Improving the efficiency of BD algorithms for biological systems simulations

Abstract

In this work, an error analysis methodology is applied to the study of various integration schemes used in Brownian Dynamics simulations of ion channels. Three algorithms have been compared for the integration of the full Langevin Equation [1]. A first-order Euler scheme [2], the Verlet-like algorithm proposed by [3], and a novel Predictor/Corrector (PC) scheme [4] have been implemented and analyzed using our assessment methodology [5]. Our results show that a significant increase in the integration timestep, and a subsequent reduction in computational cost and improvement in efficiency, can be achieved with the second order Verlet-like and PC schemes, while maintaining an excellent accuracy for the description of both structure and dynamics of the electrolyte solution. This work extends the analysis developed in [5] to dynamic properties of the solution as well as structural aspects of inhomogeneous systems such as a lipid membrane.

Brownian dynamics simulation of charge transport in ion channels

“…The integration scheme is chosen to obtain the longest timestep possible while keeping the system energetically stable. Several schemes have been implemented, with varying complexities and merits in terms of accuracy and timestep requirements [3]. In this work, the second-order Verlet-like algorithm initially proposed by van Gunsteren and Berendsen [21] is used.…”

“…Further work was conducted [3] to validate an improved implementation of the Verlet-like integration scheme used in this work. The bulk solution was simulated with an externally applied voltage to compute conductivity and the results were compared to experimental conductivity measurements, showing the possibility of using free-flight timesteps in the 100 fs range while maintaining excellent accuracy for the dynamic transport properties of the ions.…”

“…In the following section, the working principles of the BD simulation approach are introduced, and a description of the system model is offered. References will be made to previous work [2,3] conducted to validate the simulation model for electrolyte solutions and membranes in both equilibrium and dynamic settings. The subsequent section will describe the properties of the channels of interest to this work, and the simulation methodology.…”

Incorporation of Inhomogeneous Ion Diffusion Coefficients into Kinetic Lattice Grand Canonical Monte Carlo Simulations and Application to Ion Current Calculations in a Simple Model Ion Channel

“…Kinetic or dynamic lattice Monte Carlo (KLMC or DLMC) simulation algorithms [1][2][3][4] and Brownian dynamics (BD) simulation methods [5][6][7][8] are useful tools for studying ion transport in complex systems such as an ion channel. [9][10][11][12] The molecular dynamics (MD) simulation method, [13][14][15][16] which can describe ion transport at an atomistic level, is computationally too demanding to reach the time scales needed for ion transport in ion channels.…”

“…Kinetic or dynamic lattice Monte Carlo (KLMC or DLMC) simulation algorithms − and Brownian dynamics (BD) simulation methods − are useful tools for studying ion transport in complex systems such as an ion channel. − The molecular dynamics (MD) simulation method, − which can describe ion transport at an atomistic level, is computationally too demanding to reach the time scales needed for ion transport in ion channels. On the other hand, Poisson−Nernst−Planck (PNP) theory, − based on a dielectric continuum model, can be used to calculate ion currents at necessary time scales, but several important issues such as finite ion size and correlation effects are ignored in that theory.…”