Efficient Brownian dynamics simulation of DNA molecules with hydrodynamic interactions in linear flows

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 integrating factor to cope with the effect of the linear flow of the surrounding fluid and applies the Metropolis method (MM) by Bou-Rabee, Donev, and 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 λ-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.

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

“…In bead-spring models, the fiber is represented as a chain of rigid spheres [YM95,YM96,FYJ15] or el-lipsoids [RK97] linked by inextensible connectors with finite bending rigidity [JF01] or by springs with given tensile and bending stiffnesses [RK97,NF07]. The system is evolved by imposing the balance between hydrodynamic and elastic forces and torques on all beads.…”

“…Versions of particle-based methods include bead-spring models, regularized Stokes, variations of dissipative particle dynamics [CWG11,Gro12], and slender-body theory (which we use in this work). In bead-spring models, the fiber is represented as a chain of rigid spheres [YM95,YM96,FYJ15] or el-lipsoids [RK97] linked by inextensible connectors with finite bending rigidity [JF01] or by springs with given tensile and bending stiffnesses [RK97,NF07]. The system is evolved by imposing the balance between hydrodynamic and elastic forces and torques on all beads.…”