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Kjellander R. A multiple decay-length extension of the Debye-Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes. Phys Chem Chem Phys 2020; 22:23952-23985. [PMID: 33073810 DOI: 10.1039/d0cp02742a] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Poisson-Boltzmann and Debye-Hückel approximations for the pair distributions and mean electrostatic potential in electrolytes predict that these entities have one single decay mode with a decay length equal to the Debye length 1/κD, that is, they have a characteristic contribution that decays with distance r like e-κDr/r. However, in reality, electrolytes have several decay modes e-κr/r, e-κ'r/r etc. with different decay lengths, 1/κ, 1/κ' etc., that in general are different from the Debye length. As an illustration of the significance of multiple decay modes in electrolytes, the present work uses a very simple extension of the Debye-Hückel approximation with two decay lengths, which predicts oscillatory modes when appropriate. This approach gives very accurate results for radial distribution functions and thermodynamic properties of aqueous solutions of monovalent electrolytes for all concentrations investigated, including high ones. It is designed to satisfy necessary statistical mechanical conditions for the distributions. The effective dielectric permittivity of the electrolyte plays an important role in the theory and each mode has its own value of this entity. Electrolytes with high electrostatic coupling, like those with multivalent ions and/or with solvent of low dielectric constant, have decay lengths in dilute solutions that substantially deviate from the Debye length. It is shown that this is caused by nonlinear ion-ion correlation effects and the origin of under-screening, i.e., 1/κ > 1/κD, in dilute symmetric electrolytes is analyzed. The under-screening is accompanied by an increase in the effective dielectric permittivity that is also caused by these correlations. The theoretical results for the decay length are successfully compared with recent experimental data for simple electrolytes in various solvents. The paper includes background material on electrolyte theory and screening in order to be accessible for nonexperts in the field.
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Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden.
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2
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Sukhomlinov SV, Müser MH. A mixed radial, angular, three-body distribution function as a tool for local structure characterization: Application to single-component structures. J Chem Phys 2020; 152:194502. [PMID: 33687244 DOI: 10.1063/5.0007964] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A mixed radial, angular three-body distribution function g3(rBC, θABC) is introduced, which allows the local atomic order to be more easily characterized in a single graph than with conventional correlation functions. It can be defined to be proportional to the probability of finding an atom C at a distance rBC from atom B while making an angle θABC with atoms A and B, under the condition that atom A is the nearest neighbor of B. As such, our correlation function contains, for example, the likelihood of angles formed between the nearest and the next-nearest-neighbor bonds. To demonstrate its use and usefulness, a visual library for many one-component crystals is produced first and then employed to characterize the local order in a diverse body of elemental condensed-matter systems. Case studies include the analysis of a grain boundary, several liquids (argon, copper, and antimony), and polyamorphism in crystalline and amorphous silicon including that obtained in a tribological interface.
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Affiliation(s)
- Sergey V Sukhomlinov
- Department of Materials Science and Engineering, Universität des Saarlandes, Saarbrücken, Germany
| | - Martin H Müser
- Department of Materials Science and Engineering, Universität des Saarlandes, Saarbrücken, Germany
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3
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Vögele M, Köfinger J, Hummer G. Finite-Size-Corrected Rotational Diffusion Coefficients of Membrane Proteins and Carbon Nanotubes from Molecular Dynamics Simulations. J Phys Chem B 2019; 123:5099-5106. [PMID: 31132280 PMCID: PMC6750896 DOI: 10.1021/acs.jpcb.9b01656] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
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We investigate
system-size effects on the rotational diffusion of membrane proteins
and other membrane-embedded molecules in molecular dynamics simulations. We find that
the rotational diffusion coefficient slows down relative to the infinite-system
value by a factor of one minus the ratio of protein and box areas.
This correction factor follows from the hydrodynamics of rotational
flows under periodic boundary conditions and is rationalized in terms
of Taylor–Couette flow. For membrane proteins like transporters,
channels, or receptors in typical simulation setups, the protein-covered
area tends to be relatively large, requiring a significant finite-size
correction. Molecular dynamics simulations of the protein adenine
nucleotide translocase (ANT1) and of a carbon nanotube porin in lipid
membranes show that the hydrodynamic finite-size correction for rotational
diffusion is accurate in standard-use cases. The dependence of the
rotational diffusion on box size can be used to determine the membrane
viscosity.
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Affiliation(s)
- Martin Vögele
- Department of Theoretical Biophysics , Max Planck Institute of Biophysics , Max-von-Laue Str. 3 , 60438 Frankfurt am Main , Germany
| | - Jürgen Köfinger
- Department of Theoretical Biophysics , Max Planck Institute of Biophysics , Max-von-Laue Str. 3 , 60438 Frankfurt am Main , Germany
| | - Gerhard Hummer
- Department of Theoretical Biophysics , Max Planck Institute of Biophysics , Max-von-Laue Str. 3 , 60438 Frankfurt am Main , Germany.,Institute for Biophysics , Goethe University Frankfurt , 60438 Frankfurt am Main , Germany
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4
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Kawashima Y, Ishimura K, Shiga M. Ab initio quantum mechanics/molecular mechanics method with periodic boundaries employing Ewald summation technique to electron-charge interaction: Treatment of the surface-dipole term. J Chem Phys 2019; 150:124103. [DOI: 10.1063/1.5048451] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Y. Kawashima
- RIKEN Center for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - K. Ishimura
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - M. Shiga
- CCSE, Japan Atomic Energy Agency (JAEA), 178-4-4, Wakashiba, Kashiwa, Chiba 277-0871, Japan
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5
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Ekimoto T, Yamane T, Ikeguchi M. Elimination of Finite-Size Effects on Binding Free Energies via the Warp-Drive Method. J Chem Theory Comput 2018; 14:6544-6559. [DOI: 10.1021/acs.jctc.8b00280] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Toru Ekimoto
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Tsutomu Yamane
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Mitsunori Ikeguchi
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
- RIKEN Medical Sciences Innovation Hub Program, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
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6
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Brown JR, Seo Y, Hall LM. Ion Correlation Effects in Salt-Doped Block Copolymers. PHYSICAL REVIEW LETTERS 2018; 120:127801. [PMID: 29694088 DOI: 10.1103/physrevlett.120.127801] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Revised: 12/12/2017] [Indexed: 06/08/2023]
Abstract
We apply classical density functional theory to study how salt changes the microphase morphology of diblock copolymers. Polymers are freely jointed and one monomer type favorably interacts with ions, to account for the selective solvation that arises from different dielectric constants of the microphases. By including correlations from liquid state theory of an unbound reference fluid, the theory can treat chain behavior, microphase separation, ion correlations, and preferential solvation, at the same coarse-grained level. We show good agreement with molecular dynamics simulations.
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Affiliation(s)
- Jonathan R Brown
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 West Woodruff Avenue, Columbus, Ohio 43210, USA
| | - Youngmi Seo
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 West Woodruff Avenue, Columbus, Ohio 43210, USA
| | - Lisa M Hall
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 West Woodruff Avenue, Columbus, Ohio 43210, USA
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7
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Isaka Y, Ekimoto T, Kokabu Y, Yamato I, Murata T, Ikeguchi M. Rotation Mechanism of Molecular Motor V 1-ATPase Studied by Multiscale Molecular Dynamics Simulation. Biophys J 2017; 112:911-920. [PMID: 28297650 PMCID: PMC5355535 DOI: 10.1016/j.bpj.2017.01.029] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2016] [Revised: 01/06/2017] [Accepted: 01/30/2017] [Indexed: 11/28/2022] Open
Abstract
Enterococcus hirae V1-ATPase is a molecular motor composed of the A3B3 hexamer ring and the central stalk. In association with ATP hydrolysis, three catalytic AB pairs in the A3B3 ring undergo conformational changes, which lead to a 120° rotation of the central stalk. To understand how the conformational changes of three catalytic pairs induce the 120° rotation of the central stalk, we performed multiscale molecular dynamics (MD) simulations in which coarse-grained and all-atom MD simulations were combined using a fluctuation matching methodology. During the rotation, a catalytic AB pair spontaneously adopted an intermediate conformation, which was not included in the initial inputs of the simulations and was essentially close to the “bindable-like” structure observed in a recently solved crystal structure. Furthermore, the creation of a space between the bindable-like and tight pairs was required for the central stalk to rotate without steric hindrance. These cooperative rearrangements of the three catalytic pairs are crucial for the rotation of the central stalk.
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Affiliation(s)
- Yuta Isaka
- Graduate School of Medical Life Science, Yokohama City University, Tsurumi, Yokohama, Japan
| | - Toru Ekimoto
- Graduate School of Medical Life Science, Yokohama City University, Tsurumi, Yokohama, Japan
| | - Yuichi Kokabu
- Graduate School of Medical Life Science, Yokohama City University, Tsurumi, Yokohama, Japan
| | - Ichiro Yamato
- Department of Biological Science and Technology, Tokyo University of Science, Katsushika-ku, Tokyo, Japan
| | - Takeshi Murata
- Department of Chemistry, Graduate School of Science, Chiba University, Inage, Chiba, Japan; JST, PRESTO, Inage, Chiba, Japan
| | - Mitsunori Ikeguchi
- Graduate School of Medical Life Science, Yokohama City University, Tsurumi, Yokohama, Japan.
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8
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Ekimoto T, Matubayasi N, Ikeguchi M. Finite-size effect on the charging free energy of protein in explicit solvent. J Chem Theory Comput 2016; 11:215-23. [PMID: 26574219 DOI: 10.1021/ct5008394] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
The finite-size effect in periodic system is examined for the charging free energy of protein in explicit solvent over a variety of charged states. The key to the finite-size correction is the self-energy, which is defined as the interaction energy of the solute with its own periodic images and the neutralizing background. By employing the thermodynamic-integration method with systematically varied sizes of the unit cell of molecular dynamics (MD) simulations, we show for ubiquitin that the self-energy corrects the finite-size effect on the charging free energy within 1 kcal/mol at total charges of -5e, -1e, neutral, and +1e and within 5 kcal/mol even for a highly charged state with +8e. We then sought the additional correction from the solvation effect using the numerical solution to the Poisson equation of the protein with implicit solvent. This correction reduces the cell-size dependence of the charging free energy at +8e to 3 kcal/mol and is well expressed as the self-energy divided by the dielectric constant of solvent water.
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Affiliation(s)
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University , Toyonaka, Osaka 560-8531, Japan.,Elements Strategy Initiative for Catalysts and Batteries, Kyoto University , Katsura, Kyoto 615-8520, Japan
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9
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Remsing RC, Liu S, Weeks JD. Long-ranged contributions to solvation free energies from theory and short-ranged models. Proc Natl Acad Sci U S A 2016; 113:2819-26. [PMID: 26929375 PMCID: PMC4801310 DOI: 10.1073/pnas.1521570113] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Long-standing problems associated with long-ranged electrostatic interactions have plagued theory and simulation alike. Traditional lattice sum (Ewald-like) treatments of Coulomb interactions add significant overhead to computer simulations and can produce artifacts from spurious interactions between simulation cell images. These subtle issues become particularly apparent when estimating thermodynamic quantities, such as free energies of solvation in charged and polar systems, to which long-ranged Coulomb interactions typically make a large contribution. In this paper, we develop a framework for determining very accurate solvation free energies of systems with long-ranged interactions from models that interact with purely short-ranged potentials. Our approach is generally applicable and can be combined with existing computational and theoretical techniques for estimating solvation thermodynamics. We demonstrate the utility of our approach by examining the hydration thermodynamics of hydrophobic and ionic solutes and the solvation of a large, highly charged colloid that exhibits overcharging, a complex nonlinear electrostatic phenomenon whereby counterions from the solvent effectively overscreen and locally invert the integrated charge of the solvated object.
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Affiliation(s)
- Richard C Remsing
- Institute for Physical Science and Technology and Chemical Physics Program, University of Maryland, College Park, MD 20742; Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
| | - Shule Liu
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742; Department of Chemistry, James Franck Institute and Computation Institute, University of Chicago, Chicago, IL 60637
| | - John D Weeks
- Institute for Physical Science and Technology and Chemical Physics Program, University of Maryland, College Park, MD 20742; Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742;
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11
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Moucka F, Bratko D, Luzar A. Electrolyte pore/solution partitioning by expanded grand canonical ensemble Monte Carlo simulation. J Chem Phys 2015; 142:124705. [DOI: 10.1063/1.4914461] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Filip Moucka
- Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23221, USA
- Faculty of Science, J. E. Purkinje University, 400 96 Ústí nad Labem, Czech Republic
| | - Dusan Bratko
- Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23221, USA
| | - Alenka Luzar
- Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23221, USA
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12
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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: 169] [Impact Index Per Article: 15.4] [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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Luchko T, Joung IS, Case DA. Integral Equation Theory of Biomolecules and Electrolytes. INNOVATIONS IN BIOMOLECULAR MODELING AND SIMULATIONS 2012. [DOI: 10.1039/9781849735049-00051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
The so-called three-dimensional version (3D-RISM) can be used to describe the interactions of solvent components (here we treat water and ions) with a chemical or biomolecular solute of arbitrary size and shape. Here we give an overview of the current status of such models, describing some aspects of “pure” electrolytes (water plus simple ions) and of ionophores, proteins and nucleic acids in the presence of water and salts. Here we focus primarily on interactions with water and dissolved salts; as a practical matter, the discussion is mostly limited to monovalent ions, since studies of divalent ions present many difficult problems that have not yet been addressed. This is not a comprehensive review, but covers a few recent examples that illustrate current issues.
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Affiliation(s)
- Tyler Luchko
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
| | - In Suk Joung
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
| | - David A. Case
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
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14
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Janeček J, Netz RR. Effective screening length and quasiuniversality for the restricted primitive model of an electrolyte solution. J Chem Phys 2009; 130:074502. [DOI: 10.1063/1.3058777] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Bhattacharjee A, Hofer TS, Rode BM. Local density corrected three-body distribution functions for probing local structure reorganization in liquids. Phys Chem Chem Phys 2008; 10:6653-7. [DOI: 10.1039/b807305h] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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16
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Stern HA. Molecular simulation with variable protonation states at constant pH. J Chem Phys 2007; 126:164112. [PMID: 17477594 DOI: 10.1063/1.2731781] [Citation(s) in RCA: 79] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
A new method is presented for performing molecular simulations at constant pH. The method is a Monte Carlo procedure where trial moves consist of relatively short molecular dynamics trajectories, using a time-dependent potential energy that interpolates between the old and new protonation states. Conformations and protonation states are sampled from the correct statistical ensemble independent of the trial-move trajectory length, which may be adjusted to optimize efficiency. Because moves are not instantaneous, the method does not require the use of a continuum solvation model. It should also be useful in describing buried titratable groups that are not directly exposed to solvent, but have strong interactions with neighboring hydrogen bond partners. The feasibility of the method is demonstrated for a simple test case: constant-pH simulations of acetic acid in aqueous solution with an explicit representation of water molecules.
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Affiliation(s)
- Harry A Stern
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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Kastenholz MA, Hünenberger PH. Development of a lattice-sum method emulating nonperiodic boundary conditions for the treatment of electrostatic interactions in molecular simulations: A continuum-electrostatics study. J Chem Phys 2006; 124:124108. [PMID: 16599663 DOI: 10.1063/1.2177249] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Artifacts induced by the application of periodic boundary conditions and lattice-sum methods in explicit-solvent simulations of (bio-)molecular systems are nowadays a major concern in the computer-simulation community. The present article reports a first step toward the design of a modified lattice-sum algorithm emulating nonperiodic boundary conditions, and therefore exempt of such periodicity-induced artifacts. This result is achieved here in the (more simple) context of continuum electrostatics. It is shown that an appropriate modification of the periodic Poisson equation and of its boundary conditions leads to a continuum-electrostatics scheme, which, although applied under periodic boundary conditions, exactly mimics the nonperiodic situation. The possible extension of this scheme to explicit-solvent simulations is outlined and its practical implementation will be described in more details in a forthcoming article.
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Affiliation(s)
- Mika A Kastenholz
- Laboratorium für Physikalische Chemie, ETH Zürich, CH-8093 Zürich, Switzerland
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18
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Heinz TN, Hünenberger PH. Combining the lattice-sum and reaction-field approaches for evaluating long-range electrostatic interactions in molecular simulations. J Chem Phys 2005; 123:34107. [PMID: 16080730 DOI: 10.1063/1.1955525] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new scheme, the lattice-sum-emulated reaction-field (LSERF) method, is presented that combines the lattice-sum (LS) and reaction-field (RF) approaches for evaluating electrostatic interactions in molecular simulations. More precisely, the LSERF scheme emulates a RF calculation (based on an atomic cutoff) via the LS machinery. This is achieved by changing the form of the electrostatic interactions in a standard LS calculation (Coulombic) to the form corresponding to RF electrostatics (Coulombic plus quadratic reaction-field correction term, truncated at the cutoff distance). It is shown (both analytically and numerically) that in the limit of infinite reciprocal-space accuracy, (i) the LSERF scheme with a finite reaction-field cutoff and a given reaction-field permittivity is identical to the RF scheme with the same parameters (and an atomic cutoff), and (ii) the LSERF scheme is identical to the LS scheme in the limit of an infinite reaction-field cutoff, irrespective of the reaction-field permittivity. This new scheme offers two key advantages: (i) from a conceptual point of view, it shows that there is a continuity between the RF and LS schemes and unifies them into a common framework; (ii) from a practical point of view, it allows us to perform RF calculations with arbitrarily large reaction-field cutoff distances for the same computational costs as a corresponding LS calculation. The optimal choice for the cutoff will be the one that achieves the best compromise between artifacts arising from the dielectric heterogeneity of the system (short cutoff) and its artificial periodicity (long cutoff). The implementation of the LSERF method is extremely easy, requiring only very limited modifications of any standard LS code. For practical applications to biomolecular systems, the use of the LSERF scheme with large reaction-field cutoff distances is expected to represent a significant improvement over the current RF simulations involving comparatively much shorter cutoffs.
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Affiliation(s)
- Tim N Heinz
- Laboratorium für Physikalische Chemie, Eidgenössìsche Technische Hochschule Hönggerberg, Zürich, Switzerland
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Yeh IC, Hummer G. System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions. J Phys Chem B 2004. [DOI: 10.1021/jp0477147] [Citation(s) in RCA: 912] [Impact Index Per Article: 45.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Hanassab S, VanderNoot† T. Monte Carlo Simulations of Primitive Model (PM) Electrolytes in Non-Euclidean Geometries. MOLECULAR SIMULATION 2004. [DOI: 10.1080/08927020410001662624] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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21
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Kastenholz MA, Hünenberger PH. Influence of Artificial Periodicity and Ionic Strength in Molecular Dynamics Simulations of Charged Biomolecules Employing Lattice-Sum Methods. J Phys Chem B 2003. [DOI: 10.1021/jp0350924] [Citation(s) in RCA: 115] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mika A. Kastenholz
- Laboratorium für Physikalische Chemie, ETH Zürich, CH-8093 Zürich, Switzerland
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22
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Ghosh T, García AE, Garde S. Water-Mediated Three-Particle Interactions between Hydrophobic Solutes: Size, Pressure, and Salt Effects. J Phys Chem B 2002. [DOI: 10.1021/jp0220175] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tuhin Ghosh
- Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 and T-10, Theoretical Biology and Biophysics Group, MS K710 Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Angel E. García
- Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 and T-10, Theoretical Biology and Biophysics Group, MS K710 Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Shekhar Garde
- Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 and T-10, Theoretical Biology and Biophysics Group, MS K710 Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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Monte Carlo simulations of restricted primitive model (RPM) electrolytes in non-Euclidean geometries. J Electroanal Chem (Lausanne) 2002. [DOI: 10.1016/s0022-0728(02)00909-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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24
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Ghosh T, García AE, Garde S. Enthalpy and entropy contributions to the pressure dependence of hydrophobic interactions. J Chem Phys 2002. [DOI: 10.1063/1.1431582] [Citation(s) in RCA: 76] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Degrève L, Carlos Borin A, Mazzé FM, Rodrigues AL. Molecular simulation of a phase separation in a non-primitive electrolyte solution. Chem Phys 2001. [DOI: 10.1016/s0301-0104(01)00279-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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26
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Hünenberger PH, McCammon JA. Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study. Biophys Chem 1999; 78:69-88. [PMID: 10343384 DOI: 10.1016/s0301-4622(99)00007-1] [Citation(s) in RCA: 195] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity; (ii) a solute size which is non-negligible compared to the size of the unit cell; and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.
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Affiliation(s)
- P H Hünenberger
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla 92093-0365, USA.
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Georgalis Y, Umbach P, Saenger W, Ihmels B, Soumpasis DM. Ordering of Fractal Clusters in Crystallizing Lysozyme Solutions. J Am Chem Soc 1999. [DOI: 10.1021/ja982407y] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yannis Georgalis
- Contribution from the Institut für Kristallographie, Freie Universität Berlin, Takustrasse 6, 14195 Berlin, Germany, and Max-Planck Institut fur Biophysikalische Chemie, Biocomputation Group, Postfach 2841, 37018 Göttingen, Germany
| | - Patrick Umbach
- Contribution from the Institut für Kristallographie, Freie Universität Berlin, Takustrasse 6, 14195 Berlin, Germany, and Max-Planck Institut fur Biophysikalische Chemie, Biocomputation Group, Postfach 2841, 37018 Göttingen, Germany
| | - Wolfram Saenger
- Contribution from the Institut für Kristallographie, Freie Universität Berlin, Takustrasse 6, 14195 Berlin, Germany, and Max-Planck Institut fur Biophysikalische Chemie, Biocomputation Group, Postfach 2841, 37018 Göttingen, Germany
| | - Bernd Ihmels
- Contribution from the Institut für Kristallographie, Freie Universität Berlin, Takustrasse 6, 14195 Berlin, Germany, and Max-Planck Institut fur Biophysikalische Chemie, Biocomputation Group, Postfach 2841, 37018 Göttingen, Germany
| | - Dikeos Mario Soumpasis
- Contribution from the Institut für Kristallographie, Freie Universität Berlin, Takustrasse 6, 14195 Berlin, Germany, and Max-Planck Institut fur Biophysikalische Chemie, Biocomputation Group, Postfach 2841, 37018 Göttingen, Germany
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Hünenberger PH, McCammon JA. Ewald artifacts in computer simulations of ionic solvation and ion–ion interaction: A continuum electrostatics study. J Chem Phys 1999. [DOI: 10.1063/1.477873] [Citation(s) in RCA: 294] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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29
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Hummer G, Pratt LR, García AE. Molecular Theories and Simulation of Ions and Polar Molecules in Water. J Phys Chem A 1998. [DOI: 10.1021/jp982195r] [Citation(s) in RCA: 165] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Gerhard Hummer
- Theoretical Division, Mail Stop B268, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Lawrence R. Pratt
- Theoretical Division, Mail Stop B268, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Angel E. García
- Theoretical Division, Mail Stop B268, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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Georgalis Y, Umbach P, Soumpasis DM, Saenger W. Dynamics and Microstructure Formation during Nucleation of Lysozyme Solutions. J Am Chem Soc 1998. [DOI: 10.1021/ja973614l] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yannis Georgalis
- Contribution from the Institut für Kristallographie Freie Universität Berlin, Takustrasse 6, 14195 Berlin, and Biocomputation Group, Max-Planck-Institut für Biophysikalische Chemie, P.O. Box 28141, 37018 Göttingen, Germany
| | - Patrick Umbach
- Contribution from the Institut für Kristallographie Freie Universität Berlin, Takustrasse 6, 14195 Berlin, and Biocomputation Group, Max-Planck-Institut für Biophysikalische Chemie, P.O. Box 28141, 37018 Göttingen, Germany
| | - Dikeos Mario Soumpasis
- Contribution from the Institut für Kristallographie Freie Universität Berlin, Takustrasse 6, 14195 Berlin, and Biocomputation Group, Max-Planck-Institut für Biophysikalische Chemie, P.O. Box 28141, 37018 Göttingen, Germany
| | - Wolfram Saenger
- Contribution from the Institut für Kristallographie Freie Universität Berlin, Takustrasse 6, 14195 Berlin, and Biocomputation Group, Max-Planck-Institut für Biophysikalische Chemie, P.O. Box 28141, 37018 Göttingen, Germany
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Hummer G, Pratt LR, García AE, Garde S, Berne BJ, Rick SW. Reply to Comment on “Electrostatic Potentials and Free Energies of Solvation of Polar and Charged Molecules”. J Phys Chem B 1998. [DOI: 10.1021/jp980145g] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gerhard Hummer
- Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Lawrence R. Pratt
- Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Angel E. García
- Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Shekhar Garde
- Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Bruce J. Berne
- Department of Chemistry and Center for Biomolecular Simulation, Columbia University, New York, New York 10027
| | - Steven W. Rick
- Frederick Cancer Research and Development Center, National Cancer Institute, Frederick, Maryland 21702
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32
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Garde S, Hummer G, Paulaitis ME. Free energy of hydration of a molecular ionic solute: Tetramethylammonium ion. J Chem Phys 1998. [DOI: 10.1063/1.475526] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Costa D, Saija F, Giaquinta P. Angular correlations and statistical entropy of hard spherocylinders: the isotropic–nematic transition. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(97)01299-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Hummer G, Pratt LR, García AE. Multistate Gaussian Model for Electrostatic Solvation Free Energies. J Am Chem Soc 1997. [DOI: 10.1021/ja971148u] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Gerhard Hummer
- Contribution from the Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Lawrence R. Pratt
- Contribution from the Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Angel E. García
- Contribution from the Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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Pellegrini M, Gro/nbech‐Jensen N, Doniach S. Potentials of mean force for biomolecular simulations: Theory and test on alanine dipeptide. J Chem Phys 1996. [DOI: 10.1063/1.471552] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ashbaugh HS, Paulaitis ME. Entropy of Hydrophobic Hydration: Extension to Hydrophobic Chains. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp952387b] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Henry S. Ashbaugh
- Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
| | - Michael E. Paulaitis
- Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
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Affiliation(s)
- Gerhard Hummer
- Theoretical Biology and Biophysics Group T-10, MS K710, Center for Nonlinear Studies, MS B258, and Theoretical Chemistry and Molecular Physics Group T-12, MS B268, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Lawrence R. Pratt
- Theoretical Biology and Biophysics Group T-10, MS K710, Center for Nonlinear Studies, MS B258, and Theoretical Chemistry and Molecular Physics Group T-12, MS B268, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Angel E. García
- Theoretical Biology and Biophysics Group T-10, MS K710, Center for Nonlinear Studies, MS B258, and Theoretical Chemistry and Molecular Physics Group T-12, MS B268, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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Figueirido F, Del Buono GS, Levy RM. On finite‐size effects in computer simulations using the Ewald potential. J Chem Phys 1995. [DOI: 10.1063/1.470721] [Citation(s) in RCA: 139] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hummer G, Soumpasis DM. Statistical mechanical treatment of the structural hydration of biological macromolecules: Results for B-DNA. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:5085-5095. [PMID: 9962594 DOI: 10.1103/physreve.50.5085] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Abascal J, Bresme F, Turq P. The influence of concentration and ionic strength on the cluster structure of highly charged electrolyte solutions. Mol Phys 1994. [DOI: 10.1080/00268979400100101] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Hummer G, Soumpasis DM. Computation of the water density distribution at the ice-water interface using the potentials-of-mean-force expansion. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:591-596. [PMID: 9961250 DOI: 10.1103/physreve.49.591] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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45
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Bresme F, Abascal JLF. Pair connectedness functions and percolation in highly charged electrolyte solutions. J Chem Phys 1993. [DOI: 10.1063/1.465571] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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