Fig. 2
From: Transition path times of coupled folding and binding reveal the formation of an encounter complex
Quantifying transition path times. a The two kinetic models compared in the maximum likelihood analysis include the unbound (U) and bound (B) states; the second model accounts for a finite duration of a transition path by also including an intermediate state (I) with transfer efficiency EI and mean lifetime τI. b Log likelihood difference (\({\Delta\ln{L}}\)) plots for binding transitions (ionic strength 108 mM, viscosity 1.28 cP). The 2D contour plot (lower panel) shows the total \(\Delta\ln L\) of all 686 transitions for different values of τI and EI. The maximum yields \(\hat \tau _{\sf {I}}\) and \(\hat E_{\sf{I}}\), the most likely values of τI and EI, respectively, with \(\hat \tau _{\sf {I}} = \left\langle {{t}_{{\mathrm {TP}}}} \right\rangle\). The top graph shows the \({{\Delta\ln}}L\) plots for \(\hat {E}_{\sf {I}}\) (black dashed line in the contour plot). The \({\mathrm{\Delta}}\ln{L}_{j}\) plots of all individual measurements are shown (orange lines, right scale), with their average (red dashed line, right scale) and their sum (black line, left scale). c \({{\Delta {\ln}}}{L}\) contour plots of transitions measured at different solvent viscosities (η). From the lowest to the highest viscosity, sample sizes were 686, 331, 285, and 378 transitions (see Supplementary Table 3). d Solvent viscosity dependence of 〈tTP〉 (with linear fit, constrained to 〈tTP〉 ≥ 0 at zero viscosity, and 90% confidence interval) and \(\hat {E}_{\sf {I}}\) (average: solid line; standard deviation: dashed lines). Error bars indicate standard errors obtained from 1000 bootstrapping trials
