Rate Constant and Reaction Coordinate of Trp-Cage Folding in Explicit Water

Abstract

We report rate constant calculations and a reaction coordinate analysis of the rate-limiting folding and unfolding process of the Trp-cage mini-protein in explicit solvent using transition interface sampling. Previous transition path sampling simulations revealed that in this (un)folding process the protein maintains its compact configuration, while a (de)increase of secondary structure is observed. The calculated folding rate agrees reasonably with experiment, while the unfolding rate is 10 times higher. We discuss possible origins for this mismatch. We recomputed the rates with the forward flux sampling method, and found a discrepancy of four orders of magnitude, probably caused by the method's higher sensitivity to the choice of order parameter with respect to transition interface sampling. Finally, we used the previously computed transition path-sampling ensemble to screen combinations of many order parameters for the best model of the reaction coordinate by employing likelihood maximization. We found that a combination of the root mean-square deviation of the helix and of the entire protein was, of the set of tried order parameters, the one that best describes the reaction coordination.

Sampling the equilibrium kinetic network of Trp-cage in explicit solvent

“…They performed a full TIS calculation of the folding and unfolding process between intermediate loop state and the native state. 25 The unfolding rate turned out one order-of-magnitude higher than the measured experimental value, while the folding rate was in agreement with experiment. A later study of the transition employing optimized forward flux sampling (FFS) methods yielded results consistent with the TIS simulations.…”

“…For state I and W , we kept the uniform random selection of shooting point, while for state U, we employed a Gaussian bias (with a standard deviation of 0.1 nm from the interface) to select shooting points. 25 The acceptance ratio for shooting was 55%, for interface exchange 43%. For state I, W , and U, respectively, 4333, 4803, and 2665 paths were collected.…”

The reweighted path ensemble

“…In addition, we apply it to a more realistic system, the Trp-cage folding transition, which we studied in atomistic detail in a previous paper. 21,22 We end with concluding remarks.…”

“…22 The Trp-cage is a small protein consisting of 20 residues. In the native folded state it adopts an ␣-helix ͑residues 2-8͒, a 3-helix ͑residues 11-14͒ and a polyproline II helix ͑residues 17-19͒ ͑see Fig.…”

Onsager–Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways

“…This is also the case for conformational change of large protein systems with several domains, which is relevant to the understanding of the functions of proteins [1]. Therefore, alternative approaches to sample path ensembles should be established, and novel hardware strategy [2] and novel theoretical algorithms including transition interface sampling [30], milestoning [31], and Markov state models [32] have been developed in the last decade.…”