Forester radius

The Förster radius ( R ₀ ) or Förster distance , which was named after the German physical chemist Theodor Förster , describes the distance between two dyes (donor and acceptor) at which the efficiency E of a radiation-free energy transfer via Förster resonance energy transfer between the two 50% dyes is:

${\displaystyle E={\frac {1}{1+(r/R_{0})^{6}}}\!}$,

where r is the distance between the two dyes.

The Förster radius depends on the quantum yield of the donor without energy transfer Q ₀ , the dipole orientation factor κ , the refractive index n of the medium at the wavelengths relevant for energy transfer and the integral J from the overlapping spectra of donor and acceptor:

${\displaystyle {R_{0}}^{6}={\frac {9\cdot (\ln 10)\cdot (\kappa ^{2}\,n^{-4}\,Q_{0}\,J)}{128\,\pi ^{5}\,N_{A}}}=8,8\cdot 10^{-28}\cdot (\kappa ^{2}\,n^{-4}\,Q_{0}\,J)}$.

Here J depends on the normalized radiation emission intensity of the donor f _D (λ) at the wavelength λ and the extinction coefficient of the acceptor ε _A (λ) :

${\displaystyle J=\int f_{\rm {D}}(\lambda )\,\epsilon _{\rm {A}}(\lambda )\,\lambda ^{4}\,d\lambda }$.

The orientation factor κ ² depends on the angle between the emission dipole of the donor and the absorption dipole of the acceptor θ _DA as well as the angles between both dipoles and the connection vector between donor and acceptor θ _D and θ _A :

${\displaystyle \kappa ^{2}=(\cos \theta _{DA}-3\cos \theta _{D}\cos \theta _{A})^{2}\!}$,

where κ ² can assume values ​​between 0 and 4. With orthogonality of the dipoles, κ ^{2 is} 0, with parallel arrangement 1 and with collinearly arranged dipoles 4. For freely moving dyes, for example when investigating processes in solution, κ ^{2 is} 2/3.

The Förster radii determined for some frequently used donor-acceptor pairs are shown in the following table:

Donor	Acceptor	R 0 (nm)
Tryptophan	Dansyl	2.1
Dansyl	FITC	3.3-4.1
eCFP	eGFP	4.7-4.9
Cyanine Cy3	Cyanine Cy5	> 5.0
6-carboxyfluorescein	Texas Red	5.1
Fluorescein	Tetramethylrhodamine	5.5
eGFP	eYFP	5.5-5.7
Cyanine Cy5	Cyanine Cy5.5	> 8.0

Individual evidence

1. ^ Robert M. Clegg: Forster resonance energy transfer - FRET what is it, why do it, and how it's done . In: Theodorus WJ Gadella (Ed.): FRET and FLIM techniques . Elsevier, Amsterdam 2009, ISBN 0-08-054958-6 , pp. 1-58.
2. ↑ Olympus: Applications in Confocal Microscopy: Fluorescence Resonance Energy Transfer (FRET) Microscopy ( en ) Archived from the original on May 9, 2015. Retrieved July 13, 2016.

literature

• Entry on Förster-resonance-energy transfer (FRET) . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.FT07381 Version: 2.3.1.