Extracting physically intuitive reaction coordinates from transition networks of a beta-sheet miniprotein

Simulations are important for understanding complex reactions, but their interpretation is challenging owing to the large number of degrees of freedom typically involved. To address this issue, various means for relating the dynamics of a stochastic system to its structural and energetic features have been introduced. Here, we show how two leading approaches can be combined to advantage. We use the network of transitions observed in a reversible folding/unfolding simulation of a 20-residue three-stranded antiparallel β-sheet peptide (β3s) to estimate the probabilities of committing to stable states (the native state and major nonnative states), and these then serve as the basis for an efficient statistical procedure for identifying physical variables that describe the dynamics. We find that a single coordinate that jointly characterizes the formation of the two native turns of β3s can adequately describe the overall folding process, despite its complex nature. Additional features associated with major pathways leading from individual nonnative states are resolved; indeed, a key result is an improved understanding of the unfolded state. Connections to other methods for analyzing complex reactions are discussed.

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