Theory of the energy transfer efficiency and fluorescence lifetime distribution in single-molecule FRET

In single-molecule FRET experiments with pulsed lasers, not only the colors of the photons but also the fluorescence lifetimes can be monitored. Although these quantities appear to be random, they are modulated by conformational dynamics. In order to extract information about such dynamics, we develop the theory of the joint distribution of FRET efficiencies and fluorescence lifetimes determined from bins (or bursts) of photons. Our starting point is a rigorous formal expression for the distribution of the numbers of donor and acceptor photons and donor lifetimes in a bin that treats the influence of conformational dynamics on all timescales. This formula leads to an analytic result for a two-state system interconverting on a timescale slower than the interphoton time and to an efficient simulation algorithm for multistate dynamics. The shape of the joint distribution contains more information about conformational dynamics than the FRET efficiency histogram alone. In favorable cases, the connectivity of the underlying conformational states can be determined directly by simple inspection of the projection of the joint distribution on the efficiency-lifetime plane.