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Fig. 7. Distribution of fraction of native contacts (Q) and cluster P_fold in the wild-type peptide simulations. The color scale ranging from red to blue corresponds to high and low density, respectively. While structures with very large Q (Q >0.8) or very low Q (Q <0.2) have a cluster P_fold close to 1 or 0, respectively, conformations with intermediate values of Q span all of the allowed spectrum of cluster P_fold values.

Fig. 8. (Left and Center) Comparison between free-energy changes calculated with the kinetic or cluster P_fold data. The correlation coefficient is 0.73 and 0.99 for D D G_TS–D and D D G_N–D, respectively. (Right) Distribution of cluster P_fold for the wild-type simulations and identification of the native, TS, and denatured state ensemble.

The value of cluster P_fold obtained with the procedure exposed in Methods does not depend strongly on the criterion used to define commitment to fold (unfold) (1), i.e., Q >0.85 (Q <0.15), because in the near-equilibrium trajectories, the relaxation time within the folded (or unfolded) basin is 2 orders of magnitude shorter than the average unfolding (or folding) time (data not shown). Thus, instead of searching for observables that correlate with P_fold, we just identify a feature that unequivocally belongs to folded (unfolded) conformations, i.e., very high (low) Q. When the system undergoes a folding (unfolding) transition, it explores rapidly, with respect to folding/unfolding times, the folded (unfolded) basin, and reaches the conformations with high (low) Q. This unequivocally signals the occurrence of the transition event. Although Q can distinguish fully folded and fully denatured structures, it does not help distinguishing structures with properties intermediate between the native and denatured state. Indeed, structures with a Q as large as 0.7 may have cluster P_fold = 0 and, vice versa, a Q as low as 0.3 may correspond to structures with cluster P_fold = 1 (See Fig. 7). The procedure to compute standard P_fold with multiple runs starting from the same structure is extremely CPU expensive whereas the cluster P_fold calculations requires only a few seconds if near-equilibrium trajectories and an efficient clustering algorithm are available.

1. Hubner, I. A, Shimada, J. & Shakhnovic, E. I. (2004) J. Mol. Biol. 336, 745-761.