128 4.3  Förster Resonance Energy Transfer

electronic energy levels for excitation and emission overlap significantly, and so the term

fluorescent energy resonance transfer is sometimes applied, though the physical process of

FRET in itself does not necessarily require fluorescence. The length scale of operation of

FRET is comparable to that of many biomolecules and molecular machines and so can be

used as a metric for molecular interaction between two different molecules if one is labeled

with a donor and the other with an appropriate acceptor molecule.

In FRET, the donor fluorophore emits at a lower peak wavelength than the acceptor

fluorophore. Resonance transfer of energy between the two is therefore manifest as a small

reduction in fluorescence emission intensity from the donor, and a small increase in fluor­

escence emission intensity of the acceptor (Figure 4.2c and d). The length scale of energy

transfer is embodied in the Förster radius, R0, which is the distance separation that yields

a FRET efficiency of exactly 0.5. The efficiency ε of the energy transfer as a function of the

length separation R of the donor–​acceptor pair is characterized by

(4.7)

ε =

=

+

+

=

=

∑

∑

k

k

k

k

k

k

FRET

i

donors

i

radiative

j

other donors

1

1

FRET

FRET

j

R R

=

+(

)

1

1

0

6

/

The constant kFRET is the rate of energy transfer from donor to acceptor by FRET, whereas

the summed parameters Σki are the energy transfer rates from the donor of all energy

transfer processes, which include FRET and radiative processes plus various non-​FRET and

nonradiative processes (Σki). With no acceptor, a donor transfers energy at rate (kradiative +​

Σki), and so the mean donor lifetime TD is equal to 1/​(kradiative +​ Σki). With an acceptor pre­

sent, FRET occurs at a rate kFRET such that the donor lifetime τDA is then equal to (R0/​R)⁶/​kFRET,

indicating that ε =​ 1 − τDA/​τD.

We can also write ε =​ 1 − IDA/​ID where IDA and ID are the total fluorescence emission

intensities of the donor in the presence and the absence of the acceptor, respectively; in prac­

tice, the intensity values are those measured through an emission filter window close to the

emission peak of the donor fluorophore in question. Similarly, we can say that ε =​ (IAD −

IA)/​IA where IAD and IA are the total fluorescence emission intensities of the acceptor in the

presence and the absence of the donor, respectively. These formulations assume that there is

minimal fluorophore cross talk between the two excitation lasers used for the acceptor and

donor (i.e., that the donor is not significantly excited by the acceptor laser, and the acceptor

is not significantly excited by the donor laser). Also, that there is minimal bleed-​through

between the fluorescence emissions of each fluorophore between the two detector emission

channels. A simpler formulation involves the relative FRET efficiency used in ratiometric

FRET, of εrel =​ IA/​(IA +​ ID) with IA and ID being the total fluorescence intensities for acceptor

and donor, respectively, following excitation of just the donor. However, if the acceptor and

donor emission spectra overlap, then this mixed spectrum must be decomposed into the

separate component spectra to accurately measure IA and ID, which is often nontrivial. Rarely,

one can equate εrel to the actual FRET efficiency (ε) in the case of minimal laser/​fluorophore

cross talk, in practice, though converting εrel to the actual FRET efficiency (ε) usually requires

two correction factors of the contribution from direct acceptor excitation to IA and the ratio

between the donor and the acceptor fluorescence emission quantum yields. Additionally,

corrections may be needed to account for any fluorescence bleed-​through between the

acceptor and donor detector channels.

Note that sometimes a FRET pair can actually consist of a dye molecule and a nearby

quencher molecule, instead of a donor and acceptor molecule. Here, the distance depend­

ence between the dye and quencher is the same as that of a donor and acceptor molecule

since the mechanism of nonradiative energy transfer is the same. However, the quencher

does not emit fluorescence, and so the drop in normalized intensity of a dye molecule under­

going quenching is 1 − ε.