A one-dimensional reaction coordinate for identification of transition states from explicit solvent P(fold)-like calculations

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.