Ollivier Persistent Ricci Curvature-Based Machine Learning for the Protein-Ligand Binding Affinity Prediction

Curvature-enhanced graph convolutional network for biomolecular interaction prediction

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local geometric properties and enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further incorporated into the weight function for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and analyzed in details using a series of well-designed simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negative-curvature ratios, network densities, and network sizes (when larger than 500).

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.

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.

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

A Multi-perspective Model for Protein-Ligand-Binding Affinity Prediction

Gathering information from multi-perspective graphs is an essential issue for many applications especially for protein-ligand-binding affinity prediction. Most of traditional approaches obtained such information individually with low interpretability. In this paper, we harness the rich information from multi-perspective graphs with a general model, which abstractly represents protein-ligand complexes with better interpretability while achieving excellent predictive performance. In addition, we specially analyze the protein-ligand-binding affinity problem, taking into account the heterogeneity of proteins and ligands. Experimental evaluations demonstrate the effectiveness of our data representation strategy on public datasets by fusing information from different perspectives. All codes are available in the https://github.com/Jthy-af/HaPPy .

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.

Artificial intelligence-aided protein engineering: from topological data analysis to deep protein language models

Protein engineering is an emerging field in biotechnology that has the potential to revolutionize various areas, such as antibody design, drug discovery, food security, ecology, and more. However, the mutational space involved is too vast to be handled through experimental means alone. Leveraging accumulative protein databases, machine learning (ML) models, particularly those based on natural language processing (NLP), have considerably expedited protein engineering. Moreover, advances in topological data analysis (TDA) and artificial intelligence-based protein structure prediction, such as AlphaFold2, have made more powerful structure-based ML-assisted protein engineering strategies possible. This review aims to offer a comprehensive, systematic, and indispensable set of methodological components, including TDA and NLP, for protein engineering and to facilitate their future development.

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.

Fingerprint-Enhanced Graph Attention Network (FinGAT) Model for Antibiotic Discovery

Artificial Intelligence (AI) techniques are of great potential to fundamentally change antibiotic discovery industries. Efficient and effective molecular featurization is key to all highly accurate learning models for antibiotic discovery. In this paper, we propose a fingerprint-enhanced graph attention network (FinGAT) model by the combination of sequence-based 2D fingerprints and structure-based graph representation. In our feature learning process, sequence information is transformed into a fingerprint vector, and structural information is encoded through a GAT module into another vector. These two vectors are concatenated and input into a multilayer perceptron (MLP) for antibiotic activity classification. Our model is extensively tested and compared with existing models. It has been found that our FinGAT can outperform various state-of-the-art GNN models in antibiotic discovery.

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.

A fully differentiable ligand pose optimization framework guided by deep learning and a traditional scoring function

The recently reported machine learning- or deep learning-based scoring functions (SFs) have shown exciting performance in predicting protein-ligand binding affinities with fruitful application prospects. However, the differentiation between highly similar ligand conformations, including the native binding pose (the global energy minimum state), remains challenging that could greatly enhance the docking. In this work, we propose a fully differentiable, end-to-end framework for ligand pose optimization based on a hybrid SF called DeepRMSD+Vina combined with a multi-layer perceptron (DeepRMSD) and the traditional AutoDock Vina SF. The DeepRMSD+Vina, which combines (1) the root mean square deviation (RMSD) of the docking pose with respect to the native pose and (2) the AutoDock Vina score, is fully differentiable; thus is capable of optimizing the ligand binding pose to the energy-lowest conformation. Evaluated by the CASF-2016 docking power dataset, the DeepRMSD+Vina reaches a success rate of 94.4%, which outperforms most reported SFs to date. We evaluated the ligand conformation optimization framework in practical molecular docking scenarios (redocking and cross-docking tasks), revealing the high potentialities of this framework in drug design and discovery. Structural analysis shows that this framework has the ability to identify key physical interactions in protein-ligand binding, such as hydrogen-bonding. Our work provides a paradigm for optimizing ligand conformations based on deep learning algorithms. The DeepRMSD+Vina model and the optimization framework are available at GitHub repository https://github.com/zchwang/DeepRMSD-Vina_Optimization.

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.

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.

Inferring functional communities from partially observed biological networks exploiting geometric topology and side information

Cellular biological networks represent the molecular interactions that shape function of living cells. Uncovering the organization of a biological network requires efficient and accurate algorithms to determine the components, termed communities, underlying specific processes. Detecting functional communities is challenging because reconstructed biological networks are always incomplete due to technical bias and biological complexity, and the evaluation of putative communities is further complicated by a lack of known ground truth. To address these challenges, we developed a geometric-based detection framework based on Ollivier-Ricci curvature to exploit information about network topology to perform community detection from partially observed biological networks. We further improved this approach by integrating knowledge of gene function, termed side information, into the Ollivier-Ricci curvature algorithm to aid in community detection. This approach identified essential conserved and varied biological communities from partially observed Arabidopsis protein interaction datasets better than the previously used methods. We show that Ollivier-Ricci curvature with side information identified an expanded auxin community to include an important protein stability complex, the Cop9 signalosome, consistent with previous reported links to auxin response and root development. The results show that community detection based on Ollivier-Ricci curvature with side information can uncover novel components and novel communities in biological networks, providing novel insight into the organization and function of complex networks.

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.

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.

Protein pKa Prediction by Tree-Based Machine Learning

Protonation states of ionizable protein residues modulate many essential biological processes. For correct modeling and understanding of these processes, it is crucial to accurately determine their pKa values. Here, we present four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. We observed similar performance among the four machine learning algorithms. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA and 15% better than the published result from the pKa prediction method DelPhiPKa. The overall root-mean-square error (RMSE) for this model is 0.69, with surface and buried RMSE values being 0.56 and 0.78, respectively, considering six residue types (Asp, Glu, His, Lys, Cys, and Tyr), and 0.63 when considering Asp, Glu, His, and Lys only. We provide pKa predictions for proteins in human proteome from the AlphaFold Protein Structure Database and observed that 1% of Asp/Glu/Lys residues have highly shifted pKa values close to the physiological pH.

Dowker complex based machine learning (DCML) models for protein-ligand binding affinity prediction

With the great advancements in experimental data, computational power and learning algorithms, artificial intelligence (AI) based drug design has begun to gain momentum recently. AI-based drug design has great promise to revolutionize pharmaceutical industries by significantly reducing the time and cost in drug discovery processes. However, a major issue remains for all AI-based learning model that is efficient molecular representations. Here we propose Dowker complex (DC) based molecular interaction representations and Riemann Zeta function based molecular featurization, for the first time. Molecular interactions between proteins and ligands (or others) are modeled as Dowker complexes. A multiscale representation is generated by using a filtration process, during which a series of DCs are generated at different scales. Combinatorial (Hodge) Laplacian matrices are constructed from these DCs, and the Riemann zeta functions from their spectral information can be used as molecular descriptors. To validate our models, we consider protein-ligand binding affinity prediction. Our DC-based machine learning (DCML) models, in particular, DC-based gradient boosting tree (DC-GBT), are tested on three most-commonly used datasets, i.e., including PDBbind-2007, PDBbind-2013 and PDBbind-2016, and extensively compared with other existing state-of-the-art models. It has been found that our DC-based descriptors can achieve the state-of-the-art results and have better performance than all machine learning models with traditional molecular descriptors. Our Dowker complex based machine learning models can be used in other tasks in AI-based drug design and molecular data analysis.

With the ever-increasing accumulation of chemical and biomolecular data, data-driven artificial intelligence (AI) models will usher in an era of faster, cheaper and more-efficient drug design and drug discovery. However, unlike image, text, video, audio data, molecular data from chemistry and biology, have much complicated three-dimensional structures, as well as physical and chemical properties. Efficient molecular representations and descriptors are key to the success of machine learning models in drug design. Here, we propose Dowker complex based molecular representation and Riemann Zeta function based molecular featurization, for the first time. To characterize the complicated molecular structures and interactions at the atomic level, Dowker complexes are constructed. Based on them, intrinsic mathematical invariants are derived and used as molecular descriptors, which can be further combined with machine learning and deep learning models. Our model has achieved state-of-the-art results in protein-ligand binding affinity prediction, demonstrating its great potential for other drug design and discovery problems.

Artificial intelligence in the prediction of protein-ligand interactions: recent advances and future directions

New drug production, from target identification to marketing approval, takes over 12 years and can cost around $2.6 billion. Furthermore, the COVID-19 pandemic has unveiled the urgent need for more powerful computational methods for drug discovery. Here, we review the computational approaches to predicting protein-ligand interactions in the context of drug discovery, focusing on methods using artificial intelligence (AI). We begin with a brief introduction to proteins (targets), ligands (e.g. drugs) and their interactions for nonexperts. Next, we review databases that are commonly used in the domain of protein-ligand interactions. Finally, we survey and analyze the machine learning (ML) approaches implemented to predict protein-ligand binding sites, ligand-binding affinity and binding pose (conformation) including both classical ML algorithms and recent deep learning methods. After exploring the correlation between these three aspects of protein-ligand interaction, it has been proposed that they should be studied in unison. We anticipate that our review will aid exploration and development of more accurate ML-based prediction strategies for studying protein-ligand interactions.

Protein pK a Prediction with Machine Learning

Protein pK _a prediction is essential for the investigation of the pH-associated relationship between protein structure and function. In this work, we introduce a deep learning-based protein pK _a predictor DeepKa, which is trained and validated with the pK _a values derived from continuous constant-pH molecular dynamics (CpHMD) simulations of 279 soluble proteins. Here, the CpHMD implemented in the Amber molecular dynamics package has been employed (Huang Y.J. Chem. Inf. Model.2018, 58, 1372-1383). Notably, to avoid discontinuities at the boundary, grid charges are proposed to represent protein electrostatics. We show that the prediction accuracy by DeepKa is close to that by CpHMD benchmarking simulations, validating DeepKa as an efficient protein pK _a predictor. In addition, the training and validation sets created in this study can be applied to the development of machine learning-based protein pK _a predictors in the future. Finally, the grid charge representation is general and applicable to other topics, such as the protein-ligand binding affinity prediction.

Prediction of Binding Free Energy of Protein-Ligand Complexes with a Hybrid Molecular Mechanics/Generalized Born Surface Area and Machine Learning Method

Accurate prediction of protein-ligand binding free energies is important in enzyme engineering and drug discovery. The molecular mechanics/generalized Born surface area (MM/GBSA) approach is widely used to estimate ligand-binding affinities, but its performance heavily relies on the accuracy of its energy components. A hybrid strategy combining MM/GBSA and machine learning (ML) has been developed to predict the binding free energies of protein-ligand systems. Based on the MM/GBSA energy terms and several features associated with protein-ligand interactions, our ML-based scoring function, GXLE, shows much better performance than MM/GBSA without entropy. In particular, the good transferability of the GXLE model is highlighted by its good performance in ranking power for prediction of the binding affinity of different ligands for either the docked structures or crystal structures. The GXLE scoring function and its code are freely available and can be used to correct the binding free energies computed by MM/GBSA.

Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash

In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.