Biased Brownian dynamics for rate constant calculation

An enhanced sampling method-biased Brownian dynamics-is developed for the c alculation of diffusion-limited biomolecular association reaction rates wit h high energy or entropy barriers. Biased Brownian dynamics introduces a bi asing force in addition to the electrostatic force between the reactants, a nd it associates a probability weight with each trajectory. A simulation lo ses weight when movement is along the biasing force and gains weight when m ovement is against the biasing force. The sampling of trajectories is then biased, but the sampling is unbiased when the trajectory outcomes are multi plied by their weights. With a suitable choice of the biasing force, more r eacted trajectories are sampled, As a consequence, the variance of the esti mate is reduced, in our test case, biased Brownian dynamics gives a sevenfo ld improvement in central processing unit (CPU) time with the choice of a s imple centripetal biasing force.