Describing protein folding kinetics by molecular dynamics simulations. 1. Theory

A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.