Improved Estimation of Long-Time Kinetics using Non-Markovian Analysis of Trajectory Segments: Application to Protein Folding and Unfolding

Abstract

What is the best way to estimate long-time kinetics from finite trajectory data for molecular simulations? A range of sophisticated Markov-model schemes have been developed to analyze behavior arising from discretization of a continuous configuration space into states. However, discretization into finite states leads intrinsically to non-Markovian behavior, and hence to bias in Markov-based estimates of quantities such as the mean first-passage time (MFPT). We have shown previously that it is sufficient to include just part of the history information [JCTC 2014, 10, pp 2658-2667] to correct bias in MFPT estimation. Here, we attempt to develop practical non-Markovian analyses applicable to protein simulations. The schemes are tested using μsec−msec-scale simulation data [Science 2011, 334(6055), pp 517-520], which provide reference MFPT values. We progressively reduce the amount of data used by the non-Markovian estimators by cutting the trajectories in small fragments and selecting just a fraction of them. In every case we are able to obtain reasonably good results for both folding and unfolding MFPTs even when the total length of trajectory data used is well below the longer of the MFPTs. Our estimators are relatively insensitive to the construction of states, reducing the bias over a wide range of lag times, yielding reasonable MFPT values even with very crude discretizations.