Linear approaches to intramolecular Förster resonance energy transfer probe measurements for quantitative modeling

Numerous unimolecular, genetically-encoded Förster Resonance Energy Transfer (FRET) probes for monitoring biochemical activities in live cells have been developed over the past decade. As these probes allow for collection of high frequency, spatially resolved data on signaling events in live cells and tissues, they are an attractive technology for obtaining data to develop quantitative, mathematical models of spatiotemporal signaling dynamics. However, to be useful for such purposes the observed FRET from such probes should be related to a biological quantity of interest through a defined mathematical relationship, which is straightforward when this relationship is linear, and can be difficult otherwise. First, we show that only in rare circumstances is the observed FRET linearly proportional to a biochemical activity. Therefore in most cases FRET measurements should only be compared either to explicitly modeled probes or to concentrations of products of the biochemical activity, but not to activities themselves. Importantly, we find that FRET measured by standard intensity-based, ratiometric methods is inherently non-linear with respect to the fraction of probes undergoing FRET. Alternatively, we find that quantifying FRET either via (1) fluorescence lifetime imaging (FLIM) or (2) ratiometric methods where the donor emission intensity is divided by the directly-excited acceptor emission intensity (denoted R(alt)) is linear with respect to the fraction of probes undergoing FRET. This linearity property allows one to calculate the fraction of active probes based on the FRET measurement. Thus, our results suggest that either FLIM or ratiometric methods based on R(alt) are the preferred techniques for obtaining quantitative data from FRET probe experiments for mathematical modeling purposes.