Question 19.5: You are designing a FRET experiment to determine the magnitu...
You are designing a FRET experiment to determine the magnitude of the structural change introduced by substrate binding to an enzyme. Using site specific mutagenesis, you have constructed a mutant form of the enzyme that possesses a single tyrosine residue and a single tryptophan residue, and these residues are separated by 11 \mathring{A}. You would like to determine if the distance between these residues changes with substrate binding. The fluorescence of tyrosine overlaps with the tryptophan absorption; therefore, these two amino acids form a FRET pair for which r_{0}=9 \mathring{A}, determined using the absorption and emission spectra in combination with Equation (19.181). Calculate the FRET efficiency at 11 \mathring{A} separation and how much this distance must increase in order for the efficiency to decrease by 20\%, the experimental detection limit.
r_{0}\left(\mathring{A}\right)=8.79 ×10^{-5}\left( \frac{k^{2}J\Phi_{f}}{n^{4}} \right)^{1/6} (19.181)
Using the initial separation distance and r_{0}, the efficiency is determined as follows:
E_{ff}=\frac{r_{0}^{6}}{r_{0}^{6}+r^{6}}=\frac{\left( 9 \mathring{A}\right)^{6}}{\left( 9 \mathring{A}\right)^{6}+\left( 11 \mathring{A} \right)^{6}}=0.23The detection limit corresponds to E_{ff}=0.18 . Solving for r yields:
E_{ff}=0.18=\frac{r_{0}^{6}}{r_{0}^{6}+r^{6}}=\frac{\left( 9 \mathring{A}\right)^{6}}{\left( 9 \mathring{A}\right)^{6}+r^{6}}\frac{\left( 9 \mathring{A}\right)^{6}}{0.18}=\left( 9 \mathring{A}\right)^{6}+r^{6}
2.42×10^{6} \mathring{A}^{6}=r^{6}
11.6 \mathring{A} =r
Notice that for this FRET pair the modification of the tyrosine–tryptophan separation accompanying substrate binding can be measured for a relatively limited change in r. This example illustrates the importance of choosing FRET pairs having r_{0} values that are close to the length scale of interest.