Learning from history: Non-Markovian analyses of complex trajectories for extracting long-time behavior

A number of modern sampling methods probe long time behavior in complex biomolecules using a set of relatively short trajectory segments. Markov state models (MSMs) can be useful in analyzing such data sets, but in particularly complex landscapes, the available trajectory data may prove insufficient for constructing valid Markov models. Here, we explore the potential utility of history-dependent analyses applied to relatively poor decompositions of configuration space for which MSMs are inadequate. Our approaches build on previous work [Suarez et. al., JCTC 2014] showing that, with sufficient history information, unbiased equilibrium and non-equilibrium observables can be obtained even for arbitrary non-Markovian divisions of phase space. We explore a range of non-Markovian approximations using varying amounts of history information to model the finite length of trajectory segments, applying the analyses to toy models as well as several proteins previously studied by microsec-milisec scale atomistic simulations [Lindorff-Larsen et. al., Science 2011].