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Currently, there is neither effective antiviral drugs nor vaccine for coronavirus disease 2019 (COVID-19) caused by acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Due to its high conservativeness and low similarity with human genes, SARS-CoV-2 main protease (Mpro) is one of the most favorable drug targets. However, the current understanding of the molecular mechanism of Mpro inhibition is limited by the lack of reliable binding affinity ranking and prediction of existing structures of Mpro–inhibitor complexes. This work integrates mathematics (i.e., algebraic topology) and deep learning (MathDL) to provide a reliable ranking of the binding affinities of 137 SARS-CoV-2 Mpro inhibitor structures. We reveal that Gly143 residue in Mpro is the most attractive site to form hydrogen bonds, followed by Glu166, Cys145, and His163. We also identify 71 targeted covalent bonding inhibitors. MathDL was validated on the PDBbind v2016 core set benchmark and a carefully curated SARS-CoV-2 inhibitor dataset to ensure the reliability of the present binding affinity prediction. The present binding affinity ranking, interaction analysis, and fragment decomposition offer a foundation for future drug discovery efforts., By integrating algebraic topology and deep learning, we provide a reliable ranking of binding affinities, binding site analysis, and fragment decomposition for 137 SARS-CoV-2 main protease inhibitors.

Machine learning approaches have had tremendous success in various disciplines. However, such success highly depends on the size and quality of datasets. Scientific datasets are often small and difficult to collect. Currently, improving machine learning performance for small scientific datasets remains a major challenge in many academic fields, such as bioinformatics or medical science. Gradient boosting decision tree (GBDT) is typically optimal for small datasets, while deep learning often performs better for large datasets. This work reports a boosting tree-assisted multitask deep learning (BTAMDL) architecture that integrates GBDT and multitask deep learning (MDL) to achieve near-optimal predictions for small datasets when there exists a large dataset that is well correlated to the small datasets. Two BTAMDL models are constructed, one utilizing purely MDL output as GBDT input while the other admitting additional features in GBDT input. The proposed BTAMDL models are validated on four categories of datasets, including toxicity, partition coefficient, solubility, and solvation. It is found that the proposed BTAMDL models outperform the current state-of-the-art methods in various applications involving small datasets.

We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method for docking pose predictions has significantly improved from our previous ones., Comment: 24 pages, 9 figure, and one table

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.

The ability of molecular property prediction is of great significance to drug discovery, human health, and environmental protection. Despite considerable efforts, quantitative prediction of various molecular properties remains a challenge. Although some machine learning models, such as bidirectional encoder from transformer, can incorporate massive unlabeled molecular data into molecular representations via a self-supervised learning strategy, it neglects three-dimensional (3D) stereochemical information. Algebraic graph, specifically, element-specific multiscale weighted colored algebraic graph, embeds complementary 3D molecular information into graph invariants. We propose an algebraic graph-assisted bidirectional transformer (AGBT) framework by fusing representations generated by algebraic graph and bidirectional transformer, as well as a variety of machine learning algorithms, including decision trees, multitask learning, and deep neural networks. We validate the proposed AGBT framework on eight molecular datasets, involving quantitative toxicity, physical chemistry, and physiology datasets. Extensive numerical experiments have shown that AGBT is a state-of-the-art framework for molecular property prediction., Despite considerable efforts, quantitative prediction of various molecular properties remains a challenge. Here, the authors propose an algebraic graph-assisted bidirectional transformer, which can incorporate massive unlabeled molecular data into molecular representations via a self-supervised learning strategy and assisted with 3D stereochemical information from graphs.

Current drug discovery is expensive and time-consuming. It remains a challenging task to create a wide variety of novel compounds that not only have desirable pharmacological properties but also are cheaply available to low-income people. In this work, we develop a generative network complex (GNC) to generate new drug-like molecules based on the multiproperty optimization via the gradient descent in the latent space of an autoencoder. In our GNC, both multiple chemical properties and similarity scores are optimized to generate drug-like molecules with desired chemical properties. To further validate the reliability of the predictions, these molecules are reevaluated and screened by independent 2D fingerprint-based predictors to come up with a few hundreds of new drug candidates. As a demonstration, we apply our GNC to generate a large number of new BACE1 inhibitors, as well as thousands of novel alternative drug candidates for eight existing market drugs, including Ceritinib, Ribociclib, Acalabrutinib, Idelalisib, Dabrafenib, Macimorelin, Enzalutamide, and Panobinostat.

Wuhan coronavirus, called 2019-nCoV, is a newly emerged virus that infected more than 9692 people and leads to more than 213 fatalities by January 30, 2020. Currently, there is no effective treatment for this epidemic. However, the viral protease of a coronavirus is well-known to be essential for its replication and thus is an effective drug target. Fortunately, the sequence identity of the 2019-nCoV protease and that of severe-acute respiratory syndrome virus (SARS-CoV) is as high as 96.1%. We show that the protease inhibitor binding sites of 2019-nCoV and SARS-CoV are almost identical, which means all potential anti-SARS-CoV chemotherapies are also potential 2019-nCoV drugs. Here, we report a family of potential 2019-nCoV drugs generated by a machine intelligence-based generative network complex (GNC). The potential effectiveness of treating 2019-nCoV by using some existing HIV drugs is also analyzed.

The coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has infected near 5 million people and led to over 0.3 million deaths. Currently, there is no specific anti-SARS-CoV-2 medication. New drug discovery typically takes more than ten years. Drug repositioning becomes one of the most feasible approaches for combating COVID-19. This work curates the largest available experimental dataset for SARS-CoV-2 or SARS-CoV main protease inhibitors. Based on this dataset, we develop validated machine learning models with relatively low root mean square error to screen 1553 FDA-approved drugs as well as other 7012 investigational or off-market drugs in DrugBank. We found that many existing drugs might be potentially potent to SARS-CoV-2. The druggability of many potent SARS-CoV-2 main protease inhibitors is analyzed. This work offers a foundation for further experimental studies of COVID-19 drug repositioning., Comment: 20 pages, 6 figures and 6 tables

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

It remains a challenging task to generate a vast variety of novel compounds with desirable pharmacological properties. In this work, a generative network complex (GNC) is proposed as a new platform for designing novel compounds, predicting their physical and chemical properties, and selecting potential drug candidates that fulfill various druggable criteria such as binding affinity, solubility, partition coefficient, etc. We combine a SMILES string generator, which consists of an encoder, a drug-property controlled or regulated latent space, and a decoder, with verification deep neural networks, a target-specific three-dimensional (3D) pose generator, and mathematical deep learning networks to generate new compounds, predict their drug properties, construct 3D poses associated with target proteins, and reevaluate druggability, respectively. New compounds were generated in the latent space by either randomized output, controlled output, or optimized output. In our demonstration, 2.08 million and 2.8 million novel compounds are generated respectively for Cathepsin S and BACE targets. These new compounds are very different from the seeds and cover a larger chemical space. For potentially active compounds, their 3D poses are generated using a state-of-the-art method. The resulting 3D complexes are further evaluated for druggability by a championing deep learning algorithm based on algebraic topology, differential geometry, and algebraic graph theories. Performed on supercomputers, the whole process took less than one week. Therefore, our GNC is an efficient new paradigm for discovering new drug candidates., Comment: 22 pages, 12 figures

Advanced mathematics, such as multiscale weighted colored graph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R grand challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 (GC2) focused on the pose prediction and binding affinity ranking and free energy prediction for Farnesoid X receptor ligands. Our models obtained the top place in absolute free energy prediction for free energy Set 1 in Stage 2. The latest competition, D3R Grand Challenge 3 (GC3), is considered as the most difficult challenge so far. It has 5 subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-$\alpha$, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of 26 official competitive tasks., Comment: 15 pages, 4 figures

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, ΔGel, and binding free energy, ΔΔGel, is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with solvent excluded surfaces for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of ΔGel obtained at the grid spacing of 1.0 A compared to ΔGel at 0.2 A averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 A ensures accuracy and reliability in ΔΔGel calculation. In fact, the grid spacing of 1.1 A appears to deliver adequate accuracy for high throughput screening. © 2017 Wiley Periodicals, Inc.