Ion Flow through Narrow Membrane Channels: Part II

Barcilon, Victor; Chen, D.-P.; Eisenberg, Robert S.

doi:10.1137/0152081

Cited by 149 publications

(141 citation statements)

References 10 publications

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“…Subscripts x, y or z will be dropped throughout: when necessary it will be explicitly noted in the text which direction is relevant. (8) where is the normalized VACF of the ion. Laplace transforming this equation with gives:…”

Section: Theorymentioning

confidence: 99%

“…With the availability of detailed atomistic structures of several ion channels (Gramicidin A (GA) [1], KcsA potassium channel [2], α-hemolysin [3], ClC chloride channel [4]) it has become feasible to do accurate theoretical modeling of ion currents in order to understand the mechanisms of ion transport through biological channels. At present, the most popular methods of ion current modeling are PoissonNernst-Planck (PNP) [5][6][7][8][9][10], Brownian Dynamics (BD) [11][12][13][14][15][16] and Non-equilibrium Molecular dynamics (NEMD) [17][18][19]. Of these methods PNP is the most primitive but fastest method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…Of course, the relative importance of surface phenomena also increases with miniaturization. Micro-electrochemical systems of current interest include ion channels in biological membranes [3,4,5] and thin-film batteries [6,7,8,9, 10], which could revolutionize the design of modern electronics with distributed on-chip power sources. In the latter context, the internal resistance of the battery is related to the nonlinear current-voltage characteristics of the separator, consisting of a thin-film electrolyte (solid, liquid, or gel) sandwiched between flat electrodes and interfacial layers where Faradaic electron-transfer reactions occur [11].…”

mentioning

confidence: 99%

Current-Voltage Relations for Electrochemical Thin Films

Bazant¹,

Chu²,

Bayly³

2005

SIAM J. Appl. Math.

266

393

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Abstract. The dc response of an electrochemical thin film, such as the separator in a microbattery, is analyzed by solving the Poisson-Nernst-Planck equations, subject to boundary conditions appropriate for an electrolytic/galvanic cell. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer, which mediates Faradaic reactions with nonlinear Butler-Volmer kinetics. Analytical results are obtained by matched asymptotic expansions in the limit of thin double layers and compared with full numerical solutions. The analysis shows that (i) decreasing the system size relative to the Debye screening length decreases the voltage of the cell and allows currents higher than the classical diffusion-limited current; (ii) finite reaction rates lead to the important possibility of a reaction-limited current; (iii) the Stern-layer capacitance is critical for allowing the cell to achieve currents above the reaction-limited current; and (iv) all polarographic (current-voltage) curves tend to the same limit as reaction kinetics become fast. Dimensional analysis, however, shows that "fast" reactions tend to become "slow" with decreasing system size, so the nonlinear effects of surface polarization may dominate the dc response of thin films.Key words. Poisson-Nernst-Planck equations, electrochemical systems, thin films, polarographic curves, Butler-Volmer reaction kinetics, Stern layer, surface capacitance. AMS subject classifications. 34B08, 34B16, 34B60, 34E05, 80A30Introduction. Micro-electrochemical systems pose interesting problems for applied mathematics because traditional "macroscopic" approximations of electroneutrality and thermal equilibrium [1], which make the classical transport equations more tractable [2], break down at small scales, approaching the Debye screening length. Of course, the relative importance of surface phenomena also increases with miniaturization. Micro-electrochemical systems of current interest include ion channels in biological membranes [3,4,5] and thin-film batteries [6,7,8,9, 10], which could revolutionize the design of modern electronics with distributed on-chip power sources. In the latter context, the internal resistance of the battery is related to the nonlinear current-voltage characteristics of the separator, consisting of a thin-film electrolyte (solid, liquid, or gel) sandwiched between flat electrodes and interfacial layers where Faradaic electron-transfer reactions occur [11]. Under such conditions, the internal resistance is unlikely to be simply constant, as is usually assumed.Motivated by the application to thin-film batteries, here we revisit the classical problem of steady conduction between parallel, flat electrodes, studied by Nernst [12] and Brunner [13, 14] a century ago. As in subsequent studies of liquid [15,16] and solid [17,18] electrolytes, we do not make Nernst's assumption of bulk electroneutrality and work instead with the Poisson-Nernst-Planck (PNP) equations, allowing for diffuse charge in solution [1...

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“…Since the classical papers by Planck [1] and Goldman [2], much work has been done on finding steady-state solutions of the NPP equations, e.g. modeling of ion transport through liquid junctions [3], protein channels [4,5], and synthetic nanopores [6,7]. However, very little is known about the time-dependent behavior of electrodiffusion systems.…”

Section: Numerical Solutions Of the Full Set Of The Time-dependent Nementioning

confidence: 99%

Numerical simulations of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion on a simple ion channel.

Valent¹

2012

JCIS

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The concept of electrodiffusion based on the Nernst-Planck equations for ionic fluxes coupled with the Poisson equation expressing relation between gradient of the electric field and the charge density is widely used in many areas of natural sciences and engineering. In contrast to the steady-state solutions of the Nernst-Planck-Poisson (abbreviated as NPP or PNP) equations, little is known about the time-dependent behavior of electrodiffusion systems. We present numerical solutions of an NPP system modeling dynamics in the interior of a membrane channel containing an electrolyte after a potential jump at one side of the membrane (voltage-clamp). The NPP equations were solved using the VLUGR2 solver based on an adaptive-grid finite-difference method with an implicit timestepping. The used approach allows for solving the full set of the NPP equations without approximations such as the electroneutrality or constant-field assumptions. Calculations reveal interesting nonlinear time evolution of the ionic concentrations and potential.

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Ion Flow through Narrow Membrane Channels: Part II

Cited by 149 publications

References 10 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

Current-Voltage Relations for Electrochemical Thin Films

Numerical simulations of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion on a simple ion channel.

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