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Cao X, Hummel MH, Wang Y, Simmerling C, Coutsias EA. Exact Analytical Algorithm for the Solvent-Accessible Surface Area and Derivatives in Implicit Solvent Molecular Simulations on GPUs. J Chem Theory Comput 2024; 20:4456-4468. [PMID: 38780181 DOI: 10.1021/acs.jctc.3c01366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2024]
Abstract
In this paper, we present differentiable solvent-accessible surface area (dSASA), an exact geometric method to calculate SASA analytically along with atomic derivatives on GPUs. The atoms in a molecule are first assigned to tetrahedra in groups of four atoms by Delaunay tetrahedralization adapted for efficient GPU implementation, and the SASA values for atoms and molecules are calculated based on the tetrahedralization information and inclusion-exclusion method. The SASA values from the numerical icosahedral-based method can be reproduced with >98% accuracy for both proteins and RNAs. Having been implemented on GPUs and incorporated into AMBER, we can apply dSASA to implicit solvent molecular dynamics simulations with the inclusion of this nonpolar term. The current GPU version of GB/SA simulations has been accelerated up to nearly 20-fold compared to the CPU version, outperforming LCPO, a commonly used, fast algorithm for calculating SASA, as the system size increases. While we focus on the accuracy of the SASA calculations for proteins and nucleic acids, we also demonstrate stable GB/SA MD mini-protein simulations.
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Affiliation(s)
- Xin Cao
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794, United States
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
| | - Michelle H Hummel
- Sandia National Laboratories, Albuquerque, New Mexico 87123, United States
| | - Yuzhang Wang
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States
| | - Carlos Simmerling
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794, United States
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
| | - Evangelos A Coutsias
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794, United States
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
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Huang H, Simmerling C. Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs. J Chem Theory Comput 2018; 14:5797-5814. [PMID: 30303377 DOI: 10.1021/acs.jctc.8b00413] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.
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Affiliation(s)
- He Huang
- Laufer Center for Physical and Quantitative Biology , Stony Brook University , Stony Brook , New York 11794 , United States.,Department of Chemistry , Stony Brook University , Stony Brook , New York 11794 , United States
| | - Carlos Simmerling
- Laufer Center for Physical and Quantitative Biology , Stony Brook University , Stony Brook , New York 11794 , United States.,Department of Chemistry , Stony Brook University , Stony Brook , New York 11794 , United States
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Zhang B, Kilburg D, Eastman P, Pande VS, Gallicchio E. Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units. J Comput Chem 2017; 38:740-752. [PMID: 28160511 DOI: 10.1002/jcc.24745] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2016] [Revised: 01/05/2017] [Accepted: 01/08/2017] [Indexed: 11/07/2022]
Abstract
We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Baofeng Zhang
- Department of Chemistry, Brooklyn College of the City University of New York, 2900 Bedford Avenue, Brooklyn, New York, 11210
| | - Denise Kilburg
- Department of Chemistry, Brooklyn College of the City University of New York, 2900 Bedford Avenue, Brooklyn, New York, 11210.,Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York, 10016
| | - Peter Eastman
- Department of Bioengineering, Stanford University, Stanford, California, 94035
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California, 94035
| | - Emilio Gallicchio
- Department of Chemistry, Brooklyn College of the City University of New York, 2900 Bedford Avenue, Brooklyn, New York, 11210.,Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York, 10016
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Cai Q, Ye X, Wang J, Luo R. On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods. J Chem Theory Comput 2011; 7:3608-3619. [PMID: 24772042 PMCID: PMC3998210 DOI: 10.1021/ct200389p] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.
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Affiliation(s)
- Qin Cai
- Department of Biomedical Engineering, University of California, Irvine, California
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
| | - Xiang Ye
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
- Department of Physics, Shanghai Normal University, Shanghai, China
| | - Jun Wang
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
| | - Ray Luo
- Department of Biomedical Engineering, University of California, Irvine, California
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
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Rychkov G, Petukhov M. Joint neighbors approximation of macromolecular solvent accessible surface area. J Comput Chem 2007; 28:1974-89. [PMID: 17407094 DOI: 10.1002/jcc.20550] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
A new method for approximate analytical calculations of solvent accessible surface area (SASA) for arbitrary molecules and their gradients with respect to their atomic coordinates was developed. This method is based on the recursive procedure of pairwise joining of neighboring atoms. Unlike other available methods of approximate SASA calculations, the method has no empirical parameters, and therefore can be used with comparable accuracy in calculations of SASA in folded and unfolded conformations of macromolecules of any chemical nature. As shown by tests with globular proteins in folded conformations, average errors in absolute atomic surface area is around 1 A2, while for unfolded protein conformations it varies from 1.65 to 1.87 A2. Computational times of the method are comparable with those by GETAREA, one of the fastest exact analytical methods available today.
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Affiliation(s)
- Georgy Rychkov
- Division of Molecular and Radiation Biophysics, St. Petersburg Nuclear Physics Institute, The Russian Academy of Sciences (PNPI RAS), Gatchina, St. Petersburg 188300, Russia.
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Lee MS, Feig M, Salsbury FR, Brooks CL. New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations. J Comput Chem 2003; 24:1348-56. [PMID: 12827676 DOI: 10.1002/jcc.10272] [Citation(s) in RCA: 400] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
In a recent article (Lee, M. S.; Salsbury, F. R. Jr.; Brooks, C. L., III. J Chem Phys 2002, 116, 10606), we demonstrated that generalized Born (GB) theory provides a good approximation to Poisson electrostatic solvation energy calculations if one uses the same definitions of molecular volume for each. In this work, we present a new and improved analytic method for reproducing the Lee-Richards molecular volume, which is the most common volume definition for Poisson calculations. Overall, 1% errors are achieved for absolute solvation energies of a large set of proteins and relative solvation energies of protein conformations. We also introduce an accurate SASA approximation that uses the same machinery employed by our GB method and requires a small addition of computational cost. The combined methodology is shown to yield an efficient and accurate implicit solvent representation for simulations of biopolymers.
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Affiliation(s)
- Michael S Lee
- Department of Molecular Biology (TPC 6), The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037, USA
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