Brownian dynamics simulations of ions channels: A general treatment of electrostatic reaction fields for molecular pores of arbitrary geometry

Im, Wonpil; Roux, Benoı̂t

doi:10.1063/1.1390507

Cited by 72 publications

(107 citation statements)

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“…The random chaotic movements of ions through a molecular pore is also affected by processes that are intrinsically dynamical and dissipative. Effective dynamical models, such as the GLE, LE or BD incorporate the influence of such factors into the memory function, friction coefficient c, or diffusion coefficient D. The ion diffusion coefficient at different position inside the pore is a particularly important parameter in a number of theoretical models of permeation (Chiu et al 1993 ;McGill & Schumaker, 1996 ;Kurnikova et al 1999 ;Smith & Sansom, 1999 ;Im et al 2000 ;Allen & Chung, 2001 ;Im & Roux, 2001). The diffusion coefficient is often defined in terms of the average mean-square displacement (MSD) (Einstein, 1926),…”

Section: Friction and Diffusion Coefficient Techniquesmentioning

confidence: 99%

“…These difficulties are circumvented by expressing the ion charge distribution in the simulation region using a set of normalized basis functions (Im & Roux, 2001). Lastly, it should be noted that, while the decomposition described by Eq.…”

Section: The Gcmc/bd Algorithmmentioning

confidence: 99%

“…(125), they are simply superimposed in w sf (r). The contribution of the reaction field to the multi-ion PMF can be expressed as (Im & Roux, 2001)…”

Section: The Gcmc/bd Algorithmmentioning

confidence: 99%

“…In particular, macroscopic continuum electrostatic calculations, in which the polar solvent is represented as a structureless dielectric medium, can help reveal the dominant energetic factors related to ion permeation and, thus, serve to illustrate fundamental principles in a particularly clear fashion (Roux, 1999a ;Roux et al 2000). Brownian dynamics (BD), which consists in integrating stochastic equation of motions describing the displacement of the ions with some effective potential function, generally calculated on the basis of a continuum electrostatic approximation (Cooper et al 1985 ;Chung et al 1998), is also an attractive computational approach for simulating the permeation process over long time-scales without having to treat all the solvent molecules explicitly Im et al 2000 ;Allen & Chung, 2001 ;Im & Roux, 2001 ;Mashl et al 2001 ;Phale et al 2001 ;Burykin et al 2002Burykin et al , 2003. Lastly, there are continuum electrodiffusion theories, such as Poisson-Nernst-Planck (PNP), which attempt to represent average ion fluxes directly in terms of concentration gradient and average electric field (Onsager, 1926(Onsager, , 1927Schuss et al 2001).…”

Section: Introductionmentioning

confidence: 99%

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Theoretical and computational models of biological ion channels

Roux

Allen

Bernèche

et al. 2004

Quart. Rev. Biophys.

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383

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Abstract. The goal of this review is to establish a broad and rigorous theoretical framework to describe ion permeation through biological channels. This framework is developed in the context of atomic models on the basis of the statistical mechanical projection-operator formalism of Mori and Zwanzig. The review is divided into two main parts. The first part introduces the fundamental concepts needed to construct a hierarchy of dynamical models at different level of approximation. In particular, the potential of mean force (PMF) as a configuration-dependent free energy is introduced, and its significance concerning equilibrium and non-equilibrium phenomena is discussed. In addition, fundamental aspects of membrane electrostatics, with a particular emphasis on the influence of the transmembrane potential, as well as important computational techniques for extracting essential information from all-atom molecular dynamics (MD) simulations are described and discussed. The first part of the review provides a theoretical formalism to 'translate ' the information from the atomic structure into the familiar language of phenomenological models of ion permeation. The second part is aimed at reviewing and contrasting results obtained in recent computational studies of three very different channels : the gramicidin A (gA) channel, which is a narrow one-ion pore (at moderate concentration), the KcsA channel from Streptomyces lividans, which is a narrow multi-ion pore, and the outer membrane matrix porin F (OmpF) from Escherichia coli, which is a trimer of three b-barrel subunits each forming wide aqueous multi-ion pores. Comparison with experiments demonstrates that current computational models are approaching semi-quantitative accuracy and are able to provide significant insight into the microscopic mechanisms of ion conduction and selectivity. We conclude that all-atom MD with explicit water molecules can represent important structural features of complex biological channels accurately, including such features as the location of ion-binding sites along the permeation pathway. We finally discuss the broader issue of the validity of ion permeation models and an outlook to the future.

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Section: Friction and Diffusion Coefficient Techniquesmentioning

confidence: 99%

Section: The Gcmc/bd Algorithmmentioning

confidence: 99%

“…(125), they are simply superimposed in w sf (r). The contribution of the reaction field to the multi-ion PMF can be expressed as (Im & Roux, 2001)…”

Section: The Gcmc/bd Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Theoretical and computational models of biological ion channels

Roux

Allen

Bernèche

et al. 2004

Quart. Rev. Biophys.

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383

419

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“…38,39 In general, U A (Z) is dependent on a potential of mean force that, in principle, may be derived from molecular dynamics simulations based on an atomic model of the ion channel VSD. 40 However, in this paper, it is assumed that U A (Z) = U (Z, θ L (Z)) and the rotation θ L (Z) is a linear function of Z between adjacent energy wells. By approximating the potential function U A (Z) by a squarewell potential with minimum displacements of the helix, the sequential translocation of an S4 sensor through a membrane may be represented by transitions between the regions R i .…”

Section: The Activation Of a Voltage Sensormentioning

confidence: 99%

Voltage dependence of a stochastic model of activation of an alpha helical S4 sensor in a K channel membrane

Vaccaro¹

2011

The Journal of Chemical Physics

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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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Crowded Charges in Ion Channels

Eisenberg

2011

Advances in Chemical Physics

129

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Physical Chemistry and Life. Ions in water are the liquid of life. Life occurs almost entirely in 'salt water'. Life began in salty oceans. Animals kept that salt water within them when they moved out of the ocean to drier surroundings. The plasma and blood that surrounds all cells are electrolytes more or less resembling sea water. The plasma inside cells is an electrolyte solution that more or less resembles the sea water in which life began. Water itself (without ions) is lethal to animal cells and damaging for most proteins. Water must contain the right ions in the right amounts if it is to sustain life.Physical chemistry is the language of electrolyte solutions and so physical chemistry, and biology, particularly physiology, have been intertwined since physical chemistry was developed some one hundred fifty years ago. Physiology, of course, was studied by the Greeks some millennia earlier, but the biological role of electrolyte solutions could not be understood until ions were discovered by chemists some 2,000 years later.Physical chemists and biologists come from different traditions that separated for several decades as biologists identified and described the molecules of life. Communication is not easy between a fundamentally descriptive tradition and a fundamentally analytical one. Biologists have now learned to study their well defined systems with physical techniques, of considerable interest to physical chemists. Physical chemists are increasingly interested in spatially inhomogeneous systems with structures on the atomic scale so common in biology. Physical chemists will find it productive to work on well defined systems built by evolution to be reasonably robust, with input output relations insensitive to environmental insults. The overlap in science is clear. The human overlap is harder because the fields have grown independently for some time, and the knowledge base, assumptions, and jargon of the fields do not coincide. Indeed, they sometimes seem disjoint, without overlap.This article deals with properties of ion channels that in my view can be dealt with by 'physics as usual', with much the same tools that physical chemists apply to other systems. Indeed, I introduce and use a tool of physicists-a field theory (and boundary conditions) based on an energy variational approach developed by Chun Liu 141,575,766,806,944 -not too widely used among physical chemists. My goal is to provide the knowledge base, and identify the assumptions, that biologists use in studying ion channels, avoiding jargon. Although we do not know enough to write atomic, detailed physical models of the process by which ions move through channels, rather simple models of selectivity and permeation work quite well in important cases. Those physical models and cases are the main focus of this review because they demonstrate the strong essential link between the traditional treatments of ions in chemical physics, and the biological function of ion channels.At first, ion channels may seem to be an extreme system. They are as smal...

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Brownian dynamics simulations of ions channels: A general treatment of electrostatic reaction fields for molecular pores of arbitrary geometry

Cited by 72 publications

References 44 publications

Theoretical and computational models of biological ion channels

Theoretical and computational models of biological ion channels

Voltage dependence of a stochastic model of activation of an alpha helical S4 sensor in a K channel membrane

Crowded Charges in Ion Channels

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