Figure 11.

Relative error of a normalized donor–acceptor distance, δ(R_DA/R₀), depends on the normalized donor–acceptor distance, R_DA/R₀, and a number of experimental parameters. Estimated relative uncertainties δ(R_DA/R₀) of the DA distance, R_DA, for a given number of detected photons, N, with dependence of the distance R_DA/R₀ for time-correlated single photon counting (TCSPC), intensity-based measurements by multiparameter fluorescence detection (MFD) with one-color excitation (OCE), and pulsed-interleaved excitation (PIE). On the top the contributions of the shot noise and the relevant calibration/correction parameters (colored solid lines) are shown. The resulting total uncertainty is shown as a dotted line. On the bottom, the distance-dependent scaling of the total uncertainty is shown for a different number of photons. The uncertainties for TCSPC were estimated by eqs 46–51 using a radiative rate constant of k_F,D = 0.25 ns^–1 and a relative error corresponding to the donor fluorescence variation among different protein samples in Figure 1 (τ_D(0) = 3.9 ± 0.2 ns). The time-window, T = 16 ns, of the fluorescence decay histogram was separated into 53 detection channels resulting in a detection channel width of 0.3 ns (the typical width of an instrument response function in single-molecule (sm) detection). The uncertainties of the MFD-OCE and MFD-PIE measurements were calculated by eqs 35–45. In both cases the fluorescence quantum yield of the donor and acceptor were Φ_F,D = 0.8 and Φ_F,A = 0.3, respectively. In the MFD-OCE and MFD-PIE plots, α = 0.02 ± 0.005, γ′ = 0.8 ± 0.05, and Φ_F,A = 0.3. The relative fractions of the nonfluorescent background were B_G|G/I_G|G = 0.02 and B_R|G/I_R|G = 0.01. In MFD-PIE, B_R|R/I_R|R = 0.02, η = 0.02 ± 0.01, and β = 0.3 ± 0.1. In MFD-OCE, ΔΦ_F,A = 0.05.