Brownian dynamics simulations

Brownian dynamics simulations is a powerful tool to study the kinetics of association of large proteins. They diffuse randomly in an implicite solvent until they enter into the electrostatic field of each other. In this region they move by directional diffusion toward the encounter complex.

Researcher of this topic is: Denitsa Alamanova

The Brownian dynamics simulation technique is a mesoscopic method in which explicit solvent molecules are replaced by a stochastic force.
The technique takes advantage of the fact that there is a large separation in time scales between the rapid motion of solvent molecules and the more sluggish motion of polymers or colloids. The ability to coarse-grain out these fast modes of the solvent allows one to simulate much larger time scales than in a molecular dynamics simulation.
At the core of a Brownian dynamics simulation is a stochastic differential equation which is integrated forward in time to create trajectories of molecules. Time enters naturally into the scheme allowing for the study of the temporal evolution and dynamics of complex fluids (e.g. polymers, large proteins, DNA molecules and colloidal solutions). Hydrodynamic and body forces, such as magnetic or electric fields, can be added in a straightforward way.
Brownian dynamics simulations are particularly well suited to studying the structure and rheology of complex fluids in hydrodynamic flows and other nonequilibrium situations.

Protein protein association involves processes on different length and time scales. At large distances, only the relative motion of the two centers of mass is important. In this regime, the free energy landscape can be sampled by brownian dynamics. The spatial dynamics of individual proteins takes place on a coarse grained lattice.
Here we consider the problem of how to correctly model diffusion on a coarse grid, given the microscopic diffusion coefficient. In contrast to the time independent random walk methods, our requirement is that transition probabilities are modeled correctly for jumps beyond the next neighbors, too. From the condition that such a propagation should reproduce the diffusive evolution of a free particle at finite times, we derive a condition for iscretizing the stepsizes for arbitrary gridspacings, timesteps and diffusion coefficients.