Extended Data Fig. 3: Polarization-resolved fluorescence probing rotational effects.
a. Donor and acceptor emission autocorrelations (green and red, respectively; parallel vs perpendicular channels) and donor-acceptor crosscorrelation (purple; sum of correlations of respective parallel and perpendicular channels) of the FRET-active subpopulation of labeled ProTαC in the dense phase when a polarizing beam splitter is used show an asymmetry of the branches for positive and negative lag-times, τ, in the positively correlated component (correlation time of 30 ns). In contrast, this component is more symmetric when a 50-50 beam splitter is used (b), indicating that the component is caused by residual polarization anisotropy104. (c–h) Time-resolved anisotropy decays, r(t), measured for double-labeled ProTαC unbound (c,d), in the dimer (e,f), and in the dense phase (g,h) with pulsed interleaved excitation using (c,e,g) photons from donor-only bursts (transfer efficiency < 0.1, excitation at 532 nm) or (d,f,h) acceptor photons from bursts with transfer efficiency >0.2 (excitation at 635 nm). Data were fitted with the function \(r(t)={r}_{0}((1-{A}_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}){e}^{-t/{\tau }_{{\rm{f}}{\rm{a}}{\rm{s}}{\rm{t}}}}+{A}_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}){e}^{-t/{\tau }_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}}\) (dashed black lines)105 with \({r}_{0}\) = 0.4. No significant amplitude \({A}_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}\) for a slow component is present for free ProTαC (c, d), and only a small amplitude in the dimer (e,f). In the dense phase (g,h), a distinct slow decay component is observed in the anisotropy decay, which is well described with the decay time τslow = 30 ns from the correlated component of the nsFCS (a,b). This agreement further supports the role of residual rotation as the source of the latter. (i,j) Time-resolved anisotropy decays for free Cy3B in the dilute (i) and dense phase (j). The dilute-phase decay was fit with a single exponential, \(r\left(t\right)={r}_{0}\,{e}^{-t/\tau }\), and the resulting value of \(\tau =0.53\) ns was used to obtain the hydrodynamic radius of Cy3B based on the Stokes-Einstein-Debye relation, \(\tau =({\eta }_{{\rm{e}}{\rm{f}}{\rm{f}}}\,\frac{4}{3}\pi {R}_{{\rm{p}}{\rm{r}}{\rm{o}}{\rm{b}}{\rm{e}}}^{3})/({k}_{{\rm{B}}}T)\). With the viscosity of water (\(0.0010\,{\rm{P}}{\rm{a}}\,{\rm{s}}\)), we obtained 0.80 nm for the radius of Cy3B, within the range of the previously reported values (0.76 ± 0.04 nm)76. (j) The anisotropy decay in the dense phase was fit with a sum of two exponentials, \(r(t)={r}_{0}((1-{A}_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}){e}^{-t/{\tau }_{{\rm{f}}{\rm{a}}{\rm{s}}{\rm{t}}}}+{A}_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}\,{e}^{-t/{\tau }_{{\rm{s}}{\rm{l}}{\rm{o}}{\rm{w}}}})\). The effective viscosities obtained by means of the Stokes-Einstein-Debye relation from the fast and slow components, \({\tau }_{{fast}}\) and \({\tau }_{{slow}}\), are reported in Fig. 1e, and we assign the fast component to the rotational diffusion of the dye virtually unaffected by attractive protein interactions. Note that despite the slow rotational component of Cy3B, almost no partitioning of the dye into the droplets was observed (partition constant <1.05 from confocal fluorescence microscopy images).
