  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.
