PaperlayerView exact revision on arXiv

Source-linked AI summary

Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges

Duc Duy Nguyen, Zixuan Cang, Kedi Wu, Menglun Wang, Yin Cao, Guo-Wei Wei

arXiv:1804.10647v1q-bio.BM

TL;DR

The paper addresses pose prediction and binding-affinity ranking in difficult drug-design benchmarks. It integrates multiscale weighted colored graphs, element-specific persistent homology, and machine learning, achieving top performance in GC2 and across many GC3 tasks.

  • Problem

    The study targets pose prediction, binding-affinity ranking, and free-energy prediction in computer-aided drug design challenges.

  • Method

    The models combine multiscale weighted colored graph and element-specific persistent homology descriptors with random forest and deep learning methods.

  • Results

    The models ranked 1st in 10 of 26 GC3 tasks and achieved the top place in GC2 free-energy Set 1 Stage 2.

  • Takeaways & Limitations

    The reported results support the practical use of mathematical deep learning models for pose and binding-affinity prediction in drug discovery.

Abstract

from arXiv · show

Advanced mathematics, such as multiscale weighted colored graph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R grand challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 (GC2) focused on the pose prediction and binding affinity ranking and free energy prediction for Farnesoid X receptor ligands. Our models obtained the top place in absolute free energy prediction for free energy Set 1 in Stage 2. The latest competition, D3R Grand Challenge 3 (GC3), is considered as the most difficult challenge so far. It has 5 subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-$α$, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of 26 official competitive tasks.

I Introduction

The paper motivates mathematical deep learning for virtual screening, combining molecular interaction descriptors, topological representations, and machine learning to predict poses and binding affinities in D3R challenges.

  • Virtual screening combines ligand-pose generation with binding-affinity prediction, making both stages important components of computer-aided drug design.
  • Machine-learning scoring functions can characterize non-additive contributions of functional groups in protein–ligand interactions.
  • Persistent homology encodes geometric information through filtration-dependent topological invariants that track components, rings, and cavities across scales.
  • Topological descriptors have previously supported deep-learning predictions for protein-folding stability, toxicity, solubility, partition coefficient, binding affinity, and virtual screening.
  • The study evaluates mathematical deep learning models for pose selection, affinity ranking, and free-energy prediction in D3R GC2 and GC3.

II.B Protein structures selection and preparation

The workflow prepares receptor and ligand structures, generates poses with multiple docking strategies, and trains a machine-learning scoring function to rerank them by predicted quality.

  • Receptor structures are obtained through homology modeling for sequence-based targets and supplemented with available Protein Data Bank crystal structures.
  • The workflow uses four docking strategies—align-close, align-target, close-dock, and cross-dock—alongside induced-fit docking procedures.
  • A topological deep-learning scoring function is trained on docking decoys labeled by RMSD and then used to rerank poses generated for target ligands.
  • Align-close selects the most chemically similar PDB ligand and aligns it flexibly before minimization.
  • Align-target constructs receptor structures from sequences and minimizes aligned ligands with respect to the corresponding receptors.

Protocol 3: Align-target

The described docking protocols generate and select candidate poses, while weighted colored graph descriptors represent protein–ligand atomic interactions across element-specific and multiscale settings.

  • Protocol 3: Align-target: Close-dock and cross-dock use Autodock Vina with chemically similar receptors, selecting poses by binding energy.
  • Multiscale weighted colored graph representation: Weighted colored graphs encode protein–ligand interactions as element- and molecule-labeled atomic vertices connected within a distance cutoff.
  • Multiscale weighted colored graph representation: The construction partitions protein–ligand atom types into 36 ordered interaction sets and produces 36 corresponding graph centralities.
  • Multiscale weighted colored graph representation: The graph kernel uses interatomic distance, radial-basis type, scale factor, and power parameters to characterize pairwise correlations.
  • Multiscale weighted colored graph representation: The method extends centrality using correlation-weighted atomic interactions and aggregates node centralities to describe the whole graph.
  • Multiscale weighted colored graph representation: Varying kernel parameters creates multiscale centralities, yielding 72 descriptors for a two-scale weighted colored graph.

II.E Algebraic topology based molecular signature

Algebraic-topology representations use biomolecular geometry and interaction patterns to construct topological spaces that capture multiscale structural and physical–chemical information.

  • Topological analysis captures multiscale geometry, interaction networks in arbitrary dimensions, and key physical and chemical information about biomolecular systems.
  • The approach builds topological spaces from the geometry and complex interaction patterns of biomolecular systems.

II.E.1 Persistent homology

Persistent homology represents molecular topology through chains, cycles, and homology groups, then tracks topological features across a filtration to obtain a robust multiscale description.

  • II.E.1 Persistent homology: A simplicial complex discretely represents a topological space through points, edges, triangles, and higher-dimensional simplices satisfying face and intersection conditions.Chains are formal sums of simplices, with coefficients drawn from a chosen coefficient set such as a finite field.
  • II.E.1 Persistent homology: Boundary operators connect chain groups across dimensions, and their composition is zero, ensuring boundary groups are contained within cycle groups.This relation supports the quotient construction used to define homology groups.
  • II.E.1 Persistent homology: The kth homology group is the quotient Z_k(X)/B_k(X), capturing k-dimensional holes that are cycles but not boundaries.Here, Z_k(X) is the kernel of the boundary operator and B_k(X) is the image of the next boundary operator.
  • II.E.1 Persistent homology: Persistent homology tracks the birth and death of homology generators across a filtration, producing a robust multiscale description of molecular topology.A filtration is a sequence of subspaces connected by inclusion-induced maps.

II.E.2 Topological description of molecular systems

Persistent homology models molecular systems by treating atoms as vertices and selecting filtrations that encode protein geometry or protein-ligand interaction patterns across scales.

  • II.E.2 Topological description of molecular systems: Atoms serve as vertices in persistent-homology models, while different filtration constructions reveal different aspects of molecular systems.Filtration design determines which structural or interaction features are represented.
  • II.E.2 Topological description of molecular systems: Alpha-complex filtrations describe complex protein geometry by adding simplices according to intersections of Voronoi cells and radius-based balls.The filtration parameter ϵ determines the associated subcomplex.
  • II.E.2 Topological description of molecular systems: Vietoris-Rips filtrations represent protein-ligand interactions through pairwise distance thresholds, with the distance function chosen to emphasize desired molecular properties.Assigning infinite distance to atoms within the same molecule emphasizes interactions between protein and ligand atoms.
  • II.E.2 Topological description of molecular systems: Element-specific persistent-homology barcodes can be compared with Wasserstein metrics or converted into fixed-length feature vectors for machine learning.These representations support methods including nearest neighbors, manifold learning, and other predictive models.

II.F Machine learning algorithms

The paper combines ensemble-of-trees methods and deep learning within a mathematical deep learning framework for analyzing protein-ligand representations.

  • II.F Machine learning algorithms: The mathematical deep learning framework uses ensemble-of-trees methods and deep learning, with its overall workflow illustrated in Figure 1.The figure is described as a schematic illustration of the modeling approach.
  • II.F Machine learning algorithms: Ensemble-of-trees models combine multiple decision trees to improve learning capability beyond individual weak learners.Individual trees identify key features at decision nodes but are limited for highly nonlinear or high-dimensional problems.

Ensemble of trees

Deep learning is used when molecular features are complex or contain an underlying dimension, including the filtration dimension in persistent-homology representations.

  • Ensemble of trees: Convolutional neural networks can exploit the spatial dimension associated with filtration parameters in persistent-homology representations.The paper connects this representation to the success of convolutional neural networks in computer vision.

Deep Learning

The models were evaluated across GC3’s 26 competitive tasks, with first-place results in 10 tasks and especially strong performance on Cathepsin S when crystallographic poses removed pose-error effects.

  • Grand Challenge 3: 10 of 26 GC3 competitive tasks received first-place predictions across five subchallenges and two pose-prediction challenges.GC3 included affinity and pose-prediction submissions involving Cathepsin S and kinase targets.
  • Subchallenge 1: The models attained first places for free-energy prediction in Stage 1 and for scoring and free-energy prediction in Stage 2 of the Cathepsin S subchallenge.Stage 2 provided experimental structures, whereas Stage 1 remained affected by pose-prediction errors.
  • Grand Challenge 3: Figure 2 marks the GC3 tasks in which the predictions ranked first, while Figure 3 compares submissions for Stage 2 affinity ranking.The figures provide overview and participant-comparison views of the reported GC3 results.
  • Subchallenge 1: Kendall’s τ = 0.54 was the top affinity-ranking result for 19 crystallographic-pose ligands in Stage 2 of Subchallenge 1.The best prediction had receipt ID 6jekk.

Subchallenge 2

Across GC3 subchallenges 2–5, the models achieved several top-ranked affinity, classification, and free-energy results, although performance varied by task.

  • Subchallenge 2: 0.48 MCC was the best reported result for VEGFR2 active/inactive classification.The result came from submissions with receipt IDs qikvs and rtv8m.
  • Subchallenge 3: 1.06 kcal/mol RMSEc earned first place for JAK2 binding-energy prediction, while affinity ranking was not impressive.The models also ranked second in JAK2 active/inactive classification with MCC = 0.23.
  • Subchallenge 4: 0.78 MCC ranked first for TIE2 active/inactive classification, while the model also ranked first across all evaluation metrics for that subchallenge.The TIE2 results included top Kendall’s τ and Spearman correlation values of 0.57 and 0.76, respectively.
  • Subchallenge 4: 1.02 kcal/mol RMSEc was the lowest among submissions for TIE2 Set 2 absolute free-energy prediction.The result used receipt ID 5g8ed.
  • Subchallenge 5: 0.52 Kendall’s τ was the best result for ABL1 affinity ranking excluding Kds > 10 µM.The task ranked mutants for two ligands across five ABL1 mutants.

Subchallenge 5

For GC2, the models improved free-energy prediction in Stage 2 and achieved the highest Kendall’s τ for Set 1, while the broader GC3 evaluation showed strong but docking-limited performance.

  • III.B Grand challenge 2: GC2 Stage 2 repeated the earlier affinity and free-energy tasks after released structures, except that pose prediction was omitted.The second-stage comparison therefore focused on affinity-related predictions rather than pose prediction.
  • III.B Grand challenge 2: τ = 0.41 ranked first among all submissions for GC2 Stage 2 free-energy Set 1, improving on Stage 1’s RMSEc = 0.68 kcal/mol second-place result.The Stage 2 result used receipt ID 4rbjk and is shown in Figure 4.
  • IV Conclusion: 10 of 26 GC3 official evaluation tasks ranked the submissions first, while GC2 achieved the top free-energy prediction for Set 1 in Stage 2.The models used multiscale weighted colored graphs, element-specific persistent homology, random forests, and deep convolutional neural networks.
  • IV Conclusion: The docking protocols did not show a dominant role in GC3 binding-affinity accuracy, making docking accuracy a bottleneck.The authors identify improved docking as a major task for predicting binding energies when crystallographic structures are unavailable.
Loading 1804.10647v1…