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Fluorescence Correlation Spectroscopy Output Parameters

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)

Note About the QuantumXpert FCS Spectrometer

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.

Correlation Time (τ_D)back to top

Correlation Time is Related to Diffusion and Molecular Size

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.

Detecting Molecular Interactions by Measuring Changes in Correlation Time

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.

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

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.

Average Number of Particles (N_p)back to top

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).

Average Sample Intensityback to top

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.

Relative Concentration of Each Componentback to top

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.

Counts Per Particleback to top

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.