Fig. 4: Impact of photobleaching and dye brightness on FRET correlation functions.

a FRET efficiency histograms (corrected) for a two-state model (\(k=3\,{\rm{{ms}}}^{-1}\), \({\varepsilon }_{1}=0.1\), \({\varepsilon }_{2}=0.9\)) without (left) and with (middle) photobleaching. The gray shaded area indicates donor-only molecules that were excluded from the analysis (\(\widetilde{E} < 0\) due to acceptor direct excitation). The FRET efficiency histogram with photobleaching but filtered for unbleached bursts (right). b Normalized correlation ratios \({f}_{{AA}}\left(\tau \right)\) (red), \({f}_{{DD}}\left(\tau \right)\) (green), \({f}_{{AD}}\left(\tau \right)\) and \({f}_{{DA}}\left(\tau \right)\) (blue) for the data in (a). The correlation ratios are plotted for positive and negative lag time to better identify asymmetries of the cross-correlation ratios. c FRET correlation function for the data in (a). Black solid line is an exponential fit to the FRET correlation function in the absence of photobleaching. d Kinetic scheme of the 2-state model with dye brightness independent of the conformational state. e Analytical solution of the FRET correlation function for the 2-state model for \(a=d\) (\(\gamma=1\), black) and \(a=10d\) (\(\gamma=10\), red). The dashed line is the re-scaled correlation function shown for the case \(\gamma=10\). f Deviation of the relaxation rate from the true value without (solid black) and with background (dashed black). To highlight the difference, we used an unrealistic high background (10% of the acceptor signal). g The amplitude of the measured FRET correlation function relative to the value of the true amplitude is plotted as function of the correction factor. Solid and dashed lines are the same as in (f). h Kinetic scheme of the 2-state model with state-dependent dye brightness. i Analytical solutions of the FRET correlation function for identical brightness of all dyes and states (black line) and for a mixed case (red). The dashed red line is the rescaled correlation function shown as a solid red line. j Maps to indicate the relative deviation of the apparent relaxation rate (color scale) for the model in (h). Empty regions correspond to deviations <2%. A white cross indicates the case shown in (i).