Efficient Brownian Dynamics Simulation of Single DNA with Hydrodynamic Interactions in Linear Flows

TL;DR

This paper introduces an efficient Brownian dynamics algorithm for simulating single DNA molecules in linear flows, enabling larger time steps and long-term simulations while maintaining accuracy and stability.

Contribution

The authors develop a novel BD simulation method using an integrating factor and Metropolis method, allowing larger time steps and improved efficiency for long-time DNA simulations.

Findings

Numerical results match experimental data and previous simulations.

The method is scalable and parallelizable with fast algorithms.

Enables practical long-time large-scale DNA simulations.

Abstract

The coarse-grained molecular dynamics (MD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the so-called hydrodynamic interactions (HIs). In this paper, an efficient algorithm is proposed to simulate the motion of a single DNA molecule in linear flows. The algorithm utilizes the integraing factor to cope with the effect of the linear flow of the surrounding fluid and applies the Metropolis method (MM) in [N. Bou-Rabee, A. Donev, and E. Vanden-Eijnden, Multiscale Model. Simul. 12, 781 (2014)] to achieve more efficient BD simulation. Thus our method permits much larger time step size than previous methods while still maintaining the stability of the BD simulation, which is advantageous for long-time BD simulation. Our numerical results on $\lambda$-DNA agree very well with both experimental data and previous simulation results. Finally, when combined with fast algorithms such as the fast multipole method which has nearly optimal complexity in the total number of beads, the resulting method is parallelizable, scalable to large systems, and stable for large time step size, thus making the long-time large-scale BD simulation within practical reach. This will be useful for the study of membranes, long-chain molecules, and a large collection of molecules in the fluids.