Fluorescence Correlation Spectroscopy (FCS)

FCS is a method for high-resolution spatial and temporal analysis of low concentrated fluorescent bio-molecules. Unlike microscopy, FACS or fluorometry, the goal here is not to measure fluorescent emission intensity per se, or visualize the fluorescent molecules, but rather to follow minute fluctuations of fluorescent intensity that deviate from thermal equilibrium. Yeh, I don’t fully understand that either, but since I’m going to use that methods soon, I will try hard.

In general, FCS can be used to measure local concentration (at the nanomolar scale), mobility coefficients (i.e. the rate of movement) and rate constants of molecular interactions (e.g. association-disassociation). Here is a good site that teaches FCS.

I will briefly go into the microscope setup:

An excitation laser beam is directed to the objective lens via a dichroic mirror. Objectives should have high numerical aperture values (>0.9). The fluorescent light from the sample is collected by the same objective, passes through the dichroic mirror and emission filter. The light is focused on the detector with single photon sensitivity. The microscope type used is a Confocal microscope. In a nutshell, a pinhole in the image plane (field aperture) blocks any fluorescence not coming from the focal plane, thus reducing background and enhancing resolution. The excitation and emission filters’ efficiencies should be critically taken into consideration, since the signal-to-noise ratio of the FCS curves largely depends on these factors.

The use of the confocal microscope creates a small volume that is “in focus”, i.e. the sample in this volume can be efficiently detected. This volume is usually in the order of a few femtoliters, and its size and shape are dependent on the beam radius, the NA and the wavelength. I will not go into the formulas now. However, calculating the size & shape is important.

Photons intensities are measured over time. These measurements are then autocorrelated or cross-correlated, depending on the application used (single or multiple colors).

Autocorrelation means that we calculate the correlation coefficient of the intensity (I(t)) of each time point compared to time 0  (I(0)). Here is the equation:

m is an integer multiple of the time interval τ such that ∆t=mτ.  (0≤m<M). I(t) is the intensity at each time point t, with data points M+1 spanning from  t=0 to t=Mτ.  < I > is the mean intensity over all t values.

So, what does it mean in practice?

Suppose we measure the intensity over 1 milisecond intervals, for a period of 1 second (the measurement is continuo for the whole 1sec). We get a plot the intensity over time.

We can then try to correlate the data of each time interval (1ms in our example) with the intensity of the next time interval, or the second next, third next etc… for each time interval we calculate the correlation coefficient, R:

(SD – standard deviation, M total number of measurments).

As the shift in time increases, we expect the R to decrease, thus, R(∆t) represents the probability of correlation at time interval ∆t. Essentially, it expresses the correlation between the fluctuation from mean intensity. In the equation for R(∆t), the normalization is with SD2. This, apparently, causes a loss of data of the number of fluorescent molecules detected in the confocal volume. Therefore, a different equation is derived, g(∆t) by normalizing on the square mean intensity. As it is, g(∆t) is hard to calculate, due to the need to maintain a running measure of mean intensity (at this point I’m a bit lost, mathematically). Therefore, G(∆t) is used, which represents the correlation of intensity between I(0) and intensity at some later time I(t).

I will not go into cross correlation now, except mention that the two (or more) colors are correlated to each other enabling, for example, measurements of co-association or movement together.

The fluctuations in fluorescence are affected by the kinetics of movement in and out of the confocal volume, by association with other molecules, by change in size or shape etc…

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