A Combined Molecular Dynamics and Diffusion Model of Single Proton Conduction through Gramicidin

Schumaker, Mark F.; Pomès, Régis; Roux, Benoı̂t

doi:10.1016/s0006-3495(00)76522-2

Cited by 65 publications

(89 citation statements)

References 40 publications

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“…In the 10<s<30 range it has a relatively linear shape and bends up at s>30 ps −1 . We found that at very small s the smooth shape of D̂ (s) function is corrupted by a singularity near s=0, as has been observed previously [42]. We observed that the location of the singularity depends on the amount of MD sampling: longer simulations shifted the singularity to smaller s. For a 30 ns MD simulation the onset of the singularity went down to s=0.05 ps −1 .…”

Section: Calculation Of Diffusion Constant Of K + In Bulk Watersupporting

confidence: 83%

Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods

Mamonov

Kurnikova

Coalson

2006

Biophysical Chemistry

124

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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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Section: Calculation Of Diffusion Constant Of K + In Bulk Watersupporting

confidence: 83%

Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods

Mamonov

Kurnikova

Coalson

2006

Biophysical Chemistry

124

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“…(120) satisfies the condition of detailed balance under equilibrium conditions in the absence of net flux, and the stochastic evolution of the system obeys the multi-dimensional Smoluchowski diffusion Eq. (10) as dz becomes increasingly small (McGill & Schumaker, 1996;Schumaker et al 2000Schumaker et al , 2001. The resulting equations are closely related to the coupled multi-ion diffusion theory that was formulated by Stephan et al (1983).…”

Section: Discrete-state Markov Chainsmentioning

confidence: 71%

“…We will review the single-ion NP model (Lewitt, 1986 ;McGill & Schumaker, 1996), which is of particular interest because it can be solved analytically. We will also describe framework models based on continuous time discrete-state Markov chains, which can handle multi-ion pores (McGill & Schumaker, 1996;Schumaker et al 2000Schumaker et al , 2001Bernèche & Roux, 2003). Such framework models are the most convenient and powerful approaches to incorporate the information extracted from MD simulations, such as the PMF and the diffusion coefficient.…”

Section: From MD To I-v : a Practical Guidementioning

confidence: 99%

Theoretical and computational models of biological ion channels

Roux

Allen

Bernèche

et al. 2004

Quart. Rev. Biophys.

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387

419

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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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“…The stochastic Brownian motion of the multiion system was implemented as a continuous-time Markov chain with discrete states corresponding to the ion positions, and the state-to-state random walk was constructed by generating exponentially distributed random survival times. Such a Markov random walk satisfies the condition of detailed balance under equilibrium conditions in the absence of net flux, and the stochastic evolution of the system obeys a multidimensional Smulochowsky (Nernst-Planck) diffusion equation as ␦Z becomes increasingly small (30)(31)(32). The forward and backward transition rates are given by (e.g., for ion 1)…”

Section: Theory and Methodsmentioning

confidence: 99%

A microscopic view of ion conduction through the K+ channel

Bernèche

Roux²

2003

Proc. Natl. Acad. Sci. U.S.A.

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229

260

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Recent results from x-ray crystallography and molecular dynamics free-energy simulations have revealed the existence of a number of specific cation-binding sites disposed along the narrow pore of the K ؉ channel from Streptomyces lividans (KcsA), suggesting that K ؉ ions might literally ''hop'' in single file from one binding site to the next as permeation proceeds. In support of this view, it was found that the ion configurations correspond to energy wells of similar depth and that ion translocation is opposed only by small energy barriers. Although such features of the multiion potential energy surface are certainly essential for achieving a high throughput rate, diffusional and dissipative dynamical factors must also be taken into consideration to understand how rapid conduction of K ؉ is possible. To elucidate the mechanism of ion conduction, we established a framework theory enabling the direct simulation of nonequilibrium fluxes by extending the results of molecular dynamics over macroscopically long times. In good accord with experimental measurements, the simulated maximum conductance of the channel at saturating concentration is on the order of 550 and 360 pS for outward and inward ions flux, respectively, with a unidirectional flux-ratio exponent of 3. Analysis of the ionconduction process reveals a lack of equivalence between the cation-binding sites in the selectivity filter. molecular dynamics ͉ Brownian dynamics ͉ potential of mean force ͉ membrane potential ͉ Poisson-Boltzmann equation P otassium channels are transmembrane proteins that have the ability to conduct K ϩ ions at nearly the diffusion limit while remaining very selective (1). The availability of high-resolution crystallographic structures (2-4), together with the development of sophisticated computer models (5-10), is providing us with a unique opportunity to refine our understanding of these systems at an unprecedented level. Although the complexity of these channels does present a formidable challenge to biomolecular modeling, it is particularly encouraging to note that many of the recent results from molecular dynamics (MD) simulations based on realistic all-atom models have been consistent with the information emerging from higher-resolution structural data (for a recent review, see ref. 11). In particular, the free-energy profile, or potential of mean force (PMF), associated with the position of three K ϩ along the axis of the pore was calculated with umbrella sampling simulations of the K ϩ channel from Streptomyces lividans (KcsA) embedded in a phospholipid membrane with explicit solvent (5). This MD calculation reproduced the four cation-binding sites (S 1 -S 4 ) located in the narrow selectivity filter that were already known from x-ray diffraction data at 3.2-Å resolution (3) and also anticipated the existence of two additional sites (S ext and S 0 ) located on the extracellular side of the channel, which were observed independently in diffraction data at 2.0-Å resolution (2). This result increased the confidence in the abili...

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A Combined Molecular Dynamics and Diffusion Model of Single Proton Conduction through Gramicidin

Cited by 65 publications

References 40 publications

Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods

Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods

Theoretical and computational models of biological ion channels

A microscopic view of ion conduction through the K+ channel

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