A generalized Langevin algorithm for studying permeation across biological ion channels

Gordon, Dan; Krishnamurthy, Vikram; Chung, Shin-Ho

doi:10.1080/00268970802169145

Cited by 17 publications

(11 citation statements)

References 17 publications

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“…Such behavior has already been mentioned and explained in the literature: the velocity autocorrelation function for the ad-atom shows both a ballistic and a diffusive regime, the width, roughlyτ R of the balistic regime, is related tõ τ c . 13 At odds, when the stochastic force is large (D = 0.01), the possibility for the ad-atom to cross an effective poten-tial barrier on the simulation time scale increases withτ c : we report in Fig. 6a the trajectories of the ad-atom as a function of time for the three different mentioned values ofτ c .…”

Section: Retarded Effectsmentioning

confidence: 99%

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Unidimensional model of adatom diffusion on a substrate submitted to a standing acoustic wave. II. Solutions of the adatom motion equation

2012

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The ad-atom dynamic equation, a Langevin type equation is analyzed and solved using some non-linear analytical and numerical tools. We noticeably show that the effect of the surface acoustic wave is to induce an effective potential that governs the diffusion of the ad-atom: the minima of this effective potential correspond to the preferential sites in which the ad-atom spends more time. The strength of this effective potential is compared to the destructuring role of the thermal diffusion and to the crystalline potential induced by the substrate.

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Section: Retarded Effectsmentioning

confidence: 99%

“…23 while the integral of the friction term including the memory kernel are calculated using the algorithm given in Ref. 13.…”

Section: Retarded Effectsmentioning

confidence: 99%

Unidimensional model of adatom diffusion on a substrate submitted to a standing acoustic wave. II. Solutions of the adatom motion equation

2012

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“…The nonlinear generalized Langevin equation is solved using an extension of the leapfrog method as outlined in Gordon et al 34 (further detail is also provided by Nilsson and Padró 35 and Wan et al 36 ).…”

Section: Distributional Molecular Dynamicsmentioning

confidence: 99%

Synthetic cation-selective nanotube: Permeant cations chaperoned by anions

Hilder

Gordon

Chung

2011

The Journal of Chemical Physics

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The ability to design ion-selective, synthetic nanotubes which mimic biological ion channels may have significant implications for the future treatment of bacteria, diseases, and as ultrasensitive biosensors. We present the design of a synthetic nanotube made from carbon atoms that selectively allows monovalent cations to move across and rejects all anions. The cation-selective nanotube mimics some of the salient properties of biological ion channels. Before practical nanodevices are successfully fabricated it is vital that proof-of-concept computational studies are performed. With this in mind we use molecular and stochastic dynamics simulations to characterize the dynamics of ion permeation across a single-walled (10, 10), 36 Å long, carbon nanotube terminated with carboxylic acid with an effective radius of 5.08 Å. Although cations encounter a high energy barrier of 7 kT, its height is drastically reduced by a chloride ion in the nanotube. The presence of a chloride ion near the pore entrance thus enables a cation to enter the pore and, once in the pore, it is chaperoned by the resident counterion across the narrow pore. The moment the chaperoned cation transits the pore, the counterion moves back to the entrance to ferry another ion. The synthetic nanotube has a high sodium conductance of 124 pS and shows linear current-voltage and current-concentration profiles. The cation-anion selectivity ratio ranges from 8 to 25, depending on the ionic concentrations in the reservoirs.

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“…In this step, the simulation is carried out by solving the nonlinear generalized Langevin equation, as described in other papers. 17,33,34 However, there are several complications, for example, involving the boundary conditions for simulation space, that also need to be dealt with. 35 Our stochastic dynamics setup for ion channels is shown schematically in Fig.…”

Section: B Carrying Out the Distributional MD Simulationmentioning

confidence: 99%

“…In practice, the assumption often works, but the interpretation of when and why this is the case is open to question. It is known that system memory may in some circumstances lead to different barrier crossing rates and other dynamics, 16,17 and we aim to develop a fairly general theory that will automatically take such considerations into account. The aim of reproducing the distribution of MD trajectories leads us to refer to this approach as "distributional MD."…”

Section: Introductionmentioning

confidence: 99%

Generalized Langevin models of molecular dynamics simulations with applications to ion channels

Gordon

Krishnamurthy

Chung

2009

The Journal of Chemical Physics

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We present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as "distributional molecular dynamics," and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MD-derived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a current-voltage curve closely matching experimental results.

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A generalized Langevin algorithm for studying permeation across biological ion channels

Cited by 17 publications

References 17 publications

Unidimensional model of adatom diffusion on a substrate submitted to a standing acoustic wave. II. Solutions of the adatom motion equation

Unidimensional model of adatom diffusion on a substrate submitted to a standing acoustic wave. II. Solutions of the adatom motion equation

Synthetic cation-selective nanotube: Permeant cations chaperoned by anions

Generalized Langevin models of molecular dynamics simulations with applications to ion channels

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