1
|
Lin H, Nie Z, Shang E, Dai S. An Adaptive Local Iterative Method for Fast Calculation of Electrostatic Interactions between Charged Polymers in Dielectric Inhomogeneous System. ADVANCED THEORY AND SIMULATIONS 2023. [DOI: 10.1002/adts.202200776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Affiliation(s)
- Hao Lin
- School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China
| | - Zhiji Nie
- School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China
| | - Enlong Shang
- School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China
| | - Shuyang Dai
- School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China
| |
Collapse
|
2
|
Saurabh K, Solovchuk M, Sheu TWH. A detailed study of ion transport through the SARS-CoV-2 E protein ion channel. NANOSCALE 2022; 14:8291-8305. [PMID: 35648036 DOI: 10.1039/d2nr01385a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The envelope (E) protein encoded in the genome of an RNA virus is crucial for the replication, budding and pathophysiology of the virus. In the light of the ongoing pandemic, we explored similarities/differences between SARS-CoV-1 and SARS-CoV-2 E protein ion channels in terms of their selectivity. Further, we also examined the impact of variation of the bath concentration and introduction of potential and concentration gradients across the channel on the binding ratios of sodium and chloride ions for the SARS-CoV-2 E protein. Ion transport is described through the fourth-order Poisson-Nernst-Planck-Bikerman (4PNPBik) model which generalizes the traditional model by including ionic interactions between ions and their surrounding medium and non-ionic interactions between particles due to their finite size. Governing equations are solved numerically using the immersed boundary-lattice Boltzmann method (IB-LBM). The mathematical model has been validated by comparing analytical and experimental ion activity. The SARS-CoV-1 E protein ion channel is found to be more permeable to cationic ions, while the SARS-CoV-2 E protein has similar selectivity for both cationic and anionic species. For SARS-CoV-2, an increase in the bath concentration results in an increase in the binding ratio for sodium ions. Furthermore, the chloride binding ratio increases as the concentration gradient increases. A potential gradient has a minimal effect on the binding ratio. The SARS-CoV-2 E protein was found to support higher ionic currents than the SARS-CoV-1 E protein. Furthermore, the ionic current increased with increasing bath concentrations.
Collapse
Affiliation(s)
- Kumar Saurabh
- Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 10617.
- Institute of Biomedical Engineering and Nanomedicine, National Health Research Institutes, Zhunan, Taiwan 35053.
- NTU High Performance and Scientific Computing Center, National Taiwan University, Taipei, Taiwan 10617
| | - Maxim Solovchuk
- Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 10617.
- Institute of Biomedical Engineering and Nanomedicine, National Health Research Institutes, Zhunan, Taiwan 35053.
- Tissue Engineering and Regenerative Medicine, National Chung Hsing University, Taichung, Taiwan 40227
| | - Tony Wen-Hann Sheu
- Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 10617.
- NTU High Performance and Scientific Computing Center, National Taiwan University, Taipei, Taiwan 10617
- Center for Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taipei, Taiwan 10617
| |
Collapse
|
3
|
Volkmer HW, Xie D. Analytical solution of a linear nonlocal Poisson-Boltzmann equation with multiple charges in a spherical solute region surrounded by a water spherical shell. Phys Rev E 2022; 105:015305. [PMID: 35193245 DOI: 10.1103/physreve.105.015305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Accepted: 12/27/2021] [Indexed: 06/14/2023]
Abstract
In this paper, an analytical solution of a linear nonlocal Poisson-Boltzmann equation (NPBE) test model with multiple charges in a spherical solute region surrounded by a water spherical shell is derived as a single series of Legendre polynomials and modified spherical Bessel functions. The classic Kirkwood ball model is then shown to be a special case of the NPBE test model so that its analytical solution is regained from a double series of associated Legendre polynomials (derived by Kirkwood in 1934) to a new single series of Legendre polynomials, sharply reducing its computational cost. As an application of these series solutions, a comparison study is done to demonstrate the differences between the Kirkwood and NPBE test models.
Collapse
Affiliation(s)
- Hans W Volkmer
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201-0413, USA
| | - Dexuan Xie
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201-0413, USA
| |
Collapse
|
4
|
Xiao T, Zhou Y. A nonlocal electrostatics model for ions in concentrated primitive electrolyte solutions. Electrochim Acta 2021. [DOI: 10.1016/j.electacta.2021.139040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
5
|
Monet G, Bresme F, Kornyshev A, Berthoumieux H. Nonlocal Dielectric Response of Water in Nanoconfinement. PHYSICAL REVIEW LETTERS 2021; 126:216001. [PMID: 34114838 DOI: 10.1103/physrevlett.126.216001] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Revised: 04/19/2021] [Accepted: 04/29/2021] [Indexed: 06/12/2023]
Abstract
Recent experiments reporting a very low dielectric permittivity for nanoconfined water have renewed the interest in the structure and dielectric properties of water in narrow gaps. Here, we describe such systems with a minimal Landau-Ginzburg field theory composed of a nonlocal bulk-determined term and a local water-surface interaction term. We show how the interplay between the boundary conditions and intrinsic bulk correlations encodes the dielectric properties of confined water. Our theoretical analysis is supported by molecular dynamics simulations and comparison with the experimental data.
Collapse
Affiliation(s)
- G Monet
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France
| | - F Bresme
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, W12 0BZ 2AZ London, United Kingdom
| | - A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, W12 0BZ 2AZ London, United Kingdom
| | - H Berthoumieux
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France
| |
Collapse
|
6
|
Zhou YC, Argudo D, Marcoline F, Grabe M. A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface. JOURNAL OF COMPUTATIONAL PHYSICS 2020; 422:109755. [PMID: 32921806 PMCID: PMC7480790 DOI: 10.1016/j.jcp.2020.109755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.
Collapse
Affiliation(s)
- Y. C. Zhou
- Department of Mathematics, Colorado State University, Fort Collins, CO 80523
| | - David Argudo
- Department of Pharmaceutical Chemistry and Cardiovascular Research Institute, University of California, San Francisco, CA 94143
| | - Frank Marcoline
- Department of Pharmaceutical Chemistry and Cardiovascular Research Institute, University of California, San Francisco, CA 94143
| | - Michael Grabe
- Department of Pharmaceutical Chemistry and Cardiovascular Research Institute, University of California, San Francisco, CA 94143
| |
Collapse
|
7
|
Physical origin of Na+/Cl− selectivity of tight junctions between epithelial cells. Nonlocal electrostatic approach. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113884] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
|
8
|
Vatin M, Porro A, Sator N, Dufrêche JF, Berthoumieux H. Electrostatic interactions in water: a nonlocal electrostatic approach. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1825849] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- M. Vatin
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
- ICSM/LMCT Site de Marcoule, Bagnols sur Céze Cedex, France
| | - A. Porro
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
| | - N. Sator
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
| | - J.-F. Dufrêche
- ICSM/LMCT Site de Marcoule, Bagnols sur Céze Cedex, France
| | - H. Berthoumieux
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
| |
Collapse
|
9
|
Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model. ENTROPY 2020; 22:e22050550. [PMID: 33286322 PMCID: PMC7517072 DOI: 10.3390/e22050550] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Revised: 05/11/2020] [Accepted: 05/12/2020] [Indexed: 12/21/2022]
Abstract
We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.
Collapse
|
10
|
Vorotyntsev MA, Rubashkin AA. Uniformity ansatz for inverse dielectric function of spatially restricted nonlocal polar medium as a novel approach for calculation of electric characteristics of ion–solvent system. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2019.01.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
11
|
Berthoumieux H, Paillusson F. Dielectric response in the vicinity of an ion: A nonlocal and nonlinear model of the dielectric properties of water. J Chem Phys 2019; 150:094507. [PMID: 30849905 DOI: 10.1063/1.5080183] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The goal of this work is to propose a simple continuous model that captures the dielectric properties of water at the nanometric scale. We write an electrostatic energy as a functional of the polarisation field containing a term in P4 and non-local Gaussian terms. Such a hamiltonian can reproduce two key properties of water: the saturation of the polarisation response of water in the presence of a strong electrostatic field and the nanometric dipolar correlations of the solvent molecules modifying the long range van der waals interaction. This model explores thus two fundamental aspects that have to be included in implicit models of electrolytes for a relevant description of electrostatic interactions at nanometric scales.
Collapse
Affiliation(s)
| | - F Paillusson
- School of Mathematics and Physics, University of Lincoln, Lincoln LN6 7TS, United Kingdom
| |
Collapse
|
12
|
Ying J, Xie D. An accelerated nonlocal Poisson-Boltzmann equation solver for electrostatics of biomolecule. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e3129. [PMID: 30021243 DOI: 10.1002/cnm.3129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Revised: 06/26/2018] [Accepted: 07/05/2018] [Indexed: 06/08/2023]
Abstract
The nonlocal modified Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly used dielectric continuum model, the Poisson-Boltzmann equation (PBE), for computing electrostatics of biomolecules. In this paper, an accelerated NMPBE solver is constructed by finite element and finite difference hybrid techniques. It is then programmed as a software package for computing electrostatic solvation and binding free energies for a protein in a symmetric 1:1 ionic solvent. Numerical results validate the new solver and its numerical stability. They also demonstrate that the new solver has much better performance than the corresponding finite element solver in terms of computer CPU time. Furthermore, they show that the binding free energies produced by NMPBE can match chemical experiment data better than those by PBE.
Collapse
Affiliation(s)
- Jinyong Ying
- School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
| | - Dexuan Xie
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
| |
Collapse
|
13
|
Vorotyntsev MA, Rubashkin AA, Antipov AE. A New Approach in the Theory of Spatially-Restricted Nonlocal Dielectric Media. RUSS J ELECTROCHEM+ 2018. [DOI: 10.1134/s1023193518130505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
14
|
Bohinc K, Bossa GV, May S. Incorporation of ion and solvent structure into mean-field modeling of the electric double layer. Adv Colloid Interface Sci 2017; 249:220-233. [PMID: 28571611 DOI: 10.1016/j.cis.2017.05.001] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Revised: 04/28/2017] [Accepted: 05/02/2017] [Indexed: 01/13/2023]
Abstract
An electric double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the electric double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded volume effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theoretical models predict structural properties of the electric double layer such as the differential capacitance and compare some of these predictions with computer simulations.
Collapse
Affiliation(s)
- Klemen Bohinc
- Faculty of Health Sciences, University of Ljubljana, Ljubljana SI-1000, Slovenia.
| | | | - Sylvio May
- Department of Physics, North Dakota State University, Fargo, ND 58108-6050, USA
| |
Collapse
|
15
|
Wang J. Experimental charge density from electron microscopic maps. Protein Sci 2017; 26:1619-1626. [PMID: 28543856 DOI: 10.1002/pro.3198] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Accepted: 05/17/2017] [Indexed: 12/23/2022]
Abstract
The charge density (CD) distribution of an atom is the difference per unit volume between the positive charge of its nucleus and the distribution of the negative charges carried by the electrons that are associated with it. The CDs of the atoms in macromolecules are responsible for their electrostatic potential (ESP) distributions, which can now be visualized using cryo-electron microscopy at high resolution. CD maps can be recovered from experimental ESP density maps using the negative Laplacian operation. CD maps are easier to interpret than ESP maps because they are less sensitive to long-range electrostatic effects. An ESP-to-CD conversion involves multiplication of amplitudes of structure factors as Fourier transforms of these maps in reciprocal space by 1/d2 , where d is the resolution of reflections. In principle, it should be possible to determine the charges carried by the individual atoms in macromolecules by comparing experimental CD maps with experimental ESP maps.
Collapse
Affiliation(s)
- Jimin Wang
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut, 06520
| |
Collapse
|
16
|
Kjellander R. Nonlocal electrostatics in ionic liquids: The key to an understanding of the screening decay length and screened interactions. J Chem Phys 2016; 145:124503. [DOI: 10.1063/1.4962756] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
17
|
Qin J, de Pablo JJ, Freed KF. Image method for induced surface charge from many-body system of dielectric spheres. J Chem Phys 2016; 145:124903. [DOI: 10.1063/1.4962832] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
|
18
|
Buyukdagli S, Blossey R. Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:343001. [PMID: 27357125 DOI: 10.1088/0953-8984/28/34/343001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics and has been applied to numerous physical chemistry and biophysics problems. Its essential limitations are in its neglect of correlation effects and fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review, we provide an update on the developments achieved in the self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce a corresponding system of coupled non-linear equations for both continuum electrostatics with a uniform dielectric constant, and a structured solvent-a dipolar Coulomb fluid-including non-local effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows us to include physically relevant effects, as we show for a range of applications of these equations.
Collapse
Affiliation(s)
- S Buyukdagli
- Department of Physics, Bilkent University, Ankara 06800, Turkey
| | | |
Collapse
|
19
|
Xie D, Liu JL, Eisenberg B. Nonlocal Poisson-Fermi model for ionic solvent. Phys Rev E 2016; 94:012114. [PMID: 27575084 DOI: 10.1103/physreve.94.012114] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 06/06/2023]
Abstract
We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.
Collapse
Affiliation(s)
- Dexuan Xie
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, 53201-0413, USA
| | - Jinn-Liang Liu
- Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu 300, Taiwan
| | - Bob Eisenberg
- Department of Molecular Biophysics and Physiology, Rush University, Chicago, Illinois 60612, USA
| |
Collapse
|
20
|
Tabrizi AM, Knepley MG, Bardhan JP. Generalising the mean spherical approximation as a multiscale, nonlinear boundary condition at the solute–solvent interface. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1198503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | - Matthew G. Knepley
- Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA
| | - Jaydeep P. Bardhan
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA
| |
Collapse
|
21
|
Reif MM, Hünenberger PH. Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited. J Phys Chem B 2016; 120:8485-517. [PMID: 27173101 DOI: 10.1021/acs.jpcb.6b02156] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The asymmetric solvation of ions can be defined as the tendency of a solvent to preferentially solvate anions over cations or cations over anions, at identical ionic charge magnitudes and effective sizes. Taking water as a reference, these effects are quantified experimentally for many solvents by the relative acity (A) and basity (B) parameters of the Swain scale. The goal of the present study is to investigate the asymmetric solvation of ions using molecular dynamics simulations, and to connect the results to this empirical scale. To this purpose, the charging free energies of alkali and halide ions, and of their hypothetical oppositely charged counterparts, are calculated in a variety of solvents. In a first set of calculations, artificial solvent models are considered that present either a charge or a shape asymmetry at the molecular level. The solvation asymmetry, probed by the difference in charging free energy between the two oppositely charged ions, is found to encompass a term quadratic in the ion charge, related to the different solvation structures around the anion and cation, and a term linear in the ion charge, related to the solvation structure around the uncharged ion-sized cavity. For these simple solvent models, the two terms are systematically counteracting each other, and it is argued that only the quadratic term should be retained when comparing the results of simulations involving physical solvents to experimental data. In a second set of calculations, 16 physical solvents are considered. The theoretical estimates for the acity A are found to correlate very well with the Swain parameters, whereas the correlation for B is very poor. Based on this observation, the Swain scale is reformulated into a new scale involving an asymmetry parameter Σ, positive for acitic solvents and negative for basitic ones, and a polarity parameter Π. This revised scale has the same predictive power as the original scale, but it characterizes asymmetry in an absolute sense, the atomistic simulations playing the role of an extra-thermodynamic assumption, and is optimally compatible with the simulation results. Considering the 55 solvents in the Swain set, it is observed that a moderate basity (Σ between -0.9 and -0.3, related to electronic polarization) represents the baseline for most solvents, while a highly variable acity (Σ between 0.0 and 3.0, related to hydrogen-bond donor capacity modulated by inductive effects) represents a landmark of protic solvents.
Collapse
Affiliation(s)
- Maria M Reif
- Physics Department (T38), Technische Universität München , D-85748 Garching, Germany
| | | |
Collapse
|
22
|
Xie D, Volkmer HW, Ying J. Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere. Phys Rev E 2016; 93:043304. [PMID: 27176425 DOI: 10.1103/physreve.93.043304] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2015] [Indexed: 11/07/2022]
Abstract
The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.
Collapse
Affiliation(s)
- Dexuan Xie
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201-0413, USA
| | - Hans W Volkmer
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201-0413, USA
| | - Jinyong Ying
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201-0413, USA
| |
Collapse
|
23
|
Buyukdagli S. Electrostatic interactions in charged nanoslits within an explicit solvent theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:455101. [PMID: 26443128 DOI: 10.1088/0953-8984/27/45/455101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Within a dipolar Poisson-Boltzmann theory including electrostatic correlations, we consider the effect of explicit solvent structure on solvent and ion partition confined to charged nanopores. We develop a relaxation scheme for the solution of this highly non-linear integro-differential equation for the electrostatic potential. The scheme is an extension of the approach previously introduced for simple planes (Buyukdagli and Blossey 2014 J. Chem. Phys. 140 234903) to nanoslit geometry. We show that the reduced dielectric response of solvent molecules at the membrane walls gives rise to an electric field significantly stronger than the field of the classical Poisson-Boltzmann equation. This peculiarity associated with non-local electrostatic interactions results in turn in an interfacial counterion adsorption layer absent in continuum theories. The observation of this enhanced counterion affinity in the very close vicinity of the interface may have important impacts on nanofluidic transport through charged nanopores. Our results indicate the quantitative inaccuracy of solvent implicit nanofiltration theories in predicting the ionic selectivity of membrane nanopores.
Collapse
|
24
|
Schaaf C, Gekle S. Dielectric response of the water hydration layer around spherical solutes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032718. [PMID: 26465509 DOI: 10.1103/physreve.92.032718] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 06/05/2023]
Abstract
We calculate the local dielectric function ɛ(r) inside the hydration layer around a spherical solute (i) from molecular dynamics simulations including explicit solutes and (ii) theoretically using the nonlocal dielectric function of bulk water which includes the radial electric field, but not the explicit solute. The observed agreement between the two concepts shows that while ɛ(r) is strongly different from bulk, this difference is not due to restructuring of the hydrogen bond network but is mostly a consequence of the field geometry. The dielectric response differs for anions and cations, yielding a natural explanation for the well-known charge asymmetry of ionic solvation in agreement with experimental data.
Collapse
Affiliation(s)
- Christian Schaaf
- Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| |
Collapse
|
25
|
Bardhan JP, Knepley MG, Brune P. Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators. MOLECULAR BASED MATHEMATICAL BIOLOGY 2015; 3:1-22. [PMID: 26273581 DOI: 10.1515/mlbmb-2015-0001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.
Collapse
Affiliation(s)
- Jaydeep P Bardhan
- Dept. of Mechanical and Industrial Engineering, Northeastern University, Boston MA 02115
| | | | | |
Collapse
|
26
|
Rubashkin AA. The role of spatial dispersion of the dielectric constant of spherical water cavity in the lowering of the free energy of ion transfer to the cavity. RUSS J ELECTROCHEM+ 2014. [DOI: 10.1134/s1023193514110093] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
27
|
Bardhan JP, Knepley MG. Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions. J Chem Phys 2014; 141:131103. [PMID: 25296776 PMCID: PMC4193973 DOI: 10.1063/1.4897324] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2014] [Accepted: 09/25/2014] [Indexed: 01/28/2023] Open
Abstract
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
Collapse
Affiliation(s)
- Jaydeep P Bardhan
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Matthew G Knepley
- Computation Institute, The University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
28
|
Sahin B, Ralf B. Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:285101. [PMID: 24920153 DOI: 10.1088/0953-8984/26/28/285101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.
Collapse
Affiliation(s)
- Buyukdagli Sahin
- Biological Nanosystems, Interdisciplinary Research Institute, Université des Sciences et des Technologies de Lille (USTL), USR CNRS 3078, 50 Avenue Halley, 59568 Villeneuve d'Ascq, France
| | | |
Collapse
|
29
|
Buyukdagli S, Blossey R. Dipolar correlations in structured solvents under nanoconfinement. J Chem Phys 2014; 140:234903. [DOI: 10.1063/1.4881604] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
|
30
|
Buyukdagli S, Ala-Nissila T. Microscopic formulation of nonlocal electrostatics in polar liquids embedding polarizable ions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063201. [PMID: 23848796 DOI: 10.1103/physreve.87.063201] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2012] [Revised: 03/26/2013] [Indexed: 06/02/2023]
Abstract
Nonlocal electrostatic interactions associated with finite solvent size and ion polarizability are investigated within the mean-field linear response theory. To this end, we introduce a field-theoretic model of a polar liquid composed of linear multipole solvent molecules and embedding polarizable ions modeled as Drude oscillators. Unlike previous dipolar Poisson-Boltzmann formulations treating the solvent molecules as point dipoles, our model is able to qualitatively reproduce the non-local dielectric response behavior of polar liquids observed in molecular dynamics simulations and atomic force microscope experiments for water solvent at charged interfaces. The present theory explains the formation of the associated interfacial hydration layers in terms of a cooperative dipolar response mechanism driven by the reaction of the solvent molecules to their own polarization field. We also incorporate into the theory the relative multipole moments of water molecules obtained from quantum mechanical calculations and show that the multipolar contributions to the dielectric permittivity are largely dominated by the dipolar one. We find that this stems from the mutual cancellation of the first two interfacial hydration layers of opposite net charge for multipolar liquids. Within the same nonlocal dielectric response theory, we show that the induced ion polarizability reverses the interfacial ion density trends predicted by the Poisson-Boltzmann theory, resulting in a surface affinity of coions and exclusion of counterions. The results indicate that the consideration of the discrete charge composition of solvent molecules and ions is the key step towards a microscopic understanding of nonlocal electrostatic effects in polar solvents.
Collapse
Affiliation(s)
- Sahin Buyukdagli
- Department of Applied Physics and COMP Center of Excellence, Aalto University School of Science, P. O. Box 11000, FI-00076 Aalto, Espoo, Finland.
| | | |
Collapse
|
31
|
Bardhan JP, Jungwirth P, Makowski L. Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies. J Chem Phys 2013; 137:124101. [PMID: 23020318 DOI: 10.1063/1.4752735] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).
Collapse
Affiliation(s)
- Jaydeep P Bardhan
- Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, Illinois 60612, USA
| | | | | |
Collapse
|
32
|
Hughes J, Krebs EJ, Roundy D. A classical density-functional theory for describing water interfaces. J Chem Phys 2013; 138:024509. [DOI: 10.1063/1.4774155] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
|
33
|
|
34
|
Storey BD, Bazant MZ. Effects of electrostatic correlations on electrokinetic phenomena. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:056303. [PMID: 23214872 DOI: 10.1103/physreve.86.056303] [Citation(s) in RCA: 75] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2012] [Indexed: 05/17/2023]
Abstract
The classical theory of electrokinetic phenomena is based on the mean-field approximation that the electric field acting on an individual ion is self-consistently determined by the local mean charge density. This paper considers situations, such as concentrated electrolytes, multivalent electrolytes, or solvent-free ionic liquids, where the mean-field approximation breaks down. A fourth-order modified Poisson equation is developed that captures the essential features in a simple continuum framework. The model is derived as a gradient approximation for nonlocal electrostatics of interacting effective charges, where the permittivity becomes a differential operator, scaled by a correlation length. The theory is able to capture subtle aspects of molecular simulations and allows for simple calculations of electrokinetic flows in correlated ionic fluids. Charge-density oscillations tend to reduce electro-osmotic flow and streaming current, and overscreening of surface charge can lead to flow reversal. These effects also help to explain the suppression of induced-charge electrokinetic phenomena at high salt concentrations.
Collapse
Affiliation(s)
- Brian D Storey
- Franklin W. Olin College of Engineering, Needham, Massachusetts 02492, USA
| | | |
Collapse
|
35
|
Designing electrostatic interactions in biological systems via charge optimization or combinatorial approaches: insights and challenges with a continuum electrostatic framework. Theor Chem Acc 2012. [DOI: 10.1007/s00214-012-1252-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
|
36
|
Enami S, Mishra H, Hoffmann MR, Colussi AJ. Hofmeister effects in micromolar electrolyte solutions. J Chem Phys 2012; 136:154707. [PMID: 22519343 DOI: 10.1063/1.4704752] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Shinichi Enami
- The Hakubi Center, Kyoto University, Kyoto 606-8302, Japan.
| | | | | | | |
Collapse
|
37
|
Faraudo J. The missing link between the Hydration Force and interfacial water: Evidence from computer simulations. Curr Opin Colloid Interface Sci 2011. [DOI: 10.1016/j.cocis.2011.04.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
38
|
Bardhan JP. Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins. J Chem Phys 2011; 135:104113. [PMID: 21932882 DOI: 10.1063/1.3632995] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Å containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.
Collapse
Affiliation(s)
- Jaydeep P Bardhan
- Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, Illinois 60612, USA.
| |
Collapse
|
39
|
Bazant MZ, Storey BD, Kornyshev AA. Double layer in ionic liquids: overscreening versus crowding. PHYSICAL REVIEW LETTERS 2011; 106:046102. [PMID: 21405339 DOI: 10.1103/physrevlett.106.046102] [Citation(s) in RCA: 500] [Impact Index Per Article: 38.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2010] [Indexed: 05/17/2023]
Abstract
We develop a simple Landau-Ginzburg-type continuum theory of solvent-free ionic liquids and use it to predict the structure of the electrical double layer. The model captures overscreening from short-range correlations, dominant at small voltages, and steric constraints of finite ion sizes, which prevail at large voltages. Increasing the voltage gradually suppresses overscreening in favor of the crowding of counterions in a condensed inner layer near the electrode. This prediction, the ion profiles, and the capacitance-voltage dependence are consistent with recent computer simulations and experiments on room-temperature ionic liquids, using a correlation length of order the ion size.
Collapse
Affiliation(s)
- Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | | |
Collapse
|
40
|
Paillusson F, Blossey R. Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:052501. [PMID: 21230529 DOI: 10.1103/physreve.82.052501] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2010] [Indexed: 05/30/2023]
Abstract
Polar liquids like water carry a characteristic nanometric length scale, the correlation length of orientation polarizations. Continuum theories that can capture this feature commonly run under the name of "nonlocal" electrostatics since their dielectric response is characterized by a scale-dependent dielectric function ε(q), where q is the wave vector; the Poisson(-Boltzmann) equation then turns into an integro-differential equation. Recently, "local" formulations have been put forward for these theories and applied to water, solvated ions, and proteins. We review the local formalism and show how it can be applied to a structured liquid in slit and plate geometries, and solve the Poisson-Boltzmann theory for a charged plate in a structured solvent with counterions. Our results establish a coherent picture of the local version of nonlocal electrostatics and show its ease of use when compared to the original formulation.
Collapse
|
41
|
Hollenbeck D, Martini KM, Langner A, Harkin A, Ross DS, Thurston GM. Model for evaluating patterned charge-regulation contributions to electrostatic interactions between low-dielectric spheres. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031402. [PMID: 21230072 PMCID: PMC5830138 DOI: 10.1103/physreve.82.031402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2010] [Indexed: 05/30/2023]
Abstract
We study the electrostatic contribution to the effective potential between two spherical low-dielectric particles that carry proton-titratable sites within a linearized setting. To evaluate the needed work of charging for each possible proton occupancy configuration, together with its crucial dependence on sphere separation, we numerically solve a coarse-grained linear Debye-Hückel model that incorporates nonuniform dielectric and ionic solution properties at a series of intersphere separations and for chosen titratable charge locations on each sphere. We combine the resulting work-of-charging matrix with site-specific chemical potentials of proton binding to construct the Boltzmann-weighted probabilities of each possible occupancy pattern of the titratable sites as functions of intersphere separation. With the use of these probabilities we find that a nonmonotonic average electrostatic potential can result that is repulsive at larger sphere separations but attractive at close separations. The nonmonotonic potential corresponds to particular choices of site-specific unoccupied charge values and their corresponding proton affinities, and its occurrence is dependent on pH in relation to the pKa values of the titratable groups. For the chosen titratable groups, we identify the particular change from repulsive to attractive proton occupancy patterns with decreasing intersphere separation that gives rise to the modeled nonmonotonic dependence and derive more general conditions under which such a nonmonotonic dependence can occur. Within the present model we find that stationary points of the charge-regulated average electrostatic potential, considered as a function of intersphere separation, occur when a normalized Boltzmann-averaged intersphere charge number product equals its covariance with an average free energy of charging divided by k(B)T. We derive more general conditions for the location and nature of critical points in the electrostatic intersphere potential, which are not dependent on the validity of the present linear model. Analysis of the present simple prototype model can be a helpful step toward developing a framework for predicting when (i) patterned charge-regulated occupancy patterns, (ii) orientation-dependent attractions due to relatively fixed heterogeneous charging patterns, and (iii) screened net protein charge could separately dominate the electrostatic portion of the interactions between model biological macromolecules and other nanoparticles.
Collapse
Affiliation(s)
- Dawn Hollenbeck
- Department of Physics, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
| | - K. Michael Martini
- Department of Physics, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
| | - Andreas Langner
- Department of Chemistry, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
| | - Anthony Harkin
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
| | - David S. Ross
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
| | - George M. Thurston
- Department of Physics, Rochester Institute of Technology, Rochester, New York 14623-5603, USA
| |
Collapse
|
42
|
Affiliation(s)
- M. N. Tamashiro
- Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970, Campinas, São Paulo, Brazil
| | - M. A. Constantino
- Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970, Campinas, São Paulo, Brazil
| |
Collapse
|
43
|
Rottler J, Krayenhoff B. Numerical studies of nonlocal electrostatic effects on the sub-nanoscale. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:255901. [PMID: 21828443 DOI: 10.1088/0953-8984/21/25/255901] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study nonlocal electrostatics in inhomogeneous dielectric environments on the sub-nanometer scale using a recently introduced polarization energy functional. This functional is able to generate a wavevector-dependent dielectric function ϵ(q) that reflects local correlations in the medium's polarization. Its longitudinal component either decays continuously from its macroscopic continuum value to one at large q, or additionally exhibits two poles with a negative band at intermediate wavevectors (overscreening), which is characteristic of polar fluids such as water. We show that the functional reproduces known nonlocal electrostatic effects: the pair potential between point charges or Born ions in water at distances less than 5 Å is strongly modified, and the Born solvation energy is found to either decrease or increase relative to its local electrostatics value, depending on which approximation is chosen for ϵ(q). We then apply the functional to geometries that can no longer be treated analytically, such as a molecular pore of finite length. In such an anisotropic dielectric background transverse correlations in the polarization field no longer vanish and can contribute to substantial modifications of the dielectric barrier for ion translocation in the regime of intermediate pore diameters of 6-10 Å.
Collapse
Affiliation(s)
- Jörg Rottler
- Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC, V6T 1Z1, Canada
| | | |
Collapse
|
44
|
Bell RC, Wu K, Iedema MJ, Schenter GK, Cowin JP. The oil-water interface: mapping the solvation potential. J Am Chem Soc 2009; 131:1037-42. [PMID: 19154174 DOI: 10.1021/ja805962x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
An ion moving across an oil-water interface experiences strong solvation changes. We have directly measured the solvation potential from 0.4 to 4 nm for Cs(+) ions approaching the oil-water interface from the oil side ("oil" = 3-methylpentane). The interfaces were built at 30 K using molecular beam epitaxy. Ions were precisely placed within the film during its growth using a soft-landing ion beam. The ion's collective electric field was progressively increased (by adding more ions) until it balanced the individual ion's solvation potential slope. As the samples were slowly warmed, near 90 K the ions began moving, as measured by a Kelvin probe. Their motion precisely determines the local slope of the solvation potential, which was integrated to get the potential. The potential is Born-like for z > 0.4 nm away from the oil-water interface. Our method could provide important tests of theoretical estimates of ion motion at biological interfaces and in atmospheric aerosols.
Collapse
Affiliation(s)
- Richard C Bell
- Chemistry Department, The Pennsylvania State University, Altoona College, Altoona, Pennsylvania 16601, USA
| | | | | | | | | |
Collapse
|
45
|
Dong F, Wagoner JA, Baker NA. Assessing the performance of implicit solvation models at a nucleic acid surface. Phys Chem Chem Phys 2008; 10:4889-902. [PMID: 18688533 PMCID: PMC2538626 DOI: 10.1039/b807384h] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Implicit solvation models are popular alternatives to explicit solvent methods due to their ability to "pre-average" solvent behavior and thus reduce the need for computationally-expensive sampling. Previously, we have demonstrated that Poisson-Boltzmann models for polar solvation and integral-based models for nonpolar solvation can reproduce explicit solvation forces in a low-charge density protein system. In the present work, we examine the ability of these continuum models to describe solvation forces at the surface of a RNA hairpin. While these models do not completely describe all of the details of solvent behavior at this highly-charged biomolecular interface, they do provide a reasonable description of average solvation forces and therefore show significant promise for developing more robust implicit descriptions of solvent around nucleic acid systems for use in biomolecular simulation and modeling. Additionally, we observe fairly good transferability in the nonpolar model parameters optimized for protein systems, suggesting its robustness for modeling general nonpolar solvation phenomena in biomolecular systems.
Collapse
Affiliation(s)
- Feng Dong
- Merck & Co., Inc., 770 Sumneytown Pike, P.O. Box 4, WP42-330, West Point, PA 19486, USA. E-mail:
| | - Jason A. Wagoner
- Department of Chemistry, Stanford University, 333 Campus Drive #121, Mailbox 13, Stanford, CA 94305-5080, USA. E-mail:
| | - Nathan A. Baker
- To whom correspondence should be addressed. Department of Biochemistry and Molecular Biophysics, Center for Computational Biology, Washington University in St. Louis, 700. S. Euclid Ave., St. Louis, MO 63110, USA. E-mail:
| |
Collapse
|
46
|
Cheng J, Hoffmann MR, Colussi AJ. Anion Fractionation and Reactivity at Air/Water:Methanol Interfaces. Implications for the Origin of Hofmeister Effects. J Phys Chem B 2008; 112:7157-61. [DOI: 10.1021/jp803184r] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Jie Cheng
- W. M. Keck Laboratories, California Institute of Technology, Pasadena, California 91125
| | - Michael R. Hoffmann
- W. M. Keck Laboratories, California Institute of Technology, Pasadena, California 91125
| | - A. J. Colussi
- W. M. Keck Laboratories, California Institute of Technology, Pasadena, California 91125
| |
Collapse
|
47
|
Staritzbichler R, Gu W, Helms V. Are solvation free energies of homogeneous helical peptides additive? J Phys Chem B 2007; 109:19000-7. [PMID: 16853446 DOI: 10.1021/jp052403x] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We investigated the additivity of the solvation free energy of amino acids in homogeneous helices of different length in water and in chloroform. Solvation free energies were computed by multiconfiguration thermodynamic integration involving extended molecular dynamics simulations and by applying the generalized-born surface area solvation model to static helix geometries. The investigation focused on homogeneous peptides composed of uncharged amino acids, where the backbone atoms are kept fixed in an ideal helical conformation. We found nonlinearity especially for short peptides, which does not allow a simple treatment of the interaction of amino acids with their surroundings. For homogeneous peptides longer than five residues, the results from both methods are in quite good agreement and solvation energies are to a good extent additive.
Collapse
|
48
|
Cheng J, Vecitis CD, Hoffmann MR, Colussi AJ. Experimental anion affinities for the air/water interface. J Phys Chem B 2007; 110:25598-602. [PMID: 17181193 DOI: 10.1021/jp066197k] [Citation(s) in RCA: 119] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Anion affinities, gammaX-, for the aerial interface of aqueous (Br- + NO3- + I- + SCN- + BF4- + ClO4-) solutions are determined by electrospray ionization mass spectrometry. The composition of the ions ejected from the surface of fissioning nanodroplets shows that gammaX- increase (decrease) exponentially with anionic radii, aX-(dehydration free energies, dGX-), and selectively respond to the presence of surfactants. BF4-, the least hydrated and polarizable anion of the set, has one of the largest gammaX- values. Non-ionic surfactants decrease gammaI- and gammaSCN- but increase gammaBF4-. Cetyltrimethyl ammonium markedly enhances the gammaX- of smaller anions. A similar but weaker effect is observed upon lowering the pH of the bulk solutions from 8.2 to 3.0. Dodecyl sulfate has a negligible effect on gammaX-. Considering that (i) universal many-body electrodynamic interactions will progressively stabilize the interfacial layer as its dielectric permittivity falls relative to that of the bulk solution and (ii) water permittivity is uniformly depressed by increasing concentrations of these anions, we infer that the observed Hofmeister correlation, ln gammaX- infinity - dGX-, is consistent with the optimal depression of the permittivity of the drier interfacial layer by the least hydrated ions. Interfacial ion-ion interactions can significantly influence gammaX- in environmental aqueous media.
Collapse
Affiliation(s)
- Jie Cheng
- W. M. Keck Laboratories, California Institute of Technology, Pasadena, California 91125, USA
| | | | | | | |
Collapse
|
49
|
Hildebrandt A, Blossey R, Rjasanow S, Kohlbacher O, Lenhof HP. Electrostatic potentials of proteins in water: a structured continuum approach. Bioinformatics 2007; 23:e99-103. [PMID: 17237112 DOI: 10.1093/bioinformatics/btl312] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Electrostatic interactions play a crucial role in many biomolecular processes, including molecular recognition and binding. Biomolecular electrostatics is modulated to a large extent by the water surrounding the molecules. Here, we present a novel approach to the computation of electrostatic potentials which allows the inclusion of water structure into the classical theory of continuum electrostatics. Based on our recent purely differential formulation of nonlocal electrostatics [Hildebrandt, et al. (2004) Phys. Rev. Lett., 93, 108104] we have developed a new algorithm for its efficient numerical solution. The key component of this algorithm is a boundary element solver, having the same computational complexity as established boundary element methods for local continuum electrostatics. This allows, for the first time, the computation of electrostatic potentials and interactions of large biomolecular systems immersed in water including effects of the solvent's structure in a continuum description. We illustrate the applicability of our approach with two examples, the enzymes trypsin and acetylcholinesterase. The approach is applicable to all problems requiring precise prediction of electrostatic interactions in water, such as protein-ligand and protein-protein docking, folding and chromatin regulation. Initial results indicate that this approach may shed new light on biomolecular electrostatics and on aspects of molecular recognition that classical local electrostatics cannot reveal.
Collapse
Affiliation(s)
- Andreas Hildebrandt
- Center for Bioinformatics, Saarland University PO 15 11 50, 66041 Saarbrücken, Germany.
| | | | | | | | | |
Collapse
|
50
|
Blossey R. Regulating chromatin: on code and dynamic models. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 19:371-3. [PMID: 16470339 DOI: 10.1140/epje/i2005-10052-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2005] [Accepted: 01/02/2006] [Indexed: 05/06/2023]
Abstract
In this short comment on the contributions by Arndt Benecke, Francois Fuks and Helmut Schiessel I refer to some recent experimental work which sheds light on the histone code hypothesis. Further, I make some remarks on the role theoretical approaches can play in decoding chromatin regulation.
Collapse
Affiliation(s)
- R Blossey
- Interdisciplinary Research Institute, IEMN, Avenue Poincaré, F-59652, Villeneuve d'Ascq, France
| |
Collapse
|