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      Non-Equilibrium Dynamics Contribute to Ion Selectivity in the KcsA Channel

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          Abstract

          The ability of biological ion channels to conduct selected ions across cell membranes is critical for the survival of both animal and bacterial cells. Numerous investigations of ion selectivity have been conducted over more than 50 years, yet the mechanisms whereby the channels select certain ions and reject others are not well understood. Here we report a new application of Jarzynski’s Equality to investigate the mechanism of ion selectivity using non-equilibrium molecular dynamics simulations of Na + and K + ions moving through the KcsA channel. The simulations show that the selectivity filter of KcsA adapts and responds to the presence of the ions with structural rearrangements that are different for Na + and K +. These structural rearrangements facilitate entry of K + ions into the selectivity filter and permeation through the channel, and rejection of Na + ions. A mechanistic model of ion selectivity by this channel based on the results of the simulations relates the structural rearrangement of the selectivity filter to the differential dehydration of ions and multiple-ion occupancy and describes a mechanism to efficiently select and conduct K +. Estimates of the K +/Na + selectivity ratio and steady state ion conductance for KcsA from the simulations are in good quantitative agreement with experimental measurements. This model also accurately describes experimental observations of channel block by cytoplasmic Na + ions, the “punch through” relief of channel block by cytoplasmic positive voltages, and is consistent with the knock-on mechanism of ion permeation.

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          Most cited references39

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          Empirical force fields for biological macromolecules: overview and issues.

          Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed. Copyright 2004 Wiley Periodicals, Inc.
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            Adaptive biasing force method for scalar and vector free energy calculations.

            In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.
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              Energetics of ion conduction through the K+ channel.

              K+ channels are transmembrane proteins that are essential for the transmission of nerve impulses. The ability of these proteins to conduct K+ ions at levels near the limit of diffusion is traditionally described in terms of concerted mechanisms in which ion-channel attraction and ion-ion repulsion have compensating effects, as several ions are moving simultaneously in single file through the narrow pore. The efficiency of such a mechanism, however, relies on a delicate energy balance-the strong ion-channel attraction must be perfectly counterbalanced by the electrostatic ion-ion repulsion. To elucidate the mechanism of ion conduction at the atomic level, we performed molecular dynamics free energy simulations on the basis of the X-ray structure of the KcsA K+ channel. Here we find that ion conduction involves transitions between two main states, with two and three K+ ions occupying the selectivity filter, respectively; this process is reminiscent of the 'knock-on' mechanism proposed by Hodgkin and Keynes in 1955. The largest free energy barrier is on the order of 2-3 kcal mol-1, implying that the process of ion conduction is limited by diffusion. Ion-ion repulsion, although essential for rapid conduction, is shown to act only at very short distances. The calculations show also that the rapidly conducting pore is selective.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2014
                17 January 2014
                : 9
                : 1
                : e86079
                Affiliations
                [1 ]Department of Physics and Astronomy, University of Southern California, Los Angeles, California, United States of America
                [2 ]Department of Biomedical Sciences, Cedars Sinai Medical Center, Los Angeles, California, United States of America
                [3 ]Department of Physiology and Biophysics, University of Southern California, Keck School of Medicine, Los Angeles, California, United States of America
                University of Calgary, Canada
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: VN DS RAF. Performed the experiments: VN DS. Analyzed the data: VN DS RAF. Contributed reagents/materials/analysis tools: VN DS SH RAF. Wrote the paper: RAF VN DS SH.

                Article
                PONE-D-13-44156
                10.1371/journal.pone.0086079
                3895005
                d99fb76d-698e-4d0e-b1ac-a38c0c823849
                Copyright @ 2014

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 28 October 2013
                : 9 December 2013
                Page count
                Pages: 12
                Funding
                VN was supported by grant DOE-FG03-01ER45908 to SH. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology
                Biochemistry
                Metabolism
                Biological Transport
                Proteins
                Ion Channels
                Protein Structure
                Transmembrane Transport Proteins
                Biophysics
                Biophysics Simulations
                Computational Biology
                Macromolecular Structure Analysis
                Protein Structure
                Neuroscience
                Cellular Neuroscience
                Ion Channels
                Chemistry
                Computational Chemistry
                Molecular Dynamics
                Physics
                Biophysics
                Biophysics Simulations

                Uncategorized
                Uncategorized

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