# FRET Efficiency Calculator

Created by Davide Borchia
Last updated: Nov 30, 2022

At the atomic scale, molecules interact through interesting and elegant processes: learn how a non-radiative transfer of energy has become a useful tool in biochemistry with our FRET efficiency calculator!

When biochemistry became interested in phenomena at the scale of a protein or a cell membrane, many of the techniques in use lacked sufficient resolution: the activities of molecules were mostly hidden by physics. The discovery of a process where the signal is both strongly dependent on the distance and extremely sensitive in the nanometer scale opened the world to studying a small, active world.

With our FRET efficiency calculator, you will learn:

• What is the Förster resonance energy transfer;
• How is it used as a detection technique in biochemistry;
• How to calculate the characteristic FRET distance of a transfer;
• How to calculate the FRET efficiency.

If you're a chemist, then be sure also to check the theoretical yield calculator, which is a great tool assisting you during the synthesis.

## What is FRET?

The Förster resonance energy transfer (FRET) is a process involving two molecules sensitive to light that sees the transfer of energy through a process of resonant relaxation and excitation.

The process requires the presence of two molecules:

• A donor; and
• An acceptor.

The process begins with the donor in an excited electronic state (one of its outer shell electrons lies in a higher energy level). After an eventual relaxation, the donor can return to the ground state, transferring a certain amount of energy to the acceptor through long-range dipole-dipole interactions.

The transfer of energy between the donor and the acceptor is highly dependent on distance: studying the emission of the photon energy and light intensity from the relaxation of the acceptor gives important information on the proximity of a pair of molecules and of changes in the chemical surroundings.

🔎 Genetic engineering helped make up for the relative rarity of light-sensitive and fluorescent molecules, for example, by genetically encoding photosensitive features in proteins.

## How to calculate the critical distance in a FRET process

The critical distance of a FRET process is the distance at which the transfer has $50\%$ efficiency (half of the energy of the donor's relaxation is used by the acceptor). The equation for the FRET critical distance is:

$R_0 = 0.2108\cdot (n^{-4}\!\cdot\! \Phi_{\text{D}}\!\cdot\! \kappa^2\!\cdot\! J)^{\frac{1}{6}}$

Where:

• $n$ is the index of refraction of the solution;
• $\phi_{\text{D}}$ is the donor fluorescence quantum yield;
• $\kappa^2$ is the orientation factor for the transition dipoles; and
• $J$ is the overlap between the emission and absorption spectra of donor and acceptor.

For a situation with the following parameters:

• $n=1.45$;
• $\kappa^2 = 0.667$;
• $\phi_{\text{D}} = 1$; and
• $J = 6.83\cdot10^{9}$;

we find that the FRET distance for half efficiency is:

$R_0 = 0.98\ \text{nm}$

## How to calculate the FRET efficiency

The FRET efficiency is the quantum yield of the energy transfer process. The non-radiative transfer has a strong dependency on the distance, as you can clearly see from the FRET efficiency equation:

$E = \frac{1}{1+\left(\frac{r}{R_0}\right)^6}$

Where:

• $r$ is the distance between donor and acceptor; and
• $R_0$ is the Förster distance.

The dependence of the FRET efficiency on the distance with exponent $6$ makes this phenomenon extremely sensitive to small changes in the separation between donor and acceptor. Older fluorescence methods used in biochemistry lacked resolution (being limited by the wavelength of the light used).

Taking as an example the previously calculated FRET distance, we can find the efficiency of the transfer at the intermolecular distance r=0.87\ text{nm}. Plug these values in the FRET efficiency equation:

$E = \frac{1}{1+\left(\frac{0.87}{0.98}\right)^6} = 0.68$
Davide Borchia
Donor fluorescence quantum yield (ϕD)
Orientation factor for the transition dipoles (κ²)
Refractive index (n)
Spectra overlap (J)
x10¹⁶
nm⁴/(M⋅cm)
Distance (r)
nm
Förster distance (R₀)
nm
FRET efficienciy (E)
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