Improved Estimates of Folding Stabilities and Kinetics\nwith Multiensemble Markov Models

Markov\nState Models (MSMs) have been widely applied to understand\nprotein folding mechanisms by predicting long time scale dynamics\nfrom ensembles of short molecular simulations. Most MSM estimators\nenforce detailed balance, assuming that trajectory data are sampled\nat an equilibrium. This is rarely the case for ab initio folding studies,\nhowever, and as a result, MSMs can severely underestimate protein\nfolding stabilities from such data. To remedy this problem, we have\ndeveloped an enhanced-sampling protocol in which (1) unbiased folding\nsimulations are performed and sparse tICA is used to obtain features\nthat best capture the slowest events in folding, (2) umbrella sampling\nalong this reaction coordinate is performed to observe folding and\nunfolding transitions, and (3) the thermodynamics and kinetics of\nfolding are estimated using multiensemble Markov models (MEMMs). Using\nthis protocol, folding pathways, rates, and stabilities of a designed\nα-helical hairpin, Z34C, can be predicted in good agreement\nwith experimental measurements. These results indicate that accurate\nsimulation-based estimates of absolute folding stabilities are within\nreach, with implications for the computational design of folded miniproteins\nand peptidomimetics.