Computational Fragment-Based Design of Chemically Modified Oligonucleotides for Selective Protein Inhibition: BACE1 as a Case Study
- Facultad/Centro
- Facultad de Química
- Programa Académico
- es-ES Ciencias Químicas
- Título
- en-US Computational Fragment-Based Design of Chemically Modified Oligonucleotides for Selective Protein Inhibition: BACE1 as a Case Study
- es-ES Diseño computacional basado en fragmentos de oligonucleótidos modificados químicamente para la inhibición selectiva de proteínas: BACE1 como estudio de caso
- Autor
- González Alemán, Roy
- Fecha de Defensa
- 2023
- Cantidad de páginas
- 211
- Fecha de entrega
- jueves, 21 de diciembre de 2023
- Grado
- Tesis de Doctorado
- Idioma
- spa
- Derechos
- acceso abierto
- Tipo
- info:eu-repo/semantics/publishedVersion
- es-ES info:eu-repo/semantics/doctoralThesis
- Licencia
- CC BY-NC-ND 3.0
- Formato
- application/pdf
- Objetivo de Desarrollo Sostenible (ODS) y Sector Estratégico
- es_ES SE9. Industria farmacéutica, biotecnológica y producciones biomédicas
- Derechos de acceso
- Los materiales en este sitio se proporcionan para uso educativo bajo el uso justo como se describe en la ley vigente de Derechos de autor de Cuba. Siempre que haga uso de la imagen usted debe indicar que es parte de la colección de la Biblioteca Central de la Universidad de La Habana. Usted es libre de compartir (copiar y redistribuir el material en cualquier medio o formato) bajo las condiciones que se establecen en la licencia CC BY-NC-ND 3.0. Se debe obtener un permiso por escrito de la Universidad de La Habana o del titular de los derechos antes de utilizar una imagen con fines comerciales o de publicación.
- Resumen
- en-US Drug discovery is a complex and lengthy process that involves several stages, from identifying a biological target to approving a new drug by regulatory agencies. The task can take several years and billions of dollars, with a high failure rate at each stage1. The first of these stages involves identifying a biological target that plays a role in a disease process. Once identified, researchers use various approaches to discover potential drug candidates that can interact with the target and modulate its activity
- es-ES El descubrimiento de fármacos es un proceso largo y complejo que implica varias etapas, desde la identificación de un objetivo biológico hasta la aprobación de un nuevo fármaco por parte de las agencias reguladoras. La tarea puede llevar varios años y miles de millones de dólares, con una alta tasa de fracaso en cada etapa1. La primera de estas etapas implica la identificación de un objetivo biológico que desempeña un rol en el proceso de una enfermedad. Una vez identificados, los investigadores utilizan varios enfoques para descubrir posibles fármacos candidatos que puedan interactuar con el objetivo y modular su actividad.
- extracted text
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Computational Fragment-Based Design of
Chemically Modified Oligonucleotides for
Selective Protein Inhibition:
BACE1 as a Case Study
Doctoral thesis from the University of Havana and the
University of Paris-Saclay
École doctorale n◦ 577: Structure et Dynamique des Systèmes Vivants
Spécialité de doctorat: Sciences de la vie et de la santé
Graduate School : Life Sciences and Health, Référent : —
Thesis prepared at the Laboratorio de Química Computacional y Teórica (LQCT)
and the Laboratoire Séquence Structure et Fontion des ARN (SSFA), under the
joint supervision of Luis MONTERO CABRERA and Fabrice LECLERC
Thesis defended at La Havana, the 18th December of 2023, by
Jury composition
NNT : 2020UPASA001
THESE DE DOCTORAT
Roy GONZÁLEZ-ALEMÁN
Maykel Marquez-Mijares
Dr. C., University of Havana
Ricardo Bringas-Pérez
Dr. C., Center for Genetic Engineering and Biotechnology
Matthieu Montès
PhD, Conservatoire National des Arts et Métiers
Karina García-Martínez
Dra. C., Center of Molecular Immunology
Tâp Ha-Duong
PhD, Université Paris Saclay
Luis Montero-Cabrera
PhD, University of Havana
Fabrice Leclerc
PhD, Université Paris Saclay
President
Rapporteur
Rapporteur
Examinatrice
Examinateur
Directeur de thèse
Directeur de thèse
Title: Computational fragment-based design of chemically modified oligonucleotides for selective protein inhibition: BACE1 as a case study
Keywords: fragment-based drug design, BACE1, modified oligonucleotides, conformational clustering
Abstract: Fragment-based drug design (FBDD)
has become an increasingly popular approach in
ligand design, boasting numerous success stories
within the drug discovery process. Despite some
challenges relating to synthetic accessibility and
ligand-design strategies, FBDD remains a promising method for addressing chemical space, molecular complexity, binding probability, and ligand efficiency. RNA therapeutics are rapidly expanding,
undergoing a resurgence due to the several advantages of these molecules over traditional drugs
and antibodies, including their small size, ease of
synthesis, stability, and lack of immunogenicity.
However, like many other drugs, off-target effects
(where inhibitors designed for a specific molecule
inadvertently inhibit others unintended) can hinder their usage. In this study, we introduce an
in silico strategy for the fragment-based designing of a promising class of ligands: chemically
modified oligonucleotides that exhibit potential se-
lectivity for their intended targets. As a proof
of concept, we employed the BACE1 enzyme, a
well-established therapeutic target for Alzheimer’s
disease. The fragments library exploration was
conducted through extensive docking simulations
of mono-nucleotides using the Multiple Copy Simultaneous Search method, whose docking and
screening power were rigorously assessed through
a comprehensive benchmark of 121 nucleotideprotein complexes for the first time. An efficient
nucleotide assembler was developed to link the
best hits obtained in docking stages. Differential analysis of the best-scored oligonucleotides allowed us to find specific binding modes to BACE1
over BACE2. At a methodological level, we also
propose substantial memory optimization of four
widely employed clustering algorithms, which allow the identification of essential structural features for ligand-receptor binding, an integral part
of any FBDD campaign.
List of Tables
1.1
1.2
Bitwise operators logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spatial complexity of reviewed clustering algorithms . . . . . . . . . . . . . . . . . . . . .
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2.1
Benchmarked clustering algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4.1
4.2
4.3
4.4
4.5
4.6
Run time and RAM consumption of QT implementations . . . . . . . . . . . . .
Run time and RAM consumption of Daura implementations . . . . . . . . . . . .
Number and percent of elements shared by BitClust and Daura clusters . . . . .
Run time and RAM consumption of DP implementations . . . . . . . . . . . . .
Run time and RAM consumption of MDSCAN vs. HDBSCAN* implementations
ARI of clustering outputs obtained with different HDBSCAN implementations .
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5.1
5.2
5.3
NUCLEAR explorations to retrieve native-like structures for the 2XNR protein . . . . . .
NUCLEAR explorations to retrieve native-like structures for the 5WWX protein . . . . .
NUCLEAR explorations to retrieve native-like structures for the 5ELH protein. . . . . . .
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6.1
Descriptors of potential selective inhibitors of BACE-X . . . . . . . . . . . . . . . . . . .
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9.1
Frequencies of occurrences for molecular features in the Top-10 for non-optimal (good)
predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Impact of the nonbonded model and phosphate patch on the recovery effect of the Top-10
no-prediction subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Variations in the binding site’s volume for complexes with no prediction in the Top-10 . . .
9.4 Frequencies of occurrences for molecular features in the Top-10 for non-predicted cases of
STDW-310 versus benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5 Protein-nucleotide benchmark composition . . . . . . . . . . . . . . . . . . . . . . . . . .
9.6 Frequencies of occurrences for molecular features in the Top-10 non-predicted cases versus
benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.7 Impact of the vp-tree encoding on MDSCAN . . . . . . . . . . . . . . . . . . . . . . . . .
9.8 Equivalence of representative clusters in the 6 kF trajectory . . . . . . . . . . . . . . . . .
9.9 Equivalence of representative clusters in the 30 kF trajectory . . . . . . . . . . . . . . . .
9.10 NUCLEAR performance in oligonucleotide searches . . . . . . . . . . . . . . . . . . . .
9.11 Representative structures after the HDBSCAN clustering procedure. . . . . . . . . . . .
III
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List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
Typical steps involved in an FBDD campaign . . . . . . . . . . . . . . .
Non-bonded models used in the MCSS calculations . . . . . . . . . . .
Common strategies in aptamers modification . . . . . . . . . . . . . . .
Agents in clinical trials for the treatment of Alzheimer’s Disease in 2021
The amyloidogenic pathway of the Amyloid Precursor Protein . . . . . .
Binding pocket of BACE1 . . . . . . . . . . . . . . . . . . . . . . . . .
Mechanism of action of the catalytic aspartic acid residues of BACE1 . .
Some familiar algorithms’ order of growth . . . . . . . . . . . . . . . .
Illustration of basic concepts of graph theory. . . . . . . . . . . . . . . .
Graphical description of the depth-first search order . . . . . . . . . . .
Partition of a bi-dimensional space using a kd-tree . . . . . . . . . .
Partition of a database via the vantage point p . . . . . . . . . . . . . .
Condensed hierarchy of clusters produced by HDBSCAN . . . . . . . . .
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2.1
2.2
2.3
Schematic description of the benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . .
Workflow followed for BACE1 protein candidate selection. . . . . . . . . . . . . . . . . .
Protonation protocol of proteins’ titratable residues. . . . . . . . . . . . . . . . . . . . . .
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
Distribution of molecular functions and nucleotide types in the benchmark . . . . . . .
Molecular and energy features of the benchmark’s nucleotide-binding sites . . . . . . .
Nucleotide breakdown of atomic contacts . . . . . . . . . . . . . . . . . . . . . . . . .
Number of poses generated for 5’ patched nucleotides . . . . . . . . . . . . . . . . . .
Fraction of native poses generated for 5’ patched nucleotides . . . . . . . . . . . . . .
Top-i ranked native poses per nucleotide patch . . . . . . . . . . . . . . . . . . . . .
Docking powers for different scoring functions using the patch R310 . . . . . . . . . .
Impact of the clustering filtering in the docking power of different scoring functions . .
Nucleotide decomposition of the success rates for each solvent model and patch . . . .
Binding selectivity predictions for 1KTG . . . . . . . . . . . . . . . . . . . . . . . . .
Binding selectivity predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Screening powers on common predictions to the SCAL and STW models . . . . . . . .
Distributions of the nucleotide-dependent MCSS score for the SCAL or STDW models
Decomposition of screening powers per nucleotide type . . . . . . . . . . . . . . . . .
Upset diagrams of the impact of molecular features on the Top-10 predictions . . . . .
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
RMSD distributions of supposedly QT implementations’ clusters . . . . . . . . .
First iteration of the binary heuristic for searching cliques implemented in BitQT.
Distributions of clusters diameters returned by BitQT for each analyzed trajectory.
ARI between QTPy and BitQT partitions for all clusters in several trajectories . .
Workflow of the binary Daura algorithm implemented in the BitClust code . . . .
Graph-theoretical view of an MD trajectory before and after applying DP . . . . .
DP+ main objects and operations involved in the computation of ρi and ηi . . .
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5.1
5.2
5.3
5.4
NUCLEAR workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Workflow for the hotspots identification in a receptor protein using NUCLEAR.
Hotspots search using NUCLEAR’s low-res fingerprints . . . . . . . . . . . . .
Graph view of the NUCLEAR sequence search procedure . . . . . . . . . . . .
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6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
NUCLEAR search region definition from hotspots . . . . . . . . . . . .
NUCLEAR search region definition from selectivity maps . . . . . . . .
NUCLEAR search region definition from protein-inhibitors contacts . . .
General workflow to retrieve selective CMO for BACE-X proteins. . .
Binding mode of potential selective inhibitors of BACE-X . . . . . . .
BACE1’s and BACE2’s “near-10s loop region” ’s key residues . . . . .
BACE1’s and BACE2’s view of the active site region’s key residues . .
Count of molecular interactions of the CMOs targeted against BACE1
Count of molecular interactions of the CMOs targeted against BACE2
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9.1
9.2
9.3
9.4
9.5
9.6
9.7
Decomposition of docking powers per nucleotide type . . . . . . . . . . . . . . . . . . . .
Impact of the conformational features on the Top-10 predictions . . . . . . . . . . . . . .
Variations in the volume of the binding site . . . . . . . . . . . . . . . . . . . . . . . . . .
Stacking contributions for the Top-10 predictions . . . . . . . . . . . . . . . . . . . . . .
Distributions of water molecules and impact on the binding sites . . . . . . . . . . . . . .
Distribution of the torsion angles observed in the bound ligands . . . . . . . . . . . . . . .
Scoring offset between the global best-ranked pose and the best-ranked pose for the native
nucleotide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The first five clusters retrieved by QT and Daura on the 6 kF trajectory . . . . . . . . . .
Iterative gap-based method of Flores and Garza as implemented in RCDPeaks . . . . . . .
Second cluster of trajectory 6 kF after DP and RCDPeaks . . . . . . . . . . . . . . . . . .
Equivalence of clusters detected by MDSCAN and HDBSCAN* variants . . . . . . . . .
Plot of distance R vs. pseudo-dihedral psi of BACE1 structures similar to 1SGZ-A . . . . .
Superposition of the four BACE1 selected conformations . . . . . . . . . . . . . . . . . .
A-derived modified nucleotides present at the MCSS library. . . . . . . . . . . . . . . . .
C-derived modified nucleotides present at the MCSS library. . . . . . . . . . . . . . . . .
G-derived modified nucleotides present at the MCSS library. . . . . . . . . . . . . . . . .
U-derived modified nucleotides present at the MCSS library. . . . . . . . . . . . . . . . .
U-derived modified nucleotides present at the MCSS library (continuation of Figure 9.17).
“Near-10s loop region” of BACE1 (A) and BACE2 (B) colored by residue type. . . . . .
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9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
9.19
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Contents
List of Tables
III
List of Figures
IV
List of Abbreviatures and Acronyms
IX
List of Publications
XII
INTRODUCTION
1
1 BIBLIOGRAPHIC REVIEW
1.1 Fragment-based drug design . . . . . . . . . . . . . .
1.1.1 Target characterization . . . . . . . . . . . .
1.1.2 Fragment library design . . . . . . . . . . . .
1.1.3 Fragment screening . . . . . . . . . . . . . .
1.1.4 Hit-to-lead optimization . . . . . . . . . . . .
1.1.5 Lead optimization . . . . . . . . . . . . . . .
1.2 Docking simulations . . . . . . . . . . . . . . . . . .
1.2.1 Multiple Copy Simultaneous Search (MCSS)
1.3 Oligonucleotide therapeutics . . . . . . . . . . . . . .
1.3.1 Aptamers and related molecules . . . . . . . .
1.4 BACE1 as molecular target in the Alzheimer’s Disease
1.4.1 BACE1 and BACE2 structural similarities . .
1.5 Mathematical background . . . . . . . . . . . . . . .
1.5.1 Big-O notation . . . . . . . . . . . . . . . . .
1.5.2 Basics of graph theory . . . . . . . . . . . .
1.5.3 Similarity measures . . . . . . . . . . . . . .
1.5.4 Essential data structures . . . . . . . . . . .
1.5.5 Bitwise operations . . . . . . . . . . . . . . .
1.6 Clustering of molecular ensembles . . . . . . . . . . .
1.6.1 Types of clustering . . . . . . . . . . . . . .
1.6.2 Molecular clustering . . . . . . . . . . . . . .
1.6.2.1 Quality Threshold . . . . . . . . . .
1.6.2.2 Daura . . . . . . . . . . . . . . . .
1.6.2.3 Density Peaks . . . . . . . . . . . .
1.6.2.4 HDBSCAN . . . . . . . . . . . . .
1.6.3 Spatial complexity of reviewed algorithms . .
4
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2 METHODS, MODELS AND COMPUTATIONAL DETAILS
2.1 MCSS-based predictions of binding and selectivity of nucleotides
2.1.1 Protein-nucleotide benchmark design . . . . . . . . . . .
2.1.2 Patches, charges, and solvent models . . . . . . . . . . .
2.1.3 MCSS docking protocol . . . . . . . . . . . . . . . . . .
2.1.4 Clustering of MCSS distributions . . . . . . . . . . . . .
2.1.5 Docking and screening power . . . . . . . . . . . . . . .
2.1.6 Molecular features . . . . . . . . . . . . . . . . . . . . .
2.2 Reinventing the wheel of molecular clustering . . . . . . . . . .
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3 MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
3.1 Protein-nucleotide benchmark: general insights . . . . . . . . . . . . . .
3.2 Models and poses . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Docking power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Screening power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Molecular features . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NUCLEOTIDES
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4 REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
4.1 BitQT: a graph-theoretical approach to the QT clustering . . . . . .
4.1.1 Inaccurate implementations of QT . . . . . . . . . . . . . . .
4.1.2 From QT to the Maximum Clique Problem . . . . . . . . . .
4.1.3 Binary encoding of RMSD pairwise similarity . . . . . . . . .
4.1.4 A heuristic search of big cliques . . . . . . . . . . . . . . . . .
4.1.5 Performance benchmark of valid QT variants . . . . . . . . .
4.1.6 Equivalence between BitQT and QT . . . . . . . . . . . . . .
4.2 BitClust: the first binary implementation of Daura clustering . . . . .
4.2.1 Translating Daura clustering to bitwise operations . . . . . . .
4.2.2 Performance benchmark of Daura variants . . . . . . . . . . .
4.2.3 Equivalence between BitClust and Daura . . . . . . . . . . .
4.3 DP+: Reaching linear spatial complexity in DP clustering . . . . . .
4.3.1 Computing an oriented tree instead of a complete graph . . . .
4.3.2 Refining the exact algorithm of DP . . . . . . . . . . . . . . .
4.3.3 Performance benchmark of DP variants . . . . . . . . . . . .
4.4 MDSCAN: efficient RMSD-based HDBSCAN . . . . . . . . . . . .
4.4.1 Dual-heap construction of a quasi-MST . . . . . . . . . . . .
4.4.2 Performance benchmark of HDBSCAN variants . . . . . . .
4.4.3 Equivalence between MDSCAN and HDBSCAN* alternatives
4.5 Spatial complexity of proposed algorithms . . . . . . . . . . . . . . .
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2.4
2.2.1 Molecular ensembles used to benchmark clustering algorithms
2.2.2 Benchmarked clustering algorithms and dependencies . . . .
NUCLEAR: an efficient assembler for the FBDD of CMOs . . .
2.3.1 CHARMM minimization protocol . . . . . . . . . . . . . . .
In-silico design of selective CMO against BACE1 . . . . . . . . .
2.4.1 BACE1 protein candidates selection . . . . . . . . . . . . . .
2.4.2 BACE2 protein candidates selection . . . . . . . . . . . . . .
2.4.3 MCSS library of standard and modified nucleotides . . . . .
2.4.4 Protonation state of titratable aminoacids . . . . . . . . . .
2.4.5 3D equivalence between BACE-X residues . . . . . . . . . .
5 NUCLEAR: AN EFFICIENT ASSEMBLER FOR THE FBDD
5.1 NUCLEAR overview . . . . . . . . . . . . . . . . . . . . .
5.2 Search of hotspots . . . . . . . . . . . . . . . . . . . . . . .
5.3 Search of oligonucleotides . . . . . . . . . . . . . . . . . . .
5.4 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Evaluated parameters . . . . . . . . . . . . . . . . .
5.4.2 Trends in reproducing experimental binding modes . .
5.5 NUCLEAR’s complexity notes . . . . . . . . . . . . . . . .
5.5.1 Search of hotspots . . . . . . . . . . . . . . . . . . .
5.5.2 Search of oligonucleotides . . . . . . . . . . . . . . .
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OF CMOs
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6 IN-SILICO DESIGN OF SELECTIVE CMOs AGAINST BACE-X
6.1 Modified nucleotides and BACE-X protein candidates selection . . .
6.2 Definition of the receptor region to explore . . . . . . . . . . . . . . .
6.2.1 Region definition from NUCLEAR hotspots . . . . . . . . . . .
6.2.2 Region definition from residues’ selectivity . . . . . . . . . . .
6.2.3 Region definition from experimental protein-inhibitors contacts
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6.3
Selectivity of CMOs against BACE-X . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Key interactions of CMO-BACE-X complexes . . . . . . . . . . . . . . . . . . .
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7 CONCLUSIONS
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8 PERSPECTIVES
113
9 ANNEXES
9.1 MCSS-based predictions of binding and selectivity of nucleotides . . . . . . . . . . . . .
9.2 Reinventing the wheel of molecular clustering . . . . . . . . . . . . . . . . . . . . . . .
9.2.1 Details of MD used in benchmarks . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.1 6 kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.2 30 kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.3 50 kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.4 100A kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.5 100B kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.6 250 kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.7 500 kF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1.8 1 MF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.2 Reports inaccurately claiming to perform QT clustering . . . . . . . . . . . . .
9.2.3 DP+ pseudocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.4 RCDPeaks refinements over DP . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.4.1 Automatic detection and screening of cluster centers . . . . . . . . . .
9.2.4.2 Clusters core refining . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.5 Approaches for computing the quasi-MST in the HDBSCAN* variants . . . . .
9.2.5.1 Generic-based HDBSCAN* . . . . . . . . . . . . . . . . . . . . . . .
9.2.5.2 Prim-based HDBSCAN* . . . . . . . . . . . . . . . . . . . . . . . .
9.2.6 Impact of the vp-tree encoding on MDSCAN performance . . . . . . . . . . . . .
9.2.7 Cluster composition equivalence between MDSCAN and HDBSCAN alternatives
9.3 NUCLEAR: an efficient assembler for the FBDD of CMOs . . . . . . . . . . . . . .
9.3.1 NUCLEAR performance in oligonucleotide searches . . . . . . . . . . . . . . .
9.4 In-silico design of selective CMO against BACE1 . . . . . . . . . . . . . . . . . . . .
9.4.1 BACE1 protein candidates selection . . . . . . . . . . . . . . . . . . . . . . . .
9.4.2 Modified nucleotides present at the MCSS library . . . . . . . . . . . . . . . . .
9.4.3 Key interactions of CMO-BACE-X complexes . . . . . . . . . . . . . . . . . .
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RÉSUMÉ ÉTENDU
143
10 Bibliography
153
VIII
List of Abbreviatures and Acronyms
Aβ Amyloid-beta
ABNR Adopted Basis Newton-Raphson
AD Alzheimer’s Disease
AMBER Assisted Model Building and Energy Refinement
AMP Adenosine monophosphate
APP Amyloid Precursor Protein
ARI Adjusted Rand Index
ASR Active Site Region
BACE-X BACE1 and BACE2
BACE1 β-site Amyloid Precursor Protein Cleaving Enzyme 1
BACE2 β-site Amyloid Precursor Protein Cleaving Enzyme 2
BINANA BINding ANAlyzer
CADRO Common Alzheimer’s Disease Research Ontology
CASF Comparative Assessment of Scoring Functions
CHARMM Chemistry at Harvard Molecular Mechanics
cLogP Octanol-Water Partition Coefficient
CLoNe Clustering based on Local density Neighborhoods
CMO Chemically Modified Oligonucleotide
CMP Cytidine monophosphate
CphMD Constant pH Molecular Dynamics
CRISPR Clustered Regularly Interspaced Short Palindromic Repeats
DBSCAN Density-Based Spatial Clustering of Applications with Noise
DECODE DiscovEring Clusters Of Different dEnsities
DENCLUE DENsity-based CLUstEring
DFS Depth-First Search
DMT Disease-modifying Therapy
DNA Deoxyribonucleic Acid
DP Density Peaks
FBD Fragment-Based Design
FBDD Fragment-Based Drug Design
IX
FDA United States Food and Drug Administration
GB Generalized Born
GMP Guanosine monophosphate
gRNA guide Ribonucleic Acid
GROMACS GROningen MAchine for Chemical Simulation
gSkeletonClu graph-skeleton based clustering
HDBSCAN Hierarchical Density-Based Spatial Clustering of Applications with Noise
HTS High Throughput Screening
HTVS High Throughput Virtual Screening
kd-tree k-dimensional tree
LE Ligand Efficiency
LNA Locked Nucleic Acid
MCP Maximum Clique Problem
MCSS Multiple-Copy Simultaneous Search
MD Molecular Dynamics
miRNA micro Ribonucleic Acid
ML Machine Learning
MM Molecular Mechanics
MRD Mutual Reachability Distance
mRNA messenger Ribonucleic Acid
MSF Minimum Spanning Forest
MST Minimum Spanning Tree
NMR Nuclear Magnetic Resonance
NUCLEAR NUCLEotide AssembleR
PCR Polymerase Chain Reaction
PDB Protein Data Bank
QM Quantum Mechanics
QSAR Quantitative Structure-Activity Relationships
QSPR Quantitative Structure-Property Relationships
QT Quality Threshold
RAM Random Acces Memory
X
RBP Ribonucleic Acid Binding Protein
RCDPeaks Refined-Core Density Peaks
REMD Replica Exchange Molecular Dynamics
RI Rand Index
RMSD Root Mean Square Deviation
RNA Ribonucleic Acid
RRM RNA recognition motif
SD Steepest Descent
SELEX Systematic Evolution of Ligands by Exponential Enrichment
SIGKDD Special Interest Group on Knowledge Discovery and Data Mining
siRNA small interfering Ribonucleic Acid
SOMAmer Slow Off-rate Modified Aptamer
SPR Surface Plasmon Resonance
ssRNA Single stranded RNA
TI Tanimoto Index
UMP Uridine monophosphate
VMD Visual Molecular Dynamics
vp Vantage point
vp-tree Vantage point tree
WHO World Health Organization
XRC X-Ray Cristallography
XI
List of Publications
The research comprising this thesis has resulted in several peer-reviewed publications,
which are presented below. These works represent novel scientific contributions made
throughout the doctoral program studies and have helped to advance knowledge in the
field. The publications have already gained visibility and recognition from peers, totaling
65 citations. The symbol ∗ denotes corresponding authorship.
1. González-Alemán, R.∗ , Hernández-Castillo, D., Caballero, J., and Montero-Cabrera,
L. A. Quality Threshold Clustering of Molecular Dynamics: A Word of Caution. Journal of Chemical Information and Modeling, 60(2):467–472, 2020. doi:
10.1021/acs.jcim.9b00558.
2. González-Alemán, R.∗ , Hernández-Castillo, D., Rodríguez-Serradet, A., Caballero,
J., Hernández-Rodríguez, E. W., and Montero-Cabrera, L. BitClust: Fast Geometrical Clustering of Long Molecular Dynamics Simulations. Journal of
Chemical Information and Modeling, 60(2):444–448,2020. doi: 10.1021/acs.jcim.9b00828.
3. González-Alemán, R., Chevrollier, N., Simoes, M., Montero-Cabrera, L., and Leclerc,
F. MCSS-Based Predictions of Binding Mode and Selectivity of Nucleotide
Ligands. Journal of Chemical Theory and Computation, 17(4):2599–2618, 2021.
doi: 10.1021/acs.jctc.0c01339.
4. González-Alemán, R.∗ , Platero-Rochart, D., Hernández-Castillo, D., HernándezRodríguez, E. W., Caballero, J., Leclerc, F., and Montero-Cabrera, L. BitQT:
a graph-based approach to the quality threshold clustering of molecular dynamics. Bioinformatics, 38(1):73–79, 2022. doi: 10.1093/bioinformatics/btab595.
5. Platero-Rochart, D., González-Alemán, R.∗ , Hernández-Rodriguez, E. W., Leclerc,
F., Caballero, J., and Montero-Cabrera, L. RCDPeaks: Memory-efficient density peaks clustering of long molecular dynamics. Bioinformatics, 38(7):1863–1869,
2022. doi: 10.1093/bioinformatics/btac021.
6. González-Alemán, R.∗ , Platero-Rochart, D., Rodríguez-Serradet, A., HernándezRodríguez, E. W., Caballero, J., Leclerc, F., and Montero-Cabrera, L. MDSCAN:
RMSD-based HDBSCAN clustering of long molecular dynamics. Bioinformatics (Oxford, England), 38(23):5191–5198, 2022. doi: 10.1093/bioinformatics/btac666.
XII
INTRODUCTION
Drug discovery is a complex and lengthy process that involves several stages, from
identifying a biological target to approving a new drug by regulatory agencies. The task
can take several years and billions of dollars, with a high failure rate at each stage 1 . The
first of these stages involves identifying a biological target that plays a role in a disease
process. Once identified, researchers use various approaches to discover potential drug
candidates that can interact with the target and modulate its activity 2 .
From the family of drug targets known so far, proteins are the most common members 3 . Their inhibition plays an essential role in drug discovery, as it provides a means to
suppress their participation in a particular disease. However, blocking a specific protein is
challenging and frequently encounters the so-called off-target effect. This term describes
the events that can occur when a drug binds to targets (proteins or other molecules in the
body) other than those for which it was meant to bind, causing unexpected and potentially
harmful side effects 4 .
Fragment-Based Drug Design (FBDD) is a rational way to conceive the design of
protein inhibitors. It begins with a small collection of low-molecular-mass, low-affinity
molecules called fragments and then scales them into drug leads 5 . There are several
success stories when FBDD has been applied to drug design and discovery, with more
than 30 fragment-based drug candidates entering the clinic since the mid-1990s 5–9 .
Ribonucleic Acid (RNA) and derived molecules have emerged as promising tools for
selective protein inhibition due to their high specificity, low immunogenicity, and tunable
physicochemical properties 10 . For example, the development of aptamers (short singlestranded Deoxyribonucleic Acid (DNA) or RNA oligonucleotides) as therapeutic agents
has been a subject of intense research, with numerous studies reporting their successful
application in the treatment of various diseases 11 . Aptamers’ advantages include their
ease of generation, low manufacturing cost, and low immunogenicity. However, these
molecules must undergo chemical modifications to avoid their inherent susceptibility to
nuclease hydrolysis and rapid clearance through glomerular filtration 12 .
Proven allies of experimental drug discovery campaigns are the computational or in
silico methods, which mitigate time and resource costs through virtual simulations. When
looking for new drugs, a neuralgic step is screening immense databases representative of
the drug-like chemical space to find a suitable molecular cure for a disease. Computational docking methodologies play a vital role, and numerous alternatives are available
to researchers 13 . In the FBDD arena, the Multiple-Copy Simultaneous Search (MCSS)
software 14 stands out as a pioneering virtual methodology for docking that has been
previously coupled with other software to join fragments into lead compounds 15–19 .
Clustering algorithms (devoted to grouping similar entities into sets called clusters) 20
are employed in various stages of the FBDD pipeline (though often in a transparent
manner to users), primarily to group similar fragments or compounds based on their
structural or physicochemical properties. Conceiving new efficient clustering algorithms
2
or optimizing those currently used is mandatory to face the increasing size of molecular
ensembles generated by computational techniques.
The present thesis focuses on the computational fragment-based design of chemically modified oligonucleotides (inspired by the aptamers’ development and success) for
selective protein inhibition, using β-site Amyloid Precursor Protein Cleaving Enzyme 1
(BACE1) as a case study. BACE1 is a well-established therapeutic target for the
Alzheimer’s Disease (AD) due to its essential role in the production of amyloid-beta peptides, which are the primary constituents of amyloid plaques in the brains of Alzheimer’s
patients. One of the main disadvantages of targeting BACE1 resides in the off-target inhibition evinced by a related protease, β-site Amyloid Precursor Protein Cleaving Enzyme
2 (BACE2) 21 .
Although RNA therapies (including aptamers alternatives) are becoming increasingly
popular, there is no available methodology for the rational design of selective chemically
modified oligonucleotides for medical applications, which constitutes the scientific problem here addressed.
The following work was conceived on the global hypothesis that FBDD principles
can be effectively applied to the rational in silico design of chemically modified oligonucleotides with high affinity and selectivity for protein targets.
The main objective of this thesis is to develop an integrated computational framework for the fragment-based design of chemically modified oligonucleotides with high
affinity and selectivity for protein targets, using BACE1 as a relevant proof of concept.
The specific objectives that guided our efforts are the following:
1. To asses the MCSS’s docking and screening powers on a representative benchmark
of protein-nucleotide complexes.
2. To optimize popular clustering algorithms that intervene at distinct phases of the
FBDD.
3. To implement an efficient computational linker for assembling chemically modified
nucleotides (fragments) onto oligochains (lead compounds).
4. To validate a computational workflow for proposing chemically modified oligonucleotides as selective proteins inhibitors using the BACE1 as a case study.
This manuscript contains several contributions that can be highlighted in terms of
novelty:
1. For the first time, the docking and screening power of the MCSS software was
evaluated on a set of 121 representative protein-(mono)nucleotide complexes and
compared to other established scoring functions.
2. For each of the four clustering algorithms treated in our work, a novel idea was
implemented that significantly impacted their spatial complexity.
(a) A binary encoding of the pairwise molecular similarity (as well as the ability
to translate clustering steps into bitwise operations) was applied to the Daura
and the Quality Threshold clustering.
3
(b) Also, a methodological correction was raised for these two algorithms that
were incorrectly and systematically used interchangeably.
(c) The spatial complexity of the Density Peaks and the Hierarchical DensityBased Spatial Clustering of Applications with Noise algorithms was reduced
from quadratic to linear.
3. No other published tool is available to efficiently link MCSS-generated poses of
modified nucleotides onto oligonucleotides, a task we addressed with our proposed
software NUCLEotide AssembleR (NUCLEAR).
4. To our knowledge, an attempt to provide a computational workflow yielding potentially selective oligonucleotides to inhibit protein conformations has not been
reported.
1 - BIBLIOGRAPHIC REVIEW
This chapter explains core concepts, definitions, antecedents, and motivations of the
thesis work later presented in results Chapters 3 to 6 through a deliberate organization
that covers, in the first place, the principles and rationale behind the Fragment-Based
Drug Design (FBDD) methodology, emphasizing its in silico component in Section 1.1.
As it is an integral part of the computational FBDD, the basics of docking simulations and scoring functions are reviewed in Section 1.2, highlighting the Multiple-Copy
Simultaneous Search (MCSS) alternative given the significant importance this methodology plays in our approach to conceive selective oligonucleotides.
The main motivation to our study of CMOs as potential drugs, comes from the relative success of aptamers and aptamers-like molecules. So these antecedents are described
in Section 1.3 where we also briefly touch some important aspects of Ribonucleic Acid
(RNA) therapeutics.
In Section 1.4, we detail the role of the β-site Amyloid Precursor Protein Cleaving
Enzyme 1 (BACE1) protein in the Alzheimer’s Disease (AD). In this section, we make
clear the importance of selective inhibition of this target and the usefulness of avoiding
off-target effects with the related β-site Amyloid Precursor Protein Cleaving Enzyme 2
(BACE2) protein.
As this manuscript proposes significant contributions to the field of clustering molecular ensembles, we dedicated Section 1.6 to describe the machinery of several (often
confused even) algorithms widely employed in the molecular field.
However, as a mathematical background will be necessary to comprehend this and
another essential contribution we made to link nucleotide fragments in Chapter 5, we first
gather some basic mathematical background on asymptotic analysis of function growth,
graph theory, similarity measures, essential data-structures, and bitwise operations in
Section 1.5.
1.1 . Fragment-based drug design
The drug discovery process is a complex and lengthy process that involves several
stages, starting from identifying a biological target and ending with approving a new
drug by regulatory agencies. The process can take several years and billions of dollars to
complete, with a high failure rate at each stage 1 .
The first of these stages involves identifying a biological target that plays a role in a
disease process. Once a target is identified, researchers use various approaches to identify
potential drug candidates that can interact with the target and modulate its activity 2 .
High Throughput Screening (HTS) is a drug discovery approach that involves rapidly
testing many compounds for their ability to bind to a specific target or produce a desired
biological effect. It is a widely used approach in the pharmaceutical industry and academic
research to identify potential drug candidates from vast chemical libraries. HTS typically
1.1. Fragment-based drug design
5
involves using automated technologies, such as robotics and liquid handling systems, to
perform assays on hundreds of thousands or even millions of compounds in a relatively
short time 22 .
Although HTS has revolutionized the drug discovery process and led to the discovery of many essential drugs (including some that have become blockbuster drugs in the
market), when screened against newer or more difficult targets, huge compound libraries
sometimes yielded few hits or, in more problematic cases, yielded hits that were false positives 23 . Besides, there is a growing awareness of the enormity of chemical space 24 , from
which an early estimate put the number of possible small drug-like molecules at 1060 , an
immensity compared to the fragment library sizes available up to date (in the scale of the
millions).
Unlike conventional drug discovery methods that involve screening millions of compounds to find drug-sized starting points, FBDD takes a different approach (see Figure
1.1). It begins with smaller collections of low-molecular-mass, low-affinity molecules called
fragments and then scales them up into drug leads 5 .
1
2
3
4
5
Target
Characterization
Fragment Library
Design
Fragment
Screening
Hit-to-Lead
Optimization
Lead
Optimization
Figure 1.1: Typical steps involved in an FBDD campaign.
Despite some challenges related to ligand-design strategies and synthetic accessibility, fragment-based approaches remain highly attractive as they deal more efficiently
with chemical space, molecular complexity, probability of binding, and Ligand Efficiency
(LE) 23 . After the HTS, FBDD approaches represent one of the most critical leadgeneration strategies for clinical candidates 25 . There are several examples of success
stories when FBDD has been applied to drug design and discovery, with more than 30
fragment-based drug candidates entering the clinic since the mid-1990s 5–9 .
In spite of its promising future, the current FBDD approaches may face limitations
and challenges that hinder its widespread application: (i) large-scale pure, high-quality,
and stable target proteins are required for the screening but the crystallization of certain
kinds of proteins can be expensive and time-consuming, (ii) given the relatively small sizes
of fragments, limited receptor-ligand interactions can be formed with the surrounding
residues and only a part of them is strong enough for detection, (iii) only fragments with
relatively high solubility can be suitable for the screening step, (iv) FBDD endeavors also
face the total diversity space (103 fragments can typically sample the chemical diversity
space of 109 molecules) that restrains the exploration of a larger region of the drug-like
space, (v) it is known that FBDD is more suitable for certain classes of targets (such as
kinases) whose binding site often consists of multiple distinctive sub-sites , (vi) identifying
the optimal linkers in the hit-to-lead step can be challenging and time-consuming 26 , (vii)
many proteins are flexible, which can make it cumbersome to design fragments that bind
to a specific conformation, (viii) most of the FBDD methods do not take ligand specificity
or selectivity into account.
6
1. BIBLIOGRAPHIC REVIEW
Above-mentioned restrictions progressively drove researchers to consider chemo-informatics
and computational methodologies that could help at different stages of the FBDD efficiently and cost-effectively 27,28 . However, much like the experimental FBDD, their
computational counterparts have a set of restraints mainly regarding the lack of accuracy
and reliability due to the methodological approximations that govern them 29–32 .
In silico methods can generate false positives or compounds predicted to bind to
the target protein but do not have a therapeutic effect. This can lead to wasted time
and resources in the experimental validation of compounds that are not promising drug
candidates. The takeaway lessons point, not surprisingly, to the complementary use of
both approaches to advance the field of FBDD 33 .
Next, we will give a succinct overview of the primary stages illustrated in Figure 1.1,
highlighting the role of computational methods in each step.
1.1.1 . Target characterization
Drugs are compounds that interact with a biological system to produce a biological
response. Those molecular structures with a binding site into which the drug fits and
binds are termed drug targets 34 . Although proteins are the most common drug targets,
species-specific genes, Deoxyribonucleic Acid (DNA), RNA, and membranes have also
been recognized as such 3 .
Usually considered a pre-requisite more than a first step for FBDD, drug target
identification and characterization is the first step in drug discovery 35 . The primary goal
is to identify a target macromolecule or biological pathway responsible for causing or
contributing to a specific disease. This macromolecule or pathway may serve as a point
of intervention for a potential drug to treat or manage the disease.
The target identification starts selecting a suitable disease to study. Researchers may
choose based on prevalence, disease burden, and unmet medical needs. Next, they search
for the molecular basis of the disease, often by studying the genes, proteins, and cellular
pathways involved. Several approaches can be employed in this process like genomics 36 ,
transcriptomics 37 , proteomics 38 or system biology 39 (integrating multi-omic data to create a holistic understanding of biological systems). Besides, well-established databases
and biological and Machine Learning (ML) methods exist to identify drug targets 40 .
Once a target has been identified, it is essential to characterize its biological function,
molecular interactions, and role in disease pathology. This can be achieved through
various experimental and computational methods such as structural biology, biochemical
or cell-based assays, and animal models.
1.1.2 . Fragment library design
After the target against which a drug will be designed is known, the next step in
the FBDD process that is critical to its success is to design a fragment library. It is
imperative to have a diverse fragment library encompassing a wide range of chemical
space and comprising compounds with the potential to bind to the target of interest.
Traditionally, the FBDD campaigns have been applied to design ligands assembled
using small chemical groups derived from such fragment libraries. It is common that
1.1. Fragment-based drug design
7
these libraries contain molecules that conform to the rule of three 41 , which specifies
that compounds should possess (i) a molecular weight under 300 Da, (ii) less than three
hydrogen-bond donors and acceptors, (iii) fewer than three rotatable bonds, and (iv)
an Octanol-Water Partition Coefficient (cLogP) of three or less. This rule is merely a
guideline that should not be over-emphasized, and some arguments challenge its validity 42 .
Nevertheless, it remains the preferred model for fragment selection within libraries.
As the composition of the library used in an FBDD project has a direct impact on the
outcome 43,44 , it is important to analyze commercially available fragments and fragment
libraries to make a choice that meets the primary criteria based on the profile of the target
being studied 45,46 .
Commercially available fragment libraries are typically selected based on chemical and
size diversity and different well-balanced properties to cover essential features. Natural
products or natural-product-inspired fragments can be included as they are often helpful 47 .
Additionally, identifying a series of non-commercially available fragments from synthetic
chemistry efforts, such as in-house libraries or collaborating groups, is important for future
medicinal chemistry optimization strategies 48 .
Researchers usually have their customized libraries in FBDD, and the molecular
weight of a fragment can be above 300 Da. These libraries are based on their respective experience and usually do not contain molecules that are reactive to targets, bind to
proteins unspecifically, form aggregate, or form covalent bonds with proteins 49 . Recently,
Carbery et. al. 50 showed that fragment libraries designed to be functionally diverse (ranking fragments by the number of novel interactions they introduce to the library) recover
protein critical information more efficiently than standard structurally diverse libraries.
Computational methods can be employed to quickly obtain physicochemical properties, solubility, synthetic accessibility, etc. and use them as filters for commercially available fragment databases. Additionally, these in silico methods can be utilized to remove
fragments with unwanted chemical groups and incorporate the most frequently occurring
fragments from known drugs, thus ensuring good diversity to represent drug-like chemical
space. Approaches such as Quantitative Structure-Activity Relationships (QSAR) and
Quantitative Structure-Property Relationships (QSPR) modeling can be used to predict
aqueous solubility as the fragments must be highly soluble (they are screened at high
concentrations) 51,52 .
1.1.3 . Fragment screening
Once the fragment library is conceived, screening it against the target of interest
is necessary. As fragments from the library are expected to bind weakly to the target
protein, the screening assay must be sensitive enough to detect such interactions and
robust to prevent false identification of hits, which can arise due to interference with
the assay readout. Classical biophysical assays, including Nuclear Magnetic Resonance
(NMR) spectroscopy, Surface Plasmon Resonance (SPR), and X-Ray Cristallography
(XRC), have been found to meet the requirements for sensitivity and robustness 53 .
Molecular docking is a computational method to predict small molecules’ binding
mode and affinity (ligands or fragments) to a target active site 54 . It simulates the binding
8
1. BIBLIOGRAPHIC REVIEW
process between the ligand and the target to predict the most favorable binding pose
(sampling) and the corresponding binding energy (scoring). During the fragment screening
stage, docking has been used as a pre-screen tool to reduce experimental efforts as a vital
component of High Throughput Virtual Screening (HTVS).
HTVS is a valuable tool in the early stages of drug discovery, which complements
HTS by attempting to identify potential hits. The primary distinction between HTS and
HTVS is that HTS is an experimental approach, while HTVS is a theoretical one. In
HTS, many compounds are screened to determine their ability to interact with target
molecules by assessing whether a compound reacts biochemically with the target.
While most investigators rely on a familiar or laboratory-available docking program,
this attitude may not be optimal. Instead, suppose the structure of the receptor-small
molecule complex is known (e.g., from the PDB ID of the target). In that case, multiple
docking algorithms should be employed to determine which one places the small molecule
in the same orientation as observed in the crystal structure 13 .
After identifying the docking program that replicates the experimental pose observed
in the crystal structure, the researcher should evaluate how the pose is ranked by the native
scoring function, which is included with the docking program. If the pose is ranked at
the top, this docking and scoring method should be employed in the HTVS experiment.
Otherwise, the researcher should re-score the poses using alternative scoring functions.
For the results discussed in this manuscript, the significance of the selected docking
method is prominent. Therefore, we will delve into this methodology’s fundamental principles and the rationale behind our research choice (namely MCSS) in the subsequent
Sections 1.2 and 1.2.1, respectively.
1.1.4 . Hit-to-lead optimization
Next to hit identification, the FBDD process moves to the lead-generation stage 55,56 .
The prioritization of fragment hits involves considering multiple parameters, including
biological activity, LE 57 , solubility, ease of synthesis, availability of commercial analogs,
and structural information regarding the binding mode.
Either by linking, merging or growing, prioritized fragments must be joined together 23 .
The linking strategy offers theoretically better perspectives for gaining binding energy 58 ,
as it connects two non-competitive fragments by fusing some chemical bonds or creating
some additional through a spacer molecule 59 . Computational methods (e.g. de novo
drug design algorithms 60 ) can iteratively assist the buildup of the fragment hits into a
new lead compound by virtually screening linker libraries 61 .
In bio-polymers, the chemical connectivity is well-defined, and the linking strategy
does not require a spacer to be part of the fragments. Thus, the linking solves a distanceconstraint problem in joining the connecting atoms of successive residues and guarantees
a straightforward chemical synthesis. On the other hand, the chemical diversity is reduced
to that of the residues (20 for unmodified amino acids, 4 or 5 in the case of unmodified
nucleotides).
1.1.5 . Lead optimization
1.2. Docking simulations
9
Lead optimization is a crucial process in drug discovery that involves the identification
of a pre-clinical candidate with optimal biological activity and drug-like properties 2 . Following hit-to-lead efforts, the most promising hit series are advanced to the lead optimization stage, where extensive optimization of both biological activity and physicochemical
properties is carried out 62 . This is achieved through a dedicated screening funnel of both
in vitro and in vivo assays that are designed to evaluate the physio-chemical properties
of lead compounds and identify the best ones for formulation and dosing. Lead optimization is a highly iterative process, which requires robust and efficient screening assays to
prioritize compounds with optimal drug-like properties.
1.2 . Docking simulations
The molecular docking process begins by posing small molecules in the active site.
This is challenging due to the conformational degrees of freedom that even a simple
molecule can exhibit. Sampling these degrees of freedom must be performed with sufficient
accuracy to identify the conformation that best matches the receptor structure and must
be fast enough to permit the evaluation of thousands of compounds in a given docking
run.
Posing algorithms are complemented by scoring functions that are designed to predict
the biological activity through the evaluation of interactions between compounds and
potential targets. Relatively simple scoring functions continue to be heavily used, at
least during the early stages of docking simulations. Pre-selected conformers are often
further evaluated using more complex scoring schemes with more detailed treatment of
electrostatic and van der Waals interactions, and inclusion of at least some solvation or
entropic effects 63 .
It is worth mentioning that the binding of ligands is influenced by both enthalpic and
entropic factors, and in some cases, one may dominate over the other. This can pose
a challenge for current scoring functions, as they tend to prioritize capturing energetic
effects rather than entropic ones.
In addition to problems associated with scoring of compound conformations, other
complications exist that make it challenging to accurately predict binding conformations
and compound activity. These include, among others, limited resolution of crystallographic
targets, inherent flexibility, induced fit or other conformational changes that occur on
binding, and the participation of water molecules in protein–ligand interactions 64 .
An objective test of docking methods performed in 1997 confirmed the assumption
that recognizing near-native geometries and predicting their affinities could be achieved
only with limited success, whereas the problem of generating reasonable ligand orientations is considered to be virtually resolved 65 , at least for proteins with rather rigid
binding pockets, not involving any water molecules in binding and without any change in
protonation state of either ligand or protein upon binding 66 .
As a variety of scoring functions have been developed so far, some objective benchmarks are desired for assessing their strengths and weaknesses. The Comparative Assess-
10
1. BIBLIOGRAPHIC REVIEW
ment of Scoring Functions (CASF) benchmark serves this purpose as it has been designed
as a “scoring benchmark”, where the scoring process is decoupled from the docking process
to depict the performance of scoring function more precisely.
Developers of CASF proposed four metrics in 2013 that were later improved in
2016 67 . They refer to the ability of a scoring function to: (i) produce binding scores
in a linear correlation with experimental binding data (scoring power), (ii) correctly rank
the known ligands of a certain target protein by their binding affinities when the precise
binding poses of those ligands are given (ranking power), (iii) identify the native ligand
binding pose among computer-generated decoys (docking power), and (iv) identify the
true binders to a given target protein among a pool of random molecules (screening
power).
There are various types of scoring functions available. Below, we will provide a
succinct overview of the most frequently used ones.
Forcefield- or physics-based scoring functions are extensively used due to their
ability to estimate the potential energy of a protein-ligand complex based on classical
mechanics. These scoring functions use empirical parameters to describe the interactions
between atoms and molecules, including van der Waals forces, electrostatics, and hydrogen
bonding, which makes them computationally efficient and suitable for molecular dynamics
simulations and other computational modeling studies.
Despite their advantages, forcefield-based scoring functions often neglect the contributions of entropy and solvent effects, which can limit their accuracy in predicting the
behavior of molecules in complex biological systems 59 . To improve their accuracy, researchers have incorporated additional factors, such as the torsional entropy of ligands to
account for the flexibility of the ligand molecule 68 , and solvation/desolvation effects by
using explicit solvent models 69 , implicit solvent models 70 , or a combination of both.
Scoring functions based on Quantum Mechanics (QM) have been developed
to address the challenges of covalent interactions, polarization, and charge transfer in
docking 71,72 . However, with greater accuracy comes the prohibitively computational cost.
As a result, hybrid QM/Molecular Mechanics (MM) approaches have been developed as
a compromise solution 73 .
Pason & Sotriffer defined empirical scoring functions as all functions derived from
experimental structures and affinity data by means of descriptors (of any kind) and a
statistical regression model 74 . Classical empirical scoring functions try to estimate the
affinity as a (linear) sum of individual contributions deemed to be important for the binding
free energy such as hydrogen bonds, hydrophobic effects, and steric clashes. The recent
literature makes a distinction between these functions and (usually non-linear) descriptorbased 75 or ML 76 scoring functions, although such a taxonomy is rather arbitrary.
The development of empirical scoring functions is based on three components: (i) a
training set of experimental protein-ligand complex structures along with their affinities,
(ii) descriptors that capture numerically the structural features of the protein-ligand interaction, and (iii) a regression method to establish a quantitative relationship between
the descriptor-encoded structural information and the experimental affinity 74 .
1.2. Docking simulations
11
Although the empirical scoring functions decompose protein–ligand binding affinities
into several individual energy terms, similar to physic-based scoring functions, they usually
employ a flexible and intuitive functional form other than using the well- established models
that physics-based scoring functions use.
Because of their simple energy terms, these scoring functions are good at predicting
binding affinity, ligand pose, and virtual screening with low computing cost 77 , but they
are poorly suited for describing the relationship between binding affinity and the crystal structures and they encounter double-counting problems. Autodock Vina 32 and its
derivative Vinardo 78 are examples of this kind of scoring functions.
In Vina, the binding energy is predicted as the sum of distance-dependent atom pair
interactions (see Equation 1.1).
E=
X
(1.1)
epair (d)
Here d is the surface distance calculated with Equation 1.2, where r is the inter-atomic
distance and Ri and Rj are the radii of the atoms in the pair.
d = r − Ri − Rj
(1.2)
Every atom pair interacts through a steric interaction given by the first three terms
of Equation 1.3. Also, depending on the atom type, there could be hydrophobic and
non-directional H-bonding interactions, given by the last two terms of Equation 1.3.
w1 ∗ Gauss1 (d)+
w2 ∗ Gauss2 (d)+
epair (d) = w3 ∗ Repulsion(d)+
w4 ∗ Hydrophobic(d)+
w ∗ HBond(d)+
5
(1.3)
Steric interaction in Vina is assessed using three terms (Equations 1.4 to 1.6). If both
atoms in the pair are hydrophobic the linear function in Equation 1.7 is included. Also,
if the pair consists of an H-bond donor and an H-bond acceptor, Equation 1.8 is added.
These last two equations are simple piecewise linear and their effect can be thought of as
modifying the steric interaction in order to produce an increased attraction when these
types of interaction are present.
2
Gauss1 = e−((d−o1 )/s1 )
2
Gauss2 = e−((d−o2 )/s2 )
(
Repulsion(d) =
d2 f or d ≤ 0
0 f or d = 0
(1.4)
(1.5)
(1.6)
12
1. BIBLIOGRAPHIC REVIEW
1 f or d ≤ p1
Hydrophobic(d) = p2 − d f or p1 > d < p2
0 f or d ≥ p2
1 f or d ≤ h1
d
Hbond(d) = −h
f or h1 < d < 0
1
0 f or d ≥ 0
(1.7)
(1.8)
The mechanism by which these terms were selected for the Vina scoring function, the
parameters used therein, and the weight of each term are unclear, although some kind of
non-linear regression on the PDBBIND 2007 database was used 78 .
On the other hand, Vinardo was generated by a variety of scoring functions which consisted of the inclusion/exclusion of several interaction terms to the Vina scoring function.
The terms considered for addition or exclusion were Gaussian steric attractions, quadratic
steric repulsions, Lennard-Jones potentials, electrostatic interactions, hydrophobic interactions, non-hydrophobic interactions, and non-directional hydrogen bonds. These terms
are all pairwise additive and are part of the 26 currently available in the Smina program
following a procedure detailed in reference 78.
Knowledge-based scoring functions (also known as statistical potentials) derive
pairwise potentials from three-dimensional structures of a large set of protein-ligand complexes based on the inverse Boltzmann statistic principle without requiring the fitting of
empirical parameters 79,80 . The frequency of different atom pairs at different distances is
assumed to be related to the interaction of two atoms. It is converted into the distancedependent potential of mean force.
Because they are based on the physical atomic interactions, knowledge-based scoring
functions are more interpretable and can provide insights into the underlying molecular
mechanisms. The most significant advantage of knowledge-based scoring functions is their
compromise between computing cost and predictive accuracy compared to physics-based
and empirical scoring functions.
Training sets for knowledge-based scoring functions consist only of structural information. They are independent of experimental binding affinity data, avoiding possible
binding affinity ambiguities caused by experimental conditions and making them suitable
for binding pose prediction rather than binding affinities 81 . Researchers have focused
on extending pairwise potentials to many-body potentials by introducing several new
parameters to increase predictive accuracy. Examples of these scoring functions include
DrugScore 82 , DSX 83 , M-Score 84 , and ITscorePR 85 , the latter being specifically developed
for protein-RNA interactions.
As detailed in the original publication, the basic idea behind the ITscorePR method is
to improve the inter-atomic pair potentials step by step though iterations by comparing the
predicted pair distribution functions of the protein-RNA complexes and the experimentally
observed pair distribution functions of the crystal structures in the training set. The
method can be represented mathematically by the following iterative formula:
1.2. Docking simulations
(n+1)
uij
13
(n)
(n)
(n)
(r) = uij (r) + ∆uij (r), ∆uij (r) =
1
(n)
(obs)
kB T [gij (r) − gij (r)]
2
(1.9)
where n stands for the iterative step, i and j represent the types of a pair of atoms
(obs)
in the protein and the RNA, respectively. gij (r) stands for the pair distribution function for atom pair ij calculated from the experimentally observed protein-RNA complex
structures in the training set:
(obs)
gij
(r) =
K
1 X k∗
gij (r)
K
(1.10)
k=1
where K is the total number of the protein-RNA complexes in the training data set
k∗
and gij
(r) is the pair distribution function of the k th native complex structure.
(n)
The gij (r) is the pair distribution function calculated from the ensemble of the
binding modes according to the binding score-dependent Boltzmann probabilities Pkl that
(n)
are predicted with the trial potentials uij (r) at the nth step.
(n)
gij (r)
K L
1 X X l kl
Pk gij (r)
=
K
(1.11)
k=1 l=1
kl
where gij
(r) is the pair distribution function for atom pair ij observed in the lth
binding state of the k th protein-RNA complex.
ML-based scoring functions are a type of empirical scoring function that estimate
the binding affinity or other properties of protein-ligand complexes. These scoring functions use ML algorithms, such as support vector machine, random forest, neural network,
and deep-learning, to learn the relationship between the features of a complex and its
binding affinity or other properties.
In contrast to forcefield-based scoring functions, which rely on mathematical models
based on classical mechanics to calculate the potential energy of a protein-ligand complex,
ML-based scoring functions do not require explicit modeling of the physical interactions
between atoms and molecules. Instead, they use statistical models to learn the relationship
between the features of a complex and its binding affinity, which can include the shape
and electrostatic properties of the ligand and the surface properties of the protein 86 .
ML-based scoring functions can predict the properties of novel or unconventional
molecules that have not been seen before, as they are not limited by the training set used
to derive the statistical potential. In addition, they can be more flexible and adaptable
than forcefield-based scoring functions, as they can be trained to recognize complex nonlinear relationships between features and binding affinity.
Although ML-based scoring functions may outperform their classical counterpart 87 ,
they are seldom directly incorporated into docking software but are usually used for rescoring 88 . The reason is that ML-based scoring functions rely on the training dataset 89,90 .
If the protein and ligand are docked by classical docking software, and then the docked
structure is re-scored by ML scoring functions, the accuracy tends to be improved. Despite
being less concrete on the physicochemical basis (it may be challenging to understand
14
1. BIBLIOGRAPHIC REVIEW
which features of a complex are most important for predicting its binding affinity), they
often demonstrated a superior or at least comparable performance to that of classic scoring
functions in binding affinity estimation 89 .
∆vina RF20 91 was derived from Vina under the main idea of employing random forest
to parameterize corrections to the AutoDock Vina scoring function, and thus to take
advantage of both the excellent docking power of the Vina docking function and the
strength of random forest in improving scoring accuracy. The original score calculated by
the AutoDock Vina program is in the unit of kcal/mol, and can be converted into pKd
unit with the following formula: pKd (V ina) = −0.73349E(V ina). Thus, the overall
∆vina RF scoring function can be cast into the following form:
pKd (∆vina RF ) = pKd (V ina) + ∆pKd (RF )
(1.12)
where pKd (RF ) is the correction term trained by the random forest (RF) algorithm
using pKd (train), i.e., pKd (train) − pKd (V ina).
From the numerous scoring functions that have been developed, none is universally
applicable. While some perform well on proteins related to those used to calibrate their
parameters, they may be less effective for proteins with different physicochemical properties. Additionally, each scoring function has advantages and disadvantages concerning
the model formulated to describe the process of ligand-receptor association. Nevertheless, these characteristics suggest that multiple scoring functions must capture different
information.
Based on this idea, consensus scoring was introduced by combining the predictions of
multiple scoring functions. In the words of their authors: “The only potential disadvantage
we can envision regarding consensus scoring is that it may not perform as well as any
specific function in a specific instance, since the intersection of two nonidentical lists is,
by definition, smaller than the individual lists. However, since one never knows which
function might be optimal upfront, we believe the consistency and efficiency gained by
consensus scoring outweighs any potential limitation.” 92
Several strategies varying in combining each score have been attempted and have
shown improvement in predicting binding mode, affinity, or identifying ligands that can
effectively bind to a receptor in virtual screening 93–95 . Examples of software using consensus scoring are MultiScore 96 , GFscore 97 , SeleX-CS 98 , and VoteDock 99 .
1.2.1 . Multiple Copy Simultaneous Search (MCSS)
MCSS is a computational method used within the framework of FBDD approaches,
although it does not include any fragment-assembly strategy 14 . MCSS mainly performs local and iterative docking calculations based on an efficient sampling method 100
which is implemented in the Chemistry at Harvard Molecular Mechanics (CHARMM)
program 101 . MCSS is used as a first step in the FBDD process as it generates distributions of functional groups or fragments at the surface of a protein target composed
of clustered docking poses 14 . Thus, it is possible to perform virtual screening using
pre-defined 14,102,103 or customized fragment libraries 104 .
1.3. Oligonucleotide therapeutics
15
MCSS-based FBDD approaches were applied repetitively to the design of peptides
or peptidomimetics 18,19,102,105–107 or to other bio-molecules such as aminoglycosides 108 .
MCSS has gained popularity in FBDD approaches in conjunction with fragment-linking/merging
methods such as HOOK 15 , DLD 16 , or CAVEAT 17 for chemical groups, and OLIGO 18 for
oligopeptides or SiteMap for peptidomimetics 19 .
The MCSS scoring function is based on the CHARMM energy function; different
strategies have been applied to improve its performance using more accurate methods
and implicit solvent models. The first strategy includes post-processing of the MCSS
fragment poses recalculating the score function by adding solvation terms 109 , or by rescoring (single-point energy) using a Generalized Born (GB) model 110,111 .
The second less time-consuming strategy is to include solvent effects in the energy
function during the MCSS calculations using, for example, a distance-dependent dielectric model 109 or an alternative charge model 108 . Although implicit solvent models have
become very popular, their accuracy remains limited for calculating solvation-free energies 112 .
The MCSS score is defined by the electrostatic and van der Waals contributions to
the interaction energy plus a penalty term corresponding to the deviation of the fragment’s
conformation from its energy minimum:
binding
f ragment
inter
inter
∆EMCSS
= ∆Econf
+ ∆Evdw
+ ∆Eel
(1.13)
The van der Waals contribution to the score is calculated in the same way for all
solvent models:
X Aij
Bij
2
2
2
sw(rij
, ron
, rof
(1.14)
Evdw =
f)
12 − r 6
rij
ij
excl(i,j)=1
while the electrostatic contribution depends on the solvent model used. In the case of the
“FULL” model, it is calculated using the standard charges as follows:
ϵ=1
X
Eel =
excl(i,j)=1
qi qj
4πϵ0 rij
(1.15)
In the case of the other models using either scaled charges (i.e., “SCAL”) or standard
charges (i.e., “STD”) (Figure 1.2), it is calculated this way:
Eel =
ϵ=3
X
excl(i,j)=1
qi qj
2
2
2
2 sw(rij , ron , rof f )
4πϵ0 rij
(1.16)
where the dielectric constant is set up according to some previous work 108 .
1.3 . Oligonucleotide therapeutics
In the past, RNA was not widely regarded as a viable option for therapeutic use due
to its short half-life in vivo. However, with advancements in stabilization chemistry and
R
Base
O
OH
OH
SCAL
STD,FULL
R010 = -0.05
-0.10
-0.39
C5'
O
R010 = -0.53
0.10
-0.78
C5'
O
P
O
-0.37
1.20
P
O
-0.57
O
1.50
O
-0.39
-0.78
R110 = 0.00
0.23
R110 = 0.00
0.23
C5'
C5'
H 0.43
O
-0.66
R210 = -0.32
-0.10
-0.41
C5'
O
O
-0.39
1.20
R210 = -1.00
O
C5'
P
O
O -0.41
HO
-0.82
0.10
-0.62
-0.41
R310 = -0.32
0.10
C5'
O
C5'
P
-0.39
O
1.50
P
O -0.78
-0.57
H3CO
H3CO
-0.41
-0.47
R410 = -0.64
R410 = -2.00
-0.45
0.22
C5'
O
C5'
O
O -0.82
-0.78
O
O -0.41
-0.10
-0.29
P
HO
R310 = -1.00
-0.41
1.20
1.50
-0.34
-0.10
O
H 0.43
O
-0.66
0.90
O
-0.45
P
-0.90
O
O
O -0.45
-0.62
1.10
O
P
O -0.90
-0.90
Figure 1.2: Non-bonded models used in the MCSS calculations. The R group corresponding to the 5’ end of the nucleotide includes five flavors: R010 (standard nucleotide residue),
2−
R110 (5’OH patch), R210 (5’PO4 H− ), R310 (5’PO4 CH−
3 ), and R410 (5’PO4 ). Three solvent models were used: the SCAL model was based on reduced charges on the phosphate group
according to Manning’s Theory 113 and applied to nucleic acids 108 ; the STD (standard) or
FULL models were based on standard charges. The electrostatic contribution to the interaction energy was calculated based on a constant dielectric formulation for the FULL
model. The SCAL and STD models were based on a distance-dependent dielectric model.
The van der Waals contribution was calculated using the standard CHARMM27 potential
energy function 114 .
16
1. BIBLIOGRAPHIC REVIEW
a better understanding of the clinical value of short-lived molecules, this skepticism has
primarily been dispelled 115 . As a result, RNAs have become increasingly recognized as
valuable tools and targets for therapeutic interventions 10 .
RNAs can adopt complex conformations that enable them to specifically bind to proteins, small molecules, or other nucleic acids. There are four main classes of therapeutic
RNAs based on their modes of action 115 : (i) encoding therapeutic proteins or vaccine
antigens (mRNAs), (ii) inhibiting pathogenic RNA activity (siRNAs, miRNAs, and
antisense RNAs), (iii) modulating protein activity (RNA aptamers), and (iv) reprogramming genetic information (trans-splicing ribozymes and CRISPR gRNAs). This wide
range of options for therapeutic targeting of RNA has garnered significant interest from
academic research institutions and pharmaceutical companies, with a growing number of
approved RNA therapeutics now generating significant profits 116 .
In 2019, twelve molecules were approved by the United States Food and Drug Administration (FDA) for treating various pathologies. This includes nine RNA drugs in the
form of siRNA or antisense oligonucleotides, two small molecules targeting RNA targets,
and one aptamer 117–119 . In addition, research in vaccinology has led to the development
of two mRNA-based vaccines 120,121 . With the discovery of new activities performed by
RNAs, coupled with the growing recognition that transient induction of a therapeutic effect can lead to long-lasting health benefits, it is anticipated that the clinical development
pipeline will continue to be enriched with therapeutic RNAs in the future 115 .
1.3.1 . Aptamers and related molecules
Aptamers are short single-stranded DNA or RNA oligonucleotides, typically 15 to
100 bases in length that can specifically recognize targets with high affinity and selectivity. Often called “chemical antibodies” because of this ability, they adopt stable threedimensional shapes both in vitro and in vivo 11 . As proteins are the most common drug
targets in drug discovery, RNA aptamers that modulate protein activity are increasingly
attractive.
Aptamers have a broad range of potential therapeutic applications 122 . Macugen 123 is
an example used to treat age-related macular degeneration by targeting vascular endothelial growth factor. AS1411 124 has shown promise in oncology by targeting nucleolin, an
over-expressed protein in cancer cells. NOX-A12 125 is another aptamer that has shown
potential in oncology by targeting the chemokine CXCL12, which is involved in tumor
growth and metastasis.
They also have potential applications in other disease areas. For example, NOXE36 126 targets the inflammatory cytokine interleukin-6 and has shown promise in treating
type 2 diabetes and NOX-H94 127 the pro-inflammatory protein HMGB1 (so having potential applications in treating inflammatory disorders). ARC1779 128 is an aptamer that
interacts with the von Willebrand factor and has potential applications in the treatment
of thrombotic disorders. Furthermore, aptamers have been developed to diagnose and
treat tuberculosis 129 .
These molecules are selected from large libraries of random oligonucleotides containing up to 1016 unique sequences. The process of aptamer selection, termed Systematic
1.3. Oligonucleotide therapeutics
17
Evolution of Ligands by Exponential Enrichment (SELEX), was first developed in 1990
by Tuerk and Gold 130 , and Ellington and Szostak 131 . The selection cycle, whether for
DNA or RNA sequences, on proteins, on cellular levels, or in living animals, requires
three main steps: (i) incubating a target with a library containing randomized sequences,
(ii) partitioning bound sequences from non-bound ones, and (iii) recovering and Polymerase Chain Reaction (PCR) amplifying the bound sequences 132 . The selection cycle
is repeated until the sequence is enriched with the desired affinity.
While still considered a gold standard for aptamers generation, SELEX techniques
have traditionally been laborious and time-consuming. Recent research efforts have been
made to enhance and streamline the screening process. Innovative techniques that preserve the benefits of SELEX while simplifying the screening process for improved efficiency have been introduced and reviewed extensively (refer to reference 133).
Figure 1.3: Common strategies in the chemical modifications of nucleic acid aptamers
and their purposes. Taken from reference 134.
Considerable progress on aptamers modifications has been made by the company SomaLogic, which uses chemical modifications on bases to give aptamers more structural
diversity and more robust target binding ability. Their Slow Off-rate Modified Aptamers
(SOMAmers) demonstrate enhanced binding affinities and kinetics compared to traditional aptamers.
By substituting dT bases in oligonucleotide libraries with a modified dU base at the
5-position of the heterocyclic base, this approach has led to the discovery of many new
aptamers for targets that were previously unselectable. Also, by incorporating various
hydrophobic groups (benzyl, naphthyl, and indole) at the 5-position, researchers have
expanded the range of potential targets that can be effectively bound and identified 134 .
Additionally, modifications on the sugar ring, including 2’-F-ribose, 2’-NH2-ribose, 2’OMe-ribose, or Locked Nucleic Acids (LNAs) that bridge the 2’ and 4’-ribose positions
covalently, have been introduced by incorporating unnatural nucleotides into oligonucleotides using the mutational T7 RNA polymerase, enzymatically. All these techniques
18
1. BIBLIOGRAPHIC REVIEW
effectively improve the stability against nucleases and prolong serum half-life 135–137 .
Phosphate linkage modifications can also be introduced into aptamers for stabilizing
the chains of nucleic acids by replacing conventional phosphate backbones with sulfurcontaining phosphate ester bonds 138–140 , including phosphorothioate and phosphorodiothioate bonds 141,142 .
Kimoto et al. reported the incorporation of up to three unnatural nucleotides with
the 7-(2-thienyl)imidazo- [4,5-b]pyridine (Ds base) nucleotides into an oligonucleotide
library. The resulting DNA aptamers against vascular endothelial cell growth factor-165
and interferon-γ had Kd values of 0.65 pM and 0.038 nM, respectively, with more than a
100-fold improvement in affinities compared to the aptamers containing natural bases 143 .
The invention of mirror image aptamers or spiegelmers was a creative approach to
bypass the degradation of nucleases in the body. To identify spiegelmers, conventional
aptamers with a D-configuration are generated to target a mirror image of the desired
biological target. The identified aptamers’ sequence is then produced in its respective
mirror-image configuration using non-natural L-nucleotides. Guided by symmetry principles, the resulting L-aptamers bind to the natural target with the same affinity as the
D-aptamers bind to the mirror-image target 144 .
Other modification strategies to protect aptamers against exonucleases use the 3’-3’
and 5’-5’ capping methods with an inverted nucleotide in the terminus 145 or even the
cyclization of nucleic acids by linking 5’- and 3’-termini 146 .
Despite all synthetic efforts and achievements to make aptamers more stable, there is
an inherently limited chemical diversity compared to antibodies, which makes it more challenging to find high-affinity binders for some targets, especially those lacking well-defined
binding pockets. Furthermore, the SELEX methodology cannot guarantee that the best
binders have been selected (due to the sequence space’s combinatorial complexity) and
can result in batch-to-batch variability, where each round of selection yields slightly different sequences and affinities. This can complicate manufacturing and hinder regulatory
approval.
While modified nucleotides can improve nuclease resistance, aptamers and SOMAmers
still generally have more limited serum stability than antibodies and while less immunogenic, they can still elicit immune responses, especially for therapeutic applications. Modifying nucleotides and pegylation helps reduce immunogenicity but does not eliminate it.
1.4 . BACE1 as molecular target in the Alzheimer’s Disease
Presently, more than 50 million individuals globally have dementia. This number is
predicted to nearly double every 20 years, reaching 82 and 152 million in 2030 and 2050,
respectively. Most of this rise is expected to occur in developing nations, where 60%
of dementia patients currently reside. However, by 2050, this percentage is projected to
increase to 71% 147 . Roughly 60 to 70% of dementia cases worldwide are attributed to
AD, affecting approximately 35 million individuals.
This neurodegenerative condition is linked to aging and is experienced by 15% of those
1.4. BACE1 as molecular target in the Alzheimer’s Disease
19
aged 80 years or above. This situation escalates in developed and emerging nations and
is among France and Cuba’s six primary causes of death. The global cost of dementia, as
estimated by the World Health Organization (WHO), is $604 billion annually, surpassing
the combined expenses of cancer, cardiovascular disease, and stroke 148,149 .
AD dementia is preceded by a pre-clinical phase that may last for 15 to 20 years
and a prodromal period that persists for 3 to 6 years before the onset of dementia. Primary symptoms include difficulty remembering information that interferes with everyday
activities, struggles with problem-solving and planning ahead, finding it hard to complete
previously familiar tasks (whether at home, work, or in leisure activities), feeling confused
about the time or place, having difficulty recognizing visual images and spatial relationships, new difficulties with expressing verbally or in writing, demonstrating poor judgment
or decision-making skills, withdrawing from social or work-related activities, and changes
in mood and personality 150 .
In a comprehensive report of 2022, 143 agents were reported in 172 trials assessing
new therapies for AD: 31 agents in Phase 3 trials, 82 in Phase 2, and 30 in Phase 1.
Figure 1.4 shows all pharmacologic compounds currently in clinical trials for AD.
The most common agents being studied are Disease-modifying Therapy (DMT) (119
agents; 83.2% of the total number of agents in trials); 24 (16.8%) are symptomatic agents,
including 14 (9.8% of all agents in trials) targeting cognitive enhancement and 10 (6.9%
of all agents in trials) intending to treat neuropsychiatric and behavioral symptoms. Of
the DMTs, 40 (33.6% of DMTs) are biologics and 79 (66.4% of DMTs) are small
molecules. Twenty (16.8%) DMTs have amyloid, 13 (10.9%) have tau, 23 (19.3%) have
inflammation, and 19 (16%) have synaptic plasticity/neuroprotection as their primary
mechanistic targets. Considering DMTs only, 21 (67.8%) of Phase 3 agents are DMTs;
71 (86.6%) Phase 2 drugs are DMTs; and 27 (90%) Phase 1 agents are DMTs. There
are 53 repurposed agents in the pipeline comprising 37.1% of the candidate therapies (all
phases combined) 151 .
Some molecular and neuropathological manifestations of AD include impairment of
N-methyl-D-aspartate receptor-related signaling pathways, intracellular accumulation of
hyperphosphorylated tau protein, extracellular deposition of amyloid-beta, oxidative stress,
metal ion metabolism disorders, abnormalities of lipid metabolism, and disturbances 152 .
AD ’s two essential pathological aspects are related to forming plaques of Amyloid-beta
(Aβ) peptides and tangles of tau proteins.
Although the physio-pathology of AD is not fully known, the currently most accepted
model and the one investigated with a therapeutic objective is based on the amyloid hypothesis 153 . The accumulation of Aβ peptides in the brain tissue constitutes the starting
point for the characteristic pathological changes of the disease. From the physiological
point of view, the formation of amyloid plaques would give rise to synaptic dysfunction
that leads to dementia.
At the molecular level, the joint action of BACE1 and γ secretases on Amyloid
Precursor Protein (APP) produces Aβ peptides of variable lengths (see Figure 1.5),
but mostly between 39 and 42 amino acids (Aβ-39, Aβ-40, Aβ-42). These peptides
Figure 1.4: The agents are categorized by phase of the clinical trial (Phase 1, 2, or 3)
and by type of pharmacological compound (biologics, disease-modifying small molecules,
or symptomatic agents). The shape of the icon represents the population of the trial,
and the color represents the Common Alzheimer’s Disease Research Ontology (CADRO)based class of the agent. The "Other" category includes CADRO classes with three or
fewer agents in trials. Agents that are new to the pipeline since 2020 are underlined.
Taken from reference 151.
20
1. BIBLIOGRAPHIC REVIEW
can aggregate to form oligomers called amyloid fibrils, among which certain aggregated
forms of Aβ42 have been structurally characterized 154 . Therefore, many drug candidates
targeted at β- or γ-secretase have been developed to treat AD.
Figure 1.5: The amyloidogenic pathway of Amyloid Precursor Protein (APP) involves the
sequential cleavage of APP by β -secretase.The remaining fragment is then cleaved by γ secretase, resulting in the formation of the Aβ peptide. Due to its high propensity to aggregate, Aβ peptide oligomerizes, accumulates, and forms amyloid senile plaques leading
to the documented alterations in Alzheimer’s disease.Taken from reference 155.
γ-secretase inhibitors and modulators were the first to be tested in clinical trials.
However, all the trials have had to be halted due to lack of efficacy or sometimes severe
side effects 156 . γ-secretase has many other biological substrates that could explain the
adverse effects, and therefore, the focus turned to β-secretase inhibitors 157 .
There is considerable evidence regarding the involvement of BACE1 in AD pathogenesis. Increased protein levels and activity of BACE1 have been reported in the normal
aging brain and to an even more considerable extent in the AD brain 158–160 . In addition, a mutation in APP resulting in increased BACE1 cleavage (called the Swedish
mutation) results in increased Aβ production and a familial form of AD (FAD) 161 . On
the contrary, the so-called Icelandic mutation in APP 162 alters one amino acid at the
BACE1 cleavage site of APP, reducing the ability of BACE1 to cleave APP by about
30% 163 , is strongly protective against AD. Therefore, various small molecules inhibiting
BACE1 were developed and brought to clinical trials.
Clinical trials of BACE1 inhibitors for treating AD patients have yielded disappointing results. Despite their ability to reduce Aβ plaque load 164,165 in both animals and
humans 166,167 , they have not demonstrated improvements in cognitive function 164,165 , so
they have been discontinued during phase II or III trials due to a lack of efficacy, side
effects, or both, including cognitive decline 167 .
Despite the recurrence of failure observed in clinical trials of BACE1 inhibitors, recent
studies have shed light on potential explanations for their negative impact on synaptic
transmission. It has been suggested that the adverse effects could be attributed to the
high concentrations of inhibitors used in those studies. Conversely, low-dose BACE1
inhibition, which results in a moderate reduction (30-50%) of Aβ peptides, has shown no
significant impact on synaptic transmission 168 .
In the pursuit of improving cognition in AD, various strategies have been explored,
1.4. BACE1 as molecular target in the Alzheimer’s Disease
21
including BACE1 inhibition and immunotherapy aimed at clearing brain amyloid plaques
or neurofibrillary tangles 157,169 . Recent research has highlighted previously overlooked
benefits associated with targeted BACE1 inhibition in microglia. These benefits include
enhanced amyloid clearance and improved cognitive performance 170,171 .
1.4.1 . BACE1 and BACE2 structural similarities
Similar to BACE1 (52% sequence identity and 68% sequence similarity 172 ), BACE2
is a type I transmembrane protein that belongs to the peptidase A1 family (also called
the pepsin family) of aspartyl proteases. Unlike BACE1, which is highly expressed in
the brain, BACE2 is more prominently found in peripheral tissues (colon, kidney, and
pancreas) 173 . There are hints, however, indicating that side effects caused by BACE2
cross-inhibition in the brain may become apparent upon inflammation events characteristic
of the AD 174 .
BACE1 and BACE2 (referred as BACE-X from now on) are close homologs that
share sequence similarity and highly similar 3D structures. Mirsafian et. al. conducted an
evolutionary trace study for the structural comparison of BACE-X 21 . They performed
the superposition of the crystal structures of BACE1 (PDB ID: 1FKN) and BACE2
(PDB ID: 2EWY) yielded an RMSD of 1.46 Å over 373 C-alpha atoms, indicating that
these structures are remarkably similar to each other. The researchers also identified 123
group-specific residues (present only in one of the two proteins) accounting for 24.5% of
human BACE1 and 23.7% of human BACE2).
The BACE-X active site comprises the catalytic aspartic acid dyad residues, the
flap region, and 10s loop (see Figure 1.6). The amino acids within the active sites
of BACE-X are very well-conserved at greater than 80% identity, making the design
of selective BACE1 or BACE2 inhibitors exceptionally challenging 175 . Interestingly,
there are group-specific residues in this region also; Pro70, Ile110, Ile126, and Asn233
of BACE1 substituting Lys86, Leu126, Leu142, and Leu246 of BACE2, respectively.
These four residues are expected to play a pivotal role in determining the selectivity of
enzymatic activity, especially Pro70, since the proline’s cyclic property may affect the flap
region’s flexibility.
The structural similarity of these two enzymes is at the root of the off-target effect
they exhibit. Off-target inhibition is a term that describes the effects that can occur
when a drug binds to targets (proteins or other molecules in the body) other than those
for which the drug was meant to bind. This can lead to unexpected potentially harmful
side effects 4 . The majority of BACE1 inhibitors in past and current clinical trials do
not show significant selectivity for BACE1 over BACE2. To prevent such potential
undesired physiologic effects, selectivity for BACE1 over BACE2 has been targeted by
several companies 172,176 .
The activation and inhibition of BACE1 exhibit a distinctive feature characterized by
its sensitivity to pH levels. Results from fluorescence experiments reveal that the peptide
cleavage activity of BACE1 is highly specific to a narrow pH range, with optimal activity
occurring at pH 4.5. However, this activity sharply decreases when the pH falls below 4
or rises above 5.9, as demonstrated by the same experiments 177,178 .
22
1. BIBLIOGRAPHIC REVIEW
Figure 1.6: The binding pocket of BACE1. Three important parts are highlighted in red; the
flap region (the most flexible part of the binding site controlling the access of substrates),
the catalytic aspartic acid dyad (crucial for the proteolytic activity of BACE1), and the 10
seconds loop (10s loop).
The enzyme’s catalytic action involves the following steps (see Figure 1.7): (i) the
substrate binds to the enzyme’s active site, and the catalytic dyad activates a water
molecule by forming a hydrogen bond, (ii) the activated water molecule makes a nucleophilic attack on the scissile carbonyl in the peptide, leading to the formation of a diol
intermediate. This intermediate is stabilized by forming hydrogen bonds with the carboxyl
group of aspartates in the catalytic dyad. (iii) Ultimately, a proton is transferred from
Asp to the leaving amino group, resulting in the peptide bond cleavage 179 .
Figure 1.7: Mechanism of action of the catalytic aspartic acid residues of BACE1.
Taken from reference 180.
The intricate mechanism behind BACE1’s pH-regulated enzymatic activity and peptideinhibitor binding has been explored through computational studies. Contrary to previous
assumptions that dehydration at low pH was responsible for inactivation, Constant pH
Molecular Dynamics (CphMD) simulations demonstrate that the active site maintains
hydration but assumes a self-inhibited state involving Tyr71 flap residue 181 . This finding is
consistent with an earlier structural report that identified eight conserved water molecules
in the BACE1 active site, five of which were conserved in 90% of 153 studied structures
and the remaining three in 70-80% of the structures 182 .
1.5. Mathematical background
23
1.5 . Mathematical background
It is natural for methodological contributions in computational chemistry, to integrate
diverse mathematical concepts. This is because mathematics offers a rigorous framework
for formulating models, analyzing data, and making predictions. In this section, we aim
to provide a clear understanding of those key definitions necessary to comprehend the
algorithms we propose in Chapters 4 and 5.
1.5.1 . Big-O notation
During the software development process, it is essential to evaluate how well a computer program performs in various potential scenarios. The number of fundamental operations an algorithm executes as a function of the length of its input will typically be used
to assess its computational efficiency.
A function T from the set N of natural numbers to itself can be used to determine
an algorithm’s efficiency if T (n) is equal to the number of most basic operations the
algorithm can perform on inputs of length n. However, the low-level specifics of what a
fundamental operation is, can sometimes make this function T overly dependent on them.
The well-known Big-O notation helps to ignore these low-level details and concentrate on
the big picture 183 , allowing to classify algorithms according to how their run time or space
requirements grow as the input size grows (a.k.a asymptotic analysis of function growth).
A formal definition of Big-O can be stated as follows: If f , g are two functions from
N to N, then we say that f = O(g) if there exists a constant c such that f (n) ≤ c ∗ g(n)
for every sufficiently large n. By using the Big-O notation, we ignore (i) behavior on small
inputs (because programs typically run fast enough on small test cases), and (ii) multiplicative constants (because they are extremely sensitive to details of the implementation,
hardware platform, etc.) 183 .
Assume that f (n) = n and g(n) = n2 . n2 is smaller for low positive input values.
They have the same value for input 1, but then g grows and rapidly diverges to become
significantly larger than f . We will only be interested in the faster-growing term when a
function is the sum of faster and slower-growing terms. For instance, n2 will be equal to
n2 + 7n + 105. The term with the fastest growth controls the behavior of the function
as the input n increases (the first term in this case) 184 .
Some familiar order of growth in computer science are illustrated in Figure 1.8. Constant growth is represented by O(1); linear growth is O(n); logarithmic growth is O(logn);
log-linear growth is O(nlogn); polynomial growth is O(nk ); exponential growth is O(k n );
factorial growth is O(n!). These growths can be compared from best to worst as follows:
O(1) < O(logn) < O(n) < O(nlogn) < O(nk ) < O(k n ) < O(n!)
1.5.2 . Basics of graph theory
Graph Theory is a branch of mathematics devoted to studying abstract objects called
graphs, which represent numerous situations in which several elements are mutually related. Applications of graphs are diverse and widespread. Much of this area’s success is
24
1. BIBLIOGRAPHIC REVIEW
Figure 1.8: Some familiar algorithms’ order of growth. Taken from reference 185.
due to the ease at which ideas and proofs may be communicated pictorially in place of,
or in conjunction with, the use of purely formal symbolism 20 .
A graph G = (V, E) is a pair of a set of vertices (a.k.a nodes) V and a set of edges
E. Each edge is a two-element subset of V and denotes the adjacency between the nodes
it connects. In Figure 1.9A, V = {1, 2, 3, 4, 5, 6, 7} and E = {{1, 3}, {2, 3}, {2, 4}, {3, 4}, {3, 5}, {3, 6}, {4, 5}, {4, 6},
Two connected nodes are called neighbors, and the number of neighbors of a given
node constitutes its degree. In Figure 1.9A, {2, 3, 5, 6} are neighbors of 4, whose degree
is 4.
A path is a non-empty graph P = (V, E) of the form V = x0 , x1 , ..., xk , E =
x0 x1 , x1 x2 , ..., xk−1 xk , where the xi are all distinct. The vertices x0 and xk are linked
by P and are called its ends; the vertices x1 , ..., xk−1 are the inner vertices of P . The
number of edges of a path constitutes its length. In Figure 1.9A, nodes {1, 3, 2, 4, 6}
form a path of length 3 with ends {1, 6} and inner vertices {3, 2, 4}.
An edge with identical ends is called a loop, and an edge with different ends is a link.
Two or more links with the same pair of ends are said to be parallel edges. In Figure
1.9A, node 6 has a loop and nodes {3, 5} are the ends of two parallel edges.
A graph is simple if it has no loops or parallel edges. A complete graph is a simple
graph in which any two vertices are adjacent. Figure 1.9B represents a simple graph which
is also complete.
A graph G is connected if for any two vertices a and b there is a path from a to b.
Connectivity of simple graphs can be represented using its adjacency matrix, a symmetric
matrix M in which Mij = 1 if nodes i and j are connected and Mij = 0 otherwise. If
there is no directionality in the definition of the edges and no data associated with them, it
is said that the graph is undirected and unweighted, respectively. Figure 1.9C exemplify
the adjacency matrix of the connected, undirected, and unweighted graph of Figure 1.9B.
If P = x0 ...xk−1 is a path and k ≥ 3, then the graph C := P + xk−1 x0 is called
a cycle.The length of a cycle is its number of edges (or vertices). Notice that if a
1.5. Mathematical background
25
Figure 1.9: Illustration of basic concepts of graph theory.
connected graph contains a cycle, removing an edge from the cycle will not disconnect
the graph. Nodes {2, 3, 4} of graph in Figure 1.9A make a cycle of length 3.
An acyclic graph, one not containing any cycles, is called a forest. A connected
forest is called a tree. Thus, a forest is a graph whose components are trees. The vertices
of degree 1 in a tree are its leaves, the others are its inner vertices. Figure 1.9D depicts
a forest formed by two trees.
A sub-graph of a graph G is a graph H such that every vertex of H is a vertex
of G, and every edge of H is an edge of G also. In other words, V (H) ⊆ V (G) and
E(H) ⊆ E(G). In Figure 1.9E, the graph H is a sub-graph of the graph G.
A spanning sub-graph of a graph G is a sub-graph obtained by edge deletions only,
in other words, a subgraph whose vertex set is the entire vertex set of G. If S is the set
of deleted edges, this sub-graph of G is denoted G \ S. Observe that every simple graph
is a spanning sub-graph of a complete graph. In Figure 1.9E, the graph I is a spanning
sub-graph of G.
A sub-tree of a graph is a sub-graph that is a tree. If this tree is a spanning sub-graph,
it is called a spanning tree of the graph. A connected spanning subgraph of minimum
26
1. BIBLIOGRAPHIC REVIEW
weight is called minimum spanning tree. The Figure 1.9F represents a weighted graph
(left) and its minimum spanning tree (right).
Algorithms for graph search (or graph traversal) examine a graph for broad discovery or explicit search and are typically used as a foundation for additional procedures.
They will attempt to visit as much of the graph as possible, but there is no assumption
that the pathways they take will be computationally optimal.
Depth-first search (DFS) is a tree-search in which the vertex added to the tree T at
each stage is a neighbor of the most recent addition to T as possible. In other words, we
first scan the adjacency list of the most recently added vertex x for a neighbor not in T .
If there is such a neighbor, we add it to T . If not, we backtrack to the vertex added to
T just before x, examine its neighbors, and so on. The resulting spanning tree is called a
depth-first search tree or DFS-tree (see Figure 1.10)).
1
2
3
4
5
1
1
1
2
4
2
3
5
1 -> 2
4
1
3
5
1 -> 2 -> 4
2
4
1
3
5
1 -> 2 -> 4 -> 5
2
4
3
5
1 -> 2 -> 4 -> 5 -> 3
Figure 1.10: Graphical description of the depth-first search order.
A clique is a sub-graph in which vertices are all pairwise adjacent. If a clique is not
contained in any other clique, it is said to be maximal, while the term maximum clique
denotes the maximal clique with a maximum number of nodes (maximum cardinality).
The Maximum Clique Problem (MCP) deals with the challenge of finding the maximum
clique inside a given graph. In Figure 1.9G, nodes {1, 2, 3} denote a maximal clique.
Similarly, nodes {2, 3, 4, 5} also denote a maximal clique that turns out to be the maximum
clique of the graph. Graph in Figure 1.9B is also a clique.
A central idea of MCP algorithms is the notion of vertex coloring. A proper
vertex coloring refers to assigning a particular color (or any other unique label) to each
vertex of a graph so that adjacent vertices do not share the same color. The Vertex
Coloring Problem consists of finding a proper coloring that uses the fewest number of
colors, known as the graph’s chromatic number (χ). It is common to employ coloring
techniques because χ is an upper bound to a graph’s maximum clique size. This property
is exploited to discard impossible solutions and guide the search for cliques. Graph in
Figure 1.9G has χ = 4 .
In computer science, there exists a category of problems known as NP-complete.
These problems are characterized by the property that no known algorithm can solve them
exactly in polynomial time. The MCP and the Vertex Coloring Problem are examples of
NP-complete problems.
While finding an exact solution to these problems is computationally infeasible for
large instances, there are approximate algorithms and heuristics that can provide rea-
1.5. Mathematical background
27
sonable solutions within a reasonable amount of time. Heuristic methods utilize logical
assumptions and techniques to satisfactorily solve complex problems.
Despite this limitation, heuristics are extensively utilized in practical applications
where a slight deviation from the optimal solution is acceptable and does not significantly impact the overall outcome. These heuristics offer a practical trade-off between
computational efficiency and solution quality, enabling us to effectively address real-world
instances of NP-complete problems.
1.5.3 . Similarity measures
The term similarity measure refers to a function used for comparing objects of any
type. Thus, the input of a similarity measure is two objects, and the output is generally a
number between 0 (entirely dissimilar) and 1 (identical). Similarity is related to distance,
which is its inverse. A similarity of 1 implies a distance of 0 between two objects. The
selection of the proper similarity function is a critical parameter in many applications. For
example, in molecular clustering (see Section 1.6), among the most common analyses that
explicitly rely on molecular similarity, one is interested in grouping molecules conformations
based on their geometrical similarity.
There are two major classes of similarity functions: metric functions and non-metric
functions. In order for a function d to be a metric it has to satisfy all the following three
properties for any objects X, Y , Z:
1. d(X, Y ) = 0 if X = Y (identity axiom)
2. d(X, Y ) = d(Y, X) (symmetry axiom)
3. d(X, Y ) + d(Y, Z) ≥ d(X, Z) (triangle inequality)
Metric similarity functions are very widely used in search operations because of their
support of the triangle inequality. The triangle inequality can help prune a lot of the
search space, by eliminating objects from examination that are guaranteed to be distant
to the given query. The most frequently used metric similarity function is the Euclidean
distance.
For two objects X and Y that are characterized by set of n features X = (x1 , x2 , . . . , xn )
and similarly Y = (y1 , y2 , . . . , yn) the Euclidean distance is defined as
v
u n
uX
D = t (xi − yi )2
(1.17)
i=1
When comparing molecular structures, however, the Root Mean Square Deviation
(RMSD) is the most universally employed similarity function. It is computed as the average distance between every pair of equivalent positions (Equation 1.18). When molecules
are aligned first (to minimize the RMSD value by ignoring translation and rotations),
this function is referred to as optimal RMSD (RMSDopt ).
s
RMSD =
PN
i=1
N
di 2
(1.18)
28
1. BIBLIOGRAPHIC REVIEW
Despite its practical utility, the RMSD has punctual drawbacks already described 186 ,
being the most remarkable its inherent difficulty in characterizing very flexible zones of a
molecular structure 187 . Although some authors have proposed normalized and weighted
schemes to work with RMSD 188,189 that could alleviate these inconveniences, they are
more computationally demanding alternatives less frequently employed.
Euclidean or Euclidean-like metrics are exploited in molecular similarity comparison
applications under the assumption that they are faster to compute than the optimal
RMSD (as fewer unitary operations are involved and also because no alignment is performed between every pair of structures). An example of this philosophy is the software
qtcluster of the ORAC suite (see Section 1.6) that employs the maximum difference between corresponding pairs of atoms (Equation 1.19) to compare molecules. Under this
metric, the similarity of two elements Sm and Sn is assessed by the absolute maximum
value of the difference between their inter-atomic distances.
dSm ,Sn = maxi,j |dij (Sm ) − dij (Sn )|
(1.19)
Clustering results of two different procedures can be also compared using several
indices or scores from which the Adjusted Rand Index (ARI) stands out. Let’s consider
an MD trajectory T as a set of N elements (frames) T = {t1 , t2 , ..., tN }. The outcome
of applying a given clustering algorithm on T is a partition P of the N objects into C
clusters, P = {p1 , p2 , ..., pC }, such that the union of all the subsets in P is equal to T
and the intersection of any two subsets in P is empty.
Considering N2 = N (N − 1)/2 as the total number of element pairs (ti , tj ) in T ,
there exist four classifications of pairs when comparing Q and B; (a) elements in a pair
are placed in the same group in Q, and the same group in B (true positives), (b) elements
in a pair are placed in the same group in Q, and different groups in B (false negatives),
(c) elements in a pair are placed in the same group in B, and different groups in Q
(false positives), and (d) elements in a pair are placed in different groups in Q and B
(true negatives). It is possible to assess the equivalence between Q and B based on the
number of pairs of elements lying in any of these four categories.
The Rand Index (RI) 190 (Equation 1.20) expresses the fraction of pairs of elements
on which two clusterings coincide (from 0 for unrelated to 1 in a perfect match). However,
RI approaches its upper limit as the number of clusters increases because d tends to grow
even for poorly related partitions, giving a high score.
RI =
a+d
a+b+c+d
(1.20)
An Adjusted Rand Index (ARI) 191,192 corrected against “agreements-by-chance” has
been extensively used (Equation 1.21) to measure the correspondence between partitions
created by clustering algorithms. ARI extends from non-bounded negative values (poorly
related partitions) to 1 (highly similar partitions).
ARI =
N
2
(a + d) − [(a + b)(a + c) + (c + d)(b + d)]
N 2
− [(a + b)(a + c) + (c + d)(b + d)]
2
(1.21)
1.5. Mathematical background
29
The Tanimoto Index (TI), also known as the Tanimoto coefficient or the Jaccard
index, is a commonly employed similarity measure for comparing the diversity of sample
sets 193 . It is defined as the ratio of the size of the intersection of two sets divided by the
size of their union. The TI ranges from 0 to 1, with 0 indicating no similarity between
two sets and 1 indicating identical sets. Typically, a TI greater than 0.7 is considered
a good indicator that two molecules or samples are similar though this thresholds can
vary based on the data and application. The TI is popular due to its simple formulation,
bounded range, and interpretability, providing a straightforward quantitative measure of
similarity for binary sample sets.
1.5.4 . Essential data structures
Data structures can be defined as the organization of data in a logical or mathematical
model. It must be simple enough that one can effectively process the data when necessary.
The data present in the data structure are processed using several operations like traversing
(access to each element present in the data structure exactly once), searching (finding the
location of a particular element with a key attribute), inserting (adding new elements),
and deleting (removing old elements) 194 .
Below we briefly describe a set of data structures that were relevant in the development
of the algorithms we designed in Chapters 4 and 5).
An array is an ordered collection of elements of the same type, the number of elements
being fixed unless the array is flexible. Each element in an array is distinguished by a unique
list of index values that determine its position in the array. Each index is of a discrete type.
The number of indices is fixed, and the number and ordering of the indices determines
the dimensionality of the array 195 .
A one-dimensional array, or vector (v), consists of a list of elements distinguished by
a single index. If v is a one-dimensional array and i is an index value, then vi refers to
the ith element of v. If the index ranges from L through U then the value L is called
the lower bound of v and U is the upper bound. Usually in mathematics and often in
mathematical computing the index type is taken as integer and the lower bound is taken
as one 195 .
In a two-dimensional array, or matrix, the elements are ordered in the form of a table
comprising a fixed number of rows and a fixed number of columns. Each element in such
an array is distinguished by a pair of indexes. The first index gives the row and the second
gives the column of the array in which the element is located. The element in the ith
row and j th column is called the i, j th element of the array 195 . Of specially interest for
our work are bit-arrays (bit-vectors and bit-matrices) in which the type of the element are
bits.
A heap 196 is made up of nodes that contain values. A typical heap has a root node
at the top, which may have two or more child nodes directly below it. Each node can
have two or more child nodes, which means the heap becomes wider with each child node.
When displayed visually, a heap looks like an upside down tree and the general shape is a
heap.
While each node in a heap may have two or more children, most heaps limit each
30
1. BIBLIOGRAPHIC REVIEW
node to two children. These types of heaps are also called binary heaps and may be used
for storing sorted data. For example, a binary min heap stores the lowest value in the
root node. The second and third lowest values are stored in the child nodes of the root
node. Throughout the tree, each node has a greater value than either of its child nodes.
A "binary max heap" is the opposite.
Space partitioning is the process of dividing a space (usually a Euclidean space) into
two or more non-overlapping regions. Any point in the space can then be identified to
lie in exactly one of the regions. A k-dimensional tree (kd-tree) 197 (see Figure 1.11)
is a space-partitioning data structure for organizing points in a k-dimensional space. A
kd-tree is constructed through iterative bisections of the input data along a single
coordinate. These cuts are made at points producing a maximum spread in the selected
coordinate’s distribution.
Every non-leaf node in the tree acts as a hyperplane, dividing the space into two partitions. This hyperplane is perpendicular to the chosen axis, which is associated with one
of the k dimensions. There are different strategies for choosing an axis when dividing, but
the most common one would be to cycle through each of the k dimensions repeatedly and
select a midpoint along it to divide the space. For instance, in the case of 2-dimensional
points with x and y axes, we first split along the x-axis, then the y-axis, and then the
x-axis again, continuing in this manner until all points are accounted for.
Figure 1.11:
Partition
Taken from reference 198.
of
a
bi-dimensional
space
using
a
kd-tree.
kd-trees are a useful data structure for several applications, such as searches involving a multidimensional search key like nearest neighbor searches. Unfortunately, efficient
usage cases of kd-trees are restricted to Euclidean metric spaces of low dimensionality.
Such limitation prevents their utilization in the high-dimensional spaces that characterize
molecular conformations.
Vantage point trees (vp-trees) 199 are an alternative to kd-trees that were conceived to work with general metrics in high-dimensional spaces. Rather than performing
cuts among the coordinates values, nodes of the vp-tree split the database into smaller
subspaces employing distinctive elements known as Vantage points (vps). By convention, near-to-vp instances constitute the left subspace, while far points are grouped into
1.5. Mathematical background
31
the right subspace. The recursive partition of the input database then leads to a binary
tree. In a vp-tree, every frame has a "perspective" on the entire T via their distance
to all other frames. This notion of "perspective" is a direct consequence of the triangle
inequality represented in Equation 1.22 that holds for every pair of frames (a, b) ∈ T . In
Equation 1.22, d(a, b) denotes the distance between two points a and b, which will always
be greater or equal to the absolute value of the difference between distances from p to a
and b, respectively.
d(a, b) ≥ |d(p, a) − d(p, b)|
(1.22)
Given a metric space (S, d) and some finite subset (T ∈ S) representing a given
molecular ensemble, the goal of a vp-tree encoding is to organize T in a way that the k
nearest neighbors of every query frame q, may be located faster than the naive approach
of visiting all frames in T for each query. Suppose that for some frame p ∈ T , the median
(µ) of the p-versus-all distances is determined. Then T can be split into two subspaces;
the left subspace (or inside sphere Spl ), containing frames closer than µ to p, and the
right subspace (or outside sphere Spr ), containing frames at µ or larger distance values
from p (see Figure 1.12). Spl and Spr will have roughly the same size if there are relatively
few frames that lie exactly at µ.
Figure 1.12: Partition of a database via the vp p. Elements closer than µ to p form the left
subspace (inside the sphere in light gray) while the rest form the right subspace (outside
the sphere in dark gray). q and k denote a query point and its k th nearest neighbor,
respectively. τ and d(p, q) represent the distances from q to k and to p respectively.
Now suppose that for a query frame q ∈ Spl the k th nearest neighbors is solicited.
By only visiting frames inside Spl , it is possible to define a variable τ storing the distance
from q to the k th neighbor found so far. The relevance of vp-trees comes from the fact
that if d(p, q) ≥ µ + τ , then the Spr subspace can be safely removed from consideration
as searching their elements would not lead to a τ ≤ d(p, q). Similarly, if q ∈ Spr and
d(p, q) ≤ µ − τ , searching the Spl subspace is unnecessary. In both cases, a single point’s
"perspective" sufficed to prune the search significantly. However, if µ − τ < d(p, q) <
µ + τ no such reduction is possible and the whole T must be explored. Details on the
32
1. BIBLIOGRAPHIC REVIEW
mathematical validity of described notions is available in the fundamental publication of
Yianilos on vp-trees 199 .
1.5.5 . Bitwise operations
Bitwise operations are those that operate on a bit string, a bit array, or a binary
numeral at an individual bit level. These are primitive fast actions directly supported by
microprocessors that always get executed through bitwise operators. Table 1.1 contains
the results of applying four binary operations on two bit arrays X and Y . As illustrated,
AND operator only lights positions where both arrays are turned on. Inclusive OR light
positions where at least one of two bits compared is turned on. Exclusive OR, or XOR,
light positions where only one of two bits compared is turned on, while the complement
or negation operator (NOT) inverts the bit values of the passed operand.
Table 1.1: Bitwise operators logic.
X
Y
0
0
1
1
0
1
0
1
X&Y
X AND Y
0
0
0
1
X|Y
X OR Y
0
1
1
1
X^Y
X XOR Y
0
1
1
0
~X
NOT X
1
1
0
0
When properly combined, these operations may translate algorithms’ steps (checking,
erasing, combining, intersecting, etc.) into binary logic, potentially diminishing the global
run times and memory consumption.
1.6 . Clustering of molecular ensembles
Formally conceptualized as an unsupervised ML technique, clustering is a ubiquitous
tool across many branches of science that allows for grouping similar elements into sets
called clusters. Intuitively, entities within a cluster are more similar than elements from
other clusters 20,200,201 . Clustering methods play a fundamental role in extracting useful
information from big datasets and are applied in numerous and diverse tasks 202–205 .
In fields like computational chemistry, chemo- and bioinformatics, geometrical clustering of molecular data produced by docking, Molecular Dynamics (MD) and related
simulations 206,207 is one of the most frequently found analyses. In the particular subdomain of FBDD, clustering is employed in various stages, primarily to group similar
fragments or compounds based on their structural or physicochemical properties.
For example, clustering is used to create a diverse and representative fragment library
by grouping similar compounds and selecting an exemplar from each cluster. This ensures
a broad coverage of the chemical space and reduces redundancy in the library 208,209 .
Also, after screening the fragment library against the target protein, the hits are clustered
based on their structural or physicochemical properties, which helps prioritize the most
promising cases for further optimization and reduces the number of redundant or similar
compounds that will be progressed.
1.6. Clustering of molecular ensembles
33
Likewise, clustering algorithms can be used to compare the binding modes of lead
compounds to different proteins or targets. By identifying clusters of lead compounds that
bind to multiple targets, it is possible to predict potential off-target effects and optimize
the compounds to reduce their promiscuous binding. As well crucial for the FBDD is
the ability to find receptor hotspots (sites having a high propensity for ligand binding 210 )
that could provide insights into the most promising regions where a lead should bind.
These hotspots are generally obtained as the clustering output of probe explorations on
the receptor’s surface 211 .
1.6.1 . Types of clustering
After choosing an adequate metric that reflects the desired notion of similarity, selecting a clustering algorithm in line with the specific application is necessary. Many
options are available to the user, but their results are not always analogous (as they assume different cluster definitions), and none should be taken as an all-purpose tool. Due
to the inherent subjectivity associated with classification (the same set of elements can
be grouped according to many different criteria), some authors consider clustering as an
art 212 .
Different starting criteria can give rise to diverse taxonomies of clustering algorithms.
While it is challenging to define a singular, universal category that encompasses the vast
array of clustering algorithms, there is a consensus within the field of bioinformatics regarding the following families: partitional clustering, hierarchical clustering, fuzzy clustering,
neural network-based clustering, mixture model clustering, graph-based clustering, and
consensus clustering 213 .
An important distinction between types of clustering regards whether retrieved clusters
are hierarchical (nested) or partitional (unnested). An algorithm is said to be partitional
when the dataset gets divided into non-overlapping subsets (i.e. each element is in exactly
one subset). Using this broad definition, partitional clustering could cover many clustering
families.
By permitting clusters to have sub-clusters, it is possible to obtain a hierarchical
clustering, which is a set of nested clusters that are organized as a tree. Each node
(cluster) in the tree (except for the leaf nodes) is the union of its children (sub-clusters),
and the root is the cluster containing all the objects. It is worth noting that a hierarchical
clustering can be perceived as a sequence of partitional clusterings, which are retrievable
by cutting the tree at a particular level.
Exclusive clustering algorithms assign each object to a single cluster. However, this
restriction is often inadequate if elements can be reasonably placed in more than one
cluster, and in such cases, an overlapping (non-exclusive) algorithm may be more appealing. Instead of performing arbitrary labeling of the object to a single cluster, overlapping
clusterings place them in all the “equally good” clusters. On the other hand, a fuzzy clustering puts every object in every cluster and assigns them a membership score ranging
from 0 (absolutely does not belong) to 1 (absolutely belongs). An additional constraint
is often imposed on the fuzzy algorithm; the sum of the membership scores for each
object must equal 1. Note that a fuzzy clustering result can be converted to an exclusive
34
1. BIBLIOGRAPHIC REVIEW
clustering by assigning each object to the cluster in which its membership score is highest.
Clustering based on neural networks begins with a set of nodes, also known as
neurons, that are initially similar except for some randomly initialized parameters, which
cause each node to behave slightly differently. These nodes then learn from the data in
a competitive manner: active nodes reinforce their proximity within certain regions while
inhibiting the activities of other nodes.
Clustering based on mixture models is another significant family of clustering
techniques that has gained increasing interest recently. It involves formulating a clustering
kernel for each component in terms of a sampling density p(X|θ) where θ is an unknown
parameter set. Compared to algorithms based on Euclidean distance, mixture model
clustering often produces more meaningful results in cases where Euclidean distance-based
algorithms fail, particularly for time series and categorical data sets.
Graph-based clustering arises when data is depicted as a graph, where the nodes are
elements and the edges represent connections among objects. Thus a cluster is defined
as a connected component; a group of nodes connected to one another, but not to nodes
outside the group. Other types of graph-based clusters are also possible, for instance
clique clusters.
Combining multiple clustering results, called ensemble clustering, consensus clustering, or cluster aggregation, has received significant attention. It has been proposed to
address the inconsistency of stochastic clustering algorithms and clusterings produced with
different parameters. The underlying concept of ensemble clustering is that combining
various clusterings into a single consensus solution can highlight the common organization across different results. Ensemble clustering aims to produce a stable and robust final
clustering by merging results that may differ due to random initialization or algorithmic
variations.
1.6.2 . Molecular clustering
The upcoming sections focus on four molecular clustering algorithms that, in our
view, represent some of the most widely used or promising clustering methods that have
already been applied to molecular ensembles: (i) Quality Threshold (QT), covered in
Section 1.6.2.1, (ii) Daura, discussed in Section 1.6.2.2, (iii) Density Peaks (DP), detailed
in Section 1.6.2.3, and (iv) Hierarchical Density-Based Spatial Clustering of Applications
with Noise (HDBSCAN), explored in Section 1.6.2.4.
1.6.2.1
Quality Threshold
The QT clustering was initially designed for grouping gene expression patterns. First
proposed by Heyer et al. in 1999 214 , the authors intended to overcome severe limitations
inherent to other available clustering algorithms like k-means, self-organizing maps, and
hierarchical variants. Since then, besides its usage in clustering gene expression, QT has
been employed in fields other than microbiology 215–218 , and in particular to deal with
molecular ensembles like MD trajectories 219,220 .
This algorithm excels in cases where strongly geometrically correlated conformations
1.6. Clustering of molecular ensembles
35
need to be returned as clusters. Several tools like VMD 221 (through its measure cluster command), ORAC 220 (through its qtcluster procedure), WORDOM 222 (through its
qt-like option) and a standalone script contributed by Melvin et al. in 2016 described as
"A python implementation of the quality threshold clustering algorithm of Heyer, 1999,
specialized to molecular dynamics trajectories" 223 . These variants all assert to use clustering procedures based on QT, but the veracity of this claim is thoroughly discussed in
Section 4.1.1.
If we define the diameter of a cluster C as the maximum distance between any pair
of its elements (Equation 1.23), the original QT formulation can be described as follows.
After the user sets a similarity threshold k (maximum diameter of clusters to be returned),
one arbitrary element is selected and marked as a candidate cluster C1 . The remaining
elements are iteratively added to C1 if and only if two conditions hold: Condition 1- the
entering frame minimizes the increase of C1 diameter, and Condition 2- the diameter of
C1 does not exceed the threshold k. A second candidate cluster is formed by starting with
another element and repeating the procedure. Note that all elements are made available
to the second candidate cluster (i.e., elements from the first candidate cluster are not
discarded from consideration). This process continues for all elements n in the trajectory
until Cn candidate clusters have been formed. The one with more elements is set as a
cluster, removed from further consideration, and the entire process repeated until no more
clusters can be discovered. In Algorithm 1 it is shown a pseudocode for this procedure.
diam(Cn ) = max(dij ) | ∀ (i, j) ∈ Cn
(1.23)
Algorithm 1: Pseudocode for the QT clustering algorithm
1: qt_clustering(G, d){
2: for pi ∈ G do
3:
f lag = T rue
4:
Ci = {pi }
5:
while (f lag = T rue) AN D (Ci ̸= G) do
6:
find pj ∈ (G − Ci ) f or which diameter (Ci ∪ pj ) is minimum
7:
if diameter (Ci ∪ pj ) > dc then
8:
f lag = F alse
9:
else
10:
Ci = {Ci ∪ pj }
11:
12:
13:
14:
identify set C ∈ {C1 , C2 , . . . , C|G| } with maximum cardinality
output C
call qt_clustering(G − C, d)
}
The crucial aspect of the above-described workflow lies in its ability to guarantee that
all pairwise similarities inside a cluster will remain under the threshold k. This aspect is
assured entirely by Condition 2. It should be stressed that Condition 1 merely limits
the size of retrieved clusters but has no impact on maintaining their collective similarity.
36
1. BIBLIOGRAPHIC REVIEW
While being a powerful algorithm, QT is a costly solution whose naive implementation
leads to a prohibitively O(n5 ) temporal complexity 219 .
1.6.2.2
Daura
The clustering algorithm described by Daura et al. 224 is a fast and powerful approach
to partitioning molecular datasets. Although Daura does not guarantee the collective
similarity of returned clusters as QT does, it may be considered as a trade-off for systems
bigger than what QT can process.
This algorithm has been implemented in the popular suites GROMACS, WORDOM,
and VMD in which it may run in a slow or memory inefficient way when processing
large ensembles. It is available under distinct and even confusing names. GROMACS,
WORDOM and VMD packages termed this algorithm as gromos, qt-like (qt standing for
quality threshold) and quality threshold respectively. In a recent contribution by Melvin
and Salsbury 223 , a supposedly QT clustering implementation is proposed that also turned
out to be Daura (see Section 4.1.1 and 4.2.3 for a detailed discussion).
In order to find clusters in a trajectory, the Daura algorithm works as follows. The
number of neighbors is determined for each element in the analyzed dataset. We denote
neighbors as those pairs of frames with a distance value less than a previously specified
cutoff dc . The frame with most neighbors (and all its neighbors) gets saved as a cluster
and removed from further consideration in successive steps. The process starts again
from the beginning until no more clusters can be found. In Algorithm 2 it is shown a
pseudocode for this clustering.
Algorithm 2: Pseudocode for the Daura clustering algorithm
1: daura_clustering(G, d){
2: for pi ∈ G do
3:
Ci = {pi }
4:
while Ci ̸= G do
5:
find pj ∈ (G − Ci ) f or which distance(Ci ∪ pj ) ≤ dc
6:
Ci = {Ci ∪ pj }
7:
8:
9:
10:
identify set C ∈ {C1 , C2 , . . . , C|G| } with maximum cardinality
output C
call daura_clustering(G − C, d)
}
1.6.2.3
Density Peaks
Though a wide variety of geometrical clustering algorithms has been proposed and continuously optimized to deal with the growing size of molecular ensembles, the famous DP
alternative 225 stands out for its simple yet powerful definitions. In DP, cluster centers
are spotted as those elements displaying both a high density of neighbors and a relatively
large distance from other high-density elements.
1.6. Clustering of molecular ensembles
37
As it has already been pointed out 226 , the previous statement fits the nature of a
converged MD simulation, where relevant biological states would lie in denser regions
separated by lower-density zones of transitional basins.
Despite its theoretical convenience, DP has some practical limitations that have
given rise to diverse enhancement proposals (see references 227 and 228 for a review)
typically addressed to one of the following aspects: (i) the robust estimation of each
element’s density 229,230 , (ii) the selection of an adequate distance metric 231 , (iii) reducing
the complexity of computing the local density of each component and their distance to
neighbors of higher density 232 , (iv) the automatic determination of clusters centers 228,233 ,
and (v) optimizing the process of assigning elements to clusters 227,234 .
There are a few implementations of DP specifically designed to treat molecular ensembles. The cpptraj module of the AMBER suite 235 is equipped with an exact variant
while a recent contribution has proposed Clustering based on Local density Neighborhoods
(CLoNe) 226 , a robust improvement of the original algorithm.
In DP formalism, cluster centers are surrounded by neighbors of lower local density
and distant from any point with high local density. This simple statement rules the
algorithm, described as follows when processing a molecular dataset. Two magnitudes
are computed for each frame i after setting a distance cutoff (dc ); its local density (ρi
in Equation 1.24) and its minimum distance to a neighbor of higher local density, (δi in
Equation 1.25). Both quantities depend on the distances between data points dij . In
Equation 1.24 the term χ(x) = 1 if x < 0 or zero otherwise so this is equivalent to define
ρi as the number of i neighbors whose distance from i is under the dc cutoff.
ρi =
X
χ(dij − dc )
(1.24)
j
In Equation 1.25, an exception is made for the frame of maximum ρi , which is
conventionally set to max(dij ). Note that δi is significantly larger than the typical nearest
neighbor distance only for those frames that are local or global maxima in ρ. Higher values
of δi are a distinctive hallmark of cluster centers. Previous information can be condensed
and visually inspected in the decision graph of the trajectory, a 2D representation of ρ
versus δ in which cluster centers are spotted at higher values of these two magnitudes.
After selecting cluster centers from the decision graph, each remaining frame is assigned
to the same cluster as its nearest neighbor of higher ρ.
δi = min(dij ) : ρj > ρi
(1.25)
To account for the notion of noise, DP defines a boundary region for each cluster
Ci consisting of frames previously assigned to Ci but being within a distance dc from
frames belonging to other clusters. The maximum density value of the boundary region
is designated as ρb and compared to the ρi of every frame in Ci . If ρi > ρb , the frame
belongs to the core region (robust assignation). Otherwise, it can be considered in the
halo zone (noisy assignation). In Algorithm 3 it is shown a pseudocode for DP.
38
1. BIBLIOGRAPHIC REVIEW
Algorithm 3: Pseudocode for the DP clustering algorithm
Require: G, dc
▶ 1. Compute the pairwise similarity matrix
1: rmsd_matrix = calc_rmsd_matrix(G)
▶ 2. Compute ρ values for each node
2: rho_values = {}
3: for pi ∈ G do
4:
pi _vector = rmsd_matrix[pi ]
5:
rho_values[pi ] = count_elements(pi _vector < dc )
▶ 3. Compute δ values for each node
6: delta_values = {}
7: for pi ∈ G do
8:
pi _vector = rmsd_matrix[pi ]
9:
pi _rho = rho_values[pi ]
10:
pi _sorted = sort_elements(pi _vector)
11:
for pj ∈ pi _sorted do
12:
pj _rho = rho_values[pj ]
13:
if pj _rho > pi _rho then
14:
delta_values[pi ] = rmsd_matrix[pi ][pj ]
15:
16:
if delta_values[pi ] == N one then
delta_values[pi ] = get_max_value(rmsd_matrix)
▶ 4. Select cluster centers from the Decision Graph
17: decision_graph = plot(rho_values, delta_values)
18: rho_cut, delta_cut = select_cutoffs(decision_graph)
19: centers = select_centers(decision_graph, rho_cut, delta_cut)
▶ 5. Assign remaining elements
20: clusters = assign_elements(elements, centers)
1.6.2.4
HDBSCAN
Density-based clustering variants represent clusters as regions of high density surrounded
by noisy low-density zones. This notion, translated to the MD jargon, is the equivalent
of defining a cluster as a temporary stable region of the conformational landscape. From
the density-based clustering alternatives, the HDBSCAN 236 has proved one of the most
robust currently accessible solutions. This method generates a complete hierarchy of the
most significant and stable clusters through two intuitive parameters (easily fixable to
get a pseudo-non-parametric algorithm). According to classifications discussed in Section
1.6, HDBSCAN is a hierarchical, exclusive, and partial algorithm that generates densitybased clusters.
Among the HDBSCAN ’s advantages described in the original paper, the following
are of particular interest: (i) the ability to characterize datasets with nested clusters or
1.6. Clustering of molecular ensembles
39
clusters of different densities (a challenging task with other variants like Density-Based
Spatial Clustering of Applications with Noise (DBSCAN) 237 or DENsity-based CLUstEring (DENCLUE) 238 ), (ii) the straightforward simplification of the cluster hierarchy into
an easily interpretable representation of the most significant clusters, as opposed to methods like graph-skeleton based clustering (gSkeletonClu) 239 , (iii) the fact of not being
circumscribed to specific classes of problems, like gSkeletonClu or element sets in the
real coordinate space (like DiscovEring Clusters Of Different dEnsities (DECODE) 240 or
generalized Single-Linkage 241 , and (iv) the non-reliance on multiple (often critical) input
parameters like the mentioned algorithms and many others.
From the previous list, DBSCAN (implemented in the cpptraj module of the AMBER is an appealing choice for the analysis of MD trajectories. As stated by Schubert 237 ,
it is an algorithm proven to work in practical situations that received the Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD) test-of-time Award in
2014. Conceptually, HDBSCAN supersedes DBSCAN, reporting clusters over all values of the DBSCAN’s distance scale parameter ϵ and finding those clusters that persist
for many values of this magnitude.
Though not primarily conceived to deal with molecular ensembles, HDBSCAN has
been used successfully in the conformational study of MD simulations 242,243 through a
deeply optimized implementation referred to as HDBSCAN* from now on 244 . HDBSCAN*’s authors creatively addressed each major step of the original version, reducing
their time complexity from O(n2 ) to near O(n log n) in the average case. Even in the
worst cases, a fast sub-quadratic time complexity of the algorithm is expected. The main
steps of HDBSCAN are detailed in Algorithm 4.
Algorithm 4: Main steps for the HDBSCAN clustering algorithm
Require: G, m
1:
2:
3:
4:
Compute the mutual reachability distance (MRD) matrix of G (Equation 1.26)
Build a MST of G
Compute the condensed cluster hierarchy from the MST of G (Figure 1.13) using m
Select the most stable clusters (Equation 1.27)
HDBSCAN formally defines the density of each frame i in terms of a core distance
κ(i); the distance from i to its k th nearest neighbor. Note that the chosen metric for
κ(i) can be Euclidean, RMSD, or any other selected by the user. Computing κ(i) for
every frame of the trajectory permits to effectively spread apart denser frames from noise
by defining a new similarity metric, the Mutual Reachability Distance (MRD) (Equation
1.26), in which d(i, j) is the distance between elements i and j in the input metric. Under
MRD, dense conformations (having low κ(i)) remain at the same original distance from
each other while sparser frames are “pushed” to be at least their core distance away from
any other point.
40
1. BIBLIOGRAPHIC REVIEW
(
dmr (i, j) =
max{ κ(i), κ(j), d(i, j) },
0,
i ̸= j
i=j
(1.26)
From a graph-theoretic point of view, a molecular trajectory can be seen as a complete
graph (T ) in which nodes represent frames, and pairwise edges hold the MRD distance
between nodes. In this scenario, creating a hierarchical divisive partition of T can proceed
by setting a high threshold value (dist) at which to start erasing edges in a way that
T would pass from a complete graph to a completely disconnected one. As this naive
approach is computationally prohibitive, HDBSCAN recurs to construct a Minimum
Spanning Tree (MST) whose progressive disconnection leads to the same hierarchy of
components described. An MST of T is a subset of T edges that connects all T nodes
(without forming cycles) with the minimum total weight.
The MST inferred from T can be progressively disconnected to produce a hierarchy
of clusters. HDBSCAN introduces a parameter m that represents the minimum number
of points in a component to classify it as a cluster. m allows condensing the cluster
hierarchy because now, cutting an edge that produces a component with less than m
points is considered a “just-loosing-elements” cluster and not an independent one.
Concretely, the MST disconnection process (Figure 1.13) proceeds in this fashion: A
new magnitude λ is defined as the inverse of the MRD distance (λ = 1/dist). MST
edges are sorted in increasing order of their λ value (high distances edges come first).
Successive edge cutting produces two child sub-trees at each cleavage, giving rise to one
of the following situations: (i) one of the child sub-trees contains m or fewer points, (ii)
both child sub-trees include m or fewer points, and (iii) both child sub-trees carries more
than m points. In the first situation, a component without the lost members is retained,
and the split is considered spurious. No child is returned, only a shrink component. The
second situation marks the MST disconnection endpoint, as no further valid components
will be produced. The third case corresponds to a“true split” and effectively separates the
parent component into two new independent ones.
The extraction of final clusters from the condensed hierarchy takes place according
to the definition of cluster stability (σ(Ci ), Equation 1.27). First, for a given cluster
Ci (see C2 in Figure 1.13) let’s define its λbirth and λdeath as the λ values at which
Ci becomes a cluster and disappears, respectively. Inside Ci , for each element e, the
λe value denotes when e "abandons" Ci , either as a spurious or a true split (note that
λbirth < λe < λdeath ). Then the stability of Ci is calculated through the Equation 1.27.
σ(Ci ) = Σe∈Ci (λe − λbirth )
(1.27)
Once σ(Ci ) of all hierarchical clusters are computed, the final step is to find a flat
(non-hierarchical) set of disjoint clusters with maximum stability. To that end, the cluster
tree is processed from the leaves (C3 , C9 , C10 , C8 , C5 , and C6 in Figure 1.13) upwards.
Initially, all leaves are declared as clusters. Then, the stabilities of sibling leaves i, j
(sharing the same parent k) are summed, and the result is compared to the stability of
their parent. If σ(i) + σ(j) > σ(k), σ(k) is set to σ(i) + σ(j), but i and j (not k) are still
1.6. Clustering of molecular ensembles
41
Figure 1.13: Condensed hierarchy of clusters produced by the HDBSCAN’s disconnection
process. The stability of cluster Cx is inside parentheses. The final selected clusters have
an asterisk. Their relative width scales components’ size.
considered the selected clusters. On the contrary, if σ(i) + σ(j) ≤ σ(k), σ(k) conserve
its value, k is marked as selected cluster, and all descendants of k are unselected.
In Figure 1.13 (cluster stability values are inside parentheses) we can start the previously described process from leaves C9 and C10 . As 3 + 3 > 2, σ(C7 ) is set to 6, but
C7 is not selected as cluster. Repeating with C7 and C8 results in selecting C4 as cluster
and unselecting C9 , C10 , and C8 (6 + 2 < 9). Continuing with C3 and C4 excludes the
possibility to select C1 as a final cluster because 8 + 9 > 8. Note that no comparison
is ever made against C0 . Similarly, for the right section of the tree, C2 is selected as a
cluster (excluding C5 and C6 ), giving that 3 + 2 < 6. In this manner, final clusters with
maximal stability are C3 , C4 , and C2 .
1.6.3 . Spatial complexity of reviewed algorithms
Molecular clustering algorithms can be found as standalone software or as modules
integrated within molecular simulation or analysis packages, such as VMD 221 , AMBER 235 , ORAC 220 , and GROMACS 245 . These packages have gained wide acceptance
among users. However, the ever-increasing volume of molecular ensembles generated by
computational techniques has outpaced the advancements made in the clustering algorithms integrated within these suites. This widening gap between data generation and
clustering capabilities necessitates the development of more efficient clustering algorithms
or the optimization of existing ones to avoid RAM crashes or impractical run times during
post-simulation analyses.
The algorithms discussed so far, vary in temporal complexities, so some execute faster
than others, regardless of the programming languages in which they are implemented. All
of them, however, have proven beneficial, and even the most time-consuming ones have
found a niche in the molecular simulation field. Their runtime is affordable because
clustering analyses typically take significantly less time to complete than the simulations
generating the data to be clustered. Thus, it is not much of a concern if running these
42
1. BIBLIOGRAPHIC REVIEW
analyses spans days or even weeks. In most cases, the time complexity is not the bottleneck.
The substantial constraint arises from their usually quadratic spatial complexity (Table
1.2). While users can decide to run their clustering jobs longer in High-Performance
Computing facilities, they usually do not possess the spatial resources (RAM or HDD)
needed to execute them on a large trajectory. The simple but ineffective solution to this
issue has been arbitrarily selecting a portion of the trajectory instead of addressing the
spatial complexity of these procedures.
Table 1.2: Spatial complexity of reviewed clustering algorithms
Software (Suite)
qtcluster (ORAC)
gromos (GROMACS)
qt-like (WORDOM)
measure cluster (VMD)
pyMS
TTClust
cpptraj (AMBER)
CLoNe
gen.-RMSD (HDBSCAN*)
gen.-Euclidean (HDBSCAN*)
Algorithm
QT
Daura
Hierarchicals
DP
HDBSCAN
m (bytes)
4
4
4
4
4
8
4
4
8
8
VRAM
m·n· natoms·(natoms−1)
2
230
m·n2
230
m·n
Spatial complexity
O(n · natoms2 )
O(n2 )
O(n)
m·n2
230
m· n·(n−1)
2
230
O(n2 )
m·n2
230
Two primary components consume memory resources when clustering molecular data:
the “trajectory" file, which stores snapshots of molecular ensembles generated by simulations, and the data structure that contains pairwise similarity values. By storing these
components in RAM or disk, clustering algorithms enhance time performance, ensuring
fast accessibility to all the required information and eliminating the need for redundant
recalculations each time a cluster is processed. However, it is important to note that this
approach requires a sufficient amount of spatial resources in the system.
The amount of space needed for the storage of the similarity matrix (expressed in GB)
can be calculated using the equations on column VRAM of Table 1.2, where n signifies
the total count of elements in the trajectory, while m denotes the size (in bytes) of the
numeric type used to express the similarity values. Being the RMSD a float number
ranging from 0.0 to infinite, it is conventional to employ floating numeric types for the
representation of inter-element similarity. Although the valuable information is contained
in one of the triangles, many current clustering software preserves the whole matrix to
avoid the performance penalty of working with “triangular" data structures.
Some clustering alternatives like TTClust 246 use the costly choice of double-precision
float (m = 8). Other options like GROMACS 245 and WORDOM 222 packages use
single-precision floats (m = 4), saving half of RAM just by adjusting the precision used
to express RMSD. The minimum size of standard available floats is a half-precision value
(m = 2), which is (from the author’s perspective) enough for most molecular clustering
but not much implemented. Even when lowering the value of m does not imply improving
the spatial complexity of these algorithms (that remains quadratic), this simple detail does
significantly decrease the amount of space they need to run.
1.6. Clustering of molecular ensembles
43
In cases where the RMSD is not the chosen metric, other approaches are followed
to hold the similarity information in RAM. An example is the qtcluster package, which
employs the maximum difference between corresponding pairs of atoms (Equation 1.19).
This means holding the square matrix of the selected inter-atomic distances for each
conformation in RAM is necessary. In practice, qtcluster allocates the values of only one
triangle of that matrix for every conformation. The RAM used by its similarity matrix
(in GB) is expressed in Table 1.2, where natoms is the number of selected atoms.
2 - METHODS, MODELS AND COMPUTATIONAL DETAILS
As general remark, all protein-ligand contacts were retrieved using the program BINding ANAlyzer (BINANA) 247 . Molecular visualizations were produced using VMD 221
v1.9.3. Plotting of data was addressed with matplotlib Python’s library and flowcharts
were depicted using draw.io v13.0.3. The following sections describe the methods, models
and computational details proper to each result Chapter.
2.1 . MCSS-based predictions of binding and selectivity of nucleotides
2.1.1 . Protein-nucleotide benchmark design
The Protein Data Bank (PDB) was filtered out to select a set of protein-nucleotide
complexes based on different structural criteria to evaluate the Multiple-Copy Simultaneous Search (MCSS) docking and screening powers’ performance. A first query was
conducted to find protein complexes with each of the four nucleotides as ligands and
annotated in the PDB by the following labels: AMP, C5P, 5GP, and U5P. An additional criterion used a cutoff value of 2 Å resolution to select only high-resolution X-Ray
Cristallography (XRC) structures.
The resulting complexes were then clustered according to their sequence similarities to
remove redundancy. If any protein’s chain of a complex had at least 30% sequence identity
with a chain in the protein from another complex, the two complexes were grouped into
the same cluster. Each group’s crystal structure with the best resolution was selected as
the cluster’s representative.
The 188 complexes thus selected by pulling down the results from the four queries
(AMP-bound: 123, C5P-bound: 18, 5GP-bound: 21, U5P-bound: 27) were then curated
to retain those that exhibit a known binding preference for the crystallized ligand. This
feature was established based on the literature and the annotation of the protein (e.g.,
a C nucleotide for CMP-kinase, etc.). After curation, the dataset was reduced to 132
complexes.
An additional restriction was performed to eliminate some potential redundancy associated with the presence of similar binding sites for different types of nucleotides. The
procedure followed consisted of superimposing all the protein structures using the program
TM-align 248 and reviewing all of them that are similar based on the TM-score (TM-score
≥ 0.8). Two binding sites were considered non-redundant if they differed by only one
amino acid residue in direct contact with the ligand. According to this criterion, only
one complex was removed from the dataset in the case of the proteins corresponding to
the PDB IDs: 3DXG (U5P ligand) and 3DJX (C5P ligand); the latter was conserved to
compensate for the minor under-representation of C5P. The whole procedure ended up
2.1. MCSS-based predictions of binding and selectivity of nucleotides45
with a dataset of 131 protein-nucleotide complexes.
After a review of the MCSS docking calculations (see Section 2.1.3), ten proteinnucleotide complexes resulted in non-productive and were then removed from further
analyses. The resulting benchmark is thus composed of 121 protein-nucleotide complexes
associated with 13 known biological functions (Annex Table 9.5). The binding features
of these complexes were characterized by (i) the number of contacts between the protein
and its ligand, (ii) the fraction of buried surface area, (iii) the number of H-bonds in
the binding site, and (iv) the energy of interaction as calculated by the MCSS scoring
function.
2.1.2 . Patches, charges, and solvent models
Several phosphate group patches were used in the MCSS calculations to determine
the optimal parameters for mapping nucleotides at the protein surface (see Section 2.1.3).
The five different phosphate models correspond to 5’ patches (R010, R110, R210, R310,
and R410) that differ by the valence and charge of the phosphate group (Figure 1.2).
The R010 patched nucleotide corresponds to the standard nucleotide residue defined in
CHARMM, and it was the only fragment with an unfilled valence shell at the 5’ end.
All the partial charges on the phosphate groups were derived from the CHARMM
parameters. They correspond to the original CHARMM charges or were derived based
on Manning’s theory of counter-ion condensation to account for the partial neutralization
of the negative charges of poly-electrolytes solution 113 . In this latter case, the net charge
on the phosphate group was scaled down according to the implicit solvent model previously
used in MCSS calculations performed on nucleic acids 108 .
The SCAL charges model (Figure 1.2 left) was combined with a distance-dependent
dielectric (Equation 1.16) with or without water molecules: SCAL and SCALW, respectively. The default charges model STD or FULL (Figure 1.2 right) was combined with explicit solvent representation and a distance-dependent dielectric (Equation 1.16): STDW,
or with a constant dielectric (Equation 1.15): FULLW.
2.1.3 . MCSS docking protocol
The 121 selected proteins were prepared using the CHARMM-GUI interface 249 to
convert the PDB files into CRD and PSF formats. After removing all heteroatoms,
hydrogens are added to the protein using the HBUILD command from CHARMM.
Water molecules were present in all the protein-nucleotide complexes, particularly in the
binding site. Depending on the solvent representation (implicit/hybrid), they were either
removed or included before energy minimization.
The protein targets were then submitted to an energy minimization (tolerance gradient
of 0.1 kcal/mol/Å). The average deviation between the experimental structure and the
minimized was around 1.0 Å for the structures optimized without water molecules and
0.5 Å for those optimized with the crystallized water molecules (Annex Figure 9.5).
The nucleotide library of fragments includes multiple conformations, 5’ and 3’ patches
(see MCSS documentation: https://www.mcss.cnrs.fr/MCSSDOC). The initial default conformation used in the calculations was a C3’-endo/anti ribonucleotide with typi-
46
2. METHODS, MODELS AND COMPUTATIONAL DETAILS
cal values of the seven torsion angles (phosphodiester backbone and base orientation). A
set of five different patches on the 5’ end is used in the current study with this nucleotide
conformation: R010, R110, R210, R310, and R410. The nucleotide fragments are fully
flexible during the calculations and are prone to adjustments of the torsion angles to better
fit in the binding site (Annex Figure 9.6). Each binding region is defined by a 17Å3 cubic
box centered on the ligand centroid where all the inorganic compounds or organic ligands
were removed (Figure 2.1).
x5
(5’-terminus)
x4
(A,C,G,U)
charge model
(std / scal)
x4
(solvent)
it
lic
imp
x121
(complexes)
rid
hyb
Figure 2.1: Schematic description of the MCSS calculations performed on the proteinnucleotide benchmark. Five chemical structures of the 5’-terminus are considered (R010,
R110, R210, R310, R410). For each 5’-terminus, the four standard nucleotides (A, C, G, U) are
also considered. The phosphate group is enclosed into a cylinder: the bigger the cylinder,
the bigger sterically, the darker red, the more negative charge (the gray color indicates
a null charge). Four solvent models are evaluated depending on the charge model (std:
standard, scal: scaled) and the solvent representation (implicit, or hybrid: implicit and
explicit). A protein target is represented in cartoon mode with the indication of the cubic
box corresponding to the explored region.
The initial distributions of fragments were generated using 2000 groups distributed
randomly and repeatedly among 25 iterations. These parameters guarantee that fragments fully saturate the binding region of all the protein-nucleotide complexes in the
benchmark, i.e., the atomic density of the fragments mapped into the box was at least
twice that of the maximum carbon density. During the calculations, the protein targets
were considered rigid. Final poses (minima) generated by MCSS were ranked by their
score (Equations 1.13-1.15) in ascending order.
In the explicit solvent models (SCALW, STDW, and FULLW), the water molecules
were treated independently from the fragments, which were replicated from their initial
distribution during each iteration. The number of water molecules was conserved during
the calculations, and they were free to move around without any constraint. However,
they were not considered in the scoring as described below.
2.1. MCSS-based predictions of binding and selectivity of nucleotides47
The MCSS software may be obtained after signing a license agreement upon request
to Martin Karplus (marci@tammy.harvard.edu). The source code can be obtained from a
Git repository on the I2BC software forge https://forge.i2bc.paris-saclay.fr).
2.1.4 . Clustering of MCSS distributions
A fast and straightforward clustering procedure inspired on BitClust (see Section
4.2)was performed on the MCSS distributions. The first pose (best ranked) was taken
as the seed of the first cluster, and all other poses in the exploration with an RMSD less
equal than 1 Å to the seed (redundant poses) were removed from the dataset. The seed
was preserved, and the process resumed by taking the next best-ranked available pose as
seed and performing the same comparison against the remaining poses. In the end, a set
of geometrically non-redundant seeds was obtained. The MCSS results presented include
the analyses of the raw (R) and clustered (C) distributions.
2.1.5 . Docking and screening power
The docking power was defined as the ability of the scoring functions to identify the
native ligand binding pose with respect to the non-native poses generated by MCSS for
the native nucleotide ligand (single nucleotide distribution). The MCSS predictions were
ranked according to the success rate for the identification of at least one native pose
obtained on the entire benchmark in the Top-i (Top Native in the best ranked i poses)
with i taking values of 1, 5, 10, 50, and 100.
The scoring functions used were those implemented into MCSS with the four solvent
models which were evaluated (see Section 2.1.2). Four alternative scoring functions used
in the Comparative Assessment of Scoring Functions (CASF) challenges 32,67 have been
used, as well as two Molecular Mechanics (MM)-Generalized Born (GB) models through
a re-scoring scheme based on single-point calculations to assess the relative performance of
MCSS in docking power. The two MM-GB models were CHARMM implementations:
GBSW 250 and GBMV 251 . The other four selected scoring functions were either generic
(Autodock Vina 252 and Vinardo 78 ), or specialized on nucleic acids ligands (ITscorePR 85
and ∆vina RF20 253 ).
To evaluate the screening power, the MCSS distributions from the four nucleotides
were merged and sorted according to their score in increasing order as in the nucleotidespecific distributions (from the more negative to the less negative or positive). In each
Top-i , a prediction was considered optimal if two conditions were met: (i) it corresponds
to a native pose (RMSD ≤ 2.0 Å), (ii) the native nucleotide was ranked ahead of the
three other non-native nucleotides. For example, an optimal prediction in the Top-1 means
a native pose was found with the best score from the merged distributions.
Since the scoring function was still an estimate and raw approximation of the relative
binding energy, we consider as good predictions the cases where the native nucleotide was
predicted within a 2 kcal/mol range from the best ranked non-native nucleotide. This
threshold value corresponds to a maximum offset of 2 kcal/mol in 90% of the benchmark
(STDW model), where the offset was defined as the difference between the best-ranked
pose, whatever the nucleotide type, and the best-ranked pose for the nucleotide corre-
48
2. METHODS, MODELS AND COMPUTATIONAL DETAILS
sponding to the native ligand (Annex Figure 9.7). Predictions that do not satisfy these
criteria were considered poor.
The scores calculated with all the scoring functions: ITscorePR 85 , ∆vina RF20 253 ,
Autodock Vina score 252 , Vinardo 78 , and the MM-GB models correspond to single-point
calculations on the MCSS-generated poses.
2.1.6 . Molecular features
The molecular features were analyzed on a benchmark subset corresponding to the
17 protein-nucleotide complexes not generating any prediction in the Top-10 without
any distinction from the model and patch. We consider that a given feature significantly
impacted the prediction when it was found to be associated with the absence of prediction
at a higher frequency than that in the benchmark (Table 9.6).
The volume calculation of the binding site was performed using the PyVOL python
package 254 . PyVOL was used with the pocket corresponding to the nucleotide-binding
site as input (coordinates of the nucleotide ligand of interest). The threshold value to
discriminate between high or low binding volume was set to 635 Å3 , which was the average
value of the distribution (30% high and 70% low). The other molecular features comprise
the number of water molecules around the nucleotidic ligand and the presence of metals
or other nucleotidic ligands close to the binding site. The threshold value for the number
of water molecules between nwat high and low was set to 6 (nwat.low ≤ 6 & nwat.high
> 6), which was the average value of the distribution (38% high and 62% low).
The interaction features (base contacts, clashes, salt bridge, stacking) were extracted
from the analysis of the binding site using BINANA 247 and OpenEye 255 software.
2.2 . Reinventing the wheel of molecular clustering
2.2.1 . Molecular ensembles used to benchmark clustering algorithms
The molecular ensembles used to benchmark the clustering implementations proposed
in this thesis correspond exclusively to Molecular Dynamics (MD) trajectories that are
generically denoted by their size (1 kF = 1000, 1 MF = 1000000 frames). The nomenclature along all the manuscript is as follows: 6 kF: a 6001 frames Replica Exchange Molecular Dynamics (REMD) simulation of the Tau peptide 256 , 30 kF: a 30605 frames MD
of villin headpiece based on PDB 2RJY 242 , 50 kF: a 50000 frames MD of serotype 18C
of Streptococcus pneumoniae, 100A kF: a 100000 frames MD of Cyclophilin A based on
PDB 2N0T, 100B kF: 100000 frames of an MD simulation on the bovine-rhodopsin
structure embedded inside a palmitoyl-oleoyl-phosphatidylcholine hydrated membrane,
250 kF: a 250000 frames MD of four chains of the Tau peptide that corresponds to
the MD simulation of an extended Tau peptide (PDB PHF8, Álvarez-Ginarte et al., unpublished work), 500 kF: a 500000 frames MD toy trajectory constructed from randomly
selected conformations of 6 kF, and 1 MF: a one-million frames MD of ubiquitin based
on PDB 1UBQ.
All trajectory and structure files above-mentioned can be found online at the following
2.2. Reinventing the wheel of molecular clustering
49
addresses: 6, 50, 100, 250, and 500 kF at https://doi.org/10.6084/m9.figshare.
c.5403930.v1, 30 kF at https://doi.org/10.6084/m9.figshare.3983526.v1, and
1 MF at https://lbqc.ucm.cl/ubiquitin_1MF/. More details about the generation
of these trajectories can be found in Annex 9.2.1.
2.2.2 . Benchmarked clustering algorithms and dependencies
The novel clustering algorithms implementations developed in this thesis (QTPy,
BitQT, BitClust, RCDPeaks, and MDSCAN) were programmed under the Python 3 language (https://docs.python.org) avoiding any platforms-dependent code to maximize
portability between Linux, Windows and Mac operative systems. The same language was
used for all scripted analyses (except the explicit mention of the contrary).
MDTraj 257 suite (v1.9.2 or higher) was among the most important dependencies
of proposed clustering procedures as it allowed a high-speed parallel calculation of pairwise optimal RMSD distances. The bitarray dependency on the other hand (https:
//github.com/ilanschnell/bitarray), provided a bit vector data structure unavailable in pure Python and all the necessary bit operations used in the binary proposals
BitQT and BitClust (v1.6.1 and v1.2.1, respectively).
In Table 2.1 it is detailed the versions, references, and source code address of the
different clustering algorithms benchmarked in this work. All cutoff values in clustering
jobs were set after a trial/error procedure aided by visual inspection of the generated
clusters’ uniformity. As qtcluster does not use the RMSD metric, we adjusted the dc
values for each trajectory analyzed with this software. We multiplied the corresponding dc
by 2.4, in analogy with a previously published report of qtcluster’s authors (see Supporting
information of reference 258).
Table 2.1: Benchmarked clustering algorithms.
Software
QTPy
BitQT
BitClust
RCDPeaks
MDSCAN
measure cluster (VMD)
pyMS
qt-like (WORDOM)
gromos (GROMACS)
median-linkage (TTClust)
qtcluster (ORAC)
DP (cpptraj-AMBER)
CLoNe
HDBSCAN*
Version
0.0.1
0.0.1
0.0.13
0.0.1
0.0.1
1.9.3
0.0.1
0.22-rc2
2018.1
4.6.3
6.0.1
4.25.6
0.0.1
0.8.11
Reference
novel
novel
novel
novel
novel
221
223
222
245
246
220
235
226
244
Source Code
https://github.com/rglez/QT.git/
https://github.com/LQCT/BitQT.git
https://pypi.org/project/bitclust/
https://github.com/LQCT/RCDPeaks.git
https://pypi.org/project/mdscan/
https://www.ks.uiuc.edu/Research/vmd/doxygen/MeasureCluster_8C-source.html
https://github.com/melvrl13/python-quality-threshold
http://www.wordom.sf.net
https://github.com/gromacs/gromacs/blob/main/src/gromacs/gmxana/gmx_cluster.cpp
https://github.com/tubiana/TTClust
http://www1.chim.unifi.it/orac/
https://github.com/Amber-MD/cpptraj/blob/master/src/Cluster/
https://github.com/LBM-EPFL/CLoNe
https://github.com/scikit-learn-contrib/hdbscan
RCDPeaks and DP at AMBER’s cpptraj, used the same distance cutoff value for
every trajectory; 2.5 Å for 6 and 500 kF, 4 Å for 30 kF, 1 Å for 50, 100A kF and 1
MF, and 2 Å for 250 kF. These values were set after a trial/error procedure aided by
visual inspection of the number of possible centers in the decision graph. The only input
parameter of CLoNe is a user-defined percentage pdc of all pairwise similarity distances.
This parameter was set to 0.4 for 6 kF (corresponding to dc = 2.6) and to 4.4 for 30 kF
(corresponding to dc = 4.0) after author ’s recommendations. The remaining trajectories
could not be analyzed by CLoNe due to its excessive memory consumption.
50
2. METHODS, MODELS AND COMPUTATIONAL DETAILS
The benchmark of all clustering algorithms was performed on an AMD Ryzen5 hexacore workstation with a processor speed of 3.6GHz and 64 GB RAM under the 64-bit
Xubuntu 18.04 operating system. Run times and RAM peaks were recorded with the
/usr/bin/time Linux command.
2.3 . NUCLEAR: an efficient assembler for the FBDD of CMOs
2.3.1 . CHARMM minimization protocol
Carbohydrates, protein, nucleic acids, ions, waters, and general small molecules parameters and topologies defined in version 36 of the CHARMM force field were employed
in all minimization jobs. The coordinates of unlinked mono-nucleotides constituting each
chain retrieved by NUCLEAR are loaded together with every chain of the protein and
the corresponding water molecules. A four-step minimization protocol is followed in which
different atom selections can move, always specifying a tolerance value applied to the average gradient during minimization cycles (TOLGRD); if the average gradient is less than
or equal to TOLGRD, the minimization routine exits.
In the first stage, only water molecules and atoms linking nucleotides can move during
1000 steps of the Steepest Descent (SD) algorithm (TOLGRD = 10) and 10000 steps of
the Adopted Basis Newton-Raphson (ABNR) algorithm (TOLGRD = 0.1). The second
stage allows the motion of the phosphodiester skeleton and water molecules in a similar
combination of algorithms and tolerances mentioned above. Water molecules and RNA
atoms can move in a third minimization stage (10000 steps of SD with TOLGRD of 10
and 10000 steps of ABNR with TOLGRD of 0.1). In the final minimization phase, all
atoms can move with the same combination of algorithms and tolerances followed in the
previous stage.
2.4 . In-silico design of selective CMO against BACE1
2.4.1 . BACE1 protein candidates selection
Figure 2.2 summarizes the process followed to select the BACE1 protein coordinates
we employed in our work. The complete description of each stage can be found on Section
9.4.1.
2.4.2 . BACE2 protein candidates selection
The PDB database was queried using the string beta secretase 2 OR Macromolecule
Name CONTAINS PHRASE “Beta secretase 2” but unlike for the BACE1 case, only
17 structures were retrieved and none of them had the complete set of coordinates determined. We then restricted the candidates having at least the full coordinates of the
active site and the exosite, selecting 2EWY (absence of ligand at the exosite) and 3ZKM
(absence of ligand at the active site).
2.4.3 . MCSS library of standard and modified nucleotides
2.4. In-silico design of selective CMO against BACE1
PDB query:
beta secretase 1 OR
beta-secretase 1
Remove cases with
missing residues
445 structures
171 structures
Splitting
in chains and models
693 structures
51
Clustering
884 structures
4 structures
Sequence alignment
against 1SGZ-A
1SGZ, 4GID, 5MCQ, 6WUU
only keeping similars > 75%
Figure 2.2: Workflow followed for BACE1 protein candidate selection.
Apart from the standard nucleotides (A, C, G, U/T), all the other nucleotides from
the library include a modified nucleic acid base derived from the corresponding standard
one; 19 A-derived (Figure 9.14), 18 C-derived (Figure 9.15), 29 G-derived (Figure 9.16),
and 45 U/T derived (Figures 9.17 and 9.18).
2.4.4 . Protonation state of titratable aminoacids
For setting a specific protonation state for each of the titratable residues of proteins
models, we first computed the local pKa of amino acids using propka 259,260 . Then the
protonation state was decided by comparing the crystal resolution pH to pKa . For Asp
and Glu, a strict comparison between the local pKa of each residue and the pH was
performed; If pKa < pH, the residue was set as not protonated. If pKa was in the range
(pH - 0.1; pH + 0.1), we conducted a minimization for each possible state and set as
final the less deviated in RMSD. Otherwise, residues were set as protonated.
Protocol for histidine residues protonation is depicted in Figure 2.3. Histidine residues
were treated as a pair if they were at a distance less than 6Å . At acidic pH, if the pKa
> 1 pH unit, the histidine was set as protonated (HSP); otherwise, it can be protonated
(HSP) or not (HSD or HSE). At neutral pH, if the pKa < 1 pH unit, the histidine was
set as not protonated (HSD or HSE); otherwise, it can be protonated (HSP) or not (HSD
or HSE). To discriminate one state from another of a histidine (or a pair of histidines),
the RMSD at 6.0 A around this histidine (or the whole pair) is calculated, and the final
state is set as the less deviated in RMSD.
2.4.5 . 3D equivalence between BACE-X residues
The three-dimensional equivalence between BACE-X residues was done pairwise by
setting the 4GID BACE1 conformation as the reference and 2EWY or 3ZKM BACE2
conformations as the target. After parsing structures and selecting all protein atoms
of each one, we superposed the target onto reference via the matchAlign function of
the prody package. Then we encoded the two sets of coordinates as kd-trees using the
52
2. METHODS, MODELS AND COMPUTATIONAL DETAILS
Figure 2.3: Protonation protocol of proteins’ titratable residues.
cKDTree class in the spatial module of the scipy Python library. Later we computed for
every atom in the target the nearest neighbor in the reference. Finally, as the target’s
equivalent residue, we assigned the one containing more neighbors to each residue in the
reference.
3 - MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF NUCLEOTIDES
Frequently, virtual FBD workflows present a significant limitation; the docking methods’ lack of performance due to the approximate nature of their scoring functions. A fundamental assumption of this manuscript is that by employing the Multiple-Copy Simultaneous Search (MCSS) software, increased performance in the docking and the screening
power (Section 2.1.5) is possible, making this tool a suitable choice for fragment-based
drug design procedures involving nucleotides.
A previously published protein-nucleotide benchmark avoided the mentioned inconvenience 261 . The authors chose 62 complexes to evaluate the docking power of three
methods: AutoDock (4.2.3), GOLD (5.1), and MOLSDOCK. However, that report is
mainly outdated, with only 40% complexes with an atomic resolution less than 2.0 Å and
thus not representative of the currently available structural data. Besides, the methods
were tested under biased conditions: the docked region was restricted to the native ligand
pose (5 Å3 ), and the high-occupancy water molecules of the binding site were preserved
within a rigid receptor.
This Chapter presents an updated and representative dataset of high-resolution proteinnucleotide complexes in which only nucleotide mono-phosphate ligands, as single-residue
ligands, are included. Section 3.1 details the overall composition of the benchmark. The
molecular descriptors employed to characterize the binding sites under study are presented
there, and the distribution of contacts is analyzed. Section 3.2 analyzes the effect of solvent models and phosphate patches on the number of generated poses and the fraction
of native-like poses obtained. After that, the docking power of MCSS (and six other
scoring functions), as well as its screening power, is respectively assessed in Sections 3.3
and 3.4. Section 3.5 closes the Chapter by presenting the molecular features associated
with the lack of predictions.
3.1 . Protein-nucleotide benchmark: general insights
The protein-nucleotide benchmark includes a non-redundant set of 121 complexes associated with 13 known molecular functions and a wide variety of binding modes (Figure
3.1, generated from Annex Table 9.5). The selection criteria retained to build the benchmark are detailed in Section 2.1.1. Proteins binding Adenosine monophosphate (AMP)
are over-represented in PDB concerning those binding Cytidine monophosphate (CMP),
Guanosine monophosphate (GMP), or Uridine monophosphate (UMP). The ligand composition in the benchmark is biased accordingly with 72% of AMP-bound complexes; the
other complexes are represented in a similar proportion between 7 to 10%.
A series of molecular descriptors compose the features used to characterize the 121
nucleotide-binding sites. These features include standard contacts (closed contacts, H-
54
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
Figure 3.1: Distribution of molecular functions and nucleotide types in the proteinnucleotide benchmark. The external wheel depicts the general distribution of molecular
functions. The internal wheel shows the nucleotide-specific distribution for each function
(AMP, GMP, CMP, UMP).
bonds, and hydrophobic contacts), nucleic acid-specific contacts (stacking contacts, and
salt bridges), and energy-related descriptors (buried fraction of ligand and binding energy
score).
Broad distributions are observed for the standard contacts (Figure 3.2). Given that
only the nucleic acid base moiety allows the chemical distinction between the four nucleotide ligands, their contacts should be represented enough in number and frequency
for a reliable evaluation of the screening power (because they determine the selectivity
for one specific nucleotide). The decomposition of the contacts based on the phosphate,
ribose, and base moieties reveals that the base contacts are slightly more represented.
They are still somewhat less frequent, especially for close contacts (Figure 3.2A-B).
Figure 3.2: Molecular and energy features of the nucleotide-binding sites from the benchmark of 121 complexes. A-1: Histogram of the number of
contacts; A-2: Smooth histogram with decomposition per nucleotide moiety (base, ribose, phosphate); B-1: Histogram of the number of close contacts;
B-2: Same as A-2 for close contacts; C-1: Histogram of the number of H-bonds; C-2: Same as A-2 for H-bonds; D-1: Histogram of the number of C-C
contacts; D-2: Same as A-2 for C-C contacts; E-1: Histogram of the number of stacking contacts; E-2: Smooth histogram with decomposition per stacking
types; F: Histogram of the number of salt-bridges; G: Histogram of the buried fraction of ligand (calculated from the solvent accessible surface); H-1:
Histogram of the MCSS scores calculated for the ligands optimized in their binding site; H-2: Smooth histogram with decomposition per contribution
types (electrostatics, van der Waals, conformational).
3.1. Protein-nucleotide benchmark: general insights
55
In more than 10% of the benchmark (15 protein-nucleotide complexes), there is no
direct base contact suggesting that the binding selectivity may be hard to predict in those
cases and would negatively impact the screening power. Nucleic acid-specific contacts
are only represented in about half of the benchmark (Figure 3.2E-F). However, the buried
fraction of the ligands is more than 50% except in a single case (Figure 3.2G), indicating
that the nucleotide generally binds in some well-defined cavity.
The breakdown of the contacts per nucleotide type shows a bias towards AMP, the
nucleotide with almost ten times more contacts than the other nucleotides. However, the
contact profile (the proportion of different kinds of contacts) is similar between the four
nucleotides (Figure 3.3). Thus, we may expect AMP binding to be easier to predict, i.e.,
to provide better performance in docking and screening powers.
The docking power, in particular, depends on both the quality of sampling and scoring.
A baseline for the default MCSS scoring function (SCAL model) was established on the
benchmark after minimization of the ligand by re-insertion within the optimized binding
site and calculating its score (Figure 3.2H). The decomposition of the MCSS score into its
different contributions (see Equation 1.13) shows that the van der Waals term dominates.
Although the conformational penalty is a minor contribution (mean value of 5.5 kcal/mol),
it is still significant. It stresses the importance of evaluating this term properly concerning
the other contributions, given that nucleotides are very flexible (six torsion angles in
nucleotide ligands). For that, good sampling is also required.
In traditional fragment-based approaches, it is recommended to use small ligands,
which are easier to sample 262 . Large ligands such as nucleotides have many degrees
of freedom, making computational sampling more difficult. Only a unique standard nucleotide conformation is used in MCSS while the benchmark include a large diversity
of bound conformations (Annex Figure 9.6). Thus, the sampling should be efficient in
identifying bound conformations that deviate from the standard (unbound) conformation,
such as syn conformations found in 10% of the benchmark where the base orientation
is opposite from the standard anti conformation. On the other hand, the contributions
to the MCSS score should be well-balanced (the conformational penalty should not be
under or over-estimated to guarantee accurate predictions).
The benchmark’s high-resolution protein-nucleotide complexes include water molecules
around the protein surface and the binding region. The ligand and water molecules were removed in the SCAL model, leading to some distortions of the binding sites after minimization. In the other solvent models where the crystallized water molecules were included,
the original experimental coordinates were more preserved: 0.5 Å versus 1.0 Å (Annex Figure 9.5A). However, other artifacts associated with the water molecules also exist (Annex
Figure 9.5B). The minimization induces displacements of water molecules in the binding
region primarily due to the removal of the ligand leading to variations in their number and
distribution (Annex Figure 9.5B-C). All the mentioned biases and issues will be addressed
by comparing the docking and screening powers for the different solvent models (Sections
3.3 and 3.4, respectively).
Figure 3.3: Nucleotide breakdown of atomic contacts. A: all contacts; B: specific contacts (C-C contacts, close contacts, H-bonds, stacking contacts,
salt-bridges); C: ratio of each type of specific contacts. The number of contacts correspond to the average value over the full benchmark.
56
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
3.2 . Models and poses
The identification of native poses, according to standard criteria (Section 2.1.5),
depends primarily on the number of generated poses and the quality of the sampling. The
first MCSS parameters evaluated are the nucleotide ligands: R010 to R410 (Figure 2.1).
Since their charge and size differ, they are evaluated in combination with the different
solvent models. The raw distributions generally include up to several thousands of poses.
The total number of poses generated depends mostly on the solvent model and the
phosphate patch to a lesser extent.
The presence of explicit water molecules partially reduces the molecular volume accessible for nucleotides in the binding region. Thus, the number of poses generated with
the SCAL model is much larger than that generated with any of the hybrid solvent models: SCALW, FULLW, and STDW (Figure 3.4). The comparison of the raw and clustered
distributions also shows that the SCAL model exhibits the highest redundancy in the
generated poses, demonstrated by the larger difference between the raw and clustered
distributions for each patch.
Figure 3.4: Boxplot representation of the number of poses generated for the 121 proteinnucleotide complexes for each 5’ patched nucleotide (010, 110, 210, 310, 410). Results for
raw (R) and clustered (C) distributions are shown.
3.3. Docking power
57
Although the electrostatic contribution is not the major one in the default scoring
function with an implicit solvent model (Figure 3.3), it significantly impacts the number
of generated poses. Both the charge and the dielectric model have to be considered.
In the SCAL model based on a distance-dependent dielectric, the observed trend is that
the more negative the charge on the phosphate group (from R110 to R010, R210/R310,
and R410), the higher the number of generated poses except for the more charged patch
R410 (Figure 3.4). The more charged the phosphate group is, the higher the electrostatic
contribution, and the more likely the pose can pass the energy threshold value of the
MCSS score. The R210 and R310 patches give equivalent results with the same net
charge on the phosphate group. On the other hand, a too highly charged phosphate
group (R410) may also produce unfavorable interactions with negative charges at the
protein surface.
In the other hybrid models, the trend is not dominated by the charge but rather by the
fragment’s size. The larger the patch is (from R110 to R010, R410, R210, and R310), the
lower the number of generated poses and the lower the accessible volume, as mentioned
above. The models based on a distance-dependent dielectric, SCALW and STDW, also
follow this trend, given that R210 and R410 only differ by a proton. In the particular case
of the constant dielectric model FULLW, both the charge and size effects explain why
R410 is not on the lines with the other patches (Figure 3.4).
The fraction of native poses over the entire MCSS distribution for all solvent models
and patches is shown in Figure 3.5. This fraction is similar for all patches in the four
models, except for R310. The patch R310 carries a methyl group in one of the phosphate
oxygen. This group confers the ability to establish more hydrophobic contacts than other
patches. The SCAL model shows a significantly lower fraction of native poses than
solvated models despite a much larger number of generated poses (Figure 3.4). As for the
number of poses, the raw and clustered distributions are more scattered in the absence of
water molecules. In solvated models, the fractions of native poses for SCALW and STDW
are very similar. On the other hand, the FULLW model has more cases where no native
pose is found, as seen by the displacement to zero of the first interquartile section for the
boxplots (Figure 3.4).
3.3 . Docking power
The performance in docking power is evaluated on all models and patches using
the standard metrics based on the native poses found in the Top-1 to Top-100 scores
with the intermediate ranks: Top-5, Top-10, and Top-50 (see Section 2.1.5). The best
performances are obtained with the SCALW and STDW models, whatever the patch used
(Figure 3.6). The STDW model slightly outranks the SCALW model in the Top-1 and
Top-10 for all the patches (except for R310, where the performance is equivalent for the
Top-10), while the performance is pretty similar for the Top-50 and Top-100.
The best performance is obtained for patch R310. It has a success rate of 45% in
the Top 1, more than 60% for the Top 10, and more than 80% in the Top-100. However,
58
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
Figure 3.5: Boxplot representation of the fraction of native poses generated for the 121
protein-nucleotide complexes for each 5’ patched nucleotide (010, 110, 210, 310, 410). Results
for raw (R) and clustered (C) distributions are shown.
the gain in performance concerning the other patches is tiny in the Top-10 and Top-50.
The clustering does not change the general trends observed in the raw distributions, but
it slightly increases the performance in the Top-100 and, to a lesser extent, in the lower
Top-i .
The better performance of hybrid solvent models SCALW and STDW over the SCAL
implicit model is partly due to the conformational penalty term (Equation 1.13) corresponding to the deformation of the fragment from its optimal conformation. Although
this term is generally a minor contribution, it may vary depending on the non-bonded
model.
We can compare the torsion angles observed in the MCSS minima to the known
ideal values and values observed in the native bound conformations of the nucleotides
from the benchmark (Annex Figure 9.6). The absence of water molecules in the SCAL
model reveals a few biases where, for example, the syn conformation is more populated
than expected as compared with the experimental or the ideal values collected from the
experimental structures of nucleic acids 263,264 . The SCALW and the STDW model are
also biased but to a lesser extent. Only the FULLW model is exempted.
3.3. Docking power
59
Figure 3.6: Stacked histogram representation of the Top-i ranked native poses generated
for the 121 protein-nucleotide complexes for each nucleotide patch. R: raw (upper) and C:
clustered (bottom) distributions are shown.
Another common bias in models (except for FULLW) is the over-representation of
the ribose’s C2’-endo conformation, while the initial conformation is always a C3’-endo
conformation. It is partly due to the non-bonded model and the absence of complete
solvation of the ribose moiety. In FULLW, the C3’-endo/C2’-endo representation is more
balanced. Still, the phosphodiester backbone (torsion angles α and β) deviates from the
optimal values because of some distortion of the phosphate group, which is highly charged
and tends to stick closely to the protein surface in the absence of any screening effect
(constant dielectric model).
Implicit solvent models such as MM-GB models 110,111 have been applied to the rescoring of MCSS minima. A few other scoring functions also perform well in the CASF
challenges 32,67 . Six alternative scoring functions have been selected; two correspond
to MM-GB models (see Methods, section 2.1.5). The results show that the standard
MCSS scoring function corresponding to the SCAL model (MCSS-SCAL) has a similar
performance to Vina, slightly below that of ∆vina RF20 (Figure 3.7). The Vinardo scoring
function performs slightly better than both MCSS-SCAL or ∆vina RF20 . The other three
scoring functions (ITscorePR, MM-GBSW, MM-GBMV) have a low performance. The
clustering protocol described in Section 2.1.4 improves the performance of MCSS-SCAL,
slightly exceeding that of Vina or ∆vina RF20 (Annex Figure 3.8).
The MCSS scoring function associated with the STDW model still outperforms all the
alternative scoring functions in the Top-1 to Top-10 in both raw and clustered distributions
(Figure 3.6). In the CASF-2016 benchmark, the docking power ranges from around
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
60
100
Top 1
Top 5
Top 10
Top 50
Top 100
90
Ratio of native poses (%)
80
70
60
50
40
30
20
10
0
Vinardo
MCSS
DVRF20
Vina
ITscorePR
MM-GBMV MM-GBSW
scoring functions
Figure 3.7: Docking powers (Top-1 to Top-100) for Vinardo, MCSS, ∆vina RF20 , Vina,
ITscorePR, MM-GBMV, and MM-GBSW using the patch R310. The two MM-GB models use
the molecular mechanics terms from CHARMM (MCSS with SCAL model) and the solvation contribution from the respective Generalized Born models implemented in CHARMM
(see Section 2.1.5).
100
R
C
Top 1
Top 5
Top 10
Top 50
Top 100
90
Ratio of native poses (%)
80
70
60
50
40
30
20
10
0
Vinardo
MCSS
DVRF20
Vina
ITscorePR
scoring functions
Figure 3.8: Docking powers (Top-1 to Top-100) for Vinardo, MCSS, ∆vina RF20 , Vina, and
ITscorePR and the impact of the clustering filtering (using the patch R310). Left bar (R): no
clustering; Right bar (C): clustering.
30% to 90% for a variety of scoring functions 67 . The docking power is around 90% for
both Vina and ∆vina RF20 . On the current benchmark, their performance is only 33%,
3.4. Screening power
61
indicating the challenging task of scoring charged ligands such as nucleotides. Vinardo
performs slightly better (42%) and also MCSS-STDW (45%).
Because of the composition bias in the benchmark, the performance was then analyzed by nucleotide type. Since the adenosine is over-represented in the benchmark, the
performance for that specific nucleotide generally follows the global trend described above
(Figure 3.9). However, the performance for guanosine decreases for the larger patches
R210 to R410, whatever the model used. Only the smaller patches R010 and R110 give
a similar performance or better in some cases; the success rate with R110 is even better
from Top-1 to Top-50, indicating the existence, as discussed before, of a size effect that
drives down the performance (guanine is slightly more voluminous than adenine).
Consistently, the performance generally improves for pyrimidines (C or U), which are
smaller than purines. On the other hand, the performance is degraded in the smaller
nucleoside ligands (R110) that do not carry any phosphate group (uncharged). The
pyrimidic nucleotides are better predicted, especially for the two best models, SCALW
and STDW, with R310. The predictions are equivalent or degraded for the more highly
charged patch R410, especially with U. The analysis of the clustered distributions confirms
the observed trends of the raw distributions, with improved performances reaching 90%
to 100% for the Top-100 in a more significant number of models and patches (Annex
Figure 9.1).
Figure 3.9: Nucleotide decomposition of the success rates obtained for each solvent model
and patch. The data are shown for the raw distribution (without clustering) and each Topi.
3.4 . Screening power
In the benchmark, we assume that the crystallized nucleotide is always the native and
more specific nucleotide, i.e., it is the only nucleotide ligand with a detectable affinity or
62
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
the best binder among the four nucleotides. Based on this assumption, we defined the
screening power as the ability to rank the native nucleotide ahead of the other three nucleotides. In that case, we will refer to optimal predictions as the native pose is identified,
and the native nucleotide is ranked first. The other predictions are considered poor even
if native poses are found for the native nucleotide. As an illustration, we show the results
obtained for one protein-nucleotide complex (PDB ID: 1KTG) for both SCAL and STDW
models (Figure 3.10).
Figure 3.10: Binding selectivity predictions for 1KTG. Left: SCAL model (R310); right: STDW
model (R310); the interval of MCSS scores corresponding to a 2 kcal/mol range is indicated
by the green bar. Each Top-i for i > 1 is represented by a single point corresponding to all
its members’ average RMSD and score.
The best-ranked nucleotide is the native one (A) in the STDW model; other poses
of the native nucleotide are also identified (Top-5, Top-10, etc.), but only one is within
the 2 kcal/mol score range (good prediction). Some poses corresponding to non-native G
nucleotides are within the MCSS score range of 2 kcal/mol. The prediction is optimal in
the STDW model since the best-ranked pose corresponds to the native nucleotide. In the
SCAL model, the pose with the best score corresponds to a non-native G nucleotide, but
the Top-1 for the native nucleotide is within the 2 kcal/mol range; it is not considered
optimal but a good prediction. The other poses for the native nucleotide, which lie out
of the 2 kcal/mol range (Top-5, Top-10, etc.), correspond to poor predictions.
The results’ analysis focuses on comparing the standard SCAL model (without explicit
solvent) and the hybrid STDW model with the R310 patch. The STDW model shows a
significant performance gain with explicit water molecules (Figure 3.11). In the optimal
predictions, the STDW outperforms by 15 to more than 30% from the Top-1 to Top-100,
respectively. In all Top-i , the STDW optimal predictions consistently exceed the SCAL
3.4. Screening power
63
total predictions. Moreover, the ratio of optimal/good predictions is always much higher
in STDW (Figure 3.11).
Figure 3.11: Binding selectivity predictions. Optimal: native nucleotide as the best ranked;
good: native nucleotide ranked within a 2 kcal/mol range from the best ranked non-native
nucleotide; poor: native nucleotide ranked out of the 2 kcal/mol range.
The docking power determines in part the magnitude of the screening power, i.e., the
more native poses, the more likely the native nucleotide is well ranked and associated with
an optimal or good prediction. Considering only the cases where both models generate at
least one native pose in the respective Top-i , we exclude the contribution of the docking
power to the screening power (Figure 3.12).
These results show that the STDW model still has a better screening power, indicating
that the hybrid solvent model can intrinsically better discriminate the native nucleotide
from the non-native ones. The analysis of the score distributions by nucleotide type
suggests that the reason for the better screening power of STDW lies in a scoring bias.
In the SCAL model, purines that are composed of more atoms are slightly better scored
than pyrimidines (C or U), with a preference for G over A nucleotides (Figure 3.13).
In contrast, A nucleotides scored better in the STDW model, while the other three
have similar distributions. Another difference is the much more extensive range of scores
for all four nucleotides. The more favorable scoring of A is consistent with more tightly
binding modes, a known bias of the benchmark as mentioned previously (Figure 3.3).
Moreover, the nucleotide decomposition of the screening power shows no significant difference in performance between A and the other three nucleotides, although it is slightly
better in the Top-100 (Figure 3.14). Thus, the absence of any apparent bias in the
64
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
Figure 3.12: Screening powers on the benchmark subset corresponding to the predictions
common to the SCAL and STW models. Optimal: native nucleotide as the best ranked;
good: native nucleotide in the ranked within a 2 kcal/mol range from the best ranked
non-native nucleotide; poor: native nucleotide ranked out of the 2 kcal/mol range.
Figure 3.13: Distributions of the nucleotide-dependent MCSS score for the SCAL or STDW
models (R310).
3.5. Molecular features
65
STDW scoring makes it more efficient in terms of screening power. The main difference
between the SCAL and STDW models is the presence of explicit water molecules, leading
to increased sampling and scoring performance.
The current scoring functions (tested on the CASF-2016 benchmark) do not exhibit
high screening powers, which reach 30% or a bit more than 40% for the highest success
rates in the Top1% and a bit more than 60% in the Top10% 67 . The comparison with the
results of this study (Figure 3.11) is risky because the Top1% or Top10% would represent
a two- or three-fold number of poses (Figure 3.4) concerning the approximate 1000 poses
generated in the CASF-2016 scoring benchmark 67 . Furthermore, the molecular diversity
of the four nucleotides is limited to the few atoms of the nucleic acid base, making the
discriminatory scoring much more challenging.
Figure 3.14: Decomposition of screening powers per nucleotide type. Optimal: native
nucleotide as the best ranked; good: native nucleotide in the ranked within a 2 kcal/mol
range from the best ranked non-native nucleotide; poor: native nucleotide ranked out of
the 2 kcal/mol range.
3.5 . Molecular features
We define a series of representative features for nucleotide ligands to understand better
the role of solvent and other molecular properties associated directly or indirectly with
water molecules. Then, we determine the relationships between these features and the
lack of prediction, which are represented by logic diagrams (Upset plots). We classify the
features into three main groups related to: (i) the binding site properties (volume, number
of water molecules, presence of metals or other nucleotidic ligands), (ii) the conformational
properties (purine/pyrimidine, syn/anti), and (iii) the interaction properties (contacts,
clashes, stacking, salt bridges). Whether a feature is statistically significant is determined
by its relative frequency in the subset of the benchmark with no prediction (Section 2.1.6).
The only binding site feature that correlates significantly with the absence of prediction is a low volume of the binding site (Figure 3.15A), as calculated by PyVOL 254
(Section 2.1.6). On the contrary, a low number of water molecules within the binding
66
3. MCSS-BASED PREDICTIONS OF BINDING AND SELECTIVITY OF
NUCLEOTIDES
site is not particularly detrimental. Metal ions usually stabilize the phosphate group and
occupy some volume in the binding site (it is correlated with a low volume of the binding
site and a low number of water molecules). Although it is removed from each protein
target, its absence in the calculations is not particularly detrimental either.
Among the conformational features, none is an impacting feature (Annex Figure 9.2).
It is noteworthy that the syn conformation is not associated with the lack of prediction
(Annex Table 9.6), while the initial conformation of all nucleotides is anti, confirming the
quality of the MCSS sampling. On the other hand, three interaction features negatively
impact the performance: the absence of salt bridges, the presence of clashes with water
molecules, and to a lesser extent, the absence of stacking contact (Figure 3.15B). Among
these latter contacts, the π-π interactions contribute more to the negative impact on
the predictions (Annex Figure 9.4). The presence of clashes with water molecules might
induce some distortions within the binding site during the protein target’s preparation.
Suppose we focus on the non-predicted cases specific to the STDW model with the
R310 patch. In that case, the observations described above remain valid with very similar
trends for all the molecular features (Annex Table 9.4). Nevertheless, the syn conformations are slightly more frequent in the no-prediction cases (Annex Table 9.4), indicating
a less efficient sampling for the larger R310 patch in size. In the non-optimal predictions, which fail to score the native nucleotide as the best ranked (i.e., good predictions,
Figure 3.11), similar trends are again observed but with two specificities associated with
the metals and stacking contacts (Annex Table 9.1). First, metals’ presence negatively
impacts the performance suggesting that metals contribute directly or indirectly to the nucleotide selectivity. Second, the absence of stacking contacts makes it more challenging to
score the native nucleotide properly; the binding selectivity of purines versus pyrimidines,
in particular, can be easier to identify in the presence of stacking contacts.
67
Figure 3.15: Upset diagrams of the impact of molecular features on the Top-10 predictions. A: binding site features. B: interaction features. The
intersections with only one member are not shown; others: presence of additional nucleotidic (nucleic acid) fragment in the binding site; no.pred: no
prediction; metals: presence of metal(s) in the binding site; nwat.low: presence of a number of water molecules below the threshold value; vol.low:
volume of the binding site below the threshold value; no.base.contacts: absence of contacts with the nucleic acid base; clash_aa: clash(es) with
amino-acid residues; clash_w: clash(es) with water molecules; no.salt.bridges: absence of salt-bridge; no.stacking: absence of stacking.
3.5. Molecular features
67
As described above, a low volume of the binding site is detrimental per se to the
prediction performance. Once the experimental structure is optimized after the removal of
the ligand (metal and the water molecules in the SCAL model), the volume can sometimes
undergo significant variations: either decreasing or increasing (Annex Figure 9.3). The
average variation shrinks the binding site by 27 to 30 Å3 for the SCAL and STDW models,
respectively. In two-thirds of the benchmark, the binding site shrinks by an average of 87
(SCAL) to 92 Å3 (STDW). In one-third of the benchmark, the binding site expands by an
average of 92 (STDW) to 95 Å3 (SCAL). Thus, a similar trend of variations is observed
for both SCAL and STDW models.
However, only the STDW is significantly impacted in the performance for the prediction of the Top-10 (Annex Table 9.3); the shrinking of the binding site combined with the
presence of water molecules prevents the identification of any native pose in the Top-10
in the concerned cases. This is confirmed by the fact that 9 of the 17 proteins in the
subset with no predictions in the Top-10 exhibit recovered predictions in the upper Top-i
with a smaller patch such as R110 (Annex Table 9.2). In six other cases, the absence
of predictions with the STDW model can be imputed to the presence of water molecules
(Annex Table 9.2). Finally, only two cases do not provide any prediction in the Top-i .
4 - REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
There is a popular advice for beginner researchers that intends to avoid them a waste
of time and efforts whenever a valid solution already exist for they problems: Do not
reinvent the wheel ! As much solid as this maxim may sound, there are circumstances
when a "wheel" should (or must) be reinvented to accomplish a particular need. We
were persuaded (and we proved it right later) that in the clustering field of molecular
ensembles, a re-optimization of popular and effective algorithms was possible and needed
in order to fulfill our particular goals and potentially, those of many other users.
In the workflow we are following to design oligonucleotides through a fragment-based
approach, there is a compulsory need to perform clustering analyses (see Section 1.6).
Although not included in the work described by this thesis, the conformational dynamics
of generated inhibitor candidates are envisaged to be analyzed via MD simulations, whose
trajectories would also require efficient clustering algorithms to be processed.
In this chapter, we present our efforts to diminish the spatial resources of four geometrical clustering algorithms already applied to molecular ensembles: (i) the Quality
Threshold (QT, Section 4.1), (ii) the Daura (Section 4.2), (iii) the Density Peaks (DP,
Section 4.3), and (iv) the Hierarchical Density-Based Spatial Clustering of Applications
with Noise (HDBSCAN, Section 4.4) algorithms.
The implementations proposed in this work were benchmarked against the most widely
used related alternative methods. It is important to note that the benchmarks were
designed to compare software tools that may have differing time and spatial complexities.
While complexity analysis provides insight into algorithmic scaling, empirical benchmarks
on real-world datasets can still offer a meaningful performance assessment from the user
perspective. Thus, the presented comparisons remain valid as they quantify trade-offs
and aid in software selection for specific use cases.
It should be noted that not all methods were tested on the same trajectory datasets.
This situation occurred as the inherent non-linearity of scientific research led to the completion of some implementations earlier than others, and trajectories available for recent
alternatives had not yet been generated initially. Although an ideal benchmark would
gather all algorithms and datasets, this elegance was sacrificed due to practical constraints regarding access to computational resources. Despite variations in trajectory
lengths across methods, these benchmarks constitutes helpful evaluations. The central
insights and relative performance discussions can characterize the strengths and weaknesses of each clustering procedure.
4.1 . BitQT: a graph-theoretical approach to the QT clustering
4.1. BitQT: a graph-theoretical approach to the QT clustering
69
The advantages of QT clustering were already discussed in Section 1.6.2.1. The
guarantee to produce clusters in which the collective similarity of elements is preserved
captures the attention of many users. However, when cautiously examined, we noted
that the mainstream alternatives available were either flawed or significantly inefficient .
This fact led us to develop a proof of concept to demonstrate their wrongness and later
to conceive a computationally accessible solution that could be readily used to process
molecular ensembles.
4.1.1 . Inaccurate implementations of QT
The QT original formulation has two clear implications (see Section 1.6.2.1): (i)
No pairwise distance inside a cluster can be greater than a predetermined threshold (a
measure of quality), and (ii) the cluster diameter must be minimum. The first criterion is
the heart of the algorithm (and the one that should be preserved in any valid variation),
while the second merely limits the size of recovered clusters. Visibly, there is no sense in
guaranteeing the latter if the former is not met, and no implementation of this algorithm
should be taken as correct if those conditions do not hold. Variations of QT do exist 265,266
in which the core idea of respecting a quality threshold is never violated.
The VMD’s documentation stated that the measure cluster command was based on
the QT algorithm from version 1.9 (released in 2011) to 1.9.4a20 (under development
in 2019). As a consequence, numerous reports in the literature (even in book chapters)
describe the use of VMD to perform QT. A report of the QT algorithm was published
by Melvin et al. in 2016 223 . The source code (referred to as pyMS from now on) exhibits
a similar workflow to that spotted in the measure cluster command of VMD (see Figure
4.1). The same results of pyMS are retrieved WORDOM 222 , which proposes a clustering
option supposedly similar to QT. In Figure 4.1 we demonstrate that all these variants are
wrong in their claim of performing QT.
Clustering analysis of a short MD trajectory corresponding to the tau peptide 256 was
conducted using (i) the VMD’s measure cluster internal command, (ii) the WORDOM’s
qt-like method, (iii) the pyMS script, and (iv) an implementation of the original QT
algorithm developed by us (available at https://github.com/rglez/qt). For all runs, an
RMSD cutoff of 4 Å was set and the first five clusters requested with an atom selection
corresponding to all protein atoms.
Next, RMSD pairwise distances between all the elements inside every cluster returned
by each method were measured and plotted in the corresponding graph (Figure 4.1). If
any algorithm could perform QT, none of the plotted values would have been greater
than the specified cutoff; i.e., the quality guarantee of at least 4 Å should have held
between all pairs of elements inside a cluster. As shown in Figure 4.1, only our in-house
implementation of QT satisfies the discussed constraint.
The pyMS script gives precisely the same results as WORDOM and is not visible in
Figure 4.1 because of superposition. Nitpicked examinations of VMD, WORDOM, and
pyMS were conducted to realize the causes behind the displayed inconsistencies. The
source code of the measure cluster and that of pyMS revealed that they are implementing
an algorithm commonly credited to Daura 224 (see Section 1.6.2.2) that is available in the
70
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
Figure 4.1: All vs. all RMSD values of structures contained in each of the first five clusters (C1, C2, C3, C4, and C5, respectively) retrieved by supposedly QT clustering algorithms
implemented in VMD (black), pyMS (blue), and WORDOM (green, invisible due to superposition with WORDOM values). Our implementation of the original algorithm is highlighted
in red. The broken line indicates the specified cutoff of 4 Å.
GROMACS package through the gromos clustering option. The same statement applies
to the qt-like method in WORDOM, which returns the same information as pyMS.
The simplistic approach followed in Daura clustering steps only guarantees that all
elements inside a cluster have a similarity distance less than a specified threshold when
compared to the seed of the cluster (see Section 1.6.2.2). No restriction concerning the
collective intra-cluster similarity is applied, which explains why the snapshots represented
in Figure 4.1 repeatedly exceed the threshold compared to all others in the same cluster.
Some scientific reports inaccurately claiming to perform QT clustering, as well as the
potential implications of their confusion are detailed in Annex 9.2.2.
Although we proposed a freely available implementation of QT for MD (referred
to as QTPy from now on), it is not suitable to be used with relatively big molecular
ensembles because it takes long run times. However, this proof of concept could be used
to analyze small molecular ensembles or refine clusters obtained by other algorithms saved
as independent trajectories. From a developer’s point of view, our proposal can serve as a
gold standard to benchmark future versions aiming to be faster. In light of the precedent
situation, we created BitQT, a heuristic variation of QT that can output equivalent results
to the original algorithm at a much less computational cost. It has been devised using a
parallel with the Maximum Clique Problem (see Section 1.5.2).
4.1. BitQT: a graph-theoretical approach to the QT clustering
71
4.1.2 . From QT to the Maximum Clique Problem
We have already discussed that the crucial aspect of the QT algorithm lies in its ability
to guarantee that all pairwise similarities inside a cluster will remain under a threshold
k. During the execution of the algorithm (see Algorithm 1), two conditions must hold
to populate clusters under creation: Condition 1- the entering element minimizes the
increase of the cluster diameter under construction, and Condition 2- the diameter of the
cluster under construction does not exceed the threshold k.
To make a parallel between QT and the MCP, we can represent each element of an
MD trajectory as a node of an undirected graph in which edges depict RMSD similarity
between nodes. Only edges with an RMSD less or equal to the threshold k are allowed.
In that context, QT can be seen as an iterative search of cliques. However, QT cliques
are not necessarily maximum due to Condition 1 of the algorithm, which ensures that they
should have a minimum weight instead of a maximum cardinality. Condition 1 requires
the diameter of the clusters to be minimum. Still, it is Condition 2 that ensures not to
exceed the quality threshold in the pairwise similarity of retrieved clusters.
Conveniently, the QT algorithm could be redefined to search for maximum-sized
clusters instead of minimum-weighted ones without compromising the pairwise similarity
assured by the second condition. In most clustering applications, maximizing the size of
the clusters is a desirable feature. Relaxation of Condition 1 automatically converts QT
in an MCP problem, accessible by the graph theory tools. This approach profoundly
impacts how molecular similarity can be encoded and the efficiency of algorithms used to
solve the problem, as discussed in the following sections.
4.1.3 . Binary encoding of RMSD pairwise similarity
As the ultimate goal of our clustering proposal is to partition all MD trajectory
elements, all the pairwise similarities should be analyzed. This information can be saved
in RAM as a matrix to accelerate the algorithm’s run time. However, instead of using
floats as the numeric type, we followed a different approach to diminish the value of m
in Table 1.2.
If we conceive the QT algorithm as an MCP problem, after considering the relaxation
of Condition 1 our search will be focused on finding cliques of maximum cardinality, and
no helpful information is extracted from the weight of the edges other than its absence or
existence. This information can therefore be encoded as a binary matrix M where Mij = 1
if nodes i and j are similar (RMSDij ≤ k) or 0 otherwise. Note that M contains the
same information that the adjacency matrix of the graph except for the diagonal, which in
this case will always be one instead of zero (RMSDii ≡ 0.0). For the sake of simplicity,
we will refer to M as the adjacency matrix of the trajectory graph.
By using the binary adjacency matrix, we reduce the RAM consumption of this object
(m = 81 ) by 16, 32, or 64 times compared to other software that deals with half, single or
double-precision float values to represent the RMSD (see Table 1.2). Besides the RAM
saving, expressing similarity as a binary matrix offers the possibility to perform the search
of cliques using binary operators (AND and XOR, see Section 1.5.5), contributing to the
72
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
speedup of the heuristic clique search algorithm we propose in the following section.
4.1.4 . A heuristic search of big cliques
Next, we describe the workflow of the BitQT clustering algorithm, which is built upon
a not previously published heuristic for searching big cliques. A formal review of the many
MCP heuristics available is out of this thesis scope and can be found elsewhere (see
reference 267). In our case, we want to keep the common similarity of QT clusters, but
their size is not a big concern. After all, the original QT does not provide either maximum
cliques.
We start with calculating the binary similarity matrix that will be stored in RAM. The
float vector containing the one-versus-all RMSD similarity of each element is transformed
into a bit-vector Bi (B1 to B9 in Matrix 1, Figure 4.2) in which Bij = 1 if RMSDij ≤ k,
zero otherwise. Each vertex’s degree is calculated as the total number of switched-on
positions in the Bi vector (D column in Matrix 1, Figure 4.2). Note that Bi vectors always
have 1 at the ith position (RMSDii == 0 ≤ k), so D column actually contain degree + 1
of each vertex in the trajectory graph. Then, the subsequent steps are followed.
1- Vertex coloring: Each vertex of the input graph (Graph 1, Figure 4.2) is ranked
(column R, Matrix 1, Figure 4.2) in descending order of their corresponding degrees
(column D, Matrix 1, Figure 4.2. Following the rank order, each vertex takes a color label
that it shares with all other vertices that are neither colored nor neighbors (column C,
Matrix 1, Figure 4.2).
2- Clique search from the maximum degree node: After all vertices are colored,
the search of a clique starts considering only neighbors of the maximum degree node of the
graph (Graph 1A, Figure 4.2) which is called the seed of the clique (node 1 in Matrix 1A,
Graph 1A, Figure 4.2). Neighbors of the seed are strictly ordered for further processing by
following three criteria (DCg ordering); descending order of their degrees, ascending order
of their color class, and ascending order of the degeneracy of the color class (columns D,
C, and g, respectively, Matrix 1A, Figure 4.2). For our purposes, degeneracy is perceived
as the number of nodes of the color class in the context of the neighbors of a seed node,
not in the entire graph (in which case, using it for order would be meaningless).
Following this ordering, the first node is selected to start a clique, and subsequent
nodes will be added to it if they have a still-not-explored color and are adjacent to previously explored nodes (clique propagation).
BitQT performs this search using bitwise operations. The bit-vector Bi corresponding
to the maximum degree node is set as the clique bit-vector (B1 in Heuristic search of Graph
1A, Figure 4.2. Following the DCg ordering, an AND operation is performed between the
clique bit-vector and the next node bit-vector if it has a new color (B6 in Heuristic search
of Graph 1A, Figure 4.2. Indices corresponding to bits that become zero by this operation
are discarded from further consideration (B2, B3, B4, and B5) as they are not adjacent to
processed nodes (B1 and B6). The resulting bit-vector becomes the new clique bit-vector
used for the AND operation, with the next candidate following the DCg ordering (B9).
The bit-vector resulting from the iterative AND operations contains the members of the
first clique.
Figure 4.2: First iteration of the binary heuristic for searching cliques implemented in BitQT.
4.1. BitQT: a graph-theoretical approach to the QT clustering
73
3- Clique search from promising nodes: Once the clique retrieved by using the
maximum degree node as the seed is found in the previous step, the same exploration
strategy is conducted for every promising node in the original graph (Graph 1). A promising node (B8 in Graph 1, Figure 4.2 is defined as a node with a color not present in
the first clique and whose degree is higher than the number of nodes in the first clique.
Using such nodes as seeds for propagation might lead to forming a more prominent clique
(Heuristic search of Graph 1B, Figure 4.2).
4- Conclusion and updating: When the maximum degree node and all promising
nodes have been used as seeds, the maximum clique found is picked as a cluster, and
its members removed from the input graph (the corresponding Bi vectors removed from
the binary matrix). An updating of the remaining bit-vector is necessary to set all entries
corresponding to nodes that formed the cluster as zero, which will not be available for
subsequent iterations. This updating is bitwise encoded as a consecutive AND/XOR operation between the remaining bit-vectors and the clique bit-vector (Conclusion of iteration
1, Figure 4.2. The same steps are repeated from Step 2 until no more cliques can be
found.
During the execution of BitQT, some scenarios leading to ties may arise, for instance,
selecting the node of the highest degree as seed (in "2-Clique search from the maximum
degree node" and "3-Clique search from promising nodes"), or selecting the maximum
clique (in "4-Conclusion and updating"). BitQT solves these cases by choosing the element with the lowest index among the available options as the "winner" of the tie. These
ties can also appear in the original QT algorithm (when selecting the candidate cluster
with most neighbors as a cluster). Choosing one or another "winner" does impact the
outcome of algorithms in terms of cluster composition. However, the choice of a "winner"
in a tied scenario will never invalidate the discussed guarantees of BitQT or QTPy.
4.1.5 . Performance benchmark of valid QT variants
In this section, we compare the run time and memory usage of BitQT, QTPy and
qtcluster, which are the only QT implementations for molecular ensembles that we have
found in the literature. These parameters are shown in Table 4.1 for the clustering of six
different MD trajectories described in Section 2.2.1 (6, 30, 50, 100A, and 250 kF).
Given that software under evaluation is programmed by using distinct algorithms and
programming languages (Fortran 90 for qtcluster and Python 3 for BitQT and QTPy),
we are only able to provide general insights into the disparate performances observed in
Table 4.1.
74
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
Table 4.1: Run time and RAM consumption of analyzed QT implementations on different
trajectories.1
Traj. Name
6 kF
30 kF
50 kF
100A kF
250 kF
# atoms
(selection)
217 (all)
64 (CA)
78 (no H)
660 (backbone)
160 (backbone)
BitQT
Run time RAM peak
h:mm:ss
GB
0:00:08
0.101
0:02:15
0.470
0:12:34
0.435
1:15:37
4.355
6:36:04
8.128
qtcluster
Run time RAM peak
h:mm:ss
GB
0:08:21
0.529
0:18:55
0.270
1:14:08
1.526
0:00:49
81.014
130:18:06
17.476
QTPy
Run time RAM peak
h:mm:ss
GB
0:04:36
0.181
3:41:11
2.710
181:51:57
7.101
200:00:00
18.626
0:00:03
116.415
1
Bold entries denote either a time crash (job taking more than 200 h) or a memory crash (job carrying
more than 64 GB). In memory crash cases, the run time it took until crashing and an estimate of the
lowest RAM needed to run the job is presented.
Of the three options, QTPy is the only one that always creates a square float matrix
for saving the RMSD distances, so its RAM peak is expected to be the highest. The
only exception is 6 kF, where the pairwise matrix uses only about 69 MB of RAM,
so other data structures (or merely the molecular trajectory) will be responsible for the
peak. RAM usage of BitQT also grows quadratically with the number of elements in the
trajectory. However, as it uses bits instead of half-precision floats, there is a 16X memory
saving in this object’s construction compared to QTPy.
The memory usage of qtcluster may be confusing at first sight, as it can process a
250 kF trajectory but produces a memory crash when dealing with a simulation of 100
kF elements. It is clear why qtcluster crashed at 100A kF but could process 250 kF; the
100A kF trajectory contained 660 atoms and 250 kF only 160. Substituting in the VRAM
formula of qtcluster (Table 1.2) and taking m = 4 we obtain 81 GB for 100A kF and
about 12 GB for 250 kF. Inconveniently, qtcluster can analyze big trajectories only when
the number of selected atoms is relatively small.
While the three algorithms have quadratic spatial complexity, the costs of BitQT and
QTPy are governed by the trajectory size. In contrast, qtcluster is dependent on the size
of the atomic selection.
Run time reported in Table 4.1 exhibits a general trend; QTPy is the slowest choice,
followed by qtcluster, which is greatly outperformed by BitQT. QTPy is the only one that
implements the original version of QT 214 . As we have commented, the original QT has
a very high computational cost evinced in the QTPy run times. The RMSD computation
step can be safely discarded as the main contributor to the slow time performance of QTPy
because it employs the same library that BitQT for this purpose (MDTraj) 257 . QTPy
applications are limited to processing small trajectories or as a reference for developing
future QT variants applied to the MD field.
qtcluster was designed as a high-speed QT alternative for the partitioning of MD.
The similarity metric employed by this script (Equation 1.19) is cheaper than the more
customary RMSD and avoids alignment. Perhaps the essential feature that makes qtcluster a fast QT implementation lies in the fact that it only preserves one condition
from the originally formulated QT; that one assuring the collective similarity of retrieved
clusters. For big trajectories, however,it is not a fast option.
Comparatively, BitQT has the best run time performance allowing it to handle rel-
4.1. BitQT: a graph-theoretical approach to the QT clustering
75
atively long MD trajectories. The accelerated computing of optimal RMSD distances
through the MDTraj engine joined to the developed binary-based heuristic for searching
cliques are the cornerstones of its cheaper cost.
4.1.6 . Equivalence between BitQT and QT
As we discussed earlier in Section 4.1.2, BitQT was conveniently designed to relax the
Condition 1 regarding the diameter of the cluster under construction, but it must carefully
preserve the Condition 2 concerning the clusters collective similarity. The previous claim
implies that all groups returned by BitQT must have a diameter less or equal than the
user-defined quality threshold k.
Figure 4.3 shows the distribution of all clusters’ diameter for every analyzed trajectory.
It is appreciated that pairwise distances between elements of the same cluster never exceed
the predefined quality threshold k (4 Å for 6 and 30 kF, 3 Å for 250 kF, and 2 Å for 50
and 100A kF).
Figure 4.3: Distributions of clusters diameters returned by BitQT for each analyzed trajectory.
Figure 4.3 also demonstrates that BitQT clusters are cliques in the MD trajectory
graph. As mentioned in Section 4.1.3, an edge between two nodes i and j of the trajectory
graph is set if and only if dij ≤ k. If all pairwise distances between elements in every
cluster are under k, then the corresponding nodes of the trajectory graph are pairwise
connected, implying that clusters are indeed cliques.
The respect for collective similarity indicates an essential equivalence between BitQT
and QT, but it does not quantitatively compare the outcomes of these algorithms. An
Adjusted Rand Index (ARI) analysis between partitions obtained with QTPy (Q) and
76
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
BitQT (B) for trajectories 6, 30, and 50 kF is shown at Figure 4.4. Note that instead
of reporting just the global ARI between Q and B, we explicitly compared the ARI
between both partitions at the top-X clusters (QX and BX ), taking X from 1 (the first
cluster) to C (the total number of clusters). Consequently, the global ARI between Q
and B corresponds to the last point of each curve. The remaining points indicate the
correspondence between the first X clusters of Q and B.
The global ARI for 6, 30, and 50 kF are 0.87, 0.87, and 0.91 respectively, indicating a
good agreement between clusters produced by QTPy and BitQT. An even higher index is
reported for the first X clusters with sizes bigger than 1% of the trajectory size (ARI1% ).
These most populated clusters are often considered the most relevant of the trajectory
as they groups the representative conformational states explored in an MD simulation.
ARI1% (represented by a bold point in Figure 4.4A-C) is 0.96, 0.88 and 0.88 for trajectories 6, 30, and 50 kF, respectively. This indicates an excellent agreement between the
most popular clusters obtained by QTPy and BitQT.
Figure 4.4: Adjusted Rand Index (ARI) between partitions obtained with QTPy and BitQT
for all clusters in trajectories 6 kF, 30 kF, and 50 kF (A, B, and C respectively). The ARI of
the first X clusters with sizes bigger than 1% of the trajectory size is located to the left of
the bold point of each graph.
Observed ARI fluctuations at different top-X are expected because both algorithms
pick their seeds to form clusters differently. It is possible that at a given value of X, clusters
formed by QTPy were still not recovered by BitQT or vice versa. However, fluctuations
are more pronounced for the less populated clusters.
4.2 . BitClust: the first binary implementation of Daura clustering
The advantages and limitations of Daura algorithm are reviewed in Section 1.6.2.2.
This methodology stands up as a compromise alternative to QT when big molecular
ensembles must be processed within a reasonable run time. However, after carefully
inspecting its most popular alternatives, we noted that they were either inefficient (in
terms of run time and RAM consumption) or even inaccurate.
Hence, we propose BitClust, a novel, faster implementation of Daura algorithm designed to process big molecular ensembles. BitClust offers a classic trade-off, RAM for
speed, to boost time performance by increasing memory storage. However, the necessary amount of RAM has been significantly optimized by encoding pairwise similarity
4.2. BitClust: the first binary implementation of Daura clustering
77
distances as bits.
4.2.1 . Translating Daura clustering to bitwise operations
The first step in BitClust is similar to that of BitQT; the binary encoding of RMSD
pairwise similarity. Both implementations of these objects encoding are analogous and
already discussed in Section 4.1.3.
With the binary matrix loaded in RAM, two special vectors are constructed from
the beginning of the clustering process and iteratively updated during the following steps.
Firstly, a bit vector A is declared (iteration 1, Figure 4.5), which contains as 1 those indices
available to form a cluster at a given moment. In the beginning, all A bits are set to 1
as all elements are available to form clusters. As the algorithm iterates, indices already
clustered are set to 0 in A, reflecting that they are no longer available for consideration
to form other clusters.
Figure 4.5: Workflow of the binary Daura algorithm implemented in the BitClust code
Secondly, a vector D of integers is declared (matrix 1, Figure 4.5), containing the
degree (Di) of each Bi present in the matrix. Di is defined as the total number of
indices 1 in the bit vector that results from the bitwise operation Bi AN D A (Di =
sum(Bi AN D A)) and not as the total number of indices 1 of Bi. The vector A here
acts as a bit-mask that helps to elucidate how many elements of Bi are available to form
78
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
clusters. The initial bit values of Bi are never altered, only A and D change between
iterations (matrix 1, 2 and 3 in Figure 4.5).
Once A and D vectors have been initialized, the workflow of BitClust has four main
steps that repeat iteratively until no more elements can be clustered: (i) detect Bi with the
maximum degree and define as Bmax the bit vector resulting from the binary operation
Bi AN D A (step I, Figure 4.5).
Note that if two or more Bi vectors have the same maximum degree, the algorithm
arbitrarily processes the Bi with the lowest index i as if it were the maximum, (ii) saves
all set indices of Bmax as members of a cluster and delete their corresponding Bi vectors
from the matrix (step II, Figure 4.5), (iii) update the bit vector of available conformations
A by setting as 0 those entries that were clustered in the previous step (step III, Figure
4.5), and (iv) update degrees of remaining Bi (step IV, Figure 4.5).
4.2.2 . Performance benchmark of Daura variants
A set of commonly used software for clustering MD simulations has been chosen for
performance comparison against BitClust. Run time and memory consumption of each
method is reported in Table 4.2 for the three trajectories 6, 100B, and 500 kF (see Section
2.2.1).
The clustering method selected in each case was as follows; Daura for BitClust and
GROMACS (through the gromos option), quality threshold for py-MS and VMD, qt-like
for WORDOM and median-linkage for TTClust.
We want to stress that despite the native denomination in their original software,
the chosen algorithms (except the median-linkage) correspond all to Daura (see Section
4.1.1). In the case of VMD, we decided to show the performance of processing five
(VMD-5, the default value) and all (VMD-ALL) clusters to evaluate the usefulness of
its implementation, which is specially conceived for preserving memory resources.
Table 4.2: Run time and RAM consumption of analyzed Daura implementations on different trajectories.1
Software
BitClust
pyMS
WORDOM
VMD-5
VMD-all
TTClust
GROMACS
Trajectory 6 kF
Run time RAM Peak
mm:ss
GB
0:04
0.15
0:11
0.41
1:52
0.10
0:14
0.09
2:05
0.10
1:30
1.16
2:10
0.16
Trajectory 100B kF
Run time RAM Peak
hh:mm:ss
GB
1:25:28
9.41
1:46:02
61.54
1:26:13
37.25
4:59:22
6.97
5:08:10
6.97
0:01:59
74.51
26:13:29
52.22
Trajectory 500 kF
Run time RAM Peak
hh:mm:ss
GB
6:00:08
33.84
3:03:49
—2
2:54:23
931.32
29:34:43
4.13
60:00:00
4.14
0:00:37
1862.65
01:09:03
931.32
1
VMD-5 and VMD-ALL notations refer to clustering jobs performed using VMD software and requesting
five and all clusters, respectively. Bold entries denote either a time crash (jobs taking more than 72 h) or a
memory crash (jobs carrying more than 64 GB). In memory crash cases, the run time it took until crashing
and an estimate of the lowest RAM needed to run the job is presented. 2 Impossible to determine as this
algorithm does not load a matrix in RAM.
The calculation of the pairwise similarity values occurs in the first place for every soft-
4.2. BitClust: the first binary implementation of Daura clustering
79
ware. This is the most CPU-consuming step that governs overall run time. GROMACS
is the slowest option (6 and 100B kF trajectories for GROMACS in Table 4.2) because
its implementation of this first step is not parallelized.
Run times for processing five and all clusters with VMD (VMD-5 and VMD-ALL
respectively in Table 4.2) are significantly different. This behavior is associated with the
fact that VMD does not save the pairwise similarity information, which is calculated to
retrieve a particular cluster. Instead, it recalculates all the information every time a cluster
is found. While this characteristic puts VMD as the most memory-efficient alternative
among the studied ones, it is the cause of its time performance of VMD when more than
a few clusters are requested.
Suppose the trajectory has few clusters grouping most of the elements (trajectory
100B kF in Table 4.2). In that case, the recalculation takes less time as fewer elements
are available to form clusters (VMD-ALL, Table 4.2). However, suppose many evenly
distributed clusters are present in the trajectory (trajectories 6 and 500 kF in Table 4.2).
In that case, recalculations are more time-consuming as many elements are available to
form clusters after each iteration (VMD-ALL, Table 4.2).
WORDOM has an intermediate time performance in the trajectory it could handle
(trajectory 6 kF for WORDOM in Table 4.2). The faster options are BitClust and py-MS
implementations which can interface to the fast MDTraj engine 257 for the calculation
of the pairwise similarity matrix. Even though TTClust does not implement Daura, it
interfaces with MDTraj for calculating the RMSD matrix. We included it to illustrate
some aspects of memory management.
Among the analyzed options, the most memory-consuming is TTClust. It saves the
pairwise similarity matrix directly in RAM using a 64-bit float for every entry (m = 8
in VRAM equation of Table 1.2). For short trajectories (as TTClust authors point out
in their manuscript), this is affordable for most workstations, but as trajectory size gets
bigger, TTClust starts showing a prohibitively RAM consumption.
Although it also employs a 64-bit float for every entry of the similarity matrix, py-MS
has an improved approach. It saves the square matrix to a temporary file in the disk and
loads in RAM only those values having an RMSD distance less than the specified cutoff.
While the py-MS strategy can save RAM, enough space must be available on disk. In
the worst case (for higher values of cutoff leading to a situation where all elements are
neighbors), the whole file is loaded to memory, incurring the same expensive behavior that
TTClust.
GROMACS saves the similarity matrix into memory using a 32-bit float (m = 4 in
VRAM equation of Table 1.2) for each entry, requiring more than 50 GB to process the
100B kF trajectory (see Table 4.2). WORDOM saves the matrix using the same numeric
type (32-bit float) that GROMACS. However, other internal data structures make it a
more memory-consuming alternative, impeding the processing of the 100B kF trajectory.
VMD is the unique alternative that does not create a matrix in RAM or the disk.
It only retains the most significant cluster found during iterations. As a result, it must
recalculate redundant information every time a cluster is found, leading to poor time
80
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
performance when many clusters are requested. Note that this is the only variant that
requires the number of clusters to retrieve as a mandatory argument.
As discussed in Section 4.2.1, BitClust saves the whole square pairwise similarity
matrix directly in RAM. Nevertheless, it does not use float values but bits, encoding if a
particular entry has an RMSD value less equal or greater than the specified cutoff. The
use of bits results in a significant reduction of the memory requirement of the RMSD
matrix. The less precise float (half-precision float) consumes 2 bytes or 16 bits to represent
a value. On the other hand, BitClust only needs 1 bit, as discussed earlier, so a saving of
16X is achieved for the total resources consumed by the matrix. It is worth noting that
most implementations use 4 or 8 bytes (32 or 64-bit) for the single and double precision
float values, which means that BitClust builds an RMSD matrix that saves RAM by a
factor of 32X or 64X concerning such variants.
4.2.3 . Equivalence between BitClust and Daura
In order to assess the correctness of BitClust implementation, we compared elements
of the first five clusters retrieved by Daura implementations from the 6 kF trajectory. In
Table 4.3, it is reported not only the number of elements of every cluster but also the
percentage of elements contained in the corresponding cluster returned by BitClust. To effectively compare the resemblance of two conformations, they should be superposed before
the RMSD calculation; however, some analyses might require ignoring this superposition
step. In the case of WORDOM, both options were reported in Table 4.3.
Table 4.3: Number of elements and percent of elements shared by the first five clusters
retrieved by Daura alternatives against BitClust.1
Cluster ID
1
2
3
4
5
BitClust
pyMS
465 (100)
346 (100)
153 (100)
146 (100)
136 (100)
465 (100)
346 (100)
153 (100)
146 (100)
136 (100)
No. of elements (% intersection)
WORDOM
VMD
(superpose) (no superpose)
465 (100)
444 (100)
444 (100)
346 (100)
343 (100)
343 (100)
153 (100)
141 (86)
141 (86)
146 (100)
140 (90)
140 (90)
136 (100)
133 (100)
133 (100)
GROMACS
628 (6)
380 (16)
205 (9)
202 (1)
187 (1)
1
Superposition of elements before RMSD calculation was explicitly requested in the case of WORDOM
(superpose).
BitClust, py-MS, and WORDOM (superpose) retrieve exactly the same information for
the first five cluster reported (see Table 4.3). It is worth noting that WORDOM qualifies its
qt-like method as a variant of the QT algorithm, and py-MS affirms to be performing QT.
This comparison further asserts that WORDOM and py-MS implement Daura algorithm
(see discussion in Section 4.1). VMD documentation also reports the application of the
QT algorithm. However, the comparison between VMD and WORDOM (no-superpose)
in Table 4.3 demonstrates that VMD results coincide with those coming from a Daura
implementation when no superposition is performed on the analyzed elements.
GROMACS results invite a detailed analysis as none of the retrieved clusters exhibited a similarity higher than 20% to BitClust. It should be noted that only the GRO-
4.3. DP+: Reaching linear spatial complexity in DP clustering
81
MACS documentation explicitly recognizes Daura algorithm application through the gromos method, referring the readers to the original publication of this routine. However,
we think the analyzed version of gromos algorithm is incorrectly implemented. From
the 6000 elements analyzed in trajectory 6 kF, only 1000 are reported in the output
file. In addition, all conformations appeared six times in different clusters except for
the first (index zero), which appeared seven times in the output file. After these inconsistencies, it is an unreliable option. Besides our findings, a descriptive report in
the literature explains in detail the implementation pitfall contained in the source code
of this ubiquitous tool (https://mailman-1.sys.kth.se/pipermail/gromacs.org_
gmx-users/2015-April/096367.html).
4.3 . DP+: Reaching linear spatial complexity in DP clustering
The theoretical background of the DP algorithm is discussed in Section 1.6.2.3. Even
though a myriad of variants exists for this clustering procedure, none has been able to
eliminate its quadratic memory complexity so far. Here we propose DP+, a methodology
to derive the exact DP partitioning of elements without constructing a square similarity
matrix. Instead, a double-heap approach produces an oriented tree where every node is
connected to its nearest neighbor of higher density by a weighted edge.
Built upon DP+, we designed RCDPeaks, a refined variant of the original DP.
Employing DP+, RCDPeaks processed a one-million elements trajectory using less than
4.5 GB of RAM, a task that would have taken more than 2 TB (and about 3X more
time) with the most competitive alternative.
4.3.1 . Computing an oriented tree instead of a complete graph
The typical workflow used in exact or modified DP variants saves the pairwise similarity of elements into a square float matrix. This strategy may offer a fast determination
of ρi and δi (see Section 1.6.2.3) but inconveniently limits the algorithm’s application to
problems whose similarity matrix could fit in available RAM. Next, we describe DP+,
an alternative approach to DP that avoids the construction and storage of such a matrix
and hence can be applied to treat much longer ensembles.
DP+ exploits the graph-theoretical view of a molecular ensemble by considering it as
a graph T in which all nodes are pairwise connected. In T , nodes represent 3D coordinates,
and their pairwise similarity distance weights undirected edges (Figure 4.6A). If ρ values
are assigned as the weights of T nodes, then the goal of DP can be stated as transforming
T into an oriented tree T ′ that contains only one outgoing edge per node pointing to
its nearest neighbor of higher ρ. The weights of edges in T ′ correspond to δ values in
Equation 1.25 (Figure 4.6B).
For every element i, DP+ computes ρi from the i-versus-all RMSD vector (RMSDix ),
by counting the number of elements j whose RMSDij < dc . As δi refers to the distance
from i to its nearest neighbor of higher ρ, computing this magnitude requires iterative
queries to the sorted RMSDix vector. However, the complete sorting of RMSDix is
an expensive O(n ∗ log(n)) operation. DP+ makes a faster partial ordering (O(n) time
82
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
Figure 4.6: Graph-theoretical view of an MD trajectory before and after applying DP. A) Complete graph T in which nodes correspond to 3D coordinates and undirected edges
denote pairwise similarity B-) Oriented tree T ′ obtained after applying DP to T . Each node
(weighted by its ρ value) contains a single outgoing edge pointing to its nearest neighbor
of higher density.
complexity) of RMSDix at the k th position and then a complete ordering of the much
smaller k-neighborhood (denoted as η from now on). The value of k is internally defined
as 0.02 ∗ N (although users can modify it), where N is the total number of elements in
the ensemble. DP+ relies on the assumption that most elements will find their nearest
neighbor of higher ρ inside this sorted η.
Figure 4.7 illustrates the previous procedure using the RMSD0x vector of a tenelements trajectory where dc = 0.36 nm and k = 5. In Figure 4.7A, ρ0 (the number of
elements j for which RMSD0j < dc ) is set as 7 (bold entries). In 4.7B, the partial sorting
of RMSD0x at k = 5 is exemplified. Note that this process returns the first unsorted k
elements with the lowest values. Figure 4.7C shows the last ordering stage in which only
the first k elements of RMSD0x are completely sorted. This vector corresponds to ηi .
Figure 4.7: DP+ main objects and operations involved in the computation of ρi and ηi
for a ten-elements ensemble (dc = 0.36 nm and k = 5). A-) RMSD0x vector. Bold entries
correspond to elements closer than dc from element 0. B-) RMSD0x partially sorted at
k = 5. C-) Complete ordering of first k values of RMSD0x (η0 ). D-) Main heap. E-) Auxiliary
heap.
4.3. DP+: Reaching linear spatial complexity in DP clustering
83
DP+ gradually constructs T ′ using data distributed in two separate heaps to avoid
storing T information as a square matrix. The main heap will contain the ρi , i, and ηi
for a subset of elements (Figure 4.7D), while an auxiliary heap will store those elements
whose nearest neighbor of higher density could not be found inside their ηi (Figure 4.7E).
The importance of using a heap data structure lies in its ability to quickly retrieve an
extreme value (minimum in our case) of the collections it contains. If we introduce several
tuples containing ρi and ηi , a so-called "min heap" can return the minimum weighted
element and its corresponding ηi in logarithmic time. Through heaps, DP+ speeds up
the construction of T ′ , exploiting the observation that elements with lower ρ are more
likely to find their nearest neighbor of higher density inside η.
Concretely, after defining a local density cutoff dc , DP+ follows the next steps to
construct T ′ (see Algorithms 6 and 5): A still not analyzed element i is chosen from the
trajectory. This action will occur whenever the main heap is empty. RMSDix is then
calculated and ρi computed counting the number of elements j with RMSDij < dc .
Through the already mentioned sorting strategy, ηi is obtained and DP+ proceeds to
search the first element Xj ∈ ηi having ρj > ρi . If such an element is found, a directed
edge from i to j is created, and δi is set to dij . During this process, all inspected j for
which ρj ≤ ρi are transferred to the main heap as a tuple containing ρj , j index and ηj .
If the opposite situation happens, i.e., an element j whose ρj > ρi is not found in ηi ,
then a tuple containing ρi and i index is passed to a secondary heap for future processing.
The previous process goes on until all elements have been considered.
At that point, the elements i not finding their nearest neighbor inside ηi are already
stored in the auxiliary heap. For each one of them, DP+ recalculates RMSDix and
finds the element j with ρj > ρi to set δi . In the special case where i has the maximum
value of ρ (so it is impossible to find ρj > ρi ), δi is set to max(RMSDix ). Experiments
show that the average size of the auxiliary heap is always a small percent of N .
4.3.2 . Refining the exact algorithm of DP
As explained in Section 4.3.1, DP+ is an exact implementation of the original DP.
DP+ avoids the quadratic memory complexity using heap-based data structures. Having
equivalent results, DP and DP+ share the same shortcomings, among which are: (i)
the consideration of very similar center candidates as independent cluster seeds (in the
user-selected region of the decision graph, no checking is performed on centers to ensure
their pairwise geometrical separation), (ii) the impossibility of running an automatic job
(given that ρ and δ cutoffs must be manually selected from the decision graph), and (iii)
the excessive flexibility of core and halo definitions for applications regarding molecular
ensembles (see Figure 9.10). In Section 9.2.4, we describe Refined-Core Density Peaks
(RCDPeaks), built upon DP+, and addressing the limitations mentioned above.
4.3.3 . Performance benchmark of DP variants
The run time and RAM consumption of RCDPeaks, cpptraj, and CLoNe when
processing different MD trajectories are compared in Table 4.4. To our knowledge, these
three software are the only publicly available DP implementations specifically designed
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4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
to deal with MD simulations. While cpptraj implements the original algorithm, CLoNe
was inspired by DP to overcome several of its limitations.
Table 4.4: Run time and RAM consumption of analyzed DP implementations.1
Trajectory
6 kF
30 kF
50 kF
100A kF
250 kF
500 kF
1 MF
No. of atoms
(selection)
217 (all)
64 (CA)
78 (no H)
660 (backbone)
160 (backbone)
217 (all)
304 (backbone)
RCDPeaks
Run time RAM peak
h:mm:ss
GB
0:00:05
0.14
0:00:42
0.16
0:02:00
0.19
0:41:59
0.92
1:14:04
0.87
6:47:12
2.03
33:21:10
4.16
cpptraj
Run time RAM peak
h:mm:ss
GB
0:00:10
0.09
0:01:46
1.78
0:05:59
4.71
2:10:23
19.38
0:00:04
125.50
0:00:09
499.99
0:00:26
2048
Run time
h:mm:ss
0:00:40
0:23:22
0:11:29
NR
NR
NR
NR
CLoNe
RAM peak
GB
2.35
39.72
64.00
74.51
465.66
1862.65
7452.07
Disk space
GB
0.21
6.30
15.00
57.22
359.06
1430.51
5723.20
1
Bold entries denote a memory crash (jobs carrying more than 64 GB). The run time software took until
crashing and an estimate of the lowest RAM needed to run the job (and also the amount of HDD space
for CLoNe) is presented. NR means Not Ran Job.
As shown in Table 4.4, CLoNe has the highest RAM consumption, which only
permitted processing the small trajectories of 6 and 30 kF. This variant also uses substantial disk space resources if the similarity metric is not euclidean (RMSD in our case),
as the user must provide a text file with the pairwise similarity information. Although
CLoNe also has the slowest run time (about 30X slower than RCDPeaks for the 30
kF trajectory), this is not a critical aspect when dealing with the short trajectories it can
manage.
The cpptraj alternative is considerably less RAM consuming than CLoNe. The
memory peak for each analyzed trajectory roughly corresponds to the storage of a halfprecision float square matrix (pairwise RMSD information). For short and medium-sized
MD trajectories (see 100A kF in Table 4.4), cpptraj has an affordable memory cost.
However, if relatively long trajectories must be processed, the quadratic RAM complexity
of cpptraj becomes a major limitation. Regarding run time, cpptraj is also faster than
CLoNe but still about 3X slower than RCDPeaks. It is worth noting that developers
of cpptraj have marked their implementation as experimental. This software will produce
neither the calculated clusters’ core nor the boundary regions.
The fastest and the most memory-efficient software is RCDPeaks. The key factors
contributing to the speed up of this variant are the use of MDTraj 257 for computing the
optimal RMSD distances and, to a lesser extent, the sorting procedure to get ηi (see
Section 4.3.1). On the other hand, the RAM consumption of RCDPeaks is remarkably
low, mainly due to the small size of the main heap (see Section 4.3.1).
4.4 . MDSCAN: efficient RMSD-based HDBSCAN
We highlighted in Section 1.6.2.4 that we found no report of an HDBSCAN implementation specifically designed for handling molecular ensembles. Although a deeply
optimized and widely spread software exists for conducting HDBSCAN analysis using
several low-dimensional metrics (termed as HDBSCAN* by its authors), it excludes the
RMSD, a metric that remains the de facto choice in molecular similarity analyses. HDB-
4.4. MDSCAN: efficient RMSD-based HDBSCAN
85
SCAN* can receive a pre-processed RMSD float square matrix, but its explicitly fixed
double-precision float data type bounds the range of applications to tiny datasets.
Next, we propose MDSCAN, a fast and memory-efficient RMSD-based implementation of HDBSCAN that is suitable for processing big molecular datasets with no distance
matrix involved. MDSCAN, similar to HDBSCAN*, is an approximate approach to the
reference implementation 236 whose moderate deviations make a suitable compromise between the computational cost of the clustering job and the quality of returned clusters.
The encoding of molecular ensembles as a distinctive variant of vp-trees that join
leaves into buckets of elements or sub-datasets (decreasing the run times of RMSD
computation up to a half), and a double-heap approach to calculate a quasi-minimum
spanning tree of the MD trajectory’s complete graph (significantly decreasing the RAM
usage) are the significant methodological contributions of this work.
4.4.1 . Dual-heap construction of a quasi-MST
Although HDBSCAN can be helpful in multiple fields, we will focus on how simple
observations lead to substantial memory savings of optimal RMSD-based implementations for processing big datasets.
In Section 1.6.2.4, κ(i) was defined as the distance from i to its k th nearest neighbor.
Consequently, the k-neighborhood of i (denoted by η(i)) can be defined as the set of
nodes j for which d(i, j) ≤ κ(i). As a derivation of Equation 1.26, it can be stated that:
Any node j belonging to η(i) and having a core distance κ(j) ≤ κ(i), leads to a minimum
value of dmr (i, j) = κ(i) (Equation 4.1).
dmr (i, j) = {κ(i) | ∀j ∈ η(i) : κ(j) ≤ κ(i)}
(4.1)
This means that if we would like to construct an MST from T nodes, joining i to any
node j ∈ η(i) with κ(j) ≤ κ(i) would create a minimum weighted edge of that MST.
In the hypothetical case in which all nodes of T get connected as a tree following the
particular case in Equation 4.1, we would end up with an MST from which the final steps
of HDBSCAN may continue (see Section 1.6.2.4).
Although possible, the described scenario is unlikely to occur for a real dataset. The
principal assumption of MDSCAN is that it happens for most nodes, generating not an
MST but a Minimum Spanning Forest (MSF), a collection of disconnected minimum
spanning trees of T nodes. The number of MST inside the MSF equals the number of
nodes that could not find another node j satisfying Equation 4.1. For those disconnected
i, it is still possible to find a node j in one of the MST ∈ MSF whose dmr (i, j) though
not minimal, would be small enough.
Joining all disconnected nodes in the MSF without creating cycles gives a quasi-MST
(instead of an exact one). This quasi-MST could be used later to perform subsequent
steps of the original formulation of HDBSCAN. The capital importance of this workflow
to get a quasi-MST is that no similarity matrix must be stored in RAM.
Nodes i more likely to find a neighbor j satisfying Equation 4.1 are those with a high
value of κ(i). As MDSCAN continuously checks for Equation 4.1 to hold, we used a heap
86
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
data structure that retrieves the node with maximum κ(i) found so far in logarithmic
time. MDSCAN uses two heaps; the first (main heap) will contain some next-to-analyze
nodes, while an auxiliary heap involves already analyzed nodes failing Equation 4.1 that
will be re-processed after exhaustion of the main heap.
The algorithm starts by randomly choosing a not-analyzed node i from the dataset.
This will occur whenever the main heap is empty, so it is impossible to choose its first
element (highest core distance found so far). To retrieve the η(i) and κ(i) of every node,
MDSCAN queries the vantage tree data structure described in Section 1.5.4. Then, the
software searches nodes j ∈ η(i) having κ(j) ≤ κ(i). If such a node is found, a directed
edge from i to j is created, and its weight set as dmr (i, j) = κ(i).
During this process, all inspected j for which κ(j) ≥ κ(i) are transferred to the main
heap as a tuple containing κ(j), j index, and η(j). If the opposite situation happens, i.e.
a node j whose κ(j) ≤ κ(i) is not found in η(i), then a tuple containing κ(i) and i index
is passed to an auxiliary heap for future processing. The previous process goes on until
consideration of all nodes. At the end of this stage, an MSF is achieved. The deviation
from an exact MST will thus arise from the connection of nodes in the auxiliary heap.
The less populated this heap is, the smaller the deviation.
To join the remaining nodes at the auxiliary heap, MDSCAN runs the following steps
for each. First, the RMSDix vector, containing distances from i to all other nodes in
T , is calculated. Then, the dmr (i, j) is calculated for all nodes j that are not in the
same tree that i. The smallest value of these MRD is taken as the weight of a directed
connection from i to j. Once the quasi-MST is constructed, MDSCAN continues with
the building of a cluster hierarchy and the extraction of the most stable clusters just as it
was described in Section 1.6.2.4 (see Algorithm 4 and Figure 1.13).
4.4.2 . Performance benchmark of HDBSCAN variants
HDBSCAN* implementations were compared against MDSCAN in terms of run time
and memory consumption: (i) the HDBSCAN* ’s generic option using RMSD, (ii) the
HDBSCAN* ’s generic options using Euclidean distance, and (iii) the HDBSCAN*’s
Prim option using Euclidean metric. The Prim and generic labels of HDBSCAN* refer
to the approach followed for constructing the quasi-MST (see Annex 9.2.5). Note that
if the Prim algorithm is specified, it is impossible inHDBSCAN* to pass a similarity
matrix.
In Table 4.5 it is appreciated that MDSCAN is the fastest option in all cases except
for the smallest 6 kF dataset, where the effort of constructing a vpb -tree is significant
compared to the time taken by the computation of pairwise similarities. MDSCAN’s time
efficiency comes mainly from the accelerated RMSD computations offered by the MDTraj
suite and from our vpb -tree encoding. Indeed, results showed that while the quasi-MST’s
weight computed by MDSCAN with and without using vpb -tree is equivalent, the run
time decreases up to a half when the vp-tree encoding is exploited (see Annex 9.2.6).
4.4. MDSCAN: efficient RMSD-based HDBSCAN
87
Table 4.5: Run time and memory consumption of HDBSCAN* vs. MDSCAN on different
datasets.1
Traj. Name
6 kF
30 kF
50 kF
100A kF
250 kF
500 kF
1 MF
Traj. Size
(GB)
0.02
0.02
0.05
0.75
0.47
1.25
3.47
# Atoms
(selection) 2
217 (all)
64 (CA)
78 (no H)
660 (back)
160 (back)
217 (all)
304 (back)
MDSCAN
[RMSD]
Run time RAM peak
(hh:mm:ss)
(GB)
0:00:06
0.18
0:00:19
0.21
0:01:37
0.26
0:36:42
1.78
0:37:46
1.20
6:42:18
2.83
21:01:06
7.67
HDBSCAN*
[generic-RMSD]
Run time RAM peak
(hh:mm:ss)
(GB)
0:00:04
1.49
0:00:53
35.90
0:00:02
83.82
0:00:09
335.28
0:00:03
2103.87
0:00:08
8381.90
0:00:35
33534.32
HDBSCAN*
[generic-Euclidean]
Run time RAM peak
(hh:mm:ss)
(GB)
0:00:02
1.29
0:00:25
29.01
0:00:44
74.60
0:00:02
299.49
0:00:02
1863.54
0:00:03
7453.01
0:00:06
29809.12
HDBSCAN*
[Prim-Euclidean]
Run time RAM peak
(hh:mm:ss)
(GB)
0:00:30
0.15
0:02:14
0.18
0:04:28
0.26
2:31:14
2.58
5:52:37
1.64
21:00:04
4.41
72:00:00
14.23
1
Bold entries denote either a time crash (jobs taking more than 72 h) or a memory crash (jobs carrying
more than 64 GB). In memory crash cases, the run time it took until crashing and an estimate of the lowest
RAM needed to run the job is presented. 2 all: all atoms, CA: alpha carbon atoms, no H: non-hydrogen
atoms, back: backbone atoms.
While the generic implementations of HDBSCAN* (RMSD and Euclidean-based)
have run times comparable to MDSCAN (Table 4.5), their high RAM consumption only
permitted them to process the two smallest datasets. HDBSCAN* ’s generic implementations are fast primarily because they use a single-linkage approach to get a tree and do
not provide an exact MST.
The HDBSCAN* ’s Prim-Euclidean alternative could analyze all datasets (except
the 1 MF job that was stopped after running for 72h) but taking up to nine more times
than MDSCAN (see Traj.250 kF in Table 4.5). This option neither constructs an exact
MST from the input data, though a less simplistic approach than a single-linkage is
followed to construct a tree (see Annex 9.2.5).
Regarding the RAM management, the only efficient alternatives are MDSCAN and
HDBSCAN* ’s Prim-Euclidean, which does not employ square pairwise similarity matrices to derive the required tree. They both have a similar consumption for the smallest
datasets (from 6 to 50 kF, Table 4.5), with MDSCAN displaying the best behavior for
the longest cases (from 100A kF to 1 MF, Table 4.5).
Within MDSCAN, the RAM is consumed mainly by the dataset file. One copy of
this object is needed to instantiate the vpb -tree data structure and to make the similarity
recalculations to complete the final quasi-MST. Another copy is created when producing
the vantage tree’s buckets. As it is shown in Annex 9.2.6, using MDSCAN without a vpb tree encoding is more memory-friendly (as the second copy never gets created). However,
we are persuaded that this small memory trade-off is justified given the speed reached
with the vp-based alternative.
The generic-RMSD and generic-Euclidean options of HDBSCAN* carry the highest
memory consumption because, besides the input, these implementations produce another
four double-precision float matrices living simultaneously on memory. The estimated
RAM consumption of these five objects (Equation 4.2) is reported in Table 4.5 for those
datasets that produced a memory crash.
(M ∗ m1 + 4m2 ) ∗ N
(4.2)
230
In Equation 4.2, m1 is the size of the float data type employed in the input matrix
(m1 = 4), m2 is the size of the float data type employed internally by HDBSCAN*
VRAM =
88
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
(m2 = 8), N denotes the number of conformations in the dataset, and M represents
the number of columns in the input matrix (M = N for the generic-RMSD, while
M = 3 ∗ number_of _atoms in the generic-Euclidean variant).
4.4.3 . Equivalence between MDSCAN and HDBSCAN* alternatives
As stated before, the HDBSCAN clustering alternatives analyzed in this work are
expected to produce distinct partitions for each dataset, mainly because the algorithm
for the MST construction drastically varies among them. However, it is worth assessing
the impact of this methodological divergence on the outcome clusters produced by each
variant.
The upper triangle of each matrix in Table 4.6 shows the global ARI between the
MDSCAN (A), the generic RMSD-based HDBSCAN* (B), the generic Euclidean-based
HDBSCAN* (C), and the Prim Euclidean-based HDBSCAN* (D) implementations.
As envisioned, the global similarity of clusterings is far from 1.00 in every case. However,
there is an appreciable resemblance in clusterings produced by generic implementations
of HDBSCAN* using RMSD or Euclidean metric in the 6 and 30 kF datasets. In
the particular case of the 30 kF dataset, all clusterings coming from HDBSCAN* are
correlated but not analogous to MDSCAN outcomes. For datasets bigger than 30 kF,
only MDSCAN and Euclidean-based HDBSCAN* produced results, and they were also
divergent.
Table 4.6: Adjusted Rand Index (ARI) of clustering outputs obtained with different HDBSCAN implementations for each analyzed dataset. The upper triangle of each matrix corresponds to the global ARI, while in the lower triangle, only the ARI of those clusters whose
population is higher than 1% of the dataset size is depicted.1
A
B
C
D
A
1.00
0.74
0.74
0.74
A
B
C
D
A
1.00
—
—
0.80
6 kF
B
C
0.34 0.35
1.00 0.66
1.00 1.00
0.99 0.99
100A kF
B
C
—
—
1.00
—
—
1.00
—
—
D
0.34
0.32
0.38
1.00
A
1.00
0.34
0.46
0.50
D
-0.02
—
—
1.00
A
1.00
—
—
-4.8
30 kF
B
C
0.24 0.44
1.00 0.61
0.49 1.00
0.55 0.76
250 kF
B
C
—
—
1.00
—
—
1.00
—
—
D
0.48
0.64
0.76
1.00
A
1.00
—
—
0.00
D
-3.66
—
—
1.00
A
1.00
—
—
1.00
50 kF
B
C
—
—
1.00
—
—
1.00
—
—
500 kF
B
C
—
—
1.00
—
—
1.00
—
—
D
0.00
—
—
1.00
D
-27.61
—
—
1.00
1
Each different HDBSCAN variant is represented by a letter: A-) MDSCAN, B-) the generic RMSD-based
HDBSCAN*, C-) the generic Euclidean-based HDBSCAN*, and D-) the Prim Euclidean-based HDBSCAN*.
When clustering MD simulations, users are often more interested in the representative, more significant clusters found in datasets. The lower triangle of each matrix in
Table 4.6 shows the pairwise ARI of previous clusterings when considering only clusters
whose population is higher than 1% of the corresponding dataset size. The ARI between
MDSCAN and the other alternatives doubles 6 kF. For this dataset, the most populated
4.5. Spatial complexity of proposed algorithms
89
clusters reported by all software are similar (clusterings from all variants of HDBSCAN*
are equivalent). This fortuitous agreement is dataset-dependent, as appreciated in the 30
kF case for which no such prominent improvement of the clustering analogy is attained.
While the ARI can globally inform on partitions similarity, it yields no clues on the
equivalence of individual clusters fetched by every software. In Annex 9.2.7, we present
the quantitative equivalence between representative clusters (those whose population is
higher than 1% of their corresponding trajectory size) detected in trajectories 6 (Table
9.8) and 30 kF (Table 9.9) with MDSCAN (A) and the HDBSCAN* variants; generic
RMSD-based (B), generic Euclidean-based (C), and Prim RMSD-based (D).
As a general trend, clusters from all implementations are interconnected. MDSCAN often produces smaller groups of frames with the advantage of them having a
higher collective similarity (shorter average diameter). The smaller size of some clusters
produced by MDSCAN (together with the fact that they are tighter than those seized
with Euclidean-based options of HDBSCAN*) is a direct consequence of the pairwise
superposition followed when using the RMSD metric. Having tight clusters is the desired
behavior when clustering MD as more related frames get included in the same group, facilitating the visual analysis or quantitative averages calculated from clustered structures.
4.5 . Spatial complexity of proposed algorithms
Our motivation for enhancing widely used or promising clustering algorithms in the
molecular simulation domain is primarily driven by the bottleneck created by their quadratic
spatial complexity. Accordingly, this section provides a succinct overview of our proposed
methods’ performance in this context. It is crucial to underscore that while reducing the
time complexity of these procedures or their equivalents is undeniably significant, this was
not the objective pursued in the current study. Consequently, an in-depth assessment,
despite our implementations’ often-accelerated performance, lies beyond this manuscript’s
scope.
QTPy (refer to Section 4.1.1) was only suggested as a proof of concept to highlight
the inaccuracies of other clustering alternatives that flawlessly claim to perform QT. It
does not constitute a proper optimization, and its spatial complexity is O(n2 ). Nonetheless, we employed half-precision float values to represent RMSD, thereby enabling the
QTPy similarity matrix to consume half the space required by alternatives that utilize
similarity matrices of single-precision floats, such as the gromos option of GROMACS.
BitQT (see Section 4.1) and BitClust (refer to Section 4.2) adopt the same approach to shorten the memory requirements of the Daura and QT algorithms by encoding
RMSD pairwise distances as bits. Therefore, despite their quadratic spatial complexity,
they can process considerably larger trajectories than existing implementations. Given the
inherent sparsity across its columns, compressing the binary matrix could feasibly yield
sub-quadratic performance for most real-world scenarios. However, at the time of implementation, the bitarray library used for binary encoding did not possess this capability.
The DP+ algorithm represents an attempt to alleviate the quadratic spatial com-
90
4. REINVENTING THE WHEEL OF MOLECULAR CLUSTERING
plexity intrinsic to Density Peaks (DP) approaches. Instead of constructing a complete
matrix, our method operates on transient vectors of size N (where N is the number of
frames) and two heaps that may expand memory usage. The secondary heap comprises
tuples (i, ρ), representing the frame’s index and density value. In the worst-case scenario,
this heap expands to N entries with a spatial complexity of N · (O(1) + O(1)) ≡ O(N ),
thereby demonstrating linear scaling with trajectory length. The primary heap includes
the above-mentioned elements and a smaller subset ηi of size 0.02 · N . If we treat this
as a constant factor c, even if the main heap reaches its maximum size of N tuples, the
complexity remains N · (O(1) + O(1) + O(c)) ≡ O(cN ), still linear. It is worth noting
that such extreme scenarios are unlikely with prudent parameter selection.
MDSCAN’s primary objective was to mitigate the quadratic complexity of available
HDBSCAN* alternatives when utilizing high-dimensional metrics like the RMSD. Strikingly similar to DP+, MDSCAN employs the same heap data structures and transient
vectors already detailed. The sole distinction is in the type of information these heaps
contain; hence, the worst-case spatial complexity analysis presented for DP applies to
MDSCAN. However, MDSCAN processes the trajectory file differently from all other software proposed here, as a vantage point tree is constructed, necessitating a copy of the
trajectory. This processing does not increase the algorithm’s spatial complexity, although
it requires more space compared to DP.
5 - NUCLEAR: AN EFFICIENT ASSEMBLER
FOR THE FBDD OF CMOs
As we stated in this document’s introductory Chapter , our main goal is the in silico
fragment-based design of oligonucleotides showing selective affinity for their intended
target. After we assessed the reliable docking and screening powers of the MCSS scoring
function in Chapter 3, the next natural stage of the design is to link the most promising
fragments into oligonucleotide chains.
Although several tools for linking fragments are available in the literature, none is
suitable to be included in our approach mainly due to the following reasons: (i) they
cannot work with the file formats coming from MCSS and CHARMM software (PSF,
DCD), (ii) they are not designed to link oligonucleotides from C5’ to O3’ guaranteeing
clash-free solutions, and most important (iii) they are unable to process high volumes of
data.
In this Chapter, we present a novel software called NUCLEotide AssembleR (NUCLEAR), addressing the above limitations. NUCLEAR can perform different kinds
of oligonucleotide searches and retrieve hotspots in the receptor from the distributions of
docked fragments.
Section 5.1 succinctly presents the workflows available in NUCLEAR. Next, Section
5.2 details the protocol for searching hotspots at the receptor’s surface. In Section 5.3
the sequence- and spatial-constrained searches of oligonucleotides are described. Finally,
Section 5.4 is devoted to the reproduction of four crystal structures using NUCLEAR,
to discuss the computational cost of the algorithm’s main steps, and to delve into its
limitations.
5.1 . NUCLEAR overview
In a NUCLEAR single job, users can request one of two exclusive explorations (as
depicted in Figure 5.1): either a molecular hotspots search (to gain insights into the most
accessible regions of the receptor) or an oligonucleotide search. In the latter case, the
oligo-nucleotide sequence and the receptor region to consider can also be specified.
There are two common steps for hotspots and oligonucleotide search; (i) the parsing
of the main configuration file and (ii) the processing of MCSS docking distributions.
In the former, the specification of all parameters (visit https://rglez.github.io/
nuclear_docs/ for the complete list) occurs through a user-customized configuration
file. NUCLEAR parses this file and checks that all keys have reasonable values specified
(e.g., the minimum length of requested sequences must be an integer greater than 1).
Some essential options to specify in this file are the size range of sequences to search, the
number of best-scored solutions to output, and the possibility to cluster the input docking
distributions (in terms of RMSD similarity). Besides, the inter-related parameters are
92
5. NUCLEAR: AN EFFICIENT ASSEMBLER FOR THE FBDD OF CMOs
Parse
config file
by sequence
unconstrained
search
Process
MCSS dockings
Search
Hotspots
Search
oligonucleotides
by region
constrained
search
global
search
local
search
Minimization
Figure 5.1: Diagram of NUCLEAR workflows. Users may request one of two exclusive
explorations in a single job: (i) a molecular hotspots search or (ii) an oligonucleotide
search (in which case the oligonucleotide sequence and the receptor region to consider
can also be specified).
checked for consistency (e.g., if clustering is not requested, no distance cutoff should be
specified).
On the other hand, (ii) consists mainly of parsing and clustering MCSS docking
distributions, which may involve many poses exhibiting some geometrical redundancy
(see Section 3.2). NUCLEAR offers two ways for reducing the number of input poses
to process: by filtering them according to their number of contacts with the protein
(poses with fewer contacts than a user-specified cutoff are discarded) and by performing
a BitClust-inspired clustering step (see Section 2.1.4). Both alternatives are optional and
can be used together. Note that these reductions occur independently for each distribution
(every single CRD file out of the several specified is independently reduced). The similarity
metric employed between poses is their pairwise RMSD (discarding hydrogen atoms).
Once the MCSS distributions have been parsed and eventually reduced through the
number of contacts filter or by the clustering procedure, all remaining poses (coming from
each considered CRD distribution) are concatenated. Hence, they yield the NUCLEAR
search space, which can be used to search hotspots or oligonucleotide sequences.
5.2 . Search of hotspots
Detecting protein hotspots is a usual step of FBDD workflows. Though several
definitions exist, a hotspot is associated with either of two complementary concepts; (i)
a residue or cluster of residues contributing majorly to the binding free energy, or (ii)
a site on a target protein having a high propensity for ligand binding 210 . NUCLEAR
can detect hotspots following the latter interpretation, aiding to discriminate the most
favorable sites where considered fragments could bind and subsequently be joined to make
an oligonucleotide.
Figure 5.2 shows the main steps to perform the NUCLEAR’s hotspots search. Each
5.2. Search of hotspots
93
MCSS exploration comes in a CRD file from which every replica (coordinates, names, and
scoring) is extracted and their Cartesian coordinates saved as a kd-tree data structure.
The Cartesian coordinates of the protein are also kept as a kd-tree. The fingerprints are
then computed for each replica in each MCSS exploration provided. In this context,
a fingerprint is the contact between a particular replica and the protein. NUCLEAR
considers as a contact, the protein’s first atom under a cutoff distance from a ligand
atom. Note that fingerprints can be expressed at least with two resolutions: high-res
(or atomic-res): where the residue and the particular atom involved in the contact are
indicated, and low-res (or residue-res): where only the residue involved in the interaction
is indicated.
Figure 5.2: Workflow for the hotspots identification in a receptor protein using NUCLEAR.
NUCLEAR uses low-res fingerprints to locate and cluster the interacting regions
of the protein (see Figure 5.3A-B). The rationale behind this clustering approach is that
more extensive contact zones can represent many smaller ones (Figure 5.3B-C), and the
most populated clusters will inform on suitable binding sites.
The clustering of fingerprints occurs as follows: (i) all fingerprints are sorted by increasing order of their size (from biggest to smallest) (Figure 5.3E), (ii) the most extensive
fingerprint is taken as the seed of a cluster in which all other fingerprints that are proper
subsets of the seed will be grouped (Figure 5.3F), (iii) clustered fingerprints are removed
from consideration, and (iv) the process restarts from (ii) until no more fingerprints are
available for clustering.
Once we have obtained the subset clusters, they can be filtered by size. However,
the size of the clusters is not normalized by the number of residues it contains. To
leverage this situation, NUCLEAR employs a cluster’s normalized ([0, 1]) density as a
population criterion to select the most representative. The density of a particular cluster
is calculated as the number of replicas it contains divided by the count of unique residues.
These numbers are normalized, and users can effectively discern the most representative
clusters in size through a density cutoff parameter.
Each subset cluster already described has an associated seed that "represents" all
other smaller fingerprints in the same cluster. As these seeds correspond to a protein
region, they may overlap, giving rise to the potential need to merge similar areas. This
merging of clusters happens in NUCLEAR right after the density filter step and will
use the Tanimoto Index (TI) between seeds to decide if two clusters should be joined.
The process always merges worst-ranked clusters with the best-ranked ones if their TI is
below the user-specified threshold.
94
5. NUCLEAR: AN EFFICIENT ASSEMBLER FOR THE FBDD OF CMOs
Figure 5.3: Hotspots search using NUCLEAR’s low-res fingerprints. A: An example of lowres contacts between a replica and a protein. Unique residues are colored in red, and a
colon separates them). B: Five low-res fingerprints (represented as sets of residue numbers). C: Overlap of the fingerprints in B. D: An schematic representation of several fingerprints before clustering. E: Fingerprints are sorted by increasing order of their size. F:
Clusters of fingerprints. Each color denotes a cluster whose seed is the biggest fingerprint
not previously clustered and whose members are all fingerprints that are proper subsets
of the seed. G: Classification of clusters (spots) depending on their best-ranked replica
score and their population
NUCLEAR reports as spots, every cluster generated from the procedure described
above. Depending on the best-ranked replica score contained in a cluster and each cluster’s
population, a qualitative classification of spots can be made into four categories (see Figure
5.3G): (i) hotspots (clusters with high population and with a low-ranked replica), (ii)
warm spots (clusters with high-ranked replicas but highly populated), (iii) specific spots
(clusters with a low-ranked replica and low population), and (iv) noise (small clusters with
high-ranked replicas).
5.3 . Search of oligonucleotides
When the attention goes to searching oligonucleotide sequences, NUCLEAR’s primary goal is simple: to find all geometrically suitable arrangements by joining reachable
poses. Two poses i, j are considered reachable if the distance between the C5’ atom of i
and the O3’ atom of j is under a distance cutoff and other atoms do not produce steric
clashes. NUCLEAR stores this information in a non-symmetric binary matrix R, the
reachability matrix (see Figure 5.4A), whose length equals the number of poses in the
search space. In R, each position Rij = 1 if atoms C5’ of i and O3’ of j are under a
cutoff distance and no pair of ij heavy atoms produce clashes (Rij = 0 otherwise). A
directed graph G, the reachability graph, can be pictured from matrix R (See Figure 5.4D).
The sequence search followed by NUCLEAR comprises retrieving all simple paths
found in G (iteratively starting with each node as the source of the paths) following a
Depth-First Search (DFS) strategy. However, this DFS is constrained because, in the
expansion of a particular source, produced paths must not contain nodes having steric
clashes, in which case the entire branch under expansion gets pruned. While reachable
nodes in G will not produce clashes, there is no way to assert this for two non-adjacent
Figure 5.4: Graph view of the NUCLEAR sequence search procedure. A: Reachability matrix. B: Clash matrix. C: Score of nodes. D: Reachability graph.
E: Example of sequence search starting from node 9.
5.3. Search of oligonucleotides
95
ones. That is why NUCLEAR stores another symmetrical binary matrix C, the clash
matrix (see 5.4B) of the same length that R. In C, each position Cij = 1 if there is at
least one clash between heavy atoms of poses i and j (Cij = 0 otherwise).
The example in Figure 5.4E starts from node 9, which can be expanded to node 2 or
3. NUCLEAR always starts expansions with the lowest index, so sequence 9-2 is created
in a second step. Following this behavior, the sequence 9-2-3 is created. NUCLEAR
can expand node 3 to nodes 4, 5, or 6. However, adding nodes 4 or 6 would produce
clashes in the growing sequence (with 2 and 9, respectively), so the only possibility is
that 9-2-3-5 gets created. As the only expansion of node 5 (4) would produce clashes,
the branch expansion stops, and NUCLEAR backtracks to the next feasible branch, in
this case, 9-2-7. As neither node 2 nor 7 has expansion choices, NUCLEAR backtracks
again to node 9, producing 9-3, 9-3-4, and 9-3-5.
Although in Figure 5.4E, we have illustrated the sequence search process in terms of
intuitive operations, NUCLEAR implements the most important steps as binary operations, profiting from the binary encoding displayed by R and C matrices. For instance,
clashes are recorded by an OR operation of the bit vectors in C that corresponds to the
current sequence’s nodes. Similarly, the constrained DFS is conducted by pushing to and
popping from a stack of bit-vectors calculated through a consecutive XOR/AND operation
that removes the clashes from the currently expanded sequence.
To have an exhaustive exploration, the described DFS must be repeated, starting
from all nodes in G that are not leaves and saving all paths with two or more nodes.
However, the number of retrieved paths quickly explodes even for small search spaces.
Considering that only the subset of better-ranked sequences is of interest at the end
of the search, NUCLEAR proposes a pruning strategy that considerably reduces the
computational cost of the described approach.
Concretely, a fixed-size heap data structure is used to store generated sequences.
Using a heap, it is possible to quickly retrieve the worst-scored sequence generated so far
and use that scoring value to stop the expansion of paths leading to a worse score, as these
paths will never be selected in the output top-N. Another advantage of this approach is
that not all sequences get written to the disk (a considerable bottleneck when millions of
solutions are available), but only the top-N better-scored ones.
NUCLEAR can localize the search for oligonucleotides in a particular receptor region
if a valid atomic selection is provided in the configuration file. This local search causes
only fingerprints intersecting the selected residues get considered (see local search in Figure 5.1). Equally appealing is the NUCLEAR ability to specify oligonucleotide sequence
constraints to the search (see constrained search in Figure 5.1). Both options significantly help to reduce the computational cost of the DFS procedure in knowledge-guided
explorations.
Once the top-N best-scored sequences have been written to disk as PDB files, NUCLEAR generates a CHARMM minimization script for each one. In the declared
minimization process, both the receptor and ligands can move. Slight deviations in the
pre and post-minimization oligonucleotide may appear because of the phosphodiester links
96
5. NUCLEAR: AN EFFICIENT ASSEMBLER FOR THE FBDD OF CMOs
reorganization.
5.4 . Case studies
5.4.1 . Evaluated parameters
As stated, NUCLEAR’s primary goal is the fragment-based design of oligonucleotides exhibiting an affinity for a particular therapeutic target (usually a protein). In
line with this general objective, only fragments in contact with the receptor are considered
in the different available searches. Although this peculiarity does not entirely prevent the
tool from reproducing experimental ssRNA-protein complexes, only cases where contacts
between crystallized ligands and the receptor exist would be suitable for reproduction. The
success of these in-silico reproductions is then greatly conditioned by the ability of the
docking software (MCSS in our case) to capture native-like conformations of the fragments involved, as discussed in Section 3.3.
With the previous limitation in mind, the NUCLEAR ability to detect experimental binding modes of oligonucleotides crystallized within a protein was evaluated through
four high-resolution complexes involving Ribonucleic Acid Binding Proteins (RBPs) belonging to the three families most represented in humans 268 : (i) the RNA recognition
motif (RRM) of the protein Nab3 bound to its UCUU recognition sequence (PDB ID:
2XNR) 269 , (ii) a group of three CCCH zinc finger (Zn-Fs) domains of the Unkempt protein linked to a UUAUU chain (PDB ID: 5ELH) 270 , (iii) the KH2 domain of the MEX-3C
protein linked to a CAGAGCU chain (PDB ID: 5WWX) 271 , and (iv) the poly(A)-binding
protein in complex with an AAAAAAAA chain (PDB ID: 1CVJ) 272 .
For the three first cases, only three successive nucleotides in the RNA sequence are
directly involved in specific recognition, so only these triplets were kept to define the
RNA chains used as reference (UCU for 2XNR, UUA for 5ELH, and AGA for 5WWX).
Note that the discarded nucleotides either show ambiguous electron density or make little
or no contact with the domain of the asymmetric unit.
When designing inhibitors against a receptor protein, it is common practice to restrict
the search space of docking simulations to regions encompassing the known binding site.
We denoted as “global searches” those performed using all replicas present in this relatively
ambiguous (17 Å3 ) and not restricted to specific residues region of the protein. A more
constrained but still valid approach would be to limit the oligonucleotide search space
(not the docking region) to replicas involved in interactions with (or close to) the protein
residues interacting with ligands in experimental structures. These latter kinds of jobs are
referred to as “local searches”.
As detailed in Section 5.3, NUCLEAR uses a fixed-size heap to keep only the
most energetically favored oligonucleotides out of the potentially millions of generated
solutions. This strategy guarantees that only a relevant subset of chains is retained to
save on disk and minimize subsequently. However, there is no robust way to estimate
the energy that retrieved oligonucleotides would have after minimization. NUCLEAR
uses the pre-scoring to decide which chains will be included in the heap. This pre-scoring
5.4. Case studies
97
can be calculated in several ways, but we evaluated it as the arithmetic or the geometric
mean of the MCSS score of replicas composing the oligonucleotide chains. In theory, the
geometric mean would account for an inherent weighting of significantly different scored
replicas appearing in the same oligonucleotide.
One of the most neuralgic points of NUCLEAR is the combinatorial explosion that
quickly occurs as the number of replicas to analyze increases. So a pre-clustering step
(described in Section 2.1.4) can be set to reduce the number of MCSS poses for each
fragment (as exemplified in Section 5.1). We evaluated the effect of no clustering and
using 1 or 2 Å as RMSD cutoff for clustering MCSS docking distributions previous to
NUCLEAR searches.
The last parameter we varied in the present case studies was the maximum distance
from C5’ to O3’ of contiguous nucleotides to be considered linkable. This parameter
strongly impacts the number of chains NUCLEAR can mark as valid. The larger the
distance, the less restrictive the search becomes, as more continuous nucleotides would be
considered linkable. The distance to consider a clash between ligand and protein atoms
was fixed to 1.5 Å .
From now on, we will use the XYij notation when referring to NUCLEAR explorations conducted with the parameters detailed so far. Under this nomenclature, X refers
to the exploration’s extension and can be either G or L for a global or a local search,
respectively. Y denotes the kind of pre-scoring employed by NUCLEAR and can be A
(arithmetic) or G (geometric). The RMSD clustering cutoff i can take values of 0 (no
clustering), 1, and 2 Å, while j being the d(C5’-O3’) takes values of 3, 4, 5, or 6 Å. We will
denote as equivalent searches those with the same ij and a pertinent combination of XY;
GAij/GGij and LAij/LGij (where the effect of arithmetic vs. geometric pre-scoring can be
assessed) or GAij/LAij and GGij/LGij (where the effect of global vs. local search space
can be assessed). Note that each XYij exploration produces a distribution of linkable
oligo-nucleotide candidates from which only the top 5000 best-scored (heap size) were
minimized.
5.4.2 . Trends in reproducing experimental binding modes
In each individual protein, the initial number of mono-nucleotides (#mono in Tables
5.1-5.3) is identical for equivalent searches because this magnitude gets computed after
clustering but before selecting the region to consider. Evidently, #mono suffers a considerable reduction if a clustering step is conducted. The higher the RMSD cutoff, the
more considerable this reduction becomes (up to 70, 67, and 73% for 2XNR, 5WWX, and
5ELH respectively when passing from no clustering to a 2 Å cutoff clustering).
As an expected trend, for a particular combination of XY (M ethod in Tables 5.15.3), increasing the maximum allowed linkable distance from C5’ to O3’ (d(C5′ − O3′ ) in
Tables 5.1-5.3), the number of oligo-nucleotides that NUCLEAR outputs also increases
in two or three orders of magnitude in the explored range of 3-6 Å, reaching more than 34,
98, and 25 million of solutions for 2XNR, 5WWX, and 5ELH respectively in the searches
where d(C5’-O3’) was set to 6 Å and no clustering was performed.
The effect of conducting a local vs. global search in the number of oligo-nucleotides
LG
LA
GG
GA
Method
2
1
0
2
1
0
2
1
0
2
1
0
RMSD [Å]
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
d(C5’-O3’) [Å]
2696
5552
9075
2696
5552
9075
2696
5552
9075
2696
5552
9075
#mono
15694
677268
6492116
34213514
3849
164885
1595613
8447693
338
17638
176381
953535
15694
677268
6492116
34213514
3849
164885
1595613
8447693
338
17638
176381
953535
15694
677268
6492116
34213514
3849
164885
1595613
8447693
338
17638
176381
953535
15694
677268
6492116
34213514
3849
164885
1595613
8447693
338
17638
176381
953535
#oligo
-45.90
-50.33
-57.23
-59.90
-44.95
-50.38
-54.16
-54.16
-44.87
-46.76
-54.16
-54.16
-45.90
-50.33
-57.23
-57.28
-44.95
-50.38
-54.16
-54.16
-45.90
-46.76
-54.16
-54.16
-45.90
-50.33
-57.23
-59.90
-44.95
-50.38
-54.16
-59.90
-44.87
-46.76
-54.16
-54.16
-49.90
-50.33
-57.23
-57.28
-44.95
-50.38
-54.16
-54.16
-44.87
-46.76
-54.16
-54.16
min E [kcal/mol]
235
541
58
168
4
11
255
495
53
166
4
12
235
541
58
168
4
11
255
495
53
166
4
12
#native
E [kcal/mol]
-47.35
-48.51
-48.99
-48.05
-42.08
-48.38
-48.99
-48.51
-48.99
-48.99
-42.08
-48.38
-47.35
-48.51
-48.99
-48.51
-42.08
-48.38
-48.99
-48.51
-48.99
-48.99
-42.08
-48.38
native-like most similar
RMSD [Å] pre-Rank post-Rank
1.05
578
644
0.93
4071
571
1.00
973
46
1.06
4419
234
1.73
97
145
1.18
4903
21
1.00
3193
304
0.93
4237
599
1.00
486
43
1.00
3643
129
1.73
54
138
1.18
2863
22
1.05
578
644
0.93
4071
571
1.00
973
46
0.93
4071
571
1.73
97
145
1.18
4903
21
1.00
3193
304
0.93
4237
599
1.00
486
43
1.00
3643
129
1.73
54
138
1.18
2863
22
dRMSD [Å]
1.86
1.84
2.58
1.80
1.93
2.02
2.58
1.84
2.58
2.58
1.93
2.02
1.86
1.84
2.58
1.84
1.93
2.02
2.58
1.84
2.58
2.58
1.93
2.02
E [kcal/mol]
-51.47
-53.06
-50.55
-51.68
-45.28
-48.89
-51.47
-53.06
-50.55
-51.68
-45.28
-48.89
-51.47
-53.06
-50.55
-53.06
-45.28
-48.89
-51.47
-53.06
-50.55
-51.68
-45.28
-48.89
native-like best ranked
RMSD [Å] pre-Rank post-Rank
1.40
1335
95
1.43
778
53
1.75
5
24
1.61
1388
23
1.98
72
41
1.35
1122
15
1.40
699
96
1.43
872
54
1.75
8
22
1.61
1201
23
1.98
40
40
1.35
832
15
1.40
1335
95
1.43
778
53
1.75
5
24
1.43
778
53
1.98
72
41
1.35
1122
15
1.40
699
96
1.43
872
54
1.75
8
22
1.61
1201
23
1.98
40
40
1.35
832
15
Table 5.1: NUCLEAR explorations to retrieve native-like structures for the 2XNR protein.
dRMSD [Å]
1.68
1.40
1.98
1.84
1.40
1.50
1.68
1.40
1.98
1.84
1.40
1.50
1.68
1.40
1.98
1.40
1.40
1.50
1.68
1.40
1.98
1.84
1.40
1.50
GG
GA
BG
BA
Method
2
1
0
2
1
0
2
1
0
2
1
0
RMSD [Å]
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
d(C5’-O3’) [Å]
7494
14664
22818
7494
14664
22818
7494
14664
22818
7494
14664
22818
#mono
37619
1658706
17435561
98355759
9001
412382
4337966
24619477
1130
50568
537549
3068691
37619
1658706
17435561
98355759
9001
412382
4337966
24619477
1130
50568
537549
3068691
35521
1564586
16313232
91164053
8267
382221
3999686
22544353
1044
46327
491288
2783304
35521
1564586
16313232
91164053
8267
382221
3999686
22544353
1044
46327
491288
2783304
#oligo
-68.95
-68.95
-70.85
-70.90
-67.86
-68.40
-70.14
-69.65
-58.84
-64.05
-68.63
-69.65
-68.95
-68.95
-70.85
-70.90
-67.86
-68.40
-70.14
-73.53
-58.84
-64.05
-68.63
-69.65
-68.95
-68.95
-70.85
-70.90
-67.86
-68.40
-70.14
-69.65
-58.84
-64.05
-68.63
-69.65
-68.95
-68.95
-70.85
-70.90
-67.86
-68.40
-70.14
-73.53
-58.84
-64.05
-68.63
-69.65
min E [kcal/mol]
4
7
2
1
7
7
2
1
4
7
2
1
7
7
2
1
#native
E [kcal/mol]
-61.81
-60.82
-61.73
-61.73
-61.81
-60.82
-61.73
-61.73
-61.81
-60.82
-61.73
-61.73
-61.81
-60.82
-61.73
-61.73
native-like most similar
RMSD [Å] pre-Rank post-Rank
1.06
994
827
1.06
3370
611
1.96
1920
481
1.96
675
149
1.06
923
1004
1.06
3075
620
1.96
2184
534
1.96
737
152
1.06
989
831
1.06
3310
616
1.96
1893
486
1.96
659
149
1.06
922
1005
1.06
3044
624
1.96
2167
538
1.96
726
153
dRMSD [Å]
1.23
2.22
1.40
1.40
1.23
2.22
1.40
1.40
1.23
2.22
1.40
1.40
1.23
2.22
1.40
1.40
E [kcal/mol]
-64.95
-64.22
-64.19
-61.73
-64.95
-64.22
-64.19
-61.73
-64.95
-64.22
-64.19
-61.73
-64.95
-64.22
-64.19
-61.73
native-like best ranked
RMSD [Å] pre-Rank post-Rank
1.89
2827
256
1.35
3635
122
1.97
2437
161
1.96
675
149
1.89
2728
296
1.35
3222
122
1.97
1711
182
1.96
737
152
1.89
2810
257
1.35
3572
122
1.97
2407
162
1.96
659
149
1.89
2721
296
1.35
3191
122
1.97
1697
185
1.96
726
153
Table 5.2: NUCLEAR explorations to retrieve native-like structures for the 5WWX protein.
dRMSD [Å]
2.17
1.91
2.50
1.40
2.17
1.91
2.50
1.40
2.17
1.91
2.50
1.40
2.17
1.91
2.50
1.40
LG
LA
GG
GA
Method
2
1
0
2
1
0
2
1
0
2
1
0
RMSD [Å]
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
d(C5’-O3’) [Å]
2262
4881
8473
2262
4881
8473
2262
4881
8473
2262
4881
8473
#mono
14965
562254
5008076
25863579
3037
114771
1056292
5508112
245
11335
110845
596755
14965
562254
5008076
25863579
3037
114771
1056292
5508112
245
11335
110845
596755
14710
540879
4766315
24379553
2934
107945
981253
5074824
222
10052
95757
513748
14710
540879
4766315
24379553
2934
107945
981253
5074824
222
10052
95757
513748
#oligo
-60.40
-71.13
-71.75
-70.04
-58.29
-69.63
-72.88
-74.19
-53.98
-59.20
-72.88
-74.19
-60.40
-71.76
-71.75
-70.04
-58.29
-69.63
-72.88
-74.19
-53.98
-59.20
-72.88
-74.19
-60.4
-71.13
-71.75
-70.04
-58.29
-69.63
-72.88
-74.19
-53.98
-59.20
-72.88
-74.19
-60.40
-71.76
-71.75
-70.04
-58.29
-69.63
-72.88
-74.19
-53.98
-59.20
-72.88
-74.19
min E [kcal/mol]
7
1
7
1
8
1
7
1
-
#native
E [kcal/mol]
-55.85
-51.42
-55.85
-51.42
-55.85
-51.42
-55.85
-51.42
-
native-like most similar
RMSD [Å] pre-Rank post-Rank
1.46
877
490
1.82
2107
1133
1.46
3930
522
1.82
3630
1223
1.46
864
486
1.82
2077
1109
1.46
3890
517
1.82
3566
1201
dRMSD [Å]
1.30
1.37
1.30
1.37
1.30
1.37
1.30
1.37
-
E [kcal/mol]
-61.64
-51.42
-61.64
-51.42
-61.64
-51.42
-61.64
-51.42
-
native-like best ranked
RMSD [Å] pre-Rank post-Rank
1.71
138
63
1.82
2107
1133
1.71
1026
76
1.82
3630
1223
1.71
138
64
1.82
2077
1109
1.71
1018
77
1.82
3566
1201
-
Table 5.3: NUCLEAR explorations to retrieve native-like structures for the 5ELH protein.
dRMSD [Å]
1.29
1.37
1.29
1.37
1.29
1.37
1.29
1.37
-
98
5. NUCLEAR: AN EFFICIENT ASSEMBLER FOR THE FBDD OF CMOs
found by NUCLEAR (#oligo in Tables 5.1-5.3) pass from null in the 2XNR case (where
equivalent searches gives the same number of solutions) to modest in 5WWX and 5ELH
where local searches produce on average 7.5% and 7.4% less solutions than global ones,
respectively.
As a global behavior, the minimum energy (min E in Tables 5.1-5.3) of minimized
oligo-nucleotides slightly decreases (or stays constant) with the increase of d(C5’-O3’) for
a given value of RMSD cutoff, meaning that bigger search spaces may help in finding
less energetic solutions. This trend is consistently followed in the 2XNR case, with only
an exception in 5WWX (LA15) and some slight anomalies in 5ELH (XY06 cases).
When min E is compared between equivalent searches (GA vs. GG and LA vs. LG
to assess the effect of arithmetic vs. geometric pre-scoring or GA vs. LA and GG vs.
LG to assess the effect of global vs. local search space), there are only minor differences
indicating no clear trend for crowning a best XY methodology.
As the search space grows (either by increasing d(C5’-O3’) or by clustering with low
values of RMSD cutoff), the probability of finding native-like structures (#native in
Tables 5.1-5.3) also augments because there are more native-like mono-nucleotides being
considered. For 2XNR, only searches performed at d(C5’-O3’) of 5 or 6 Å produced
native-like solutions, with a maximum of 541 structures (GA06, LA06) and a minimum of
4 (GA25, GG25, LA25, LG25). In 5WWX the number of native-like structures considerably
drops down to a maximum of 7 (XY15, GG06, and LG06) and a minimum of 1 (XY26).
In 5ELH the trend resembles 5WWX, with a maximum of native-like structures retrieved
of 8 (LA06), and a minimum of 1 (XY16). In this latter case, explorations conducted
after clustering with 2Å RMSD cutoff did not report any native-like structure.
As the primary goal of this section was to reproduce crystal structures, our attention
was focused on two distinctive solutions for each XYij distribution; (i) the most similar
solution to the experimental one and (ii) the best-scored solution among the native-like
ones.
In the 2XNR case, the most similar solution to the experimental one is almost always
the same for equivalent searches, except in GG05 vs. GA05, GG16 vs. GA16 LA16
vs. GA16, LG05 vs. LA05, and LG16 vs. LA16. The biggest energy gap between these
divergent cases was 1.64 kcal/mol. These structures’ similarities against the reference vary
from 0.93 to 1.73 Å. For 5WWX and 5ELH the most similar solution to the experimental
one is always the same for equivalent searches and their resemblance fluctuates from 1.06
to 1.96 Å and from 1.46 to 1.82 Å, respectively.
The most similar solutions are ranked before and after minimization in their corresponding XYij distribution. In 2XNR their ranking before and after minimization ranges
from 54 to 4903 and from 21 to 644, respectively. In 5WWX the ranks fluctuates from
659 to 3370 before and from 149 to 1005 after minimization. For 5ELH pre-minimization
ranks of the most similar solution to the experimental one ranges from 864 to 3930 while
they drops from 486 to 1223 after minimization. This is indicative that the pre-score of
oligo-nucleotides is not linearly related to the score they will have after minimization. Note
that the energies of these structures are distant from the global minimum of their XYij
5.5. NUCLEAR’s complexity notes
99
distribution (5.2-12.08 kcal/mol, 7.9-11.8 kcal/mol, and 14.2-22.8 kcal/mol for 2XNR,
5WWX, and 5ELH respectively). The RMSD deviation after the linking process of connectable nucleotides found by NUCLEAR with respect to the original positions initially
found by MCSS are in the interval 1.80-2.58 Å in 2XNR, 1.23-2.22 Å in 5WWX, and
1.30-1.37 Å in 5ELH.
Concerning the best-scored solutions found by NUCLEAR among the native-likes
for each XYij distribution, only in the 2XNR case there are divergences in equivalent
searches (LA16 vs. GA16 and LA16 vs. LG16 ). The similarities of these best-scored
native likes structures vary from 1.35 to 1.98 Å in 2XNR, from 1.35 to 1.97 Å in 5WWX,
and from 1.71 to 1.82 Å in 5ELH. Let us analyze their ranking inside the XYij distribution in which they were obtained before and after minimization: 5-1388 and 15-96 for
2XNR, 659-3635 and 122-296 for 5WWX, and 138-3630 and 63-1223 for 5ELH. It is
worth noting that the energy of these structures are distant from the global minimum of
their XYij distribution (2.48-8.88 kcal/mol, 5.46-9.34 kcal/mol, and 8.4-22.7 kcal/mol for
2XNR, 5WWX, and 5ELH respectively). The RMSD deviation after the linking process
of connectable nucleotides found by NUCLEAR with respect to the original positions
initially found by MCSS are in the interval 1.40-1.98 Å in 2XNR, 1.40-2.50 Å in 5WWX,
and 1.29-1.37 Å in 5ELH.
5.5 . NUCLEAR’s complexity notes
In Figure 5.1, we detailed the general workflow for NUCLEAR software. Two
different tasks can be accomplished: searching for either hotspots or oligonucleotides.
In this Section we advance some notes on the temporal and spatial complexities of the
different steps conducted by NUCLEAR. It is important to note that even if algorithm
complexity gives idea on the worst performances an algorithm can have, real situations
often are better than the worst case and carefully chosen parameters could help in reaching
practical performances. Table 9.10 was constructed to grab an idea on the NUCLEAR’s
running times and memory consumption for the case studies presented in Section 5.4.2.
In Figure 5.1, we detailed the general workflow for the NUCLEAR software, which
can accomplish two distinct tasks: searching for either hotspots or oligonucleotides. This
section analyzes the time and space complexities of the various steps conducted by NUCLEAR. It is important to note that while algorithmic complexity provides insight into
the worst-case runtime, real-world situations are often better than the theoretical worst
case. Careful parameter selection can aid in achieving practical performance. Table 9.10
was constructed to showcase NUCLEAR’s running times and memory usage on the case
studies presented in Section 5.4.2, giving empirical measurements.
Though some steps exhibit high polynomial complexities, appropriate cutoffs allow
NUCLEAR to perform reasonably on test cases, avoiding the deterioration predicted by
worst-case analysis. Still, future work could aim to reduce the complexity of critical steps,
such as clustering and construction of the clash/reachability matrices. With algorithmic
improvements, NUCLEAR may scale more efficiently to large numbers of fragments and
100 5. NUCLEAR: AN EFFICIENT ASSEMBLER FOR THE FBDD OF CMOs
replicas while retaining its demonstrated utility for FBDD efforts.
5.5.1 . Search of hotspots
In Figure 5.2, the main steps for a NUCLEAR oligonucleotide search are shown: (i)
parsing molecular data, (ii) calculating interaction fingerprints, (iii) clustering fingerprints
into proper subsets, (iv) filtering, and (v) merging similar clusters.
Parsing molecular files can be regarded as an O(n) operation concerning the number
of fragment conformations to analyze. Interaction fingerprints are computed using the
protein coordinates for each fragment conformation and can be assumed as a constant
operation O(k) since the time to compute a given fingerprint is independent of the total
number of fragments. As this step is executed for every fragment, the overall complexity
is O(kn) ≡ O(n).
The clustering step (described previously in Section 2.1.4) depends on the number
of fragments. In the worst case where no fragment can be designated as similar, the
procedure attempts for each fragment (O(n)) to compute its similarity (O(k)) against all
available fragments (O(n)), thus reaching an overall complexity of O(n) · O(k) · O(n) →
O(kn2 ) ≡ O(n2 ).
Filtering against a cutoff value is a constant action performed n times in the worst
case, so this step is linear (O(n)). The worst case for the final operation occurs if no
cluster can be merged, a failed constant action repeated n times (O(n)). After summing
the previous contributions, we can conclude that the NUCLEAR search of hotspots has
the quadratic time complexity of its dominant term, the clustering step.
The spatial complexity of hotspots search can be evaluated by analyzing the objects
loaded into RAM at each previously mentioned step. Parsing molecular data requires
linear space with respect to the number of fragments to analyze (O(n)). The fingerprint
calculation generates one fingerprint (O(k)) for every fragment (O(n)), thus also consuming linear space. Clustering fingerprints necessitates loading all fragments into memory
(O(n)). Since the similarity computations are performed in situ, once per element, and
all elements appended to a cluster are eliminated from further consideration, this step
also exhibits linear spatial complexity (no similarity matrix is used). The filtering and
merging operations do not increase the spatial complexity either, so the dominant term
of the complete procedure is linear.
5.5.2 . Search of oligonucleotides
The primary steps involved in NUCLEAR’s oligonucleotide search are (i) clustering
of MCSS docking distributions, (ii) construction of reachability and clash matrices, and
(iii) linking mono-nucleotides to produce sequences.
As previously discussed, the BitClust-inspired clustering is executed independently
for each docking distribution, requiring O(n2 ) time (n being the number of replicas per
distribution). Thus, for m distributions, the time complexity of this step is quadratic,
O(mn2 ). A kd-tree containing two atoms per replica (O3′ and C5) is utilized to
construct the reachability matrix. With the kd-tree built, each O3′ atom searches in
logarithmic time O(nlogn) for neighboring atoms within a cutoff. The clash matrix uses
5.5. NUCLEAR’s complexity notes
101
a kd-tree of all replica atoms. Detecting clashes between a replica’s atoms and others’
is done by finding nearest neighbors within a cutoff, an O(nlogn) operation.
Finally, mono-nucleotide linking follows a DFS traversal of the reachability graph
in O(n + e) time (n = replicas, e = graph edges) since each node and edge is visited
once. Currently, NUCLEAR performs this from every node, increasing the complexity
to O(n2 + ne). Overall, quadratic terms plague NUCLEAR’s performance. However,
as Table 9.10 shows, carefully chosen cutoffs can prevent deteriorated performance.
As discussed in Section 5.5.1, NUCLEAR clustering has linear spatial complexity.
The constructed binary matrices are quadratic, dominating overall spatial complexity.
In the linking stage, each connected node saves a reachability matrix vector. In the
worst case, where all nodes are linkable, this grows quadratically. Nevertheless, linkable
nucleotides (b) are limited for practical use, giving O(bn) complexity.
6 - IN-SILICO DESIGN OF SELECTIVE CMOs
AGAINST BACE-X
Once the required methodological scaffold developed, we can tackle this work’s primary goal: the in-silico fragment-based design of selective Chemically Modified Oligonucleotides (CMOs) as potential protein inhibitors. We will use the BACE-X protein as a
relevant case study.
After presenting the nature of the chemically modified mono-nucleotides and the
protein conformations under consideration (Section 6.1), we illustrate how to attack the
problem of assembling oligonucleotides in two situations. Where practical information
on protein-inhibitor interactions is limited or unavailable (Sections 6.2.1 and 6.2.2), and
where knowledge on these interactions is accessible through molecular databases (Section
6.2.3). In the last part of the chapter, we then focus our attention on discerning if produced oligonucleotides have the potential to be selective against the BACE1 protein over
BACE2 by implementing several selection constraints to their binding modes (Section
6.3).
6.1 . Modified nucleotides and BACE-X protein candidates selection
As already discussed in Section 1.4.1, most inhibitors designed against BACE1
present off-target interactions with the conformationally similar protein BACE2, a negative side effect that leads to the inhibition of both proteins. Hence the primary motivation
of our workflow is to design oligonucleotides binding BACE1 preferentially.
After a full search for representative conformations of BACE1 and BACE2 proteins
in the PDB (see Sections 2.4.1 and 2.4.2 for details), we chose four models of the first
one (1SGZ, 4GID, 5MCQ, and 6UVV) and two of the latter one (2EWY and 3ZKM).
Once the protein models were established, the MCSS nucleotide fragments were
selected. A total of 111 mono-phosphate (including standard and chemically modified
nucleotides) were considered (see Section 2.4.3 for the complete list). The chemical
modifications in the library of the MCSS include all of the natural nucleotides found in
living organisms. They are available from commercial providers to guarantee that the
designed oligonucleotides can be chemically synthesized.
Apart from the standard nucleotides (A, C, G, U/T), all the other nucleotides from
the library include a modified nucleic acid base derived from the corresponding standard
one (19 A-derived, 18 C-derived, 29 G-derived, 45 U/T derived). In addition to the nucleobase’s modification, some also include a modification on the ribose with a 2’-OMe group.
The 2’-OMe modification has been widely used to produce synthetic oligonucleotides and
has been shown to improve the therapeutic index 273 .
Each fragment (mono-nucleotide) was docked onto the entire surface of each protein
6.2. Definition of the receptor region to explore
103
conformation (not only their binding site) via MCSS software, yielding 666 distributions
of about 10000 replicas that constitute the underlying data for the rest of the design
workflow.
6.2 . Definition of the receptor region to explore
When we analyzed the performance of NUCLEAR in Section 5.1, it became evident
that the selection of even a moderate number of linkable nucleotides (docked at the protein
surface) may lead to a combinatorial explosion of the oligonucleotide candidates to output.
The most natural choice to deal with this problem is to reduce the number of nucleotides
to connect in a particular search. This reduction can be accomplished in the NUCLEAR
context at least by three strategies; (i) performing a clustering step before starting the
oligonucleotide search, (ii) constraining the sequence to search for, and (iii) focusing the
search on a docked sub-region of interest at the receptor.
Clustering the docked distributions reduces the search’s exhaustiveness but at the
expense of eliminating poses that might lead to the best hits. We evaluated this effect
in Section 5.4 when struggling to find native-like poses of known oligonucleotide-protein
complexes. So we consider that it is more appropriate to do so as an optional second pass
to discover non-similar oligonucleotides.
As we are at the initial stages of the design of oligonucleotides, there is no particular
reason to introduce a bias in favor of a given sequence neither, so limiting the search to a
particular sub-region was the chosen way to deal with the aforementioned combinatorial
explosion.
However, discriminating essential protein sub-regions from the irrelevant ones is not
trivial in cases where there is no previous knowledge of how the protein binds to its
inhibitors and, more specifically, to the particular (potentially novel) fragments we want
to explore in the design. Next, we detail three approaches to restrict the exploration
regions: through the detection of hotspots (Section 6.2.1), from selectivity analyses of
the protein residues (Section 6.2.2), and from experimental knowledge of the alreadyknown binding sites of the protein (Section 6.2.3).
6.2.1 . Region definition from NUCLEAR hotspots
Information about the protein regions having a high propensity for ligand binding, also
known as hotspots, is essential in FBDD workflows. That is why NUCLEAR incorporates the ability to detect such hotspots, helping to ignore unimportant binding regions
(relative to the fragments under concern) and consequently improving the performance
of subsequent oligonucleotide searches.
For every conformation of BACE-X, we instructed NUCLEAR to execute a hotspots
search (described in Section 5.2) from the corresponding distributions of non-clustered
docked fragments. All protein atoms (but only no-patch fragment atoms) were evaluated
for determining NUCLEAR fingerprints. Only spots with a relative density greater than
0.05 were considered, and those whose seeds’ Tanimoto Index (TI) was under 0.25 were
merged.
104
6. IN-SILICO DESIGN OF SELECTIVE CMOs AGAINST BACE-X
The spots found with the previous procedure for the 4GID conformation of BACE1
are depicted in Figure 6.1 for illustration purposes. Note that some of them may appear
small because of the superposition with adjacent ones. In other applications, users may
want to focus the search on a subset of adjacent spots. However, we decided to use them
all for a more encompassing search area. So for every BACE-X conformation, all spots
having at least one fingerprint coming from a fragment ranked in the first top 100 of its
particular MCSS distribution were selected.
Figure 6.1: NUCLEAR hotspots detected in 4GID protein. (A) Protein side containing the
experimental binding site (in red). (B) The opposite side (180 deg. rotation around the yaxis from side A).
6.2.2 . Region definition from residues’ selectivity
The previous search region definition is relative to the particular conformation for
which the NUCLEAR search of spots was conducted. Such an approach provides no
insightful information on the average selectivity or binding preference of fragments against
one or another protein. As we are interested in designing selective oligonucleotides against
BACE1 (and not just against a particular conformation), we found it reasonable to define
the exploration region upon those residues showing a consensus selectivity for BACE1
over BACE2. These details may be challenging to obtain from experiments but are
recoverable from an in-silico approach.
Suppose that for a given BACE-X conformation, we compute the fingerprints of all
fragment poses issued from the MCSS docking. Each of those fingerprints comprises
several protein residues (see Section 5.2). By concatenating all fingerprints found on a
given conformation j, it is possible to count the total number of times a protein residue
i gets involved in contacts (countsij ).
Let us define the BACE-X counts of a residue i, as its average count for each BACEX conformation: BX_countsi = countsij : ∀ j in BACE-X_list, where X can be
1 or 2 and BACE-X_list comprises 1SGZ, 4GID, 5MCQ, and 6UVV conformations for
6.2. Definition of the receptor region to explore
105
X = 1, and 2EWY and 3ZKM conformations for X = 2. In this context, the BACE1
selectivity of a residue i was computed as:
Si (B1) = B1_countsi /(B1_countsi + B2_countsi )
(6.1)
While residues of the identical BACE-X conformations can be trivially re-numbered
to have an equivalent enumeration, BACE1 and BACE2 do not have complete sequence
identity. Then, a residue i on BACE1 may not exist or be displaced in the BACE2
sequence and vice versa. So, for determining the residue’s selectivity, we faced the nontrivial problem of finding a three-dimensional equivalence between BACE-X residues
identity and enumeration that we approached as explained in Section 2.4.5.
It is clear that the selectivity notion of Equation 6.1 offers just a piece of approximate
information on residue binding preference. The panorama would have changed if another set of conformations were selected for BACE-X (or the evaluated fingerprints were
restricted to the best-ranked top-X). In any case, the derived selectivity maps advance
valuable clues on the overall binding preferences of proteins.
As it is verified in Figure 6.2, vast regions are selective to BACE1 (intense blue). Note
that although the map has been projected onto a particular BACE1 conformation (4GID),
the selectivity per residue could have been mapped to any other BACE-X conformation.
Suppose we concentrate on the lower region of Figure 6.2B. In that case, we observe
that it appears highly selective to BACE2, the reason behind hotspots’ absence in this
region for BACE1 conformations (see the equivalent region in Figure 6.1). So for every
BACE-X conformation, the region search defined from selectivity information consisted
of residues with more than S >= 0.5 for BACE1 and S < 0.5 for BACE2.
Figure 6.2: Selectivity map of residues computed from NUCLEAR fingerprints projected
onto the 4GID BACE1 conformation. (A) Protein side containing the experimental binding
site. (B) The opposite side (180 deg. rotation around the y-axis from side A). BACE1 selectivity of residues are color coded from zero (red residues selective to BACE2) to one (blue
residues).
106
6. IN-SILICO DESIGN OF SELECTIVE CMOs AGAINST BACE-X
6.2.3 . Region definition from experimental protein-inhibitors contacts
Previous definitions of the region to explore lead to a considerable shrink of the
receptor surface to evaluate. They are both in-silico-inspired reductions that have no
ultimate link with experimental knowledge of the protein’s binding site. Provided this
knowledge exists, one could use it to define where to conduct NUCLEAR searches. As
described in Section 2.4.1, we downloaded BACE-X inhibitors reported on the PDB
database and computed their fingerprints using the BINANA software to gather the
interacting residues.
In Figure 6.3, it is appreciated how by only selecting those residues that interact with
an experimentally tested inhibitor, the search space is now much more reduced than the
formerly defined in Sections 6.2.1 and 6.2.2. From a design perspective, this characteristic
limits the amount of novel binding areas to consider. Nevertheless, at the same time, it
provides a zone that may contain a lot of well-ranked oligonucleotides.
Figure 6.3: Region definition from protein-inhibitors contacts computed with BINANA for
(A) BACE1 and (B) BACE2 conformations.
Note that as the number of BACE1 inhibitors reported in PDB is more prominent
than for BACE2, the latter has a slightly smaller region defined by this methodology.
They are spatially equivalent, in any case.
6.3 . Selectivity of CMOs against BACE-X
The general workflow to retrieve selective CMO against BACE-X is depicted in
Figure 6.4. After choosing one of the approaches mentioned above to define the protein’s
region where the NUCLEAR oligonucleotide search should proceed (Sections 6.2.16.2.3), resulting selections were used to search for the 1000 best-ranked chains with sizes
between 2 and 6 nucleotides onto the surface of each protein conformation. The first 100
best-ranked poses of every fragment distribution obtained by the MCSS docking were
6.3. Selectivity of CMOs against BACE-X
107
considered. The distance to catch an atomic clash between protein and fragment atoms
was set to 1.5 Å and the maximum distance to join nucleotides (from O3′ to O5′ ) to 6
Å.
Total of oligo-nucleotide chains
# protein conformation: 6
(1SGZ, 2EWY, 3ZKM, 5MCQ, 6WUU)
# selections: 3
(inhibitord, hotspots, selectivity)
# chain's size requested: 5
(2, 3, 4, 5, 6)
# chains / protein / selection : top-1000
88 112 chains
Minimization
(CHARMM)
Filter #1
(RMSD < 1A)
BACE1 design
9302 chains
BACE2 design
Filter #2
Filter #2
(BACE1 selectivity > 0.75)
(BACE2 selectivity > 0.75)
5321 chains
1861 chains
Compute NUCLEAR
fingerprints
Compute NUCLEAR
fingerprints
Clustering
Clustering
(overlap > 0.85)
(overlap > 0.85)
228 clusters +
149 singletons
176 clusters +
144 singletons
Figure 6.4: General workflow to retrieve selective CMO for BACE-X proteins.
The 88112 found oligonucleotides were then submitted to a minimization protocol
using CHARMM (see Section 2.3.1). At this point, a necessary clarification should be
made; for a given MCSS exploration conducted on a particular protein conformation,
NUCLEAR searches deliver unique oligonucleotide conformations. In the same job,
for example, it is possible to output the sequence ADE GUA THY more than once,
ranked differently depending on the conformation it adopts upon protein binding after
minimization.
In a post-minimization stage, the following descriptors were requested for each produced chain in order to derive rules for later selecting the most appropriate candidates
to inhibitors: (i) their interaction energy (EINT) with the protein (requested in the
CHARMM minimization script), (ii) their post-minimization ranking (after sorting by
their EINT), (iii) their number of contacts with the protein (after minimization) (iv) the
108
6. IN-SILICO DESIGN OF SELECTIVE CMOs AGAINST BACE-X
Tanimoto Index (TI) of the pre and post-minimization NUCLEAR fingerprints, (v) the
RMSD of the pre and post-minimized coordinates, (vi) their number of conformers, and
(vii) their BACE1 selectivity (computed after Equation 6.1).
Selecting a potential inhibitor against BACE1 is a challenging task that can not be
estimated using only these descriptors. We proceeded with that information because no
other analyses were implemented when writing this manuscript. We are still confident
that the chosen ones (easily derived with NUCLEAR) furnish users with practical power
to discern potential hits from sub-optimal solutions. Also, the cutoffs used to restrict
the number of sequences to analyze and the choice of the different top-X should not be
blindly embraced as gold standards and are provided in a demonstrative basis.
The ensemble of chains was arranged in a tabular data structure and ordered by
EINT (ascending), selectivity to BACE1 conformations (descending), and the number
of contacts (descending). Then two ramifications were followed to generate BACE1 or
BACE2 selective CMOs. Those sequences whose RMSD after minimization was less
than 1 Å or whose BACE-X selectivity was above 0.75 were conserved (5321 chains for
BACE1 and 1861 chains for BACE2).
The conserved sequences were submitted to the clustering procedure described in
Section 2.1.4. The similarity criteria, however, was the overlap of their fingerprints (those
overlapping more than 0.85 were considered similar). In this way, 228 clusters (plus
149 singletons) were obtained for BACE1 and 176 clusters (plus 144 singletons) were
retrieved for BACE2. In Figure 6.5, the first five best ranked seeds for each protein are
shown, while more information about these seeds is reported in Table 6.1.
As shown in Table 6.1, the clusters of BACE1 contain a higher percentage (13%) of
the selected chains (5321 in total) compared to the clusters of BACE2, which account
for approximately 6% of the selected chains (1861 in total). All the seeds in both clusters
are hexamers, which aligns with the maximum chain size requested in the NUCLEAR jobs.
Despite the lack of direct comparability and variations in interaction energy among
the different seeds, they are all well-ranked within their respective NUCLEAR distribution
(from a minimum of 3 to 174 out of the 1000 solutions requested). It is noteworthy that
the selected CMOs exhibit a low deviation before and after minimization, as evidenced
by their TI and RMSD values. Lastly, it is important to highlight that all compared
seeds demonstrate complete selectivity towards the protein in which they were identified.
The seeds of the first five clusters associated with potential selective inhibitors of
BACE-X are depicted in Figure 6.5. In the case of BACE1, despite being the highestranked solution, C1 adopts a U-like conformation and does not contact the active site
region. Similarly, C2 does not introduce a complete nucleotide into the active site; only
the T6A nucleobase is present, resulting in a T-like conformation. In contrast, C3 and C5
exhibit a more conventional curvilinear arrangement, effectively crossing the active site
region and establishing a characteristic set of interactions with the flap region through
their common 7OU and OAU mono-nucleotides. The most atypical CMO binding mode
retrieved for BACE1 is C4. In this case, the hexamer lands over the left side of the flap
and extends until the final, unmodified GUA nucleotide, gets inside the active site.
Figure 6.5: First five clusters’ seeds of BACE-X’s potential selective inhibitors. Red, blue, and green regions correspond to the active site, the flap, and
the 10s loop regions, respectively. Oligonucleotides are represented without protons and phosphorus atoms have been highlighted for improved visual
clarity. The red nucleotide starts the oligomer whose sequence is shown in Table 6.1.
108
6. IN-SILICO DESIGN OF SELECTIVE CMOs AGAINST BACE-X
Regarding BACE2, the hexamers C1 and C2 exhibit a shared terminal motif (PBGOMG), giving rise to a distinctive interaction pattern. In this pattern, PBG covers the
upper-right side of the flap, while OMG is inserted within the active site region. In a
reversed orientation, C3 replicates the aforementioned binding mode, featuring a lateral
interaction between BUG and the flap, while ADE is inserted into the active site. On the
other hand, C4 and C5 seeds are situated significantly distant from the active site region.
6.3.1 . Key interactions of CMO-BACE-X complexes
The molecular basis underlying the binding modes of Figure 6.5 was investigated by
examination of the close contacts, hydrogen bonds, salt bridges, hydrophobic, π − π,
T-stacking, and π−cation interactions between the CMOs and BACE-X. This analysis
was conducted utilizing the default’s geometrical values of the BINANA program and
for all members of the inspected clusters. The outcomes are presented in Figure 6.8 for
BACE1 and Figure 6.9 for BACE2.
For BACE1, residues in the “near-10s loop region” displayed the highest interaction
frequency (except for cluster 4, which does not extend to that area). This region includes
the residues LYS-9, GLN-12, ASN-111, GLN-163, ARG-307, VAL-309, GLU-310, ASP311, and LYS-321 (refer to Figure 6.6A). Interactions with LYS-9, GLU-310, and ASP-311
are particularly prevalent in clusters 1 and 2, exhibiting close contacts, hydrogen bonds,
hydrophobic interactions, and salt bridges. ARG-307 and LYS-321 are also among the
most frequent residues, forming similar types of interactions. Though rare, LYS21 can form
π−cation interactions with a few exemplars. While GLN-12 can form hydrogen bonds,
hydrophobic interactions are more common. VAL-309 only gives rise to hydrophobic
interactions. ASN-111 and GLN-163 interact with members across the four clusters,
though their frequency is low.
Figure 6.6: BACE1’s (A) and BACE2’s (B) “near-10s loop region” key residues interacting
with the members of the first five clusters of selective CMOs retrieved by NUCLEAR.
6.3. Selectivity of CMOs against BACE-X
109
By contrast, the “near-10s loop region” of BACE2 (Figure 6.6B) contains more and
different residues with prevalent interactions: GLY8, ASP9, GLY11, ARG12, GLY112,
LYS114, GLY165, ASN167, LEU264, MET306, MET307, GLU314 and ARG317. This
region is shared by the two significantly distinct binding modes that CMOs adopts in this
protein: that of clusters 1, 2, and 3 (that also covers the active site region) and the one
seen in clusters 4 and 5 (positioned in the outer right side of the 10s loop, without any
contact with the active site and thus not essential to the present study). Consequently,
interacting residues are seldom present with the same prevalence across the five clusters.
The ARG12, able to form hydrogen bonds across all clusters and salt bridges in C1 to
C3, stands as one of the residues with more interactions. LYS114 is the only residue
in the region to establish π−cation interactions with a few exemplars. From the two
consecutive methionines, MET307 forms hydrogen bonds across all clusters, though they
seem stronger for clusters 3, 4, and 5, where close contacts are detected with this residue.
In Figure 9.19, the interacting residues of this region are colored by their type. In
BACE1, there are three basic residues together: an acidic dyad and a polar sub-region.
There is no close acidic pair for BACE2, and a non-polar chain outlines one of the
two basic residues. The distinctive composition of this particular area, coupled with
the significant frequency of interactions established with the CMOs, strongly suggests
their relevance for the design of BACE-X selective inhibitors (currently focused on the
protein’s active site).
Examining the active site region (refer to Figure 6.7), we observe distinct differences
in the composition and significance of the interacting residues in each protein. Notably,
the flap region (TYR71, THR72, GLN73) remains conserved between both proteins. The
claw-like interaction observed in clusters 3 and 5 of BACE1 results from π − π stacking
with TYR71 and hydrogen bonds with THR72. These residues also exist in BACE2,
although the π − π stacking is observed solely in cluster 3. GLN73 is more prevalent in
BACE2 clusters than in BACE2.
A critical distinction between BACE-X interaction patterns pertains to the catalytic
aspartic dyad (ASP32-ASP228 in BACE1, ASP32-ASP225 in BACE2). A limited number of members from cluster 4 in BACE1 exhibit hydrogen bonds with ASP228 and
close contacts with ASP32. This particular location assumes a more significant role in
BACE2, where members of clusters 1, 2, and 3 can establish hydrogen bonds, salt
bridges, or hydrophobic interactions with ASP32 or ASP225.
The unusual binding mode of cluster 4 in BACE1, supported by π − π stacking
(TYR68), hydrogen bonds (LYS75, GLU77, SER328), and salt bridges interactions (LYS75
and GLU77), does not have a counterpart in BACE2. This binding, while anomalous,
aligns with other authors’ recommendations of targeting the flap region, where the shape
and flexibility differ between BACE-X enzymes 21,172 .
Overall, despite the claimed similarity between BACE-X proteins, our analysis reveals
that the highest-ranked CMOs interacting with them are positioned differently, not just
within the active site but also in other protein sub-sites crucial for molecular anchoring.
110
6. IN-SILICO DESIGN OF SELECTIVE CMOs AGAINST BACE-X
Figure 6.7: BACE1’s top (A) and BACE2’s right lateral (B) view of the active site region’s key
residues interacting with the members of the first five clusters of selective CMOs retrieved
by NUCLEAR.
Clust. size
105
268
119
160
36
16
11
36
8
34
Clust. ID
1
2
3
4
5
1
2
3
4
5
Protein
BACE1
BACE2
3MC-YYG-K2C-3AU-PBG-OMG
5CU-PBG-K2C-3AU-PBG-OMG
ADE-BUG-5HU-5CU-MAU-BUG
R2C-BUG-MSU-R2C-ADE-HWG
R2C-BUG-THY-R2C-5HU-PBG
R2C-OAU-1MA-OAU-3MC-R2C
HWG-R2C-OAU-1MG-T6A-SIA
13P-70U-OAU-BUG-6IA-HWG
HNA-OAU-K2C-HCU-OAU-GUA
OAU-70U-OAU-BUG-MMA-HWG
Chain
-180.66
-178.5
-168.2
-159.84
-159.32
EINT
[kcal/mol]
-177.46
-170.97
-165.99
-165.77
-163.89
10
18
174
20
22
13
11
22
3
43
Rank
31
34
28
27
27
24
29
31
23
28
#contacts
0.77
0.78
0.71
0.83
0.93
0.82
0.90
0.88
0.88
0.87
TI
0.98
0.99
0.98
1.00
0.93
RMSD
[Å]
1.00
0.97
0.92
1.00
0.88
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Selectivity
Table 6.1: Descriptors of potential selective inhibitors of BACE-X. The Selectivity column refers to Si (B1) or Si (B2) for BACE1 or BACE2, respectively.
Figure 6.8: Count of molecular interactions formed between all constituents of the first five clusters (C1 to C5) of the CMOs targeted against BACE1.
Residues on the x-axis are colored red, blue, or green if they are part of the active site region, flap, or 10s loop, respectively.
Figure 6.9: Count of molecular interactions formed between all constituents of the first five clusters (C1 to C5) of the CMOs targeted against BACE2.
Residues on the x-axis are colored red, blue, or green if they are part of the active site region, flap, or 10s loop, respectively.
7 - CONCLUSIONS
1. The Multiple-Copy Simultaneous Search software was evaluated for docking nucleotides on a benchmark of 121 protein complexes. Different solvent and phosphate models were tested to optimize the success rate for identifying native poses
(docking power) and the actual native nucleotide (screening power). As a result,
the combined STDW model with the phosphate patch R310 appears to give the
best performance, outperforming several scoring functions. The presence of water
molecules in the preparation and optimization of the protein structure allows the
minimized structure to deviate less from the experimental structure.
2. Four popular clustering algorithms were significantly optimized to enable their application at distinct phases of the Fragment-Based Drug Design. Through binary
storage, binary translation of the primary operations, or complete reformulation
of the algorithms, exact (BitClust, DP+) and modified (BitQT, RCDPeaks, MDSCAN) versions of the original proposal were presented and thoroughly benchmarked. A methodological confusion between Quality Threshold and Daura’s algorithms was exposed to the community.
3. An efficient computational linker for assembling Chemically Modified Oligonucleotides (fragments) onto oligochains (lead compounds) was developed. Our
NUCLEotide AssembleR was able to return clash-free sequences following distinct
constraints (in sequence or exploration region) and could identify (despite inherent
limitations) several experimental binding modes in three case studies. Another
necessary functionality of this software is the determination of hotspots at the
target’s surfaces for guiding the Fragment-Based Drug Design.
4. We designed an in silico fragment-based workflow that produces low-energy binding modes of Chemically Modified Oligonucleotides (obtained by the NUCLEotide
AssembleR after Multiple-Copy Simultaneous Search docking) evincing structural
selectivity against β-site Amyloid Precursor Protein Cleaving Enzyme 1 enzyme
over the related β-site Amyloid Precursor Protein Cleaving Enzyme 2. The topranked BACE1 binding modes are able to linearly traverse the active site region
or concurrently interact with the top side of the flap and the active site, while
similar binding modes are not detected for BACE2.
8 - PERSPECTIVES
1. Integrating optimized clustering algorithms into the NUCLEAR software could
enhance performance and scalability. Other approaches could be explored as alternatives to the current BitClust-inspired implementation to reduce computational
complexity for extensive fragment collections.
2. Calculating physicochemical and drug-likeness molecular descriptors could enable
rational filtering of non-viable oligonucleotide sequences identified by NUCLEAR.
Descriptors related to solubility, cell permeability, and synthetic accessibility could
be computed to screen for promising sequences worth experimental validation.
3. Performing MD simulations on the NUCLEAR-generated complexes would allow evaluating their geometrical stability and dynamics. These simulations could
identify unstable or unfavorable interactions that may preclude function, informing
on oligonucleotide sequence optimization and guiding synthetic efforts toward productive candidates. Longer timescale simulations may also reveal conformational
changes relevant to the inhibition mechanism. Beyond geometrical stability, simulations could also probe oligonucleotide binding kinetics and affinity with receptors
to establish viable complexes. Free energy calculations could quantify the relative
strengths of binding.
4. Collaborations with synthetic chemists will be crucial to experimentally produce
and characterize oligonucleotide candidates proposed by NUCLEAR. These validations will demonstrate real-world utility.
9 - ANNEXES
9.1 . MCSS-based predictions of binding and selectivity of nucleotides
Figure 9.1: Decomposition of docking powers per nucleotide type. The data are shown for
the clustered distribution and each Top-i .
9.2 . Reinventing the wheel of molecular clustering
9.2.1 . Details of MD used in benchmarks
9.2.1.1
6 kF
All details on generation of the 6 kF trajectory has been previously published by Shea and
Levine 256 .
9.2.1.2
30 kF
All details on generation of the 30 kF trajectory has been previously published by Melvin
et al. 242 .
9.2.1.3
50 kF
The initial coordinates of the repetitive unit of serotype 18C of Streptococcus pneumoniae
were obtained with CarbBuilder 274 . The system with dimensions 32 × 32 × 43 Å contains
1202 water molecules and was neutralized using N a+ and Cl− ions at near-physiological
9.2. Reinventing the wheel of molecular clustering
115
80
72
Intersection Size
60
40
20
18
12
11
4
3
1
0
syn
●
no.pred
●
pyr
pur
100
75
50
25
●
●
●
●
●
●
●
●
●
●
●
0
Set Size
Figure 9.2: Upset diagram of the impact of the conformational features on the Top-10
predictions. The intersections with only one member are not shown; syn: syn conformation
of the nucleic acid base; pyr: pyrimidine; pur: purine.
1400
1200
1000
800
3
Volume (A )
600
400
200
0
−200
−400
−600
−800
5x0j
5v1m
5v0i
5t8s
5k1d
5jda
5gmd
5ed3
5d4n
5cot
5bph
5b8f
5b6d
4zfn
4zcp
4x9d
4ww7
4uuw
4r78
4pno
4p86
4ozl
4o6m
4ndf
4mx2
4mpo
4ma0
4m9d
4m0k
4kbf
4jem
4ike
4ijn
4ig1
4he2
4h2w
4g0p
4fe3
4fbc
4eum
4eql
4emd
4eei
4d7a
4d05
4cs3
4co4
4brq
4blw
3w07
3uwq
3uq8
3ttf
3sf0
3rpz
3rl4
3pln
3omf
3o0m
3nyq
3nua
3n1s
3m84
3lkm
3lfr
3kgd
3kd6
3ib8
3gru
3glv
3g1z
3fwz
3feg
3ewy
3dlz
3djx
3ddj
3cls
3cj9
3c85
3c4z
3ake
2yvo
2yrx
2yab
2xwm
2xbu
2vfk
2uv4
2r85
2qrk
2oun
2jbh
2jb7
2j91
2ii6
2gxq
2g1u
2fjb
2ffc
2eqa
2cnq
2a7x
1z4m
1y1p
1xtt
1wxi
1uuy
1uj2
1ucd
1ua4
1s68
1rao
1qgx
1qf9
1nh8
1ktg
1jp4
1iyb
1hdi
1ex7
PDB ID
Figure 9.3: Variations in the volume of the binding site. Black line: experimental structure;
Blue line: optimized structure for the SCAL model; Red line: optimized structure for the
STDW model. The histograms indicate a decreasing of the volume for the negative values
and an increasing for the positive values. The calculation of volume does not take into
account the water molecules.
concentration (150 mM). The solvating water molecules were described with the TIP3P
model ( 275 ).
The MD trajectory was computed with NAMD (v2.12) program 276 , using the CHARMM36
force field 277,278 and periodic boundary conditions (PBC). Long-range interactions for the
full system with PBC were handled by means of the particle-mesh Ewald method 279 with
a grid resolution of less than 1 Å, while all other non-bonded interactions were computed
with a cutoff of 12 Å. SHAKE constrains 280 were applied to water molecules bonds. A
time step of 1 fs was used, saving all frames every 1 ps to obtain 50000 conformations
116
9. ANNEXES
Features
nwat.low
vol.low
binding site
others
metals
syn
conformational
pur
pyr
no.base.contacts
no.salt.bridges
interaction
no.stacking
clash aa
clash w
Freq. Benchmark
62
69
12
36
12
79
21
12
44
49
22
33
Freq. good
60
70
10
60
0
80
0
30
30
70
20
40
Table 9.1: Frequencies of occurrences for molecular features in the Top-10 for non-optimal
(good) predictions. Others: presence of additional nucleotidic (nucleic acid) fragment
in the binding site; metals: presence of metal(s) in the binding site; nwat.low: presence
of number of water molecules below the threshold value; vol.low: volume of the binding site below the threshold value; syn: syn conformation of the nucleic acid base; pyr:
pyrimidine; pur: purine; no.base.contacts: absence of contacts with the nucleic acid base;
clash_aa: clash(es) with amino-acid residues; clash_w: clash(es) with water molecules;
no.salt.bridges: absence of salt-bridge; no.stacking: absence of stacking.
50
Intersection Size
40
27
20
10
9
8
8
5
2
1
1
0
no.pred
●
no.pp_stacking
●
no.pi.cat_stacking
●
●
●
●
no.t_stacking
90
60
30
●
no.stacking
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0
Set Size
Figure 9.4: Upset diagram of stacking contributions for the Top-10 predictions. no.pp_satcking: no π -π stacking; no.pi.cat_stacking: no π -cation stacking; no.t_stacking: no t
stacking.
contained in the 50 kF (kF=1000 Frames) trajectory. The production MD simulation was
performed at a constant temperature of 300 K and a pressure of 1 bar (NPT ensemble)
by using the Nosé-Hoover thermostat and barostat 281 .
9.2. Reinventing the wheel of molecular clustering
1rao
1wxi
1xtt
2g1u
2xbu
2xwm
3gru
3m84
3nua
3omf
3sf0
4eei
4ijn
4zfn
5ed3
5jda
5v0i
stdw-R110
Y
Y
Y
Y
Y
N
N
Y
N
Y
N
N
N
Y
Y
N
N
117
scal-R310
scal-R110
Y
N
N
N
Y
Y
Y
Y
Y
N
N
Table 9.2: Impact of the nonbonded model and phosphate patch on the recovery effect
of the Top-10 no-prediction subset. Y: recovered prediction using a different model and
patch; N: no recovered prediction with the given model and patch.
Volumes
UP
SCAL
DOWN
UP
STDW
DOWN
Freq. Benchmark
12
19
13
21
Freq. nopred.
0
18
0
35
Table 9.3: Variations in the binding site’s volume for the subset of protein-nucleotides
complexes with no prediction in the Top-10. The volume of reference corresponds to that
of the experimental structure; the modified volumes are calculated for both the SCAL and
STDW models. Only the cases where the variation equals or exceeds 100Å3 are considered.
UP: increase of the binding site’s volume. DOWN: decrease of the binding site’s volume.
9.2.1.4
100A kF
A structural model of Cyclophilin A (PDB ID 2N0T 282 ) was embedded into an octahedral
box. The system with dimensions 89 × 89 × 95 Å contains 22083 water molecules and
was neutralized at near-physiological concentration (150 mM), using N a+ and Cl− ions.
The water molecules were described with the TIP3P model 275 . At least 15 Å of space was
left between the Cyclophilin structure and the simulation cell boundaries, keeping more
than 50 Å of distance between protein copies of neighboring cells during MD runs.
The MD trajectory was computed with NAMD (v2.13) program 276 , using the CHARMM36
118
9. ANNEXES
Features
nwat.low
vol.low
binding site
others
metals
syn
conformational
pur
pyr
no.base.contacts
no.salt.bridges
interaction
no.stacking
clash aa
clash w
Freq. Benchmark
62
69
12
36
12
79
21
12
44
49
22
33
Freq. STDW(R310)
51
72
6
30
17
83
17
11
62
49
21
40
Table 9.4: Frequencies of occurrences for molecular features in the Top-10 for nonpredicted cases of STDW-310 versus benchmark. Others: presence of additional nucleotidic (nucleic acid) fragment in the binding site; metals: presence of metal(s) in the binding
site; nwat.low: presence of number of water molecules below the threshold value; vol.low:
volume of the binding site below the threshold value; syn: syn conformation of the nucleic
acid base; pyr: pyrimidine; pur: purine; no.base.contacts: absence of contacts with the
nucleic acid base; clash_aa: clash(es) with amino-acid residues; clash_w: clash(es) with
water molecules; no.salt.bridges: absence of salt-bridge; no.stacking: absence of stacking.
force field 277,278 and periodic boundary conditions (PBC). Long-range interactions for the
full system with PBC were handled by means of the particle-mesh Ewald method 279 with
a grid resolution of less than 1 Å, while all other non-bonded interactions were computed
with a cutoff of 12 Å. SHAKE constrains 280 were applied to water molecules bonds. A
time step of 1.0 fs was used, saving all frames every 1 ps to obtain 100000 conformations
contained in the 100A kF trajectory. The production MD simulation was performed at a
constant temperature of 310 K and a pressure of 1.0 bar (NPT ensemble) by using the
Nosé-Hoover thermostat and barostat 281 .
9.2.1.5
100B kF
The 2.2 Å X-ray bovine-rhodopsin structure (Protein Data Bank code: 1U19)1,2 was embedded inside a palmitoyl-oleoyl-phosphatidylcholine (POPC) hydrated membrane. The
protonation states of the titratable amino-acid residues were assigned according to the
protocol described by 283 . The internal water molecules were conserved in the rhodopsin
model. The rhodopsin/POPC/water system was neutralized at near-physiological concentration (150 mM) using Na+ and Cl− ions, where at least 15.0 Å of space was left
between the rhodopsin structure and cell boundaries. The TIP3P model 275 was used for
all water molecules. The two palmitoyl residues covalently linked to the residues Cys322
and Cys323 were kept in the three-dimensional structure, as well as the Cys110-Cys187
disulfide bridge.
9.2. Reinventing the wheel of molecular clustering
119
Table 9.5: Protein-nucleotide benchmark composition.
PDB-ID
1ex7
1hdi
1iyb
1jp4
1ktg
1nh8
1qf9
1qgx
1rao
1s68
1ua4
1ucd
1uj2
1uuy
1wxi
1xtt
1y1p
1z4m
2a7x
2cnq
2eqa
2ffc
2fjb
2g1u
2gxq
2ii6
2j91
2jb7
2jbh
2oun
2qrk
2r85
2uv4
2vfk
2xbu
2xwm
2yab
2yrx
2yvo
3ake
3c4z
3c85
3cj9
3cls
3ddj
3djx
3dlz
3ewy
3feg
3fwz
3g1z
3glv
3gru
3ib8
3kd6
3kgd
3lfr
3lkm
3m84
3n1s
3nua
Nuc-ID
5GP
AMP
5GP
AMP
AMP
AMP
C5P
AMP
AMP
AMP
AMP
U5P
C5P
AMP
AMP
U5P
AMP
U5P
AMP
AMP
AMP
U5P
AMP
AMP
AMP
C5P
AMP
AMP
5GP
AMP
AMP
AMP
AMP
AMP
5GP
C5P
AMP
AMP
AMP
C5P
AMP
AMP
AMP
AMP
AMP
C5P
AMP
U5P
AMP
AMP
AMP
AMP
AMP
AMP
AMP
AMP
AMP
AMP
AMP
5GP
AMP
Resolution
1.90
1.80
1.50
1.69
1.80
1.80
1.70
1.60
1.56
1.90
1.90
1.30
1.80
1.45
1.70
1.80
1.60
1.70
1.70
1.00
1.80
1.70
1.70
1.50
1.20
1.75
1.80
1.65
1.70
1.56
1.75
1.70
1.33
1.50
1.80
1.80
1.90
1.90
1.67
1.50
1.84
1.90
1.80
1.65
1.80
1.69
1.85
1.10
1.30
1.79
1.95
1.99
1.60
1.80
1.88
1.68
1.53
1.60
1.70
1.45
1.40
Classification
TRANSFERASE
TRANSFERASE
HYDROLASE
HYDROLASE
HYDROLASE
TRANSFERASE
TRANSFERASE
HYDROLASE
TRANSFERASE
LIGASE
TRANSFERASE
HYDROLASE
TRANSFERASE
CHELATASE
LIGASE
TRANSFERASE
OXIDOREDUCTASE
HYDROLASE
LIGASE
LIGASE
NA BINDING PROTEIN
LYASE
OXIDOREDUCTASE
MEMBRANE PROTEIN
HYDROLASE
TRANSFERASE
LYASE
UNKNOWN FUNCTION
TRANSFERASE
HYDROLASE
OXIDOREDUCTASE
UNKNOWN FUNCTION
TRANSFERASE
HYDROLASE
TRANSFERASE
TRANSFERASE
TRANSFERASE
LIGASE
HYDROLASE
TRANSFERASE
TRANSFERASE
MEMBRANE PROTEIN
HYDROLASE
ELECTRON TRANSPORT
UNKNOWN FUNCTION
HYDROLASE
TRANSFERASE
LYASE
TRANSFERASE
MEMBRANE PROTEIN
LIGASE
BIOSYNTHETIC PROTEIN
TRANSFERASE
HYDROLASE
TRANSFERASE
LIGASE
MEMBRANE PROTEIN
TRANSFERASE
LIGASE
HYDROLASE
LIGASE
PDB-ID
3nyq
3o0m
3omf
3pln
3rl4
3rpz
3sf0
3ttf
3uq8
3uwq
3w07
4blw
4brq
4co4
4cs3
4d05
4d7a
4eei
4emd
4eql
4eum
4fbc
4fe3
4g0p
4h2w
4he2
4ig1
4ijn
4ike
4jem
4kbf
4m0k
4m9d
4ma0
4mpo
4mx2
4ndf
4o6m
4ozl
4p86
4pno
4r78
4uuw
4ww7
4x9d
4zcp
4zfn
5b6d
5b8f
5bph
5cot
5d4n
5ed3
5gmd
5jda
5k1d
5t8s
5v0i
5v1m
5x0j
Nuc-ID
AMP
AMP
AMP
U5P
5GP
AMP
AMP
AMP
AMP
U5P
U5P
AMP
AMP
AMP
AMP
AMP
AMP
AMP
C5P
AMP
AMP
AMP
U5P
U5P
AMP
AMP
AMP
AMP
AMP
C5P
AMP
AMP
AMP
AMP
AMP
AMP
AMP
C5P
AMP
5GP
U5P
AMP
AMP
AMP
U5P
C5P
5GP
C5P
C5P
AMP
AMP
AMP
AMP
AMP
AMP
5GP
AMP
AMP
U5P
AMP
Resolution
1.43
1.90
1.80
1.50
1.29
1.51
1.35
1.92
1.70
1.80
1.03
1.95
1.45
1.50
1.50
1.65
1.80
1.92
1.75
1.80
1.80
1.70
1.74
1.80
1.95
1.60
1.43
1.70
1.48
1.55
1.90
1.40
1.82
1.98
1.90
1.90
1.94
1.90
1.49
1.93
0.97
1.45
1.98
1.67
1.50
1.98
1.90
1.65
1.45
1.70
1.69
1.60
1.31
1.50
1.40
1.94
1.70
1.90
1.47
1.43
Classification
LIGASE
HYDROLASE
METAL BINDING PROTEIN
OXIDOREDUCTASE
HYDROLASE
LYASE
HYDROLASE
TRANSFERASE
LIGASE
LYASE
LYASE
TRANSFERASE
HYDROLASE
SIGNALING PROTEIN
LIGASE
LIGASE
LIGASE
LYASE
TRANSFERASE
LIGASE
TRANSFERASE
HYDROLASE
HYDROLASE
GENE REGULATION
LIGASE
HYDROLASE
HYDROLASE
TRANSFERASE
TRANSFERASE
HYDROLASE
HYDROLASE
TRANSFERASE
LIGASE
LYASE
HYDROLASE
LYASE
NA BINDING PROTEIN
TRANSFERASE
SIGNALING PROTEIN
TRANSFERASE
NA BINDING PROTEIN
TRANSFERASE
BIOSYNTHETIC PROTEIN
TRANSFERASE
NA BINDING PROTEIN
TRANSFERASE
TRANSFERASE
TRANSFERASE
LYASE
LIGASE
LIGASE
SIGNALING PROTEIN
HYDROLASE
LYASE
TRANSFERASE
HYDROLASE
TRANSFERASE
LIGASE
HYDROLASE
TRANSFERASE
A 100-ns MD trajectory was computed with the NAMD (v2.12) 276 program, using the
CHARMM36 force field 277,278 . The system was simulated at the constant temperature
of 310 K and pressure of 1.0 bar by using the Nosé-Hoover thermostat and barostat 281 .
A time-step of 1.0 fs was used for the production 100-ns run, and the frames were saved
every 1 ps, which allowed to obtain a MD trajectory containing 100000 frames. A cutoff of
120
9. ANNEXES
Figure 9.5: Distributions of water molecules and impact on the binding sites. A-1.: Histogram of RMSD in presence/absence of water molecules; A-2.: Same as A-1 with a smooth
histogram; B-1.: the number of water molecules around the ligand (distance cutoff of
4.0Å); B-2.: Same as B-1 with decomposition per nucleotide moiety; C-1.: Number of water
molecules within the binding site as defined in MCSS by the box parameters (see Section
2.1.3); C-2.: displacements (Å) of water molecules from their crystallized positions.
12 Å was used to compute the other non-bonded interactions. The system was simulated
using periodic boundary conditions (PBC), which were considered in the calculations of
long-range interactions for the full system, using the particle-mesh Ewald method 279 with
a grid resolution less than 1.0 Å.
A first minimization-equilibration cycle was performed while both all rhodopsin atoms
and internal water molecules were fixed, and the solvating water molecules were relaxed
by a 10000-step conjugated gradient (CG) minimization, followed by 4-ns NVT MD simulation. In the second minimization-equilibration cycle, the protein backbone atoms were
fixed and the system was again subjected to a 10000-step CG minimization, followed by
4-ns NPT simulation. Subsequently, a third 8-ns NPT equilibration cycle was performed
9.2. Reinventing the wheel of molecular clustering
121
Figure 9.6: Torsion angles. Non-bonded models and associated patches (R010 to R410): A.
SCAL, B. FULLW, C. SCALW, D. STDW. In blue, the distribution of the torsion angles observed
in the MCSS minima. In red, the distribution of the torsion angles observed in the bound
ligands.
122
9. ANNEXES
Figure 9.7: Scoring differences (offset) between the best-ranked pose whatever the nucleotide type and the best-ranked pose for the nucleotide corresponding to the native ligand. Top: STDW model; bottom: SCAL model. The color code indicates the nucleotide type.
with the protein free to move. Finally, a production 100-ns NPT run was performed
without applying any restraint to obtain the 100K trajectory.
9.2.1.6
250 kF
The coordinates of the PHF8 tetramer were derived from the biological assembly of the
Tau peptide (PDB ID 2ON9). All the MD settings were defined using the CHARMM-GUI
interface 249,284,285 and the CHARMM36m force-field 286 . An octahedral water box was
defined using a 10 Å edge distance. Na+ and Cl− ions were added using a physiological
concentration (150 mM) and assigned via the Monte-Carlo protocol.
The MD simulation were carried through NAMD (v2.12) 287 using the TIP3P water
model at 298.15K. The constant temperature was maintained using Langevin dynamics.
All bonds involving hydrogen atoms were constrained with the SHAKE algorithm with
a time step of 2 fs. The minimized structures of the tetramers were subjected to an
equilibration of 1 ns in the NVT ensemble. The production was carried out in the NPT
ensemble. The pressure of 1 atm was maintained with the Nosé-Hoover-Langevin piston
algorithm. Electrostatic interactions were computed with the smooth particle-mesh Ewald
sum 279 ; the real-space part of the Ewald sum and the Lennard-Jones interactions were
truncated using a smooth switching function between 10 and 12 Å.
9.2. Reinventing the wheel of molecular clustering
Features
nwat.low
vol.low
binding site
others
metals
syn
conformational
pur
pyr
no.base.contacts
no.salt.bridges
interaction
no.stacking
clash aa
clash w
Freq. Benchmark
62
69
12
36
12
79
21
12
44
49
22
33
123
Freq. no.pred
59
82
6
24
0
71
23
12
59
53
18
41
Table 9.6: Frequencies of occurrences for molecular features in the Top-10 non-predicted
cases versus benchmark. Others: presence of additional nucleotidic (nucleic acid) fragment in the binding site; metals: presence of metal(s) in the binding site; nwat.low: presence of number of water molecules below the threshold value; vol.low: volume of the
binding site below the threshold value; syn: syn conformation of the nucleic acid base; pyr:
pyrimidine; pur: purine; no.base.contacts: absence of contacts with the nucleic acid base;
clash_aa: clash(es) with amino-acid residues; clash_w: clash(es) with water molecules;
no.salt.bridges: absence of salt-bridge; no.stacking: absence of stacking.
9.2.1.7
500 kF
To generate the 500 kF trajectory, 100000 frames randomly combined 6 kF were concatenated five times.
9.2.1.8
1 MF
The atomic coordinates of a 1.8 Å resolution crystal structure of ubiquitin (PDB ID
1UBQ). The system was inserted in an octahedral box with initial dimensions 70 × 72
× 76 Å, containing 11815 water molecules described with the TIP3P 275 model. The
system was neutralized at near-physiological concentration (150 mM) using Na+ and Cl−
ions. At least 50 Å of distance was left between protein copies of neighboring cells during
molecular dynamics (MD) runs, keeping more than 15.0 Å of space between the ubiquitin
structural model and simulation cell boundaries.
The MD simulation was performed with NAMD (v2.13) 288,289 , applying the CHARMM36 277,278
force field and SHAKE 280 constrains to water molecules bonds. Long-range interactions
were calculated for the full system with periodic boundary conditions (PBC), using the
particle-mesh Ewald method 279 and a grid resolution of less than 1.0 Å, as well as, a cutoff
of 12 Å to compute all other non-bonded interactions. A 100 ns MD run was carried out
at a constant temperature of 310 K and pressure of 1.0 atm by using the Nosé-Hoover
thermostat and barostat 281 while a time-step of 1.0 fs was applied, saving all frames every
124
9. ANNEXES
Figure 9.8: Graphical ribbons representation of 6kF trajectory (backbone) for the first five
clusters retrieved by QT and their related counterpart determined by Daura algorithm.
0.1 ps to obtain 1000000 conformations.
9.2.2 . Reports inaccurately claiming to perform QT clustering
On a careful analysis of 30 scientific works claiming to use QT to retrieve clusters
from MD trajectories, we identify two common pitfalls (labeled as P1 and P2) that appear
in the current literature. In the first group of works (P1) 290–299 , the authors explicitly
describe the algorithm they were using as if it were QT, citing the original paper of Heyer
et al. 214 . Only one of them correctly described the algorithm as Daura clustering 296 but
still cited the incorrect reference, Heyer et al. 214 .
In the second group of works (P2) 300–319 , the authors do not thoroughly describe the
algorithm used but do affirm performing QT when they execute Daura clustering. While
both groups of authors might have wanted to select QT because of the high uniformity
of returned clusters, those in P1, which explicitly describe the foundations of QT, are
more affected because part of their research was built based on incorrect assumptions.
In Figure 9.8, a relationship is established between clusters retrieved by QT and
Daura algorithm. Graphical representation corresponds to ribbons of the 6 kF trajectory’s
backbone. The numbering of clusters (CX) is consistent with that in Figure 4.1. Note
that both algorithms return clusters in decreasing order of size, but this does not imply
that conformations contained in equally numbered clusters are the same. Figure 9.8A
shows that all elements of the first cluster returned by QT (QT-C1) are contained in the
second cluster reported by Daura (Daura-C2). As it is easy to note, Daura-C2 contains, in
addition, many elements (in red) that do not fit well in the uniform conformation depicted
by QT-C1 (black).
The first cluster retrieved by Daura (Daura-C1, Figure 9.8B) is a critical example of
the algorithm selection implications and the risks of confusing both. Retrieved conformations by Daura-C1 are dispersed. It groups two QT clusters, QT-C2 (black) and QT-C3
(blue), representing highly correlated sets of distinct conformations. It is worth noting
that Daura-C1 could be erroneously qualified as the most representative cluster of the
9.2. Reinventing the wheel of molecular clustering
125
simulation, given that it is the most populated one.
The fourth and fifth clusters retrieved by QT (QT-C4 and QT-C5, respectively)
also present a uniform conformation and are entirely contained at Daura-C5 and DauraC4, respectively (Figure 9.8C and D). Once again, clusters retrieved by Daura algorithm
contain elements that deviate from the uniform pattern that QT clusters exhibit. Marked
dispersion of groups returned by Daura method could alter those analyses based on intracluster average properties.
9.2.3 . DP+ pseudocode
Algorithm 5: Get ρ and η for a particular node i
1: function get_node_info(i, k, dc , trajectory )
2:
i_vector = calc_rmsd_vector(i, trajectory)
3:
i_rho = count_elements(i_vector < dc )
4:
i_partition = partial_sort_elements(i_vector, k)
5:
i_eta_elements = sort_elements(i_partition[0 : k])
6:
i_eta_rmsd = i_vector[i_eta_elements]
7:
i_eta = join(i_eta_elements, i_eta_rmsd)
8:
return (i_rho, i, i_eta)
126
9. ANNEXES
Algorithm 6: Compute the Oriented Tree of an MD trajectory
1: function compute_oriented_tree(k, dc , trajectory )
▶ 1. Initialize containers
2:
elements = {1, 2, 3, ..., trajectory.size}
3:
main_heap = create_heap()
4:
auxiliary _heap = create_heap()
5:
rho_inf o = {}
6:
delta_inf o = {}
7:
nearest_neighbors = {}
▶ 2. Find node i whose neighborhood will be analyzed
8:
while T rue do
9:
if main_heap ̸= ∅ then
10:
i, i_rho, i_eta = pop_first_from(main_heap)
11:
else if elements ̸= ∅ then
12:
i = pop_any_from(elements)
13:
i_rho, i, i_eta = get_node_info(i, k, dc , trajectory)
14:
else
15:
break
▶ 3. Try to find j inside ηi
16:
while T rue do
17:
if i_eta ̸= ∅ then
18:
j, rmsd_ij = next(i_eta)
19:
else
20:
send((i_rho, i), auxiliary _heap)
21:
break
22:
if j ∈ elements then
23:
j _rho, j, j _eta = get_node_info(j, k, dc , trajectory)
24:
send((j _rho, j, j _eta), main_heap)
25:
rho_inf o[j] = j _rho
26:
remove_from(elements, j)
27:
else
28:
j _rho = rho_inf o[j]
if j _rho > i_rho then
nearest_neighbors[i] = j
delta_inf o[i] = rmsd_ij
break
▶ 4. Processing the auxiliary heap
33:
while T rue do
34:
if auxiliary _heap ̸= ∅ then
35:
i_rho, i = pop_first_from(auxiliary _heap)
36:
i_vector = calc_rmsd_vector(i, trajectory)
37:
denser_j = get_elements(rho_inf o > i_rho)
38:
j _vector = i_vector[denser_j]
39:
if j _vector ̸= ∅ then
40:
j = get_min_element(j _vector)
41:
delta_inf o[i] = i_vector[j]
42:
nearest_neighbors[i] = j
43:
else
44:
delta_inf o[i] = get_max_value[i_vector]
45:
nearest_neighbors[i] = i
29:
30:
31:
32:
46:
else
47:
break
48: return (delta_inf o, rho_inf o, edges)
9.2. Reinventing the wheel of molecular clustering
127
9.2.4 . RCDPeaks refinements over DP
9.2.4.1
Automatic detection and screening of cluster centers
In the original DP, users must select the cluster centers from the decision graph before the
DP algorithm can assign the remaining elements to each cluster (Figure 9.9A). This selection introduces a potentially biased, user-dependent step that prevents automatic runs.
Several authors have used statistical mechanisms to bypass this step (see reference 228 for
a review) by detecting clusters centers as ρ, δ or γ outliers (Equation 9.1).
γi = ρi ∗ δ i
(9.1)
The gap-based centers selection method proposed by Flores and Garza 228 proceeds
as follows: First, a subset P1 containing elements whose ρ and δ values are higher than
the average defined (discontinue lines in Figure 9.9B). P1 is sorted in descending order of
each γi score. The consecutive point distance (Equation 9.2) between all candidates, as
well as the average point distance (Equation 9.3) are then computed. In this context, a
¯ The last gap in P1 (formed by elements i and i + 1)
gap is formally defined as a di ≥ d.
is considered a threshold and all elements before i are marked as cluster centers.
di = abs(γi − γi+1 )
d¯ =
X di
|Pi |
(9.2)
(9.3)
i∈Pi
The described methodology produced many cluster centers for the trajectories analyzed in this work. Instead of stopping the algorithm after the first loop, RCDPeaks makes
another iteration on a new subset P2 , containing only elements whose ρ and δ values are
higher than the average in P1 (Figure 9.9C). This procedure effectively reduces the number
of candidate clusters, which are intuitively a subset of the original P1 . Iteration continues
until the one-member set Pn is found (Figure 9.9D). All sets from P1 to Pn may be
considered valid automatic guesses of cluster centers. Each of the Pn guesses made by
RCDPeaks will be further processed in n distinct clustering jobs of the same oriented tree
represented by the decision graph in Figure 9.9A. In the analyzed trajectories, n varies
from 2 to 3.
Although RCDPeaks implements the Flores and Garza method, users still have the
choice to set ρ and δ values manually. Also, as the most time-consuming part of RCDPeaks consists of computing those two magnitudes for each element, the software saves
the decision graph. This inexpensive saving allows users to experiment independently
with the result of different ρ and δ cutoffs for cases where the automatic guesses do not
perform as expected.
Centers retrieved by either an automatic or a manual selection may lie within a dc
radius. The original DP unsuccessfully handles these cases by considering all centers as
good choices. RCDPeaks avoids taking into account similar centers through a screening
128
9. ANNEXES
Figure 9.9: Iterative gap-based method of Flores and Garza implemented in RCDPeaks for
the automatic detection of cluster centers. A-) Decision graph. B-D-) Consecutive iterations
of the method produce several automatic guesses of cluster centers.
process that iteratively takes the center of highest γi from Pi as a reference and removes
other centers within a dc distance from further consideration.
9.2.4.2
Clusters core refining
MD clusters generated by the original version of DP usually contain structurally unrelated
elements. Definitions of the core and halo zones (see Section 1.6.2.3) contribute to some
extent to the separation of highly similar elements (core) from more loosely related ones
(halo). However, the original cores obtained by the DP clustering may still display a high
level of dissimilarity, as can be appreciated in Figure 9.10.
Since cluster centers have a preponderant significance in DP, it is reasonable to expect
their geometrical resemblance to elements in their respective cores. RCDPeaks follows a
simple procedure to extract a set of exemplar elements (a refined core), evincing a higher
degree of collective similarity than what can be obtained from the original definition of
core zones in DP. For each cluster Ci , its refined core will consist of those elements
within a dc distance from its cluster center. As shown in Figure 9.10C, this restrained set
9.2. Reinventing the wheel of molecular clustering
129
Figure 9.10: Second cluster of trajectory 6 kF. A-) The raw cluster obtained by the original
DP approach. B-) Cluster core obtained by the original DP approach. C-) refined cluster
core obtained by RCDPeaks.
exhibits considerable uniformity.
9.2.5 . Approaches for computing the quasi-MST in the HDBSCAN* variants
Computing a minimum spanning tree (MST) is an important step of the HDBSCAN
methodology. However, determining the exact MST is a time-consuming task approachable from a heuristic perspective. In HDBSCAN* software, two such heuristics are
employed: (i) the generic and (ii) the Prim alternatives.
9.2.5.1
Generic-based HDBSCAN*
The generic option of HDBSCAN* adopt the Single Linkage (SL) algorithm to obtain
the approximate MST. SL is an agglomerative scheme that groups together elements in a
bottom-up fashion. HDBSCAN* implements SL using three vectors called left (L), right
(R), and current_distances (C). L and R contain the distances to be compared while C
holds the results of such comparison. Concretely, for a trajectory T={1, 2, 3, ..., N}, the
generic implementations of HDBSCAN* work as follows:
1. Initialization of L: L is defined as a vector of length N, filled with an infinite value
at each index.
2. Initialization of R: an element i from T is selected, and R is filled with the distances
from i to all not analyzed elements in T.
3. Initialization of C: the array C gets created and holds the minima of the elementwise comparison of R and L.
4. Edge formation and updating: the minimum distance in C (dij , i ̸= j) is selected
as the weight of a new edge between i and j. L is redefined as R and j becomes
the next element to analyze.
Steps from 2 are repeated until all nodes in T gets analyzed.
130
9. ANNEXES
9.2.5.2
Prim-based HDBSCAN*
Constructing an MST from a set of nodes through the Prims’ algorithm can be done
following the next iterative steps:
1. Find an edge between nodes i and j with the lowest distance.
2. Connect i and j if the resulting graph does not present cycles or self-connections.
The implemented Prims’ algorithm in HDBSCAN* is slightly different from the
original one. It starts selecting the first frame (i) as root node (instead of finding the
lowest distance edge). An edge between i and its nearest neighbor j is created and j is
taken as the next node to analyze. Then the lowest distance of the remaining points and
j is selected as the weight of a new edge. Analyzing non-previously seen vertices, the
algorithm is able to avoids cycles and self-connected nodes. However, it is not possible to
obtain the MST because in each iteration, only the distances associated to a single node
are taken into account.
9.2.6 . Impact of the vp-tree encoding on MDSCAN performance
Table 9.7: Impact of the vp-tree encoding on MDSCAN run time, RAM consumption, and
quasi-MST weight for each analyzed trajectory.
Traj. Name
6 kF
30 kF
50 kF
100A kF
250 kF
500 kF
1 MF
MDSCAN [with vptree]
Run time RAM peak q-MST weight
hh:mm:ss
GB
mrd
0:00:06
0.18
1565.6521
0:00:19
0.21
5286.8418
0:01:37
0.26
2713.9600
0:36:42
1.78
5516.5962
0:37:46
1.20
17354.6699
6:42:18
2.83
1258.8015
21:01:06
7.67
39514.9727
MDSCAN [without vptree]
Run time RAM peak q-MST weight
hh:mm:ss
GB
mrd
0:00:04
0.10
1565.6497
0:00:40
0.12
5286.8511
0:02:00
0.16
2713.9534
0:46:05
0.88
5516.4922
1:16:55
0.67
17354.6445
12:25:49
1.61
1238.6390
37:20:55
4.10
39514.6328
9.2.7 . Cluster composition equivalence between MDSCAN and
HDBSCAN alternatives
In the corresponding graphs of Figure 9.11, nodes depict clusters. The label of each
node is composed of a letter and a cluster ID (ordering starts from 1, the most populated
cluster for a particular letter). Each node’s size correlates to its population, while its
color corresponds to the average diameter of the represented cluster (the darker the node,
the bigger its average diameter). We define as diameter the maximum pairwise distance
between any cluster’s frames. Edges exist if linked nodes have shared frames. Edges’
color and size are consistent with the number of shared frames (the darker and broader
the edge, the greater the number of common frames between linked nodes).
In the 6 kF trajectory (Figure 9.11A, Table 9.8), a total equivalence of the third and
fourth clusters retrieved by all software is appreciated. A similar agreement is shown for
cluster 5 of MDSCAN and the sixth one reported by the HDBSCAN* variants.
9.2. Reinventing the wheel of molecular clustering
131
Figure 9.11: Equivalence of clusters detected in trajectories 6 and 30 kF (A and B sections
respectively) with software A- MDSCAN, B- the generic RMSD-based HDBSCAN*, C- the
generic Euclidean-based HDBSCAN*, and D- the Prim Euclidean-based HDBSCAN*. Each
node represents a cluster. Nodes color corresponds to the average diameter of the cluster
(the darker the node, the bigger its average diameter) while nodes’ size correlates to their
population. The color and size of edges map to the number of common frames between
two clusters (the darker and wider the edge, the greater the number of common frames
between the linked nodes.)
Interestingly, the first and second clusters produced by all variants of HDBSCAN*
are identical but MDSCAN splits each of them in two smaller groups of less diameter;
A2 and A6 for the first cluster, and A1 and A12 for the second cluster. A9 is fully contained in the bigger and wider cluster 5 produced by HDBSCAN* alternatives. Finally,
HDBSCAN* variants reported a seventh cluster not detected with MDSCAN, while
MDSCAN identified another four clusters not recognized with any of the HDBSCAN*
implementations: A7, A8, A10, and A11.
The relationship between the representative clusters reported for trajectory 30 kF
(Figure 9.11B, Table 9.9) is not as pronounced as in the 6 kF case.
The only instance of total equivalence among the HDBSCAN* implementations is
for their first cluster, which is split by MDSCAN in five smaller and tighter clusters (A3,
A5, A6, A11, and A12). A high overlap (though not total) is also observed in several cases:
(i) between the seventh cluster of MDSCAN and the fifth of HDBSCAN* variants, (ii)
between B4, C6, and D7 (which contain some frames of A4), (iii) between A1, C3, and
D2, and finally (iv) between A2, C4, and D3 (this partition is split by the generic RMSDbased, implementation of HDBSCAN* in B2 and B3). The big cluster C2 produced by
the generic Euclidean-based implementation of HDBSCAN* contain frames that have
been split into several smaller and tighter clusters by MDSCAN (A8, A9, A10, and A15),
and by the Prim Euclidean-based HDBSCAN* (D4, D6, D8, and D10). Also, C2 shares
some frames with the generic RMSD-based variant (B6).
132
9. ANNEXES
Table 9.8: Equivalence of representative clusters in the 6 kF trajectory
generic-Eucl.
Prim-Eucl.
HDBSCAN*
generic-RMSD
MDSCAN
Software
Cluster-ID
Size
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
B1
B2
B3
B4
B5
B6
B7
C1
C2
C3
C4
C5
C6
C7
D1
D2
D3
D4
D5
D6
D7
213
210
200
145
131
99
80
79
78
74
70
62
363
287
200
145
135
131
73
363
287
200
145
135
131
73
363
285
200
145
135
131
73
Average Diameter
()
2.36
2.61
2.81
3.41
2.27
2.67
4.44
4.91
2.48
5.33
3.08
2.07
3.10
2.56
2.81
3.41
3.05
2.27
2.33
3.10
2.56
2.81
3.41
3.05
2.27
2.33
3.10
2.55
2.81
3.41
3.05
2.27
2.33
Intersecting clusters
(# common frames)
B2(213), C2(213), D2(211)
B1(210), C1(210), D1(210)
B3(200), C3(200), D3(200)
B3(145), C3(145), D3(145)
B6(131), C6(131), D6(131)
B1(99), C1(99), D1(99)
B5(78), C5(78), D5(78)
B2(62), C2(62), D2(62)
A2(210), A6(99), C1(363), D1(363)
A1(213), A12(62), C2(287), D2(285)
A3(200), C3(200), D3(200)
A4(145), C4(145), D4(145)
A9(78), C5(135), D5(135)
A5(131), C6(131), D6(131)
C7(73), D7(73)
A2(210), A6(99), B1(363), D1(363)
A1(213), A12(62), B2(287), D2(285)
A3(200), B3(200), D3(200)
A4(145), B4(145), D4(145)
A9(78), B5(135), D5(135)
A5(131), B6(131), D6(131)
B7(73), D7(73)
A2(210), A6(99), B1(363), C1(363)
A1(211), A12(62), B2(285), C2(285)
A3(200), B3(200), C3(200)
A4(145), B4(145), C4(145)
A9(78), B5(135), C5(135)
A5(131), B6(131), C6(131)
C7(73), D7(73)
9.3 . NUCLEAR: an efficient assembler for the FBDD of CMOs
9.3.1 . NUCLEAR performance in oligonucleotide searches
9.4 . In-silico design of selective CMO against BACE1
9.4.1 . BACE1 protein candidates selection
The PDB database was queried using the string beta secretase 1 OR beta-secretase 1,
returning 415 structures. PDB files header contains a field of related_entries that could
be useful to analyze, so we adjusted these 40 related structures for completeness to the
already found (415 + 40 = 455). Fetched PDBs contain chains and models that must be
split into individual files for further analyses. The splitting stage produced 884 individual
132
9. ANNEXES
Table 9.9: Equivalence of representative clusters composition in the 30 kF trajectory
generic-Eucl.
Prim-Eucl.
HDBSCAN*
generic-RMSD
MDSCAN
Software
Cluster-ID
Size
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
B1
B2
B3
B4
B5
B6
C1
C2
C3
C4
C5
C6
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
D11
4251
2646
1754
999
870
735
680
641
506
471
468
445
394
379
336
6541
1939
702
698
651
640
6541
4632
3986
2642
644
550
6541
4090
2638
893
672
636
552
507
401
372
372
Average Diameter
()
2.8
5.76
2.71
4.11
2.52
2.98
2.65
2.95
3.04
2.71
4.87
2.97
1.83
4.82
3.37
4.63
5.57
4.87
3.29
2.5
2.95
4.63
5.89
2.7
5.76
2.48
2.80
4.63
2.73
5.76
4.89
2.59
2.93
2.80
2.81
4.08
2.89
4.44
Intersecting clusters
(# common frames)
C3(3986), D2(4090)
B2(1939), B3(702), C4(2642), D3(2637)
B1(1754), C1(1754), D1(1754)
B4(599), C6(550), D7(552)
B1(870), C1(870), D1(870)
B1(735), C1(735), D1(735)
B5(651), C5(644), D5(672)
B6(640), C2(641), D6(636)
C2(506)
C2(471), D8(412)
B1(468), C1(468), D1(468)
B1(445), C1(445), D1(445)
C2(336), D4(328)
A3(1754), A5(870), A6(735), A11(468), A12(445), C1(6541), D1(6541)
A2(1939), C4(1938), D3(1935)
A2(702), C4(702), D3(701)
A4(599), C6(550), D7(552)
A7(651), C5(644), D5(651)
A8(640), C2(640), D6(636)
A3(1754), A5(870), A6(735), A11(468), A12(445), B1(6541), D1(6541)
A8(641), A9(506), A10(471), A15(336), B6(640), D4(893), D6(636), D8(507), D10(372)
A1(3986), D2(3981)
A2(2642), B2(1938), B3(702), D3(2637)
A7(644), B5(644), D5(644)
A4(550), B4(550), D7(549)
A3(1754), A5(870), A6(735), A11(468), A12(445), B1(6541), C1(6541)
A1(4090), C3(3981)
A2(2637), B2(1935), B3(701), C4(2637)
A15(328), C2(893)
A7(672), B5(651), C5(644)
A8(636), B6(636), C2(636)
A4(552), B4(552), C6(549)
A10(412), C2(507)
C2(372)
-
structures filtered to preserve only those similar to a BACE1 reference (1SGZ-A).
A pairwise sequence alignment was performed between the 884 targets against the
1SGZ-A reference. The alignment score (ranging from 0 to 100) was calculated as follows,
where nresids_aligned represents the number of residues in the target that aligns to the
reference and nresids_reference is the total number of residues in the reference:
score = (nresids_aligned/nresids_ref erence) ∗ 100
(9.4)
The following fields for each structure were computed: (i) a unique identifier {PDB
code}-{chain/model}, (ii) the score (by Equation 9.4), (iii) the sequence identity, (iv) the
sequence overlap, (v) the crystallization pH, (vi) the resolution, (vii) R (distance from
CG-Asp32 to OH-Tyr71 ), and (i) psi (pseudo-dihedral C-Trp76, N-Val69, CA-Thr72,
CA-Gln73 ).
Structures with sequence identity less or equal to 75% against 1SGZ-A were removed
from further analyses. There were many presenting gaps from the remaining 693 structures similar to 1SGZ-A. We defined a gap as a protein’s region with missing residues
(discontinuities in the residue enumeration) and discarded affected structures.
The 171 structures without gaps were submitted to a clustering procedure aiming
to select just a few geometrically distant models for docking stages. We conserved all
9.4. In-silico design of selective CMO against BACE1
133
Table 9.10: NUCLEAR performance for the global geometric (GG) oligonucleotide searches
performed on proteins 2XNR, 5WWX, and 5ELH. The following timings are reported: (i) the
time taken to parse the MCSS docking distributions (t1), (ii) the time taken to construct both
binary matrices (t2), and (iii) the time taken to perform the actual search of chains (t3).
Additionally, the total elapsed time and the peak memory usage for each job is reported.
Protein
RMSD
d(C5′ − O3′ )
#Poses
#Chains
t1
15694
677268
6492116
34213514
3849
164885
1595613
8447693
338
17638
176381
953535
37619
1658706
17435561
98355759
9001
412382
4337966
24619477
1130
8334
537549
3068691
14965
562254
5008076
25863579
3037
114771
1056292
5508112
245
11335
110845
596755
2
2
2
2
46
44
44
47
17
17
19
20
6
6
6
6
194
192
191
206
79
80
82
93
2
2
2
2
35
34
35
38
13
12
13
15
[Å]
0
2XNR
1
2
0
5WWX
1
2
0
5ELH
1
2
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
9075
5552
2696
22818
14664
7494
8473
4881
2262
t2
t3
Total time
[seconds]
64
5
71
63
13
78
62
82
146
69
425
496
24
4
74
23
6
73
21
22
87
24
103
174
3
0
20
3
4
24
4
7
30
5
17
42
315
5
326
309
27
342
301 241
548
349 1396
1751
112
5
311
111
10
313
110
61
362
124 343
673
22
1
102
27
5
112
26
11
119
29
44
166
81
5
88
99
22
123
79
64
145
92
328
422
26
3
64
25
6
65
25
17
77
27
71
136
3
0
16
8
0
20
5
5
23
5
12
32
RAM Peak
[MB]
396
269
265
396
396
224
225
396
396
219
219
396
396
517
396
396
396
393
523
396
396
301
301
396
396
272
271
396
396
213
215
396
396
209
209
396
equivalent atoms between the 171-group (2798). The Active Site Region (ASR) was
defined as the atoms within 8Å of the residues Asp32 and Asp228 plus the atoms involved
in the flap region (residues from 67 to 77). Then we used the BitQT formalism (see
Section 4.1) with a cutoff of 1Å on the RMSD matrix of the 171-group ASRs.
Nevertheless, the ASR is rigid, exhibiting only modest conformational variability in
the flap zone. By using BitQT, five homogeneous clusters were obtained. However, the
RMSD metric is inaccurate to capture the Tyr-71 orientation, an essential residue in the
BACE1 active site and the most significant source of conformational diversity in the
clustered structures.
In the particular case of the BACE1 ASR, a couple of order parameters character-
134
9. ANNEXES
izing the flap conformation have been previously identified: R and psi. We plotted the R
vs. psi values of the 693 individual structures similar to 1SGZ-A. As it can be appreciated
in Figure 9.12A, the R/psi regions observed roughly correspond to the regions described
in the MD explorations of holo/apo BACE1 181 .
To produce Figure 9.12B, we used the density-based clustering algorithm HDBSCAN
in the Cartesian space of R/psi values (both normalized to 0-1 range beforehand). Seven
dense clusters were found.
Keeping the previous cluster labels, we restricted the analysis to the 171-structures
group without gaps. As depicted in Figure 9.12C, six clusters were retrieved. In Table
9.11, we detail some information on the representative structure of each.
Table 9.11: Representative structures after the HDBSCAN clustering procedure.
Cluster
1
2
3
4
5
6
6
Selected
1SGZ-A
3SKG-D
6UVV-A
4FSL-A
6BFW-A
5MCQ-A
4GID-A
pH
6.5
6.2
7.4
6.2
N/A
4.5
6.5
Resolution
1.80
2.88
1.63
2.50
1.84
1.82
2.00
R / Psi
11.29 / 10.77
7.52 / 12.71
7.6 / -6.28
6.64 /-19.39
6.68 / 19.21
6.60 / -2.15
6.44 / -9.15
#waters
234
20
588
215
416
551
316
# waters@ASR
13
2
20
13
17
14
9
It should be highlighted that cluster 2 only has 1 member with poor resolution,
cluster 4 has only 2 structures with poor resolution and similar to cluster 6, while cluster
5 structures are similar to cluster 6. So the final set of BACE1 conformations comprises
clusters 1, 3, and 6 as candidates to start docking studies. These structures have good
resolution and an appropriate number of water molecules at the ASR.
There is a region of BACE proteins called exosite surrounded by three loops where
inhibitors also bind preferentially (loop C, D, and F comprising residues 254-257, 270-274,
and 309-320, respectively) 320 . Apart from the three structures selected (1SGZ, 4GID, and
6UVV), which are conformationally different at the ASR, we chose 5MCQ, which belongs
to cluster 6 (so having a similar arrangement of the ASR that 4GID) but whose exosite
presents a different conformation.
9.4.2 . Modified nucleotides present at the MCSS library
9.4.3 . Key interactions of CMO-BACE-X complexes
135
Figure 9.12: Plot of distance R vs. pseudo-dihedral psi of the 693 individual structures similar to 1SGZ-A)
136
9. ANNEXES
Figure 9.13: Superposition of the four BACE1 selected conformations; 1SGZ (red), 4GID
(blue), 5MCQ (orange), and 6UVV (purple).
Figure 9.14: A-derived modified nucleotides present at the MCSS library.
Figure 9.15: C-derived modified nucleotides present at the MCSS library.
Figure 9.16: G-derived modified nucleotides present at the MCSS library.
Figure 9.17: U-derived modified nucleotides present at the MCSS library.
Figure 9.18: U-derived modified nucleotides present at the MCSS library (continuation of
Figure 9.17).
142
9. ANNEXES
Figure 9.19: “Near-10s loop region” of BACE1 (A) and BACE2 (B) colored by residue type.
RÉSUMÉ ÉTENDU
INTRODUCTION
La découverte de médicaments est un processus complexe et long qui comporte
plusieurs étapes, de l’identification d’une cible biologique à l’approbation d’un nouveau
médicament par les organismes de réglementation. La tâche peut prendre plusieurs années
et des milliards de dollars, avec un taux d’échec élevé à chaque étape 1 . La première de
ces étapes consiste à identifier une cible biologique qui joue un rôle dans le processus de
la maladie. Une fois identifiés, les chercheurs utilisent diverses approches pour découvrir
des candidats-médicaments potentiels qui peuvent interagir avec la cible et moduler son
activité 2 .
De la famille de cibles médicamenteuses connues jusqu’à présent, les protéines sont
les membres les plus courants 3 . Leur inhibition joue un rôle essentiel dans la découverte
de médicaments, car elle fournit un moyen de supprimer leur participation à une maladie
particulière. Cependant, le blocage d’une protéine spécifique est difficile et rencontre
souvent l’effet dit off-target. Ce terme décrit les événements qui peuvent se produire
lorsqu’un médicament se lie à des cibles (protéines ou autres molécules dans le corps)
autres que celles pour lesquelles il était censé se lier, provoquant des effets secondaires
inattendus et potentiellement nocifs 4 .
La conception de médicaments par fragments (FBDD) est un moyen rationnel de
concevoir la conception d’inhibiteurs de protéines. Il commence par une petite collection
de molécules de faible masse moléculaire et de faible affinité appelées fragments, puis
les intègre dans les médicaments de plus haut poids moléculaire 5 . Il y a plusieurs cas de
réussite lorsque FBDD a été appliqué à la conception et à la découverte de médicaments,
avec plus de 30 candidats à base de fragments entrant dans la clinique depuis le milieu
des années 1990 5–9 .
L’acide ribonucléique (RNA) et les molécules dérivées sont apparus comme des outils
prometteurs pour l’inhibition sélective des protéines en raison de leur spécificité élevée,
de leur faible immunogénicité et de leurs propriétés physico-chimiques ajustables 10 . Par
exemple, le développement d’aptamères (oligonucléotides courts simple brin d’acide désoxyribonucléique (DNA) ou RNA comme agents thérapeutiques a fait l’objet d’intenses
recherches, de nombreuses études faisant état de leur application réussie dans le traitement de diverses maladies 11 . Les avantages des aptamers comprennent leur facilité de
génération, leur faible coût de fabrication et leur faible immunogénicité. Cependant, ces
molécules doivent subir des modifications chimiques pour éviter leur susceptibilité inhérente à l’hydrolyse des nucléases et à une clairance rapide par filtration glomérulaire 12 .
Les alliés éprouvés des campagnes expérimentales de découverte de médicaments
sont les méthodes computationnelles ou in silico, qui réduisent les coûts de temps et
de ressources grâce à des simulations virtuelles. Lorsque l’on recherche de nouveaux
médicaments, une étape névralgique consiste à examiner d’immenses bases de données
144
9. ANNEXES
représentatives de l’espace chimique du médicament pour trouver un remède moléculaire
approprié à une maladie. Les méthodes d’amarrage informatique jouent un rôle essentiel, et de nombreuses alternatives sont disponibles pour les chercheurs 13 . Dans l’arène
FBDD, le logiciel Multiple-Copy Simultaneous Search (MCSS) 14 se distingue comme
une méthodologie virtuelle pionnière pour l’amarrage qui a été précédemment couplée
à d’autres logiciels pour joindre des fragments dans des composés de départ sujets à
optimisation 15–19 .
Les algorithmes de clustering (dédiés au regroupement d’entités similaires en ensembles appelés clusters) 20 sont utilisés à différentes étapes du pipeline FBDD (bien que
souvent de manière transparente pour les utilisateurs), principalement pour regrouper
des fragments ou des composés similaires en fonction de leurs propriétés structurales
ou physicochimiques. La conception de nouveaux algorithmes de clustering efficaces ou
l’optimisation de ceux actuellement utilisés est obligatoire pour faire face à la taille croissante des ensembles moléculaires générés par les techniques de calcul.
La présente thèse porte sur la conception computationnelle basée sur des fragments
d’oligonucléotides chimiquement modifiés (inspirés par le développement et le succès des
aptamères) pour l’inhibition sélective des protéines, en utilisant β-site Amyloid Precursor Protein Cleaving Enzyme 1 (BACE1) comme étude de cas. BACE1 est une cible
thérapeutique bien établie pour la maladie d’Alzheimer (AD) en raison de son rôle essentiel dans la production de peptides amyloïdes-bêta, qui sont les principaux constituants
des plaques amyloïdes dans le cerveau des patients atteints de la maladie d’Alzheimer.
L’un des principaux inconvénients du ciblage de BACE1 réside dans l’inhibition hors
cible démontrée par une protéase apparentée, β-site Amyloid Precursor Protein Cleaving
Enzyme 2 (BACE2) 21 .
Bien que les thérapies RNA (y compris les alternatives d’aptamères) soient de
plus en plus populaires, il n’existe pas de méthodologie pour la conception rationnelle
d’oligonucléotides chimiquement modifiés sélectifs pour des applications médicales, ce qui
constitue le problème scientifique ici adressé.
Le travail suivant a été conçu sur l’hypothèse globale hypothèse que les principes
FBDD peuvent être appliqués efficacement à la conception rationnelle in silico d’oligonucléotides
chimiquement modifiés avec une affinité et une sélectivité élevées pour les cibles protéiques.
L’objectif principal de cette thèse est de développer un cadre de calcul intégré pour la
conception par fragments d’oligonucléotides chimiquement modifiés avec une affinité et
une sélectivité élevées pour les cibles protéiques, en utilisant BACE1 comme preuve de
concept pertinente. Les objectifs spécifiques qui ont guidé nos efforts sont les suivants :
1. Évaluer les pouvoirs d’arrimage et de criblage de la methodologie MCSS sur un
benchmark représentatif de complexes nucléotidiques de protéines.
2. Optimiser des algorithmes de clustering populaires qui interviennent à des phases
distinctes du FBDD.
3. Mettre en œuvre un schema informatique efficace pour assembler des nucléotides
9.4. In-silico design of selective CMO against BACE1
145
(fragments) chimiquement modifiés sur des oligochaînes.
4. Valider un workflow de calcul pour proposer des oligonucléotides chimiquement
modifiés comme inhibiteurs de protéines sélectives en utilisant BACE1 comme
étude de cas.
Main results
PRÉDICTIONS DE LA LIAISON ET LA SÉLECTIVITÉ DES NUCLÉOTIDES AVEC MCSS
Fréquemment, les workflows virtuels de conception de médicaments par fragments
présentent une limitation significative; le manque de performance des méthodes d’amarrage
en raison de la nature approximative de leurs fonctions de score. Une hypothèse fondamentale de ce manuscrit est qu’en employant le logiciel MCSS, une performance accrue
dans l’amarrage et la puissance de criblage est possible, faisant de cet outil un choix approprié pour les procédures de conception de médicaments à base de fragments impliquant
des nucléotides.
Nous avons présenté un ensemble de données actualisé et représentatif de complexes
protéine-nucléotide à haute résolution dans lesquels seuls les ligands mono-phosphate de
nucléotide, en tant que ligands mono-résidu, sont inclus. La composition globale du
référentiel, les descripteurs utilisés pour caractériser les sites de liaison à l’étude et la
répartition des contacts sont analysés.
Nous avons accordé une attention particulière à l’effet des modèles de solvants et
des patchs de phosphate sur le nombre de poses générées et la fraction de poses natives
obtenues. Le nombre total de poses générées dépend principalement du modèle de solvant
et du timbre de phosphate dans une moindre mesure.
La présence de molécules d’eau explicites réduit partiellement le volume moléculaire
accessible pour les nucléotides dans la région de liaison. Ainsi, le nombre de poses générées
avec le modèle SCAL est beaucoup plus grand que celui généré avec l’un des modèles
de solvants hybrides : SCALW, FULLW et STDW (Figure 9.20). La comparaison des
distributions brutes et en cluster montre également que le modèle SCAL présente la
redondance la plus élevée dans les poses générées, démontrée par la plus grande différence
entre les distributions brutes et en cluster pour chaque patch.
La fraction des poses natives sur l’ensemble de la distribution MCSS pour tous
les modèles et patchs de solvants est similaire, sauf pour R310. Le patch R310 porte un
groupe méthyle dans l’un des phosphates oxygène. Ce groupe confère la capacité d’établir
plus de contacts hydrophobes que les autres patchs. Le modèle SCAL montre une fraction
significativement plus faible de poses natives que les modèles solvatés malgré un nombre
beaucoup plus important de poses générées (Figure 9.20).
Quant au nombre de poses, les distributions brutes et groupées sont plus dispersées
en l’absence de molécules d’eau. Dans les modèles solvatés, les fractions de poses natives
pour SCALW et STDW sont très similaires. D’autre part, le modèle FULLW a plus de
cas où aucune pose native n’est trouvée, comme le montre le déplacement à zéro de la
146
9. ANNEXES
Figure 9.20: Nombre de poses générées pour les 121 complexes protéine-nucléotide pour
chaque nucléotide 5’ patché (010, 110, 210, 310, 410). Les résultats pour les distributions
brutes (R) et groupées (C) sont affichés.
première section inter-quartile sur les boxplots (Figure 9.20).
Après cela, la puissance d’amarrage de MCSS, ainsi que sa puissance de criblage,
ont été respectivement évaluées. La performance en puissance d’amarrage est évaluée sur
tous les modèles et patchs en utilisant les mesures standard basées sur les poses natives
trouvées dans les scores Top-1 à Top-100 avec les rangs intermédiaires: Top-5, Top-10 et
Top-50. Les meilleures performances sont obtenues avec les modèles SCALW et STDW,
quel que soit le patch utilisé (Figure 9.21). Le modèle STDW surpasse légèrement le
modèle SCALW dans le Top-1 et le Top-10 pour tous les patchs (sauf pour R310, où la
performance est équivalente pour le Top-10).
La meilleure performance est obtenue pour le patch R310. Il a un taux de réussite
de 40% dans le Top 1, plus de 60% dans le Top 10 et plus de 80% dans le Top 100.
Cependant, le gain de performance concernant les autres patchs est infime dans le Top10 et le Top-50. Le clustering ne modifie pas les tendances générales observées dans les
distributions brutes, mais il augmente légèrement la performance dans le Top-100 et, dans
une moindre mesure, dans le Top-i . La discussion s’est terminée par la présentation des
caractéristiques moléculaires associées au manque de prédictions.
9.4. In-silico design of selective CMO against BACE1
147
Figure 9.21: Représentation de l’histogramme empilé des poses natives classées Top-i
générées pour les 121 complexes protéine-nucléotide pour chaque patch nucléotidique. Les
distributions brutes (en haut) et groupées (en bas) de textbfR: et de textbfC: sont affichées.
RÉINVENTER LA ROUE DU REGROUPEMENT MOLÉCULAIRE
Nous avons présenté nos efforts pour diminuer les ressources spatiales de quatre
algorithmes de clustering géométriques déjà appliqués aux ensembles moléculaires : (i) les
algorithmes Quality Threshold (QT), (ii) le Daura, (iii) le Density Peaks (DP), et (iv) le
Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN).
Nos implémentations ont été comparées aux méthodes alternatives les plus utilisées.
Pour chacun d’entre eux, une nouvelle idée qui a eu un impact significatif sur leur consommation de mémoire a été développée. Un encodage binaire de la similarité moléculaire par
paires (ainsi que la possibilité de traduire les étapes de clustering en opérations bit à bit)
a été appliqué au clustering de Daura et du Quality Threshold. En outre, une correction
méthodologique a été soulevée pour ces deux algorithmes qui ont été incorrectement et
systématiquement utilisés de manière interchangeable.
QTPy a seulement été suggéré comme preuve de concept pour mettre en évidence
les inexactitudes des autres alternatives de clustering qui prétendent sans faille effectuer
QT. Il ne constitue pas une optimisation correcte, et sa complexité spatiale est O(n2 ).
Néanmoins, nous avons utilisé des valeurs flottantes de demi-précision pour représenter
RMSD, permettant ainsi à la matrice de similarité QTPy de consommer la moitié de
l’espace requis par les alternatives qui utilisent des matrices de similarité de flotteurs de
précision simple, telles que l’option gromos de GROMACS.
BitQT et BitClust adoptent la même approche pour raccourcir les exigences de
mémoire des algorithmes Daura et QT en codant les distances entre paires RMSD en
148
9. ANNEXES
bits. Par conséquent, malgré leur complexité spatiale quadratique, ils peuvent traiter des
trajectoires considérablement plus grandes que les implémentations existantes.
L’algorithme DP+ représente une tentative d’atténuer la complexité spatiale quadratique intrinsèque aux approches DP. Au lieu de construire une matrice complète, notre
méthode fonctionne sur des vecteurs transitoires de taille N (où N est le nombre de
conformations moleculaires) et deux tas qui peuvent étendre l’utilisation de la mémoire.
Le tas secondaire comprend les tuples (i, rho), qui représentent l’indice et la valeur de
densité de la trame.
Dans le pire des cas, ce tas s’étend aux entrées N avec une complexité spatiale
de N · (O(1) + O(1)) ≡ O(N ), démontrant ainsi une mise à l’échelle linéaire avec la
longueur de la trajectoire. Le tas primaire comprend les éléments mentionnés ci-dessus et
un sous-ensemble plus petit etai de taille 0.02 · N . Si nous traitons ceci comme un facteur
constant c, même si le tas principal atteint sa taille maximale de N tuples, la complexité
reste N · (O(1) + O(1) + O(c)) ≡ O(cN ), toujours linéaire. Il convient de noter que de
tels scénarios extrêmes sont peu probables avec une sélection prudente des paramètres.
L’objectif principal de MDSCAN était d’atténuer la complexité quadratique des alternatives HDBSCAN* disponibles lors de l’utilisation de mesures de grande dimension
comme la RMSD. Remarquablement similaire à DP+, MDSCAN utilise les mêmes structures de données de tas et vecteurs transitoires déjà détaillés. La seule distinction réside
dans le type d’information que ces tas contiennent; par conséquent, l’analyse de complexité spatiale du pire des cas présentée pour DP s’applique à MDSCAN. Cependant,
MDSCAN traite le fichier de trajectoire différemment de tous les autres logiciels proposés
ici, car un arbre de “vantage points” est construit, nécessitant une copie de la trajectoire.
Ce traitement n’augmente pas la complexité spatiale de l’algorithme, bien qu’il nécessite
plus d’espace par rapport à DP.
NUCLEAR: UN ASSEMBLEUR EFFICACE POUR LA CONCEPTION PAR FRAGMENTS D´OLIGONUCLÉOTIDES CHIMIQUEMENT MODIFIÉS
Bien que plusieurs outils de liaison de fragments soient disponibles dans la littérature,
aucun ne convient à être inclus dans notre approche principalement pour les raisons
suivantes : (i) ils ne peuvent pas fonctionner avec les formats de fichiers provenant des
logiciels MCSS et CHARMM (PSF, DCD), (ii) ils ne sont pas conçus pour lier les
oligonucléotides de C5’ à O3’ garantissant des solutions sans conflit, et surtout (iii) ils
sont incapables de traiter de gros volumes de données.
En tenant compte des limites susmentionnées, nous avons présenté un nouveau logiciel
appelé NUCLEotide AssembleR (NUCLEAR). NUCLEAR peut effectuer différents
types de recherches d’oligonucléotides et récupérer des “hotspots” dans le récepteur à
partir des distributions de fragments ancrés. Après avoir présenté les flux de travail
disponibles dans NUCLEAR, nous avons détaillé le protocole de recherche des points
chauds à la surface du récepteur.
Plus tard, les recherches d’oligonucléotides sous contrainte de séquence et spatiale
sont décrites. Enfin, nous avons essayé la reproduction de trois structures cristallines en
9.4. In-silico design of selective CMO against BACE1
149
utilisant NUCLEAR comme études de cas pour discuter du coût de calcul des principales
étapes de l’algorithme, et pour approfondir ses limites.
CONCEPTION IN-SILICO D´OLIGONUCLÉOTIDES CHIMIQUEMENT MODIFIÉS SELECTIFS CONTRE BACE-X
Une fois que la nature des mono-nucléotides modifiés chimiquement et les conformations protéiques considérées sont présentées, nous illustrons comment attaquer le problème
de l’assemblage des oligonucléotides dans deux situations; quand des informations pratiques sur les interactions protéines-receptor sont limitées ou indisponibles, et quand les
connaissances sur ces interactions sont accessibles via des bases de données moléculaires.
Dans la dernière partie de la discussion, nous nous concentrons ensuite sur le discernement si les oligonucléotides produits ont le potentiel d’être sélectifs contre la protéine
BACE1 sur BACE2 en implémentant plusieurs contraintes de sélection à leurs modes
de liaison. La base moléculaire sous-jacente aux modes de liaison de la Figure 9.22 a été
étudiée en examinant les contacts étroits, les liaisons hydrogène, les ponts salins, les interactions hydrophobes, π − π, T-stacking et π−cation entre l’CMOs et l’BACE-X. Cette
analyse a été effectuée en utilisant les valeurs géométriques par défaut du programme
BINANA et pour tous les membres des clusters inspectées.
Le mode de liaison inhabituel du groupe 4 chez BACE1, soutenu par l’empilement
de π − π (TYR68), les liaisons hydrogène (LYS75, GLU77, SER328) et les interactions
des ponts de sel (LYS75 et GLU77), n’a pas de contrepartie chez BACE2. Cette liaison,
bien qu’anormale, s’aligne sur les recommandations d’autres auteurs de cibler la région du
lambeau, où la forme et la flexibilité diffèrent entre les enzymes BACE-X 21,172 . Dans
l’ensemble, malgré la similitude revendiquée entre les protéines BACE-X, notre analyse
révèle que les CMOs les mieux classés interagissant avec elles sont positionnés différemment, non seulement dans le site actif, mais aussi dans d’autres sous-sites protéiques
cruciaux pour l’ancrage moléculaire.
Conclusions
1. Le logiciel Multiple-Copy Simultaneous Search a été évalué pour l’ancrage des nucléotides sur un benchmark de 121 complexes protéiques. Différents modèles de
solvant et de phosphate ont été testés pour optimiser le taux de réussite pour identifier les poses natives (puissance d’amarrage) et le nucléotide natif réel (puissance
de criblage). En conséquence, le modèle STDW combiné avec le patch phosphate
R310 semble donner les meilleures performances, surpassant plusieurs fonctions
de score. La présence de molécules d’eau dans la préparation et l’optimisation de
la structure protéique permet à la structure minimisée de s’écarter moins de la
structure expérimentale.
2. Quatre algorithmes de clustering populaires ont été significativement optimisés
pour permettre leur application à des phases distinctes de l’Fragment-Based Drug
Design. Grâce au stockage binaire, la traduction binaire des opérations primaires,
150
Figure 9.22: Les cinq premiers clusters des inhibiteurs sélectifs potentiels de BACE-X. Les régions rouges, bleues et vertes correspondent respectivement
au site actif, au “flap” et aux régions de boucle 10s. Les oligonucléotides sont représentés sans protons et les atomes de phosphore ont été mis en
évidence pour une meilleure clarté visuelle. Le nucléotide rouge démarre l’oligomère dont la séquence est présentée dans le tableau 9.12.
9.4. In-silico design of selective CMO against BACE1
151
ou la reformulation complète des algorithmes, les versions exactes (BitClust, DP+)
et modifiées (BitQT, RCDPeaks, MDSCAN) de la proposition originale ont été
présentées et soigneusement comparées. Une confusion méthodologique entre
Quality Threshold et les algorithmes de Daura a été exposée à la communauté.
3. Un liant informatique efficace pour l’assemblage d’Chemically Modified Oligonucleotides (fragments) sur des oligochaînes a été développé. Notre NUCLEotide
AssembleR a été capable de renvoyer des séquences sans conflits geometriques
suivant des contraintes distinctes (en séquence ou région d’exploration) et a pu
identifier (malgré des limitations inhérentes) plusieurs modes de liaison expérimentaux dans trois études de cas. Une autre fonctionnalité nécessaire de ce logiciel
est la détermination des “hotspots” à la surface de la cible pour guider l’FragmentBased Drug Design.
4. Nous avons conçu un flux de travail basé sur des fragments in silico qui produit des
modes de liaison à faible énergie d’Chemically Modified Oligonucleotides (obtenus
par l’amarrage NUCLEotide AssembleR après Multiple-Copy Simultaneous Search)
démontrant une sélectivité structurelle contre l’enzyme BACE1 sur les BACE2.
Les modes de liaison BACE1 les mieux classés peuvent traverser linéairement la
région active du site ou interagir simultanément avec le côté supérieur du volet et
le site actif, tandis que des modes de liaison similaires ne sont pas détectés pour
BACE2.
152
Clust. size
105
268
119
160
36
16
11
36
8
34
Clust. ID
1
2
3
4
5
1
2
3
4
5
Protein
BACE1
BACE2
3MC-YYG-K2C-3AU-PBG-OMG
5CU-PBG-K2C-3AU-PBG-OMG
ADE-BUG-5HU-5CU-MAU-BUG
R2C-BUG-MSU-R2C-ADE-HWG
R2C-BUG-THY-R2C-5HU-PBG
R2C-OAU-1MA-OAU-3MC-R2C
HWG-R2C-OAU-1MG-T6A-SIA
13P-70U-OAU-BUG-6IA-HWG
HNA-OAU-K2C-HCU-OAU-GUA
OAU-70U-OAU-BUG-MMA-HWG
Chain
-180.66
-178.5
-168.2
-159.84
-159.32
EINT
[kcal/mol]
-177.46
-170.97
-165.99
-165.77
-163.89
10
18
174
20
22
13
11
22
3
43
Rank
31
34
28
27
27
24
29
31
23
28
#contacts
0.77
0.78
0.71
0.83
0.93
0.82
0.90
0.88
0.88
0.87
TI
0.98
0.99
0.98
1.00
0.93
RMSD
[Å]
1.00
0.97
0.92
1.00
0.88
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Selectivity
Table 9.12: Descripteurs d’inhibiteurs sélectifs potentiels de BACE-X. La colonne Selectivity fait référence à Si (B1) ou Si (B2) pour BACE1 ou BACE2,
respectivement.
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