Question

A protein has three identical sites arranged at the vertices of an equilateral triangle. With one site filled with donor dye, the quantum yield \(\phi_D\) is \(0.5\). Filling one site with donor and a second with acceptor gives \(\phi_D=0.25\). Find \(\phi_D\) when one site has donor and the other two have acceptor dyes (rounded to three decimals).

Hint:

FRET/quencher effects add as rates: \(\phi=\dfrac{k_f}{k_f+k_{nr}+\sum k_{ET,i}}\).

Answer 1

Correct Answer: 0.165

Step 1: Let \(k_f\) be donor radiative rate and \(k_{nr}\) non-radiative rate. With no acceptor: \(\phi_1=\dfrac{k_f}{k_f+k_{nr}}=0.5 \Rightarrow k_f+k_{nr}=2k_f\).
Step 2: With one acceptor, extra transfer rate \(k_{ET}\) adds: \[ \phi_2=\frac{k_f}{k_f+k_{nr}+k_{ET}}=\frac{k_f}{2k_f+k_{ET}}=0.25 \Rightarrow 2+\frac{k_{ET}}{k_f}=4 \Rightarrow k_{ET}=2k_f. \] Step 3: With two identical acceptors, total transfer rate \(=2k_{ET}=4k_f\). Hence \[ \phi_3=\frac{k_f}{k_f+k_{nr}+2k_{ET}} =\frac{k_f}{2k_f+4k_f}=\frac{1}{6}=0.166\overline{6}\approx \boxed{0.167}. \]