A second-order algorithm for the simulation of the Brownian dynamics of macromolecular models

Abstract

Most recent works on Brownian dynamics simulation employ a first-order algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)]. In this work we propose the use of a second-order algorithm in which the step is a combination of two first-order steps, like in the second-order Runge–Kutta method for differential equations. Although the computer time per step is roughly doubled, the second-order algorithm is more efficient than the previous one because a given accuracy in the results can be achieved with less than half the number of steps. The new algorithm also allows for longer time steps without divergence. The advantage of the new procedure is illustrated in the simulation of four macromolecular systems: A quasirigid dumbbell, a semiflexible trumbbell, a semiflexible hinged rod, and a Gaussian polymer chain.

Diffusion of a ring polymer in good solution via the Brownian dynamics with no bond crossing

“…Here k B denotes the Boltzmann constant. We employ the predictor-corrector version [20] of the Ermak-McCammon algorithm [21] for generating the time evolution of a ring polymer in solution. The details are given in Appendix A.…”

“…In the paper we have simulated linear and ring polymers in a good solvent with hydrodynamic interaction by the revised version of the Brownian dynamics [21] with respect to the first-order predictor-corrector [20]. Let us explain the original version of the Brownian dynamics [21].…”

“…Here we note that dimensionless parameters and variables are obtained by dividing length, time and energy by b, ζb 2 /kT and kT , respectively. The first-order predictor-corrector version [20] Here R j obey the Gaussian distribution where the average value is zero and the variance-covariance is given by the following: .10) …”

Internal motion of supercoiled DNA: brownian dynamics simulations of site juxtaposition

“…We used the second-order BD algorithm (Iniesta & Garcia de la Torre, 1990) in which the chain displacement during a time interval Át is calculated in two steps. If r n i is a current position of bead i, an auxiliary position of the bead, r Ä n 1 i , is calculated according to the ®rst-order algorithm of Ermak & McCammon (1978):…”

On Algorithms for Brownian Dynamics Computer Simulations

“…Algorithms along this line has been proposed e.g., by Helfand [3], Iniesta and Torre [4], and recently one rigorously developed for the one-variable case by Honeycutt [5], All these methods, like the deterministic Runge-Kutta methods, require more than one evaluation of the particle force per time step, which clearly reduces its efficiency. From the other hand they employ larger time step and it has been argued that stochastic Runge-Kutta (SRK) approach gives, more accurate results than the conventional BD (for the same amount of computer time) [4].…”