FRET Theory

Förster Resonance Energy Transfer

FRET efficiency \(E\) depends on the distance \(r\) between a donor and an acceptor fluorophore according to the Förster equation:

\[E = \frac{1}{1 + (r/R_0)^6}\]

where \(R_0\) is the Förster distance at which the transfer efficiency is 50%.

The Orientation Factor (\(\kappa^2\))

The Förster distance \(R_0\) depends on the relative orientation of the donor and acceptor transition dipoles, described by the orientation factor \(\kappa^2\):

\[\kappa^2 = (\cos \theta_T - 3 \cos \theta_D \cos \theta_A)^2\]

While \(\kappa^2 = 2/3\) is often assumed for randomly oriented dyes, diff-fret implements the Dale-Eisinger-Blumberg (1979) model to estimate the upper and lower bounds of \(\kappa^2\) based on measured fluorescence anisotropy \(r_{obs}\):

\[\langle \kappa^2 \rangle_{max} = \frac{2}{3} (1 + d_D + d_A + 3 d_D d_A)$$ $$\langle \kappa^2 \rangle_{min} = \frac{2}{3} \left[ 1 - \frac{1}{2}(d_D + d_A) \right]\]

where \(d = \sqrt{r_{obs}/r_{0}}\) is the axial depolarization factor.