Fig. 3 | Nature Communications

Fig. 3

From: Diffusion-limited association of disordered protein by non-native electrostatic interactions

Fig. 3

Measurement of the lifetime of transient complex. a Selected donor and acceptor fluorescence trajectories (left) and FRET efficiency trajectories (right) collected at high illumination intensity (200 μs bin time) that exhibit gradual changes in the fluorescence intensities and FRET efficiency (yellow shade) during association and dissociation. The accurate lifetime of TC was determined using the maximum likelihood analysis of photon trajectories without binning (see e). b Three-state model to determine the lifetime of TC (tTC). The two rate coefficients of the transitions from TC to the bound and unbound states are set to be equal (kTC) for the convenience of the analysis, which does not reflect the actual relative heights of the two barriers in Fig. 4c. c The difference of log-likelihood (Δln L) plots for binding of TAD and NCBD as a function of tTC at various NaCl concentrations (quoted numbers). Δln L = ln L(tTC) − ln L(0) compares the likelihood of the three-state model with a finite lifetime, tTC, with the model with an instantaneous transition (tTC = 0). The FRET efficiency of TC is assumed to be the average of the bound and unbound FRET efficiencies (ETC = (EB + EU)/2). When the peak of the likelihood is significantly higher than the 95% confidence level (Δln L = +3, upper dashed line), tTC can be determined from the time at the maximum. When there is no significant peak, the upper bound of the lifetime can be determined from the time where Δln L crosses the lower 95% confidence level (Δln L = −3, lower dashed line). d Δln L plotted for binding of barnase and barstar at 0 mM NaCl. e The dependence of tTC on the NaCl concentration. tTC of TAD and NCBD binding is determined from either the maximum of Δln L in c (blue) or by maximizing Δln L with ETC as a free parameter (red, see Methods). Fitted values of ETC are shown in the inset. Green filled squares are the upper bound of tTC at 90 and 150 mM NaCl. A purple filled square is the upper bound of tTC of barnase and barstar binding at 0 mM NaCl in d. Fitting parameters are also listed in Supplementary Table 2. Errors are standard deviations obtained from the diagonal elements of the covariance matrix calculated at the maximum of the likelihood function

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