Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

PMSPcnn: Predicting protein stability changes upon single point mutations with convolutional neural network

Protein missense mutations and resulting protein stability changes are important causes for many human genetic diseases. However, the accurate prediction of stability changes due to mutations remains a challenging problem. To address this problem, we have developed an unbiased effective model: PMSPcnn that is based on a convolutional neural network. We have included an anti-symmetry property to build a balanced training dataset, which improves the prediction, in particular for stabilizing mutations. Persistent homology, which is an effective approach for characterizing protein structures, is used to obtain topological features. Additionally, a regression stratification cross-validation scheme has been proposed to improve the prediction for mutations with extreme ΔΔG. For three test datasets: Ssym, p53, and myoglobin, PMSPcnn achieves a better performance than currently existing predictors. PMSPcnn also outperforms currently available methods for membrane proteins. Overall, PMSPcnn is a promising method for the prediction of protein stability changes caused by single point mutations.

Recent advances in computational and experimental protein-ligand affinity determination techniques

INTRODUCTION

Modern drug discovery revolves around designing ligands that target the chosen biomolecule, typically proteins. For this, the evaluation of affinities of putative ligands is crucial. This has given rise to a multitude of dedicated computational and experimental methods that are constantly being developed and improved.

AREAS COVERED

In this review, the authors reassess both the industry mainstays and the newest trends among the methods for protein - small-molecule affinity determination. They discuss both computational affinity predictions and experimental techniques, describing their basic principles, main limitations, and advantages. Together, this serves as initial guide to the currently most popular and cutting-edge ligand-binding assays employed in rational drug design.

EXPERT OPINION

The affinity determination methods continue to develop toward miniaturization, high-throughput, and in-cell application. Moreover, the availability of data analysis tools has been constantly increasing. Nevertheless, cross-verification of data using at least two different techniques and careful result interpretation remain of utmost importance.

Water Network-Augmented Two-State Model for Protein-Ligand Binding Affinity Prediction

Water network rearrangement from the ligand-unbound state to the ligand-bound state is known to have significant effects on the protein-ligand binding interactions, but most of the current machine learning-based scoring functions overlook these effects. In this study, we endeavor to construct a comprehensive and realistic deep learning model by incorporating water network information into both ligand-unbound and -bound states. In particular, extended connectivity interaction features were integrated into graph representation, and graph transformer operator was employed to extract features of the ligand-unbound and -bound states. Through these efforts, we developed a water network-augmented two-state model called ECIFGraph::HM-Holo-Apo. Our new model exhibits satisfactory performance in terms of scoring, ranking, docking, screening, and reverse screening power tests on the CASF-2016 benchmark. In addition, it can achieve superior performance in large-scale docking-based virtual screening tests on the DEKOIS2.0 data set. Our study highlights that the use of a water network-augmented two-state model can be an effective strategy to bolster the robustness and applicability of machine learning-based scoring functions, particularly for targets with hydrophilic or solvent-exposed binding pockets.

PLANET: A Multi-objective Graph Neural Network Model for Protein-Ligand Binding Affinity Prediction

Predicting protein-ligand binding affinity is a central issue in drug design. Various deep learning models have been published in recent years, where many of them rely on 3D protein-ligand complex structures as input and tend to focus on the single task of reproducing binding affinity. In this study, we have developed a graph neural network model called PLANET (Protein-Ligand Affinity prediction NETwork). This model takes the graph-represented 3D structure of the binding pocket on the target protein and the 2D chemical structure of the ligand molecule as input. It was trained through a multi-objective process with three related tasks, including deriving the protein-ligand binding affinity, protein-ligand contact map, and ligand distance matrix. Besides the protein-ligand complexes with known binding affinity data retrieved from the PDBbind database, a large number of non-binder decoys were also added to the training data for deriving the final model of PLANET. When tested on the CASF-2016 benchmark, PLANET exhibited a scoring power comparable to the best result yielded by other deep learning models as well as a reasonable ranking power and docking power. In virtual screening trials conducted on the DUD-E benchmark, PLANET's performance was notably better than several deep learning and machine learning models. As on the LIT-PCBA benchmark, PLANET achieved comparable accuracy as the conventional docking program Glide, but it only spent less than 1% of Glide's computation time to finish the same job because PLANET did not need exhaustive conformational sampling. Considering the decent accuracy and efficiency of PLANET in binding affinity prediction, it may become a useful tool for conducting large-scale virtual screening.

An ensemble-based approach to estimate confidence of predicted protein-ligand binding affinity values

When designing a machine learning-based scoring function, we access a limited number of protein-ligand complexes with experimentally determined binding affinity values, representing only a fraction of all possible protein-ligand complexes. Consequently, it is crucial to report a measure of confidence and quantify the uncertainty in the model's predictions during test time. Here, we adopt the conformal prediction technique to evaluate the confidence of a prediction for each member of the core set of the CASF 2016 benchmark. The conformal prediction technique requires a diverse ensemble of predictors for uncertainty estimation. To this end, we introduce ENS-Score as an ensemble predictor, which includes 30 models with different protein-ligand representation approaches and achieves Pearson's correlation of 0.842 on the core set of the CASF 2016 benchmark. Also, we comprehensively investigate the residual error of each data point to assess the normality behavior of the distribution of the residual errors and their correlation to the structural features of the ligands, such as hydrophobic interactions and halogen bonding. In the end, we provide a local host web application to facilitate the usage of ENS-Score. All codes to repeat results are provided at https://github.com/miladrayka/ENS_Score.

GSScore: a novel Graphormer-based shell-like scoring method for protein-ligand docking

Protein-ligand interactions (PLIs) are essential for cellular activities and drug discovery. But due to the complexity and high cost of experimental methods, there is a great demand for computational approaches to recognize PLI patterns, such as protein-ligand docking. In recent years, more and more models based on machine learning have been developed to directly predict the root mean square deviation (RMSD) of a ligand docking pose with reference to its native binding pose. However, new scoring methods are pressingly needed in methodology for more accurate RMSD prediction. We present a new deep learning-based scoring method for RMSD prediction of protein-ligand docking poses based on a Graphormer method and Shell-like graph architecture, named GSScore. To recognize near-native conformations from a set of poses, GSScore takes atoms as nodes and then establishes the docking interface of protein-ligand into multiple bipartite graphs within different shell ranges. Benefiting from the Graphormer and Shell-like graph architecture, GSScore can effectively capture the subtle differences between energetically favorable near-native conformations and unfavorable non-native poses without extra information. GSScore was extensively evaluated on diverse test sets including a subset of PDBBind version 2019, CASF2016 as well as DUD-E, and obtained significant improvements over existing methods in terms of RMSE, $R$ (Pearson correlation coefficient), Spearman correlation coefficient and Docking power.

Enhancing Generalizability in Protein-Ligand Binding Affinity Prediction with Multimodal Contrastive Learning

Improving the generalization ability of scoring functions remains a major challenge in protein-ligand binding affinity prediction. Many machine learning methods are limited by their reliance on single-modal representations, hindering a comprehensive understanding of protein-ligand interactions. We introduce a graph-neural-network-based scoring function that utilizes a triplet contrastive learning loss to improve protein-ligand representations. In this model, three-dimensional complex representations and the fusion of two-dimensional ligand and coarse-grained pocket representations converge while distancing from decoy representations in latent space. After rigorous validation on multiple external data sets, our model exhibits commendable generalization capabilities compared to those of other deep learning-based scoring functions, marking it as a promising tool in the realm of drug discovery. In the future, our training framework can be extended to other biophysical- and biochemical-related problems such as protein-protein interaction and protein mutation prediction.

Directional ΔG Neural Network (DrΔG-Net): A Modular Neural Network Approach to Binding Free Energy Prediction

The protein-ligand binding free energy is a central quantity in structure-based computational drug discovery efforts. Although popular alchemical methods provide sound statistical means of computing the binding free energy of a large breadth of systems, they are generally too costly to be applied at the same frequency as end point or ligand-based methods. By contrast, these data-driven approaches are typically fast enough to address thousands of systems but with reduced transferability to unseen systems. We introduce DrΔG-Net (or simply Dragnet), an equivariant graph neural network that can blend ligand-based and protein-ligand data-driven approaches. It is based on a 3D fingerprint representation of the ligand alone and in complex with the protein target. Dragnet is a global scoring function to predict the binding affinity of arbitrary protein-ligand complexes, but can be easily tuned via transfer learning to specific systems or end points, performing similarly to common 2D ligand-based approaches in these tasks. Dragnet is evaluated on a total of 28 validation proteins with a set of congeneric ligands derived from the Binding DB and one custom set extracted from the ChEMBL Database. In general, a handful of experimental binding affinities are sufficient to optimize the scoring function for a particular protein and ligand scaffold. When not available, predictions from physics-based methods such as absolute free energy perturbation can be used for the transfer learning tuning of Dragnet. Furthermore, we use our data to illustrate the present limitations of data-driven modeling of binding free energy predictions.

Machine Learning for Sequence and Structure-Based Protein-Ligand Interaction Prediction

Developing new drugs is too expensive and time -consuming. Accurately predicting the interaction between drugs and targets will likely change how the drug is discovered. Machine learning-based protein-ligand interaction prediction has demonstrated significant potential. In this paper, computational methods, focusing on sequence and structure to study protein-ligand interactions, are examined. Therefore, this paper starts by presenting an overview of the data sets applied in this area, as well as the various approaches applied for representing proteins and ligands. Then, sequence-based and structure-based classification criteria are subsequently utilized to categorize and summarize both the classical machine learning models and deep learning models employed in protein-ligand interaction studies. Moreover, the evaluation methods and interpretability of these models are proposed. Furthermore, delving into the diverse applications of protein-ligand interaction models in drug research is presented. Lastly, the current challenges and future directions in this field are addressed.

EGGNet, a Generalizable Geometric Deep Learning Framework for Protein Complex Pose Scoring

Computational prediction of molecule-protein interactions has been key for developing new molecules to interact with a target protein for therapeutics development. Previous work includes two independent streams of approaches: (1) predicting protein-protein interactions (PPIs) between naturally occurring proteins and (2) predicting binding affinities between proteins and small-molecule ligands [also known as drug-target interaction (DTI)]. Studying the two problems in isolation has limited the ability of these computational models to generalize across the PPI and DTI tasks, both of which ultimately involve noncovalent interactions with a protein target. In this work, we developed Equivariant Graph of Graphs neural Network (EGGNet), a geometric deep learning (GDL) framework, for molecule-protein binding predictions that can handle three types of molecules for interacting with a target protein: (1) small molecules, (2) synthetic peptides, and (3) natural proteins. EGGNet leverages a graph of graphs (GoG) representation constructed from the molecular structures at atomic resolution and utilizes a multiresolution equivariant graph neural network to learn from such representations. In addition, EGGNet leverages the underlying biophysics and makes use of both atom- and residue-level interactions, which improve EGGNet's ability to rank candidate poses from blind docking. EGGNet achieves competitive performance on both a public protein-small-molecule binding affinity prediction task (80.2% top 1 success rate on CASF-2016) and a synthetic protein interface prediction task (88.4% area under the precision-recall curve). We envision that the proposed GDL framework can generalize to many other protein interaction prediction problems, such as binding site prediction and molecular docking, helping accelerate protein engineering and structure-based drug development.

Poisson-Boltzmann-based machine learning model for electrostatic analysis

Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic solvation free energies for macromolecules due to the nonlinearity, dielectric jumps, charge singularity, and geometric complexity associated with the PB equation. The present work introduces a PB-based machine learning (PBML) model for biomolecular electrostatic analysis. Trained with the second-order accurate MIBPB solver, the proposed PBML model is found to be more accurate and faster than several eminent PB solvers in electrostatic analysis. The proposed PBML model can provide highly accurate PB electrostatic solvation free energy of new biomolecules or new conformations generated by molecular dynamics with much reduced computational cost.

TopoFormer: Multiscale Topology-enabled Structure-to-Sequence Transformer for Protein-Ligand Interaction Predictions

Pre-trained deep Transformers have had tremendous success in a wide variety of disciplines. However, in computational biology, essentially all Transformers are built upon the biological sequences, which ignores vital stereochemical information and may result in crucial errors in downstream predictions. On the other hand, three-dimensional (3D) molecular structures are incompatible with the sequential architecture of Transformer and natural language processing (NLP) models in general. This work addresses this foundational challenge by a topological Transformer (TopoFormer). TopoFormer is built by integrating NLP and a multiscale topology techniques, the persistent topological hyperdigraph Laplacian (PTHL), which systematically converts intricate 3D protein-ligand complexes at various spatial scales into a NLP-admissible sequence of topological invariants and homotopic shapes. Element-specific PTHLs are further developed to embed crucial physical, chemical, and biological interactions into topological sequences. TopoFormer surges ahead of conventional algorithms and recent deep learning variants and gives rise to exemplary scoring accuracy and superior performance in ranking, docking, and screening tasks in a number of benchmark datasets. The proposed topological sequences can be extracted from all kinds of structural data in data science to facilitate various NLP models, heralding a new era in AI-driven discovery.

An overview of recent advances and challenges in predicting compound-protein interaction (CPI)

Compound-protein interactions (CPIs) are critical in drug discovery for identifying therapeutic targets, drug side effects, and repurposing existing drugs. Machine learning (ML) algorithms have emerged as powerful tools for CPI prediction, offering notable advantages in cost-effectiveness and efficiency. This review provides an overview of recent advances in both structure-based and non-structure-based CPI prediction ML models, highlighting their performance and achievements. It also offers insights into CPI prediction-related datasets and evaluation benchmarks. Lastly, the article presents a comprehensive assessment of the current landscape of CPI prediction, elucidating the challenges faced and outlining emerging trends to advance the field.

Predicting Affinity Through Homology (PATH): Interpretable Binding Affinity Prediction with Persistent Homology

Accurate binding affinity prediction is crucial to structure-based drug design. Recent work used computational topology to obtain an effective representation of protein-ligand interactions. Although persistent homology encodes geometric features, previous works on binding affinity prediction using persistent homology employed uninterpretable machine learning models and failed to explain the underlying geometric and topological features that drive accurate binding affinity prediction. In this work, we propose a novel, interpretable algorithm for protein-ligand binding affinity prediction. Our algorithm achieves interpretability through an effective embedding of distances across bipartite matchings of the protein and ligand atoms into real-valued functions by summing Gaussians centered at features constructed by persistent homology. We name these functions internuclear persistent contours (IPCs) . Next, we introduce persistence fingerprints , a vector with 10 components that sketches the distances of different bipartite matching between protein and ligand atoms, refined from IPCs. Let the number of protein atoms in the protein-ligand complex be n , number of ligand atoms be m , and ω ≈ 2.4 be the matrix multiplication exponent. We show that for any 0 < ε < 1, after an 𝒪 ( mn log( mn )) preprocessing procedure, we can compute an ε -accurate approximation to the persistence fingerprint in 𝒪 ( m log 6 ω ( m/" )) time, independent of protein size. This is an improvement in time complexity by a factor of 𝒪 (( m + n ) 3 ) over any previous binding affinity prediction that uses persistent homology. We show that the representational power of persistence fingerprint generalizes to protein-ligand binding datasets beyond the training dataset. Then, we introduce PATH , Predicting Affinity Through Homology, an interpretable, small ensemble of shallow regression trees for binding affinity prediction from persistence fingerprints. We show that despite using 1,400-fold fewer features, PATH has comparable performance to a previous state-of-the-art binding affinity prediction algorithm that uses persistent homology features. Moreover, PATH has the advantage of being interpretable. Finally, we visualize the features captured by persistence fingerprint for variant HIV-1 protease complexes and show that persistence fingerprint captures binding-relevant structural mutations. The source code for PATH is released open-source as part of the osprey protein design software package.

Expanding Training Data for Structure-Based Receptor-Ligand Binding Affinity Regression through Imputation of Missing Labels

The success of machine learning is, in part, due to a large volume of data available to train models. However, the amount of training data for structure-based molecular property prediction remains limited. The previously described CrossDocked2020 data set expanded the available training data for binding pose classification in a molecular docking setting but did not address expanding the amount of receptor-ligand binding affinity data. We present experiments demonstrating that imputing binding affinity labels for complexes without experimentally determined binding affinities is a viable approach to expanding training data for structure-based models of receptor-ligand binding affinity. In particular, we demonstrate that utilizing imputed labels from a convolutional neural network trained only on the affinity data present in CrossDocked2020 results in a small improvement in the binding affinity regression performance, despite the additional sources of noise that such imputed labels add to the training data. The code, data splits, and imputation labels utilized in this paper are freely available at https://github.com/francoep/ImputationPaper.

A practical guide to machine-learning scoring for structure-based virtual screening

Structure-based virtual screening (SBVS) via docking has been used to discover active molecules for a range of therapeutic targets. Chemical and protein data sets that contain integrated bioactivity information have increased both in number and in size. Artificial intelligence and, more concretely, its machine-learning (ML) branch, including deep learning, have effectively exploited these data sets to build scoring functions (SFs) for SBVS against targets with an atomic-resolution 3D model (e.g., generated by X-ray crystallography or predicted by AlphaFold2). Often outperforming their generic and non-ML counterparts, target-specific ML-based SFs represent the state of the art for SBVS. Here, we present a comprehensive and user-friendly protocol to build and rigorously evaluate these new SFs for SBVS. This protocol is organized into four sections: (i) using a public benchmark of a given target to evaluate an existing generic SF; (ii) preparing experimental data for a target from public repositories; (iii) partitioning data into a training set and a test set for subsequent target-specific ML modeling; and (iv) generating and evaluating target-specific ML SFs by using the prepared training-test partitions. All necessary code and input/output data related to three example targets (acetylcholinesterase, HMG-CoA reductase, and peroxisome proliferator-activated receptor-α) are available at https://github.com/vktrannguyen/MLSF-protocol , can be run by using a single computer within 1 week and make use of easily accessible software/programs (e.g., Smina, CNN-Score, RF-Score-VS and DeepCoy) and web resources. Our aim is to provide practical guidance on how to augment training data to enhance SBVS performance, how to identify the most suitable supervised learning algorithm for a data set, and how to build an SF with the highest likelihood of discovering target-active molecules within a given compound library.

Multi-shelled ECIF: improved extended connectivity interaction features for accurate binding affinity prediction

Motivation

Extended connectivity interaction features (ECIF) is a method developed to predict protein-ligand binding affinity, allowing for detailed atomic representation. It performed very well in terms of Comparative Assessment of Scoring Functions 2016 (CASF-2016) scoring power. However, ECIF has the limitation of not being able to adequately account for interatomic distances.

Results

To investigate what kind of distance representation is effective for P-L binding affinity prediction, we have developed two algorithms that improved ECIF's feature extraction method to take distance into account. One is multi-shelled ECIF, which takes into account the distance between atoms by dividing the distance between atoms into multiple layers. The other is weighted ECIF, which weights the importance of interactions according to the distance between atoms. A comparison of these two methods shows that multi-shelled ECIF outperforms weighted ECIF and the original ECIF, achieving a CASF-2016 scoring power Pearson correlation coefficient of 0.877.

Availability and implementation

All the codes and data are available on GitHub (https://github.com/koji11235/MSECIFv2).

ViTScore: A Novel Three-Dimensional Vision Transformer Method for Accurate Prediction of Protein-Ligand Docking Poses

Protein-ligand interactions (PLIs) are essential for cellular activities and drug discovery, and due to the complexity and high cost of experimental methods, there is a great demand for computational approaches, such as protein-ligand docking, to decipher PLI patterns. One of the most challenging aspects of protein-ligand docking is to identify near-native conformations from a set of poses, but traditional scoring functions still have limited accuracy. Therefore, new scoring methods are urgently needed for methodological and/or practical implications. We present a novel deep learning-based scoring function for ranking protein-ligand docking poses based on Vision Transformer (ViT), named ViTScore. To recognize near-native poses from a set of poses, ViTScore voxelizes the protein-ligand interactional pocket into a 3D grid labeled by the occupancy contribution of atoms in different physicochemical classes. This allows ViTScore to capture the subtle differences between spatially and energetically favorable near-native poses and unfavorable non-native poses without needing extra information. After that, ViTScore will output the prediction of the root mean square deviation (rmsd) of a docking pose with reference to the native binding pose. ViTScore is extensively evaluated on diverse test sets including PDBbind2019 and CASF2016, and obtains significant improvements over existing methods in terms of RMSE, R and docking power. Moreover, the results demonstrate that ViTScore is a promising scoring function for protein-ligand docking, and it can be used to accurately identify near-native poses from a set of poses. Furthermore, the results suggest that ViTScore is a powerful tool for protein-ligand docking, and it can be used to accurately identify near-native poses from a set of poses. Additionally, ViTScore can be used to identify potential drug targets and to design new drugs with improved efficacy and safety.

Ligand binding affinity prediction with fusion of graph neural networks and 3D structure-based complex graph

Accurate prediction of protein-ligand binding affinity is pivotal for drug design and discovery. Here, we proposed a novel deep fusion graph neural networks framework named FGNN to learn the protein-ligand interactions from the 3D structures of protein-ligand complexes. Unlike 1D sequences for proteins or 2D graphs for ligands, the 3D graph of protein-ligand complex enables the more accurate representations of the protein-ligand interactions. Benchmark studies have shown that our fusion models FGNN can achieve more accurate prediction of binding affinity than any individual algorithm. The advantages of fusion strategies have been demonstrated in terms of expressive power of data, learning efficiency and model interpretability. Our fusion models show satisfactory performances on diverse data sets, demonstrating their generalization ability. Given the good performances in both binding affinity prediction and virtual screening, our fusion models are expected to be practically applied for drug screening and design. Our work highlights the potential of the fusion graph neural network algorithm in solving complex prediction problems in computational biology and chemistry. The fusion graph neural networks (FGNN) model is freely available in https://github.com/LinaDongXMU/FGNN.

Recent Developments in Ultralarge and Structure-Based Virtual Screening Approaches

Drug development is a wide scientific field that faces many challenges these days. Among them are extremely high development costs, long development times, and a small number of new drugs that are approved each year. New and innovative technologies are needed to solve these problems that make the drug discovery process of small molecules more time and cost efficient, and that allow previously undruggable receptor classes to be targeted, such as protein-protein interactions. Structure-based virtual screenings (SBVSs) have become a leading contender in this context. In this review, we give an introduction to the foundations of SBVSs and survey their progress in the past few years with a focus on ultralarge virtual screenings (ULVSs). We outline key principles of SBVSs, recent success stories, new screening techniques, available deep learning-based docking methods, and promising future research directions. ULVSs have an enormous potential for the development of new small-molecule drugs and are already starting to transform early-stage drug discovery.

Persistent topological Laplacian analysis of SARS-CoV-2 variants

Topological data analysis (TDA) is an emerging field in mathematics and data science. Its central technique, persistent homology, has had tremendous success in many science and engineering disciplines. However, persistent homology has limitations, including its inability to handle heterogeneous information, such as multiple types of geometric objects; being qualitative rather than quantitative, e.g., counting a 5-member ring the same as a 6-member ring, and a failure to describe non-topological changes, such as homotopic changes in protein-protein binding. Persistent topological Laplacians (PTLs), such as persistent Laplacian and persistent sheaf Laplacian, were proposed to overcome the limitations of persistent homology. In this work, we examine the modeling and analysis power of PTLs in the study of the protein structures of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike receptor binding domain (RBD). First, we employ PTLs to study how the RBD mutation-induced structural changes of RBD-angiotensin-converting enzyme 2 (ACE2) binding complexes are captured in the changes of spectra of the PTLs among SARS-CoV-2 variants. Additionally, we use PTLs to analyze the binding of RBD and ACE2-induced structural changes of various SARS-CoV-2 variants. Finally, we explore the impacts of computationally generated RBD structures on a topological deep learning paradigm and predictions of deep mutational scanning datasets for the SARS-CoV-2 Omicron BA.2 variant. Our results indicate that PTLs have advantages over persistent homology in analyzing protein structural changes and provide a powerful new TDA tool for data science.

Persistent Dirac for molecular representation

Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design and materials discovery have been greatly contributed by molecular representation models. In this paper, we present a computational framework for molecular representation that is mathematically rigorous and based on the persistent Dirac operator. The properties of the discrete weighted and unweighted Dirac matrix are systematically discussed, and the biological meanings of both homological and non-homological eigenvectors are studied. We also evaluate the impact of various weighting schemes on the weighted Dirac matrix. Additionally, a set of physical persistent attributes that characterize the persistence and variation of spectrum properties of Dirac matrices during a filtration process is proposed to be molecular fingerprints. Our persistent attributes are used to classify molecular configurations of nine different types of organic-inorganic halide perovskites. The combination of persistent attributes with gradient boosting tree model has achieved great success in molecular solvation free energy prediction. The results show that our model is effective in characterizing the molecular structures, demonstrating the power of our molecular representation and featurization approach.

AI in drug discovery and its clinical relevance

The COVID-19 pandemic has emphasized the need for novel drug discovery process. However, the journey from conceptualizing a drug to its eventual implementation in clinical settings is a long, complex, and expensive process, with many potential points of failure. Over the past decade, a vast growth in medical information has coincided with advances in computational hardware (cloud computing, GPUs, and TPUs) and the rise of deep learning. Medical data generated from large molecular screening profiles, personal health or pathology records, and public health organizations could benefit from analysis by Artificial Intelligence (AI) approaches to speed up and prevent failures in the drug discovery pipeline. We present applications of AI at various stages of drug discovery pipelines, including the inherently computational approaches of de novo design and prediction of a drug's likely properties. Open-source databases and AI-based software tools that facilitate drug design are discussed along with their associated problems of molecule representation, data collection, complexity, labeling, and disparities among labels. How contemporary AI methods, such as graph neural networks, reinforcement learning, and generated models, along with structure-based methods, (i.e., molecular dynamics simulations and molecular docking) can contribute to drug discovery applications and analysis of drug responses is also explored. Finally, recent developments and investments in AI-based start-up companies for biotechnology, drug design and their current progress, hopes and promotions are discussed in this article.

SS-GNN: A Simple-Structured Graph Neural Network for Affinity Prediction

Efficient and effective drug-target binding affinity (DTBA) prediction is a challenging task due to the limited computational resources in practical applications and is a crucial basis for drug screening. Inspired by the good representation ability of graph neural networks (GNNs), we propose a simple-structured GNN model named SS-GNN to accurately predict DTBA. By constructing a single undirected graph based on a distance threshold to represent protein-ligand interactions, the scale of the graph data is greatly reduced. Moreover, ignoring covalent bonds in the protein further reduces the computational cost of the model. The graph neural network-multilayer perceptron (GNN-MLP) module takes the latent feature extraction of atoms and edges in the graph as two mutually independent processes. We also develop an edge-based atom-pair feature aggregation method to represent complex interactions and a graph pooling-based method to predict the binding affinity of the complex. We achieve state-of-the-art prediction performance using a simple model (with only 0.6 M parameters) without introducing complicated geometric feature descriptions. SS-GNN achieves Pearson's R_p = 0.853 on the PDBbind v2016 core set, outperforming state-of-the-art GNN-based methods by 5.2%. Moreover, the simplified model structure and concise data processing procedure improve the prediction efficiency of the model. For a typical protein-ligand complex, affinity prediction takes only 0.2 ms. All codes are freely accessible at https://github.com/xianyuco/SS-GNN.

Multiscale Laplacian Learning

Machine learning has greatly influenced many fields, including science. However, despite of the tremendous accomplishments of machine learning, one of the key limitations of most existing machine learning approaches is their reliance on large labeled sets, and thus, data with limited labeled samples remains a challenge. Moreover, the performance of machine learning methods often severely hindered in case of diverse data, usually associated with smaller data sets or data associated with areas of study where the size of the data sets is constrained by high experimental cost and/or ethics. These challenges call for innovative strategies for dealing with these types of data. In this work, the aforementioned challenges are addressed by integrating graph-based frameworks, semi-supervised techniques, multiscale structures, and modified and adapted optimization procedures. This results in two innovative multiscale Laplacian learning (MLL) approaches for machine learning tasks, such as data classification, and for tackling data with limited samples, diverse data, and small data sets. The first approach, multikernel manifold learning (MML), integrates manifold learning with multikernel information and incorporates a warped kernel regularizer using multiscale graph Laplacians. The second approach, the multiscale MBO (MMBO) method, introduces multiscale Laplacians to the modification of the famous classical Merriman-Bence-Osher (MBO) scheme, and makes use of fast solvers. We demonstrate the performance of our algorithms experimentally on a variety of benchmark data sets, and compare them favorably to the state-of-art approaches.

SVSBI: sequence-based virtual screening of biomolecular interactions

Virtual screening (VS) is a critical technique in understanding biomolecular interactions, particularly in drug design and discovery. However, the accuracy of current VS models heavily relies on three-dimensional (3D) structures obtained through molecular docking, which is often unreliable due to the low accuracy. To address this issue, we introduce a sequence-based virtual screening (SVS) as another generation of VS models that utilize advanced natural language processing (NLP) algorithms and optimized deep K-embedding strategies to encode biomolecular interactions without relying on 3D structure-based docking. We demonstrate that SVS outperforms state-of-the-art performance for four regression datasets involving protein-ligand binding, protein-protein, protein-nucleic acid binding, and ligand inhibition of protein-protein interactions and five classification datasets for protein-protein interactions in five biological species. SVS has the potential to transform current practices in drug discovery and protein engineering.

Genomics data analysis via spectral shape and topology

Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and to retain information that may be lost using standard dimension-reduction algorithms. We propose a novel workflow to process and analyze RNA-seq data from tumor and healthy subjects integrating Mapper, differential gene expression, and spectral shape analysis. Precisely, we show that a Gaussian mixture approximation method can be used to produce graphical structures that successfully separate tumor and healthy subjects, and produce two subgroups of tumor subjects. A further analysis using DESeq2, a popular tool for the detection of differentially expressed genes, shows that these two subgroups of tumor cells bear two distinct gene regulations, suggesting two discrete paths for forming lung cancer, which could not be highlighted by other popular clustering methods, including t-distributed stochastic neighbor embedding (t-SNE). Although Mapper shows promise in analyzing high-dimensional data, tools to statistically analyze Mapper graphical structures are limited in the existing literature. In this paper, we develop a scoring method using heat kernel signatures that provides an empirical setting for statistical inferences such as hypothesis testing, sensitivity analysis, and correlation analysis.

Improving drug-target affinity prediction via feature fusion and knowledge distillation

Rapid and accurate prediction of drug-target affinity can accelerate and improve the drug discovery process. Recent studies show that deep learning models may have the potential to provide fast and accurate drug-target affinity prediction. However, the existing deep learning models still have their own disadvantages that make it difficult to complete the task satisfactorily. Complex-based models rely heavily on the time-consuming docking process, and complex-free models lacks interpretability. In this study, we introduced a novel knowledge-distillation insights drug-target affinity prediction model with feature fusion inputs to make fast, accurate and explainable predictions. We benchmarked the model on public affinity prediction and virtual screening dataset. The results show that it outperformed previous state-of-the-art models and achieved comparable performance to previous complex-based models. Finally, we study the interpretability of this model through visualization and find it can provide meaningful explanations for pairwise interaction. We believe this model can further improve the drug-target affinity prediction for its higher accuracy and reliable interpretability.

Novel Molecular Representations Using Neumann-Cayley Orthogonal Gated Recurrent Unit

Advances in deep neural networks (DNNs) have made a very powerful machine learning method available to researchers across many fields of study, including the biomedical and cheminformatics communities, where DNNs help to improve tasks such as protein performance, molecular design, drug discovery, etc. Many of those tasks rely on molecular descriptors for representing molecular characteristics in cheminformatics. Despite significant efforts and the introduction of numerous methods that derive molecular descriptors, the quantitative prediction of molecular properties remains challenging. One widely used method of encoding molecule features into bit strings is the molecular fingerprint. In this work, we propose using new Neumann-Cayley Gated Recurrent Units (NC-GRU) inside the Neural Nets encoder (AutoEncoder) to create neural molecular fingerprints (NC-GRU fingerprints). The NC-GRU AutoEncoder introduces orthogonal weights into widely used GRU architecture, resulting in faster, more stable training, and more reliable molecular fingerprints. Integrating novel NC-GRU fingerprints and Multi-Task DNN schematics improves the performance of various molecular-related tasks such as toxicity, partition coefficient, lipophilicity, and solvation-free energy, producing state-of-the-art results on several benchmarks.

Persistent topological Laplacian analysis of SARS-CoV-2 variants

Topological data analysis (TDA) is an emerging field in mathematics and data science. Its central technique, persistent homology, has had tremendous success in many science and engineering disciplines. However, persistent homology has limitations, including its inability to handle heterogeneous information, such as multiple types of geometric objects; being qualitative rather than quantitative, e.g., counting a 5-member ring the same as a 6-member ring, and a failure to describe non-topological changes, such as homotopic changes in protein-protein binding. Persistent topological Laplacians (PTLs), such as persistent Laplacian and persistent sheaf Laplacian, were proposed to overcome the limitations of persistent homology. In this work, we examine the modeling and analysis power of PTLs in the study of the protein structures of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike receptor binding domain (RBD). First, we employ PTLs to study how the RBD mutation-induced structural changes of RBD-angiotensin-converting enzyme 2 (ACE2) binding complexes are captured in the changes of spectra of the PTLs among SARS-CoV-2 variants. Additionally, we use PTLs to analyze the binding of RBD and ACE2-induced structural changes of various SARS-CoV-2 variants. Finally, we explore the impacts of computationally generated RBD structures on a topological deep learning paradigm and predictions of deep mutational scanning datasets for the SARS-CoV-2 Omicron BA.2 variant. Our results indicate that PTLs have advantages over persistent homology in analyzing protein structural changes and provide a powerful new TDA tool for data science.

GB-score: Minimally designed machine learning scoring function based on distance-weighted interatomic contact features

In recent years, thanks to advances in computer hardware and dataset availability, data-driven approaches (like machine learning) have become one of the essential parts of the drug design framework to accelerate drug discovery procedures. Constructing a new scoring function, a function that can predict the binding score for a generated protein-ligand pose during docking procedure or a crystal complex, based on machine and deep learning has become an active research area in computer-aided drug design. GB-Score is a state-of-the-art machine learning-based scoring function that utilizes distance-weighted interatomic contact features, PDBbind-v2019 general set, and Gradient Boosting Trees algorithm to the binding affinity prediction. The distance-weighted interatomic contact featurization method used the distance between different ligand and protein atom types for numerical representation of the protein-ligand complex. GB-Score attains Pearson's correlation 0.862 and RMSE 1.190 on the CASF-2016 benchmark test in the scoring power metric. GB-Score's codes are freely available on the web at https://github.com/miladrayka/GB_Score.

Persistent Path-Spectral (PPS) Based Machine Learning for Protein-Ligand Binding Affinity Prediction

Molecular descriptors are essential to quantitative structure activity/property relationship (QSAR/QSPR) models and machine learning models. Here we propose persistent path-spectral (PPS), PPS-based molecular descriptors, and PPS-based machine learning model for the prediction of the protein-ligand binding affinity, for the first time. For the graph, simplicial complex, and hypergraph representation of molecular structures and interactions, the path-Laplacian can be constructed and the derived path-spectral naturally gives a quantitative description of molecules. Further, by introducing the filtration process of the representation, the persistent path-spectral can be derived, which gives a multiscale characterization of molecules. Molecular descriptors from the persistent path-spectral attributes then are combined with the machine learning model, in particular, the gradient boosting tree, to form our PPS-ML model. We test our model on three most commonly used data sets, i.e., PDBbind-v2007, PDBbind-v2013, and PDBbind-v2016, and our model can achieve competitive results.

Reducing false positive rate of docking-based virtual screening by active learning

Machine learning-based scoring functions (MLSFs) have become a very favorable alternative to classical scoring functions because of their potential superior screening performance. However, the information of negative data used to construct MLSFs was rarely reported in the literature, and meanwhile the putative inactive molecules recorded in existing databases usually have obvious bias from active molecules. Here we proposed an easy-to-use method named AMLSF that combines active learning using negative molecular selection strategies with MLSF, which can iteratively improve the quality of inactive sets and thus reduce the false positive rate of virtual screening. We chose energy auxiliary terms learning as the MLSF and validated our method on eight targets in the diverse subset of DUD-E. For each target, we screened the IterBioScreen database by AMLSF and compared the screening results with those of the four control models. The results illustrate that the number of active molecules in the top 1000 molecules identified by AMLSF was significantly higher than those identified by the control models. In addition, the free energy calculation results for the top 10 molecules screened out by the AMLSF, null model and control models based on DUD-E also proved that more active molecules can be identified, and the false positive rate can be reduced by AMLSF.

Persistent Homology for RNA Data Analysis

Molecular representations are of great importance for machine learning models in RNA data analysis. Essentially, efficient molecular descriptors or fingerprints that characterize the intrinsic structural and interactional information of RNAs can significantly boost the performance of all learning modeling. In this paper, we introduce two persistent models, including persistent homology and persistent spectral, for RNA structure and interaction representations and their applications in RNA data analysis. Different from traditional geometric and graph representations, persistent homology is built on simplicial complex, which is a generalization of graph models to higher-dimensional situations. Hypergraph is a further generalization of simplicial complexes and hypergraph-based embedded persistent homology has been proposed recently. Moreover, persistent spectral models, which combine filtration process with spectral models, including spectral graph, spectral simplicial complex, and spectral hypergraph, are proposed for molecular representation. The persistent attributes for RNAs can be obtained from these two persistent models and further combined with machine learning models for RNA structure, flexibility, dynamics, and function analysis.

Persistent Laplacian projected Omicron BA.4 and BA.5 to become new dominating variants

Due to its high transmissibility, Omicron BA.1 ousted the Delta variant to become a dominating variant in late 2021 and was replaced by more transmissible Omicron BA.2 in March 2022. An important question is which new variants will dominate in the future. Topology-based deep learning models have had tremendous success in forecasting emerging variants in the past. However, topology is insensitive to homotopic shape evolution in virus-human protein-protein binding, which is crucial to viral evolution and transmission. This challenge is tackled with persistent Laplacian, which is able to capture both the topological change and homotopic shape evolution of data. Persistent Laplacian-based deep learning models are developed to systematically evaluate variant infectivity. Our comparative analysis of Alpha, Beta, Gamma, Delta, Lambda, Mu, and Omicron BA.1, BA.1.1, BA.2, BA.2.11, BA.2.12.1, BA.3, BA.4, and BA.5 unveils that Omicron BA.2.11, BA.2.12.1, BA.3, BA.4, and BA.5 are more contagious than BA.2. In particular, BA.4 and BA.5 are about 36% more infectious than BA.2 and are projected to become new dominant variants by natural selection. Moreover, the proposed models outperform the state-of-the-art methods on three major benchmark datasets for mutation-induced protein-protein binding free energy changes. Our key projection about BA4 and BA.5's dominance made on May 1, 2022 (see arXiv:2205.00532) became a reality in late June 2022.

MILCDock: Machine Learning Enhanced Consensus Docking for Virtual Screening in Drug Discovery

Molecular docking tools are regularly used to computationally identify new molecules in virtual screening for drug discovery. However, docking tools suffer from inaccurate scoring functions with widely varying performance on different proteins. To enable more accurate ranking of active over inactive ligands in virtual screening, we created a machine learning consensus docking tool, MILCDock, that uses predictions from five traditional molecular docking tools to predict the probability a ligand binds to a protein. MILCDock was trained and tested on data from both the DUD-E and LIT-PCBA docking datasets and shows improved performance over traditional molecular docking tools and other consensus docking methods on the DUD-E dataset. LIT-PCBA targets proved to be difficult for all methods tested. We also find that DUD-E data, although biased, can be effective in training machine learning tools if care is taken to avoid DUD-E's biases during training.

Assessment of the Generalization Abilities of Machine-Learning Scoring Functions for Structure-Based Virtual Screening

In structure-based virtual screening (SBVS), it is critical that scoring functions capture protein-ligand atomic interactions. By focusing on the local domains of ligand binding pockets, a standardized pocket Pfam-based clustering (Pfam-cluster) approach was developed to assess the cross-target generalization ability of machine-learning scoring functions (MLSFs). Subsequently, 12 typical MLSFs were evaluated using random cross-validation (Random-CV), protein sequence similarity-based cross-validation (Seq-CV), and pocket Pfam-based cross-validation (Pfam-CV) methods. Surprisingly, all of the tested models showed decreased performances from Random-CV to Seq-CV to Pfam-CV experiments, not showing satisfactory generalization capacity. Our interpretable analysis suggested that the predictions on novel targets by MLSFs were dependent on buried solvent-accessible surface area (SASA)-related features of complex structures, with greater predicted binding affinities on complexes owning larger protein-ligand interfaces. By combining buried SASA-related features with target-specific patterns that were only shared among structurally similar compounds in the same cluster, the random forest (RF)-Score attained a good performance in the Random-CV test. Based on these findings, we strongly advise assessing the generalization ability of MLSFs with the Pfam-cluster approach and being cautious with the features learned by MLSFs.

Biomolecular Topology: Modelling and Analysis

With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases. The high dimensionality, structural complexity, the nonlinearity, and entanglements of biomolecular data, ranging from DNA knots, RNA secondary structures, protein folding configurations, chromosomes, DNA origami, molecular assembly, to others at the macromolecular level, pose a severe challenge in their analysis and characterization. In the past few decades, mathematical concepts, models, algorithms, and tools from algebraic topology, combinatorial topology, computational topology, and topological data analysis, have demonstrated great power and begun to play an essential role in tackling the biomolecular data challenge. In this work, we introduce biomolecular topology, which concerns the topological problems and models originated from the biomolecular systems. More specifically, the biomolecular topology encompasses topological structures, properties and relations that are emerged from biomolecular structures, dynamics, interactions, and functions. We discuss the various types of biomolecular topology from structures (of proteins, DNAs, and RNAs), protein folding, and protein assembly. A brief discussion of databanks (and databases), theoretical models, and computational algorithms, is presented. Further, we systematically review related topological models, including graphs, simplicial complexes, persistent homology, persistent Laplacians, de Rham-Hodge theory, Yau-Hausdorff distance, and the topology-based machine learning models.

Deep learning methods for molecular representation and property prediction

With advances in artificial intelligence (AI) methods, computer-aided drug design (CADD) has developed rapidly in recent years. Effective molecular representation and accurate property prediction are crucial tasks in CADD workflows. In this review, we summarize contemporary applications of deep learning (DL) methods for molecular representation and property prediction. We categorize DL methods according to the format of molecular data (1D, 2D, and 3D). In addition, we discuss some common DL models, such as ensemble learning and transfer learning, and analyze the interpretability methods for these models. We also highlight the challenges and opportunities of DL methods for molecular representation and property prediction.

Systematic Improvement of the Performance of Machine Learning Scoring Functions by Incorporating Features of Protein-Bound Water Molecules

Water molecules at the ligand-protein interfaces play crucial roles in the binding of the ligands, but the behavior of protein-bound water is largely ignored in many currently used machine learning (ML)-based scoring functions (SFs). In an attempt to improve the prediction performance of existing ML-based SFs, we estimated the water distribution with a HydraMap (HM) method and then incorporated the features extracted from protein-bound waters obtained in this way into three ML-based SFs: RF-Score, ECIF, and PLEC. It was found that a combination of HM-based features can consistently improve the performance of all three SFs, including their scoring, ranking, and docking power. HydraMap-based features show consistently good performance with both crystal structures and docked structures, demonstrating their robustness for SFs. Overall, HM-based features, which are a statistical representation of hydration sites at protein-ligand interfaces, are expected to improve the prediction performance for diverse SFs.

Hom-Complex-Based Machine Learning (HCML) for the Prediction of Protein-Protein Binding Affinity Changes upon Mutation

Protein-protein interactions (PPIs) are involved in almost all biological processes in the cell. Understanding protein-protein interactions holds the key for the understanding of biological functions, diseases and the development of therapeutics. Recently, artificial intelligence (AI) models have demonstrated great power in PPIs. However, a key issue for all AI-based PPI models is efficient molecular representations and featurization. Here, we propose Hom-complex-based PPI representation, and Hom-complex-based machine learning models for the prediction of PPI binding affinity changes upon mutation, for the first time. In our model, various Hom complexes Hom(G₁, G) can be generated for the graph representation G of protein-protein complex by using different graphs G₁, which reveal G₁-related inner connections within the graph representation G of protein-protein complex. Further, for a specific graph G₁, a series of nested Hom complexes are generated to give a multiscale characterization of the PPIs. Its persistent homology and persistent Euler characteristic are used as molecular descriptors and further combined with the machine learning model, in particular, gradient boosting tree (GBT). We systematically test our model on the two most-commonly used data sets, that is, SKEMPI and AB-Bind. It has been found that our model outperforms all the existing models as far as we know, which demonstrates the great potential of our model for the analysis of PPIs. Our model can be used for the analysis and design of efficient antibodies for SARS-CoV-2.

Methodology-Centered Review of Molecular Modeling, Simulation, and Prediction of SARS-CoV-2

Despite tremendous efforts in the past two years, our understanding of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), virus-host interactions, immune response, virulence, transmission, and evolution is still very limited. This limitation calls for further in-depth investigation. Computational studies have become an indispensable component in combating coronavirus disease 2019 (COVID-19) due to their low cost, their efficiency, and the fact that they are free from safety and ethical constraints. Additionally, the mechanism that governs the global evolution and transmission of SARS-CoV-2 cannot be revealed from individual experiments and was discovered by integrating genotyping of massive viral sequences, biophysical modeling of protein-protein interactions, deep mutational data, deep learning, and advanced mathematics. There exists a tsunami of literature on the molecular modeling, simulations, and predictions of SARS-CoV-2 and related developments of drugs, vaccines, antibodies, and diagnostics. To provide readers with a quick update about this literature, we present a comprehensive and systematic methodology-centered review. Aspects such as molecular biophysics, bioinformatics, cheminformatics, machine learning, and mathematics are discussed. This review will be beneficial to researchers who are looking for ways to contribute to SARS-CoV-2 studies and those who are interested in the status of the field.

Scoring Functions for Protein-Ligand Binding Affinity Prediction using Structure-Based Deep Learning: A Review

The rapid and accurate in silico prediction of protein-ligand binding free energies or binding affinities has the potential to transform drug discovery. In recent years, there has been a rapid growth of interest in deep learning methods for the prediction of protein-ligand binding affinities based on the structural information of protein-ligand complexes. These structure-based scoring functions often obtain better results than classical scoring functions when applied within their applicability domain. Here we review structure-based scoring functions for binding affinity prediction based on deep learning, focussing on different types of architectures, featurization strategies, data sets, methods for training and evaluation, and the role of explainable artificial intelligence in building useful models for real drug-discovery applications.

Multiphysical graph neural network (MP-GNN) for COVID-19 drug design

Graph neural networks (GNNs) are the most promising deep learning models that can revolutionize non-Euclidean data analysis. However, their full potential is severely curtailed by poorly represented molecular graphs and features. Here, we propose a multiphysical graph neural network (MP-GNN) model based on the developed multiphysical molecular graph representation and featurization. All kinds of molecular interactions, between different atom types and at different scales, are systematically represented by a series of scale-specific and element-specific graphs with distance-related node features. From these graphs, graph convolution network (GCN) models are constructed with specially designed weight-sharing architectures. Base learners are constructed from GCN models from different elements at different scales, and further consolidated together using both one-scale and multi-scale ensemble learning schemes. Our MP-GNN has two distinct properties. First, our MP-GNN incorporates multiscale interactions using more than one molecular graph. Atomic interactions from various different scales are not modeled by one specific graph (as in traditional GNNs), instead they are represented by a series of graphs at different scales. Second, it is free from the complicated feature generation process as in conventional GNN methods. In our MP-GNN, various atom interactions are embedded into element-specific graph representations with only distance-related node features. A unique GNN architecture is designed to incorporate all the information into a consolidated model. Our MP-GNN has been extensively validated on the widely used benchmark test datasets from PDBbind, including PDBbind-v2007, PDBbind-v2013 and PDBbind-v2016. Our model can outperform all existing models as far as we know. Further, our MP-GNN is used in coronavirus disease 2019 drug design. Based on a dataset with 185 complexes of inhibitors for severe acute respiratory syndrome coronavirus (SARS-CoV/SARS-CoV-2), we evaluate their binding affinities using our MP-GNN. It has been found that our MP-GNN is of high accuracy. This demonstrates the great potential of our MP-GNN for the screening of potential drugs for SARS-CoV-2. Availability: The Multiphysical graph neural network (MP-GNN) model can be found in https://github.com/Alibaba-DAMO-DrugAI/MGNN. Additional data or code will be available upon reasonable request.

Hodge theory-based biomolecular data analysis

Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis. Here we use Hodge Laplacian and Hodge decomposition models to analyze biomolecular structures. Different from traditional graph-based methods, biomolecular structures are represented as simplicial complexes, which can be viewed as a generalization of graph models to their higher-dimensional counterparts. Hodge Laplacian matrices at different dimensions can be generated from the simplicial complex. The spectral information of these matrices can be used to study intrinsic topological information of biomolecular structures. Essentially, the number (or multiplicity) of k-th dimensional zero eigenvalues is equivalent to the k-th Betti number, i.e., the number of k-th dimensional homology groups. The associated eigenvectors indicate the homological generators, i.e., circles or holes within the molecular-based simplicial complex. Furthermore, Hodge decomposition-based HodgeRank model is used to characterize the folding or compactness of the molecular structures, in particular, the topological associated domain (TAD) in high-throughput chromosome conformation capture (Hi-C) data. Mathematically, molecular structures are represented in simplicial complexes with certain edge flows. The HodgeRank-based average/total inconsistency (AI/TI) is used for the quantitative measurements of the folding or compactness of TADs. This is the first quantitative measurement for TAD regions, as far as we know.

Machine-Learning- and Knowledge-Based Scoring Functions Incorporating Ligand and Protein Fingerprints

We propose a novel machine-learning-based scoring function for drug discovery that incorporates ligand and protein structural information into a knowledge-based PMF score. Molecular docking, a simulation method for structure-based drug design (SBDD), is expected to reduce the enormous costs associated with conventional experimental methods in terms of rational drug discovery. Molecular docking has two main purposes: to predict ligand-binding structures for target proteins and to predict protein-ligand binding affinity. Currently available programs of molecular docking offer an accurate prediction of ligand binding structures for many systems. However, the accurate prediction of binding affinity remains challenging. In this study, we developed a new scoring function that incorporates fingerprints representing ligand and protein structures as descriptors in the PMF score. Here, regression analysis of the scoring function was performed using the following machine learning techniques: least absolute shrinkage and selection operator (LASSO) and light gradient boosting machine (LightGBM). The results on a test data set showed that the binding affinity delivered by the newly developed scoring function has a Pearson correlation coefficient of 0.79 with the experimental value, which surpasses that of the conventional scoring functions. Further analysis provided a chemical understanding of the descriptors that contributed significantly to the improvement in prediction accuracy. Our approach and findings are useful for rational drug discovery.

ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE

We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.

Differences in ligand-induced protein dynamics extracted from an unsupervised deep learning approach correlate with protein-ligand binding affinities

Prediction of protein–ligand binding affinity is a major goal in drug discovery. Generally, free energy gap is calculated between two states (e.g., ligand binding and unbinding). The energy gap implicitly includes the effects of changes in protein dynamics induced by ligand binding. However, the relationship between protein dynamics and binding affinity remains unclear. Here, we propose a method that represents ligand-binding-induced protein behavioral change with a simple feature that can be used to predict protein–ligand affinity. From unbiased molecular simulation data, an unsupervised deep learning method measures the differences in protein dynamics at a ligand-binding site depending on the bound ligands. A dimension reduction method extracts a dynamic feature that strongly correlates to the binding affinities. Moreover, the residues that play important roles in protein–ligand interactions are specified based on their contribution to the differences. These results indicate the potential for binding dynamics-based drug discovery.

Differences in ligand-induced protein dynamics extracted as a single feature from a deep learning-based analysis of MD simulations correlate with ligand binding affinity.

Delta Machine Learning to Improve Scoring-Ranking-Screening Performances of Protein-Ligand Scoring Functions

Protein-ligand scoring functions are widely used in structure-based drug design for fast evaluation of protein-ligand interactions, and it is of strong interest to develop scoring functions with machine-learning approaches. In this work, by expanding the training set, developing physically meaningful features, employing our recently developed linear empirical scoring function Lin_F9 (Yang, C. J. Chem. Inf. Model. 2021, 61, 4630-4644) as the baseline, and applying extreme gradient boosting (XGBoost) with Δ-machine learning, we have further improved the robustness and applicability of machine-learning scoring functions. Besides the top performances for scoring-ranking-screening power tests of the CASF-2016 benchmark, the new scoring function Δ_{Lin_F9}XGB also achieves superior scoring and ranking performances in different structure types that mimic real docking applications. The scoring powers of Δ_{Lin_F9}XGB for locally optimized poses, flexible redocked poses, and ensemble docked poses of the CASF-2016 core set achieve Pearson's correlation coefficient (R) values of 0.853, 0.839, and 0.813, respectively. In addition, the large-scale docking-based virtual screening test on the LIT-PCBA data set demonstrates the reliability and robustness of Δ_{Lin_F9}XGB in virtual screening application. The Δ_{Lin_F9}XGB scoring function and its code are freely available on the web at (https://yzhang.hpc.nyu.edu/Delta_LinF9_XGB).