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

Question

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)

[latex]r_{0}\left(\mathring{A}\right)=8.79 ×10^{-5}\left( \frac{k^{2}J\Phi_{f}}{n^{4}} \right)^{1/6}[/latex] (19.181)

Accepted Answer

Using the initial separation distance and [latex]r_{0}[/latex], the efficiency is determined as follows:

[latex]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}}=0.23[/latex]

The detection limit corresponds to [latex]E_{ff}=0.18[/latex] . Solving for [latex]r[/latex] yields:

[latex]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}}[/latex]

[latex]\frac{\left( 9 \mathring{A}\right)^{6}}{0.18}=\left( 9 \mathring{A}\right)^{6}+r^{6}[/latex]

[latex]2.42×10^{6} \mathring{A}^{6}=r^{6}[/latex]

[latex]11.6 \mathring{A} =r[/latex]

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 [latex]r[/latex]. This example illustrates the importance of choosing FRET pairs having [latex]r_{0}[/latex] values that are close to the length scale of interest.

Question 19.5: You are designing a FRET experiment to determine the magnitu...

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