1
|
Ullah SA, Yang X, Jones B, Zhao S, Geng W, Wei GW. Bridging Eulerian and Lagrangian Poisson-Boltzmann solvers by ESES. J Comput Chem 2024; 45:306-320. [PMID: 37830273 PMCID: PMC10993026 DOI: 10.1002/jcc.27239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 08/08/2023] [Accepted: 09/24/2023] [Indexed: 10/14/2023]
Abstract
The Poisson-Boltzmann (PB) model is a widely used electrostatic model for biomolecular solvation analysis. Formulated as an elliptic interface problem, the PB model can be numerically solved on either Eulerian meshes using finite difference/finite element methods or Lagrangian meshes using boundary element methods. Molecular surface generators, which produce the discretized dielectric interfaces between solutes and solvents, are critical factors in determining the accuracy and efficiency of the PB solvers. In this work, we investigate the utility of the Eulerian Solvent Excluded Surface (ESES) software for rendering conjugated Eulerian and Lagrangian surface representations, which enables us to numerically validate and compare the quality of Eulerian PB solvers, such as the MIBPB solver, and the Lagrangian PB solvers, such as the TABI-PB solver. Furthermore, with the ESES software and its associated PB solvers, we are able to numerically validate an interesting and useful but often neglected source-target symmetric property associated with the linearized PB model.
Collapse
Affiliation(s)
| | - Xin Yang
- Department of Mathematics, Southern Methodist University, Dallas, Texas, USA
| | - Ben Jones
- Department of Mathematics, Michigan State University, East Lansing, Michigan, USA
| | - Shan Zhao
- Department of Mathematics, University of Alabama, Tuscaloosa, Alabama, USA
| | - Weihua Geng
- Department of Mathematics, Southern Methodist University, Dallas, Texas, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan, USA
| |
Collapse
|
2
|
Chen J, Xu Y, Yang X, Cang Z, Geng W, Wei GW. Poisson-Boltzmann-based machine learning model for electrostatic analysis. Biophys J 2024:S0006-3495(24)00107-3. [PMID: 38356263 DOI: 10.1016/j.bpj.2024.02.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Revised: 01/26/2024] [Accepted: 02/09/2024] [Indexed: 02/16/2024] Open
Abstract
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.
Collapse
Affiliation(s)
- Jiahui Chen
- Department of Mathematics, University of Arkansas, Fayetteville, Arkansas
| | | | - Xin Yang
- Department of Mathematics, Southern Methodist University, Dallas, Texas
| | - Zixuan Cang
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
| | - Weihua Geng
- Department of Mathematics, Southern Methodist University, Dallas, Texas.
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan; Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan.
| |
Collapse
|
3
|
Wee J, Chen J, Xia K, Wei GW. Integration of persistent Laplacian and pre-trained transformer for protein solubility changes upon mutation. Comput Biol Med 2024; 169:107918. [PMID: 38194782 PMCID: PMC10922365 DOI: 10.1016/j.compbiomed.2024.107918] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Revised: 12/21/2023] [Accepted: 01/01/2024] [Indexed: 01/11/2024]
Abstract
Protein mutations can significantly influence protein solubility, which results in altered protein functions and leads to various diseases. Despite tremendous effort, machine learning prediction of protein solubility changes upon mutation remains a challenging task as indicated by the poor scores of normalized Correct Prediction Ratio (CPR). Part of the challenge stems from the fact that there is no three-dimensional (3D) structures for the wild-type and mutant proteins. This work integrates persistent Laplacians and pre-trained Transformer for the task. The Transformer, pretrained with hundreds of millions of protein sequences, embeds wild-type and mutant sequences, while persistent Laplacians track the topological invariant change and homotopic shape evolution induced by mutations in 3D protein structures, which are rendered from AlphaFold2. The resulting machine learning model was trained on an extensive data set labeled with three solubility types. Our model outperforms all existing predictive methods and improves the state-of-the-art up to 15%.
Collapse
Affiliation(s)
- JunJie Wee
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
| | - Jiahui Chen
- Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, USA
| | - Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA; Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA.
| |
Collapse
|
4
|
Zhao S, Ijaodoro I, McGowan M, Alexov E. Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential. JOURNAL OF COMPUTATIONAL PHYSICS 2024; 497:112634. [PMID: 38045553 PMCID: PMC10688429 DOI: 10.1016/j.jcp.2023.112634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/05/2023]
Abstract
The Poisson-Boltzmann (PB) equation governing the electrostatic potential with a unit is often transformed to a normalized form for a dimensionless potential in numerical studies. To calculate the electrostatic free energy (EFE) of biological interests, a unit conversion has to be conducted, because the existing PB energy functionals are all described in terms of the original potential. To bypass this conversion, this paper proposes energy functionals in terms of the dimensionless potential for the first time in the literature, so that the normalized PB equation can be directly derived by using the Euler-Lagrange variational analysis. Moreover, alternative energy forms have been rigorously derived to avoid approximating the gradient of singular functions in the electrostatic stress term. A systematic study has been carried out to examine the surface integrals involved in alternative energy forms and their dependence on finite domain size and mesh step size, which leads to a recommendation on the EFE forms for efficient computation of protein systems. The calculation of the EFE in the regularization formulation, which is an analytical approach for treating singular charge sources of the PB equation, has also been studied. The proposed energy forms have been validated by considering smooth dielectric settings, such as diffuse interface and super-Gaussian, for which the EFE of the nonlinear PB model is found to be significantly different from that of the linearized PB model. All proposed energy functionals and EFE forms are designed such that the dimensionless potential can be simply plugged in to compute the EFE in the unit of kcal/mol, and they can also be applied in the classical sharp interface PB model.
Collapse
Affiliation(s)
- Shan Zhao
- Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
| | - Idowu Ijaodoro
- Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
| | - Mark McGowan
- Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
| | - Emil Alexov
- Department of Physics and Astronomy, Clemson University, Clemson, SC 29634, USA
| |
Collapse
|
5
|
Rana MM, Nguyen DD. EISA-Score: Element Interactive Surface Area Score for Protein–Ligand Binding Affinity Prediction. J Chem Inf Model 2022; 62:4329-4341. [DOI: 10.1021/acs.jcim.2c00697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Md Masud Rana
- Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, United States
| | - Duc Duy Nguyen
- Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, United States
| |
Collapse
|
6
|
Abstract
Monte Carlo (MC) methods are important computational tools for molecular structure optimizations and predictions. When solvent effects are explicitly considered, MC methods become very expensive due to the large degree of freedom associated with the water molecules and mobile ions. Alternatively implicit-solvent MC can largely reduce the computational cost by applying a mean field approximation to solvent effects and meanwhile maintains the atomic detail of the target molecule. The two most popular implicit-solvent models are the Poisson-Boltzmann (PB) model and the Generalized Born (GB) model in a way such that the GB model is an approximation to the PB model but is much faster in simulation time. In this work, we develop a machine learning-based implicit-solvent Monte Carlo (MLIMC) method by combining the advantages of both implicit solvent models in accuracy and efficiency. Specifically, the MLIMC method uses a fast and accurate PB-based machine learning (PBML) scheme to compute the electrostatic solvation free energy at each step. We validate our MLIMC method by using a benzene-water system and a protein-water system. We show that the proposed MLIMC method has great advantages in speed and accuracy for molecular structure optimization and prediction.
Collapse
Affiliation(s)
- Jiahui Chen
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Weihua Geng
- Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, MI 48824, USA
- Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824, USA
| |
Collapse
|
7
|
Wu CY, Ouyang M, Wang B, de Rutte J, Joo A, Jacobs M, Ha K, Bertozzi AL, Di Carlo D. Monodisperse drops templated by 3D-structured microparticles. SCIENCE ADVANCES 2020; 6:eabb9023. [PMID: 33148643 PMCID: PMC7673687 DOI: 10.1126/sciadv.abb9023] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 09/21/2020] [Indexed: 05/27/2023]
Abstract
The ability to create uniform subnanoliter compartments using microfluidic control has enabled new approaches for analysis of single cells and molecules. However, specialized instruments or expertise has been required, slowing the adoption of these cutting-edge applications. Here, we show that three dimensional-structured microparticles with sculpted surface chemistries template uniformly sized aqueous drops when simply mixed with two immiscible fluid phases. In contrast to traditional emulsions, particle-templated drops of a controlled volume occupy a minimum in the interfacial energy of the system, such that a stable monodisperse state results with simple and reproducible formation conditions. We describe techniques to manufacture microscale drop-carrier particles and show that emulsions created with these particles prevent molecular exchange, concentrating reactions within the drops, laying a foundation for sensitive compartmentalized molecular and cell-based assays with minimal instrumentation.
Collapse
Affiliation(s)
- Chueh-Yu Wu
- Department of Bioengineering, University of California, Los Angeles, CA 90095, USA
| | - Mengxing Ouyang
- Department of Bioengineering, University of California, Los Angeles, CA 90095, USA
| | - Bao Wang
- Department of Mathematics, University of California, Los Angeles, CA 90095, USA
| | - Joseph de Rutte
- Department of Bioengineering, University of California, Los Angeles, CA 90095, USA
| | - Alexis Joo
- Department of Bioengineering, University of California, Los Angeles, CA 90095, USA
| | - Matthew Jacobs
- Department of Mathematics, University of California, Los Angeles, CA 90095, USA
| | - Kyung Ha
- Department of Mathematics, University of California, Los Angeles, CA 90095, USA
| | - Andrea L Bertozzi
- Department of Mathematics, University of California, Los Angeles, CA 90095, USA
- Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
- California NanoSystems Institute, University of California, Los Angeles, CA 90095, USA
| | - Dino Di Carlo
- Department of Bioengineering, University of California, Los Angeles, CA 90095, USA.
- Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
- California NanoSystems Institute, University of California, Los Angeles, CA 90095, USA
- Jonsson Comprehensive Cancer Center, University of California, Los Angeles, CA 90095, USA
| |
Collapse
|
8
|
Abstract
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.
Collapse
Affiliation(s)
- Duc Duy Nguyen
- Department of Mathematics, Michigan State University, MI 48824, USA.
| | - Zixuan Cang
- Department of Mathematics, Michigan State University, MI 48824, USA.
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, MI 48824, USA. and Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824, USA and Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
| |
Collapse
|
9
|
Nguyen DD, Gao K, Wang M, Wei GW. MathDL: mathematical deep learning for D3R Grand Challenge 4. J Comput Aided Mol Des 2020; 34:131-147. [PMID: 31734815 PMCID: PMC7376411 DOI: 10.1007/s10822-019-00237-5] [Citation(s) in RCA: 45] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Accepted: 10/14/2019] [Indexed: 12/17/2022]
Abstract
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 on docking pose predictions has significantly improved from our previous ones.
Collapse
Affiliation(s)
- Duc Duy Nguyen
- Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA
| | - Kaifu Gao
- Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA
| | - Menglun Wang
- Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA.
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI, 48824, USA.
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, 48824, USA.
| |
Collapse
|
10
|
Zhao R, Cang Z, Tong Y, Wei GW. Protein pocket detection via convex hull surface evolution and associated Reeb graph. Bioinformatics 2019; 34:i830-i837. [PMID: 30423105 DOI: 10.1093/bioinformatics/bty598] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Motivation Protein pocket information is invaluable for drug target identification, agonist design, virtual screening and receptor-ligand binding analysis. A recent study indicates that about half holoproteins can simultaneously bind multiple interacting ligands in a large pocket containing structured sub-pockets. Although this hierarchical pocket and sub-pocket structure has a significant impact to multi-ligand synergistic interactions in the protein binding site, there is no method available for this analysis. This work introduces a computational tool based on differential geometry, algebraic topology and physics-based simulation to address this pressing issue. Results We propose to detect protein pockets by evolving the convex hull surface inwards until it touches the protein surface everywhere. The governing partial differential equations (PDEs) include the mean curvature flow combined with the eikonal equation commonly used in the fast marching algorithm in the Eulerian representation. The surface evolution induced Morse function and Reeb graph are utilized to characterize the hierarchical pocket and sub-pocket structure in controllable detail. The proposed method is validated on PDBbind refined sets of 4414 protein-ligand complexes. Extensive numerical tests indicate that the proposed method not only provides a unique description of pocket-sub-pocket relations, but also offers efficient estimations of pocket surface area, pocket volume and pocket depth. Availability and implementation Source code available at https://github.com/rdzhao/ProteinPocketDetection. Webserver available at http://weilab.math.msu.edu/PPD/.
Collapse
Affiliation(s)
- Rundong Zhao
- Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA
| | - Zixuan Cang
- Department of Mathematics, Michigan State University, East Lansing, MI, USA
| | - Yiying Tong
- Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, MI, USA
| |
Collapse
|
11
|
Lange AW, Herbert JM, Albrecht BJ, You ZQ. Intrinsically smooth discretisation of Connolly's solvent-excluded molecular surface. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1644384] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Adrian W. Lange
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA
| | - Benjamin J. Albrecht
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA
| | - Zhi-Qiang You
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA
| |
Collapse
|
12
|
Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges. J Comput Aided Mol Des 2018; 33:71-82. [PMID: 30116918 DOI: 10.1007/s10822-018-0146-6] [Citation(s) in RCA: 99] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2018] [Accepted: 08/03/2018] [Indexed: 12/18/2022]
Abstract
Advanced mathematics, such as multiscale weighted colored subgraph 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 focused on the pose prediction, 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 five subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-α, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of these 26 tasks.
Collapse
|
13
|
Wu K, Wei GW. Quantitative Toxicity Prediction Using Topology Based Multitask Deep Neural Networks. J Chem Inf Model 2018; 58:520-531. [DOI: 10.1021/acs.jcim.7b00558] [Citation(s) in RCA: 75] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kedi Wu
- Department of Mathematics, ‡Department of Electrical and Computer Engineering, and ¶Department of Biochemistry
and Molecular Biology, Michigan State University, East Lansing, Michigan 48824, United States
| | - Guo-Wei Wei
- Department of Mathematics, ‡Department of Electrical and Computer Engineering, and ¶Department of Biochemistry
and Molecular Biology, Michigan State University, East Lansing, Michigan 48824, United States
| |
Collapse
|
14
|
Zhao R, Wang M, Tong Y, Wei GW. Divide-and-conquer strategy for large-scale Eulerian solvent excluded surface. COMMUNICATIONS IN INFORMATION AND SYSTEMS 2018; 18:299-329. [PMID: 31327932 DOI: 10.4310/cis.2018.v18.n4.a5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
MOTIVATION Surface generation and visualization are some of the most important tasks in biomolecular modeling and computation. Eulerian solvent excluded surface (ESES) software provides analytical solvent excluded surface (SES) in the Cartesian grid, which is necessary for simulating many biomolecular electrostatic and ion channel models. However, large biomolecules and/or fine grid resolutions give rise to excessively large memory requirements in ESES construction. We introduce an out-of-core and parallel algorithm to improve the ESES software. RESULTS The present approach drastically improves the spatial and temporal efficiency of ESES. The memory footprint and time complexity are analyzed and empirically verified through extensive tests with a large collection of biomolecule examples. Our results show that our algorithm can successfully reduce memory footprint through a straightforward divide-and-conquer strategy to perform the calculation of arbitrarily large proteins on a typical commodity personal computer. On multi-core computers or clusters, our algorithm can reduce the execution time by parallelizing most of the calculation as disjoint subproblems. Various comparisons with the state-of-the-art Cartesian grid based SES calculation were done to validate the present method and show the improved efficiency. This approach makes ESES a robust software for the construction of analytical solvent excluded surfaces. AVAILABILITY AND IMPLEMENTATION http://weilab.math.msu.edu/ESES.
Collapse
Affiliation(s)
- Rundong Zhao
- Department of Computer Science and Engineering, Michigan State University, MI 48824, USA
| | - Menglun Wang
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Yiying Tong
- Department of Computer Science and Engineering, Michigan State University, MI 48824, USA
| | - Guo-Wei Wei
- Department of Mathematics, and Department of Electrical and Computer Engineering, and Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824, USA
| |
Collapse
|
15
|
Cang Z, Mu L, Wei GW. Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening. PLoS Comput Biol 2018; 14:e1005929. [PMID: 29309403 PMCID: PMC5774846 DOI: 10.1371/journal.pcbi.1005929] [Citation(s) in RCA: 139] [Impact Index Per Article: 23.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2017] [Revised: 01/19/2018] [Accepted: 12/15/2017] [Indexed: 12/05/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Zixuan Cang
- Department of Mathematics, Michigan State University, East Lansing, Michigan, United States of America
| | - Lin Mu
- Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States of America
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan, United States of America
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan, United States of America
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan, United States of America
| |
Collapse
|
16
|
Wang B, Wang C, Wu K, Wei G. Breaking the polar‐nonpolar division in solvation free energy prediction. J Comput Chem 2017; 39:217-233. [DOI: 10.1002/jcc.25107] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2017] [Revised: 09/02/2017] [Accepted: 10/22/2017] [Indexed: 11/12/2022]
Affiliation(s)
- Bao Wang
- Department of MathematicsMichigan State University Michigan48824
| | - Chengzhang Wang
- School of Statistics and MathematicsCentral University of Finance and EconomicsBeijing100081 China
| | - Kedi Wu
- Department of MathematicsMichigan State University Michigan48824
| | - Guo‐Wei Wei
- Department of MathematicsMichigan State University Michigan48824
- Department of Electrical and ComputerEngineering Michigan State University Michigan48824
- Department of Biochemistry and MolecularBiology Michigan State UniversityMichigan48824
| |
Collapse
|
17
|
Forouzesh N, Izadi S, Onufriev AV. Grid-Based Surface Generalized Born Model for Calculation of Electrostatic Binding Free Energies. J Chem Inf Model 2017; 57:2505-2513. [DOI: 10.1021/acs.jcim.7b00192] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Saeed Izadi
- Early Stage Pharmaceutical
Development, Genentech Inc., 1 DNA
Way, South San Francisco, California 94080, United States
| | - Alexey V. Onufriev
- Center
for Soft Matter and Biological Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
| |
Collapse
|
18
|
Cang Z, Wei GW. TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions. PLoS Comput Biol 2017; 13:e1005690. [PMID: 28749969 PMCID: PMC5549771 DOI: 10.1371/journal.pcbi.1005690] [Citation(s) in RCA: 155] [Impact Index Per Article: 22.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Revised: 08/08/2017] [Accepted: 07/18/2017] [Indexed: 11/18/2022] Open
Abstract
Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. AVAILABILITY weilab.math.msu.edu/TDL/.
Collapse
Affiliation(s)
- Zixuan Cang
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
| |
Collapse
|
19
|
Nguyen DD, Wang B, Wei GW. Accurate, robust, and reliable calculations of Poisson-Boltzmann binding energies. J Comput Chem 2017; 38:941-948. [PMID: 28211071 PMCID: PMC5844473 DOI: 10.1002/jcc.24757] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2016] [Revised: 11/28/2016] [Accepted: 01/22/2017] [Indexed: 12/18/2022]
Abstract
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 Å compared to ΔGel at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in ΔΔGel calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. © 2017 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Duc D Nguyen
- Department of Mathematics, Michigan State University, Michigan, 48824
| | - Bao Wang
- Department of Mathematics, Michigan State University, Michigan, 48824
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, Michigan, 48824
- Department of Electrical and Computer Engineering, Michigan State University, Michigan, 48824
- Department of Biochemistry and Molecular Biology, Michigan State University, Michigan, 48824
| |
Collapse
|
20
|
Wang B, Zhao Z, Nguyen DD, Wei GW. Feature functional theory–binding predictor (FFT–BP) for the blind prediction of binding free energies. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2083-1] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
|