1
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Tolokh IS, Folescu DE, Onufriev AV. Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains. J Phys Chem B 2024. [PMID: 38860842 DOI: 10.1021/acs.jpcb.4c00254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.
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Affiliation(s)
- Igor S Tolokh
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Dan E Folescu
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
- Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Alexey V Onufriev
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, United States
- Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061, United States
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2
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Fukuda I, Moritsugu K, Higo J, Fukunishi Y. A cutoff-based method with charge-distribution-data driven pair potentials for efficiently estimating electrostatic interactions in molecular systems. J Chem Phys 2023; 159:234116. [PMID: 38112509 DOI: 10.1063/5.0172270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 11/27/2023] [Indexed: 12/21/2023] Open
Abstract
We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.
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Affiliation(s)
- Ikuo Fukuda
- Graduate School of Science, Osaka Metropolitan University, 1-2 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8231, Japan
- Japan Biological Informatics Consortium, 2-4-32 Aomi, Koto-ku, Tokyo, 135-8073, Japan
| | - Kei Moritsugu
- Graduate School of Science, Osaka Metropolitan University, 1-2 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8231, Japan
| | - Junichi Higo
- Graduate School of Information Science, University of Hyogo, 7-1-28 Minatojima Minamimachi, Chuo-ku, Kobe, Hyogo650-0047, Japan
- Research Organization of Science and Technology, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
| | - Yoshifumi Fukunishi
- Cellular and Molecular Biotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 2-3-26, Aomi, Koto-ku, Tokyo 135-0064, Japan
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3
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Fukuda I, Nakamura H. Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference. Biophys Rev 2022; 14:1315-1340. [PMID: 36659982 PMCID: PMC9842848 DOI: 10.1007/s12551-022-01029-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 11/30/2022] [Indexed: 01/13/2023] Open
Abstract
In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.
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Affiliation(s)
- Ikuo Fukuda
- Graduate School of Information Science, University of Hyogo, 7-1-28 Minatojima, Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047 Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871 Japan
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4
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Zhao Q, Liang J, Xu Z. Harmonic surface mapping algorithm for fast electrostatic sums. J Chem Phys 2018; 149:084111. [DOI: 10.1063/1.5044438] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qiyuan Zhao
- Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jiuyang Liang
- School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhenli Xu
- School of Mathematical Sciences, Institute of Natural Sciences and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
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5
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Kasahara K, Sakuraba S, Fukuda I. Enhanced Sampling of Molecular Dynamics Simulations of a Polyalanine Octapeptide: Effects of the Periodic Boundary Conditions on Peptide Conformation. J Phys Chem B 2018; 122:2495-2503. [PMID: 29439570 DOI: 10.1021/acs.jpcb.7b10830] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
We investigate the problem of artifacts caused by the periodic boundary conditions (PBC) used in molecular simulation studies. Despite the long history of simulations with PBCs, the existence of measurable artifacts originating from PBCs applied to inherently nonperiodic physical systems remains controversial. Specifically, these artifacts appear as differences between simulations of the same system but with different simulation-cell sizes. Earlier studies have implied that, even in the simple case of a small model peptide in water, sampling inefficiency is a major obstacle to understanding these artifacts. In this study, we have resolved the sampling issue using the replica exchange molecular dynamics (REMD) enhanced-sampling method to explore PBC artifacts. Explicitly solvated zwitterionic polyalanine octapeptides with three different cubic-cells, having dimensions of L = 30, 40, and 50 Å, were investigated to elucidate the differences with 64 replica × 500 ns REMD simulations using the AMBER parm99SB force field. The differences among them were not large overall, and the results for the L = 30 and 40 Å simulations in the conformational free energy landscape were found to be very similar at room temperature. However, a small but statistically significant difference was seen for L = 50 Å. We observed that extended conformations were slightly overstabilized in the smaller systems. The origin of these artifacts is discussed by comparison to an electrostatic calculation method without PBCs.
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Affiliation(s)
- Kota Kasahara
- College of Life Sciences , Ritsumeikan University , 1-1-1 Noji-higashi , Kusatsu , Shiga 525-8577 , Japan
| | - Shun Sakuraba
- Graduate School of Frontier Sciences , The University of Tokyo , 5-1-5 Kashiwanoha , Kashiwa , Chiba 277-8561 , Japan
| | - Ikuo Fukuda
- Institute for Protein Research , Osaka University , 3-2 Yamada-oka , Suita , Osaka 565-0871 , Japan
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6
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Fu J, Xu Z. Accurate image-charge method by the use of the residue theorem for core-shell dielectric sphere. J Chem Phys 2018; 148:054105. [DOI: 10.1063/1.5010722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jing Fu
- School of Mathematical Sciences, Institute of Natural Sciences and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhenli Xu
- School of Mathematical Sciences, Institute of Natural Sciences and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
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7
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Onufriev AV, Izadi S. Water models for biomolecular simulations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1347] [Citation(s) in RCA: 94] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Alexey V. Onufriev
- Department of Physics; Virginia Tech; Blacksburg VA USA
- Department of Computer Science; Virginia Tech; Blacksburg VA USA
- Center for Soft Matter and Biological Physics; Virginia Tech; Blacksburg VA USA
| | - Saeed Izadi
- Early Stage Pharmaceutical Development; Genentech Inc.; South San Francisco, CA USA
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8
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Wang H, Nakamura H, Fukuda I. A critical appraisal of the zero-multipole method: Structural, thermodynamic, dielectric, and dynamical properties of a water system. J Chem Phys 2016; 144:114503. [DOI: 10.1063/1.4943956] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Han Wang
- CAEP Software Center for High Performance Numerical Simulation, Huayuan Road 6, 100088 Beijing, China and Zuse Institute Berlin (ZIB), Berlin, Germany
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Ikuo Fukuda
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
- RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
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9
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Karandur D, Pettitt B. The contribution of electrostatic interactions to the collapse of oligoglycine in water. CONDENSED MATTER PHYSICS 2016; 19:23802. [PMID: 28943833 PMCID: PMC5607018 DOI: 10.5488/cmp.19.23802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Protein solubility and conformational stability are a result of a balance of interactions both within a protein and between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide backbone, becomes more favorable with an increasing length, yet longer peptides collapse due to the formation of favorable intrapeptide interactions between CO dipoles, in some cases without hydrogen bonds. The strongly repulsive solvent cavity formation is balanced by van der Waals attractions and electrostatic contributions. In order to investigate the competition between solvent exclusion and charge interactions we simulate the collapse of a long oligoglycine comprised of 15 residues while scaling the charges on the peptide from zero to fully charged. We examine the effect this has on the conformational properties of the peptide. We also describe the approximate thermodynamic changes that occur during the scaling both in terms of intrapeptide potentials and peptide-water potentials, and estimate the electrostatic solvation free energy of the system.
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Affiliation(s)
- D. Karandur
- Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, TX 77030, USA
| | - B.M. Pettitt
- Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, TX 77030, USA
- Sealy Center for Structural Biology and Molecular Biophysics, Department of Biochemistry and Molecular Biology, University of Texas Medical Branch, 301 University Blvd., Galveston, TX 77555-0304, USA
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10
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Cumberworth A, Bui JM, Gsponer J. Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models. J Comput Chem 2015; 37:629-40. [DOI: 10.1002/jcc.24235] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Revised: 09/25/2015] [Accepted: 10/06/2015] [Indexed: 12/13/2022]
Affiliation(s)
| | | | - Jörg Gsponer
- Center for High-Throughput Biology, UBC; Vancouver Canada
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11
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Fukuda I, Kamiya N, Nakamura H. The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: analysis of the accuracy and application to liquid systems. J Chem Phys 2014; 140:194307. [PMID: 24852538 DOI: 10.1063/1.4875693] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.
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Affiliation(s)
- Ikuo Fukuda
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Narutoshi Kamiya
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
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12
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Botello-Smith WM, Cai Q, Luo R. Biological applications of classical electrostatics methods. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014. [DOI: 10.1142/s0219633614400082] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Continuum electrostatics modeling of solvation based on the Poisson–Boltzmann (PB) equation has gained wide acceptance in biomolecular applications such as energetic analysis and structural visualization. Successful application of the PB solvent models requires careful calibration of the solvation parameters. Extensive testing and validation is also important to ensure accuracy in their applications. Limitation in the continuum modeling of solvation is also a known issue in certain biomolecular applications. Growing interest in membrane systems has further spurred developmental efforts to allow inclusion of membrane in the PB solvent models. Despite their past successes due to careful parameterization, algorithm development and parallel implementation, there is still much to be done to improve their transferability from the small molecular systems upon which they were developed and validated to complex macromolecular systems as advances in technology continue to push forward, providing ever greater computational resources to researchers to study more interesting biological systems of higher complexity.
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Affiliation(s)
- Wesley M. Botello-Smith
- Chemical Physics and Material Physics Graduate Program, University of California, Irvine, CA 92697, USA
- Department of Chemistry, University of California, Irvine, CA 92697, USA
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA
| | - Qin Cai
- Department of Biomedical Engineering, University of California, Irvine, CA 92697, USA
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA
| | - Ray Luo
- Department of Biomedical Engineering, University of California, Irvine, CA 92697, USA
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA
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13
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Cisneros GA, Karttunen M, Ren P, Sagui C. Classical electrostatics for biomolecular simulations. Chem Rev 2014; 114:779-814. [PMID: 23981057 PMCID: PMC3947274 DOI: 10.1021/cr300461d] [Citation(s) in RCA: 192] [Impact Index Per Article: 19.2] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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14
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Deng S, Xue C, Baumketner A, Jacobs D, Cai W. Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions. JOURNAL OF COMPUTATIONAL PHYSICS 2013; 245:84-106. [PMID: 23913979 PMCID: PMC3728380 DOI: 10.1016/j.jcp.2013.03.027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
This paper extends the image charge solvation model (ICSM) [J. Chem. Phys. 131, 154103 (2009)], a hybrid explicit/implicit method to treat electrostatic interactions in computer simulations of biomolecules formulated for spherical cavities, to prolate spheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-spherical solutes in molecular dynamics (MD) simulations. In addition to the utilization of a general truncated octahedron as the MD simulation box, central to the proposed extension is an image approximation method to compute the reaction field for a point charge placed inside such a non-spherical cavity by using a single image charge located outside the cavity. The resulting generalized image charge solvation model (GICSM) is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulations as a reference. We find that, for improved computational efficiency due to smaller simulation cells and consequently a less number of explicit solvent molecules, the generalized model can still faithfully reproduce known static and dynamic properties of liquid water at least for systems considered in the present paper, indicating its great potential to become an accurate but more efficient alternative to the ICSM when bio-macromolecules of irregular shapes are to be simulated.
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Affiliation(s)
- Shaozhong Deng
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
| | - Changfeng Xue
- Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng, Jiangsu 224051, PR China
| | - Andriy Baumketner
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
| | - Donald Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
| | - Wei Cai
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
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15
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Song W, Lin Y, Baumketner A, Deng S, Cai W, Jacobs DJ. Effect of the Reaction Field on Molecular Forces and Torques Revealed by an Image-Charge Solvation Model. COMMUNICATIONS IN COMPUTATIONAL PHYSICS 2013; 13:129-149. [PMID: 23833681 PMCID: PMC3702192 DOI: 10.4208/cicp.290711.180711s] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We recently developed the Image-Charge Solvation Model (ICSM), which is an explicit/implicit hybrid model to accurately account for long-range electrostatic forces in molecular dynamics simulations [Lin et al., J. Chem. Phys., 131, 154103, 2009]. The ICSM has a productive spherical volume within the simulation cell for which key physical properties of bulk water are reproduced, such as density, radial distribution function, diffusion constants and dielectric properties. Although the reaction field (RF) is essential, it typically accounts for less than 2% of the total electrostatic force on a water molecule. This observation motivates investigating further the role of the RF within the ICSM. In this report we focus on distributions of forces and torques on water molecules as a function of distance from the origin and make extensive tests over a range of model parameters where Coulomb forces are decomposed into direct interactions from waters modeled explicitly and the RF. Molecular torques due to the RF typically account for 20% of the total torque, revealing why the RF plays an important role in the dielectric properties of simulated water. Moreover, it becomes clear that the buffer layer in the ICSM is essential to mitigate artifacts caused by the discontinuous change in dielectric constants at the explicit/implicit interface.
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Affiliation(s)
- Wei Song
- Departments of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
| | - Yuchun Lin
- Departments of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
- Departments of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
| | - Andrij Baumketner
- Departments of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
- On leave from Institute for Condensed Matter Physics, 1 Svientsitsky Str., Lviv 79011, Ukraine
| | - Shaozhong Deng
- Departments of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
| | - Wei Cai
- Departments of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
| | - Donald J. Jacobs
- Departments of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28262, USA
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16
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Baker K, Baumketner A, Lin Y, Deng S, Jacobs D, Cai W. ICSM: An order N method for calculating electrostatic interactions added to TINKER. COMPUTER PHYSICS COMMUNICATIONS 2013; 184:19-26. [PMID: 23087451 PMCID: PMC3472439 DOI: 10.1016/j.cpc.2012.08.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We present an order N method for calculating electrostatic interactions that has been integrated into the molecular dynamics portion of the TINKER Molecular Modeling package. This method, introduced in a previous paper [J. Chem. Phys. 131 (2009) 154103] and termed the Image-Charge Solvation Model (ICSM), is a hybrid electrostatic approach that combines the strengths of both explicit and implicit representations of the solvent. A multiple-image method is used to calculate reaction fields due to the implicit part while the Fast Multipole Method (FMM) is used to calculate the Coulomb interactions for all charges, including the explicit part. The integrated package is validated through test simulations of liquid water. The results are compared with those obtained by the Particle Mesh Ewald (PME) method that is built in the TINKER package. Timing performance of TINKER with the integrated ICSM is benchmarked on bulk water as a function of the size of the system. In particular, timing analysis results show that the ICSM outperforms the PME for sufficiently large systems with the break-even point at around 30,000 particles in the simulated system.
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Affiliation(s)
- Katherine Baker
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
| | - Andrij Baumketner
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
- On leave from the Institute for Condensed Matter Physics, NAS of Ukraine, 1 Svientsistsky Str, Lviv, 79011
| | - Yuchun Lin
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, United States
| | - Shaozhong Deng
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
| | - Donald Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
| | - Wei Cai
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States
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17
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Fukuda I, Nakamura H. Non-Ewald methods: theory and applications to molecular systems. Biophys Rev 2012; 4:161-170. [PMID: 23293678 PMCID: PMC3428531 DOI: 10.1007/s12551-012-0089-4] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2012] [Accepted: 06/21/2012] [Indexed: 11/29/2022] Open
Abstract
Several non-Ewald methods for calculating electrostatic interactions have recently been developed, such as the Wolf method, the reaction field method, the pre-averaging method, and the zero-dipole summation method, for molecular dynamics simulations of various physical systems, including biomolecular systems. We review the theories of these approaches and their potential applications to molecular simulations, and discuss their relationships.
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Affiliation(s)
- Ikuo Fukuda
- RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198 Japan
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18
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Xu Z. A fast algorithm for treating dielectric discontinuities in charged spherical colloids. Interdiscip Sci 2012; 4:19-26. [PMID: 22392273 DOI: 10.1007/s12539-012-0113-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Revised: 07/28/2011] [Accepted: 07/29/2012] [Indexed: 11/28/2022]
Abstract
Electrostatic interactions between multiple colloids in ionic fluids are attracting much attention in studies of biological and soft matter systems. The evaluation of the polarization surface charges due to the spherical dielectric discontinuities poses a challenging problem to highly efficient computer simulations. In this paper, we propose a new method for fast calculating the electric field of spaced spheres using the multiple reflection expansion. The method uses a technique of recursive reflections among the spherical interfaces based on a formula of the multiple image representation, resulting in a simple, accurate and close-form expression of the surface polarization charges. Numerical calculations of the electric potential energies of charged spheres demonstrate the method is highly accurate with small number of reflections, and thus attractive for the use in practical simulations of related problems such as colloid suspension and macromolecular interactions.
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Affiliation(s)
- Zhenli Xu
- Department of Mathematics, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China.
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Xu Z, Cai W. Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations. SIAM REVIEW. SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS 2011; 53:683-720. [PMID: 23745011 PMCID: PMC3671632 DOI: 10.1137/090774288] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson-Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods.
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Affiliation(s)
- Zhenli Xu
- Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China, and Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC 28223 ()
| | - Wei Cai
- Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC 28223 (), and Beijing International Center for Mathematical Research, Beijing, People's Republic of China, 100871
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Gan Z, Xu Z. Multiple-image treatment of induced charges in Monte Carlo simulations of electrolytes near a spherical dielectric interface. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016705. [PMID: 21867341 DOI: 10.1103/physreve.84.016705] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2011] [Revised: 05/30/2011] [Indexed: 05/31/2023]
Abstract
The polarization-induced charges of a dielectric sphere are studied for charged colloidal systems in electrolyte solutions with a primitive model. The method of constructing multiple-image charges is used to approximate the polarization potential of a microion outside the sphere; it is based on a numerical discretization of the potential's analytical integral representation, and can systematically approximate the exact potential with desired accuracy by varyiation of the number of point images. Different aspects of the image effects are then investigated by Monte Carlo simulations for several colloidal systems, in both salt-free and salty environments. Furthermore, we studied the influence of discrete surface charges of different valences, and demonstrate that the polarization charges can significantly strengthen charge reversal for the colloid-microion complex, especially for multivalent interfacial ions.
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Affiliation(s)
- Zecheng Gan
- Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China
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Abstract
We have developed a treecode-based O(N log N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge-charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.
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Affiliation(s)
- Zhenli Xu
- Department of Mathematics, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
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Lin Y, Baumketner A, Song W, Deng S, Jacobs D, Cai W. Ionic solvation studied by image-charge reaction field method. J Chem Phys 2011; 134:044105. [PMID: 21280685 PMCID: PMC3045217 DOI: 10.1063/1.3530094] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2010] [Accepted: 12/01/2010] [Indexed: 11/14/2022] Open
Abstract
In a preceding paper [J. Chem. Phys. 131, 154103 (2009)], we introduced a new, hybrid explicit/implicit method to treat electrostatic interactions in computer simulations, and tested its performance for liquid water. In this paper, we report further tests of this method, termed the image-charge solvation model (ICSM), in simulations of ions solvated in water. We find that our model can faithfully reproduce known solvation properties of sodium and chloride ions. The charging free energy of a single sodium ion is in excellent agreement with the estimates by other electrostatics methods, while offering much lower finite-size errors. Similarly, the potentials of mean force computed for Na-Cl, Na-Na, and Cl-Cl pairs closely reproduce those reported previously. Collectively, our results demonstrate the superior accuracy of the proposed ICSM method for simulations of mixed media.
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Affiliation(s)
- Yuchun Lin
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, USA
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Xu Z, Cai W, Cheng X. Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model. COMMUNICATIONS IN COMPUTATIONAL PHYSICS 2010; 9:1056-1070. [PMID: 23504509 PMCID: PMC3596020 DOI: 10.4208/cicp.160410.200910a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
A multiple-image method is proposed to approximate the reaction-field potential of a source charge inside a finite length cylinder due to the electric polarization of the surrounding membrane and bulk water. When applied to a hybrid ion-channel model, this method allows a fast and accurate treatment of the electrostatic interactions of protein with membrane and solvent. To treat the channel/membrane interface boundary conditions of the electric potential, an optimization approach is used to derive image charges by fitting the reaction-field potential expressed in terms of cylindric harmonics. Meanwhile, additional image charges are introduced to satisfy the boundary conditions at the planar membrane interfaces. In the end, we convert the electrostatic interaction problem in a complex inhomogeneous system of ion channel/membrane/water into one in a homogeneous free space embedded with discrete charges (the source charge and image charges). The accuracy of this method is then validated numerically in calculating the solvation self-energy of a point charge.
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Affiliation(s)
- Zhenli Xu
- Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Wei Cai
- Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
- Beijing International Center for Mathematical Research, Beijing 100871, China
| | - Xiaolin Cheng
- Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
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Zhang C, Raugei S, Eisenberg B, Carloni P. Molecular Dynamics in Physiological Solutions: Force Fields, Alkali Metal Ions, and Ionic Strength. J Chem Theory Comput 2010; 6:2167-75. [DOI: 10.1021/ct9006579] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Chao Zhang
- German Research School for Simulation Sciences, FZ-Juelich/RWTH Aachen University, Aachen, Germany, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99352, Rush University Medical Center, 1653 W. Congress Parkway, Chicago, Illinois 60612, and SISSA, CNR-INFN-DEMOCRITOS, and Italian Institue of Technology (IIT), SISSA Unit, Trieste, Italy
| | - Simone Raugei
- German Research School for Simulation Sciences, FZ-Juelich/RWTH Aachen University, Aachen, Germany, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99352, Rush University Medical Center, 1653 W. Congress Parkway, Chicago, Illinois 60612, and SISSA, CNR-INFN-DEMOCRITOS, and Italian Institue of Technology (IIT), SISSA Unit, Trieste, Italy
| | - Bob Eisenberg
- German Research School for Simulation Sciences, FZ-Juelich/RWTH Aachen University, Aachen, Germany, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99352, Rush University Medical Center, 1653 W. Congress Parkway, Chicago, Illinois 60612, and SISSA, CNR-INFN-DEMOCRITOS, and Italian Institue of Technology (IIT), SISSA Unit, Trieste, Italy
| | - Paolo Carloni
- German Research School for Simulation Sciences, FZ-Juelich/RWTH Aachen University, Aachen, Germany, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99352, Rush University Medical Center, 1653 W. Congress Parkway, Chicago, Illinois 60612, and SISSA, CNR-INFN-DEMOCRITOS, and Italian Institue of Technology (IIT), SISSA Unit, Trieste, Italy
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Xu Z. Treecode algorithm for pairwise electrostatic interactions with solvent-solute polarization. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:020902. [PMID: 20365522 DOI: 10.1103/physreve.81.020902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2009] [Revised: 01/18/2010] [Indexed: 05/29/2023]
Abstract
An O(N log N) treecode algorithm is presented for computing pairwise interactions of electrostatic free energy for reaction potentials with polarization effects due to the macroscopic solvent. A multipole expansion for a cluster is used to account for particles inside the cluster, where a spatial difference is applied to obtain the expansion coefficients of the polarization function. Numerical tests are performed to illustrate the accuracy and efficiency of the approach. The algorithm is significant in speeding up generalized Born methods for biomolecular simulations under the framework of macroscopically treating solvents.
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Affiliation(s)
- Zhenli Xu
- Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China and Department of Mathematics and Statistics, University of North Carolina, Charlotte, North Carolina 28223, USA.
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