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A key overall goal of biomolecular simulations is the characterization of"mechanism" -- the pathways through configuration space of processes such asconformational transitions and binding. Some amount of heterogeneity isintrinsic to the ensemble of pathways, in direct analogy to thermalconfigurational ensembles. Quantification of that heterogeneity is essential toa complete understanding of mechanism. We propose a general approach forcharacterizing path ensembles based on mapping individual trajectories intopathway classes whose populations and uncertainties can be analyzed as anordinary histogram, providing a quantitative "fingerprint" of mechanism. Incontrast to prior flux-based analyses used for discrete-state models,stochastic deviations from average behavior are explicitly included via directclassification of trajectories. The histogram approach, furthermore, isapplicable to analysis of continuous trajectories. It enables straightforwardcomparison between ensembles produced by different methods or under differentconditions. To implement the formulation, we develop approaches for classifyingtrajectories, including a clustering-based approach suitable for bothcontinuous-space (e.g., molecular dynamics) or discrete-state (e.g., Markovstate model) trajectories, as well as a "fundamental sequence" approachtailored for discrete-state trajectories but also applicable to continuoustrajectories through a mapping process. We apply the pathway histogram analysisto a toy model and an extremely long atomistic molecular dynamics trajectory ofprotein folding.

Pathway Histogram Analysis of Trajectories: A general strategy for quantification of molecular mechanisms