Fig. 1: Scheme of calculating FRET correlation functions from photon trajectories.
From: Model-free photon analysis of diffusion-based single-molecule FRET experiments
a The diffusion of donor- (D, green) and acceptor- (A, red) labeled proteins (gray) through the confocal volume (cyan, schematic) causes photon emission bursts (bursts 1–5) of limited duration (T). Each burst is characterized by a collection of arrival times and colors of the detected photons (bottom). b For each burst, we determine all possible pairs of photons together with the time that passed between each pair, which we call the lag time (\(\tau\)). This procedure generates a list of photon pairs and lag times for each burst (Burst 1,2,3…). c The lists generated in (b) is now used to sort the photon pairs according to their types (AA, DD, AD, DA) irrespective from which burst a photon pair originated (top). A histogram of the photon pairs of each photon pair type (\({N}_{{AA}}\left(\tau \right)\), \({N}_{{DD}}\left(\tau \right)\), \({N}_{{AD}}\left(\tau \right)\), \({N}_{{DA}}\left(\tau \right)\)) is constructed (bottom, schematic). The sum of these four histograms gives the histogram of all photon pairs, irrespective of color: \({N\left(\tau \right)=N}_{{AA}}\left(\tau \right)+{N}_{{DD}}\left(\tau \right)+{N}_{{AD}}\left(\tau \right)+{N}_{{DA}}\left(\tau \right)\) d Dividing the photon pair histograms by the histogram of all photon pairs \(N\left(\tau \right)\) (inset), provides the correlation ratios (\({N}_{{AA}}\left(\tau \right)/N\left(\tau \right)\), \({N}_{{DD}}\left(\tau \right)/N\left(\tau \right)\), \({N}_{{AD}}\left(\tau \right)/N\left(\tau \right)\), \({N}_{{DA}}\left(\tau \right)/N\left(\tau \right)\)). Using Eq. 2, the FRET correlation function is computed (blue circles, schematic). The timescale of diffusion is indicated as gray shaded area.
