Constrained Proper Sampling of Conformations of Transition State Ensemble during Protein Folding

Characterizing the conformations of protein in the transition state ensemble (TSE) is important for studying protein folding. A promising approach pioneered by Vendruscolo et al40 to study TSE is to generate conformations that satisfy all constraints imposed by the experimentally measured φ-values that provide information about the native-likeness of the transition states. Faisca et al12 generated conformations of TSE based on the criterion that, starting from a TS conformation, the probabilities of folding and unfolding are about equal through Metropolis Monte Carlo (MC) simulations. In this study, we use the technique of constrained sequential Monte Carlo method (CSMC)26,44 to generate TSE conformations of acylphosphatase (AcP) of 98 residues that satisfy the φ-value constraints, as well as the criterion that each conformation has a folding probability of 0.5 by Metropolis MC simulations. We adopt a two stage process and first generate 5,000 contact maps satisfying the φ value constraints. Each contact map is then used to generate 1,000 properly weighted conformations. After clustering similar conformations, we obtain a set of properly weighted samples of 4,185 candidate clusters. Representative conformation of each of these cluster is then selected and 50 runs of Markov chain Monte Carlo (MCMC) simulation are carried using a regrowth move set. We then select a subset of 1,501 conformations that have equal probabilities to fold and to unfold as the set of TSE. These 1,501 samples characterize well the distribution of transition state ensemble conformations of acylphosphatase. Compared with previous studies, our approach can access much wider conformational space and can objectively generate conformations that satisfy the φ-value constraints and the criterion of 0.5 folding probability without bias. In contrast to the previous studies, our results show that transition state conformations are very diverse and are far from native-like when measured in cRMSD (Cartesian Root-Mean-Square Deviation): the average cRMSD between TS conformations and the native structure is 9.4Å for this short protein, instead of 6Å reported in previous studies. In addition, we found that the average fraction of native contacts in the TSE is 0.37, with enrichment in native-like β-sheets and a shortage of long range contacts, suggesting such contacts form at a later stage of folding. We further calculate the first passage time of folding of TSE conformations through calculation of physical time associated with the regrowth moves in MCMC simulation through mapping such moves to a Markovian state space model with transition time obtained by Langevin dynamics simulations. Our results indicate