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# Fluorescence resonance energy transfer

Fluorescence resonance energy transfer (FRET) describes an energy transfer mechanism between two chromophores.

A donor chromophore in its excited state can transfer energy by a nonradiative, long-range dipole-dipole coupling mechanism to an acceptor chromophore in close proximity (typically <10nm). This 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.[2],[3]. In order to avoid an erroneous interpretation of the phenomenon that, even when occurring between two fluorescent molecules, is always a nonradiative transfer of energy, the name "Förster resonance energy transfer" may be preferred to "Fluorescence resonance energy transfer".

## Theoretical basis

The FRET efficiency (E) is the quantum yield of the energy transfer transition, i.e. the fraction of energy transfer event occurring per donor excitation event:

$E = \frac{k_{ET}}{k_f+k_{ET}+\sum{k_i}}$

where kET is the rate of energy transfer, kf the radiative decay rate and the ki are the rate constants of any other de-excitation pathway.

The FRET efficiency depends on many parameters that can be grouped as follows:

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

E depends on the donor-to-acceptor separation distance r with an inverse 6th power law due to the dipole-dipole coupling mechanism:

$E=\frac{1}{1+(r/R_0)^6}\!$

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:

${R_0}^6 = 8.8 \times 10^{-28} \; \kappa^2 \, n^{-4} \, Q_0 \, J$

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 molar extinction coefficient. κ2 =2/3 is often assumed. This value is obtained when both dyes are freely rotating and can be considered to be isotropically oriented during the excited state lifetime. If either dye is fixed or not free to rotate, then κ2 =2/3 will not be a valid assumption. In most cases, however, even modest reorientation of the dyes results in enough orientational averaging that κ2 = 2/3 does not result in a large error in the estimated energy transfer distance due to the sixth power dependence of R0 on κ2. Even when κ2 is quite different from 2/3 the error can be associated with a shift in R0 and thus determinations of changes in relative distance for a particular system are still valid. Fluorescent proteins do not reorient on a timescale that is faster than their fluorescence lifetime. In this case 0 ≤ κ2 ≤ 4.

The FRET efficiency relates to the quantum yield and the fluorescence lifetime of the donor molecule as follows:

$E = 1 - {\tau'_{\rm D}}/{\tau_{\rm D}} \!$

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

$E = 1 - {F'_{\rm D}}/{F_{\rm D}} \!$

where F'D and FD are the donor fluorescence intensities with and without an acceptor, respectively.

## Methods

In fluorescence microscopy, fluorescence confocal laser scanning microscopy, as well as in molecular biology, FRET is a useful tool to quantify molecular dynamics in biophysics and biochemistry, 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 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.

FRET studies are scalable: the extent of energy transfer is often quantified from the milliliter scale of cuvette-based experiments to the femtoliter scale of microscopy-based experiments. This quantification can be based directly (sensitized emission method) on detecting two emission channels under two different excitation conditions (primarily donor and primarily acceptor). However, for robustness reasons, FRET quantification is most often based on measuring changes in fluorescence intensity or fluorescence lifetime upon changing the experimental conditions (e.g. a microscope image of donor emission is taken with the acceptor being present. The acceptor is then bleached, such that it is incapable of accepting energy transfer and another donor emission image is acquired. A pixel-based quantification using the second equation in the theory section above is then possible.) An alternative way of temporarily deactivating the acceptor is based on its fluorescence saturation. Exploiting polarisation characteristics of light, a FRET quantification is also possible with only a single camera exposure.

### CFP-YFP pairs

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.

### BRET

A limitation of FRET is the requirement for external illumination to initiate the fluorescence transfer, which can lead to background noise in the results from direct excitation of the acceptor or to photobleaching. To avoid this drawback, Bioluminescence Resonance Energy Transfer (or BRET) has been developed. This technique uses a bioluminescent luciferase (typically the luciferase from Renilla reniformis) rather than CFP to produce an initial photon emission compatible with YFP.

FRET and BRET are also the common tools in the study of biochemical reaction kinetics and molecular motors.

### Other methods

A different, but related, mechanism is Dexter Electron Transfer.

An alternative method to detecting protein-protein proximity is BiFC where two halves of a YFP are fused to a protein (Hu, Kerppola et al. 2002). When these two halves meet they form a fluorophore after about 60 s - 1 hr.

## Applications

FRET has been applied in an experimental method for the detection of phosgene. In it, phosgene or rather triphosgene as a safe substitute serves as a linker between an acceptor and a donor coumarine (forming urea groups).[4] The presence of phosgene is detected at 5x10-5M with a typical FRET emission at 464 nm.

## References

1. ^ Inconspicuous Consumption: Uncovering the Molecular Pathways behind Phagocytosis. Inman M, PLoS Biology Vol. 4/6/2006, e190. doi:10.1371/journal.pbio.0040190
2. ^ Joseph R. Lakowicz, "Principles of Fluorescence Spectroscopy", Plenum Publishing Corporation, 2nd edition (July 1, 1999)
3. ^ FRET microscopy tutorial from Olympus
4. ^ A FRET approach to phosgene detection Hexiang Zhang and Dmitry M. Rudkevich Chem. Commun., 2007, 1238 - 1239, doi:10.1039/b614725a