Simultaneous computation of dynamical and equilibrium information using a weighted ensemble of trajectories

Equilibrium can be represented as an ensemble of uncoupled systems undergoing dynamics in which detailed balance is maintained. We describe a simulation protocol based on the "weighted ensemble" (WE) approach [Huber and Kim, Biophys. J., 1996], in which weak coupling between parallel simulations can capture both dynamical and equilibrium properties without statistical bias. The approach is demonstrated on molecular systems. Of particular practical importance, analysis of the weighted ensemble does not require states to be chosen in advance, and permits the calculation of rates between arbitrary states chosen after the simulation is run. We describe a history-dependent non-Markovian formulation to correct for a potentially significant bias in kinetic properties measured from equilibrium WE simulations.