Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations

Baker, Kristy Z.; Chen, Duan; Cai, Wei

doi:10.4208/cicp.130315.310815a

Cited by 7 publications

(2 citation statements)

References 35 publications

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“…However, the major drawback of the explicit method is the extremely large number of degree of freedom for the system, so the computation remains very expensive even with contemporary computer powers due to the necessarily small time step (10 −15 seconds) versus the ion permeation time scale (10 −6 seconds). Some important ion channel models in MD are referred to Baker et al (2016), Dai & Zhou (2014), Heymann et al (2013), Im & Roux (2002), Lin et al (2013), Marx & Hutter (2000), Roux (2002), Roux et al (2004), Schumaker et al (2000). Specifically, gating motion of ion channels, and their interactions between transmembrane were studied in Dai et al (2015), Dai & Zhou (2014), Heymann et al (2013), Jensen et al (2012a).…”

Section: Viiconcluding Remarks 27 I Introductionmentioning

confidence: 99%

A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge Transport ☆

Chen

Wei

2017

Reference Module in Life Sciences

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The molecular mechanism of ion channel gating and substrate modulation is elusive for many voltage gated ion channels, such as eukaryotic sodium ones. The understanding of channel functions is a pressing issue in molecular biophysics and biology. Mathematical modeling, computation and analysis of membrane channel charge transport have become an emergent field and give rise to significant contributions to our understanding of ion channel gating and function. This review summarizes recent progresses and outlines remaining challenges in mathematical modeling, simulation and analysis of ion channel charge transport. One of our focuses is the Poisson-Nernst-Planck (PNP) model and its generalizations. Specifically, the basic framework of the PNP system and some of its extensions, including size effects, ion-water interactions, coupling with density functional theory and relation to fluid flow models. A reduced theory, the PoissonBoltzmann-Nernst-Planck (PBNP) model, and a differential geometry based ion transport model are also discussed. For proton channel, a multiscale and multiphysics Poisson-Boltzmann-Kohn-Sham (PBKS) model is presented. We show that all of these ion channel models can be cast into a unified variational multiscale framework with a macroscopic continuum domain of the solvent and a microscopic discrete domain of the solute. The main strategy is to construct a total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation and chemical potential related energies. Using the Euler-Lagrange variation, the coupled PNP equations and other transport equations are derived, whose solutions lead to the minimization of the total free energy and explicit profiles of electrostatic potential and densities of charge species. Current computational algorithms and tools for numerical simulations and results from mathematical analysis of ion channel systems are also surveyed.

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Section: Viiconcluding Remarks 27 I Introductionmentioning

confidence: 99%

A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge Transport ☆

Chen

Wei

2017

Reference Module in Life Sciences

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“…However, at the atomic scale, these systems have intractable numbers of degrees of freedom. Multiscale modeling and analysis using quantum mechanics (QM), molecular mechanics (MM), and continuum mechanics (CM) offer an effective reduction in their dimensionality [12,13,14]. PDEs (e.g., Schrodinger equation, Poisson-Boltzmann equation, elasticity equation etc.…”

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confidence: 99%

Mathematics at the eve of a historic transition in biology

Wei

2017

Computational and Mathematical Biophysics

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Fractional Poisson–Nernst–Planck Model for Ion Channels I: Basic Formulations and Algorithms

Chen

2017

Bull Math Biol

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In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

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Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations

Cited by 7 publications

References 35 publications

A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge Transport ☆

A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge Transport ☆

Mathematics at the eve of a historic transition in biology

Fractional Poisson–Nernst–Planck Model for Ion Channels I: Basic Formulations and Algorithms

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