FRET rate constant

The FRET rate constant, k_{RET}, quantifies the FRET process by the number of quanta transferred from the donor’s excited state to the acceptor per time. It depends on the mutual dipole orientation of the donor and the acceptor fluorophore, the distance between the donor and acceptor, R_{DA}, the Förster radius, R_0 of the dye pair, and the corresponding fluorescence lifetime of the donor in the absence of FRET, \tau_{0}. The orientation factor \kappa^2 captures The mutual dipole orientation.

$$ k_{RET} = \frac{1}{\tau_0} \kappa^2 \left( \frac{R_0}{R_{DA}} \right)^{6} $$

Note, for the calculation of the FRET rate constant the fluorescence lifetime has to match the Förster radius. Meaning the fluorescence lifetime of the corresponding donor fluorescence quantum yield, \Phi_{F}^{D0} should be used.