Fig. 3: Recurrence analysis of the PR distributions.

a In the time-trace of the bin-wise PR (thick line), positive (red areas, above median PR) and negative (blue areas, below median PR) fluctuations are assigned to the high-FRET (HF) and low-FRET (LF) regions, respectively. For a given time delay τ, the distributions of bin-wise PR are plotted for the regions shifted by τ over the time axis from the HF regions (PR(t) | HF(t-τ), dashed red lines) or from the LF regions (PR(t) | LF(t-τ), dashed blue lines). The shifts of these distributions from the general bin-wise distribution of PR (black line) indicate a higher than random probability of finding the protein in the same state for the time points t-τ and t. b Distributions of the bin-wise PR in the regions shifted from the LF (“Start at LF”) or HF (“Start at HF”) regions by time delays τ = 1 ms and τ = 200 ms are shown for the apo and ligand-bound A_2AAR. The general distributions of bin-wise PR are shown in black. c The conditional probability of observing the positive fluctuation in PR at the time t (red areas), given that earlier, at the time t-τ, a positive fluctuation was also observed (dashed red contours), is calculated as a function p(HF(t) | HF(t-τ)) of τ (solid red line). Similarly, the probability of the positive fluctuation in PR at time t, given that a negative fluctuation was observed at time t-τ (dashed blue contours), is calculated as a function p(HF(t) | LF(t-τ)) of τ (solid blue line). On the right, two curves converge to the same value at times much longer than the inter-state exchange relaxation time of the target molecules. d Two conditional probabilities of the positive fluctuation in PR are plotted for the apo and ligand-bound A_2AAR. Two orange lines show the same curves for the simulated “static heterogeneity” scenario (p(HF(t) | HF(t-τ)) - higher line; p(HF(t) | LF(t-τ)) - lower line). The 95% confidence intervals were obtained via statistical bootstrapping (shaded colored areas)¹¹⁰.