 | Box 1
Nature Biotechnology
21, 1387 - 1395 (2003)
Published online: 31 October 2003; | doi:10.1038/nbt896
FRET imagingElizabeth A Jares-Erijman
& Thomas M Jovin | | | 
| Photophysical primer
One can regard a given fluorophore as a photophysical catalyst that in a real functional sense shares many attributes of a protein catalyst (an enzyme). That is, the steady-state formalism of the familiar Michaelis-Menten kinetics applies directly to the transformation by a fluorophore F of its 'substrate'—a photon (of wavelength  1 and energy hc/1; h, Planck's constant; and c, velocity of light)—that 'binds' (is absorbed) into a 'product'— a photon at longer wavelength 2 (and of lesser energy hc/2) with an efficiency dictated by alternative nonradiative pathways (Fig. 2).
At low 'substrate concentration,' the rate of photon emission is linearly dependent on light intensity, or more precisely, photon flux  (photons s-1 cm-2) = 5  1015 irradiance (W cm-2) wavelength (nm). The photonic 'K
M', the value of yielding half the maximal fluorescence signal, is given by [  ]-1, where is the absorption cross-section (a measure of photon capture probability, a quantity proportional to the decadic molar absorption coefficient  ; = 3.8 10-21), and is the first excited singlet state (S1 = F
*) lifetime; = k
d
-1 = [k
f + k
nr]-1; k
f and k
nr are the radiative and nonradiative deactivation rate constants, respectively, excluding for the moment other competing processes described below. The initial slope (emission versus excitation photon flux), equivalent to the enzymatic k
cat/K
M, is given by Q; the fluorescence quantum yield (Q) is defined as the ratio of emitted to absorbed photons or by the equivalent expression k
f/k
d = k
f. The process saturates at high 'substrate concentration' (irradiance; Fig. 2) because the fluorophore is maintained in the excited singlet state (assuming the absence of a finite triplet steady-state population), thus yielding a maximal 'turnover' rate equal to k
f. This maximal rate of fluorescence emission, given by the reciprocal of the radiative lifetime, is independent of Q and of the excitation light intensity and stability, implying that the most sensitive, quantitative, rapid and possibly simplest determination of molecular number, local density or concentration may often be achieved by operating at saturation instead of in the low, linear, range universally espoused for quantitative biological microscopy.
The total photon yield/fluorophore/pulse (PY) for a rectangular excitation pulse of length t =  , and photon flux  =  /() is given by equation (4), in which PYon and PYoff are the integrated photon emissions during the light (irradiation) and dark (post-irradiation decay) phases, respectively. For >> 1 (the saturation condition): PY Q(1+) and the ratio function OnOff . If is also >>1 (that is, t >> ) PY Q  k
f
t, confirming the result derived above from the steady-state solution in Figure 2.
Saturation can be achieved to any desired degree by selection of light pulses of a given repetition rate, duty cycle and duration. These parameters are generally selected so as to reduce background, triplet state buildup, photodestruction and generation of potentially cytotoxic photoproducts (see valuable discussions in refs. 23,92). One can minimize the latter two reactions by limiting the photon dose (irradiance exposure time  ).
According to equation (4), a single fluorescein-like molecule ( = 105 M-1 cm-1, = 4 ns, Q = 0.4) exposed to an 8-ns pulse of 0.2 nJ at 488 nm focused to an area of 1  m2 ( = 2, = 9.3) will on average emit 0.69 photons in the light phase and 0.36 photons in the dark phase; the OnOff ratio, 1.9, is very close to , in accordance with the limiting cases given for equation (4) (see also Fig. 1b). The ratio of PY to a given irradiation 'dose' ( = 18.5 photons in the above example) constitutes a measure of 'photon conversion efficiency' and thus of signal-to-background contrast. In the event of significant contributions from scattering and short-lived luminescent components, one may wish to gate detection during the pulsed excitation cycle, thereby restricting the signal to PYoff.
Photobleaching limits the number of cycles (photon 'turnovers') to  pb/, in which pb is the reciprocal photobleaching rate (Fig. 5). A typical value is 105 cycles (fluorescein), implying that 102 repetitions would be possible for single determinations based on 103 excitation pulses. On the other hand, photobleaching can also be exploited to obtain information, as in determinations of FRET (pbFRET, Id1 and Id2, Table 1) and of translational diffusion (FRAP, FLIP86 and FLAP93).
To explore quantitatively the region of saturation (that is, depletion of the ground state), we are obliged to expand the formalism to account for transitions to and from the triplet state, RET between donor and acceptor fluorophores and photobleaching (Fig. 5a). The corresponding rate equations for a complete kinetic scheme are first-order except for the virtual second-order RET reaction involving donor* (D*) and acceptor (A) in the forward and acceptor* (A*) and donor (D) in the reverse direction. We circumvent this difficulty by representing the system in terms of transitions between donor-acceptor pairs in the different electronic states (Fig. 5b), thereby obtaining analytical expressions that permit the exploration of arbitrary degrees of saturation of both donor and acceptor (see also ref. 29).
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