Ab Initio Derivation of the FRET Equations Resolves Old Puzzles and Suggests Measurement Strategies

Quantitative imaging methods based on Förster resonance energy transfer (FRET) rely on the determination of an apparent FRET efficiency (E_app), as well as donor and acceptor concentrations, to uncover the identity and relative abundance of the supramolecular (or quaternary) structures of associating macromolecules. Theoretical work has provided "structure-based" relationships between E_app distributions and the quaternary structure models that underlie them. By contrast, the body of work that predicates the "signal-based" dependence of E_app 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 E_app and measurable fluorescence signals. Analysis of these relationships reveals a few anticipated results and some unexpected explanations for known experimental FRET puzzles, and it provides theoretical foundations for optimizing measurement strategies.