Brownian dynamics with hydrodynamic interactions

Abstract

A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker–Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution.

Colloidal dynamics: Influence of diffusion, inertia and colloidal forces on cluster formation

“…Such an artificial increase of the kinetic energy is more significant for smaller potential well depth as can be noticed from Table 1: there is more significant difference between simulated and analytical results at the potential well depth equal to 1 kT. The results presented in Table 1 confirm that the presented mathematical model, as well as diffusional model proposed in Ref [23] enable the simulation of clustering behaviour based solely on first principles without any empirical fit. The drawback of the presented model in comparison to diffusion approximation is much smaller time step.…”

“…The matrix of hydrodynamic resistance coefficients, ςˆ, and matrix of Brownian coefficients, αˆ, are related according to the fluctuation-dissipation theorem [23]:…”

“…The advantage of this approximation is the possibility (i) of using a time step which is much larger than the momentum relaxation time and (ii) neglecting the inertial term in the Langevin equations (1) [21,23]. These simplify the calculations considerably providing nevertheless correct enough simulation results.…”

Integrative structure and functional anatomy of a nuclear pore complex

“…Distributions of the FG repeats and NTRs were computed by Brownian dynamics simulation 145 , using our protocol 146 implemented in IMP 98 , version 2.6. The simulated system included the static NPC ring determined in this study, the pore membrane, disordered and flexible FG repeat domains, as well as freely diffusing NTRs and inert macromolecules, all enclosed within a bounding box of 2,000 × 2,000 × 2,000 Å 3 .…”

Forced Unfolding Mechanism of Bacteriorhodopsin as Revealed by Coarse-Grained Molecular Dynamics

“…We developed a coarse-grained (C-G) model because the unfolding occurs on timescales much slower than those covered by typical all-atom simulations, making unfolding simulations of membrane proteins unfeasible with the finite computational resources available. The surrounding water and membrane environment were represented as an implicit medium, and the Brownian dynamics (BD) method (40)(41)(42) was employed for the simulation. Before calculations, we verified that our model system is overdamped and suitable for the BD simulation.…”