Analysis and estimation of time step sizes and stiffness parameters for efficient simulations of macromolecules with hydrodynamic interactions

Abstract

Recent studies have shown the importance of using highly resolved models for Brownian Dynamics (BD) simulations of long macromolecules. For computational efficiency, such models use stiff springs to mimic a single Kuhn step and use a single-step semi-implicit (SS) scheme. Somewhat unexpectedly, time step sizes for such a single-step method need to be reduced with increasing chain size and level of hydrodynamic interactions (HIs), for good convergence. The conventional predictor–corrector (PC) method works reasonably well but remains computationally slow, owing to multiple iterations per time step to convergence. In this study, we reveal how the time step size for the much faster SS method is tied to the physics of the problem. Using simple physical principles, we derive an analytical estimate of the upper limit on the time step size for given levels of HI, chain size, and stiffness of connecting springs. Detailed BD simulations at equilibrium and in flow fields highlight the success of our analytical estimate. We also provide a lower limit on spring stiffness parameter such that it remains effectively rigid and successfully mimics a Kuhn step. Our investigations show that the resulting BD simulations using our estimated time step size in the SS scheme are significantly faster than the conventional PC technique. The analysis presented here is expected to be useful in general for any type of simulations of macromolecules, with or without flow fields, owing to deep connections with the underlying physics.