On the structural convergence of biomolecular simulations by determination of the effective sample size

Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of simulation trajectories has remained difficult to assess. Such assessment is critical not only for establishing the relevance of any individual simulation but also in the extremely active field of developing computational methods. Here we map the trajectory assessment problem onto a simple statistical calculation of the "effective sample size", that is, the number of statistically independent configurations. The mapping is achieved by asking the question, "How much time must elapse between snapshots included in a sample for that sample to exhibit the statistical properties expected for independent and identically distributed configurations?" Our method is more general than autocorrelation methods in that it directly probes the configuration-space distribution without requiring a priori definition of configurational substates and without any fitting parameters. We show that the method is equally and directly applicable to toy models, peptides, and a 72-residue protein model. Variants of our approach can readily be applied to a wide range of physical and chemical systems.