Fig. 2.
Two-dimensional density histograms of the FRET efficiency and the ratio of the donor fluorescence lifetime in the presence and absence of acceptor (τ/τD), for a molecule with three interconverting states. (A) The histograms for three different connectivities of the states (columns) and increasing bin times (rows, top to bottom T = 1, 6, 30 ms). The full histogram corresponding to the center panel is shown in Fig. 1C. The FRET efficiencies of the states increase from left to right and their connectivity is shown at the top. All transitions are reversible with the same rate 0.1 ms-1. The FRET efficiencies are ε1 = 0.2, ε2 = 0.5, and ε3 = 0.8 and corresponding lifetime ratios are 0.8, 0.5, and 0.2. The histograms were simulated using the algorithm discussed in Methods with nAs + nDs = 100 ms-1, s = 1,2,3. (B) The superposition of the histogram for T = 6 ms with the two-state dynamic lines (black) calculated using Eq. 9 for all pairs of directly connected states.