  A key overall goal of biomolecular simulations is the characterization of
"mechanism" -- the pathways through configuration space of processes such as
conformational transitions and binding. Some amount of heterogeneity is
intrinsic to the ensemble of pathways, in direct analogy to thermal
configurational ensembles. Quantification of that heterogeneity is essential to
a complete understanding of mechanism. We propose a general approach for
characterizing path ensembles based on mapping individual trajectories into
pathway classes whose populations and uncertainties can be analyzed as an
ordinary histogram, providing a quantitative "fingerprint" of mechanism. In
contrast to prior flux-based analyses used for discrete-state models,
stochastic deviations from average behavior are explicitly included via direct
classification of trajectories. The histogram approach, furthermore, is
applicable to analysis of continuous trajectories. It enables straightforward
comparison between ensembles produced by different methods or under different
conditions. To implement the formulation, we develop approaches for classifying
trajectories, including a clustering-based approach suitable for both
continuous-space (e.g., molecular dynamics) or discrete-state (e.g., Markov
state model) trajectories, as well as a "fundamental sequence" approach
tailored for discrete-state trajectories but also applicable to continuous
trajectories through a mapping process. We apply the pathway histogram analysis
to a toy model and an extremely long atomistic molecular dynamics trajectory of
protein folding.
