FRET theoretical predictions concerning freely diffusive dyes inside spherical container: how to choose the best pair?

FRET has been massively used to see if biomolecules were bounded or not by labelling both biomolecules by one dye of a FRET pair. This should give a digital answer to the question (fluorescence of the acceptor: high FRET efficency: molecules associated, fluorescence of the donor: low FRET efficency: molecules dissociated). This has been used, inter alia, at the single-molecule scale in containers, such as liposomes. One perspective of the field is to reduce the container's size to study the effect of confinement on binding. The problem is that if the two dyes are encapsulated inside a small liposome, they could have a significant probability to be close one from the other one (and thus to undergo a high FRET efficiency event without binding). This is why we suggest here a theoretical model which gives mean FRET efficiency as a function of liposome radius (the model applies to any spherical container) and Förster radius to help the experimentalist to choose their experimental set-up. Besides, the influence of side effect on mean FRET efficiency has been studied as well. We show here that if this "background FRET" is most of the time non-quantitative, it can remain significant and which makes data analysis trickier. We could show as well that if this background FRET obviously increases when liposome radius decreases, this variation was lower than the one which could be expected because of side effect. We show as well the FRET efficiency function distribution which let the experimentalist know the probability to get one FRET efficiency value.