Ab initio derivation of the FRET equations resolves old puzzles and suggests measurement strategies

Quantitative FRET-based imaging methods rely on the determination of an apparent FRET efficiency (Eapp) as well as donor and acceptor concentrations, in order to uncover the identity and relative abundance of the oligomeric (or quaternary) structures of associating macromolecules. Theoretical work has provided \"upwards\" relationships between the experimentally determined Eapp distributions and the quaternary structure models that underlie them. By contrast, the body of work that predicates the \"downwards\" dependence of Eapp on directly measurable quantities (i.e., fluorescence emission of donors and acceptors) relies largely on plausibility arguments, one of which is the seemingly obvious assumption that the fraction of fluorescent molecules in the ground state pretty nearly equals the total concentration of molecules. In this work, we use the kinetic models of fluorescence in the presence and absence of FRET to rigorously derive useful relationships between Eapp and measurable fluorescence signals. Analysis of these relationships reveals a few anticipated surprises and some unexpected explanations for known experimental FRET puzzles, and it provides theoretical foundations for optimizing measurement strategies.