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

Abstract

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 (Mol. Phys. 1982, 45, 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. (J. Chem. Phys. 2006, 125, 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 .

Multiscale analysis of the effect of surface charge pattern on a nanopore’s rectification and selectivity properties: From all-atom model to Poisson-Nernst-Planck

“…Transport can be simulated directly using MD, Brownian Dynamics (BD) [70,71,72,73,74], or Dynamic Monte Carlo (DMC) [75,76,77], or computed with a transport equation. Direct simulation of ionic transport in the explicit-and implicit-water frameworks are done by MD and BD, respectively, by solving the Newton and the Langevin equations of motion, respectively.…”

Coulomb blockade model of permeation and selectivity in biological ion channels

“…The ions' motion through a channel can be described as an electro-diffusion process and investigated through Brownian dynamics simulations [15,30,44,45,57,[70][71][72][73] of the ionic trajectories. Taking account of the singlefiling required by electrostatics, we can solve the over-damped, time-discretized, Langevin equation numerically.…”

“…However, a multi-scale analysis is still needed [40][41][42] to build up a full picture. Self-consistent electrostatic and Brownian dynamics simulations [15,30,[43][44][45] describe ionic motion as an electro-diffusion process, leading to fast and direct estimation of the currents under non-equilibrium conditions. Such simulations have shown very clearly that the permeation and selectivity features of many channels are defined by just the basic electrostatics of narrow waterfilled channels, rather than by the details of the channel structures themselves.…”

Selecting Ions by Size in a Calcium Channel: The Ryanodine Receptor Case Study

“…Moreover, our 1D DFT RyR profiles are very similar to cross-sectional averages of full 3D simulations (Dezs} o Boda, University of Pannonia, personal communication, 2014), so it is probable that the 1D Nernst-Planck equation used here is applicable. However, more studies on crowded channels should be done, which is work we plan to continue (64)(65)(66).…”