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Petersen T. Toward Modeling the Structure of Electrolytes at Charged Mineral Interfaces Using Classical Density Functional Theory. J Phys Chem B 2024; 128:3981-3996. [PMID: 38626457 PMCID: PMC11056995 DOI: 10.1021/acs.jpcb.3c08045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 04/02/2024] [Accepted: 04/03/2024] [Indexed: 04/18/2024]
Abstract
The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article, we assemble a density functional that measures the free energy due to the interaction of water molecules and ions in electric double layers. The model accounts for the finite size of the particles using fundamental measure theory, hydrogen-bonding between water molecules using Wertheim's statistical association theory, long-range dispersion interactions using Barker and Henderson's high-temperature expansion, electrostatic correlations using a functionalized mean-spherical approximation, and Coulomb forces through the Poisson equation. These contributions are shown to produce highly correlated structures, aptly rendering the layering of counterions and co-ions at highly charged surfaces and permitting the solvation of ions and surfaces to be measured by a combination of short-range associations and long-ranged attractions. The model is tested in a planar geometry near soft, charged surfaces to reproduce the structure of water near graphene and mica. For mica surfaces, explicitly representing the density of the outer oxygen layer of the exposed silica tetrahedra allows water molecules to hydrogen-bond to the solid. When electrostatic interactions are included, water molecules assume a hybrid character, being accounted for implicitly in the dielectric constant but explicitly otherwise. The disjoining pressure between approaching like-charged surfaces is calculated, demonstrating the model's ability to probe pressure oscillations that arise during the expulsion of ions and water layers from the interfacial gap and predict strong interattractive stresses that form at narrow interfacial spacing when the surface charge is overscreened. This interattractive stress arises not due to in-plane correlations under strong electrostatic coupling but due to the out-of-plane structuring of associating ions and water molecules.
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Affiliation(s)
- Thomas Petersen
- Sonny Astani Department of
Civil and Environmental Engineering, University
of Southern California, Los Angeles, California 90089, United States
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2
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Abstract
This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.
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3
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Willems K, Ruić D, L R Lucas F, Barman U, Verellen N, Hofkens J, Maglia G, Van Dorpe P. Accurate modeling of a biological nanopore with an extended continuum framework. NANOSCALE 2020; 12:16775-16795. [PMID: 32780087 DOI: 10.1039/d0nr03114c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Despite the broad success of biological nanopores as powerful instruments for the analysis of proteins and nucleic acids at the single-molecule level, a fast simulation methodology to accurately model their nanofluidic properties is currently unavailable. This limits the rational engineering of nanopore traits and makes the unambiguous interpretation of experimental results challenging. Here, we present a continuum approach that can faithfully reproduce the experimentally measured ionic conductance of the biological nanopore Cytolysin A (ClyA) over a wide range of ionic strengths and bias potentials. Our model consists of the extended Poisson-Nernst-Planck and Navier-Stokes (ePNP-NS) equations and a computationally efficient 2D-axisymmetric representation for the geometry and charge distribution of the nanopore. Importantly, the ePNP-NS equations achieve this accuracy by self-consistently considering the finite size of the ions and the influence of both the ionic strength and the nanoscopic scale of the pore on the local properties of the electrolyte. These comprise the mobility and diffusivity of the ions, and the density, viscosity and relative permittivity of the solvent. Crucially, by applying our methodology to ClyA, a biological nanopore used for single-molecule enzymology studies, we could directly quantify several nanofluidic characteristics difficult to determine experimentally. These include the ion selectivity, the ion concentration distributions, the electrostatic potential landscape, the magnitude of the electro-osmotic flow field, and the internal pressure distribution. Hence, this work provides a means to obtain fundamental new insights into the nanofluidic properties of biological nanopores and paves the way towards their rational engineering.
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Affiliation(s)
- Kherim Willems
- KU Leuven, Department of Chemistry, Celestijnenlaan 200F, B-3001 Leuven, Belgium
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4
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Ma K, Zhu D, Zhang C, Lv L. Botulinum Toxin Type A Possibly Affects Ca v3.2 Calcium Channel Subunit in Rats with Spinal Cord Injury-Induced Muscle Spasticity. Drug Des Devel Ther 2020; 14:3029-3041. [PMID: 32801642 PMCID: PMC7395704 DOI: 10.2147/dddt.s256814] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2020] [Accepted: 06/26/2020] [Indexed: 12/12/2022] Open
Abstract
INTRODUCTION Spinal cord injury (SCI) often causes muscle spasticity, which can be inhibited by using calcium channel blocker. Botulinum toxin type A (BoT-A) shows therapeutic efficacy on spasticity and may exert inhibitory effects on the calcium channel. METHODS A rat model with muscle spasticity was established after SCI via contusion and compression. Different concentrations (0, 1, 3 and 6 U/kg) of BoT-A Botox were injected in the extensor digitorum longus (EDL) muscles of the right hindlimb in the muscle spasticity model. The changes of muscle spasticity and calcium level in EDL muscles were measured after the establishment of SCI-induced spasticity. Cav3.2 calcium channel subunit and its mutant (M1560V) were analyzed using Western blot before (input) or after immunoprecipitation with anti-FLAG antibody, and their currents were measured in motoneurons by using whole-cell voltage clamp recordings. RESULTS SCI induced muscle spasticity, whereas calcium level in EDL muscles and expression of Cav3.2 was increased in the SCI model when compared with the sham group (p < 0.05). BoT-A Botox treatment significantly reduced muscle spasticity and calcium level in EDL muscles and Cav3.2 expression in a dose-dependent way (p < 0.05). The ratio of biotinylated to total Cav3.2 was reduced in the mutant (M1560V) of Cav3.2 and lower than that in the wild Cav3.2. BoT-A Botox intervention also reduced the current values of calcium channel and the ratio in a dose-dependent way (p < 0.05). DISCUSSION BoT-A Botox possibly attenuates SCI-induced muscle spasticity by affecting the expression of Cav3.2 calcium channel subunit in the rat models. There may be multiple mechanisms for the function of BoT-A Botox. Further work is needed to be done to address these issues.
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Affiliation(s)
- Kening Ma
- Department of Pain Medicine, The First Hospital of Jilin University, Changchun130021, People’s Republic of China
| | - Dan Zhu
- Department of Neurologic Medicine, The First Hospital of Jilin University, Changchun130021, People’s Republic of China
| | - Chunguo Zhang
- Department of Pain Medicine, The First Hospital of Jilin University, Changchun130021, People’s Republic of China
| | - Lijie Lv
- Department of Medicine and Pension, The First Hospital of Jilin University, Changchun130021, People’s Republic of China
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5
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Sun L, Liang X, Solms NV, Kontogeorgis GM. Analysis of Some Electrolyte Models Including Their Ability to Predict the Activity Coefficients of Individual Ions. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.0c00980] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Li Sun
- Center for Energy Resources Engineering Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, 2800 Kgs Lyngby, Denmark
| | - Xiaodong Liang
- Center for Energy Resources Engineering Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, 2800 Kgs Lyngby, Denmark
| | - Nicolas von Solms
- Center for Energy Resources Engineering Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, 2800 Kgs Lyngby, Denmark
| | - Georgios M. Kontogeorgis
- Center for Energy Resources Engineering Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, 2800 Kgs Lyngby, Denmark
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6
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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.
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7
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Song Z, Cao X, Horng TL, Huang H. Selectivity of the KcsA potassium channel: Analysis and computation. Phys Rev E 2019; 100:022406. [PMID: 31574673 DOI: 10.1103/physreve.100.022406] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 11/07/2022]
Abstract
Ion channels regulate the flux of ions through cell membranes and play significant roles in many physiological functions. Most of the existing literature focuses on computational approaches based on molecular dynamics simulation or numerical solution of the modified Poisson-Nernst-Planck (PNP) system. In this paper, we present an analytical and computational study of a mathematical model of the KcsA potassium channel, including the effects of ion size (Bikerman model) and solvation energy (Born model). Under equilibrium conditions, we obtain an analytical solution of our modified PNP system, which is used to explain selectivity of KcsA of various ions (K^{+}, Na^{+}, Cl^{-}, Ca^{2+}, and Ba^{2+}) due to negative permanent charges inside the filter region and the effect of ion sizes. Our results show that K^{+} is always selected over Na^{+}, as smaller Na^{+} ions have larger solvation energy. As the amount of negative charges in the filter exceeds a critical value, divalent ions (Ca^{2+} and Ba^{2+}) can enter the filter region and block the KcsA channel. For the nonequilibrium cases, due to difficulties associated with a pure analytical or numerical approach, we use a hybrid analytical-numerical method to solve the modified PNP system. Our predictions of selectivity of KcsA channels and saturation phenomenon of the current-voltage (I-V) curve agree with experimental observations.
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Affiliation(s)
- Zilong Song
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
| | - Xiulei Cao
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
| | - Tzyy-Leng Horng
- Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan and National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan 10617
| | - Huaxiong Huang
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3 and Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada M5T 3J1
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8
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Misra R, de Souza JP, Blankschtein D, Bazant MZ. Theory of Surface Forces in Multivalent Electrolytes. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:11550-11565. [PMID: 31310557 PMCID: PMC6750839 DOI: 10.1021/acs.langmuir.9b01110] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Aqueous electrolyte solutions containing multivalent ions exhibit various intriguing properties, including attraction between like-charged colloidal particles, which results from strong ion-ion correlations. In contrast, the classical Derjaguin-Landau-Verwey-Overbeek theory of colloidal stability, based on the Poisson-Boltzmann mean-field theory, always predicts a repulsive electrostatic contribution to the disjoining pressure. Here, we formulate a general theory of surface forces, which predicts that the contribution to the disjoining pressure resulting from ion-ion correlations is always attractive and can readily dominate over entropic-induced repulsions for solutions containing multivalent ions, leading to the phenomenon of like-charge attraction. Ion-specific short-range hydration interactions, as well as surface charge regulation, are shown to play an important role at smaller separation distances but do not fundamentally change these trends. The theory is able to predict the experimentally observed strong cohesive forces reported in cement pastes, which result from strong ion-ion correlations involving the divalent calcium ion.
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Affiliation(s)
- Rahul
Prasanna Misra
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, 25 Ames Street, Cambridge, Massachusetts 02142, United States
| | - J. Pedro de Souza
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, 25 Ames Street, Cambridge, Massachusetts 02142, United States
| | - Daniel Blankschtein
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, 25 Ames Street, Cambridge, Massachusetts 02142, United States
- E-mail: (D.B.)
| | - Martin Z. Bazant
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, 25 Ames Street, Cambridge, Massachusetts 02142, United States
- Department
of Mathematics, Massachusetts Institute
of Technology, 182 Memorial Drive, Cambridge, Massachusetts 02142, United States
- E-mail: (M.Z.B.)
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9
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Liu JL, Eisenberg B. Poisson-Fermi modeling of ion activities in aqueous single and mixed electrolyte solutions at variable temperature. J Chem Phys 2018; 148:054501. [PMID: 29421887 DOI: 10.1063/1.5021508] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-Hückel models to calculate activity coefficients of aqueous mixtures of the most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-Hückel theory that does not take steric and correlation effects of ions and water into account. By contrast, the Poisson-Fermi theory developed in recent years treats ions and water molecules as nonuniform hard spheres of any size with interstitial voids and includes ion-water and ion-ion correlations. We present a Poisson-Fermi model and numerical methods for calculating the individual or mean activity coefficient of electrolyte solutions with any arbitrary number of ionic species in a large range of salt concentrations and temperatures. For each activity-concentration curve, we show that the Poisson-Fermi model requires only three unchanging parameters at most to well fit the corresponding experimental data. The three parameters are associated with the Born radius of the solvation energy of an ion in electrolyte solution that changes with salt concentrations in a highly nonlinear manner.
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Affiliation(s)
- Jinn-Liang Liu
- Institute of Computational and Modeling Science, National Tsing Hua University, Hsinchu 300, Taiwan
| | - Bob Eisenberg
- Department of Physiology and Biophysics, Rush University, Chicago, Illinois 60612, USA and Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
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10
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Gavish N, Elad D, Yochelis A. From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory. J Phys Chem Lett 2018; 9:36-42. [PMID: 29220577 DOI: 10.1021/acs.jpclett.7b03048] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and underscreening, which all impact the emergence of fluid/solid interfaces, and the transport in these systems. Because these phenomena are not captured by existing mean-field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquid mixtures. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing a free energy that consists of short- and long-range interactions, along with an energy dissipation mechanism obtained by Onsager's relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified by the free energy. The model equations not only provide insights into transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enable qualitative recovery of three distinct regions in the full range of the nonmonotonic electrical screening length that has been recently observed in experiments in which organic solvent is used to dilute ionic liquids.
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Affiliation(s)
- Nir Gavish
- Department of Mathematics, Technion - IIT , Haifa 3200003, Israel
| | - Doron Elad
- Department of Mathematics, Technion - IIT , Haifa 3200003, Israel
| | - Arik Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev , Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev , Be'er Sheva 8410501, Israel
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11
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Liu X, Lu B. Incorporating Born solvation energy into the three-dimensional Poisson-Nernst-Planck model to study ion selectivity in KcsA K^{+} channels. Phys Rev E 2017; 96:062416. [PMID: 29347452 DOI: 10.1103/physreve.96.062416] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2017] [Indexed: 06/07/2023]
Abstract
Potassium channels are much more permeable to potassium than sodium ions, although potassium ions are larger and both carry the same positive charge. This puzzle cannot be solved based on the traditional Poisson-Nernst-Planck (PNP) theory of electrodiffusion because the PNP model treats all ions as point charges, does not incorporate ion size information, and therefore cannot discriminate potassium from sodium ions. The PNP model can qualitatively capture some macroscopic properties of certain channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. However, the traditional PNP model is a continuum mean-field model and has no or underestimates the discrete ion effects, in particular the ion solvation or self-energy (which can be described by Born model). It is known that the dehydration effect (closely related to ion size) is crucial to selective permeation in potassium channels. Therefore, we incorporated Born solvation energy into the PNP model to account for ion hydration and dehydration effects when passing through inhomogeneous dielectric channel environments. A variational approach was adopted to derive a Born-energy-modified PNP (BPNP) model. The model was applied to study a cylindrical nanopore and a realistic KcsA channel, and three-dimensional finite element simulations were performed. The BPNP model can distinguish different ion species by ion radius and predict selectivity for K^{+} over Na^{+} in KcsA channels. Furthermore, ion current rectification in the KcsA channel was observed by both the PNP and BPNP models. The I-V curve of the BPNP model for the KcsA channel indicated an inward rectifier effect for K^{+} (rectification ratio of ∼3/2) but indicated an outward rectifier effect for Na^{+} (rectification ratio of ∼1/6).
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Affiliation(s)
- Xuejiao Liu
- State Key Laboratory of Scientific and Engineering Computing, National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Benzhuo Lu
- State Key Laboratory of Scientific and Engineering Computing, National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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12
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Kaufman IK, Fedorenko OA, Luchinsky DG, Gibby WA, Roberts SK, McClintock PV, Eisenberg RS. Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants. ACTA ACUST UNITED AC 2017. [DOI: 10.1051/epjnbp/2017003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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13
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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.
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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
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14
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Liu JL, Hsieh HJ, Eisenberg B. Poisson–Fermi Modeling of the Ion Exchange Mechanism of the Sodium/Calcium Exchanger. J Phys Chem B 2016; 120:2658-69. [DOI: 10.1021/acs.jpcb.5b11515] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jinn-Liang Liu
- Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu 300, Taiwan
| | - Hann-jeng Hsieh
- Department
of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan
| | - Bob Eisenberg
- Department of Molecular Biophysics
and Physiology, Rush University, Chicago, Illinois 60612, United States
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15
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16
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Liu JL, Eisenberg B. Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012711. [PMID: 26274207 DOI: 10.1103/physreve.92.012711] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2015] [Indexed: 05/17/2023]
Abstract
Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are known. The experimental data of both channels are then used to verify and explain novel features of PNPF as compared with previous PNP models. The PNPF currents are in accord with the experimental I-V (V for applied voltages) data of the gramicidin A channel and I-C (C for bath concentrations) data of the calcium channel with 10(-8)-fold bath concentrations that pose severe challenges in theoretical simulations.
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Affiliation(s)
- 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
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17
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18
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Ma M, Xu Z. Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media. J Chem Phys 2014; 141:244903. [DOI: 10.1063/1.4904728] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Manman Ma
- Department of Mathematics, Institute of Natural Sciences, and MoE Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhenli Xu
- Department of Mathematics, Institute of Natural Sciences, and MoE Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
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19
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Liu JL, Eisenberg B. Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels. J Chem Phys 2014; 141:22D532. [DOI: 10.1063/1.4902973] [Citation(s) in RCA: 54] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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
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20
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Liu JL, Eisenberg B. Analytical models of calcium binding in a calcium channel. J Chem Phys 2014; 141:075102. [DOI: 10.1063/1.4892839] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Qiao Y, Tu B, Lu B. Ionic size effects to molecular solvation energy and to ion current across a channel resulted from the nonuniform size-modified PNP equations. J Chem Phys 2014; 140:174102. [DOI: 10.1063/1.4872330] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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