Förster resonance energy transfer

Cartoon diagram of the concept of Förster resonance energy transfer (FRET).

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]

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 ${\displaystyle \kappa ^{2}}$ = 2/3 does not result in a large error in the estimated energy-transfer distance due to the sixth-power dependence of ${\displaystyle R_{0}}$ on ${\displaystyle \kappa ^{2}}$. Even when ${\displaystyle \kappa ^{2}}$ is quite different from 2/3, the error can be associated with a shift in ${\displaystyle R_{0}}$, 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 ≤ ${\displaystyle \kappa ^{2}}$ ≤ 4.[20]

The units of the data are usually not in SI units. Using the original units to calculate the Förster distance is often more convenient. For example, the wavelength is often in unit nm and the extinction coefficient is often in unit ${\displaystyle M^{-1}cm^{-1}}$, where ${\displaystyle M}$ is concentration ${\displaystyle mol/L}$. ${\displaystyle J}$ obtained from these units will have unit ${\displaystyle M^{-1}cm^{-1}nm^{4}}$. To use unit Å (${\displaystyle 10^{-10}m}$) for the ${\displaystyle R_{0}}$, the equation is adjusted to [17][22][23][24]

${\displaystyle {R_{0}}^{6}=8.785\times 10^{-5}{\frac {\kappa ^{2}\,Q_{D}}{n^{4}}}J}$ (Å${\displaystyle ^{6}}$)

For time-dependent analyses of FRET, the rate of energy transfer (${\displaystyle k_{\text{ET}}}$) can be used directly instead:[17]

${\displaystyle k_{\text{ET}}=({\frac {R_{0}}{r}})^{6}\,{\frac {1}{\tau _{D}}}}$

where ${\displaystyle \tau _{D}}$ is the donor's fluorescence lifetime in the absence of the acceptor.

The FRET efficiency relates to the quantum yield and the fluorescence lifetime of the donor molecule as follows:[25]

${\displaystyle E=1-\tau '_{\text{D}}/\tau _{\text{D}},}$

where ${\displaystyle \tau _{\text{D}}'}$ and ${\displaystyle \tau _{\text{D}}}$ are the donor fluorescence lifetimes in the presence and absence of an acceptor respectively, or as

${\displaystyle E=1-F_{\text{D}}'/F_{\text{D}},}$

where ${\displaystyle F_{\text{D}}'}$ and ${\displaystyle F_{\text{D}}}$ are the donor fluorescence intensities with and without an acceptor respectively.

The inverse sixth-power distance dependence of Förster resonance energy transfer was experimentally confirmed by Wilchek, Edelhoch and Brand[26] using tryptophyl peptides. Stryer, Haugland and Yguerabide[27][28] also experimentally demonstrated the theoretical dependence of Förster resonance energy transfer on the overlap integral by using a fused indolosteroid as a donor and a ketone as an acceptor. Calculations on FRET distances of some example dye-pairs can be found here.[22][24] However, a lot of contradictions of special experiments with the theory was observed under complicated environment when the orientations and quantum yields of the molecules are difficult to estimate.[29]

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. The FRET efficiency is measured and used to identify interactions between the labeled complexes. There are several ways of measuring the FRET efficiency by monitoring changes in the fluorescence emitted by the donor or the acceptor.[30]

The applications of fluorescence resonance energy transfer (FRET) have expanded tremendously in the last 25 years, and the technique has become a staple in many biological and biophysical fields. FRET can be used as a spectroscopic ruler to measure distance and detect molecular interactions in a number of systems and has applications in biology and biochemistry.[28][52]

Chemosensor

FRET-based probe that activates upon interaction with Cd2+

FRET-based probes can detect the presence of various molecules: the probe's structure is affected by small molecule binding or activity, which can turn the FRET system on or off. This is often used to detect anions, cations, small uncharged molecules, and some larger biomacromolecules as well. Similarly, FRET systems have been designed to detect changes in the cellular environment due to such factors as pH, hypoxia, or mitochondrial membrane potential.[64]

A different, but related, mechanism is Dexter electron transfer.

An alternative method to detecting protein–protein proximity is the bimolecular fluorescence complementation (BiFC), where two parts of a fluorescent protein are each fused to other proteins. When these two parts meet, they form a fluorophore on a timescale of minutes or hours.[77]

• Dexter electron transfer
• Förster coupling
• Surface energy transfer
• Time-resolved fluorescence energy transfer

• FRET effect in a thin film on YouTube
• FRET Imaging (Tutorial of Becker & Hickl, website)