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 flu...