Folding Kinetics and Unfolded State Dynamics of the GB1 Hairpin from Molecular Simulation David De Sancho, † Jeetain Mittal, ‡ and Robert B. Best* ,§ † Cambridge University, Department of Chemistry, Lensfield Road Cambridge CB2 1EW, United Kingdom ‡ Department of Chemical Engineering, 111 Research Drive, Iacocca Hall, Bethlehem, Pennsylvania 18015, United States § Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520, United States *S Supporting Information ABSTRACT: The C-terminal β-hairpin of protein G is a 16-residue peptide that folds in a two-state fashion akin to many larger proteins. However, with an experimental folding time of ∼6 μs, it remains a challenging system for all- atom, explicitly solvated, molecular dynamics simulations. Here, we use a large simulation data set (0.7 ms total) of the hairpin at 300 and 350 K to interpret its folding via a master equation approach. We find a separation of over an order of magnitude between the longest and second longest relaxation times, with the slowest relaxation corresponding to folding. However, in spite of this apparent two-state dynamics, the folding rate determined based on a first- passage time analysis depends on the initial conditions chosen, with a nonexponential distribution of first passage times being obtained in some cases. Using the master equation model, we are now able to account quantitatively for the observed distribution of first passage times. The deviation from the expected exponential distribution for a two-state system arises from slow dynamics in the unfolded state, associated with formation and melting of helical structures. Our results help to reconcile recent findings of slow dynamics in unfolded proteins with observed two-state folding kinetics. At the same time, they indicate that care is required in estimating folding kinetics from many short folding simulations. Last, we are able to use the master equation model to obtain details of the folding mechanism and folding transition state, which appear consistent with the “zipper” mechanism inferred from the experiment. ■ INTRODUCTION Although the resolution of atomistic molecular dynamics (MD) simulations of protein folding is greater than that of any experimental technique, their high computational cost and the limited accuracy of molecular mechanics force fields 1−7 make benchmarking against experimental data essential. 8 Ultrafast folding peptides and mini-proteins are well suited to such validation, 9 since they can be studied using high resolution spectroscopic techniques 10 and are also amenable to atomistic molecular simulation studies; 8 additionally simplified statistical mechanics models are analytically solvable for short sequen- ces. 11,12 From the extensive characterization of a number of ultrafast folders, a description of the folding of peptides and small proteins which is both accurate and microscopically detailed is currently emerging. 13 Here, we focus on the GB1 hairpin, the C-terminal β-hairpin of protein G 14 (see Figure 1A), which has become one of the testbeds for comparing simulations, theory, and experimental results. This 16-residue peptide was shown to fold to a native-like three-dimensional structure 15 and to exhibit two state folding from relaxation experiments using ultrafast temperature jumps, with consistent results using different experimental probes. 16,17 Since then the GB1 hairpin has been extensively characterized in multiple experimental 17−20 and simulation 21−37 studies. Sampling of folding events in all-atom simulations of protein folding is still a major challenge, and with a folding time of ∼6 μs, the GB1 hairpin is no exception. One approach to sampling folding (or unfolding) events, extensively exploited in world- wide distributed computing projects, 38 is to run many relatively short simulations, of which only a few will contain folding transitions. The folding rate can then be estimated by assuming the folding to occur according to simple two-state kinetics. 25 For example, a recent study of the GB1 hairpin used many simulations of between 0.25 and 1.5 μs each to sample folding and unfolding events, for a total of 0.7 ms of data. 39 A curious result of this work was that the apparent folding rate computed from mean first passage times depended on the choice of initial “unfolded” states. Using as starting structures a set of unfolded states chosen from the equilibrium distribution (U−A), a folding time of 59 μs was obtained, while using a subset of the unfolded state containing no α-helical structures (U−B) resulted in a folding time of 8.2 μs. This is clearly an unexpected result if the peptide indeed folds in a two-state manner: if relaxation within the unfolded state is much faster than folding, one would expect little dependence of the results Received: November 22, 2012 Published: February 7, 2013 Article pubs.acs.org/JCTC © 2013 American Chemical Society 1743 dx.doi.org/10.1021/ct301033r | J. Chem. Theory Comput. 2013, 9, 1743−1753