Feature functional theory–binding predictor (FFT–BP) for the blind prediction of binding free energies

emPDBA: protein-DNA binding affinity prediction by combining features from binding partners and interface learned with ensemble regression model

Protein-deoxyribonucleic acid (DNA) interactions are important in a variety of biological processes. Accurately predicting protein-DNA binding affinity has been one of the most attractive and challenging issues in computational biology. However, the existing approaches still have much room for improvement. In this work, we propose an ensemble model for Protein-DNA Binding Affinity prediction (emPDBA), which combines six base models with one meta-model. The complexes are classified into four types based on the DNA structure (double-stranded or other forms) and the percentage of interface residues. For each type, emPDBA is trained with the sequence-based, structure-based and energy features from binding partners and complex structures. Through feature selection by the sequential forward selection method, it is found that there do exist considerable differences in the key factors contributing to intermolecular binding affinity. The complex classification is beneficial for the important feature extraction for binding affinity prediction. The performance comparison of our method with other peer ones on the independent testing dataset shows that emPDBA outperforms the state-of-the-art methods with the Pearson correlation coefficient of 0.53 and the mean absolute error of 1.11 kcal/mol. The comprehensive results demonstrate that our method has a good performance for protein-DNA binding affinity prediction. Availability and implementation: The source code is available at https://github.com/ChunhuaLiLab/emPDBA/.

Leveraging scaffold information to predict protein-ligand binding affinity with an empirical graph neural network

Protein-ligand binding affinity prediction is an important task in structural bioinformatics for drug discovery and design. Although various scoring functions (SFs) have been proposed, it remains challenging to accurately evaluate the binding affinity of a protein-ligand complex with the known bound structure because of the potential preference of scoring system. In recent years, deep learning (DL) techniques have been applied to SFs without sophisticated feature engineering. Nevertheless, existing methods cannot model the differential contribution of atoms in various regions of proteins, and the relationship between atom properties and intermolecular distance is also not fully explored. We propose a novel empirical graph neural network for accurate protein-ligand binding affinity prediction (EGNA). Graphs of protein, ligand and their interactions are constructed based on different regions of each bound complex. Proteins and ligands are effectively represented by graph convolutional layers, enabling the EGNA to capture interaction patterns precisely by simulating empirical SFs. The contributions of different factors on binding affinity can thus be transparently investigated. EGNA is compared with the state-of-the-art machine learning-based SFs on two widely used benchmark data sets. The results demonstrate the superiority of EGNA and its good generalization capability.

A reinforcement learning approach for protein-ligand binding pose prediction

Protein ligand docking is an indispensable tool for computational prediction of protein functions and screening drug candidates. Despite significant progress over the past two decades, it is still a challenging problem, characterized by the still limited understanding of the energetics between proteins and ligands, and the vast conformational space that has to be searched to find a satisfactory solution. In this project, we developed a novel reinforcement learning (RL) approach, the asynchronous advantage actor-critic model (A3C), to address the protein ligand docking problem. The overall framework consists of two models. During the search process, the agent takes an action selected by the actor model based on the current location. The critic model then evaluates this action and predict the distance between the current location and true binding site. Experimental results showed that in both single- and multi-atom cases, our model improves binding site prediction substantially compared to a naïve model. For the single-atom ligand, copper ion (Cu²⁺), the model predicted binding sites have a median root-mean-square-deviation (RMSD) of 2.39 Å to the true binding sites when starting from random starting locations. For the multi-atom ligand, sulfate ion (SO₄^2-), the predicted binding sites have a median RMSD of 3.82 Å to the true binding sites. The ligand-specific models built in this study can be used in solvent mapping studies and the RL framework can be readily scaled up to larger and more diverse sets of ligands.

A Physics-Guided Neural Network for Predicting Protein–Ligand Binding Free Energy: From Host–Guest Systems to the PDBbind Database

Calculation of protein–ligand binding affinity is a cornerstone of drug discovery. Classic implicit solvent models, which have been widely used to accomplish this task, lack accuracy compared to experimental references. Emerging data-driven models, on the other hand, are often accurate yet not fully interpretable and also likely to be overfitted. In this research, we explore the application of Theory-Guided Data Science in studying protein–ligand binding. A hybrid model is introduced by integrating Graph Convolutional Network (data-driven model) with the GBNSR6 implicit solvent (physics-based model). The proposed physics-data model is tested on a dataset of 368 complexes from the PDBbind refined set and 72 host–guest systems. Results demonstrate that the proposed Physics-Guided Neural Network can successfully improve the “accuracy” of the pure data-driven model. In addition, the “interpretability” and “transferability” of our model have boosted compared to the purely data-driven model. Further analyses include evaluating model robustness and understanding relationships between the physical features.

Artificial intelligence in virtual screening: models versus experiments

A typical drug discovery project involves identifying active compounds with significant binding potential for selected disease-specific targets. Experimental high-throughput screening (HTS) is a traditional approach to drug discovery, but is expensive and time-consuming when dealing with huge chemical libraries with billions of compounds. The search space can be narrowed down with the use of reliable computational screening approaches. In this review, we focus on various machine-learning (ML) and deep-learning (DL)-based scoring functions developed for solving classification and ranking problems in drug discovery. We highlight studies in which ML and DL models were successfully deployed to identify lead compounds for which the experimental validations are available from bioassay studies.

Improving Structure-Based Virtual Screening with Ensemble Docking and Machine Learning

One of the main challenges of structure-based virtual screening (SBVS) is the incorporation of the receptor's flexibility, as its explicit representation in every docking run implies a high computational cost. Therefore, a common alternative to include the receptor's flexibility is the approach known as ensemble docking. Ensemble docking consists of using a set of receptor conformations and performing the docking assays over each of them. However, there is still no agreement on how to combine the ensemble docking results to obtain the final ligand ranking. A common choice is to use consensus strategies to aggregate the ensemble docking scores, but these strategies exhibit slight improvement regarding the single-structure approach. Here, we claim that using machine learning (ML) methodologies over the ensemble docking results could improve the predictive power of SBVS. To test this hypothesis, four proteins were selected as study cases: CDK2, FXa, EGFR, and HSP90. Protein conformational ensembles were built from crystallographic structures, whereas the evaluated compound library comprised up to three benchmarking data sets (DUD, DEKOIS 2.0, and CSAR-2012) and cocrystallized molecules. Ensemble docking results were processed through 30 repetitions of 4-fold cross-validation to train and validate two ML classifiers: logistic regression and gradient boosting trees. Our results indicate that the ML classifiers significantly outperform traditional consensus strategies and even the best performance case achieved with single-structure docking. We provide statistical evidence that supports the effectiveness of ML to improve the ensemble docking performance.

Computational representations of protein-ligand interfaces for structure-based virtual screening

Introduction: Structure-based virtual screening (SBVS) is an essential strategy for hit identification. SBVS primarily uses molecular docking, which exploits the protein-ligand binding mode and associated affinity score for compound ranking. Previous studies have shown that computational representation of protein-ligand interfaces and the later establishment of machine learning models are efficacious in improving the accuracy of SBVS.Areas covered: The authors review the computational methods for representing protein-ligand interfaces, which include the traditional ones that use deliberately designed fingerprints and descriptors and the more recent methods that automatically extract features with deep learning. The effects of these methods on the performance of machine learning models are briefly discussed. Additionally, case studies that applied various computational representations to machine learning are cited with remarks.Expert opinion: It has become a trend to extract binding features automatically by deep learning, which uses a completely end-to-end representation. However, there is still plenty of scope for improvement . The interpretability of deep-learning models, the organization of data management, the quantity and quality of available data, and the optimization of hyperparameters could impact the accuracy of feature extraction. In addition, other important structural factors such as water molecules and protein flexibility should be considered.

ET-score: Improving Protein-ligand Binding Affinity Prediction Based on Distance-weighted Interatomic Contact Features Using Extremely Randomized Trees Algorithm

The molecular docking simulation is a key computational tool in modern drug discovery research that its predictive performance strongly depends on the employed scoring functions. Many recent studies have shown that the application of machine learning algorithms in the development of scoring functions has led to a significant improvement in docking performance. In this work, we introduce a new machine learning (ML) based scoring function called ET-Score, which employs the distance-weighted interatomic contacts between atom type pairs of the ligand and the protein for featurizing protein-ligand complexes and Extremely Randomized Trees algorithm for the training process. The performance of ET-Score is compared with some successful ML-based scoring functions and several popular classical scoring functions on the PDBbind 2016v core set. It is shown that our ET-Score model (with Pearson's correlation of 0.827 and RMSE of 1.332) achieves very good performance in comparison with most of the ML-based scoring functions and all classical scoring functions despite its extremely low computational cost. ET-Score's codes are freely available on the web at https://github.com/miladrayka/ET_Score.

Are 2D fingerprints still valuable for drug discovery?

Recently, molecular fingerprints extracted from three-dimensional (3D) structures using advanced mathematics, such as algebraic topology, differential geometry, and graph theory have been paired with efficient machine learning, especially deep learning algorithms to outperform other methods in drug discovery applications and competitions. This raises the question of whether classical 2D fingerprints are still valuable in computer-aided drug discovery. This work considers 23 datasets associated with four typical problems, namely protein-ligand binding, toxicity, solubility and partition coefficient to assess the performance of eight 2D fingerprints. Advanced machine learning algorithms including random forest, gradient boosted decision tree, single-task deep neural network and multitask deep neural network are employed to construct efficient 2D-fingerprint based models. Additionally, appropriate consensus models are built to further enhance the performance of 2D-fingerprint-based methods. It is demonstrated that 2D-fingerprint-based models perform as well as the state-of-the-art 3D structure-based models for the predictions of toxicity, solubility, partition coefficient and protein-ligand binding affinity based on only ligand information. However, 3D structure-based models outperform 2D fingerprint-based methods in complex-based protein-ligand binding affinity predictions.

A review of mathematical representations of biomolecular data

Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of biomolecular datasets obstruct the efficient application of ML algorithms in the field. In addition to data and algorithm, an efficient ML machinery for biomolecular predictions must include structural representation as an indispensable component. Mathematical representations that simplify the biomolecular structural complexity and reduce ML dimensionality have emerged as a prime winner in D3R Grand Challenges. This review is devoted to the recent advances in developing low-dimensional and scalable mathematical representations of biomolecules in our laboratory. We discuss three classes of mathematical approaches, including algebraic topology, differential geometry, and graph theory. We elucidate how the physical and biological challenges have guided the evolution and development of these mathematical apparatuses for massive and diverse biomolecular data. We focus the performance analysis on protein-ligand binding predictions in this review although these methods have had tremendous success in many other applications, such as protein classification, virtual screening, and the predictions of solubility, solvation free energies, toxicity, partition coefficients, protein folding stability changes upon mutation, etc.

Can machine learning consistently improve the scoring power of classical scoring functions? Insights into the role of machine learning in scoring functions

How to accurately estimate protein-ligand binding affinity remains a key challenge in computer-aided drug design (CADD). In many cases, it has been shown that the binding affinities predicted by classical scoring functions (SFs) cannot correlate well with experimentally measured biological activities. In the past few years, machine learning (ML)-based SFs have gradually emerged as potential alternatives and outperformed classical SFs in a series of studies. In this study, to better recognize the potential of classical SFs, we have conducted a comparative assessment of 25 commonly used SFs. Accordingly, the scoring power was systematically estimated by using the state-of-the-art ML methods that replaced the original multiple linear regression method to refit individual energy terms. The results show that the newly-developed ML-based SFs consistently performed better than classical ones. In particular, gradient boosting decision tree (GBDT) and random forest (RF) achieved the best predictions in most cases. The newly-developed ML-based SFs were also tested on another benchmark modified from PDBbind v2007, and the impacts of structural and sequence similarities were evaluated. The results indicated that the superiority of the ML-based SFs could be fully guaranteed when sufficient similar targets were contained in the training set. Moreover, the effect of the combinations of features from multiple SFs was explored, and the results indicated that combining NNscore2.0 with one to four other classical SFs could yield the best scoring power. However, it was not applicable to derive a generic target-specific SF or SF combination.

Integrated Predictor Based on Decomposition Mechanism for PM2.5 Long-Term Prediction

It is crucial to predict PM2.5 concentration for early warning regarding and the control of air pollution. However, accurate PM2.5 prediction has been challenging, especially in long-term prediction. PM2.5 monitoring data comprise a complex time series that contains multiple components with different characteristics; therefore, it is difficult to obtain an accurate prediction by a single model. In this study, an integrated predictor is proposed, in which the original data are decomposed into three components, that is, trend, period, and residual components, and then different sub-predictors including autoregressive integrated moving average (ARIMA) and two gated recurrent units are used to separately predict the different components. Finally, all the predictions from the sub-predictors are combined in fusion node to obtain the final prediction for the original data. The results of predicting the PM2.5 time series for Beijing, China showed that the proposed predictor can effectively improve prediction accuracy for long-term prediction.

AGL-Score: Algebraic Graph Learning Score for Protein-Ligand Binding Scoring, Ranking, Docking, and Screening

Although algebraic graph theory-based models have been widely applied in physical modeling and molecular studies, they are typically incompetent in the analysis and prediction of biomolecular properties, confirming the common belief that "one cannot hear the shape of a drum". A new development in the century-old question about the spectrum-geometry relationship is provided. Novel algebraic graph learning score (AGL-Score) models are proposed to encode high-dimensional physical and biological information into intrinsically low-dimensional representations. The proposed AGL-Score models employ multiscale weighted colored subgraphs to describe crucial molecular and biomolecular interactions in terms of graph invariants derived from graph Laplacian, its pseudo-inverse, and adjacency matrices. Additionally, AGL-Score models are integrated with an advanced machine learning algorithm to predict biomolecular macroscopic properties from the low-dimensional graph representation of biomolecular structures. The proposed AGL-Score models are extensively validated for their scoring power, ranking power, docking power, and screening power via a number of benchmark datasets, namely CASF-2007, CASF-2013, and CASF-2016. Numerical results indicate that the proposed AGL-Score models are able to outperform other state-of-the-art scoring functions in protein-ligand binding scoring, ranking, docking, and screening. This study indicates that machine learning methods are powerful tools for molecular docking and virtual screening. It also indicates that spectral geometry or spectral graph theory has the ability to infer geometric properties.

DG-GL: Differential geometry-based geometric learning of molecular datasets

MOTIVATION

Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding of its potential power in dimensionality reduction and its ability to encode essential chemical and biological information in differentiable manifolds.

RESULTS

We put forward a differential geometry-based geometric learning (DG-GL) hypothesis that the intrinsic physics of three-dimensional (3D) molecular structures lies on a family of low-dimensional manifolds embedded in a high-dimensional data space. We encode crucial chemical, physical, and biological information into 2D element interactive manifolds, extracted from a high-dimensional structural data space via a multiscale discrete-to-continuum mapping using differentiable density estimators. Differential geometry apparatuses are utilized to construct element interactive curvatures in analytical forms for certain analytically differentiable density estimators. These low-dimensional differential geometry representations are paired with a robust machine learning algorithm to showcase their descriptive and predictive powers for large, diverse, and complex molecular and biomolecular datasets. Extensive numerical experiments are carried out to demonstrate that the proposed DG-GL strategy outperforms other advanced methods in the predictions of drug discovery-related protein-ligand binding affinity, drug toxicity, and molecular solvation free energy.

AVAILABILITY AND IMPLEMENTATION

http://weilab.math.msu.edu/DG-GL/ Contact: wei@math.msu.edu.

Integration of element specific persistent homology and machine learning for protein-ligand binding affinity prediction

Protein-ligand binding is a fundamental biological process that is paramount to many other biological processes, such as signal transduction, metabolic pathways, enzyme construction, cell secretion, and gene expression. Accurate prediction of protein-ligand binding affinities is vital to rational drug design and the understanding of protein-ligand binding and binding induced function. Existing binding affinity prediction methods are inundated with geometric detail and involve excessively high dimensions, which undermines their predictive power for massive binding data. Topology provides the ultimate level of abstraction and thus incurs too much reduction in geometric information. Persistent homology embeds geometric information into topological invariants and bridges the gap between complex geometry and abstract topology. However, it oversimplifies biological information. This work introduces element specific persistent homology (ESPH) or multicomponent persistent homology to retain crucial biological information during topological simplification. The combination of ESPH and machine learning gives rise to a powerful paradigm for macromolecular analysis. Tests on 2 large data sets indicate that the proposed topology-based machine-learning paradigm outperforms other existing methods in protein-ligand binding affinity predictions. ESPH reveals protein-ligand binding mechanism that can not be attained from other conventional techniques. The present approach reveals that protein-ligand hydrophobic interactions are extended to 40Å  away from the binding site, which has a significant ramification to drug and protein design.

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

This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination.