Tech note: Applying dual-colour fluctuation cross-orrelation spectroscopy to cell signaling studies

Quantitative measurements of dynamics of protein-protein interactions in cells are crucial to understand cell signaling. The fluctuation correlation spectroscopy (FCS) and dual-color fluctuation cross-correlation spectroscopy (FCCS) may open a new way to explore cell signaling mechanisms.

Principles:

1. FCS
FCS measures the fluctuation of fluorescence emitted from a small excitation spot (~0.5 fL) made by a focused laser. When the number of fluorophores in the spot is small, the fluorescence intensity fluctuates due to the in and out movement of the fluorophores (fluctuation size ~ $1/\sqrt{N}$ ). In the case the fluorophores diffuse freely, the fluctuation has the correlation time characterized by the diffusion constant and the size of laser spot. Therefore, by quantifying the correlation time using autocorrelation (or probably Fourier transformation?), the diffusion constant can be obtained. Because the diffusion constant is roughly proportional to the diameter of labeled proteins, this can be a measure of protein binding.

Analytical solution of the autocorrelation is given as follows:
$G(\tau)=\frac{\lt \delta I(t) \delta I(\tau+t) \gt}{\lt I^2 \gt}= 1 + \frac{1}{N}\frac{1}{(1+\tau/\tau_c)\sqrt{1+\tau/(q^2\tau_c)}$

where N and $\tau_c$ are the average number of fluorescent particle in the volume element and the diffusion time, respectively. q is the ratio of the exp(-2) distance in z-axis and radius in the x-y plane in the confocal space. $\tau_c$ is determined by $w_{xy}^2/4D$ where D and $w_{xy}$ are the diffusion coefficient and the exp(-2) radius. This value is the mean transit time of the molecule in the space.

2. FCCS
The fluctuation of two different fluorophores have interesting characteristics. When two dyes bind together, these dyes move in and out simultaneously, causing the high correlation between these two fluctuations. Therefore, the cross-correlation of the two fluctuation can be a good measure of the interactions between two labeled proteins.

Cross-correlation is defined as
$G_{rg}(\tau)=\frac{\lt \delta I_r(t) \delta I_g(\tau+t) \gt}{\lt I_r \gt\lt I_g \gt}$
where r and g indicate signals of different colors. Fraction of binding protein can be obtained as $G_{rg}(0) / G_r(0)$ .

APplication to studies of cellular and synaptic signaling

Both FCS and FCCS work beautifully in cuvette. However, the situation is much more complicated in cells. For example, if two proteins are in the same vesicle, they move together even if they are not bound together. Bacia K. et al. (2002, biophysical J.) used this fact to analyze vesicular movements. Also, slow movements of large organelles containing these proteins can give burst fluorescence, causing a large correlation. Non-mobile fraction of proteins can give some artificial correlations due to photo-bleaching. Thus, great cares have to be taken to interpret the correlation signal. Even with these limitation, Schwille and his colleagues (Kim et al., PNAS 2004) have shown that the techniques are useful to measure interactions between highly mobile signaling proteins in Cells.

Is it possible to apply this technique for the analysis of signaling in neuro-microcompartments such as dendritic spines ? Because dendritic spines are usually smaller than optical resolution, the fluorescence fluctuation is made by fluorophore movement through the narrow necks connecting the spines and their parent dendrite. The time constant of this diffusion coupling is about 0.1-0.8 sec for highly mobile proteins such as GFP. To obtain successful signal-to-noise ratio, the measurements of fluctuation with such the long correlation time can take minutes (hundred times correlation time). Because even a small drift of the target spine in the long time measurements can cause large artificial correlation, the measurements are challenging. If the target protein interact with synaptic proteins, as in the case of most of interesting signaling proteins, the situation can be much warse. Therefore, the FCS and FCCS applications to studies of synaptic signaling are probably very limited.

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