Analysis of Protein Dynamics Simulations by a Stochastic Point Process Approach

MD simulations can now explore the complex dynamics of proteins and their associated solvent in atomic detail on a millisecond time scale. Among the phenomena that thereby become amenable to detailed study are intermittent conformational transitions where the protein accesses transient high-energy states that often play key roles in biology. Here, we present a coherent theoretical framework, based on the stochastic theory of stationary point processes, that allows the essential dynamical characteristics of such processes to be efficiently extracted from the MD trajectory without assuming Poisson statistics. Since the complete information content of a point process is contained in the sequence of residence or interevent times, the experimentally relevant survival correlation function can be computed several orders of magnitude more efficiently than with the conventional approach, involving averaging over initial times. We also present a detailed analysis of the statistical and binning errors, of particular importance when MD results are compared with experiment. As an illustration of the general theoretical framework, we use a 1 ms MD trajectory of the protein BPTI to analyze the exchange kinetics of an internal water molecule and the dynamics of the rare conformational fluctuations that govern the rate of this exchange process.