FIG. 11.

Dynamic FRET-lines in the presence of flexible linkers. (a) and (b) Static and dynamic FRET-lines in the $(\mathit{E},{⟨{\mathit{\tau }}_{\mathit{D}\left(\mathit{A}\right)}⟩}_{\mathit{F}})$ parameter space (a) and in the moment representation (b) in the absence of flexible linkers. The static FRET-line is given in black, and the dynamic FRET-line is colored according to the relative contribution of the two species. (c) and (d) Static and dynamic FRET-lines in the presence of flexible linkers (black and colored lines) are shown in the $\left(\mathit{E},{⟨{\mathit{\tau }}_{\mathit{D}\left(\mathit{A}\right)}⟩}_{\mathit{F}}\right)$ parameter space (c) and in the moment representation (d). The FRET-lines in the absence of flexible linkers, as shown in (a) and (b), are displayed in gray. Arrows indicate the shift of the pure states after averaging over the linker distance distribution. No simple relation exists between the dynamic FRET-line in the presence and absence of flexible linkers for the $(\mathit{E},{⟨{\mathit{\tau }}_{\mathit{D}\left(\mathit{A}\right)}⟩}_{\mathit{F}})$ representation (c). In the moment representation (d), the linear relationship for the dynamic exchange is retained in the presence of flexible linkers. The dynamic FRET-line is simply obtained by connecting the shifted coordinates of the pure states in the presence of flexible linkers. The curves are obtained for a donor lifetime of ${\mathit{\tau }}_{\mathit{D}\left(0\right)}=4$ ns, a Förster radius of R₀ = 50 Å, and interdye distances of ${\mathit{R}}_{\mathit{m}\mathit{p}}^{(1)}=57.5$ Å and ${\mathit{R}}_{\mathit{m}\mathit{p}}^{(2)}=34.5$ Å. The distribution width for the linker broadening was ${\mathit{\sigma }}_{\mathit{D}\mathit{A}}=7.5$ Å. In (a), the static FRET-line (black) is given by Eq. (22) and the dynamic FRET-line (gradient line) was calculated according to Eq. (27). In (b), the static FRET line (black) is given by Eq. (45) and the dynamic FRET-line (gradient line) was calculated according to Eq. (47). In (c) and (d), the static FRET-lines and dynamic FRET-lines were computed according to Eqs. (22) and (27) for (c) and Eqs. (45) and (47) for (d) using the linker averaged moments of the lifetime distribution as given in Eqs. (66) and (68).