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Boda D, Valiskó M, Gillespie D. Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models. ENTROPY 2020; 22:e22111259. [PMID: 33287027 PMCID: PMC7711659 DOI: 10.3390/e22111259] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Revised: 10/30/2020] [Accepted: 11/02/2020] [Indexed: 01/08/2023]
Abstract
Biological ion channels and synthetic nanopores are responsible for passive transport of ions through a membrane between two compartments. Modeling these ionic currents is especially amenable to reduced models because the device functions of these pores, the relation of input parameters (e.g., applied voltage, bath concentrations) and output parameters (e.g., current, rectification, selectivity), are well defined. Reduced models focus on the physics that produces the device functions (i.e., the physics of how inputs become outputs) rather than the atomic/molecular-scale physics inside the pore. Here, we propose four rules of thumb for constructing good reduced models of ion channels and nanopores. They are about (1) the importance of the axial concentration profiles, (2) the importance of the pore charges, (3) choosing the right explicit degrees of freedom, and (4) creating the proper response functions. We provide examples for how each rule of thumb helps in creating a reduced model of device behavior.
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Affiliation(s)
- Dezső Boda
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary;
- Correspondence: ; Tel.: +36-88-624-000 (ext. 6041)
| | - Mónika Valiskó
- Department of Physical Chemistry, University of Pannonia, P.O. Box 158, H-8201 Veszprém, Hungary;
| | - Dirk Gillespie
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, IL 60612, USA;
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Fertig D, Valiskó M, Boda D. Rectification of bipolar nanopores in multivalent electrolytes: effect of charge inversion and strong ionic correlations. Phys Chem Chem Phys 2020; 22:19033-19045. [PMID: 32812580 DOI: 10.1039/d0cp03237a] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Bipolar nanopores have powerful rectification properties due to the asymmetry in the charge pattern on the wall of the nanopore. In particular, bipolar nanopores have positive and negative surface charges along the pore axis. Rectification is strong if the radius of the nanopore is small compared to the screening length of the electrolyte so that both cations and anions have depletion zones in the respective regions. The depths of these depletion zones is sensitive to sign of the external voltage. In this work, we are interested in the effect of the presence of strong ionic correlations (both between ions and between ions and surface charge) due to the presence of multivalent ions and large surface charges. We show that strong ionic correlations cause leakage of the coions, a phenomenon that is absent in mean field theories. In this modeling study, we use both the mean-field Poisson-Nernst-Planck (PNP) theory and a particle simulation method, Local Equilibrium Monte Carlo (LEMC), to show that phenomena such as overcharging and charge inversion cannot be reproduced with PNP, while LEMC is able to produce nonmonotonic dependence of currents and rectification as a function of surface charge strength.
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Affiliation(s)
- Dávid Fertig
- Department of Physical Chemistry, University of Pannonia, P. O. Box 158, H-8201 Veszprém, Hungary.
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Ion selectivity by charged spherical cavities and investigation of intersection point for average cavity density versus electric potential (a DFT study). J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112283] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Finnerty JJ, Peyser A, Carloni P. Cation Selectivity in Biological Cation Channels Using Experimental Structural Information and Statistical Mechanical Simulation. PLoS One 2015; 10:e0138679. [PMID: 26460827 PMCID: PMC4603898 DOI: 10.1371/journal.pone.0138679] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Accepted: 09/01/2015] [Indexed: 01/31/2023] Open
Abstract
Cation selective channels constitute the gate for ion currents through the cell membrane. Here we present an improved statistical mechanical model based on atomistic structural information, cation hydration state and without tuned parameters that reproduces the selectivity of biological Na+ and Ca2+ ion channels. The importance of the inclusion of step-wise cation hydration in these results confirms the essential role partial dehydration plays in the bacterial Na+ channels. The model, proven reliable against experimental data, could be straightforwardly used for designing Na+ and Ca2+ selective nanopores.
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Affiliation(s)
- Justin John Finnerty
- Computational Biophysics, German Research School for Simulation Sciences, 52425 Jülich, Germany
| | - Alexander Peyser
- Computational Biophysics, German Research School for Simulation Sciences, 52425 Jülich, Germany
- Simulation Lab Neuroscience—Bernstein Facility for Simulation and Database Technology, Institute for Advanced Simulation, Jülich Aachen Research Alliance, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Paolo Carloni
- Computational Biophysics, German Research School for Simulation Sciences, 52425 Jülich, Germany
- Computational Biomedicine, Institute for Neuroscience and Medicine (INM-9) and Institute for Advanced Simulation (IAS-5), Forschungszentrum Jülich, 52425 Jülich, Germany
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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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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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Selective transport through a model calcium channel studied by Local Equilibrium Monte Carlo simulations coupled to the Nernst–Planck equation. J Mol Liq 2014. [DOI: 10.1016/j.molliq.2013.03.015] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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Boda D. Monte Carlo Simulation of Electrolyte Solutions in Biology. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2014. [DOI: 10.1016/b978-0-444-63378-1.00005-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Kaufman I, Luchinsky DG, Tindjong R, McClintock PVE, Eisenberg RS. Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052712. [PMID: 24329301 DOI: 10.1103/physreve.88.052712] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2013] [Indexed: 06/03/2023]
Abstract
We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.
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Affiliation(s)
- I Kaufman
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - D G Luchinsky
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom and Mission Critical Technologies Inc., 2041 Rosecrans Ave. Suite 225 El Segundo, California 90245, USA
| | - R Tindjong
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - R S Eisenberg
- Department of Molecular Biophysics and Physiology, Rush Medical College, 1750 West Harrison, Chicago, Illinois 60612, USA
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Dreyer J, Strodel P, Ippoliti E, Finnerty J, Eisenberg B, Carloni P. Ion permeation in the NanC porin from Escherichia coli: free energy calculations along pathways identified by coarse-grain simulations. J Phys Chem B 2013; 117:13534-42. [PMID: 24147565 DOI: 10.1021/jp4081838] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Using the X-ray structure of a recently discovered bacterial protein, the N-acetylneuraminic acid-inducible channel (NanC), we investigate computationally K(+) and Cl(-) ions' permeation. We identify ion permeation pathways that are likely to be populated using coarse-grain Monte Carlo simulations. Next, we use these pathways as reaction coordinates for umbrella sampling-based free energy simulations. We find distinct tubelike pathways connecting specific binding sites for K(+) and, more pronounced, for Cl(-) ions. Both ions permeate the porin preserving almost all of their first hydration shell. The calculated free energy barriers are G(#) ≈ 4 kJ/mol and G(#) ≈ 8 kJ/mol for Cl(-) and K(+), respectively. Within the approximations associated with these values, discussed in detail in this work, we suggest that the porin is slightly selective for Cl(-) versus K(+). Our suggestion is consistent with the experimentally observed weak Cl(-) over K(+) selectivity. A rationale for the latter is suggested by a comparison with previous calculations on strongly anion selective porins.
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Affiliation(s)
- Jens Dreyer
- Computational Biophysics, German Research School for Simulation Sciences , D-52425 Jülich, Germany
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Boda D, Henderson D, Gillespie D. The role of solvation in the binding selectivity of the L-type calcium channel. J Chem Phys 2013; 139:055103. [DOI: 10.1063/1.4817205] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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Eisenberg B. Interacting ions in biophysics: real is not ideal. Biophys J 2013; 104:1849-66. [PMID: 23663828 PMCID: PMC3647150 DOI: 10.1016/j.bpj.2013.03.049] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2012] [Revised: 03/03/2013] [Accepted: 03/27/2013] [Indexed: 11/28/2022] Open
Abstract
Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.
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Affiliation(s)
- Bob Eisenberg
- Department of Molecular Biophysics Rush University, Chicago Illinois, USA.
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Kaufman I, Luchinsky DG, Tindjong R, McClintock PVE, Eisenberg RS. Multi-ion conduction bands in a simple model of calcium ion channels. Phys Biol 2013; 10:026007. [DOI: 10.1088/1478-3975/10/2/026007] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Abstract
Ionic solutions are dominated by interactions because they must be electrically neutral, but classical theory assumes no interactions. Biological solutions are rather like seawater, concentrated enough so that the diameter of ions also produces important interactions. In my view, the theory of complex fluids is needed to deal with the interacting reality of biological solutions.
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Affiliation(s)
- Bob Eisenberg
- Department of Molecular Biophysics and Physiology, Rush University, Chicago, Illinois
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Eisenberg B. Ionic interactions in biological and physical systems: a variational treatment. Faraday Discuss 2013; 160:279-96; discussion 311-27. [DOI: 10.1039/c2fd20066j] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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Finnerty JJ, Eisenberg R, Carloni P. Localizing the Charged Side Chains of Ion Channels within the Crowded Charge Models. J Chem Theory Comput 2012; 9:766-73. [DOI: 10.1021/ct300768j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Justin J. Finnerty
- Computational Biophysics, German
Research School for Simulation Sciences, 52425 Jülich, Germany
| | - Robert Eisenberg
- Department of Molecular Biophysics
and Physiology, Rush University, Chicago, Illinois 60612, United States
| | - Paolo Carloni
- Computational Biophysics, German
Research School for Simulation Sciences, 52425 Jülich, Germany
and Institute for Advanced Simulation IAS-5, Computational Biomedicine,
Forschungszentrum Jülich, 52425 Jülich, Germany
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Maffeo C, Bhattacharya S, Yoo J, Wells D, Aksimentiev A. Modeling and simulation of ion channels. Chem Rev 2012; 112:6250-84. [PMID: 23035940 PMCID: PMC3633640 DOI: 10.1021/cr3002609] [Citation(s) in RCA: 148] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Christopher Maffeo
- Department of Physics, University of Illinois, 1110 W. Green St., Urbana, IL
| | - Swati Bhattacharya
- Department of Physics, University of Illinois, 1110 W. Green St., Urbana, IL
| | - Jejoong Yoo
- Department of Physics, University of Illinois, 1110 W. Green St., Urbana, IL
| | - David Wells
- Department of Physics, University of Illinois, 1110 W. Green St., Urbana, IL
| | - Aleksei Aksimentiev
- Department of Physics, University of Illinois, 1110 W. Green St., Urbana, IL
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Horng TL, Lin TC, Liu C, Eisenberg B. PNP Equations with Steric Effects: A Model of Ion Flow through Channels. J Phys Chem B 2012; 116:11422-41. [DOI: 10.1021/jp305273n] [Citation(s) in RCA: 118] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Tzyy-Leng Horng
- Department of Applied Mathematics, Feng Chia University, 100 Wen-Hwa Road, Taichung, Taiwan
40724
| | - Tai-Chia Lin
- Department of Mathematics, Taida Institute for Mathematical
Sciences (TIMS), No. 1, Sec. 4, National Taiwan University, Roosevelt Road, Taipei 106, Taiwan
| | - Chun Liu
- Department of Mathematics, Pennsylvania State University University Park, Pennsylvania 16802,
United States
| | - Bob Eisenberg
- Department of Molecular Biophysics and Physiology, Rush University, 1653 West Congress Parkway, Chicago,
Illinois 60612, United States
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Dudev T, Lim C. Competition among Ca2+, Mg2+, and Na+ for model ion channel selectivity filters: determinants of ion selectivity. J Phys Chem B 2012; 116:10703-14. [PMID: 22889116 DOI: 10.1021/jp304925a] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Because voltage-gated ion channels play critical biological roles, understanding how they can discriminate the native metal ion from rival cations in the milieu is of great interest. Although Ca(2+), Mg(2+), and Na(+) are present in comparable concentrations outside the cell, the factors governing the competition among these cations for the selectivity filter of voltage-gated Ca(2+) ion channel remain unclear. Using density functional theory combined with continuum dielectric methods, we evaluate the effect of (1) the number, chemical type, and charge of the ligands lining the pore, (2) the pore's rigidity, size, symmetry, and solvent accessibility, and (3) the Ca(2+) hydration number outside the selectivity filter on the competition among Ca(2+), Mg(2+), and Na(+) in model selectivity filters. The calculations show how the outcome of this competition depends on the interplay between electronic and solvation effects. Selectivity for monovalent Na(+) over divalent Ca(2+)/Mg(2+) is achieved when solvation effects outweigh electrostatic effects; thus filters comprising a few weak charge-donating groups such as Ser/Thr side chains, where electrostatic effects are relatively weak and are easily overcome by solvation effects, are Na(+)-selective. In contrast, selectivity for divalent Ca(2+)/Mg(2+) over monovalent Na(+) is achieved when metal-ligand electrostatic effects outweigh solvation effects. The key differences in selectivity between Mg(2+) and Ca(2+) lie in the pore size, oligomericity, and solvent accessibility. The results, which are consistent with available experimental data, reveal how the structure and composition of the ion channel selectivity pore had adapted to the specific physicochemical properties of the native metal ion to enhance the competitiveness of the native metal toward rival cations.
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Affiliation(s)
- Todor Dudev
- Institute of Biomedical Sciences, Academia Sinica, Taipei 115, Taiwan
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