FIG. 14.

FRET-lines for order–disorder transitions. (a) Free energy landscape of a folding/unfolding transition. (b) Distance distribution of the folded state given by a non-central χ-distribution as given in Eq. (60), centered at 52 Å with a width parameter of 6 Å. (c) Distance distributions $\mathit{p}\left({\mathit{R}}_{\mathit{D}\mathit{A}}\right)$ for unfolded states described by the worm-like chain (WLC) model for a polymer of 120 Å length with varying stiffness κ [see the color scale in (d)]. Distance distributions were calculated as described in the supplementary material, Note 6. (d) and (e) Dynamic FRET-lines for the exchange between the folded and unfolded states in the parameter space of the experimental observables E and ${⟨{\mathit{\tau }}_{\mathit{D}\left(\mathit{A}\right)}⟩}_{\mathit{F}}$ (d) and in the moment representation (e). The folded state lies on the static FRET-line (black) for fixed distances, while all unfolded states are positioned on the dashed gray line defined by the WLC model with different stiffness κ. The WLC distance distributions of the unfolded state were calculated according to Ref. 113 and as described in the supplementary material, Note 6. The Förster radius is 52 Å and the donor lifetime in the absence of the acceptor is τ_D(0) = 4 ns. The linker-corrected static FRET-line and the polymer FRET-line for the WLC 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. (60) for the folded state and the supplementary material, Note 6 for the WLC model. Dynamic FRET-lines were computed accordingly using the mixed distance distribution given in Eq. (70) by varying the species fraction of the folded and unfolded states.