Fig. 3: Quantitative analysis of a non-equilibrium steady-state system.

a An illustration of the simulated three-state model with a counter-clockwise net flow. States (circles) are connected by forward and reverse rate constants as specified. b A simulated smFRET trace with donor and acceptor fluorescence intensity (green, red) and FRET efficiency (FRET, black), representative for the dataset used in (c, d, e): n(traces) = 150, n(datapoints) = 82,594, sampling rate = 10 Hz, time per datapoint = 100 ms. c SmFRET histogram overlaid with the inferred FRET efficiencies (right axis, numbers as in e) and assigned states on top. Sample size as in (b). The error bars represent standard deviations. d Inferred rate constants are shown in red and blue as specified. Vertical lines indicate the GT. The intrinsic uncertainty of the dataset is represented by dark gray (1σ) and light gray (2σ) intervals. Sample size as in (b). Uncertainty measures (CI, SD) as listed in Table 1. Analysis tools are numbered as in (e). e The inferred cyclic flow in the counter-clockwise direction determined by calculating ∆G from Eq. (1) and compared with the GT value (solid vertical line). The uncertainty intervals (dark and light gray) are plotted as in (d). Sample size as in (b). Uncertainty measures (CI, SD) as listed in Table 1. Additional simulations to validate the dataset are shown in Supplementary Fig. 3. ‡ denotes results that were submitted after the GT was known. Edge finding did not report uncertainties. § denotes that the misassignment of start and end states was corrected after the GT was known. Source data are provided as a Source Data file for panels (c, d, and e).