In Fluorescence Resonance Energy Transfer (FRET) the FRET efficiency may be expressed as function of distances:
E(r) = 1 / [1 + (r / R0)6],
where r = distance between donor and acceptor chromophores,
and R0 = Forster Radius with 50% Transfer Efficiency. R0 may be understood as the inflection point of the "E" vs "r" graph. Maybe that is fundamentally helpful in the understanding of R0, but if you are don't know what the distances are, how can you know what R0 is?
E can be deduced from the following relationship with the donor quenching method:
E = 1 - ( IDA / ID), where IDA is intensity of donor in presence of Acceptor and ID is the intensity of the donor in the absence of Acceptor.
So if my algebra is right, then "r" may be calculated:
r = 6√[(1 / E) - 1] * R0
So now to get the distance I just need to know R0. Is there a simple mathematical derivation for R0 or is it just constant for each pair of donor and acceptor fluorescent molecules, like R0 is fixed for Cy3 & Cy5; and GFP and YFP donor-acceptor pairs, etcetera? If so then where can I find the most reliable tables of R0 for donor-and acceptor pairs?
From my equation, it would seem that large values of the Forster Radius would allow larger distances to be measured with FRET, but if I had a Forster Radius of say 8 nanometers, then could I still measure 2 nanometer distances well with my donor-acceptor pairs, or does the Forster Radius have some reliability range? Well, from my graphs, it does not look like the case.
Thanks!
Sources:
Libretexts. “Fluorescence Resonance Energy Transfer.” Chemistry LibreTexts, National Science Foundation, 24 Sept. 2018,
chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Fundamentals/Fluorescence_Resonance_Energy_Transfer
The easiest method is to use a value of Ro that has already been reported by someone else in a similar medium.
The experimental calculation is based on measuring the overlap integral between the absorbance spectrum of the donor and the instrument-corrected fluorescence emission spectrum of the acceptor, as well as the quantum yield of the donor, the refractive index of the medium, and the orientation factor kappa2. Unfortunately, it is generally not possible to measure kappa2, so it is usually assumed to have the dynamic average value 2/3, although there is a method for estimating upper and lower bounds based on fluorescence anisotropy measurements. For the other measurements, you need a spectrophotometer, a spectrofluorometer, and a refractometer.
For an example of a measurement of Ro, see this paper:
Article Extraction of Hoechst 33342 from the Cytoplasmic Leaflet of ...
You should also read this paper:
Article Resonance Energy Transfer: Methods and Applications
The highest accuracy for the distance measurement is made close to the Ro, as you surmised from your graph. At much shorter distances, the energy transfer efficiency is close to 100%, so there is little ability to differentiate between distances. Therefore, to measure short distances you need a pair of probes with a small Ro. Also, as you said, to measure long distances requires a pair of probes with large values of Ro. Alternatively, you could increase the energy transfer efficiency by having more than one acceptor molecule present.
Second part of your question: Yes it is possible, since Ro means 50% efficiency (roughly meaning almost maximum energy transfer below Ro value and minimal above, see also reference Sahoo, 2011). You can detect energy transfer below the value of Ro.
Your other matter related to how the calculate (or measure) the distance:
There are (roughly) two ways:
1. Theoretical: the main point to focus on is the spectral overval of the emission (donor) and excitation spectrum (acceptor).
2. Experimentally: the main point is the quenching of the donor emission at various concentrations of acceptor.
See for an example:
Article Characterization of the Resonance Energy Transfer Couple Cou...
For more details on the calculation you could check the (older) publications such as:
Wolber, P. K., & Hudson, B. S. (1979). An analytic solution to the Förster energy transfer problem in two dimensions. Biophysical journal, 28(2), 197-210.
A nice way to get exercise your math skills… Some interesting background information you can find here:
Sahoo, H. (2011). Förster resonance energy transfer–A spectroscopic nanoruler: Principle and applications. Journal of Photochemistry and Photobiology C: Photochemistry Reviews, 12(1), 20-30.
Hope this is of any help to bring you further.
Dr Keller's answer is exactly right - I would point out that due to the sixth power dependence on distance, there is very little energy transfer at distances greater than Ro
The easiest method is to use a value of Ro that has already been reported by someone else in a similar medium.
The experimental calculation is based on measuring the overlap integral between the absorbance spectrum of the donor and the instrument-corrected fluorescence emission spectrum of the acceptor, as well as the quantum yield of the donor, the refractive index of the medium, and the orientation factor kappa2. Unfortunately, it is generally not possible to measure kappa2, so it is usually assumed to have the dynamic average value 2/3, although there is a method for estimating upper and lower bounds based on fluorescence anisotropy measurements. For the other measurements, you need a spectrophotometer, a spectrofluorometer, and a refractometer.
For an example of a measurement of Ro, see this paper:
Article Extraction of Hoechst 33342 from the Cytoplasmic Leaflet of ...
You should also read this paper:
Article Resonance Energy Transfer: Methods and Applications
The highest accuracy for the distance measurement is made close to the Ro, as you surmised from your graph. At much shorter distances, the energy transfer efficiency is close to 100%, so there is little ability to differentiate between distances. Therefore, to measure short distances you need a pair of probes with a small Ro. Also, as you said, to measure long distances requires a pair of probes with large values of Ro. Alternatively, you could increase the energy transfer efficiency by having more than one acceptor molecule present.
- Badges
- Science topic
- Similar topics
- Chemistry