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Vahid H, Scacchi A, Yang X, Ala-Nissila T, Sammalkorpi M. Modified Poisson–Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions. J Chem Phys 2022; 156:214906. [DOI: 10.1063/5.0092273] [Citation(s) in RCA: 1] [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 present a soft-potential-enhanced Poisson–Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulation with the explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1M and ion sizes ranging from small ions, such as Na+ or Cl−, to softer and larger ions with a size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.
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Affiliation(s)
- Hossein Vahid
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Alberto Scacchi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Xiang Yang
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
- Quantum Technology Finland Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Tapio Ala-Nissila
- Quantum Technology Finland Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
| | - Maria Sammalkorpi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Bioproducts and Biosystems, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
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2
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Fingerhut BP, Schauss J, Kundu A, Elsaesser T. Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation. Biophys J 2021; 120:5322-5332. [PMID: 34715079 PMCID: PMC8715182 DOI: 10.1016/j.bpj.2021.10.029] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2020] [Revised: 08/24/2021] [Accepted: 10/22/2021] [Indexed: 11/18/2022] Open
Abstract
The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg2+) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg2+ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg2+ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg2+-excess concentrations and comparison with fluorescence titration measurements shows that on average 20-30% of the Mg2+ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.
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3
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Koehl P, Delarue M, Orland H. Simultaneous Identification of Multiple Binding Sites in Proteins: A Statistical Mechanics Approach. J Phys Chem B 2021; 125:5052-5067. [PMID: 33973782 DOI: 10.1021/acs.jpcb.1c02658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions between charges are controlled by electrostatics, while hydrophobic interactions are modeled with a Yukawa potential. We impose steric constraints by assuming that the system is represented on a cubic lattice. We also assume incompressibility; i.e., all sites of the lattice are occupied. This model, which we refer to as the Hydrophobic Dipolar Poisson-Boltzmann Langevin (HDPBL) model, leads to a system of two equations whose solutions give the water dipole, salt, and hydrophobic molecule densities, all of them in the presence of the others in a self-consistent way. We use those to study the organization of the ions, cosolvent, and solvent molecules around proteins. In particular, peaks of densities are expected to reveal, simultaneously, the presence of compatible binding sites of different kinds on a protein. We have tested and validated the ability of HDPBL to detect pockets in proteins that bind to hydrophobic ligands, polar ligands, and charged small probes as well as to characterize the binding sites of lipids for membrane proteins.
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Affiliation(s)
- Patrice Koehl
- Department of Computer Science and Genome Center, University of California, Davis, California 95616, United States
| | - Marc Delarue
- Architecture et Dynamique des Macromolécules Biologiques, Département de Biologie Structurale et Chimie, UMR 3528 du CNRS, Institut Pasteur, 75015 Paris, France
| | - Henri Orland
- Institut de Physique Théorique, Université Paris-Saclay, CEA, 91191 Gif/Yvette Cedex, France
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4
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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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5
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Forouzesh N, Mukhopadhyay A, Watson LT, Onufriev AV. Multidimensional Global Optimization and Robustness Analysis in the Context of Protein-Ligand Binding. J Chem Theory Comput 2020; 16:4669-4684. [PMID: 32450041 PMCID: PMC8594251 DOI: 10.1021/acs.jctc.0c00142] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Accuracy of protein-ligand binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a global multidimensional optimization pipeline is developed to find optimal atomic radii specifically for protein-ligand binding calculations in implicit solvent. The computational pipeline has these three key components: (1) a massively parallel implementation of a deterministic global optimization algorithm (VTDIRECT95), (2) an accurate yet reasonably fast generalized Born implicit solvent model (GBNSR6), and (3) a novel robustness metric that helps distinguish between nearly degenerate local minima via a postprocessing step of the optimization. A graph-based "kT-connectivity" approach to explore and visualize the multidimensional energy landscape is proposed: local minima that can be reached from the global minimum without exceeding a given energy threshold (kT) are considered to be connected. As an illustration of the capabilities of the optimization pipeline, we apply it to find a global optimum in the space of just five radii: four atomic (O, H, N, and C) radii and water probe radius. The optimized radii, ρW = 1.37 Å, ρC = 1.40 Å, ρH = 1.55 Å, ρN = 2.35 Å, and ρO = 1.28 Å, lead to a closer agreement of electrostatic binding free energies with the explicit solvent reference than two commonly used sets of radii previously optimized for small molecules. At the same time, the ability of the optimizer to find the global optimum reveals fundamental limits of the common two-dielectric implicit solvation model: the computed electrostatic binding free energies are still almost 4 kcal/mol away from the explicit solvent reference. The proposed computational approach opens the possibility to further improve the accuracy of practical computational protocols for binding free energy calculations.
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Affiliation(s)
- Negin Forouzesh
- Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
| | - Abhishek Mukhopadhyay
- Department of Physics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
| | - Layne T Watson
- Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
- Department of Mathematics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
- Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
- Center for Soft Matter and Biological Physics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
| | - Alexey V Onufriev
- Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
- Department of Physics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
- Center for Soft Matter and Biological Physics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, United States
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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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A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states. J Math Biol 2019; 79:631-672. [PMID: 31030299 PMCID: PMC9841320 DOI: 10.1007/s00285-019-01372-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2018] [Revised: 12/16/2018] [Indexed: 01/18/2023]
Abstract
Calculations of electrostatic potential and solvation free energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the macromolecule and water are modeled as two-dielectric media with a sharp border. However, the dielectric property of interior cavities and ion-channels is difficult to model realistically in a two-dielectric setting. In fact, the detection of water molecules in a protein cavity remains to be an experimental challenge. This introduces an uncertainty, which affects the subsequent solvation free energy calculation. In order to compensate this uncertainty, a novel super-Gaussian dielectric PB model is introduced in this work, which devices an inhomogeneous dielectric distribution to represent the compactness of atoms and characterizes empty cavities via a gap dielectric value. Moreover, the minimal molecular surface level set function is adopted so that the dielectric profile remains to be smooth when the protein is transferred from water phase to vacuum. An important feature of this new model is that as the order of super-Gaussian function approaches the infinity, the dielectric distribution reduces to a piecewise constant of the two-dielectric model. Mathematically, an effective dielectric constant analysis is introduced in this work to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both water filled and empty cavities is employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in biomolecular electrostatic analysis.
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8
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Chakravorty A, Gallicchio E, Alexov E. A grid-based algorithm in conjunction with a gaussian-based model of atoms for describing molecular geometry. J Comput Chem 2019; 40:1290-1304. [PMID: 30698861 PMCID: PMC6506848 DOI: 10.1002/jcc.25786] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Revised: 12/12/2018] [Accepted: 01/06/2019] [Indexed: 11/06/2022]
Abstract
A novel grid-based method is presented, which in conjunction with a smooth Gaussian-based model of atoms, is used to compute molecular volume (MV) and surface area (MSA). The MV and MSA are essential for computing nonpolar component of free energies. The objective of our grid-based approach is to identify solute atom pairs that share overlapping volumes in space. Once completed, this information is used to construct a rooted tree using depth-first method to yield the final volume and SA by using the formulations of the Gaussian model described by Grant and Pickup (J. Phys Chem, 1995, 99, 3503). The method is designed to function uninterruptedly with the grid-based finite-difference method implemented in Delphi, a popular and open-source package used for solving the Poisson-Boltzmann equation (PBE). We demonstrate the time efficacy of the method while also validating its performance in terms of the effect of grid-resolution, positioning of the solute within the grid-map and accuracy in identification of overlapping atom pairs. We also explore and discuss different aspects of the Gaussian model with key emphasis on its physical meaningfulness. This development and its future release with the Delphi package are intended to provide a physically meaningful, fast, robust and comprehensive tool for MM/PBSA based free energy calculations. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Arghya Chakravorty
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634
| | | | - Emil Alexov
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634
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9
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Labat F, Civalleri B, Dovesi R. Implicit Solvation Using a Generalized Finite-Difference Approach in CRYSTAL: Implementation and Results for Molecules, Polymers, and Surfaces. J Chem Theory Comput 2018; 14:5969-5983. [PMID: 30347161 DOI: 10.1021/acs.jctc.8b00762] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the implementation of an implicit solvation model in the CRYSTAL code. The solvation energy is separated into two components: the electrostatic contribution arising from a self-consistent reaction field treatment obtained within a generalized finite-difference Poisson model, augmented by a nonelectrostatic contribution proportional to the solvent-accessible surface area of the solute. A discontinuous dielectric boundary is used, along with a solvent-excluded surface built from interlocking atom-centered spheres on which apparent surface point charges are mapped. The procedure is general and can be performed at both the Hartree-Fock and density functional theory levels, with pure or hybrid functionals, for systems periodic in 0, 1, and 2 directions, that is, for isolated molecules and extended polymers and surfaces. The Poisson equation resolution and apparent surface charge formalism is first validated on model analytical test cases. The good agreement obtained on solvation free energies is further confirmed by calculations performed on a large test set of 501 neutral molecules, for which a mean unsigned error of 1.3 kcal/mol is obtained when compared to the available experimental data. Importantly, the self-consistent reaction field procedure converges well for all molecules tested. This is further verified for all polymers and surfaces considered. In particular, for periodic systems, results obtained on an infinite glycine chain and on the wettability parameters of SiO2 surfaces are in good agreement with previously published data. The size extensivity of the energetic terms involved in the electrostatic contribution to the solvation energy is also well verified. These encouraging results constitute a first step to take into account complex environments in the CRYSTAL code, potentially allowing for a more accurate modeling of complex processes for both periodic and nonperiodic systems.
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Affiliation(s)
- Frédéric Labat
- PSL Research University, Chimie Paristech-CNRS , Institut de Recherche de Chimie de Paris , 11 rue P. et M. Curie , 75005 Paris , France
| | - Bartolomeo Civalleri
- Dipartimento di Chimica IFM , Università di Torino and NIS - Nanostructured Interfaces and Surfaces - Centre of Excellence , Via P. Giuria 7 , 10125 Torino , Italy
| | - Roberto Dovesi
- Dipartimento di Chimica IFM , Università di Torino and NIS - Nanostructured Interfaces and Surfaces - Centre of Excellence , Via P. Giuria 7 , 10125 Torino , Italy
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10
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Coons MP, Herbert JM. Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface. J Chem Phys 2018; 148:222834. [DOI: 10.1063/1.5023916] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Marc P. Coons
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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11
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Zhou HX, Pang X. Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation. Chem Rev 2018; 118:1691-1741. [PMID: 29319301 DOI: 10.1021/acs.chemrev.7b00305] [Citation(s) in RCA: 485] [Impact Index Per Article: 80.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.
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Affiliation(s)
- Huan-Xiang Zhou
- Department of Chemistry and Department of Physics, University of Illinois at Chicago , Chicago, Illinois 60607, United States.,Department of Physics and Institute of Molecular Biophysics, Florida State University , Tallahassee, Florida 32306, United States
| | - Xiaodong Pang
- Department of Physics and Institute of Molecular Biophysics, Florida State University , Tallahassee, Florida 32306, United States
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12
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Forouzesh N, Izadi S, Onufriev AV. Grid-Based Surface Generalized Born Model for Calculation of Electrostatic Binding Free Energies. J Chem Inf Model 2017; 57:2505-2513. [DOI: 10.1021/acs.jcim.7b00192] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Saeed Izadi
- Early Stage Pharmaceutical
Development, Genentech Inc., 1 DNA
Way, South San Francisco, California 94080, United States
| | - Alexey V. Onufriev
- Center
for Soft Matter and Biological Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
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13
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Lee KH, Chen J. Optimization of the GBMV2 implicit solvent force field for accurate simulation of protein conformational equilibria. J Comput Chem 2017; 38:1332-1341. [PMID: 28397268 DOI: 10.1002/jcc.24734] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2016] [Revised: 11/16/2016] [Accepted: 12/14/2016] [Indexed: 12/12/2022]
Abstract
Accurate treatment of solvent environment is critical for reliable simulations of protein conformational equilibria. Implicit treatment of solvation, such as using the generalized Born (GB) class of models arguably provides an optimal balance between computational efficiency and physical accuracy. Yet, GB models are frequently plagued by a tendency to generate overly compact structures. The physical origins of this drawback are relatively well understood, and the key to a balanced implicit solvent protein force field is careful optimization of physical parameters to achieve a sufficient level of cancellation of errors. The latter has been hampered by the difficulty of generating converged conformational ensembles of non-trivial model proteins using the popular replica exchange sampling technique. Here, we leverage improved sampling efficiency of a newly developed multi-scale enhanced sampling technique to re-optimize the generalized-Born with molecular volume (GBMV2) implicit solvent model with the CHARMM36 protein force field. Recursive optimization of key GBMV2 parameters (such as input radii) and protein torsion profiles (via the CMAP torsion cross terms) has led to a more balanced GBMV2 protein force field that recapitulates the structures and stabilities of both helical and β-hairpin model peptides. Importantly, this force field appears to be free of the over-compaction bias, and can generate structural ensembles of several intrinsically disordered proteins of various lengths that seem highly consistent with available experimental data. © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Kuo Hao Lee
- Department of Biochemistry and Molecular Biophysics, Kansas State University, Manhattan, Kansas, 66506
| | - Jianhan Chen
- Department of Biochemistry and Molecular Biophysics, Kansas State University, Manhattan, Kansas, 66506
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Ringe S, Oberhofer H, Reuter K. Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions. J Chem Phys 2017; 146:134103. [DOI: 10.1063/1.4978850] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Stefan Ringe
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Harald Oberhofer
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Karsten Reuter
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
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15
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Chakavorty A, Li L, Alexov E. Electrostatic component of binding energy: Interpreting predictions from poisson-boltzmann equation and modeling protocols. J Comput Chem 2016; 37:2495-507. [PMID: 27546093 PMCID: PMC5030180 DOI: 10.1002/jcc.24475] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Revised: 08/03/2016] [Accepted: 08/06/2016] [Indexed: 01/11/2023]
Abstract
Macromolecular interactions are essential for understanding numerous biological processes and are typically characterized by the binding free energy. Important component of the binding free energy is the electrostatics, which is frequently modeled via the solutions of the Poisson-Boltzmann Equations (PBE). However, numerous works have shown that the electrostatic component (ΔΔGelec ) of binding free energy is very sensitive to the parameters used and modeling protocol. This prompted some researchers to question the robustness of PBE in predicting ΔΔGelec . We argue that the sensitivity of the absolute ΔΔGelec calculated with PBE using different input parameters and definitions does not indicate PBE deficiency, rather this is what should be expected. We show how the apparent sensitivity should be interpreted in terms of the underlying changes in several numerous and physical parameters. We demonstrate that PBE approach is robust within each considered force field (CHARMM-27, AMBER-94, and OPLS-AA) once the corresponding structures are energy minimized. This observation holds despite of using two different molecular surface definitions, pointing again that PBE delivers consistent results within particular force field. The fact that PBE delivered ΔΔGelec values may differ if calculated with different modeling protocols is not a deficiency of PBE, but natural results of the differences of the force field parameters and potential functions for energy minimization. In addition, while the absolute ΔΔGelec values calculated with different force field differ, their ordering remains practically the same allowing for consistent ranking despite of the force field used. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Arghya Chakavorty
- Computational Biophysics and Bioinformatics, Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, 29634
| | - Lin Li
- Computational Biophysics and Bioinformatics, Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, 29634
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, 29634.
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16
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Wang C, Nguyen PH, Pham K, Huynh D, Le TBN, Wang H, Ren P, Luo R. Calculating protein-ligand binding affinities with MMPBSA: Method and error analysis. J Comput Chem 2016; 37:2436-46. [PMID: 27510546 PMCID: PMC5018451 DOI: 10.1002/jcc.24467] [Citation(s) in RCA: 156] [Impact Index Per Article: 19.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Accepted: 07/13/2016] [Indexed: 11/07/2022]
Abstract
Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here different computational alternatives were investigated to assess their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. First the performance of nonpolar solvation models was studied and it was found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the Poisson-Boltzmann methods was analyzed next. The data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 Å is already small enough to be negligible. The impact of different atomic radius sets and different molecular surface definitions was further analyzed and weak influences were found on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. The data also showed that the converged simulations caused slight reduction in the agreement with experiment. Finally the direction of estimating absolute binding free energies was briefly explored. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities were also reduced dramatically when the modern nonpolar solvent model was used, although further developments were apparently necessary to further improve the MMPBSA methods. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Changhao Wang
- Chemical and Materials Physics Graduate Program, Irvine, California, 92697
- Department of Molecular Biology and Biochemistry, Irvine, California, 92697
- Department of Physics and Astronomy, University of California, Irvine, California, 92697
| | - Peter H Nguyen
- Department of Molecular Biology and Biochemistry, Irvine, California, 92697
| | - Kevin Pham
- Department of Molecular Biology and Biochemistry, Irvine, California, 92697
| | - Danielle Huynh
- Department of Molecular Biology and Biochemistry, Irvine, California, 92697
| | | | - Hongli Wang
- Department of Molecular Biology and Biochemistry, Irvine, California, 92697
| | - Pengyu Ren
- Department of Biomedical Engineering, University of Texas, Austin, Texas, 78712
| | - Ray Luo
- Chemical and Materials Physics Graduate Program, Irvine, California, 92697.
- Department of Molecular Biology and Biochemistry, Irvine, California, 92697.
- Department of Chemical Engineering and Materials Science, Irvine, California, 92697.
- Department of Biomedical Engineering, University of California, Irvine, California, 92697.
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Sun H, Wen J, Zhao Y, Li B, McCammon JA. A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics. J Chem Phys 2015; 143:243110. [PMID: 26723595 DOI: 10.1063/1.4932336] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.
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Affiliation(s)
- Hui Sun
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail Code 0112. La Jolla, California 92093-0112, USA
| | - Jiayi Wen
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail Code 0112. La Jolla, California 92093-0112, USA
| | - Yanxiang Zhao
- Department of Mathematics, the George Washington University, Monroe Hall, 2115 G St. NW, Washington, DC 20052, USA
| | - Bo Li
- Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, Mail Code 0112. La Jolla, California 92093-0112, USA
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, and Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, USA
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18
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Seybold C, Elserafy M, Rüthnick D, Ozboyaci M, Neuner A, Flottmann B, Heilemann M, Wade RC, Schiebel E. Kar1 binding to Sfi1 C-terminal regions anchors the SPB bridge to the nuclear envelope. J Cell Biol 2015; 209:843-61. [PMID: 26076691 PMCID: PMC4477856 DOI: 10.1083/jcb.201412050] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2014] [Accepted: 05/20/2015] [Indexed: 11/22/2022] Open
Abstract
The yeast spindle pole body (SPB) is the functional equivalent of the mammalian centrosome. The half bridge is a SPB substructure on the nuclear envelope (NE), playing a key role in SPB duplication. Its cytoplasmic components are the membrane-anchored Kar1, the yeast centrin Cdc31, and the Cdc31-binding protein Sfi1. In G1, the half bridge expands into the bridge through Sfi1 C-terminal (Sfi1-CT) dimerization, the licensing step for SPB duplication. We exploited photo-activated localization microscopy (PALM) to show that Kar1 localizes in the bridge center. Binding assays revealed direct interaction between Kar1 and C-terminal Sfi1 fragments. kar1Δ cells whose viability was maintained by the dominant CDC31-16 showed an arched bridge, indicating Kar1's function in tethering Sfi1 to the NE. Cdc31-16 enhanced Cdc31-Cdc31 interactions between Sfi1-Cdc31 layers, as suggested by binding free energy calculations. In our model, Kar1 binding is restricted to Sfi1-CT and Sfi1 C-terminal centrin-binding repeats, and centrin and Kar1 provide cross-links, while Sfi1-CT stabilizes the bridge and ensures timely SPB separation.
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Affiliation(s)
- Christian Seybold
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Alliance, 69120 Heidelberg, Germany
| | - Menattallah Elserafy
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Alliance, 69120 Heidelberg, Germany
| | - Diana Rüthnick
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Alliance, 69120 Heidelberg, Germany
| | - Musa Ozboyaci
- Heidelberg Institute for Theoretical Studies, 69118 Heidelberg, Germany Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, Heidelberg University, 69120 Heidelberg, Germany
| | - Annett Neuner
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Alliance, 69120 Heidelberg, Germany
| | - Benjamin Flottmann
- Institute for Anatomy and Cell Biology, Functional Neuroanatomy, Heidelberg University, 69120 Heidelberg, Germany Institute for Physical and Theoretical Chemistry, Johann-Wolfgang-Goethe-University Frankfurt, 60438 Frankfurt am Main, Germany
| | - Mike Heilemann
- Institute for Anatomy and Cell Biology, Functional Neuroanatomy, Heidelberg University, 69120 Heidelberg, Germany Institute for Physical and Theoretical Chemistry, Johann-Wolfgang-Goethe-University Frankfurt, 60438 Frankfurt am Main, Germany
| | - Rebecca C Wade
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Alliance, 69120 Heidelberg, Germany Heidelberg Institute for Theoretical Studies, 69118 Heidelberg, Germany Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany
| | - Elmar Schiebel
- Zentrum für Molekulare Biologie der Universität Heidelberg, DKFZ-ZMBH Alliance, 69120 Heidelberg, Germany
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19
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Parameterization for molecular Gaussian surface and a comparison study of surface mesh generation. J Mol Model 2015; 21:113. [PMID: 25862632 DOI: 10.1007/s00894-015-2654-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Accepted: 03/16/2015] [Indexed: 10/23/2022]
Abstract
The molecular Gaussian surface has been frequently used in the field of molecular modeling and simulation. Typically, the Gaussian surface is defined using two controlling parameters; the decay rate and isovalue. Currently, there is a lack of studies in which a systematic approach in the determination of optimal parameterization according to the geometric features has been done. In this paper, surface area, volume enclosed by the surface and Hausdorff distance are used as three criteria for the parameterization to make the Gaussian surface approximate the solvent excluded surface (SES) well. For each of these three criteria, a search of the parameter space is carried out in order to determine the optimal parameter values. The resulted parameters are close to each other and result in similar calculated molecular properties. Approximation of the VDW surface is also done by analyzing the explicit expressions of the Gaussian surface and VDW surface, which analysis and parameters can be similarly applied to the solvent accessible surface (SAS) due to its geometric similarity to the VDW surface. Once the optimal parameters are obtained, we compare the performance of our Gaussian surface generation software TMSmesh with other commonly used software programs, focusing primarily on mesh quality and fidelity. Additionally, the Poisson-Boltzmann solvation energies based on the surface meshes generated by TMSmesh and those generated by other software programs are calculated and compared for a set of molecules with different sizes. The results of these comparisons validate both the accuracy and the applicability of the parameterized Gaussian surface.
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20
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Li L, Wang L, Alexov E. On the energy components governing molecular recognition in the framework of continuum approaches. Front Mol Biosci 2015; 2:5. [PMID: 25988173 PMCID: PMC4429657 DOI: 10.3389/fmolb.2015.00005] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2014] [Accepted: 02/04/2015] [Indexed: 01/14/2023] Open
Abstract
Molecular recognition is a process that brings together several biological macromolecules to form a complex and one of the most important characteristics of the process is the binding free energy. Various approaches exist to model the binding free energy, provided the knowledge of the 3D structures of bound and unbound molecules. Among them, continuum approaches are quite appealing due to their computational efficiency while at the same time providing predictions with reasonable accuracy. Here we review recent developments in the field emphasizing on the importance of adopting adequate description of physical processes taking place upon the binding. In particular, we focus on the efforts aiming at capturing some of the atomistic details of the binding phenomena into the continuum framework. When possible, the energy components are reviewed independently of each other. However, it is pointed out that rigorous approaches should consider all energy contributions on the same footage. The two major schemes for utilizing the individual energy components to predict binding affinity are outlined as well.
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Affiliation(s)
- Lin Li
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University Clemson, SC, USA
| | - Lin Wang
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University Clemson, SC, USA
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University Clemson, SC, USA
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21
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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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22
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Tuszynski JA, Winter P, White D, Tseng CY, Sahu KK, Gentile F, Spasevska I, Omar SI, Nayebi N, Churchill CD, Klobukowski M, El-Magd RMA. Mathematical and computational modeling in biology at multiple scales. Theor Biol Med Model 2014; 11:52. [PMID: 25542608 PMCID: PMC4396153 DOI: 10.1186/1742-4682-11-52] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2014] [Accepted: 11/25/2014] [Indexed: 01/08/2023] Open
Abstract
A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.
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Affiliation(s)
- Jack A Tuszynski
- Department of Physics and Department of Oncology, University of Alberta, Edmonton, Canada.
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23
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Wang N, Zhou S, Kekenes-Huskey PM, Li B, McCammon JA. Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers. J Phys Chem B 2014; 118:14827-32. [PMID: 25426875 PMCID: PMC4280115 DOI: 10.1021/jp511702w] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
![]()
Mean-field
methods, such as the Poisson–Boltzmann equation
(PBE), are often used to calculate the electrostatic properties of
molecular systems. In the past two decades, an enhancement of the
PBE, the size-modified Poisson–Boltzmann equation (SMPBE),
has been reported. Here, the PBE and the SMPBE are reevaluated for
realistic molecular systems, namely, lipid bilayers, under eight different
sets of input parameters. The SMPBE appears to reproduce the molecular
dynamics simulation results better than the PBE only under specific
parameter sets, but in general, it performs no better than the Stern
layer correction of the PBE. These results emphasize the need for
careful discussions of the accuracy of mean-field calculations on
realistic systems with respect to the choice of parameters and call
for reconsideration of the cost-efficiency and the significance of
the current SMPBE formulation.
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Affiliation(s)
- Nuo Wang
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - Shenggao Zhou
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - Peter M Kekenes-Huskey
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - Bo Li
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
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24
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Sakalli I, Schöberl J, Knapp EW. mFES: A Robust Molecular Finite Element Solver for Electrostatic Energy Computations. J Chem Theory Comput 2014; 10:5095-112. [DOI: 10.1021/ct5005092] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- I. Sakalli
- Freie Universität Berlin, Institute of
Chemistry and Biochemistry, Fabeckstr. 36a, Berlin 14195, Germany
| | - J. Schöberl
- Technische Universität Wien, Institute for Analysis
and Scientific Computing, Wiedner Hauptstraße 8−10, Vienna 1040, Austria
| | - E. W. Knapp
- Freie Universität Berlin, Institute of
Chemistry and Biochemistry, Fabeckstr. 36a, Berlin 14195, Germany
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25
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Li L, Li C, Alexov E. On the Modeling of Polar Component of Solvation Energy using Smooth Gaussian-Based Dielectric Function. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014; 13. [PMID: 25018579 DOI: 10.1142/s0219633614400021] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Traditional implicit methods for modeling electrostatics in biomolecules use a two-dielectric approach: a biomolecule is assigned low dielectric constant while the water phase is considered as a high dielectric constant medium. However, such an approach treats the biomolecule-water interface as a sharp dielectric border between two homogeneous dielectric media and does not account for inhomogeneous dielectric properties of the macromolecule as well. Recently we reported a new development, a smooth Gaussian-based dielectric function which treats the entire system, the solute and the water phase, as inhomogeneous dielectric medium (J Chem Theory Comput. 2013 Apr 9; 9(4): 2126-2136.). Here we examine various aspects of the modeling of polar solvation energy in such inhomogeneous systems in terms of the solute-water boundary and the inhomogeneity of the solute in the absence of water surrounding. The smooth Gaussian-based dielectric function is implemented in the DelPhi finite-difference program, and therefore the sensitivity of the results with respect to the grid parameters is investigated, and it is shown that the calculated polar solvation energy is almost grid independent. Furthermore, the results are compared with the standard two-media model and it is demonstrated that on average, the standard method overestimates the magnitude of the polar solvation energy by a factor 2.5. Lastly, the possibility of the solute to have local dielectric constant larger than of a bulk water is investigated in a benchmarking test against experimentally determined set of pKa's and it is speculated that side chain rearrangements could result in local dielectric constant larger than 80.
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Affiliation(s)
- Lin Li
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
| | - Chuan Li
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
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26
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Onufriev AV, Aguilar B. Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014; 13. [PMID: 26236064 DOI: 10.1142/s0219633614400069] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
We investigate the influence of three common definitions of the solute/solvent dielectric boundary (DB) on the accuracy of the electrostatic solvation energy ΔGel computed within the Poisson Boltzmann and the generalized Born models of implicit solvation. The test structures include small molecules, peptides and small proteins; explicit solvent ΔGel are used as accuracy reference. For common atomic radii sets BONDI, PARSE (and ZAP9 for small molecules) the use of van der Waals (vdW) DB results, on average, in considerably larger errors in ΔGel than the molecular surface (MS) DB. The optimal probe radius ρw for which the MS DB yields the most accurate ΔGel varies considerably between structure types. The solvent accessible surface (SAS) DB becomes optimal at ρw ~ 0.2 Å (exact value is sensitive to the structure and atomic radii), at which point the average accuracy of ΔGel is comparable to that of the MS-based boundary. The geometric equivalence of SAS to vdW surface based on the same atomic radii uniformly increased by ρw gives the corresponding optimal vdW DB. For small molecules, the optimal vdW DB based on BONDI + 0.2 Å radii can yield ΔGel estimates at least as accurate as those based on the optimal MS DB. Also, in small molecules, pairwise charge-charge interactions computed with the optimal vdW DB are virtually equal to those computed with the MS DB, suggesting that in this case the two boundaries are practically equivalent by the electrostatic energy criteria. In structures other than small molecules, the optimal vdW and MS dielectric boundaries are not equivalent: the respective pairwise electrostatic interactions in the presence of solvent can differ by up to 5 kcal/mol for individual atomic pairs in small proteins, even when the total ΔGel are equal. For small proteins, the average decrease in pairwise electrostatic interactions resulting from the switch from optimal MS to optimal vdW DB definition can be mimicked within the MS DB definition by doubling of the solute dielectric constant. However, the use of the higher interior dielectric does not eliminate the large individual deviations between pairwise interactions computed within the two DB definitions. It is argued that while the MS based definition of the dielectric boundary is more physically correct in some types of practical calculations, the choice is not so clear in some other common scenarios.
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Affiliation(s)
- Alexey V Onufriev
- Department of Computer Science and Department of Physics, Virginia Tech, Blacksburg, VA 24060, and Department of Computer Science, Virginia Tech, Blacksburg, VA 24060
| | - Boris Aguilar
- Department of Computer Science and Department of Physics, Virginia Tech, Blacksburg, VA 24060, and Department of Computer Science, Virginia Tech, Blacksburg, VA 24060
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27
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Qin S, Zhou HX. Using the concept of transient complex for affinity predictions in CAPRI rounds 20-27 and beyond. Proteins 2013; 81:2229-36. [PMID: 23873496 PMCID: PMC3842397 DOI: 10.1002/prot.24366] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Revised: 06/26/2013] [Accepted: 06/29/2013] [Indexed: 11/10/2022]
Abstract
Predictions of protein-protein binders and binding affinities have traditionally focused on features pertaining to the native complexes. In developing a computational method for predicting protein-protein association rate constants, we introduced the concept of transient complex after mapping the interaction energy surface. The transient complex is located at the outer boundary of the bound-state energy well, having near-native separation and relative orientation between the subunits but not yet formed most of the short-range native interactions. We found that the width of the binding funnel and the electrostatic interaction energy of the transient complex are among the features predictive of binders and binding affinities. These ideas were very promising for the five affinity-related targets (T43-45, 55, and 56) of CAPRI rounds 20-27. For T43, we ranked the single crystallographic complex as number 1 and were one of only two groups that clearly identified that complex as a true binder; for T44, we ranked the only design with measurable binding affinity as number 4. For the nine docking targets, continuing on our success in previous CAPRI rounds, we produced 10 medium-quality models for T47 and acceptable models for T48 and T49. We conclude that the interaction energy landscape and the transient complex in particular will complement existing features in leading to better prediction of binding affinities.
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Affiliation(s)
- Sanbo Qin
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
| | - Huan-Xiang Zhou
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
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28
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Rocklin GJ, Mobley DL, Dill KA, Hünenberger PH. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects. J Chem Phys 2013; 139:184103. [PMID: 24320250 PMCID: PMC3838431 DOI: 10.1063/1.4826261] [Citation(s) in RCA: 175] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2013] [Accepted: 09/30/2013] [Indexed: 01/12/2023] Open
Abstract
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.
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Affiliation(s)
- Gabriel J Rocklin
- Department of Pharmaceutical Chemistry, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA and Biophysics Graduate Program, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA
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29
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Li C, Petukh M, Li L, Alexov E. Continuous development of schemes for parallel computing of the electrostatics in biological systems: implementation in DelPhi. J Comput Chem 2013; 34:1949-60. [PMID: 23733490 PMCID: PMC3707979 DOI: 10.1002/jcc.23340] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2013] [Revised: 04/03/2013] [Accepted: 05/02/2013] [Indexed: 11/07/2022]
Abstract
Due to the enormous importance of electrostatics in molecular biology, calculating the electrostatic potential and corresponding energies has become a standard computational approach for the study of biomolecules and nano-objects immersed in water and salt phase or other media. However, the electrostatics of large macromolecules and macromolecular complexes, including nano-objects, may not be obtainable via explicit methods and even the standard continuum electrostatics methods may not be applicable due to high computational time and memory requirements. Here, we report further development of the parallelization scheme reported in our previous work (Li, et al., J. Comput. Chem. 2012, 33, 1960) to include parallelization of the molecular surface and energy calculations components of the algorithm. The parallelization scheme utilizes different approaches such as space domain parallelization, algorithmic parallelization, multithreading, and task scheduling, depending on the quantity being calculated. This allows for efficient use of the computing resources of the corresponding computer cluster. The parallelization scheme is implemented in the popular software DelPhi and results in speedup of several folds. As a demonstration of the efficiency and capability of this methodology, the electrostatic potential, and electric field distributions are calculated for the bovine mitochondrial supercomplex illustrating their complex topology, which cannot be obtained by modeling the supercomplex components alone.
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Affiliation(s)
- Chuan Li
- Computational Biophysics and Bioinformatics, Physics Department, Clemson University, Clemson, SC 29642
| | - Marharyta Petukh
- Computational Biophysics and Bioinformatics, Physics Department, Clemson University, Clemson, SC 29642
| | - Lin Li
- Computational Biophysics and Bioinformatics, Physics Department, Clemson University, Clemson, SC 29642
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Physics Department, Clemson University, Clemson, SC 29642
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30
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Fogolari F, Corazza A, Esposito G. Generalized Born forces: surface integral formulation. J Chem Phys 2013; 138:054112. [PMID: 23406103 DOI: 10.1063/1.4789537] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Generalized Born (GB) models offer a convenient alternative to Poisson-Boltzmann based models. In the last decade, the GB radii computed based on the exact results obtained for a charge embedded in a conducting sphere have proven to be accurate also for the complex molecular shapes of proteins. The surface integral formulation of the theory has been much less explored than the volume integral formulation. In this work, we provide the exact equations for the GB solvation forces in the surface integral formulation, which are non-trivial due to the non-negligible dependence of GB radii on atomic positions and due to the discontinuity in the derivative of the solvent accessible surface point positions with respect to atomic positions. The equations derived here provide a useful reference for developing faster approximations.
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Affiliation(s)
- Federico Fogolari
- Dipartimento di Scienze Mediche e Biologiche, Universita' di Udine, Piazzale Kolbe 4, 33100 Udine, Italy
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Harris RC, Boschitsch AH, Fenley MO. Influence of Grid Spacing in Poisson-Boltzmann Equation Binding Energy Estimation. J Chem Theory Comput 2013; 9:3677-3685. [PMID: 23997692 DOI: 10.1021/ct300765w] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Grid-based solvers of the Poisson-Boltzmann, PB, equation are routinely used to estimate electrostatic binding, ΔΔGel, and solvation, ΔGel, free energies. The accuracies of such estimates are subject to grid discretization errors from the finite difference approximation to the PB equation. Here, we show that the grid discretization errors in ΔΔGel are more significant than those in ΔGel, and can be divided into two parts: (i) errors associated with the relative positioning of the grid and (ii) systematic errors associated with grid spacing. The systematic error in particular is significant for methods, such as the molecular mechanics PB surface area, MM-PBSA, approach that predict electrostatic binding free energies by averaging over an ensemble of molecular conformations. Although averaging over multiple conformations can control for the error associated with grid placement, it will not eliminate the systematic error, which can only be controlled by reducing grid spacing. The present study indicates that the widely-used grid spacing of 0.5 Å produces unacceptable errors in ΔΔGel, even though its predictions of ΔGel are adequate for the cases considered here. Although both grid discretization errors generally increase with grid spacing, the relative sizes of these errors differ according to the solute-solvent dielectric boundary definition. The grid discretization errors are generally smaller on the Gaussian surface used in the present study than on either the solvent-excluded or van der Waals surfaces, which both contain more surface discontinuities (e.g., sharp edges and cusps). Additionally, all three molecular surfaces converge to very different estimates of ΔΔGel.
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Affiliation(s)
- Robert C Harris
- Department of Physics, Florida State University, Tallahasse, FL 32306
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Abstract
AbstractA stochastic generalized Born (GB) solver is presented which
can give predictions of energies arbitrarily close to those that
would be given by exact effective GB radii, and, unlike analytical
GB solvers, these errors are Gaussian with estimates
that can be easily obtained from the algorithm. This method
was tested by computing the electrostatic solvation energies
(ΔGsolv) and the electrostatic binding energies (ΔGbind) of a
set of DNA-drug complexes, a set of protein-drug complexes,
a set of protein-protein complexes, and a set of RNA-peptide
complexes. Its predictions of ΔGsolv agree with those of the
linearized Poisson-Boltzmann equation, but it does not predict
ΔGbind well, although these predictions of ΔGbind may
be marginally better than those of traditional analytical GB
solvers. Apparently, the GB model itself must be improved
before accurate estimates of ΔGbind can be obtained.
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Abstract
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.
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Li L, Li C, Zhang Z, Alexov E. On the Dielectric "Constant" of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi. J Chem Theory Comput 2013; 9:2126-2136. [PMID: 23585741 PMCID: PMC3622359 DOI: 10.1021/ct400065j] [Citation(s) in RCA: 362] [Impact Index Per Article: 32.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2013] [Indexed: 01/26/2023]
Abstract
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Implicit methods for modeling protein
electrostatics require dielectric
properties of the system to be known, in particular, the value of
the dielectric constant of protein. While numerous values of the internal
protein dielectric constant were reported in the literature, still
there is no consensus of what the optimal value is. Perhaps this is
due to the fact that the protein dielectric constant is not a “constant”
but is a complex function reflecting the properties of the protein’s
structure and sequence. Here, we report an implementation of a Gaussian-based
approach to deliver the dielectric constant distribution throughout
the protein and surrounding water phase by utilizing the 3D structure
of the corresponding macromolecule. In contrast to previous reports,
we construct a smooth dielectric function throughout the space of
the system to be modeled rather than just constructing a “Gaussian
surface” or smoothing molecule–water boundary. Analysis
on a large set of proteins shows that (a) the average dielectric constant
inside the protein is relatively low, about 6–7, and reaches
a value of about 20–30 at the protein’s surface, and
(b) high average local dielectric constant values are associated with
charged residues while low dielectric constant values are automatically
assigned to the regions occupied by hydrophobic residues. In terms
of energetics, a benchmarking test was carried out against the experimental
pKa’s of 89 residues in staphylococcal
nuclease (SNase) and showed that it results in a much better RMSD
(= 1.77 pK) than the corresponding calculations done
with a homogeneous high dielectric constant with an optimal value
of 10 (RMSD = 2.43 pK).
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Affiliation(s)
- Lin Li
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, South Carolina 29634, United States
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Fogolari F, Corazza A, Esposito G. A differential equation for the Generalized Born radii. Phys Chem Chem Phys 2013; 15:9783-91. [DOI: 10.1039/c3cp51174j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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