Single-macromolecule fluorescence resonance energy transfer and free-energy profiles

What is the dynamical and structural information contained in single-molecule fluorescence resonance energy, transfer (FRET) experiments where the donor and acceptor photons emitted during a fixed time window T are counted? To answer this question, a theory is developed to obtain the probability distribution of the energy-transfer efficiency obtained from trajectories of duration T. The efficiency is an explicit function of the distance between a fluorescent donor and acceptor attached to the macromolecule; thus, the efficiency can formally be converted to a distance. The resulting distance probability distribution or, equivalently, the potential of mean force or free-energy profile, however, depends on the size of the observation time window T. Illustrative calculations are presented for a random coil polymer and for a protein that exhibits two-state folding kinetics. It is found that the apparent free-energy profiles look physically reasonable, even for long observation times during which significant fluctuations occur. Such, profiles are, however, deceptive unless the observation time is approximately an order of magnitude smaller than the relaxation time of the donor-acceptor distance.