Molecular Fluorescence

8.7 Bibliography 245

Otherwise, depolarization would also be a result of energy transfer between probe molecules. Because the transition moments of two interacting probes are unlikely to be parallel, this e ect is indeed formally equivalent to a rotation. Moreover, artefacts may arise from scattering light that is not totally rejected in the detection system.

The fluorescence polarization technique is a very powerful tool for studying the fluidity and orientational order of organized assemblies: aqueous micelles, reverse micelles and microemulsions, lipid bilayers, synthetic nonionic vesicles, liquid crystals. This technique is also very useful for probing the segmental mobility of polymers and antibody molecules.

8.6

Concluding remarks

The various fluorescence-based methods for the determination of fluidity and molecular mobility are summarised in Table 8.1. Attention should be paid to the comments indicated in the last column.

The choice of method depends on the system to be investigated. The methods of intermolecular quenching and intermolecular excimer formation are not recommended for probing fluidity of microheterogeneous media because of possible perturbation of the translational di usion process. The methods of intramolecular excimer formation and molecular rotors are convenient and rapid, but the timeresolved fluorescence polarization technique provides much more detailed information, including the order of an anisotropic medium.

Whatever the technique used, it is important to note that (i) only an equivalent viscosity can be determined, (ii) the response of a probe may be di erent in solvents of the same viscosity but of di erent chemical nature and structure, (iii) the measured equivalent viscosity often depends on the probe and on the fluorescence technique. Nevertheless, the relative variations of the di usion coe cient resulting from an external perturbation are generally much less dependent on the technique and on the nature of the probe. Therefore, the fluorescence techniques are very valuable in monitoring changes in fluidity upon an external perturbation such as temperature, pressure and addition of compounds (e.g. cholesterol added to lipid vesicles; alcohols and oil added to micellar systems).

8.7

Bibliography

246 8 Microviscosity, fluidity, molecular mobility. Estimation by means of fluorescent probes

248 9 Resonance energy transfer and its applications

a distance r is:

where tD0 is the excited-state lifetime of the donor in the absence of transfer and R0 is the Fo¨rster critical radius (distance at which transfer and spontaneous decay of the excited donor are equally probable, i.e. kT ¼ 1=tD0 ). R0 (in A˚ ) is given by

where k2 is the orientational factor, which can take values from 0 (perpendicular transition moments) to 4 (collinear transition moments) (see Section 4.6.3 for more details on k2), FD0 is the fluorescence quantum yield of the donor in the absence of transfer, n is the average refractive index of the medium in the wavelength range where spectral overlap isÐsignificant, IDðlÞ is the fluorescence spectrum of the donor normalized so that 0y IDðlÞ dl ¼ 1, eAðlÞ is the molar absorption coe cient of the acceptor (in dm3 mol 1 cm 1) and l is the wavelength in nanometers. Values of R0 in the range of 10–80 A˚ have been reported (see below).

The transfer e ciency is given by

The sixth power dependence explains why resonance energy transfer is most sensitive to the donor–acceptor distance when this distance is comparable to the Fo¨r- ster critical radius.

It should be emphasized that the transfer rate depends not only on distance separation but also on the mutual orientation of the fluorophores. Therefore, it may be more appropriate in some cases to rewrite the transfer rate as follows:

9.2 Determination of distances at a supramolecular level using RET 249

9.2

Determination of distances at a supramolecular level using RET

9.2.1

Single distance between donor and acceptor

The Fo¨rster resonance energy transfer can be used as a spectroscopic ruler in the range of 10–100 A˚ . The distance between the donor and acceptor molecules should be constant during the donor lifetime, and greater than about 10 A˚ in order to avoid the e ect of short-range interactions. The validity of such a spectroscopic ruler has been confirmed by studies on model systems in which the donor and acceptor are separated by well-defined rigid spacers. Several precautions must be taken to ensure correct use of the spectroscopic ruler, which is based on the use of Eqs (9.1) to (9.3):

(i)The critical distance R0 should be determined under the same experimental conditions as those of the investigated system because R0 involves the quantum yield of the donor and the overlap integral, which both depend on the nature of the microenvironment. For this reason, the values of R0 reported in Table 9.1 can only be used as a guide for selection of a pair. Tryptophan can be used as a donor for distance measurements in proteins; a few R0 values are given in this table (for further values, see Berlman, 1973; Wu and Brand, 1994; and Van der Meer, 1994).

(ii)As regards the orientation factor k2, it is usually taken as 2=3, which is the isotropic dynamic average, i.e. under the assumptions that both donor and acceptor transient moments randomize rapidly during the donor lifetime and sample all orientations. However, these conditions may not be met owing to the constraints of the microenvironment of the donor and acceptor. A variation of k2 from 2=3 to 4 results in only a 35% error in r because of the sixth root of

250 9 Resonance energy transfer and its applications

Fig. 9.1. Variations in the transfer efficiency as a function of the ratio donor–acceptor distance/Forster€ critical radius.

k2 appearing in R0 (Eq. 9.2), but a variation from 2=3 to 0.01 results in a twofold decrease in r. Information on the orientational freedom of donor and acceptor and their relative orientations can be obtained from fluorescence polarization experiments (Dale et al., 1975).

(iii)Because of the sixth power dependence, the variation in FT (Eq. 9.3) is sharp around r ¼ R0, as shown in Figure 9.1: for r < R0=2, the transfer e ciency is close to 1, and for r > 2R0, it approaches 0; therefore the distance between donor and acceptor should be in the following range 0:5R0 < r < 1:5R0.

(iv)The distance to be measured should be constant during the donor lifetime.

This section deals with a single donor–acceptor distance. Let us consider first the case where the donor and acceptor can freely rotate at a rate higher than the energy transfer rate, so that the orientation factor k2 can be taken as 2=3 (isotropic dynamic average). The donor–acceptor distance can then be determined by steadystate measurements via the value of the transfer e ciency (Eq. 9.3):

Three steady-state methods can be used to determine the energy transfer e ciency. In the following description of these methods, the fluorescence intensity is indicated with two wavelengths in parentheses: the first one is the excitation wavelength, and the second is the observation wavelength. Because the characteristics of the donor and/or acceptor are measured in the presence and in the absence of transfer, the concentrations of donor and acceptor and their microenvironments must be the same under both these conditions.

Steady-state method 1: decrease in donor fluorescence Transfer from donor to acceptor causes the quantum yield of the donor to decrease. The transfer e ciency is given by

252 9 Resonance energy transfer and its applications

Steady-state method 3: Enhancement of acceptor fluorescence The fluorescence intensity of the acceptor is enhanced in the presence of transfer. Comparison with the intensity in the absence of transfer provides the transfer e ciency:

It should be noted that AAðlDÞ is often small and thus di cult to measure accurately, which may lead to large errors in FT.

Method 1 appears to be more straightforward than methods 2 and 3. However, it cannot be used in the case of very low donor quantum yields. It should also be noted that quenching of the donor by the acceptor may occur. This point can be checked by a complementary study based on observation of the acceptor fluorescence (method 2 or 3).

Time-resolved emission of the donor or acceptor fluorescence provides direct information on the transfer rate, without the di culties that may result from inner filter e ects.

Time-resolved method 1: decay of the donor fluorescence If the fluorescence decay of the donor following pulse excitation is a single exponential, the measurement of the decay time in the presence ðtDÞ and absence ðtD0 Þ of transfer is a straightforward method of determining the transfer rate constant, the transfer e ciency and the donor–acceptor distance, by using the following relations:

The advantage of this method is its ability to check whether the donor fluorescence decay in the absence and presence of acceptor is a single exponential or not. If this decay is not a single exponential in the absence of acceptor, this is likely to be due to some heterogeneity of the microenvironment of the donor. It can then be empirically modeled as a sum of exponentials:

X

iDðtÞ ¼ ai expð t=tiÞ ð9:18Þ

i

Transfer e ciency can be calculated by using the average decay times of the donor in the absence and presence of acceptor, as follows: