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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.
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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
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Nguyen DD, Wei GW. DG-GL: Differential geometry-based geometric learning of molecular datasets. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3179. [PMID: 30693661 PMCID: PMC6598676 DOI: 10.1002/cnm.3179] [Citation(s) in RCA: 47] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Revised: 11/21/2018] [Accepted: 12/06/2018] [Indexed: 05/11/2023]
Abstract
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.
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Affiliation(s)
- Duc Duy Nguyen
- Department of Mathematics, Michigan State University, East Lansing, 48824, Michigan
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, 48824, Michigan
- Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, Michigan
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Jurrus E, Engel D, Star K, Monson K, Brandi J, Felberg LE, Brookes DH, Wilson L, Chen J, Liles K, Chun M, Li P, Gohara DW, Dolinsky T, Konecny R, Koes DR, Nielsen JE, Head-Gordon T, Geng W, Krasny R, Wei GW, Holst MJ, McCammon JA, Baker NA. Improvements to the APBS biomolecular solvation software suite. Protein Sci 2017; 27:112-128. [PMID: 28836357 DOI: 10.1002/pro.3280] [Citation(s) in RCA: 1160] [Impact Index Per Article: 165.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Revised: 08/21/2017] [Accepted: 08/22/2017] [Indexed: 12/11/2022]
Abstract
The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that have provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses the three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this article, we discuss the models and capabilities that have recently been implemented within the APBS software package including a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory-based algorithm for determining pKa values, and an improved web-based visualization tool for viewing electrostatics.
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Affiliation(s)
| | - Dave Engel
- Pacific Northwest National Laboratory, Richland, Washington
| | - Keith Star
- Pacific Northwest National Laboratory, Richland, Washington
| | - Kyle Monson
- Pacific Northwest National Laboratory, Richland, Washington
| | - Juan Brandi
- Pacific Northwest National Laboratory, Richland, Washington
| | | | | | | | - Jiahui Chen
- Southern Methodist University, Dallas, Texas
| | - Karina Liles
- Pacific Northwest National Laboratory, Richland, Washington
| | - Minju Chun
- Pacific Northwest National Laboratory, Richland, Washington
| | - Peter Li
- Pacific Northwest National Laboratory, Richland, Washington
| | | | | | - Robert Konecny
- University of California San Diego, San Diego, California
| | - David R Koes
- University of Pittsburgh, Pittsburgh, Pennsylvania
| | | | | | - Weihua Geng
- Southern Methodist University, Dallas, Texas
| | | | - Guo-Wei Wei
- Michigan State University, East Lansing, Michigan
| | | | | | - Nathan A Baker
- Pacific Northwest National Laboratory, Richland, Washington.,Brown University, Providence, Rhode Island
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Wang B, Wei GW. Parameter optimization in differential geometry based solvation models. J Chem Phys 2015; 143:134119. [PMID: 26450304 PMCID: PMC4602332 DOI: 10.1063/1.4932342] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Accepted: 09/22/2015] [Indexed: 01/01/2023] Open
Abstract
Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and non-polar interactions in a self-consistent framework. Our earlier study indicates that DG based non-polar solvation model outperforms other methods in non-polar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and non-polar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.
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Affiliation(s)
- Bao Wang
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
| | - G W Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
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