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We present the theory for the distribution of the number of donor and acceptor photons detected in a time bin and the corresponding energy-transfer efficiency distribution obtained from single-molecule Forster resonance energy-transfer measurements. Photon counts from both immobilized and freely diffusing molecules are considered. Our starting point is the joint distribution for the donor and acceptor photons for a system described by an arbitrary kinetic scheme. This is simplified by exploiting the time scale separation between fast fluorescent transitions and slow processes which include conformational dynamics, intersystem conversion to a dark state, and translational diffusion in and out of the laser spot. The fast fluorescent transitions result in a Poisson distribution of the number of photons which is then averaged over slow fluctuations of the local transfer efficiency and the total number of photons. The contribution of various processes to the distribution and the variance of the energy-transfer efficiency are analyzed.
Gopich et al. (Mon,) studied this question.