Claudio Berti

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 (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 .

PACO: PArticle COunting Method To Enforce Concentrations in Dynamic Simulations.

We present PACO, a computationally efficient method for concentration boundary conditions in nonequilibrium particle simulations. Because it requires only particle counting, its computational effort is significantly smaller than other methods. PACO enables Brownian dynamics simulations of micromolar electrolytes (3 orders of magnitude lower than previously simulated). PACO for Brownian dynamics is integrated in the BROWNIES package (www.phys.rush.edu/BROWNIES). We also introduce a molecular dynamics PACO implementation that allows for very accurate control of concentration gradients.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

Particle-Based Simulation of Conductance of Solid-State Nanopores and Ion Channels

A three-dimensional numerical simulation technique based on Brownian Dynamics is presented for simulating ion currents flowing through ion channels and solid-state nanopores under various conditions. This implementation allows to perform simulations on the µ-seconds time scale in order to obtain information on the conductance of the simulated channels. Results regarding ion motion in bulk solution and concerning electrostatic calculation along channel axis for a catenary test pore are presented here. Furthermore, the calculated potential energy profiles and con- ductance of an open-state configuration of KcsA K + channel of Streptomyces Lividans bacterium are presented.

Chapter 4:Non-atomistic Simulations of Ion Channels

Mathematical modeling and numerical simulations are powerful tools for the analysis of the structure–function relation in ion channels. The continuous increase in the number of experimental structures of membrane proteins at high resolution has promoted the development of methods based on full atomistic descriptions of ion channels. However, the computational cost of atomistic simulations is still prohibitively high for a systematic study of conduction in ion channels. This chapter describes simplified models of conductions based on the implicit treatment of solvent molecules. In simplified models of ion channels, only a well-reasoned set of features is explicitly described. Thus, these methods are more than a mere way to increase the computational efficiency. Identifying which features are important, and how they impact on the functional properties, might offer a more profound understanding of the simulated systems. The chapter also discusses how to combine simplified models with atomistic simulations. These multi-scale models are a promising strategy to investigate the structure–function relation in complex biological molecules such as ion channels.

Brownian dynamics simulation of ion channels embedded in silicon membranes for sensor applications

In this work we present a three-dimensional numerical simulation technique for the study of ion permeation through ion channels embedded in silicon membranes, that can be exploited for sensor applications. The results of this work clarify how the charges embedded in the protein forming the ion channel can influence ionic conductance through silicon membrane slabs, controlling the channel conductance and selectivity with respect to ionic species.

Particle-based simulation of electrical transport in discrete-charge nanoscale systems: The electrostatic problem

We present a comparison between two different approaches to solve the electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations.