1
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Mondal R, Vaissier Welborn V. Dynamics accelerate the kinetics of ion diffusion through channels: Continuous-time random walk models beyond the mean field approximation. J Chem Phys 2024; 160:144109. [PMID: 38597306 DOI: 10.1063/5.0188469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 03/14/2024] [Indexed: 04/11/2024] Open
Abstract
Ion channels are proteins that play a significant role in physiological processes, including neuronal excitability and signal transduction. However, the precise mechanisms by which these proteins facilitate ion diffusion through cell membranes are not well understood. This is because experimental techniques to characterize ion channel activity operate on a time scale too large to understand the role of the various protein conformations on diffusion. Meanwhile, computational approaches operate on a time scale too short to rationalize the observed behavior at the microscopic scale. In this paper, we present a continuous-time random walk model that aims to bridge the scales between the atomistic models of ion channels and the experimental measurement of their conductance. We show how diffusion slows down in complex systems by using 3D lattices that map out the pore geometry of two channels: Nav1.7 and gramicidin. We also introduce spatial and dynamic site disorder to account for system heterogeneity beyond the mean field approximation. Computed diffusion coefficients show that an increase in spatial disorder slows down diffusion kinetics, while dynamic disorder has the opposite effect. Our results imply that microscopic or phenomenological models based on the potential of mean force data overlook the functional importance of protein dynamics on ion diffusion through channels.
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Affiliation(s)
- Ronnie Mondal
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Valerie Vaissier Welborn
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, Virginia 24061, USA
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2
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Li M, Muthukumar M. Electro-osmotic flow in nanoconfinement: Solid-state and protein nanopores. J Chem Phys 2024; 160:084905. [PMID: 38411234 DOI: 10.1063/5.0185574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/05/2024] [Indexed: 02/28/2024] Open
Abstract
Electro-osmotic flow (EOF) is a phenomenon where fluid motion occurs in porous materials or micro/nano-channels when an external electric field is applied. In the particular example of single-molecule electrophoresis using single nanopores, the role of EOF on the translocation velocity of the analyte molecule through the nanopore is not fully understood. The complexity arises from a combination of effects from hydrodynamics in restricted environments, electrostatics emanating from charge decorations and geometry of the pores. We address this fundamental issue using the Poisson-Nernst-Planck and Navier-Stokes (PNP-NS) equations for cylindrical solid-state nanopores and three representative protein nanopores (α-hemolysin, MspA, and CsgG). We present the velocity profiles inside the nanopores as a function of charge decoration and geometry of the pore and applied electric field. We report several unexpected results: (a) The apparent charges of the protein nanopores are different from their net charge and the surface charge of the whole protein geometry, and the net charge of inner surface is consistent with the apparent charge. (b) The fluid velocity depends non-monotonically on voltage. The three protein nanopores exhibit unique EOF and velocity-voltage relations, which cannot be simply deduced from their net charge. Furthermore, effective point mutations can significantly change both the direction and the magnitude of EOF. The present computational analysis offers an opportunity to further understand the origins of the speed of transport of charged macromolecules in restricted space and to design desirable nanopores for tuning the speed of macromolecules through nanopores.
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Affiliation(s)
- Minglun Li
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Murugappan Muthukumar
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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3
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Wilson MA, Pohorille A. Structure and Computational Electrophysiology of Ac-LS3, a Synthetic Ion Channel. J Phys Chem B 2022; 126:8985-8999. [PMID: 36306164 DOI: 10.1021/acs.jpcb.2c05965] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Computer simulations are reported on Ac-LS3, a synthetic ion channel, containing 21 residues with a Leu-Ser-Ser-Leu-Leu-Ser-Leu heptad repeat, which forms ions channels upon application of voltage. A hexameric, coiled-coil bundle initially positioned perpendicular to the membrane settled into a stable, tilted structure after 1.5 μs, most likely to improve contacts between the non-polar exterior of the channel and the hydrophobic core of the membrane. Once tilted, the bundle remained in this state during subsequent simulations of nearly 10 μs at voltages ranging from 200 to -100 mV. In contrast, attempts to identify a stable pentameric structure failed, thus supporting the hypothesis that the channel is a hexamer. Results at 100 mV were used to reconstruct the free energy profiles for K+ and Cl- in the channel. This was done by way of several methods in which results of molecular dynamics (MD) simulations were combined with the electrodiffusion model. Two of them developed recently do not require knowledge of the diffusivity. Instead, they utilize one-sided density profiles and committor probabilities. The consistency between different methods is very good, supporting the utility of the newly developed methods for reconstructing free energies of ions in channels. The flux of K+, which accounts for most of the current through the channel, calculated directly from MD matches well the total measured current. However, the current of Cl- is somewhat overestimated, possibly due to a slightly unbalanced force field involving chloride. The current-voltage dependence was also reconstructed by way of a recently developed, efficient method that requires simulations only at a single voltage, yielding good agreement with the experiment. Taken together, the results demonstrate that computational electrophysiology has become a reliable tool for studying how channels mediate ion transport through membranes.
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Affiliation(s)
- Michael A Wilson
- Exobiology Branch, MS239-4, NASA Ames Research Center, Moffett Field, California94035, United States.,SETI Institute, 189 Bernardo Avenue, Suite 200, Mountain View, California94043, United States
| | - Andrew Pohorille
- Exobiology Branch, MS239-4, NASA Ames Research Center, Moffett Field, California94033, United States.,Department of Pharmaceutical Chemistry, University of California San Francisco, San Francisco, California94132, United States
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4
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Choi I, Kim N, Song Y, Schatz GC, Hwang H. Extended kinetic lattice grand canonical Monte Carlo simulation method for transport of multicomponent ion mixtures through a model nanopore system. B KOREAN CHEM SOC 2022. [DOI: 10.1002/bkcs.12466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Inhyeok Choi
- Department of Chemistry and Institute for Molecular Science and Fusion Technology Kangwon National University Chuncheon Gangwon‐do Republic of Korea
| | - Namho Kim
- Department of Biochemistry Kangwon National University Chuncheon Gangwon‐do Republic of Korea
| | - Yeonho Song
- Department of Chemistry and Institute for Molecular Science and Fusion Technology Kangwon National University Chuncheon Gangwon‐do Republic of Korea
| | - George C. Schatz
- Department of Chemistry Northwestern University Evanston Illinois USA
| | - Hyonseok Hwang
- Department of Chemistry and Institute for Molecular Science and Fusion Technology Kangwon National University Chuncheon Gangwon‐do Republic of Korea
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5
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Guardiani C, Cecconi F, Chiodo L, Cottone G, Malgaretti P, Maragliano L, Barabash ML, Camisasca G, Ceccarelli M, Corry B, Roth R, Giacomello A, Roux B. Computational methods and theory for ion channel research. ADVANCES IN PHYSICS: X 2022; 7:2080587. [PMID: 35874965 PMCID: PMC9302924 DOI: 10.1080/23746149.2022.2080587] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 05/15/2022] [Indexed: 06/15/2023] Open
Abstract
Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.
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Affiliation(s)
- C. Guardiani
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - F. Cecconi
- CNR - Istituto dei Sistemi Complessi, Rome, Italy and Istituto Nazionale di Fisica Nucleare, INFN, Roma1 section. 00185, Roma, Italy
| | - L. Chiodo
- Department of Engineering, Campus Bio-Medico University, Rome, Italy
| | - G. Cottone
- Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Palermo, Italy
| | - P. Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Erlangen, Germany
| | - L. Maragliano
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Ancona, Italy, and Center for Synaptic Neuroscience and Technology, Istituto Italiano di Tecnologia, Genova, Italy
| | - M. L. Barabash
- Department of Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA
| | - G. Camisasca
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
- Dipartimento di Fisica, Università Roma Tre, Rome, Italy
| | - M. Ceccarelli
- Department of Physics and CNR-IOM, University of Cagliari, Monserrato 09042-IT, Italy
| | - B. Corry
- Research School of Biology, The Australian National University, Canberra, ACT 2600, Australia
| | - R. Roth
- Institut Für Theoretische Physik, Eberhard Karls Universität Tübingen, Tübingen, Germany
| | - A. Giacomello
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - B. Roux
- Department of Biochemistry & Molecular Biology, University of Chicago, Chicago IL, USA
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6
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Parvulescu VI, Epron F, Garcia H, Granger P. Recent Progress and Prospects in Catalytic Water Treatment. Chem Rev 2021; 122:2981-3121. [PMID: 34874709 DOI: 10.1021/acs.chemrev.1c00527] [Citation(s) in RCA: 67] [Impact Index Per Article: 22.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Presently, conventional technologies in water treatment are not efficient enough to completely mineralize refractory water contaminants. In this context, the implementation of catalytic processes could be an alternative. Despite the advantages provided in terms of kinetics of transformation, selectivity, and energy saving, numerous attempts have not yet led to implementation at an industrial scale. This review examines investigations at different scales for which controversies and limitations must be solved to bridge the gap between fundamentals and practical developments. Particular attention has been paid to the development of solar-driven catalytic technologies and some other emerging processes, such as microwave assisted catalysis, plasma-catalytic processes, or biocatalytic remediation, taking into account their specific advantages and the drawbacks. Challenges for which a better understanding related to the complexity of the systems and the coexistence of various solid-liquid-gas interfaces have been identified.
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Affiliation(s)
- Vasile I Parvulescu
- Department of Organic Chemistry, Biochemistry and Catalysis, University of Bucharest, B-dul Regina Elisabeta 4-12, Bucharest 030016, Romania
| | - Florence Epron
- Université de Poitiers, CNRS UMR 7285, Institut de Chimie des Milieux et Matériaux de Poitiers (IC2MP), 4 rue Michel Brunet, TSA 51106, 86073 Poitiers Cedex 9, France
| | - Hermenegildo Garcia
- Instituto Universitario de Tecnología Química, Universitat Politecnica de Valencia-Consejo Superior de Investigaciones Científicas, Universitat Politencia de Valencia, Av. de los Naranjos s/n, 46022 Valencia, Spain
| | - Pascal Granger
- CNRS, Centrale Lille, Univ. Artois, UMR 8181 - UCCS - Unité de Catalyse et Chimie du Solide, Univ. Lille, F-59000 Lille, France
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7
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Wilson MA, Pohorille A. Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations. ENTROPY 2021; 23:e23050571. [PMID: 34066581 PMCID: PMC8148522 DOI: 10.3390/e23050571] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Revised: 04/24/2021] [Accepted: 04/28/2021] [Indexed: 12/13/2022]
Abstract
We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current–voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current–voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions.
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Affiliation(s)
- Michael A. Wilson
- Exobiology Branch, MS 239-4, NASA Ames Research Center, Moffett Field, CA 94035, USA;
- SETI Institute, 189 Bernardo Ave, Suite 200, Mountain View, CA 94043, USA
| | - Andrew Pohorille
- Exobiology Branch, MS 239-4, NASA Ames Research Center, Moffett Field, CA 94035, USA;
- Department of Pharmaceutical Chemistry, University of California, San Francisco, CA 94132, USA
- Correspondence: ; Tel.: +1-650-604-5759
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8
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Prajapati JD, Kleinekathöfer U, Winterhalter M. How to Enter a Bacterium: Bacterial Porins and the Permeation of Antibiotics. Chem Rev 2021; 121:5158-5192. [PMID: 33724823 DOI: 10.1021/acs.chemrev.0c01213] [Citation(s) in RCA: 81] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Despite tremendous successes in the field of antibiotic discovery seen in the previous century, infectious diseases have remained a leading cause of death. More specifically, pathogenic Gram-negative bacteria have become a global threat due to their extraordinary ability to acquire resistance against any clinically available antibiotic, thus urging for the discovery of novel antibacterial agents. One major challenge is to design new antibiotics molecules able to rapidly penetrate Gram-negative bacteria in order to achieve a lethal intracellular drug accumulation. Protein channels in the outer membrane are known to form an entry route for many antibiotics into bacterial cells. Up until today, there has been a lack of simple experimental techniques to measure the antibiotic uptake and the local concentration in subcellular compartments. Hence, rules for translocation directly into the various Gram-negative bacteria via the outer membrane or via channels have remained elusive, hindering the design of new or the improvement of existing antibiotics. In this review, we will discuss the recent progress, both experimentally as well as computationally, in understanding the structure-function relationship of outer-membrane channels of Gram-negative pathogens, mainly focusing on the transport of antibiotics.
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Affiliation(s)
| | | | - Mathias Winterhalter
- Department of Life Sciences and Chemistry, Jacobs University Bremen, Bremen 28759, Germany
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9
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Golla VK, Prajapati JD, Kleinekathöfer U. Millisecond-Long Simulations of Antibiotics Transport through Outer Membrane Channels. J Chem Theory Comput 2021; 17:549-559. [PMID: 33378186 DOI: 10.1021/acs.jctc.0c01088] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
To reach their target site inside Gram-negative bacteria, almost all antibiotics need to cross the outer membrane. Computational modeling of such processes can be numerically demanding due to the size of the systems and especially due to the timescales involved. Recently, a hybrid Brownian and molecular dynamics approach, i.e., Brownian dynamics including explicit atoms (BRODEA), has been developed and evaluated for studying the transport of monoatomic ions through membrane channels. Later on, this numerically efficient scheme has been applied to determine the free energy surfaces of the ciprofloxacin and enrofloxacin translocation through the porin OmpC using temperature-accelerated simulations. To improve the usability and accuracy of the approach, schemes to approximate the position-dependent diffusion constant of the molecule while traversing the pore had to be established. To this end, we have studied the translocation of the charged phosphonic acid antibiotic fosfomycin through the porin OmpF from Escherichia coli devising and benchmarking several diffusion models. To test the efficiency and sensitivity of these models, the effect of OmpF mutations on the permeation of fosfomycin was analyzed. Permeation events have been recorded over millisecond-long biased and unbiased simulations, from which thermodynamics and kinetics quantities of the translocation processes were determined. As a result, the use of the BRODEA approach, together with the appropriate diffusion model, was seen to accurately reproduce the findings observed in electrophysiology experiments and all-atom molecular dynamics simulations. These results suggest that the BRODEA approach can become a valuable tool for screening numerous compounds to evaluate their outer membrane permeability, a property important in the development of new antibiotics.
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Affiliation(s)
- Vinaya Kumar Golla
- Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany
| | | | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany
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10
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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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11
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Solano CJF, Prajapati JD, Pothula KR, Kleinekathöfer U. Brownian Dynamics Approach Including Explicit Atoms for Studying Ion Permeation and Substrate Translocation across Nanopores. J Chem Theory Comput 2018; 14:6701-6713. [DOI: 10.1021/acs.jctc.8b00917] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Carlos J. F. Solano
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany
| | - Jigneshkumar D. Prajapati
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany
| | - Karunakar R. Pothula
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany
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12
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Affiliation(s)
- Mohammad Saleheen
- Department of Chemical Engineering, University of South Carolina, 301
Main Street, Columbia, South
Carolina 29208, United States
| | - Andreas Heyden
- Department of Chemical Engineering, University of South Carolina, 301
Main Street, Columbia, South
Carolina 29208, United States
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13
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Jo S, Cheng X, Lee J, Kim S, Park SJ, Patel DS, Beaven AH, Lee KI, Rui H, Park S, Lee HS, Roux B, MacKerell AD, Klauda JB, Qi Y, Im W. CHARMM-GUI 10 years for biomolecular modeling and simulation. J Comput Chem 2017; 38:1114-1124. [PMID: 27862047 PMCID: PMC5403596 DOI: 10.1002/jcc.24660] [Citation(s) in RCA: 179] [Impact Index Per Article: 25.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2016] [Revised: 10/04/2016] [Accepted: 10/18/2016] [Indexed: 12/16/2022]
Abstract
CHARMM-GUI, http://www.charmm-gui.org, is a web-based graphical user interface that prepares complex biomolecular systems for molecular simulations. CHARMM-GUI creates input files for a number of programs including CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, OpenMM, and CHARMM/OpenMM. Since its original development in 2006, CHARMM-GUI has been widely adopted for various purposes and now contains a number of different modules designed to set up a broad range of simulations: (1) PDB Reader & Manipulator, Glycan Reader, and Ligand Reader & Modeler for reading and modifying molecules; (2) Quick MD Simulator, Membrane Builder, Nanodisc Builder, HMMM Builder, Monolayer Builder, Micelle Builder, and Hex Phase Builder for building all-atom simulation systems in various environments; (3) PACE CG Builder and Martini Maker for building coarse-grained simulation systems; (4) DEER Facilitator and MDFF/xMDFF Utilizer for experimentally guided simulations; (5) Implicit Solvent Modeler, PBEQ-Solver, and GCMC/BD Ion Simulator for implicit solvent related calculations; (6) Ligand Binder for ligand solvation and binding free energy simulations; and (7) Drude Prepper for preparation of simulations with the CHARMM Drude polarizable force field. Recently, new modules have been integrated into CHARMM-GUI, such as Glycolipid Modeler for generation of various glycolipid structures, and LPS Modeler for generation of lipopolysaccharide structures from various Gram-negative bacteria. These new features together with existing modules are expected to facilitate advanced molecular modeling and simulation thereby leading to an improved understanding of the structure and dynamics of complex biomolecular systems. Here, we briefly review these capabilities and discuss potential future directions in the CHARMM-GUI development project. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Sunhwan Jo
- Leadership Computing Facility, Argonne National Laboratory, 9700 Cass Ave, Argonne, Illinois
| | - Xi Cheng
- Drug Discovery and Design Center, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica Chinese Academy of Sciences, 555 Zuchongzhi Road, Pudong, Shanghai, 201203, China
| | - Jumin Lee
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Seonghoon Kim
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Sang-Jun Park
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Dhilon S Patel
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Andrew H Beaven
- Department of Chemistry, The University of Kansas, Lawrence, Kansas
| | - Kyu Il Lee
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Huan Rui
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, Illinois
| | - Soohyung Park
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Hui Sun Lee
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, Illinois
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences School of Pharmacy, University of Maryland, Baltimore, Maryland
| | - Jeffrey B Klauda
- Department of Chemical and Biomolecular Engineering and the Biophysics Program, University of Maryland College Park, Maryland
| | - Yifei Qi
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
| | - Wonpil Im
- Department of Biological Sciences and Bioengineering Program, Lehigh University, Pennsylvania
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14
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Bargiello TA, Oh S, Tang Q, Bargiello NK, Dowd TL, Kwon T. Gating of Connexin Channels by transjunctional-voltage: Conformations and models of open and closed states. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2017; 1860:22-39. [PMID: 28476631 DOI: 10.1016/j.bbamem.2017.04.028] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2017] [Revised: 04/26/2017] [Accepted: 04/28/2017] [Indexed: 11/18/2022]
Abstract
Voltage is an important physiologic regulator of channels formed by the connexin gene family. Connexins are unique among ion channels in that both plasma membrane inserted hemichannels (undocked hemichannels) and intercellular channels (aggregates of which form gap junctions) have important physiological roles. The hemichannel is the fundamental unit of gap junction voltage-gating. Each hemichannel displays two distinct voltage-gating mechanisms that are primarily sensitive to a voltage gradient formed along the length of the channel pore (the transjunctional voltage) rather than sensitivity to the absolute membrane potential (Vm or Vi-o). These transjunctional voltage dependent processes have been termed Vj- or fast-gating and loop- or slow-gating. Understanding the mechanism of voltage-gating, defined as the sequence of voltage-driven transitions that connect open and closed states, first and foremost requires atomic resolution models of the end states. Although ion channels formed by connexins were among the first to be characterized structurally by electron microscopy and x-ray diffraction in the early 1980's, subsequent progress has been slow. Much of the current understanding of the structure-function relations of connexin channels is based on two crystal structures of Cx26 gap junction channels. Refinement of crystal structure by all-atom molecular dynamics and incorporation of charge changing protein modifications has resulted in an atomic model of the open state that arguably corresponds to the physiologic open state. Obtaining validated atomic models of voltage-dependent closed states is more challenging, as there are currently no methods to solve protein structure while a stable voltage gradient is applied across the length of an oriented channel. It is widely believed that the best approach to solve the atomic structure of a voltage-gated closed ion channel is to apply different but complementary experimental and computational methods and to use the resulting information to derive a consensus atomic structure that is then subjected to rigorous validation. In this paper, we summarize our efforts to obtain and validate atomic models of the open and voltage-driven closed states of undocked connexin hemichannels. This article is part of a Special Issue entitled: Gap Junction Proteins edited by Jean Claude Herve.
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Affiliation(s)
- Thaddeus A Bargiello
- Dominic P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, United States.
| | - Seunghoon Oh
- Department of Physiology, College of Medicine, Dankook University, Cheonan, Republic of Korea
| | - Qingxiu Tang
- Dominic P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, United States
| | - Nicholas K Bargiello
- Dominic P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, United States
| | - Terry L Dowd
- Department of Chemistry, Brooklyn College, Brooklyn, NY 11210, United States
| | - Taekyung Kwon
- Dominic P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, United States
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15
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Solano CJF, Pothula KR, Prajapati JD, De Biase PM, Noskov SY, Kleinekathöfer U. BROMOCEA Code: An Improved Grand Canonical Monte Carlo/Brownian Dynamics Algorithm Including Explicit Atoms. J Chem Theory Comput 2016; 12:2401-17. [DOI: 10.1021/acs.jctc.5b01196] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Carlos J. F. Solano
- Department
of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Karunakar R. Pothula
- Department
of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Jigneshkumar D. Prajapati
- Department
of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Pablo M. De Biase
- Centre
for Molecular Simulation, Department of Biological Sciences, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Sergei Yu. Noskov
- Centre
for Molecular Simulation, Department of Biological Sciences, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Ulrich Kleinekathöfer
- Department
of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
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16
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Pothula KR, Solano CJF, Kleinekathöfer U. Simulations of outer membrane channels and their permeability. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2015; 1858:1760-71. [PMID: 26721326 DOI: 10.1016/j.bbamem.2015.12.020] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2015] [Revised: 12/15/2015] [Accepted: 12/17/2015] [Indexed: 12/25/2022]
Abstract
Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.
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Affiliation(s)
- Karunakar R Pothula
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Carlos J F Solano
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
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17
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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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18
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De Biase PM, Markosyan S, Noskov S. BROMOC suite: Monte Carlo/Brownian dynamics suite for studies of ion permeation and DNA transport in biological and artificial pores with effective potentials. J Comput Chem 2014; 36:264-71. [PMID: 25503688 DOI: 10.1002/jcc.23799] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Revised: 10/28/2014] [Accepted: 11/03/2014] [Indexed: 01/11/2023]
Abstract
The transport of ions and solutes by biological pores is central for cellular processes and has a variety of applications in modern biotechnology. The time scale involved in the polymer transport across a nanopore is beyond the accessibility of conventional MD simulations. Moreover, experimental studies lack sufficient resolution to provide details on the molecular underpinning of the transport mechanisms. BROMOC, the code presented herein, performs Brownian dynamics simulations, both serial and parallel, up to several milliseconds long. BROMOC can be used to model large biological systems. IMC-MACRO software allows for the development of effective potentials for solute-ion interactions based on radial distribution function from all-atom MD. BROMOC Suite also provides a versatile set of tools to do a wide variety of preprocessing and postsimulation analysis. We illustrate a potential application with ion and ssDNA transport in MspA nanopore.
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Affiliation(s)
- Pablo M De Biase
- Centre for Molecular Simulation, Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4
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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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Berti C, Furini S, Gillespie D, Boda D, Eisenberg RS, Sangiorgi E, Fiegna C. Three-Dimensional Brownian Dynamics Simulator for the Study of Ion Permeation through Membrane Pores. J Chem Theory Comput 2014; 10:2911-26. [DOI: 10.1021/ct4011008] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Claudio Berti
- Department
of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago,Illinois, United States
- ARCES
and DEI, University of Bologna and IUNET, Cesena, Italy
| | - Simone Furini
- Department
of Medical Biotechnologies, University of Siena, Siena, Italy
| | - Dirk Gillespie
- Department
of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago,Illinois, United States
| | - Dezső Boda
- Department
of Physical Chemistry, University of Pannonia, Veszprém, Hungary
| | - Robert S. Eisenberg
- Department
of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago,Illinois, United States
| | | | - Claudio Fiegna
- ARCES
and DEI, University of Bologna and IUNET, Cesena, Italy
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21
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Abstract
Ion channels are membrane-bound enzymes whose catalytic sites are ion-conducting pores that open and close (gate) in response to specific environmental stimuli. Ion channels are important contributors to cell signaling and homeostasis. Our current understanding of gating is the product of 60 plus years of voltage-clamp recording augmented by intervention in the form of environmental, chemical, and mutational perturbations. The need for good phenomenological models of gating has evolved in parallel with the sophistication of experimental technique. The goal of modeling is to develop realistic schemes that not only describe data, but also accurately reflect mechanisms of action. This review covers three areas that have contributed to the understanding of ion channels: traditional Eyring kinetic theory, molecular dynamics analysis, and statistical thermodynamics. Although the primary emphasis is on voltage-dependent channels, the methods discussed here are easily generalized to other stimuli and could be applied to any ion channel and indeed any macromolecule.
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22
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Chaudhry JH, Comer J, Aksimentiev A, Olson LN. A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore. COMMUNICATIONS IN COMPUTATIONAL PHYSICS 2014; 15:10.4208/cicp.101112.100413a. [PMID: 24363784 PMCID: PMC3867981 DOI: 10.4208/cicp.101112.100413a] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current.
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Affiliation(s)
| | - Jeffrey Comer
- Department for Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Aleksei Aksimentiev
- Department for Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Luke N. Olson
- Department for Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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23
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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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24
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De Biase P, Solano CJF, Markosyan S, Czapla L, Noskov SY. BROMOC-D: Brownian Dynamics/Monte-Carlo Program Suite to Study Ion and DNA Permeation in Nanopores. J Chem Theory Comput 2012; 8:2540-2551. [PMID: 22798730 PMCID: PMC3396124 DOI: 10.1021/ct3004244] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2012] [Indexed: 11/29/2022]
Abstract
A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion-ion and ion-DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)(n) and ss-poly(dC)(n). The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.
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Affiliation(s)
| | | | | | - Luke Czapla
- Institute for Biocomplexity and Informatics, Department
of Biological Sciences, University of Calgary, Calgary, AB, Canada,
T2N 1N4
| | - Sergei Yu. Noskov
- Institute for Biocomplexity and Informatics, Department
of Biological Sciences, University of Calgary, Calgary, AB, Canada,
T2N 1N4
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25
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Berti C, Gillespie D, Bardhan JP, Eisenberg RS, Fiegna C. Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011912. [PMID: 23005457 DOI: 10.1103/physreve.86.011912] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2012] [Indexed: 06/01/2023]
Abstract
Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the two methods are essentially equivalent; i.e., they have comparable accuracies for the same number of elements. We find that ions in water--charges embedded in a high-dielectric medium--are harder to compute accurately than charges in a low-dielectric medium.
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Affiliation(s)
- Claudio Berti
- ARCES, University of Bologna and IUNET, Via Venezia 260, I-47521 Cesena, Italy.
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26
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Comer J, Aksimentiev A. Predicting the DNA sequence dependence of nanopore ion current using atomic-resolution Brownian dynamics. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2012; 116:3376-3393. [PMID: 22606364 PMCID: PMC3350822 DOI: 10.1021/jp210641j] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
It has become possible to distinguish DNA molecules of different nucleotide sequences by measuring ion current passing through a narrow pore containing DNA. To assist experimentalists in interpreting the results of such measurements and to improve the DNA sequence detection method, we have developed a computational approach that has both the atomic-scale accuracy and the computational efficiency required to predict DNA sequence-specific differences in the nanopore ion current. In our Brownian dynamics method, the interaction between the ions and DNA is described by three-dimensional potential of mean force maps determined to a 0.03 nm resolution from all-atom molecular dynamics simulations. While this atomic-resolution Brownian dynamics method produces results with orders of magnitude less computational effort than all-atom molecular dynamics requires, we show here that the ion distributions and ion currents predicted by the two methods agree. Finally, using our Brownian dynamics method, we find that a small change in the sequence of DNA within a pore can cause a large change in the ion current, and validate this result with all-atom molecular dynamics.
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Affiliation(s)
- Jeffrey Comer
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
| | - Aleksei Aksimentiev
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
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27
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Kwon T, Harris AL, Rossi A, Bargiello TA. Molecular dynamics simulations of the Cx26 hemichannel: evaluation of structural models with Brownian dynamics. J Gen Physiol 2011; 138:475-93. [PMID: 22006989 PMCID: PMC3206306 DOI: 10.1085/jgp.201110679] [Citation(s) in RCA: 72] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2011] [Accepted: 09/27/2011] [Indexed: 11/21/2022] Open
Abstract
The recently published crystal structure of the Cx26 gap junction channel provides a unique opportunity for elucidation of the structure of the conductive connexin pore and the molecular determinants of its ion permeation properties (conductance, current-voltage [I-V] relations, and charge selectivity). However, the crystal structure was incomplete, most notably lacking the coordinates of the N-terminal methionine residue, which resides within the pore, and also lacking two cytosolic domains. To allow computational studies for comparison with the known channel properties, we completed the structure. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) simulations of the completed and the published Cx26 hemichannel crystal structure indicate that the pore is too narrow to permit significant ion flux. The GCMC/BD simulations predict marked inward current rectification and almost perfect anion selectivity, both inconsistent with known channel properties. The completed structure was refined by all-atom molecular dynamics (MD) simulations (220 ns total) in an explicit solvent and POPC membrane system. These MD simulations produced an equilibrated structure with a larger minimal pore diameter, which decreased the height of the permeation barrier formed by the N terminus. GCMC/BD simulations of the MD-equilibrated structure yielded more appropriate single-channel conductance and less anion/cation selectivity. However, the simulations much more closely matched experimentally determined I-V relations when the charge effects of specific co- and posttranslational modifications of Cx26 previously identified by mass spectrometry were incorporated. We conclude that the average equilibrated structure obtained after MD simulations more closely represents the open Cx26 hemichannel structure than does the crystal structure, and that co- and posttranslational modifications of Cx26 hemichannels are likely to play an important physiological role by defining the conductance and ion selectivity of Cx26 channels. Furthermore, the simulations and data suggest that experimentally observed heterogeneity in Cx26 I-V relations can be accounted for by variation in co- and posttranslational modifications.
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Affiliation(s)
- Taekyung Kwon
- Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461
| | - Andrew L. Harris
- Department of Pharmacology and Physiology, New Jersey Medical School, University of Medicine and Dentistry of New Jersey, Newark, NJ 07103
| | - Angelo Rossi
- Department of Pharmacology and Physiology, New Jersey Medical School, University of Medicine and Dentistry of New Jersey, Newark, NJ 07103
| | - Thaddeus A. Bargiello
- Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461
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28
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Vaccaro SR. Voltage dependence of a stochastic model of activation of an alpha helical S4 sensor in a K channel membrane. J Chem Phys 2011; 135:095102. [PMID: 21913782 DOI: 10.1063/1.3630010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The voltage dependence of the ionic and gating currents of a K channel is dependent on the activation barriers of a voltage sensor with a potential function which may be derived from the principal electrostatic forces on an S4 segment in an inhomogeneous dielectric medium. By variation of the parameters of a voltage-sensing domain model, consistent with x-ray structures and biophysical data, the lowest frequency of the survival probability of each stationary state derived from a solution of the Smoluchowski equation provides a good fit to the voltage dependence of the slowest time constant of the ionic current in a depolarized membrane, and the gating current exhibits a rising phase that precedes an exponential relaxation. For each depolarizing potential, the calculated time dependence of the survival probabilities of the closed states of an alpha helical S4 sensor are in accord with an empirical model of the ionic and gating currents recorded during the activation process.
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Affiliation(s)
- S R Vaccaro
- Department of Physics, University of Adelaide, Adelaide, South Australia 5005, Australia.
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29
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Lee KI, Rui H, Pastor RW, Im W. Brownian dynamics simulations of ion transport through the VDAC. Biophys J 2011; 100:611-619. [PMID: 21281575 PMCID: PMC3030170 DOI: 10.1016/j.bpj.2010.12.3708] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2010] [Revised: 12/02/2010] [Accepted: 12/13/2010] [Indexed: 10/18/2022] Open
Abstract
It is important to gain a physical understanding of ion transport through the voltage-dependent anion channel (VDAC) because this channel provides primary permeation pathways for metabolites and electrolytes between the cytosol and mitochondria. We performed grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) simulations to explore the ion transport properties of human VDAC isoform 1 (hVDAC1; PDB:2K4T) embedded in an implicit membrane. When the MD-derived, space-dependent diffusion constant was used in the GCMC/BD simulations, the current-voltage characteristics and ion number profiles inside the pore showed excellent agreement with those calculated from all-atom molecular-dynamics (MD) simulations, thereby validating the GCMC/BD approach. Of the 20 NMR models of hVDAC1 currently available, the third one (NMR03) best reproduces both experimental single-channel conductance and ion selectivity (i.e., the reversal potential). In addition, detailed analyses of the ion trajectories, one-dimensional multi-ion potential of mean force, and protein charge distribution reveal that electrostatic interactions play an important role in the channel structure and ion transport relationship. Finally, the GCMC/BD simulations of various mutants based on NMR03 show good agreement with experimental ion selectivity. The difference in ion selectivity between the wild-type and the mutants is the result of altered potential of mean force profiles that are dominated by the electrostatic interactions.
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Affiliation(s)
- Kyu Il Lee
- Center for Bioinformatics, University of Kansas, Lawrence, Kansas; Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas
| | - Huan Rui
- Center for Bioinformatics, University of Kansas, Lawrence, Kansas; Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas
| | - Richard W Pastor
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland
| | - Wonpil Im
- Center for Bioinformatics, University of Kansas, Lawrence, Kansas; Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas.
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30
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Calero C, Faraudo J, Aguilella-Arzo M. First-passage-time analysis of atomic-resolution simulations of the ionic transport in a bacterial porin. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:021908. [PMID: 21405864 DOI: 10.1103/physreve.83.021908] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2010] [Indexed: 05/30/2023]
Abstract
We have studied the dynamics of chloride and potassium ions in the interior of the Outer membrane porin F (OmpF) under the influence of an external electric field. From the results of extensive all-atom molecular dynamics (MD) simulations of the system, we computed several first-passage-time (FPT) quantities to characterize the dynamics of the ions in the interior of the channel. Such FPT quantities obtained from MD simulations demonstrate that it is not possible to describe the dynamics of chloride and potassium ions inside the whole channel with a single constant diffusion coefficient. However, we showed that a valid, statistically rigorous description in terms of a constant diffusion coefficient D and an effective deterministic force F(eff) can be obtained after appropriate subdivision of the channel in different regions suggested by the x-ray structure. These results have important implications for popular simplified descriptions of channels based on the one-dimensional Poisson-Nernst-Planck equations. Also, the effect of entropic barriers on the diffusion of the ions is identified and briefly discussed.
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Affiliation(s)
- Carles Calero
- Institut de Ciència dels Materials de Barcelona (ICMAB-CSIC), Campus de la UAB, E-08193 Bellaterra, Spain.
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31
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Aguilella VM, Queralt-Martín M, Aguilella-Arzo M, Alcaraz A. Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity. Integr Biol (Camb) 2010; 3:159-72. [PMID: 21132209 DOI: 10.1039/c0ib00048e] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Ion channels are hollow proteins that have evolved to exhibit discrimination between charged solutes. This property, known as ion selectivity is critical for several biological functions. By using the bacterial porin OmpF as a model system of wide protein channels, we demonstrate that significant insights can be gained when selectivity measurements are combined with electrodiffusion continuum models and simulations based on the atomic structure. A correct interpretation of the mechanisms ruling the many sources of channel discrimination is a first, indispensable step for the understanding of the controlled movement of ions into or out of cells characteristic of many physiological processes. We conclude that the scattered information gathered from several independent approaches should be appropriately merged to provide a unified and coherent picture of the channel selectivity.
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Affiliation(s)
- Vicente M Aguilella
- Dept. Physics, Lab. Molecular Biophysics, Universitat Jaume I, 12080 Castellón, Spain.
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32
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Simakov NA, Kurnikova MG. Soft wall ion channel in continuum representation with application to modeling ion currents in α-hemolysin. J Phys Chem B 2010; 114:15180-90. [PMID: 21028776 DOI: 10.1021/jp1046062] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
A soft repulsion (SR) model of short-range interactions between mobile ions and protein atoms is introduced in the framework of continuum representation of the protein and solvent. The Poisson-Nernst-Plank (PNP) theory of ion transport through biological channels is modified to incorporate this soft wall protein model. Two sets of SR parameters are introduced. The first is parametrized for all essential amino acid residues using all atom molecular dynamic simulations; the second is a truncated Lennard-Jones potential. We have further designed an energy-based algorithm for the determination of the ion accessible volume, which is appropriate for a particular system discretization. The effects of these models of short-range interactions were tested by computing current-voltage characteristics of the α-hemolysin channel. The introduced SR potentials significantly improve prediction of channel selectivity. In addition, we studied the effect of the choice of some space-dependent diffusion coefficient distributions on the predicted current-voltage properties. We conclude that the diffusion coefficient distributions largely affect total currents and have little effect on rectifications, selectivity, or reversal potential. The PNP-SR algorithm is implemented in a new efficient parallel Poisson, Poisson-Boltzmann, and PNP equation solver, also incorporated in a graphical molecular modeling package HARLEM.
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Affiliation(s)
- Nikolay A Simakov
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
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33
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Egwolf B, Luo Y, Walters DE, Roux B. Ion selectivity of alpha-hemolysin with beta-cyclodextrin adapter. II. Multi-ion effects studied with grand canonical Monte Carlo/Brownian dynamics simulations. J Phys Chem B 2010; 114:2901-9. [PMID: 20146515 DOI: 10.1021/jp906791b] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In a previous study of ion selectivity of alpha-hemolysin (alphaHL) in complex with beta-cyclodextrin (betaCD) adapter, we calculated the potential of mean force (PMF) and characterized the self-diffusion coefficients of isolated K(+) and Cl(-) ions using molecular dynamics simulations (Y. Luo et al., "Ion Selectivity of alpha-Hemolysin with beta-Cyclodextrin Adapter: I. Single Ion Potential of Mean Force and Diffusion Coefficient"). In the present effort, these results pertaining to single isolated ions in the wide aqueous pore are extended to take into account multi-ion effects. The grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) algorithm is used to simulate ion currents through the wild-type alphaHL ion channel, as well as two engineered alphaHL mutants, with and without the cyclic oligosaccaride betaCD lodged in the lumen of the pore. The GCMC/BD current-voltage curves agree well with experimental results and show that betaCD increases the anion selectivity of alphaHL. Comparisons between multi-ion PMFs from GCMC/BD simulations and single-ion PMFs demonstrate that multi-ion effects and pore shape are crucial for explaining this behavior. It is concluded that the narrow betaCD adapter increases the anion selectivity of alphaHL because it reduces the pore radius locally, which decreases the ionic screening and the dielectric shielding of the strong electrostatic field induced by a nearby ring of positively charged alphaHL side chains.
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Affiliation(s)
- Bernhard Egwolf
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, Illinois, USA
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34
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Freedman H, Rezania V, Priel A, Carpenter E, Noskov SY, Tuszynski JA. Model of ionic currents through microtubule nanopores and the lumen. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:051912. [PMID: 20866266 DOI: 10.1103/physreve.81.051912] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2009] [Revised: 01/26/2010] [Indexed: 05/29/2023]
Abstract
It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores, both with and without an external potential applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear IV curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the C-terminal tails causes cations to be pumped across the microtubule wall and propagate in both directions down the microtubule through the lumen, returning to the bulk solution through its open ends. This effect is demonstrated to add directly to the longitudinal current through the lumen resulting from an external voltage source applied across the two ends of the microtubule. The predicted persistent currents directed through the microtubule wall and along the lumen could be significant in directing the dissipation of weak, endogenous potential gradients toward one end of the microtubule within the cellular environment.
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Affiliation(s)
- Holly Freedman
- Department of Oncology, Cross Cancer Institute, University of Alberta, Edmonton, Alberta, Canada
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35
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Luo Y, Egwolf B, Walters DE, Roux B. Ion selectivity of alpha-hemolysin with a beta-cyclodextrin adapter. I. Single ion potential of mean force and diffusion coefficient. J Phys Chem B 2010; 114:952-8. [PMID: 20041673 DOI: 10.1021/jp906790f] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The alpha-hemolysin (alphaHL) is a self-assembling exotoxin that binds to the membrane of a susceptible host cell and causes its death. Experimental studies show that electrically neutral beta-cyclodextrin (betaCD) can insert into the alphaHL channel and significantly increase its anion selectivity. To understand how betaCD can affect ion selectivity, molecular dynamics simulations and potential of mean force (PMF) calculations are carried out for different alphaHL channels with and without the betaCD adapter. A multiscale approach based on the generalized solvent boundary potential is used to reduce the size of the simulated system. The PMF profiles reveal that betaCD has no anion selectivity by itself but can increase the Cl(-) selectivity of the alphaHL channel when lodged into the pore lumen. Analysis shows that betaCD causes a partial desolvation of ions and affects the orientation of nearby charged residues. The ion selectivity appears to result from increased electrostatic interaction between the ion and the channel due to a reduction in dielectric shielding by the solvent. These observations suggest a reasonable explanation of the ion selectivity and provide important information for further ion channel modification.
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Affiliation(s)
- Yun Luo
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, Illinois, USA
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36
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Alkherraz A, Kamerlin SCL, Feng G, Sheikh QI, Warshel A, Williams NH. Phosphate ester analogues as probes for understanding enzyme catalysed phosphoryl transfer. Faraday Discuss 2010. [DOI: 10.1039/b908398g] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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37
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Kamerlin SCL, Haranczyk M, Warshel A. Are mixed explicit/implicit solvation models reliable for studying phosphate hydrolysis? A comparative study of continuum, explicit and mixed solvation models. Chemphyschem 2009; 10:1125-34. [PMID: 19301306 DOI: 10.1002/cphc.200800753] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Phosphate hydrolysis is ubiquitous in biology. However, despite intensive research on this class of reactions, the precise nature of the reaction mechanism remains controversial. Herein, we have examined the hydrolysis of three homologous phosphate diesters. The solvation free energy was simulated by means of either an implicit solvation model (COSMO), hybrid quantum mechanical/molecular mechanical free energy perturbation (QM/MM-FEP) or a mixed solvation model in which N water molecules were explicitly included in the ab initio description of the reacting system (where N=1-3), with the remainder of the solvent being implicitly modelled as a continuum. Here, both COSMO and QM/MM-FEP reproduce DeltaG(obs) within an error of about 1 kcal mol(-1). However, we demonstrate that in order to obtain any kind of reliable results from a mixed model, it is essential to carefully select the explicit water molecules from short QM/MM runs that act as a model for the true infinite system. Additionally, the mixed models tend to be increasingly unstable and miss larger entropic contributions as more explicit water molecules are placed into the system. Thus, our analysis indicates that this approach provides an unreliable way for modelling phosphate hydrolysis in solution.
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Affiliation(s)
- Shina C L Kamerlin
- Department of Chemistry, University of Southern California, 3620 McClintock Ave., Los Angeles, CA 90089, USA.
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38
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Abstract
The outer membrane of Gram-negative bacteria serves as a protective barrier against the external environment but is rendered selectively permeable to nutrients and waste by proteins called porins. Other outer membrane proteins (OMPs) provide the membrane with a variety of other functions including active transport, catalysis, pathogenesis and signal transduction. A relatively small number of crystal or NMR structures of these proteins are known, and it is therefore essential that the maximum possible information be extracted. In this respect, computational techniques enable extrapolation from time- and space-averaged static structures to dynamic, physiological events. Electrostatics approaches have been used to investigate the structures of porins. The stochastic simulation of ion trajectories through these channels has been possible with Brownian dynamics, which treats the membrane and solvent approximately, enabling the prediction of conduction properties. Molecular dynamics has also been applied, enabling fully atomistic descriptions of 'virtual outer membranes'. This has provided atomic resolution descriptions of solute permeation through porins. It has also yielded insights into the dynamics of gating in active transporters and ion channels, as well as providing clues to catalytic mechanisms in outer membrane enzymes. Additionally, simulations are beginning to reveal the common features of interactions between membrane proteins and lipids, with biological implications for OMP folding, stability and mechanism. Future prospects include the simulation of longer, larger and more complex outer membrane systems, with more accurate descriptions of inter-atomic forces.
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Affiliation(s)
- Peter J Bond
- Department of Biochemistry, The University of Oxford, Oxford, UK
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39
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Bardhan JP, Eisenberg RS, Gillespie D. Discretization of the induced-charge boundary integral equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:011906. [PMID: 19658728 PMCID: PMC3700357 DOI: 10.1103/physreve.80.011906] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2008] [Indexed: 05/18/2023]
Abstract
Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.
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Affiliation(s)
- Jaydeep P Bardhan
- Biosciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
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40
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Kamerlin SCL, Haranczyk M, Warshel A. Progress in ab initio QM/MM free-energy simulations of electrostatic energies in proteins: accelerated QM/MM studies of pKa, redox reactions and solvation free energies. J Phys Chem B 2009; 113:1253-72. [PMID: 19055405 PMCID: PMC2679392 DOI: 10.1021/jp8071712] [Citation(s) in RCA: 241] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Hybrid quantum mechanical/molecular mechanical (QM/MM) approaches have been used to provide a general scheme for chemical reactions in proteins. However, such approaches still present a major challenge to computational chemists, not only because of the need for very large computer time in order to evaluate the QM energy but also because of the need for proper computational sampling. This review focuses on the sampling issue in QM/MM evaluations of electrostatic energies in proteins. We chose this example since electrostatic energies play a major role in controlling the function of proteins and are key to the structure-function correlation of biological molecules. Thus, the correct treatment of electrostatics is essential for the accurate simulation of biological systems. Although we will be presenting different types of QM/MM calculations of electrostatic energies (and related properties) here, our focus will be on pKa calculations. This reflects the fact that pKa's of ionizable groups in proteins provide one of the most direct benchmarks for the accuracy of electrostatic models of macromolecules. While pKa calculations by semimacroscopic models have given reasonable results in many cases, existing attempts to perform pKa calculations using QM/MM-FEP have led to discrepancies between calculated and experimental values. In this work, we accelerate our QM/MM calculations using an updated mean charge distribution and a classical reference potential. We examine both a surface residue (Asp3) of the bovine pancreatic trypsin inhibitor and a residue buried in a hydrophobic pocket (Lys102) of the T4-lysozyme mutant. We demonstrate that, by using this approach, we are able to reproduce the relevant side chain pKa's with an accuracy of 3 kcal/mol. This is well within the 7 kcal/mol energy difference observed in studies of enzymatic catalysis, and is thus sufficient accuracy to determine the main contributions to the catalytic energies of enzymes. We also provide an overall perspective of the potential of QM/MM calculations in general evaluations of electrostatic free energies, pointing out that our approach should provide a very powerful and accurate tool to predict the electrostatics of not only solution but also enzymatic reactions, as well as the solvation free energies of even larger systems, such as nucleic acid bases incorporated into DNA.
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Affiliation(s)
- Shina C. L. Kamerlin
- Department of Chemistry, University of Southern California, 418 SGM Building, 3620 McClintock Avenue, Los Angeles, CA 90089-1062, USA
| | - Maciej Haranczyk
- Department of Chemistry, University of Southern California, 418 SGM Building, 3620 McClintock Avenue, Los Angeles, CA 90089-1062, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50F-1650, Berkeley, CA 94720-8139, USA
| | - Arieh Warshel
- Department of Chemistry, University of Southern California, 418 SGM Building, 3620 McClintock Avenue, Los Angeles, CA 90089-1062, USA
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41
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Kamerlin SCL, Florián J, Warshel A. Associative versus dissociative mechanisms of phosphate monoester hydrolysis: on the interpretation of activation entropies. Chemphyschem 2009; 9:1767-73. [PMID: 18666265 DOI: 10.1002/cphc.200800356] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Phosphate monoester and anhydride hydrolysis is ubiquitous in biology, being involved in, amongst other things, signal transduction, energy production, and the regulation of protein function. Therefore, this reaction has understandably been the focus of intensive research. Nevertheless, the precise mechanism by which phosphate monoester hydrolysis proceeds remains controversial. Traditionally, it has been assumed and frequently implied that a near-zero activation entropy is indicative of a dissociative pathway. Herein, we examine free-energy surfaces for the hydrolysis of the methyl phosphate dianion and the methyl pyrophosphate trianion in aqueous solution. In both cases, the reaction can proceed through either compact or expansive concerted (A(N)D(N)) transition states, with fairly similar barriers. We have evaluated the activation entropies for each transition state and demonstrate that both associative and dissociative transition states have near-zero entropies of activation that are in good agreement with experimental values. Therefore, we believe that the activation entropy alone is not a useful diagnostic tool, as it depends not only on bond orders at the transition state, but also on other issues that include (but are not limited to) steric factors determining the configurational volumes available to reactants during the reaction, solvation and desolvation effects that may be associated with charge redistribution upon approaching the transition state and entropy changes associated with intramolecular degrees of freedom as the transition state is approached.
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Affiliation(s)
- Shina C L Kamerlin
- Department of Chemistry, University of Southern California, 3620 McClintock Ave, Los Angeles, CA 90089, USA.
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42
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Hwang H, Schatz GC, Ratner MA. Incorporation of inhomogeneous ion diffusion coefficients into kinetic lattice grand canonical monte carlo simulations and application to ion current calculations in a simple model ion channel. J Phys Chem A 2007; 111:12506-12. [PMID: 17960920 DOI: 10.1021/jp075838o] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
To deal with inhomogeneous diffusion coefficients of ions without altering the lattice spacing in the kinetic lattice grand canonical Monte Carlo (KLGCMC) simulation, an algorithm that incorporates diffusion coefficient variation into move probabilities is proposed and implemented into KLGCMC calculations. Using this algorithm, the KLGCMC simulation method is applied to the calculation of ion currents in a simple model ion channel system. Comparisons of ion currents and ion concentrations from these simulations with Poisson-Nernst-Planck (PNP) results show good agreement between the two methods for parameters where the latter method is expected to be accurate.
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Affiliation(s)
- Hyonseok Hwang
- Department of Chemistry, Kangwon National University, Chuncheon, Kangwon 200-701, Republic of Korea.
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43
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Hwang H, Schatz GC, Ratner MA. Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system. J Chem Phys 2007; 127:024706. [PMID: 17640144 DOI: 10.1063/1.2748373] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
An algorithm in which kinetic lattice grand canonical Monte Carlo simulations are combined with mean field theory (KLGCMC/MF) is presented to calculate ion currents in a model ion channel system. In this simulation, the relevant region of the system is treated by KLGCMC simulations, while the rest of the system is described by modified Poisson-Boltzmann mean field theory. Calculation of reaction field due to induced charges on the channel/water and membrane/water boundaries is carried out using a basis-set expansion method [Im and Roux, J. Chem. Phys. 115, 4850 (2001)]. Calculation of ion currents, electrostatic potentials, and ion concentrations, as obtained from the KLGCMC/MF simulations, shows good agreement with Poisson-Nernst-Planck (PNP) theory predictions when the channel and membrane have the same dielectric constant as water. If the channel and membrane have a lower dielectric constant than water, however, there is a considerable difference between the KLGCMC/MF and PNP predictions. This difference is attributed to the reaction field, which is missing in PNP theory. It is demonstrated that the reaction field as well as fixed charges in the channel play key roles in selective ion transport. Limitations and further development of the current KLGCMC/MF approach are also discussed.
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Affiliation(s)
- Hyonseok Hwang
- Department of Chemistry, Kangwon National University, Chucheon 200-701, South Korea
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44
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Hwang H, Schatz GC, Ratner MA. Ion Current Calculations Based on Three Dimensional Poisson−Nernst−Planck Theory for a Cyclic Peptide Nanotube. J Phys Chem B 2006; 110:6999-7008. [PMID: 16571014 DOI: 10.1021/jp055740e] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Ion current calculations based on Poisson-Nernst-Planck (PNP) theory are performed for a synthetic cyclic peptide nanotube that consists of eight or ten cyclo[(-L-Trp-D-Leu-)4] embedded in a lipid bilayer membrane to investigate the ion transport properties of the nanotube. To explore systems with arbitrary geometries, three-dimensional PNP theory is implemented using a finite difference method. The influence of dipolar lipid molecules on the ion currents is also examined by turning on or off the charges of the lipid dipoles in dipalmitoylphosphatidylcholine (DPPC). Comparisons between the calculated and experimentally measured ion currents show that the PNP approach agrees well with the measurements at low ion concentrations but overestimates the currents at higher concentrations. Concentration profiles reveal the selectivity of the peptide nanotube to cations, which is attributed to the negatively charged carbonyl oxygens inside the nanotube. The dominant cation and the minimum anion concentrations inside the cyclic peptide nanotube suggest that these cyclic peptide nanotubes can be employed as ion sensors. In the case of the polar DPPC bilayer, smaller currents are obtained in the calculation. The variation of current with polarity of the lipids implies that both polar and nonpolar lipid bilayer membranes can be utilized to regulate ion currents in the peptide nanotube and other ion channels. Strengths and limitations of the PNP theory are also discussed.
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Affiliation(s)
- Hyonseok Hwang
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA
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45
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Baginski M, Cybulska B, Gruszecki WI. Chapter 9 Interaction of Polyene Macrolide Antibiotics with Lipid Model Membranes. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/s1554-4516(05)03009-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/21/2023]
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46
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47
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Woolf TB, Zuckerman DM, Lu N, Jang H. Tools for channels: moving towards molecular calculations of gating and permeation in ion channel biophysics. J Mol Graph Model 2004; 22:359-68. [PMID: 15099832 DOI: 10.1016/j.jmgm.2003.12.003] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
Recent X-ray structures of voltage gated potassium channels provide an exciting opportunity to connect molecular structures with measured biological function. Two of the most important connections for these channels are: first, to the molecular basis behind selectivity and the associated free energy profile underlying ionic current flow and, second, to a true molecular understanding of the large-scale conformational transitions that underlie voltage dependent gating. But, existing computational tools need to be further developed to reach these goals. In this contribution to the symposia on sampling methods we outline our dynamic importance sampling method for sampling large-scale conformational transitions as well as our studies with non-equilibrium work events and equilibrium overlap sampling (OS) methods for sampling events related to the calculation of relative free energies.
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Affiliation(s)
- Thomas B Woolf
- Department of Physiology, Johns Hopkins University, School of Medicine, Biophysics 206, 725 N. Wolfe Street, Baltimore, MD 21205, USA.
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48
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Noskov SY, Im W, Roux B. Ion permeation through the alpha-hemolysin channel: theoretical studies based on Brownian dynamics and Poisson-Nernst-Plank electrodiffusion theory. Biophys J 2004; 87:2299-309. [PMID: 15454431 PMCID: PMC1304654 DOI: 10.1529/biophysj.104.044008] [Citation(s) in RCA: 138] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2004] [Accepted: 06/14/2004] [Indexed: 11/18/2022] Open
Abstract
Identification of the molecular interaction governing ion conduction through biological pores is one of the most important goals of modern electrophysiology. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) and three-dimensional Poisson-Nernst-Plank (3d-PNP) electrodiffusion algorithms offer powerful and general approaches to study of ion permeation through wide molecular pores. A detailed analysis of ion flows through the staphylococcal alpha-hemolysin channel based on series of simulations at different concentrations and transmembrane potentials is presented. The position-dependent diffusion coefficient is approximated on the basis of a hydrodynamic model. The channel conductance calculated by GCMC/BD is approximately 10% higher than (electrophysiologically measured) experimental values, whereas results from 3d-PNP are always 30-50% larger. Both methods are able to capture all important electrostatic interactions in equilibrium conditions. The asymmetric conductance upon the polarity of the transmembrane potential observed experimentally is reproduced by GCMC/BD and 3d-PNP. The separation of geometrical and energetic influence of the channel on ion conduction reveals that such asymmetries arise from the permanent charge distribution inside the pore. The major determinant of the asymmetry is unbalanced charge in the triad of polar residues D127, D128, and K131. The GCMC/BD or 3d-PNP calculations reproduce also experimental reversal potentials and permeability rations in asymmetric ionic solutions. The weak anionic selectivity of the channel results from the presence of the salt bridge between E111 and K147 in the constriction zone. The calculations also reproduce the experimentally derived dependence of the reversible potential to the direction of the salt gradient. The origin of such effect arises from the asymmetrical distribution of energetic barriers along the channel axis, which modulates the preferential ion passage in different directions.
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Affiliation(s)
- Sergei Yu Noskov
- Department of Biochemistry & Structural Biology, Weill Medical College of Cornell University, New York, New York 10021, USA
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49
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Boda D, Gillespie D, Nonner W, Henderson D, Eisenberg B. Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:046702. [PMID: 15169126 DOI: 10.1103/physreve.69.046702] [Citation(s) in RCA: 92] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2003] [Revised: 12/16/2003] [Indexed: 05/24/2023]
Abstract
The efficient calculation of induced charges in an inhomogeneous dielectric is important in simulations and coarse-grained models in molecular biology, chemical physics, and electrochemistry. We present the induced charge computation (ICC) method for the calculation of the polarization charges based on the variational formulation of Allen et al. [Phys. Chem. Chem. Phys. 3, 4177 (2001)]. We give a different solution for their extremum condition that produces a matrix formulation. The induced charges are directly calculated by solving the linear matrix equation Ah=c, where h contains the discretized induced charge density, c depends only on the source charges-the ions moved in the simulation-and the matrix A depends on the geometry of dielectrics, which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. We verify the efficiency and accuracy of the method by means of Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielectric boundary is present, which allows comparison with exact results calculated using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. Our results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.
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Affiliation(s)
- Dezsö Boda
- Department of Physical Chemistry, University of Veszprém, P.O. Box 158, Veszprém, Hungary
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50
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Domene C, Bond PJ, Sansom MS. Membrane protein simulations: ion channels and bacterial outer membrane proteins. ADVANCES IN PROTEIN CHEMISTRY 2003; 66:159-93. [PMID: 14631819 DOI: 10.1016/s0065-3233(03)66005-5] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Carmen Domene
- Laboratory of Molecular Biophysics (LMB), Department of Biochemistry, University of Oxford, Oxford, United Kingdom
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