Multipoint fluorescence quenching-time statistics for single molecules with anomalous diffusion

Three-point fluorescence lifetime correlation functions are computed for the fluorescence resonance energy transfer (FRET) and electron transfer (ET) quenching mechanisms in a single donor-acceptor system of which the distance X undergoes anomalous diffusion in a harmonic potential with short-time variance scaling as similar tot(alpha). The three-point joint probability distribution of X and its moments are calculated by solving the fractional Fokker-Planck equation (FFPE). For alpha = 1, the process is stationary and the two- and three-point joint probability distribution is centered around the time-dependent average donor-acceptor separation, <X(t)>. For alpha < 1, the distribution slows down, becomes nonstationary, and remains centered at initial separation X(0) even for times exceeding the bath correlation time scale.