1
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Addison-Smith I, Guzman HV, Cooper CD. Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model. J Chem Theory Comput 2023; 19:2996-3006. [PMID: 37104704 DOI: 10.1021/acs.jctc.3c00021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here we present a calculation of the electric field on the solute-solvent interface that is exact for piecewise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a much finer mesh than in solvation energy calculations to get acceptable accuracy in the force, whereas the same surface mesh as in a standard energy calculation is appropriate for the boundary element method. Among the four evaluated alternatives of force calculation, we saw that the most accurate one is based on the Maxwell stress tensor. However, for a realistic application, like the barnase-barstar complex, the approach based on variations of the energy functional, which is less accurate, gives equivalent results. This analysis is useful toward using the Poisson-Boltzmann equation for force calculations in applications where high accuracy is key, for example, to feed molecular dynamics models or to enable the study of the interaction between large molecular structures, like viruses adsorbed onto substrates.
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Affiliation(s)
- Ian Addison-Smith
- Department of Mechanical Engineering, Universidad Técnica Federico Santa María, 2390123 Valparaíso, Chile
| | - Horacio V Guzman
- Department of Theoretical Physics, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Christopher D Cooper
- Department of Mechanical Engineering, Universidad Técnica Federico Santa María, 2390123 Valparaíso, Chile
- Centro Científico Tecnológico de Valparaíso, Universidad Técnica Federico Santa María, 2390123 Valparaíso, Chile
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2
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Cao S, Kalin ML, Huang X. EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules. J Comput Chem 2023; 44:1536-1549. [PMID: 36856731 DOI: 10.1002/jcc.27088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2022] [Revised: 12/24/2022] [Accepted: 01/29/2023] [Indexed: 03/02/2023]
Abstract
Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.
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Affiliation(s)
- Siqin Cao
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin, USA
| | - Michael L Kalin
- Biophysics Graduate Program, University of Wisconsin-Madison, Madison, Wisconsin, USA
| | - Xuhui Huang
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin, USA
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3
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Herbert JM. Dielectric continuum methods for quantum chemistry. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1519] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- John M. Herbert
- Department of Chemistry and Biochemistry The Ohio State University Columbus Ohio USA
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4
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Wei H, Luo A, Qiu T, Luo R, Qi R. Improved Poisson-Boltzmann Methods for High-Performance Computing. J Chem Theory Comput 2019; 15:6190-6202. [PMID: 31525962 DOI: 10.1021/acs.jctc.9b00602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Implicit solvent models based on the Poisson-Boltzmann equation (PBE) have been widely used to study electrostatic interactions in biophysical processes. These models often treat the solvent and solute regions as high and low dielectric continua, leading to a large jump in dielectrics across the molecular surface which is difficult to handle. Higher order interface schemes are often needed to seek higher accuracy for PBE applications. However, these methods are usually very liberal in the use of grid points nearby the molecular surface, making them difficult to use on high-performance computing platforms. Alternatively, the harmonic average (HA) method has been used to approximate dielectric interface conditions near the molecular surface with surprisingly good convergence and is well suited for high-performance computing. By adopting a 7-point stencil, the HA method is advantageous in generating simple 7-banded coefficient matrices, which greatly facilitate linear system solution with dense data parallelism, on high-performance computing platforms such as a graphics processing unit (GPU). However, the HA method is limited due to its lower accuracy. Therefore, it would be of great interest for high-performance applications to develop more accurate methods while retaining the simplicity and effectiveness of the 7-point stencil discretization scheme. In this study, we have developed two new algorithms based on the spirit of the HA method by introducing more physical interface relations and imposing the discretized Poisson's equation to the second order, respectively. Our testing shows that, for typical biomolecules, the new methods significantly improve the numerical accuracy to that comparable to the second-order solvers and with ∼65% overall efficiency gain on widely available high-performance GPU platforms.
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5
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Denton AR, Alziyadi MO. Osmotic pressure of permeable ionic microgels: Poisson-Boltzmann theory and exact statistical mechanical relations in the cell model. J Chem Phys 2019; 151:074903. [DOI: 10.1063/1.5091115] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Affiliation(s)
- Alan R. Denton
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
| | - Mohammed O. Alziyadi
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
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6
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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
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7
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Greene D, Qi R, Nguyen R, Qiu T, Luo R. Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies. J Chem Inf Model 2019; 59:3041-3056. [PMID: 31145610 PMCID: PMC7197397 DOI: 10.1021/acs.jcim.9b00363] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y12R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.
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8
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Qi R, Luo R. Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units. J Chem Inf Model 2018; 59:409-420. [PMID: 30550277 DOI: 10.1021/acs.jcim.8b00761] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Poisson-Boltzmann equation (PBE) based continuum electrostatics models have been widely used in modeling electrostatic interactions in biochemical processes, particularly in estimating protein-ligand binding affinities. Fast convergence of PBE solvers is crucial in binding affinity computations as numerous snapshots need to be processed. Efforts have been reported to develop PBE solvers on graphics processing units (GPUs) for efficient modeling of biomolecules, though only relatively simple successive over-relaxation and conjugate gradient methods were implemented. However, neither convergence nor scaling properties of the two methods are optimal for large biomolecules. On the other hand, geometric multigrid (MG) has been shown to be an optimal solver on CPUs, though no MG have been reported for biomolecular applications on GPUs. This is not a surprise as it is a more complex method and depends on simpler but limited iterative methods such as Gauss-Seidel in its core relaxation procedure. The robustness and efficiency of MG on GPUs are also unclear. Here we present an implementation and a thorough analysis of MG on GPUs. Our analysis shows that robustness is a more pronounced issue than efficiency for both MG and other tested solvers when the single precision is used for complex biomolecules. We further show how to balance robustness and efficiency utilizing MG's overall efficiency and conjugate gradient's robustness, pointing to a hybrid GPU solver with a good balance of efficiency and accuracy. The new PBE solver will significantly improve the computational throughput for a range of biomolecular applications on the GPU platforms.
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9
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Wilmott ZM, Breward CJW, Chapman SJ. Modelling Low-Salinity Oil Recovery Mechanisms Using an Ion Dissociation Model. Transp Porous Media 2018. [DOI: 10.1007/s11242-018-1220-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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10
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Xiao L, Luo R. Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid. J Chem Phys 2018; 147:214112. [PMID: 29221408 DOI: 10.1063/1.5016052] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.
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Affiliation(s)
- Li Xiao
- Departments of Biomedical Engineering, University of California, Irvine, California 92697, USA
| | - Ray Luo
- Departments of Biomedical Engineering, University of California, Irvine, California 92697, USA
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11
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Cao S, Zhu L, Huang X. 3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1416195] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Siqin Cao
- Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Lizhe Zhu
- Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen, China
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12
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Wang C, Ren P, Luo R. Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling. J Phys Chem B 2017; 121:11169-11179. [PMID: 29164898 DOI: 10.1021/acs.jpcb.7b09616] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.
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Affiliation(s)
| | - Pengyu Ren
- Department of Biomedical Engineering, University of Texas , Austin, Texas 78712, United States
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13
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Xiao L, Diao J, Greene D, Wang J, Luo R. A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins. J Chem Theory Comput 2017; 13:3398-3412. [PMID: 28564540 PMCID: PMC5728381 DOI: 10.1021/acs.jctc.7b00382] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.
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Affiliation(s)
| | | | | | - Junmei Wang
- Department of Pharmaceutical Sciences, University of Pittsburgh , Pittsburgh, Pennsylvania 15261, United States
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14
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Wang C, Xiao L, Luo R. Numerical interpretation of molecular surface field in dielectric modeling of solvation. J Comput Chem 2017; 38:1057-1070. [PMID: 28318096 PMCID: PMC5464005 DOI: 10.1002/jcc.24782] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2016] [Revised: 01/10/2017] [Accepted: 02/20/2017] [Indexed: 11/07/2022]
Abstract
Continuum solvent models, particularly those based on the Poisson-Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one-sided and two-sided methods with both first-order and second-order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one-dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface-to-atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second-order methods, including the one-dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one-dimensional method is far more efficient than standard second-order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Changhao Wang
- Chemical and Materials Physics Graduate Program, University of California, Irvine, California, 92697
- Department of Physics and Astronomy, University of California, Irvine, California, 92697
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California, 92697
| | - Li Xiao
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California, 92697
- Department of Biomedical Engineering, University of California, Irvine, California, 92697
| | - Ray Luo
- Chemical and Materials Physics Graduate Program, University of California, Irvine, California, 92697
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California, 92697
- Department of Biomedical Engineering, University of California, Irvine, California, 92697
- Department of Chemical Engineering and Materials Science, University of California, Irvine, California, 92697
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15
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Li L, Chakravorty A, Alexov E. DelPhiForce, a tool for electrostatic force calculations: Applications to macromolecular binding. J Comput Chem 2017; 38:584-593. [PMID: 28130775 PMCID: PMC5315605 DOI: 10.1002/jcc.24715] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2016] [Accepted: 12/10/2016] [Indexed: 12/31/2022]
Abstract
Long-range electrostatic forces play an important role in molecular biology, particularly in macromolecular interactions. However, calculating the electrostatic forces for irregularly shaped molecules immersed in water is a difficult task. Here, we report a new tool, DelPhiForce, which is a tool in the DelPhi package that calculates and visualizes the electrostatic forces in biomolecular systems. In parallel, the DelPhi algorithm for modeling electrostatic potential at user-defined positions has been enhanced to include triquadratic and tricubic interpolation methods. The tricubic interpolation method has been tested against analytical solutions and it has been demonstrated that the corresponding errors are negligibly small at resolution 4 grids/Å. The DelPhiForce is further applied in the study of forces acting between partners of three protein-protein complexes. It has been demonstrated that electrostatic forces play a dual role by steering binding partners (so that the partners recognize their native interfaces) and exerting an electrostatic torque (if the mutual orientations of the partners are not native-like). The output of DelPhiForce is in a format that VMD can read and visualize, and provides additional options for analysis of protein-protein binding. DelPhiForce is available for download from the DelPhi webpage at http://compbio.clemson.edu/downloadDir/delphiforce.tar.gz © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Lin Li
- Department of Physics, Clemson University, Clemson, SC 29634, USA
| | | | - Emil Alexov
- Department of Physics, Clemson University, Clemson, SC 29634, USA
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16
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Xiao L, Wang C, Ye X, Luo R. Charge Central Interpretation of the Full Nonlinear PB Equation: Implications for Accurate and Scalable Modeling of Solvation Interactions. J Phys Chem B 2016; 120:8707-21. [PMID: 27146097 DOI: 10.1021/acs.jpcb.6b04439] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Continuum solvation modeling based upon the Poisson-Boltzmann equation (PBE) is widely used in structural and functional analysis of biomolecules. In this work, we propose a charge-central interpretation of the full nonlinear PBE electrostatic interactions. The validity of the charge-central view or simply charge view, as formulated as a vacuum Poisson equation with effective charges, was first demonstrated by reproducing both electrostatic potentials and energies from the original solvated full nonlinear PBE. There are at least two benefits when the charge-central framework is applied. First the convergence analyses show that the use of polarization charges allows a much faster converging numerical procedure for electrostatic energy and forces calculation for the full nonlinear PBE. Second, the formulation of the solvated electrostatic interactions as effective charges in vacuum allows scalable algorithms to be deployed for large biomolecular systems. Here, we exploited the charge-view interpretation and developed a particle-particle particle-mesh (P3M) strategy for the full nonlinear PBE systems. We also studied the accuracy and convergence of solvation forces with the charge-view and the P3M methods. It is interesting to note that the convergence of both the charge-view and the P3M methods is more rapid than the original full nonlinear PBE method. Given the developments and validations documented here, we are working to adapt the P3M treatment of the full nonlinear PBE model to molecular dynamics simulations.
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Affiliation(s)
| | | | - Xiang Ye
- Department of Physics, Shanghai Normal University , Shanghai 200234, China
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17
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Zhou S, Cheng LT, Sun H, Che J, Dzubiella J, Li B, McCammon JA. LS-VISM: A software package for analysis of biomolecular solvation. J Comput Chem 2015; 36:1047-59. [PMID: 25766844 PMCID: PMC4412808 DOI: 10.1002/jcc.23890] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Accepted: 02/08/2015] [Indexed: 12/30/2022]
Abstract
We introduce a software package for the analysis of biomolecular solvation. The package collects computer codes that implement numerical methods for a variational implicit-solvent model (VISM). The input of the package includes the atomic data of biomolecules under consideration and the macroscopic parameters such as solute-solvent surface tension, bulk solvent density and ionic concentrations, and the dielectric coefficients. The output includes estimated solvation free energies and optimal macroscopic solute-solvent interfaces that are obtained by minimizing the VISM solvation free-energy functional among all possible solute-solvent interfaces enclosing the solute atoms. We review the VISM with various descriptions of electrostatics. We also review our numerical methods that consist mainly of the level-set method for relaxing the VISM free-energy functional and a compact coupling interface method for the dielectric Poisson-Boltzmann equation. Such numerical methods and algorithms constitute the central modules of the software package. We detail the structure of the package, format of input and output files, workflow of the codes, and the postprocessing of output data. Our demo application to a host-guest system illustrates how to use the package to perform solvation analysis for biomolecules, including ligand-receptor binding systems. The package is simple and flexible with respect to minimum adjustable parameters and a wide range of applications. Future extensions of the package use can include the efficient identification of ligand binding pockets on protein surfaces.
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Affiliation(s)
- Shenggao Zhou
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Hui Sun
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Jianwei Che
- Parallel Computing Labs, 3525 Del Mar Heights Road, No. 288, San Diego, CA 92130
| | - Joachim Dzubiella
- Soft Matter and Functional Materials, Helmholtz-Center Berlin, 14109 Berlin, Germany, and Physics Department, Humboldt-University of Berlin, 12489 Berlin, Germany
| | - Bo Li
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - J. Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, United States
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18
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Fogolari F, Corazza A, Esposito G. Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes. J Comput Chem 2015; 36:585-96. [DOI: 10.1002/jcc.23832] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2014] [Revised: 11/15/2014] [Accepted: 12/12/2014] [Indexed: 11/11/2022]
Affiliation(s)
- Federico Fogolari
- Dipartimento di Scienze Mediche e Biologiche; Universita' di Udine; Piazzale Kolbe 4-33100 Udine Italy
- Istituto Nazionale Biostrutture e Biosistemi; Viale medaglie d'Oro 305-00136 Roma Italy
| | - Alessandra Corazza
- Dipartimento di Scienze Mediche e Biologiche; Universita' di Udine; Piazzale Kolbe 4-33100 Udine Italy
- Istituto Nazionale Biostrutture e Biosistemi; Viale medaglie d'Oro 305-00136 Roma Italy
| | - Gennaro Esposito
- Dipartimento di Scienze Mediche e Biologiche; Universita' di Udine; Piazzale Kolbe 4-33100 Udine Italy
- Istituto Nazionale Biostrutture e Biosistemi; Viale medaglie d'Oro 305-00136 Roma Italy
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19
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Xiao L, Cai Q, Li Z, Zhao H, Luo R. A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation. Chem Phys Lett 2014; 616-617:67-74. [PMID: 25404761 DOI: 10.1016/j.cplett.2014.10.033] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.
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Affiliation(s)
- Li Xiao
- Department of Biomedical Engineering, University of California, Irvine, CA 92697 ; Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697
| | - Qin Cai
- Department of Biomedical Engineering, University of California, Irvine, CA 92697 ; Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697
| | - Zhilin Li
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695
| | - Hongkai Zhao
- Department of Mathematics, University of California, Irvine, CA 92697
| | - Ray Luo
- Department of Biomedical Engineering, University of California, Irvine, CA 92697 ; Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697 ; Department of Chemical Engineering and Materials Science, University of California, Irvine, CA 92697
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20
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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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21
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Zhou S, Cheng LT, Dzubiella J, Li B, McCammon JA. Variational Implicit Solvation with Poisson-Boltzmann Theory. J Chem Theory Comput 2014; 10:1454-1467. [PMID: 24803864 PMCID: PMC3985794 DOI: 10.1021/ct401058w] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2013] [Indexed: 12/26/2022]
Abstract
We incorporate the Poisson-Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems. These include some single ions, two charged particles, two charged plates, and the host-guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior and can provide accurate estimates of binding affinity of the host-guest system. We finally discuss several issues for further improvement of VISM.
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Affiliation(s)
- Shenggao Zhou
- Department
of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Li-Tien Cheng
- Department
of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Joachim Dzubiella
- Soft
Matter and Functional Materials, Helmholtz-Center Berlin, 14109 Berlin,
Germany, and Physics Department, Humboldt-University
of Berlin, 12489 Berlin, Germany
| | - Bo Li
- Department
of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - J. Andrew McCammon
- Department
of Chemistry and Biochemistry, Department of Pharmacology, Center
for Theoretical Biological Physics, and Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, United States
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22
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Abstract
Accurate and efficient treatment of electrostatics is a crucial step in computational analyses of biomolecular structures and dynamics. In this study, we have explored a second-order finite-difference numerical method to solve the widely used Poisson-Boltzmann equation for electrostatic analyses of realistic bio-molecules. The so-called immersed interface method was first validated and found to be consistent with the classical weighted harmonic averaging method for a diversified set of test biomolecules. The numerical accuracy and convergence behaviors of the new method were next analyzed in its computation of numerical reaction field grid potentials, energies, and atomic solvation forces. Overall similar convergence behaviors were observed as those by the classical method. Interestingly, the new method was found to deliver more accurate and better-converged grid potentials than the classical method on or nearby the molecular surface, though the numerical advantage of the new method is reduced when grid potentials are extrapolated to the molecular surface. Our exploratory study indicates the need for further improving interpolation/extrapolation schemes in addition to the developments of higher-order numerical methods that have attracted most attention in the field.
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