Fig. 1. Trajectories, transition path analyses, and free energy landscapes of binding-coupled-folding of pKID to KIX.

2D binding–folding free energy landscapes are calculated from REMD simulations and projected along (A) d_RMS−B, Q_F and (B) Q_B, Q_F. d_RMS−B is the root-meansquare deviation of the distances of binding native contact pairs to those in the native structure, while Q_B and Q_F are the fractions of binding and folding native contacts for pKID, respectively. The typical structures of pKID-KIX are shown corresponding to the indicated binding stages. A sample binding trajectory (C, D), 1D free energy landscape (E, F), and transition path analyses (G, H) are shown along d_RMS−B and Q_B, respectively. p(TP|x) is the conditional probability of being on a transition path, where x is the reaction coordinate. The dashed vertical lines in free energy landscapes and p(TP|x) are plotted according to the maximum values as an identification of the transition state. The values at the peak of p(TP|x) for d_RMS−B and Q_B are 0.45±0.03 and 0.35±0.01, respectively. The transition state locations are very similar, according to different identifications of the barrier of free energy landscapes and the peak of p(TP|x). In detail, for d_RMS−B, the transition states’ d_RMS−B are 1.49 and 1.52 from the free energy landscape and p(TP|x), respectively, while for Q_B, the transition states’ Q_B are 0.22 and 0.20 from the free energy landscape and p(TP|x), respectively. We denote the transition state ensembles that have p(TP|x) higher than 0.30 by gray shadow regions. The errors of p(TP|x) are calculated by analyzing different trajectories. A total of 1108 and 1099 (un)binding transition paths are observed along d_RMS−B and Q, respectively. Time is in reduced units, d_RMS−B is in units of nm, and free energy is in units of kT_B, where T_B is the binding temperature.