Most FRET methods are limited to recording a static picture - a "snapshot" of molecular proximities of the labeled biomolecules - without being able to report on the temporal stability of molecular interactions. Co-localization at the nanometer scale as revealed by FRET does not necessarily mean that the studied proteins form stable complexes with one another. The co-mobility - that is, the joint diffusive motion of proteins - is an evidence for their stable interaction, and this can be investigated by using the dynamic method of fluorescence cross-correlation spectroscopy (FCCS), the two-channel version of fluorescence correlation spectroscopy (FCS). A recent compilation on the theory and applications of FCS can be found in a publication edited by two pioneers of the technique, Rigler and El-son .
In FCS, a laser beam focused to a subfemtoliter volume element excites fluor-ophores diffusing across the sensitive volume (a prolate ellipsoid defined by the surface at which the detection efficiency drops to e-2 times the value at the center), giving rise to a fluctuating fluorescence signal. The rate of fluctuations is related to the mobility of the fluorescing molecules (i.e., the diffusion coefficient). Typically, the intensity autocorrelation function is calculated from the intensity versus time signal (either on-line by a dedicated correlator card or off-line), and this function is fitted according to model functions assuming different mechanisms of diffusion and accounting for various photophysical processes (singlet-triplet transition, dark state formation, photobleaching) or chemical reactions (e. g., protonation) taking place in the system. For a system with n different species diffusing in 2D (the plane of the plasma membrane) labeled with dyes undergoing singlet-triplet transition , the autocorrelation function is as follows:
The left part of the equation is the definition of the autocorrelation function: the square brackets refer to averaging the expression over the duration T of the meas urement, the variable t is the lag time (the time difference between the samples taken from the F(t) curve), (F) is the mean fluorescence intensity over the studied time interval, and SF(t) = F(t)-(F) is the deviation of the actual fluorescence intensity from the mean. N is the mean number of molecules in the sensitive volume, 0tr is the fraction of molecules in the triplet state, ztr is the phosphorescence lifetime, ti is the diffusion time (the mean dwell time of a molecule in the sensitive volume) and fi is the weight of the ith species. The diffusion time is inversely proportional to the diffusion coefficient Di:
with Wxy indicating the lateral radius of the sensitive volume.
Thus, the parameters of major importance derived from the autocorrelation function regarding protein-protein interactions are the diffusion coefficient and the local concentration of the labeled molecules. The value of D decreases if the labeled proteins form aggregates or interact with the cytoskeleton. Another good measure of the aggregation (homo-association) state of the studied proteins is the fluorescence intensity of the jointly diffusing units, which is simply the ratio (F)/ N.
The diffusion coefficient has only a weak dependence on the molecular weight (D ~ MW~1/3); thus, in a relatively heterogeneous system such as the plasma membrane of a live cell it is not always possible to distinguish between monomeric and dimeric states.
In FCCS, two molecular species are labeled with preferably distinctly excitable and detectable fluorophores. In case the two molecular species are associated, their joint diffusive motion will result in parallel fluctuations of the fluorescence intensities Fa(t) and Fb(t) in the two detection channels. In this case, the cross-correlation function Gx (t) (see Eq. 7.7) has a nonzero amplitude Gx (0), which is proportional to the concentration cab of the complexed fraction of molecular species "a" and "b" (see Eq. 7.8):
where Ca,tot and Cb,tot are the total concentrations of molecules a and b in free state or in complex, and Vff is the so-called effective volume. The actual form of the cross-correlation function also depends on the geometrical parameters of the laser foci and the diffusion properties of the different molecular species [57,58].
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