FCSXpert Solutions: Fluorescence Correlation Spectroscopy Simplified!.
## FCS Classroom

#### How are Physical Parameters Extracted from FCS Data?

### Extracting Parameters from Correlation Timeback to top

### Extracting Parameters from the Interceptback to top

The real power of FCS comes when one relates the intensity fluctuations observed to the underlying physical processes to determine the fundamental physical constants of the system being studied. For instance, one might fit the data to isotropic three-dimensional diffusion and obtain the diffusion coefficients.

Below, you will find discussions on extracting physical parameters from these two properties of correlation functions:

The rate of decay of the correlation over time, the so-called correlation time, τ_{D},
describes the physical phenomenon, such as diffusion, that is causing the
correlation. The longer the correlation persists, the slower the diffusion.
Correlation persists longer for slowly diffusing particles and decays quickly
for rapidly diffusing particles. In Figure 1, shifts in the correlation curve from
the left to the right represent increases in correlation time (slower diffusing
particles).

Figure 2 displays correlation times for 3D diffusion for a wide range of small molecules, macromolecules, fluorescent beads, quantum dots, and pathogens. This is based on a detection system using a confocal beam radius of approximately 1 µm (See Confocal Optics).

In Autocorrelation Due to 3D Diffusion, we calculated the value of g(Δt) at time t = 0 axis to be the reciprocal of the number of particles in the confocal volume.

,

where N_{m} is the number of particles in the confocal volume.

In General Intensity Autocorrelation, we showed that G(Δt) is simply related to g(Δt) through the following relationship:

As a result,

As illustrated in Figure 3, the intercept of the correlation function is inversely related to the number of fluorescent particles detected. As particle number decreases, the intercept increases.