Förster resonance energy transfer (FRET), fluorescence resonance energy transfer, resonance energy transfer (RET) or electronic energy transfer (EET) is a mechanism describing energy transfer between two light-sensitive molecules (chromophores).^[1] A donor chromophore, initially in its electronic excited state, may transfer energy to an acceptor chromophore through nonradiative dipole–dipole coupling.^[2] The efficiency of this energy transfer is inversely proportional to the sixth power of the distance between donor and acceptor, making FRET extremely sensitive to small changes in distance.^[3][4]

Measurements of FRET efficiency can be used to determine if two fluorophores are within a certain distance of each other.^[5] Such measurements are used as a research tool in fields including biology and chemistry.

FRET is analogous to near-field communication, in that the radius of interaction is much smaller than the wavelength of light emitted. In the near-field region, the excited chromophore emits a virtual photon that is instantly absorbed by a receiving chromophore. These virtual photons are undetectable, since their existence violates the conservation of energy and momentum, and hence FRET is known as a radiationless mechanism. Quantum electrodynamical calculations have been used to determine that radiationless (FRET) and radiative energy transfer are the short- and long-range asymptotes of a single unified mechanism.^[6][7][8]

Terminology

Förster resonance energy transfer is named after the German scientist Theodor Förster.^[9] When both chromophores are fluorescent, the term "fluorescence resonance energy transfer" is often used instead, although the energy is not actually transferred by fluorescence.^[10][11] In order to avoid an erroneous interpretation of the phenomenon that is always a nonradiative transfer of energy (even when occurring between two fluorescent chromophores), the name "Förster resonance energy transfer" is preferred to "fluorescence resonance energy transfer"; however, the latter enjoys common usage in scientific literature.^[12] FRET is not restricted to fluorescence and occurs in connection with phosphorescence as well.^[10]

Theoretical basis

The FRET efficiency (${\displaystyle E}$) is the quantum yield of the energy-transfer transition, i.e. the probability of energy-transfer event occurring per donor excitation event:^[13]

${\displaystyle E={\frac {k_{\text{ET}}}{k_{f}+k_{\text{ET}}+\sum {k_{i}}}},}$

where ${\displaystyle k_{f}}$ the radiative decay rate of the donor, ${\displaystyle k_{\text{ET}}}$ is the rate of energy transfer, and ${\displaystyle k_{i}}$ the rates of any other de-excitation pathways excluding energy transfers to other acceptors.^[14][15]

The FRET efficiency depends on many physical parameters^[16] that can be grouped as: 1) the distance between the donor and the acceptor (typically in the range of 1–10 nm), 2) the spectral overlap of the donor emission spectrum and the acceptor absorption spectrum, and 3) the relative orientation of the donor emission dipole moment and the acceptor absorption dipole moment.

${\displaystyle E}$ depends on the donor-to-acceptor separation distance ${\displaystyle r}$ with an inverse 6th-power law due to the dipole–dipole coupling mechanism:

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

with ${\displaystyle R_{0}}$ being the Förster distance of this pair of donor and acceptor, i.e. the distance at which the energy transfer efficiency is 50%.^[14] 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 all in SI units:^[17][18][19]

${\displaystyle {R_{0}}^{6}={\frac {2.07}{128\,\pi ^{5}\,N_{A}}}\,{\frac {\kappa ^{2}\,Q_{D}}{n^{4}}}J}$

where ${\displaystyle Q_{\text{D}}}$ is the fluorescence quantum yield of the donor in the absence of the acceptor, ${\displaystyle \kappa ^{2}}$ is the dipole orientation factor, ${\displaystyle n}$ is the refractive index of the medium, ${\displaystyle N_{\text{A}}}$ is the Avogadro constant, and ${\displaystyle J}$ is the spectral overlap integral calculated as

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

where ${\displaystyle f_{\text{D}}}$ is the donor emission spectrum, ${\displaystyle {\overline {f_{\text{D}}}}}$ is the donor emission spectrum normalized to an area of 1, and ${\displaystyle \epsilon _{\text{A}}}$ is the acceptor molar extinction coefficient, normally obtained from an absorption spectrum.^[20] The orientation factor κ is given by

${\displaystyle \kappa ={\hat {\mu }}_{\text{A}}\cdot {\hat {\mu }}_{\text{D}}-3({\hat {\mu }}_{\text{D}}\cdot {\hat {R}})({\hat {\mu }}_{\text{A}}\cdot {\hat {R}}),}$

where ${\displaystyle {\hat {\mu }}_{i}}$ denotes the normalized transition dipole moment of the respective fluorophore, and ${\displaystyle {\hat {R}}}$ denotes the normalized inter-fluorophore displacement.^[21] ${\displaystyle \kappa ^{2}}$ = 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 ${\displaystyle \kappa ^{2}}$ = 2/3 will not be a valid assumption. In most cases, however, even modest reorientation of the dyes results in enough orientational averaging that ${\displaystyle {\mathrm{\kappa <!--\; \kappa \; -->}}^{}}$Zdroj:https://en.wikipedia.org?pojem=Fluorescence_resonance_energy_transfer
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