FIG. 8.

Static and dynamic FRET-lines for mixtures of distinct photophysical states of the donor in the (E-${⟨{\tau }_{D\left(A\right)}⟩}_F$) parameter space [(a)–(c)] and in the moment representation [(d)–(f)]. (a) and (d) Static and binary dynamic FRET lines for a superposition of two species with distinct donor-only lifetimes of ${\tau }_{D\left(0\right)}^{\left(1\right)}$ = 4 ns and ${\tau }_{D\left(0\right)}^{\left(2\right)}$ = 1 ns, corresponding to donor quantum yields of ${\mathrm{\Phi }}_{F,D}^{(1)}$ = 0.8 and ${\mathrm{\Phi }}_{F,D}^{(2)}$ = 0.2. Static FRET-lines are shown in black. The inter-dye distances of the two FRET species are $R_{DA}^{(1)}$ = 40 Å (blue, orange) and $R_{DA}^{(2)}$ = 60 Å (teal, red). The Förster radius of the donor state with ${\tau }_{D\left(0\right)}^{\left(1\right)}$ = 4 ns is R₀ = 50 Å. The acceptor quantum yield is chosen as Φ_F,A = 0.8. In (a), the static FRET-lines are given by Eq. (22) and dynamic FRET lines were calculated according to Eq. (27). In (d), the static FRET-line is given by Eq. (45) and the limiting dynamic FRET-lines were calculated according to Eq. (47). (b) and (e) Static and binary dynamic FRET lines for the mixture of the two species shown in (a) and (d) in slow exchange, i.e., on a timescale slower than the observation time, with equilibrium fractions of $x_{D\left(0\right)}^{(1)}$ = 0.25 and $x_{D\left(0\right)}^{(2)}$ = 0.75. For the proximity ratio E_PR, a curvature of the static FRET-lines arises even in the absence of dynamics. Gray lines correspond to the ideal static FRET-lines shown in (a). Note that in (e), the moment difference $\left(1-E_{PR}\right)E_{PR,\tau }$ can assume negative values. (c) and (f) Static and binary dynamic FRET-lines for the mixture of the two species shown in (a) in fast exchange, i.e., for complete averaging during the observation time, with equilibrium fractions of $x_{D\left(0\right)}^{(1)}$ = 0.25 and $x_{D\left(0\right)}^{(2)}$ = 0.75. Solid gray lines correspond to the static FRET-lines for slow exchange as shown in (b) and (e). Dashed gray lines correspond to the ideal static FRET-lines of the two species as shown in (a) and (d). Note that the static FRET-line is convex in this case. In (b) and (c) and (e) and (f), the FRET lines are calculated from the averaged observables defined in Eqs. (53)–(55), assuming a single donor photophysical state for each line.