Steady-State Electrodiffusion from the Nernst–Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst–Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques

Correction to “Simulation of an Electrical Double Layer Model with a Low Dielectric Layer between the Electrode and the Electrolyte”

Correction to “Simulation of an Electrical Double Layer Model with a Low Dielectric Layer between the Electrode and the Electrolyte

Three-Dimensional Brownian Dynamics Simulator for the Study of Ion Permeation through Membrane Pores

A three-dimensional numerical simulator based on Brownian dynamics (BD) for the study of ion transport through membrane pores is presented. Published BD implementations suffer from severe shortcomings in accuracy and efficiency. Such limitations arise largely from (i) the nonrigorous treatment of unphysical ion configurations; (ii) the assumption that ion motion occurs always in the high friction limit, (iii) the inefficient solution of the Poisson equation with dielectric interfaces, and (iv) the inaccurate treatment of boundary conditions for ion concentrations. Here, we introduce a new BD simulator in which these critical issues are addressed, implementing advanced techniques: (i) unphysical ion configurations are managed with a novel retracing technique; (ii) ion motion is evaluated integrating the Langevin equation with the algorithm of van Gunsteren and Berendsen (<i>Mol. Phys.</i> <b>1982</b>, <i>45</i>, 637–647); (iii) dielectric response in the Poisson equation is solved at run time with the Induced Charge Computation (ICC) method of Boda et al. (<i>J. Chem. Phys</i>. <b>2006</b>, <i>125</i>, 034901); and (iv) boundary conditions for ion concentrations are enforced by an accurate Grand Canonical Monte Carlo (GCMC) algorithm. Although some of these techniques have already been separately adopted for the simulation of membrane pores, our tool is the first BD implementation, to our knowledge, that fully retrace ions to avoid unphysical configurations and that computes dielectric interactions at each time step. Most other BD codes have been used on wide channels. Our BD simulator is specifically designed for narrow and crowded ion channels (e.g., L-type calcium channels) where all the aforementioned techniques are necessary for accurate results. In this paper, we introduce our tool, focusing on the implementation and testing of key features and we illustrate its capabilities through the analysis of test cases. The source code is available for download at www.phys.rush.edu/BROWNIES