Figure 14.

Considering the simplest bimodal model with two discrete distances, the distance resolution of time-resolved fluorescence measurements is limited by the shot noise of the experiment. Statistical error estimates of a two-distance model described by eq 56 with distances and , fluorescence lifetime τ_D(0) = 4 ns, and a time-window of 12.5τ_D(0). (A) Relative standard error δ per 10⁶ photons of the distances (blue, left), (green, middle), and their difference ΔR_DA (red, right). White lines are isolines δ = 0.5 (also shown at panel D). (B) Isolines of δ(⁾) = 0.5 (blue line), δ() = 0.5 (green line), and δ(ΔR_DA)=0.5 (red line) for 10⁶ counted photons (the same as white lines at panel A). The isolines partition the parameter space in four regions: (i) All three parameters are resolved. (ii) The distances , can be reliably determined while the relative standard error of their difference δ(ΔR_DA) increases above value 0.5. (iii) Only the shorter distance is reliably estimated. The distance distribution is only partially resolved, and the species with small FRET rate constant cannot be distinguished from non-FRET species. (iv) None of the parameters is resolved. The vertical lines indicate limiting distances of the region i (red) and of the region ii (green). (C) Dependence of the limiting distances and on the number of detected photons.