Figure 11.

System transition rates ${\lambda }_{esc}$ and FRET efficiencies ${ϵ}_{FRET}$ as functions of increasing donor and acceptor background fraction ${\lambda }_{bg}/{\lambda }_{ex}$. To produce these plots, we generated synthetic data with an excitation rate of ${\lambda }_{ex}=10$ ms⁻¹, and escape rates ${\lambda }_{esc}=1$ and 2 ms⁻¹ for the two system states, respectively, same as Fig. 5, while increasing the fraction of background photons (donor and acceptor) from 0 to 50% $\left({\lambda }_{bg}/{\lambda }_{ex}=1\right)$. In each plot, the blue dots represent the median values (50% quantile), and the ends of the attached confidence intervals represent the 5 and 95% quantiles. Furthermore, ground truths are shown with red horizontal lines. In (a), we show two plots showing system transition rates estimated by the BNP-FRET sampler when corrected and uncorrected for crosstalk. We show similar plots for FRET efficiencies in (b). In all plots, we see that as background is increased, the confidence intervals get bigger (the posterior gets wider) and the estimates become unreliable after ${\lambda }_{bg}/{\lambda }_{ex}>0.6$. In addition, as expected, if unaccounted for, FRET efficiencies start to merge with increasing background as photons originating from FRET events significantly reduce.