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The ultrafast folding pathway of the engrailed homeodomain has been exceptionally well characterized by experiment and simulation. Helices II and III of the three-helix bundle protein form the native helix-turn-helix motif as an on-pathway intermediate within a few microseconds. The slow step is then the proper docking of the helices in approximately 15 mus. However, there is still the unexplained puzzle of why helix docking is relatively slow, which is part of the more general question as to why rearrangements of intermediates occur slowly. To address this problem, we performed 46 all-atom molecular dynamics refolding simulations in explicit water, for a total of 15 micros of simulation time. The simulations started from an intermediate state structure that was generated in an unfolding simulation at 498 K and was then quenched to folding-permissive temperatures. The protein refolded successfully in only one of the 46 simulations, and in that case the refolding pathway mirrored the unfolding pathway at high temperature. In the 45 simulations in which the protein did not fully fold, nonnative salt bridges trapped the protein, which explains why the protein folds relatively slowly from the intermediate state., (Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.

A properly identified transition state ensemble (TSE) in a molecular dynamics (MD) simulation can reveal a tremendous amount about how a protein folds and offer a point of comparison to experimentally derived Phi(F) values, which reflect the degree of structure in these transient states. In one such method of TSE identification, dubbed P(fold), MD simulations of individual protein structures taken from an unfolding trajectory are used to directly assess an input structure's probability of folding before unfolding, and P(fold) is, by definition, 0.5 for the TSE. Other, less computationally intensive methods, such as multidimensional scaling (MDS) of the pairwise root mean-squared deviation (RMSD) matrix of the conformations sampled in a thermal unfolding trajectory, have also been used to identify the TSE. Identification of the TSE is made from the original MD simulation without the need to run further simulations. Here we present a P(fold)-like study and describe methods for identification of the TSE through the derivation of a high fidelity, bounded, one-dimensional reaction coordinate for protein folding. These methods are applied to the engrailed homeodomain. The TSE identified by this approach is essentially identical to the TSE identified previously by MDS of the pairwise RMSD matrix. However, the cost of performing P(fold), or even our reduced P(fold)-like calculations, is at least 36,000 times greater than the MDS method.

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.

All atom molecular dynamics simulations have become a standard method for mapping equilibrium protein dynamics and non-equilibrium events like folding and unfolding. Here, we present detailed methods for performing such simulations. Generic protocols for minimization, solvation, simulation, and analysis derived from previous studies are also presented. As a measure of validation, our water model is compared with experiment. An example of current applications of these methods, simulations of the ultrafast folding protein Engrailed Homeodomain are presented including the experimental evidence used to verify their results. Ultrafast folders are an invaluable tool for studying protein behavior as folding and unfolding events measured by experiment occur on timescales accessible with the high-resolution molecular dynamics methods we describe. Finally, to demonstrate the prospect of these methods for folding proteins, a temperature quench simulation of a thermal unfolding intermediate of the Engrailed Homeodomain is described.

We have determined consensus protein-fold classifications on the basis of three classification methods, SCOP, CATH, and Dali. These classifications make use of different methods of defining and categorizing protein folds that lead to different views of protein-fold space. Pairwise comparisons of domains on the basis of their fold classifications show that much of the disagreement between the classification systems is due to differing domain definitions rather than assigning the same domain to different folds. However, there are significant differences in the fold assignments between the three systems. These remaining differences can be explained primarily in terms of the breadth of the fold classifications. Many structures may be defined as having one fold in one system, whereas far fewer are defined as having the analogous fold in another system. By comparing these folds for a nonredundant set of proteins, the consensus method breaks up broad fold classifications and combines restrictive fold classifications into metafolds, creating, in effect, an averaged view of fold space. This averaged view requires that the structural similarities between proteins having the same metafold be recognized by multiple classification systems. Thus, the consensus map is useful for researchers looking for fold similarities that are relatively independent of the method used to compare proteins. The 30 most populated metafolds, representing the folds of about half of a nonredundant subset of the PDB, are presented here. The full list of metafolds is presented on the Web.