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

#### Interpreting Fitted Fractions in FCS

##### Example Correction Applications

### Example: A Sample of Monomers & Known Oligomers

#### Sample Properties

#### Applications of this Example

#### Pre-Correction Results

#### Fraction Correction Calculation

#### Corrected Concentration Calculation

In Autocorrelation Due to Multicomponent Translational Diffusion we derived the FCS equations for multicomponent diffusion as follows:

One caveat to the general equation for multicomponent diffusion is that the counts/particle of all components is assumed to be the same. At the end of
Autocorrelation Due to Multicomponent Translational Diffusion, we derived an equation for converting fractions
resulting from fitting to the above equation, f_{1} and f_{2}, to the physical particle number fractions,
f^{P}_{1} and f^{P}_{2} as follows:

where q_{1} and q_{2} are counts/particle for component 1 and 2, respectively.

- A Sample of Monomers & Known Oligomers: Calculating f
^{P}_{1}and f^{P}_{2}

In this example we will consider the case of a fluorescent molecule, such as a fluorophore-labeled protein, that exists as an equilibrium of two forms in solution: monomeric and oligomeric. We will calculate the relative and absolute concentrations of each component from fitted FCS results.

In this example, the degree of oligomerization is known, and we will use the example of tetramerization.

This analysis might be used to determine the affect of environmental factors, such as pH or temperature, on the relative equilibrium monomer/oligomer concentrations.

An autocorrelation curve of the sample above will have two diffusing components. A fit to the autocorrelation curve will output these parameters:

- N
_{p}: total particle number - Tau
_{D1}: Correlation time of component 1 - Tau
_{D2}: Correlation time of component 2 - f
_{1}: fractional contribution of component 1 to the correlation function - f
_{2}: fractional contribution of component 2 to the correlation function

where component 2 is the larger, slower-diffusing component.

For this example, we will use the following representative results:

- N
_{p}= 50 - f
_{1}= 0.25 - f
_{2}= 0.75

and assume that the oligomer is a tetramer made up of four monomeric units, which means that q_{2} = 4q_{1} (assuming that no change in fluorophore quantum yield
is observed upon tetramerization). We will also use a confocal instrument detection volume of 20 fL (20x10^{-15} L), which means that a
particle number of N_{p} = 50 corresponds to 4.2 nM.

Because f_{1} and f_{2} aren't the physical fractions of particle number, we need to apply the correction equation to find the equilibrium
concentrations of each component.

Using the following equation,

we can calculate f^{P}_{1} / f^{P}_{2} = 5.33.

Using the condition that f^{P}_{1} + f^{P}_{2} = 1, we find that:

- f
^{P}_{1}= 0.84 - f
^{P}_{2}= 0.16

where we have corrected for the overestimation of component 2's fraction due to the 4x increase in brightness and we see that component 1 is actually the dominant component.

Finally, If we use the total conentration of 4.2 nM, we can calculate that the concentration of each component as:

- C
_{1}= 3.5 nM - C
_{2}= 0.7 nM