Past exam of the biological physics course of the University of Oxford / 2022 / 1 / d / Solution

Let $k_D$ be the donor's total decay rate without acceptors, including radiative and nonradiative decay, and let $k_T$ be its transfer rate to one acceptor. In weak excitation, independent equivalent acceptors supply additive transfer rates, so FRET efficiency isEliminating $k_T/k_D=E/(1-E)$ givesThis assumes the same Förster distance, equivalent donor–acceptor distances and unchanged donor decay, with no acceptor saturation or other transfer pathways affecting donor de-excitation.

For Förster resonance energy transfer, $k_T/k_D=(R_0/R{)}^6$, henceHere the single-pair FRET efficiency would be $E=0.60$, which indeed produces $E_2=0.75$.