FIG. 13.

FRET-lines for disordered states. (a) Unstructured biomolecules, such as intrinsically disordered proteins, rapidly interconvert between an ensemble of structures. (b) The interdye distance distributions $\mathit{p}\left({\mathit{R}}_{\mathit{D}\mathit{A}}\right)$ of an unstructured system may be described by polymer models, here given by worm-like chain (WLC) of different lengths of 60, 70, and 90 Å. The distance distributions were generated according to Eq. (69) for the ideal (Gaussian) chain and as described in the supplementary material, Note 6, for the WLC model. (c) The distance distributions define the corresponding fluorescence decays ${\mathit{f}}_{\mathit{D}|\mathit{D}}\left(\mathit{t}\right)$ according to Eq. (8). (d) FRET-lines for the WLC model at different polymer lengths and stiffness κ. The examples shown in (a) and (b) are given as colored dots. The static FRET-line for fixed dyes is given as a black line, and the FRET-line for the Gaussian chain model is given as a red line. (e) The same data as shown in (d) in the moment representation. FRET-lines were calculated for a donor-lifetime ${\mathit{\tau }}_{\mathit{D}\left(0\right)}=4$ ns, and a Förster distance R₀ = 52 Å. All FRET-lines were computed from the moments of the lifetime distribution as given in Eq. (59) using the distance distributions for the inter-dye distance as given in Eq. (69) for the ideal (Gaussian) chain and in the supplementary material, Note 6, for the WLC model.