1
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Jäger M, Koslowski T, Wolf S. Predicting Ion Channel Conductance via Dissipation-Corrected Targeted Molecular Dynamics and Langevin Equation Simulations. J Chem Theory Comput 2021; 18:494-502. [PMID: 34928150 DOI: 10.1021/acs.jctc.1c00426] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, here we applied dissipation-corrected targeted molecular dynamics in combination with Langevin equation simulations to potassium diffusion through the gramicidin A channel as a test system. Performing a nonequilibrium principal component analysis on backbone dihedral angles, we find coupled protein-ion dynamics to occur during ion transfer. The dissipation-corrected free energy profiles correspond well to predictions from other biased simulation methods. The incorporation of an external electric field in Langevin simulations enables the prediction of macroscopic observables in the form of I-V characteristics.
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Affiliation(s)
- Miriam Jäger
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Thorsten Koslowski
- Institute of Physical Chemistry, University of Freiburg, 79104 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
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2
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Flood E, Boiteux C, Lev B, Vorobyov I, Allen TW. Atomistic Simulations of Membrane Ion Channel Conduction, Gating, and Modulation. Chem Rev 2019; 119:7737-7832. [DOI: 10.1021/acs.chemrev.8b00630] [Citation(s) in RCA: 65] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Emelie Flood
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia
| | - Céline Boiteux
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia
| | - Bogdan Lev
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia
| | - Igor Vorobyov
- Department of Physiology & Membrane Biology/Department of Pharmacology, University of California, Davis, 95616, United States
| | - Toby W. Allen
- School of Science, RMIT University, Melbourne, Victoria 3000, Australia
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3
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Na S, Steinbrecher T, Koslowski T. Thermodynamic integration network approach to ion transport through protein channels: Perspectives and limits. J Comput Chem 2018; 39:2539-2550. [DOI: 10.1002/jcc.25615] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2018] [Revised: 03/27/2018] [Accepted: 09/03/2018] [Indexed: 12/20/2022]
Affiliation(s)
- Sehee Na
- Fakultät für Chemie und Pharmazie, Institut für Physikalische ChemieUniversität Freiburg Albertstraße 23a, 79104, Freiburg im Breisgau Germany
| | | | - Thorsten Koslowski
- Fakultät für Chemie und Pharmazie, Institut für Physikalische ChemieUniversität Freiburg Albertstraße 23a, 79104, Freiburg im Breisgau Germany
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4
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Adiban J, Jamali Y, Rafii-Tabar H. Modeling ion permeation through a bacterial voltage-gated calcium channel CaVAb using molecular dynamics simulations. MOLECULAR BIOSYSTEMS 2017; 13:208-214. [DOI: 10.1039/c6mb00690f] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Ca2+ion binds tightly to the center of the selectivity filter of voltage-gated calcium channels.
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Affiliation(s)
- Jamal Adiban
- Department of Medical Physics and Biomedical Engineering
- Faculty of Medicine
- Shahid Beheshti University of Medical Sciences
- Tehran
- Iran
| | - Yousef Jamali
- Department of Applied Mathematics
- School of Mathematical Sciences
- Tarbiat Modares University
- Tehran
- Iran
| | - Hashem Rafii-Tabar
- Department of Medical Physics and Biomedical Engineering
- Faculty of Medicine
- Shahid Beheshti University of Medical Sciences
- Tehran
- Iran
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5
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Setiadi J, Kuyucak S. Computational Investigation of the Effect of Lipid Membranes on Ion Permeation in Gramicidin A. MEMBRANES 2016; 6:membranes6010020. [PMID: 26999229 PMCID: PMC4812426 DOI: 10.3390/membranes6010020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Revised: 03/08/2016] [Accepted: 03/08/2016] [Indexed: 06/05/2023]
Abstract
Membrane proteins are embedded in a lipid bilayer and interact with the lipid molecules in subtle ways. This can be studied experimentally by examining the effect of different lipid bilayers on the function of membrane proteins. Understanding the causes of the functional effects of lipids is difficult to dissect experimentally but more amenable to a computational approach. Here we perform molecular dynamics simulations and free energy calculations to study the effect of two lipid types (POPC and NODS) on the conductance of the gramicidin A (gA) channel. A larger energy barrier is found for the K⁺ potential of mean force in gA embedded in POPC compared to that in NODS, which is consistent with the enhanced experimental conductance of cations in gA embedded in NODS. Further analysis of the contributions to the potential energy of K⁺ reveals that gA and water molecules in gA make similar contributions in both bilayers but there are significant differences between the two bilayers when the lipid molecules and interfacial waters are considered. It is shown that the stronger dipole moments of the POPC head groups create a thicker layer of interfacial waters with better orientation, which ultimately is responsible for the larger energy barrier in the K⁺ PMF in POPC.
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Affiliation(s)
- Jeffry Setiadi
- School of Physics, University of Sydney, Sydney NSW 2006, Australia.
| | - Serdar Kuyucak
- School of Physics, University of Sydney, Sydney NSW 2006, Australia.
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6
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Abstract
Microscopic mechanism for cation selectivity in three different ion channels is proposed using ionization energy theory supported by experimental data.
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Affiliation(s)
- Andrew Das Arulsamy
- Condensed Matter Group
- Institute of Interdisciplinary Science
- 42000 Port Klang
- Malaysia
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7
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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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8
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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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9
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Todorović M, Bowler DR, Gillan MJ, Miyazaki T. Density-functional theory study of gramicidin A ion channel geometry and electronic properties. J R Soc Interface 2013; 10:20130547. [PMID: 24068174 PMCID: PMC3808544 DOI: 10.1098/rsif.2013.0547] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2013] [Accepted: 09/03/2013] [Indexed: 01/29/2023] Open
Abstract
Understanding the mechanisms underlying ion channel function from the atomic-scale requires accurate ab initio modelling as well as careful experiments. Here, we present a density functional theory (DFT) study of the ion channel gramicidin A (gA), whose inner pore conducts only monovalent cations and whose conductance has been shown to depend on the side chains of the amino acids in the channel. We investigate the ground state geometry and electronic properties of the channel in vacuum, focusing on their dependence on the side chains of the amino acids. We find that the side chains affect the ground state geometry, while the electrostatic potential of the pore is independent of the side chains. This study is also in preparation for a full, linear scaling DFT study of gA in a lipid bilayer with surrounding water. We demonstrate that linear scaling DFT methods can accurately model the system with reasonable computational cost. Linear scaling DFT allows ab initio calculations with 10,000-100,000 atoms and beyond, and will be an important new tool for biomolecular simulations.
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Affiliation(s)
- Milica Todorović
- National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - David R. Bowler
- International Centre for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
- London Centre for Nanotechnology, UCL, 17–19 Gordon Street, London WC1H 0AH, UK
- Thomas Young Centre, Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT, UK
| | - Michael J. Gillan
- London Centre for Nanotechnology, UCL, 17–19 Gordon Street, London WC1H 0AH, UK
- Thomas Young Centre, Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT, UK
| | - Tsuyoshi Miyazaki
- National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
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10
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Kaufman I, Luchinsky DG, Tindjong R, McClintock PVE, Eisenberg RS. Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052712. [PMID: 24329301 DOI: 10.1103/physreve.88.052712] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2013] [Indexed: 06/03/2023]
Abstract
We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.
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Affiliation(s)
- I Kaufman
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - D G Luchinsky
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom and Mission Critical Technologies Inc., 2041 Rosecrans Ave. Suite 225 El Segundo, California 90245, USA
| | - R Tindjong
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - R S Eisenberg
- Department of Molecular Biophysics and Physiology, Rush Medical College, 1750 West Harrison, Chicago, Illinois 60612, USA
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11
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Gordon D, Chen R, Chung SH. Computational methods of studying the binding of toxins from venomous animals to biological ion channels: theory and applications. Physiol Rev 2013; 93:767-802. [PMID: 23589832 PMCID: PMC3768100 DOI: 10.1152/physrev.00035.2012] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
The discovery of new drugs that selectively block or modulate ion channels has great potential to provide new treatments for a host of conditions. One promising avenue revolves around modifying or mimicking certain naturally occurring ion channel modulator toxins. This strategy appears to offer the prospect of designing drugs that are both potent and specific. The use of computational modeling is crucial to this endeavor, as it has the potential to provide lower cost alternatives for exploring the effects of new compounds on ion channels. In addition, computational modeling can provide structural information and theoretical understanding that is not easily derivable from experimental results. In this review, we look at the theory and computational methods that are applicable to the study of ion channel modulators. The first section provides an introduction to various theoretical concepts, including force-fields and the statistical mechanics of binding. We then look at various computational techniques available to the researcher, including molecular dynamics, brownian dynamics, and molecular docking systems. The latter section of the review explores applications of these techniques, concentrating on pore blocker and gating modifier toxins of potassium and sodium channels. After first discussing the structural features of these channels, and their modes of block, we provide an in-depth review of past computational work that has been carried out. Finally, we discuss prospects for future developments in the field.
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Affiliation(s)
- Dan Gordon
- Research School of Biology, The Australian National University, Acton, ACT 0200, Australia.
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12
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Abstract
We review the basic physics involved in transport of ions across membrane channels in cells. Electrochemical forces that control the diffusion of ions are discussed both from microscopic and macroscopic perspectives. A case is made for use of Brownian dynamics as the minimal phenomenological model that provides a bridge between experiments and more fundamental theoretical approaches. Application of Brownian and molecular dynamics methods to channels with known molecular structures is discussed.
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Affiliation(s)
- Serdar Kuyucak
- Department of Theoretical Physics, Research School of Physical Sciences, Australian National University, Canberra, ACT 0200 Australia
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13
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Chen D, Wei GW. Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation. COMMUNICATIONS IN COMPUTATIONAL PHYSICS 2013; 13:285-324. [PMID: 23550030 PMCID: PMC3580801 DOI: 10.4208/cicp.050511.050811s] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.
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Affiliation(s)
- Duan Chen
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
- Corresponding author. (G.-W. Wei)
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14
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Affiliation(s)
| | - Sergey M. Bezrukov
- Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, U.S.A
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15
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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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16
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Abstract
The response of nanoscale electrodes displays deviations from conventional voltammetry theory that include a reduction in the limiting current and enhanced current fluctuations. We study the power spectra of these fluctuations in well characterized conical electrodes with radii between 2 and 10 nm. The fluctuations are found to display non-trivial power laws. We propose a model based on reversible adsorption of the redox species onto the nanoelectrode. This model is consistent with the non-stationary character of both the limiting current and the adsorption of molecules onto metal electrodes. Our model predicts the electrochemical reaction is nonergodic and sets fundamental limits on the sensitivity of uncoated nanoelectrodes.
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Affiliation(s)
- Diego Krapf
- Electrical and Computer Engineering and School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA.
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17
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Abstract
Carbon nanotubes offer exciting opportunities for devising highly-sensitive detectors of specific molecules in biology and the environment. Detection limits as low as 10(-11) M have already been achieved using nanotube-based sensors. We propose the design of a biosensor comprised of functionalized carbon nanotube pores embedded in a silicon-nitride or other membrane, fluorofullerene-Fragment antigen-binding (Fab fragment) conjugates, and polymer beads with complementary Fab fragments. We show by using molecular and stochastic dynamics that conduction through the (9, 9) exohydrogenated carbon nanotubes is 20 times larger than through the Ion Channel Switch ICS(TM) biosensor, and fluorofullerenes block the nanotube entrance with a dissociation constant as low as 37 pM. Under normal operating conditions and in the absence of analyte, fluorofullerenes block the nanotube pores and the polymer beads float around in the reservoir. When analyte is injected into the reservoir the Fab fragments attached to the fluorofullerene and polymer bead crosslink to the analyte. The drag of the much larger polymer bead then acts to pull the fluorofullerene from the nanotube entrance, thereby allowing the flow of monovalent cations across the membrane. Assuming a tight seal is formed between the two reservoirs, such a biosensor would be able to detect one channel opening and thus one molecule of analyte making it a highly sensitive detection design.
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Affiliation(s)
- Tamsyn A. Hilder
- Computational Biophysics Group, Research School of Biology, Australian National University, Acton, ACT 0200, Australia; E-Mail:
- Author to whom correspondence should be addressed; E-Mail: ; Tel.: +61-2-6125-4034; Fax: +61-2-6125-0739
| | - Ron J. Pace
- Biophysical Chemistry, Research School of Chemistry, Australian National University, Acton, ACT 0200, Australia; E-Mail:
| | - Shin-Ho Chung
- Computational Biophysics Group, Research School of Biology, Australian National University, Acton, ACT 0200, Australia; E-Mail:
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18
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Chen D, Wei GW. Quantum dynamics in continuum for proton transport--generalized correlation. J Chem Phys 2012; 136:134109. [PMID: 22482542 DOI: 10.1063/1.3698598] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.
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Affiliation(s)
- Duan Chen
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
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19
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Horng TL, Lin TC, Liu C, Eisenberg B. PNP Equations with Steric Effects: A Model of Ion Flow through Channels. J Phys Chem B 2012; 116:11422-41. [DOI: 10.1021/jp305273n] [Citation(s) in RCA: 118] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Tzyy-Leng Horng
- Department of Applied Mathematics, Feng Chia University, 100 Wen-Hwa Road, Taichung, Taiwan
40724
| | - Tai-Chia Lin
- Department of Mathematics, Taida Institute for Mathematical
Sciences (TIMS), No. 1, Sec. 4, National Taiwan University, Roosevelt Road, Taipei 106, Taiwan
| | - Chun Liu
- Department of Mathematics, Pennsylvania State University University Park, Pennsylvania 16802,
United States
| | - Bob Eisenberg
- Department of Molecular Biophysics and Physiology, Rush University, 1653 West Congress Parkway, Chicago,
Illinois 60612, United States
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20
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Molecular dynamics simulations of membrane proteins. Biophys Rev 2012; 4:271-282. [PMID: 28510077 DOI: 10.1007/s12551-012-0084-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Accepted: 06/06/2012] [Indexed: 10/28/2022] Open
Abstract
Membrane proteins control the traffic across cell membranes and thereby play an essential role in cell function from transport of various solutes to immune response via molecular recognition. Because it is very difficult to determine the structures of membrane proteins experimentally, computational methods have been increasingly used to study their structure and function. Here we focus on two classes of membrane proteins-ion channels and transporters-which are responsible for the generation of action potentials in nerves, muscles, and other excitable cells. We describe how computational methods have been used to construct models for these proteins and to study the transport mechanism. The main computational tool is the molecular dynamics (MD) simulation, which can be used for everything from refinement of protein structures to free energy calculations of transport processes. We illustrate with specific examples from gramicidin and potassium channels and aspartate transporters how the function of these membrane proteins can be investigated using MD simulations.
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21
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Bordin JR, Diehl A, Barbosa MC, Levin Y. Ion fluxes through nanopores and transmembrane channels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031914. [PMID: 22587130 DOI: 10.1103/physreve.85.031914] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2011] [Revised: 02/08/2012] [Indexed: 05/31/2023]
Abstract
We introduce an implicit solvent Molecular Dynamics approach for calculating ionic fluxes through narrow nanopores and transmembrane channels. The method relies on a dual-control-volume grand-canonical molecular dynamics (DCV-GCMD) simulation and the analytical solution for the electrostatic potential inside a cylindrical nanopore recently obtained by Levin [Europhys. Lett. 76, 163 (2006)]. The theory is used to calculate the ionic fluxes through an artificial transmembrane channel which mimics the antibacterial gramicidin A channel. Both current-voltage and current-concentration relations are calculated under various experimental conditions. We show that our results are comparable to the characteristics associated to the gramicidin A pore, especially the existence of two binding sites inside the pore and the observed saturation in the current-concentration profiles.
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Affiliation(s)
- J R Bordin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil
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Krishnamurthy V, Cornell B. Engineering aspects of biological ion channels--from biosensors to computational models for permeation. PROTOPLASMA 2012; 249 Suppl 1:S3-S9. [PMID: 22038117 DOI: 10.1007/s00709-011-0333-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2011] [Accepted: 10/04/2011] [Indexed: 05/31/2023]
Abstract
This paper presents two important engineering aspects of biological ion channels-how to build sensors out of gramicidin channels and how to construct computational models for ion channel permeation. We describe our recent research in these areas, potential challenges and possible solutions.
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Affiliation(s)
- Vikram Krishnamurthy
- Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, V6T 1Z4, Canada.
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Chen D, Chen Z, Wei GW. Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2012; 28:25-51. [PMID: 22328970 PMCID: PMC3274368 DOI: 10.1002/cnm.1458] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2011] [Revised: 05/25/2011] [Accepted: 06/06/2011] [Indexed: 05/11/2023]
Abstract
Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model.
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Affiliation(s)
- Duan Chen
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
| | - Zhan Chen
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
- Corresponding author. Tel: (517)353 4689, Fax:(517)432 1562,
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Krishnamurthy V, Luk KY. Semi-Markov models for brownian dynamics permeation in biological ion channels. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2011; 8:273-281. [PMID: 21071815 DOI: 10.1109/tcbb.2008.136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Constructing accurate computational models that explain how ions permeate through a biological ion channel is an important problem in biophysics and drug design. Brownian dynamics simulations are large-scale interacting particle computer simulations for modeling ion channel permeation but can be computationally prohibitive. In this paper, we show the somewhat surprising result that a small-dimensional semi-Markov model can generate events (such as conduction events and dwell times at binding sites in the protein) that are statistically indistinguishable from brownian dynamics computer simulation. This approach enables the use of extrapolation techniques to predict channel conduction when performing the actual brownian dynamics simulation that is computationally intractable. Numerical studies on the simulation of gramicidin A ion channels are presented.
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Affiliation(s)
- Vikram Krishnamurthy
- Department of Electrical and Computer Engineering, University of British Columbia, Vancouver V6T 1Z4, Canada.
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Hilder TA, Gordon D, Chung SH. Synthetic chloride-selective carbon nanotubes examined by using molecular and stochastic dynamics. Biophys J 2010; 99:1734-42. [PMID: 20858417 PMCID: PMC2941003 DOI: 10.1016/j.bpj.2010.06.034] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2010] [Revised: 06/09/2010] [Accepted: 06/11/2010] [Indexed: 11/19/2022] Open
Abstract
Synthetic channels, such as nanotubes, offer the possibility of ion-selective nanoscale pores which can broadly mimic the functions of various biological ion channels, and may one day be used as antimicrobial agents, or for treatment of cystic fibrosis. We have designed a carbon nanotube that is selectively permeable to anions. The virtual nanotubes are constructed from a hexagonal array of carbon atoms (graphene) rolled up to form a tubular structure, with an effective radius of 4.53 Å and length of 34 Å. The pore ends are terminated with polar carbonyl groups. The nanotube thus formed is embedded in a lipid bilayer and a reservoir containing ionic solutions is added at each end of the pore. The conductance properties of these synthetic channels are then examined with molecular and stochastic dynamics simulations. Profiles of the potential of mean force at 0 mM reveal that a cation moving across the pore encounters an insurmountable free energy barrier of ∼25 kT in height. In contrast, for anions, there are two energy wells of ∼12 kT near each end of the tube, separated by a central free energy barrier of 4 kT. The conductance of the pore, with symmetrical 500 mM solutions in the reservoirs, is 72 pS at 100 mV. The current saturates with an increasing ionic concentration, obeying a Michaelis-Menten relationship. The pore is normally occupied by two ions, and the rate-limiting step in conduction is the time taken for the resident ion near the exit gate to move out of the energy well.
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Affiliation(s)
- Tamsyn A Hilder
- Research School of Biology, Australian National University, Canberra, Australia.
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The gramicidin channel ion permeation free-energy profile: direct and indirect effects of CHARMM force field improvements. Interdiscip Sci 2010; 1:113-27. [PMID: 20084184 DOI: 10.1007/s12539-009-0025-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
A revised CHARMM force field for tryptophan residues is studied as well as a new grid-based correction algorithm, called CMAP, using molecular dynamics simulations of gramicidin A (1JNO) embedded in a lipid bilayer (DMPC) with 1 mol/kg NaCl or KCl saline solution. The conformational stability of the interfacial side chains is studied, which shows good stability on the 10 ns time scale. The revised force field for the tryptophan side chain produces, in the decomposition, a Na(+) PMF(Trp) profile that is consonant with the prediction from the experimental results, analyzed with rate theory by Durrant et al. (2006), but in stark contrast to the prediction of the original CHARMM force field, version 22. However, the effect is diluted in the PMF profile due to indirect effects mediated by other components of the system (polypeptide, lipid molecules, ions, and water molecules). CMAP corrections to the L-amino acids help reduce the excessive translocation barrier. Decomposition demonstrates that this effect is due to effects on the K(+) PMF(H(2)O) profile rather than on the K(+) PMF(gA) profile. The results have been confirmed to be robust using an alternative umbrella-potential method. Further force field balancing efforts (direct and indirect) are required for future studies to evaluate whether these effects give rise to predictions that are consistent with those observables extracted from real experiments.
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Bucher D, Rothlisberger U. Molecular simulations of ion channels: a quantum chemist's perspective. ACTA ACUST UNITED AC 2010; 135:549-54. [PMID: 20513756 PMCID: PMC2888055 DOI: 10.1085/jgp.201010404] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Denis Bucher
- Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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30
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Jung YW, Lu B, Mascagni M. A computational study of ion conductance in the KcsA K+ channel using a Nernst–Planck model with explicit resident ions. J Chem Phys 2009; 131:215101. [DOI: 10.1063/1.3268774] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Mustafa M, Henderson DJ, Busath DD. Free-energy profiles for ions in the influenza M2-TMD channel. Proteins 2009; 76:794-807. [PMID: 19296508 DOI: 10.1002/prot.22376] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
M(2) transmembrane domain channel (M(2)-TMD) permeation properties are studied using molecular dynamics simulations of M(2)-TMD (1NYJ) embedded in a lipid bilayer (DMPC) with 1 mol/kg NaCl or KCl saline solution. This study allows examination of spontaneous cation and anion entry into the selectivity filter. Three titration states of the M(2)-TMD tetramer are modeled for which the four His(37) residues, forming the selectivity filter, are net uncharged, +2 charged, or +3 charged. M(2)-TMD structural properties from our simulations are compared with the properties of other models extracted from NMR and X-ray studies. During 10 ns simulations, chloride ions occasionally occupy the positively-charged selectivity filter region, and from umbrella sampling simulations, Cl(-) has a lower free-energy barrier in the selectivity-filter region than either Na(+) or NH(4) (+), and NH(4) (+) has a lower free-energy barrier than Na(+). For Na(+) and Cl(-), the free-energy barriers are less than 5 kcal/mol, suggesting that the 1NYJ conformation would probably not be exquisitely proton selective. We also point out a rotameric configuration of Trp(41) that could fully occlude the channel.
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Affiliation(s)
- Morad Mustafa
- Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, USA.
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Gordon D, Krishnamurthy V, Chung SH. Generalized Langevin models of molecular dynamics simulations with applications to ion channels. J Chem Phys 2009; 131:134102. [DOI: 10.1063/1.3233945] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Nielsen CH. Biomimetic membranes for sensor and separation applications. Anal Bioanal Chem 2009; 395:697-718. [DOI: 10.1007/s00216-009-2960-0] [Citation(s) in RCA: 137] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2009] [Revised: 07/02/2009] [Accepted: 07/07/2009] [Indexed: 01/04/2023]
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Bucher D, Guidoni L, Maurer P, Rothlisberger U. Developing Improved Charge Sets for the Modeling of the KcsA K+ Channel Using QM/MM Electrostatic Potentials. J Chem Theory Comput 2009; 5:2173-9. [DOI: 10.1021/ct9001619] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Denis Bucher
- Federal Institute of Technology EPFL, Institute of Chemical Sciences and Engineering, CH-1015 Lausanne, Switzerland
| | - Leonardo Guidoni
- Federal Institute of Technology EPFL, Institute of Chemical Sciences and Engineering, CH-1015 Lausanne, Switzerland
| | - Patrick Maurer
- Federal Institute of Technology EPFL, Institute of Chemical Sciences and Engineering, CH-1015 Lausanne, Switzerland
| | - Ursula Rothlisberger
- Federal Institute of Technology EPFL, Institute of Chemical Sciences and Engineering, CH-1015 Lausanne, Switzerland
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Siu SWI, Böckmann RA. Low Free Energy Barrier for Ion Permeation Through Double-Helical Gramicidin. J Phys Chem B 2009; 113:3195-202. [DOI: 10.1021/jp810302k] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Shirley W. I. Siu
- Theoretical and Computational Membrane Biology, Center for Bioinformatics, Saarland University, P.O. Box 15 11 50, 66041 Saarbrücken, Germany
| | - Rainer A Böckmann
- Theoretical and Computational Membrane Biology, Center for Bioinformatics, Saarland University, P.O. Box 15 11 50, 66041 Saarbrücken, Germany
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36
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Forney MW, Janosi L, Kosztin I. Calculating free-energy profiles in biomolecular systems from fast nonequilibrium processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:051913. [PMID: 19113161 DOI: 10.1103/physreve.78.051913] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2008] [Indexed: 05/27/2023]
Abstract
Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing the recently proposed FR method [I. Kosztin, J. Chem. Phys. 124, 064106 (2006)], which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the position-dependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in an overdamped Brownian model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.
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Affiliation(s)
- Michael W Forney
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
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37
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Ion channel gates: comparative analysis of energy barriers. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2008; 38:347-54. [PMID: 18923825 DOI: 10.1007/s00249-008-0377-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2008] [Revised: 09/18/2008] [Accepted: 09/23/2008] [Indexed: 12/27/2022]
Abstract
The energetic profile of an ion translated along the axis of an ion channel should reveal whether the structure corresponds to a functionally open or closed state of the channel. In this study, we explore the combined use of Poisson-Boltzmann electrostatic calculations and evaluation of van der Waals interactions between ion and pore to provide an initial appraisal of the gating state of a channel. This approach is exemplified by its application to the bacterial inward rectifier potassium channel KirBac3.1, where it reveals the closed gate to be formed by a ring of leucine (L124) side chains. We have extended this analysis to a comparative survey of gating profiles, including model hydrophobic nanopores, the nicotinic acetylcholine receptor, and a number of potassium channel structures and models. This enables us to identify three gating regimes, and to show the limitation of this computationally inexpensive method. For a (closed) gate radius of 0.4 nm < R < 0.8 nm, a hydrophobic gate may be present. For a gate radius of 0.2 nm < R < 0.4 nm, both electrostatic and van der Waals interactions will contribute to the barrier height. Below R = 0.2 nm, repulsive van der Waals interactions are likely to dominate, resulting in a sterically occluded gate. In general, the method is more useful when the channel is wider; for narrower channels, the flexibility of the protein may allow otherwise-unsurmountable energetic barriers to be overcome.
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Bisset D, Chung SH. Efficacy of external tetraethylammonium block of the KcsA potassium channel: Molecular and Brownian dynamics studies. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2008; 1778:2273-82. [DOI: 10.1016/j.bbamem.2008.05.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2008] [Revised: 05/22/2008] [Accepted: 05/22/2008] [Indexed: 11/28/2022]
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Wijesinghe R, Coorey N, Kuyucak S. Charge state of the fast gate in chloride channels: Insights from electrostatic calculations in a schematic model. J Chem Phys 2007; 127:195102. [DOI: 10.1063/1.2804419] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kelkar DA, Chattopadhyay A. The gramicidin ion channel: A model membrane protein. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2007; 1768:2011-25. [PMID: 17572379 DOI: 10.1016/j.bbamem.2007.05.011] [Citation(s) in RCA: 264] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2006] [Revised: 05/09/2007] [Accepted: 05/10/2007] [Indexed: 02/07/2023]
Abstract
The linear peptide gramicidin forms prototypical ion channels specific for monovalent cations and has been extensively used to study the organization, dynamics and function of membrane-spanning channels. In recent times, the availability of crystal structures of complex ion channels has challenged the role of gramicidin as a model membrane protein and ion channel. This review focuses on the suitability of gramicidin as a model membrane protein in general, and the information gained from gramicidin to understand lipid-protein interactions in particular. Special emphasis is given to the role and orientation of tryptophan residues in channel structure and function and recent spectroscopic approaches that have highlighted the organization and dynamics of the channel in membrane and membrane-mimetic media.
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Affiliation(s)
- Devaki A Kelkar
- Centre for Cellular and Molecular Biology, Uppal Road, Hyderabad 500 007, India
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41
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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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Cheng MH, Mamonov AB, Dukes JW, Coalson RD. Modeling the fast gating mechanism in the ClC-0 chloride channel. J Phys Chem B 2007; 111:5956-65. [PMID: 17487993 DOI: 10.1021/jp063993h] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
A simplified three-dimensional model ClC-0 chloride channel is constructed to couple the permeation of Cl- ions to the motion of a glutamate side chain that acts as the putative fast gate in the ClC-0 channel. The gate is treated as a single spherical particle attached by a rod to a pivot point. This particle moves in a one-dimensional arc under the influence of a bistable potential, which mimics the isomerization process by which the glutamate side chain moves from an open state (not blocking the channel pore) to a closed state (blocking the channel pore, at a position which also acts as a binding site for Cl- ions moving through the channel). A dynamic Monte Carlo (DMC) technique is utilized to perform Brownian dynamics simulations to investigate the dependence of the gate closing rate on both internal and external chloride concentration and the gate charge as well. To accelerate the simulation of gate closing to a time scale that can be accommodated with current methodology and computer power, namely, microseconds, parameters that govern the motion of the bare gate (i.e., in the absence of coupling to the permeating ions) are chosen appropriately. Our simulation results are in qualitative agreement with experimental observations and consistent with the "foot-in-the-door" mechanism (Chen et al. J. Gen. Physiol. 2003, 122, 641; Chen and Miller J. Gen. Physiol. 1996, 108, 237), although the absolute time scale of gate closing in the real channel is much longer (millisecond time scale). A simple model based on the fractional occupation probability of the Cl- binding site that is ultimately blocked by the fast gate suggests straightforward scalability of simulation results for the model channel considered herein to experimentally realistic time scales.
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Affiliation(s)
- Mary H Cheng
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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Baştuğ T, Kuyucak S. Free energy simulations of single and double ion occupancy in gramicidin A. J Chem Phys 2007; 126:105103. [PMID: 17362089 DOI: 10.1063/1.2710267] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Simultaneous occupancy of the two binding sites in gramicidin A by monovalent cations is a well known property of this channel, but the energetic feasibility of this process in molecular dynamics simulations has not been established so far. Here the authors study the energetics of single and double ion occupancy in gramicidin A by constructing the potential of mean force for single and pair of cations. As representatives of small and large ions, they consider both Na+ and K+ ions in the calculations. Binding constants of ions are estimated from the free energy profiles. Comparisons with the experimental results indicate 3-4 kT discrepancy in the binding energies. They also study the coordination of the ions in their respective binding sites and the dynamic behavior of the channel water during the double ion binding process.
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Affiliation(s)
- Turgut Baştuğ
- School of Physics, University of Sydney, New South Wales 2006, Australia
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Baştuğ T, Patra SM, Kuyucak S. Molecular dynamics simulations of gramicidin A in a lipid bilayer: From structure–function relations to force fields. Chem Phys Lipids 2006; 141:197-204. [PMID: 16600199 DOI: 10.1016/j.chemphyslip.2006.02.012] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2005] [Accepted: 02/20/2006] [Indexed: 10/24/2022]
Abstract
Molecular dynamics simulations of membrane proteins have become a popular tool for studying their dynamic features, which are not easily accessible by experiments. Whether the force fields developed for globular proteins are adequate this purpose is an important question that is often glossed over. Here we determine the permeation properties of potassium ions in the gramicidin A channel in a lipid bilayer from free energy simulations, and compare the results to experimental data. In particular, we check the dependence of the free energy barriers ions face at the channel center on the membrane size. The results indicate that there is a serious problem with the current rigid force fields independent of the membrane size, and new, possibly polarizable, force fields need to be developed to resolve this problem.
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Affiliation(s)
- Turgut Baştuğ
- School of Physics, University of Sydney, NSW, Australia
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Krishnamurthy V, Chung SH. Adaptive Brownian Dynamics Simulation for Estimating Potential Mean Force in Ion Channel Permeation. IEEE Trans Nanobioscience 2006; 5:126-38. [PMID: 16805109 DOI: 10.1109/tnb.2006.875035] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Ion channels are biological nanotubes formed by large protein molecules in the cell membrane. This paper presents a novel multiparticle simulation methodology, which we call adaptive controlled Brownian dynamics, for estimating the force experienced by a permeating ion at each discrete position along the ion-conducting pathway. The profile of this force, commonly known as the potential of mean force, results from the electrostatic interactions between the ions in the conduit and all the charges carried by atoms forming the channel the protein, as well as the induced charges on the protein wall. The current across the channel is solely determined by the potential of mean force encountered by the permeant ions. The simulation algorithm yields consistent estimates of this profile. The algorithm operates on an angstrom unit spatial scale and femtosecond time scale. Numerical simulations on the gramicidin ion channel show that the algorithm yields the potential of mean force profile that accurately reproduces experimental observations.
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Affiliation(s)
- Vikram Krishnamurthy
- Department of Electrical and Computer Engineering, University of British Columbia, Vancouver V6T 1Z4, Canada.
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Allen TW, Andersen OS, Roux B. Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields. Biophys J 2006; 90:3447-68. [PMID: 16500984 PMCID: PMC1440729 DOI: 10.1529/biophysj.105.077073] [Citation(s) in RCA: 118] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2005] [Accepted: 02/06/2006] [Indexed: 11/18/2022] Open
Abstract
We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.
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Affiliation(s)
- Toby W Allen
- Department of Chemistry, University of California at Davis, 95616, USA.
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Allen TW, Andersen OS, Roux B. Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels. Biophys Chem 2006; 124:251-67. [PMID: 16781050 DOI: 10.1016/j.bpc.2006.04.015] [Citation(s) in RCA: 137] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2006] [Revised: 04/26/2006] [Accepted: 04/27/2006] [Indexed: 11/29/2022]
Abstract
Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.
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Affiliation(s)
- Toby W Allen
- Department of Chemistry, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA.
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Mamonov AB, Kurnikova MG, Coalson RD. Diffusion constant of K+ inside Gramicidin A: a comparative study of four computational methods. Biophys Chem 2006; 124:268-78. [PMID: 16797116 PMCID: PMC2266632 DOI: 10.1016/j.bpc.2006.03.019] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2005] [Accepted: 03/25/2006] [Indexed: 10/24/2022]
Abstract
The local diffusion constant of K(+) inside the Gramicidin A (GA) channel has been calculated using four computational methods based on molecular dynamics (MD) simulations, specifically: Mean Square Displacement (MSD), Velocity Autocorrelation Function (VACF), Second Fluctuation Dissipation Theorem (SFDT) and analysis of the Generalized Langevin Equation for a Harmonic Oscillator (GLE-HO). All methods were first tested and compared for K(+) in bulk water--all predicted the correct diffusion constant. Inside GA, MSD and VACF methods were found to be unreliable because they are biased by the systematic force exerted by the membrane-channel system on the ion. SFDT and GLE-HO techniques properly unbias the influence of the systematic force on the diffusion properties and predicted a similar diffusion constant of K(+) inside GA, namely, ca. 10 times smaller than in the bulk. It was found that both SFDT and GLE-HO methods require extensive MD sampling on the order of tens of nanoseconds to predict a reliable diffusion constant of K(+) inside GA.
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Affiliation(s)
- Artem B. Mamonov
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, United States
| | - Maria G. Kurnikova
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15260, United States
| | - Rob D. Coalson
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, United States
- * Corresponding author. Tel.: +1 412 624 8261; fax: +1 412 624 8301. E-mail address: (R.D. Coalson)
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