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

#### Fluorescence Correlation Spectroscopy Output Parameters

##### Note About the QuantumXpert FCS Spectrometer

### Correlation Time (τ_{D})back to top

#### Correlation Time is Related to Diffusion and Molecular Size

#### Detecting Molecular Interactions by Measuring Changes in Correlation Time

##### Cross-Correlation Eliminates the Need to Detect Changes in Correlation Time

### Average Number of Particles (N_{p})back to top

### Average Sample Intensityback to top

### Relative Concentration of Each Componentback to top

### Counts Per Particleback to top

FCS instruments provide a number of physically-relevant fitted parameters. These parameters are described below:

- Correlation Time (τ
_{D}) for one or more diffusing components - Average Number of Particles (N
_{p}) - Average Sample Intensity
- Relative Concentration of Each Component
- Counts per particle (CPP)

The QuantumXpert is optimized to characterize events that are relevant to biologists and biochemists -- specifically, the interactions of macromolecules (see Biological Interactions that FCS Can Detect). These events occur in the time domain of a few hundred microseconds up to a few seconds.

The QuantumXpert cannot be used to study fast photophysical events such as photon antibunching, triplet state dynamics, photoisomerization, or even rotational diffusion of molecules, all of which occur in the nanosecond to few microsecond time domain.

FCS data can report correlation time (τ_{D}) in both autocorrelation mode
and cross-correlation mode. Correlation time is related to the translational diffusion coefficient, D,
by the following relation:

where ω is the radius of the confocal detection volume.

The diffusion coefficient of a particle is in turn determined by two properties: the
viscosity of the solvent, η, and the hydrodynamic radius of the particle, R_{h} . This
relationship is described by the Einstein equation below:

where k_{B} is the Boltzmann constant (1.38x10^{-23} J/K) and T is the temperature.

For autocorrelation experiments, where a single
dye is measured in each emission channel, the magnitude of the change in
molecular weight of free dye-labeled probe and probe-bound complex is critical,
and will result in a right-ward shift in the correlation decay curve due to an increase in correlation time, as shown in **Figure 1** below.

A general rule-of-thumb is that the difference in molecular weight for the complex and the unbound probe should be between 3 to 5 fold to result in a shift in diffusion time that can be distinguished by FCS.

If two fluorescently labeled reactants are used, interaction between the two reactants can be monitored using cross-correlation and a large change in mass is not required. In this case, each fluorescent dye is detected in different emission channels, and the correlated diffusion between two channels result in the cross-correlation function.

See our mathematical discussion on cross-correlation in What is Cross-correlation?, or read a comparison on correlation types in Autocorrelation vs. Cross-correlation Assays.

FCS data also report the average number of fluorescently labeled
particles (N_{p}) in the detection volume. This value can be used to calculate the
total concentration of the fluorescent particles in a sample.

N_{p} is inversely proportional to the y-intercept, G(0), of the autocorrelation function,
so as the average number of particles decreases, the magnitude of the intercept increases.

An interesting result of the inverse relationship between N_{p} and the y-intercept is that
the quality of FCS data can often be improved by *reducing* the concentration, rather than increasing the concentration.
This is because a background FCS curve showing no correlation is centered at G = 1. Lowering the sample concentration
will separate it further from baseline FCS curve because the intercept is higher (unless the signal intensity from the lower
concentration sample becomes too faint).

FCS curves are created by correlating nanosecond fluctuations in fluorescence intensity. The steady-state average intensity can also provide useful information and is provided by most FCS instruments.

In addition to reporting a value for N_{p}, the average number of fluorescent particles, FCS
data report the fraction of N_{p} that is associated with components of different size. (Usually, components must
differ in size by 3 to 5 fold to be distinguished.) These values can be used
to calculate relative and absolute concentrations of each fluorescent species in a sample.

It is important to note that the contribution of each component to the correlation curve is related to both relative concentration and relative brightness. See Interpreting Fitted Fractions in FCS for information on how to take brightness into account when calculating relative concentrations.

The values of average intensity and number of particles can be used to calculate the average counts per particle to determine the degree of labeling of the fluorescent particles.