# Fluorescence resonance energy transfer

Fluorescence resonance energy transfer (or Förster resonance energy transfer) describes an energy transfer mechanism between two fluorescent molecules. A fluorescent donor is excited at its specific fluorescence excitation wavelength. By a long-range dipole-dipole coupling mechanism, this excited state is then nonradiatively transferred to a second molecule, the acceptor. The donor returns to the electronic ground state. The described energy transfer mechanism is termed "Förster resonance energy transfer" (FRET), named after the German scientist Theodor Förster . When both molecules are fluorescent, the term "fluorescence resonance energy transfer" is often used, although the energy is not actually transferred by fluorescence.

## Theoretical basis

The FRET efficiency is determined by three parameters:

1. The distance between the donor and the acceptor.
2. The spectral overlap of the donor emission spectrum and the acceptor absorption spectrum.
3. The relative orientation of the donor emission dipole moment and the acceptor absorption dipole moment.

The FRET efficiency E, which is defined as

E = 1 - τ'D / τD

where τ'D and τD are the donor fluorescence lifetimes in the presence and absence of an acceptor, respectively, or as

E = 1 - F'D / FD

where F'D and FD are the donor fluorescence intensities with and without an acceptor, respectively. E depends on the donor-to-acceptor separation distance r with an inverse 6th order law due to the dipole-dipole coupling mechanism:

E = 1 / (1 + (r / R0)6)

with R0 being the Förster distance of this pair of donor and acceptor at which the FRET efficiency is 50%. The Förster distance depends on the overlap integral of the donor emission spectrum with the acceptor absorption spectrum and their mutual molecular orientation as expressed by the following equation:

${R_0}^6 = 8.8 \times 10^{23} \; \kappa^2 \, n^{-4} \, Q_0 \, J$

where κ2 is the dipole orientation factor, n is the refractive index of the medium, Q0 is the fluorescence quantum yield of the donor in the absence of the acceptor, and J is the spectral overlap integral calculated as

$J = \int f_{\rm D}(\lambda) \, \epsilon_{\rm A}(\lambda) \, \lambda^4 \, d\lambda$

where fD is the normalized donor emission spectrum, and εA is the acceptor extinction coefficient. If either the donor or the acceptor is freely rotating (or both), κ2 = 2 / 3 is assumed. On this condition, the R0 value is determined only by the combination of the donor and acceptor molecules.

## Applications

In fluorescence microscopy, fluorescence confocal laser scanning microscopy, as well as in molecular biology, FRET is a useful biophysical tool to quantify molecular dynamics, such as protein-protein interactions, protein-DNA interactions, and protein conformational changes. For monitoring the complex formation between two molecules, one of them is labeled with a donor and the other with an acceptor, and these fluorophore-labeled molecules are mixed. When they are dissociated, the donor emission is detected upon the donor excitation. On the other hand, when the donor and acceptor are in close proximity (1-10 nm) due to the interaction of the two molecules, the acceptor emission is predominantly observed because of the intermolecular FRET from the donor to the acceptor. For monitoring protein conformational changes, the target protein is labeled with a donor and an acceptor at two loci. When a twist or bend of the protein brings the change in the distance or relative orientation of the donor and acceptor, FRET change is observed. If a molecular interaction or a protein conformational change is dependent on ligand binding, this FRET technique is applicable to fluorescent indicators for the ligand detection.

The most popular FRET pair for biological use is a cyan fluorescent protein (CFP)-yellow fluorescent protein (YFP) pair. Both are color variants of green fluorescent protein (GFP). While labeling with organic fluorescent dyes requires troublesome processes of purification, chemical modification, and intracellular injection of a host protein, GFP variants can be easily attached to a host protein by genetic engineering. By virtue of GFP variants, the use of FRET techniques for biological research is becoming more and more popular.

FRET is also a common tool in the study of reaction kinetics.

A different, but related, mechanism is the energy transfer of Dexter type.

## References:

Joseph R. Lakowicz, "Principles of Fluorescence Spectroscopy", Plenum Publishing Corporation, 2nd edition (July 1, 1999)

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07-14-2008 23:18:10