Fluorescence Correlation Spectroscopy (FCS)

Fluorescence Correlation Spectroscopy (FCS) probes molecular diffusion and interaction. It works best with nanomolar concentrations of protein. Typical experiments involve sample volumes as low as a few microliters. The measurements can be performed in solution and living cells.

FCS is a statistical method. It is based on the analysis of fluorescence fluctuations. Typically, they originate form Brownian motion of dye labeled molecules through a small laser spot. The mean time these molecules stay within the laser spot depends on their size. If a small, dye tagged molecule binds to a larger one, it slows down and emits photons for a longer time during its diffusion through the laser spot.

A sensitive detector records single photons emitted by the dye molecules. The result is an intensity trace representing random noise. Correlation functions are used to extract information about diffusion times (= size) and number of molecules (=concentration) in the sample. Physical models describe the source of the fluctuations and are fitted to the correlated data to quantify these information.

Beyond Brownian motion, FCS can analyze other sources of fluorescence fluctuations, including electronic properties of dyes (e.g. triplet states), restricted diffusion, active transport and changes in FRET signals due to conformational changes of molecules.

If only one type of fluorescent dye and one detector are used, the method is called auto-correlation. To distinguish between two different species of molecules or a small molecule bound to a larger one a difference of mass of at least 1.4 is required. To increase the flexibility of the method, two dyes and detectors can be used. This method is called cross-correlation. Other common methods to use fluorescence fluctuations to probe molecular interactions include Photon Counting Histograms (PCH) and Fluorescence Intensity Distribution Analysis (FIDA). Coincidence Analysis is used to probe rare events in the femto-molar range.

At the Stowers Institute we are using a ConfoCor 3 manufactured by Carl Zeiss. It is attached to a confocal microscope LSM 510 META NLO.

Stowers Links:
Imaging Facility
Adv. Instr. & Physics: Literature FCS

Literature:
Elson, E. L. and D. Magde (1974). "Fluorescence correlation spectroscopy. I. Conceptual basis and theory." Biopolymers 13(1): 1-27. Download PDF
P. Schwille, E. Haustein: Fluorescence Correlation Spectroscopy Download PDF
Wiegraebe, W. (2000). "Fluorescence correlation microscopy: Probing molecular interactions inside living cells." Am. Lab. Sept.: 44-47. Download PDF
Dancing Molecules. Download PDF

• Source of Fluctuations
• Create a Small Measurement Volume
• Detect Single Photons
• Calculate Correlation Function

Free Diffusion

The movement of small particles in solution is a random process described as Brownian Motion. Whenever a molecule tagged with a fluorescent dye diffuses through a small laser spot it will emit a burst of photons.

The probability C of finding a particle at position r, at a time t, when the particle was at the origin r = 0 at time t = 0 is

D is the diffusion coefficient. This is a solution of Fick's second law of diffusion:

The Einstein relation

links D to the absolute Temperature T, the viscosity of the medium η and the hydrodynamic radius r of the molecule. k = 1.38 x 10^-23 J/K is the Boltzman constant.

The viscosity of liquids is temperature dependent:

For globular molecules the hydrodynamic radius r can be estimated as

with molecular weight m and Avogadro's number N_A = 6.023x 10²³ mol^-1. The mean density ρ of molecules can be estimated for most applications with¹

Literature values for the diffusion constant of some molecules in water are:

For rod-like molecules the diffusion coefficient D is given by

L is the length of the molecule (e.g. 3.8 Å per DNA nucleotide) and d it's diameter (23.8 Å for double stranded DNA). A is a correction factor given as

Stowers Links:
Stowers Institute Home Page
Stowers Institute Core Facilities

Web Links:
Wikipedia: Brownian Motion

Literature:
Carl Zeiss: Applications Manual LSM 510 - ConfoCor 2 Application Download PDF

The smaller the volume the larger the signal

Fluorescence Correlation Spectroscopy (FCS) is based on the measurement of fluctuations. The fluctuation signal is higher with lower number of molecules. To measure higher concentrations a measurement volume as small as possible is created. There are about 6 molecules within 1 femto-liter (10^-15 liter) of a 10 nano-molar (10 x 10^-9 Mol) solution.

Confocal Volume

Most FCS setups use confocal optics to create a measurement volume. It's size matches physiological concentrations very well. It is easy to place within structures like cells.

A laser beam is focused to a diffraction limited spot, defining the xy size of the volume in the focal plane. A confocal pinhole limits the detection of photons to light originating from the focal plane. The optical setup is identical to a confocal Laser Scanning Microscope (LSM). Scanning mirrors are not required. Sometimes they are added for scanning FCS and easier positioning of the measurement spot within cells.

The diameter (FWHM = Full Width Half Maximum) of the diffraction limited excitation spot depends on the wavelength λ, the numerical aperture NA of the lens used and how much of the Gausian shaped laser beam fits into the back aperture of the objective (T = Truncation factor):

There is only a small dependence of the xy dimensions on the diameter of the pinhole. The pinhole diameter defines mainly the extend of the measurement volume along the optical axis (z axis):

Multi-Photon Excitation

Two or Multi-photon excitation is an other way to define a measurement volume. Two (or more) photons are required to reach the dye molecule at the same time (within about 10^-15 seconds). This happens only at the focal spot, thus no out-of-focus excitation occurs. A pinhole is not required.

The setup is similar to a two-photon microscope.

Other Setups

Any arrangement which creates a small enough measurement volume can be used for FCS.

The original setup¹ used a small cell to limit the measurement volume along the optical axis. Other setups use Total Internal Reflection (TIRF) to create a small volume.

Stowers Links:
Stowers Institute Home Page
Stowers Institute Core Facilities

Literature:
Carl Zeiss: Principles - Confocal Laser Scanning Microscopy Download PDF
Magde, D. and E. L. Elson (1974). "Fluorescence Correlation Spectroscopy. II. An Experimental Realization." Biopolymers 13: 29-61.Download PDF

While passing the measurement volume, the chromophore attached to the protein of interest emits very view photons. In solution about 5 of them are detected. The number of photons depend on the quantum efficiency of the chromophore, the size of the measurement volume and the diffusion constant of the protein - dye complex.

To detect the photons very sensitive photon counting detectors are required. Typically Avalanche Photo Detectors (APD) are used.

Adding all pulses created by photons in one time window (binning) gives traces of random noise, representing the fluorescence fluctuations within the measurement volume.

You can use our FCS data viewer and view raw data acquired with a Carl Zeiss ConfoCor 2 system to see the single photon events detected during one experiment.

Stowers Links:
Stowers: FCS data viewer
Stowers Institute Core Facilities

Web Links:
Perkin Elmer: Single Photon Counting Module

Literature:
Perkin Elmer: Single Photon-Counting Technology, Download PDF

To determine the hidden time structure of the fluctuation signal the auto-correlation function of the measured data is calculated. The auto-correlation function transforms the data from the measured time domain (=how long it took to acquire the data) to the correlation time domain (=how fast the fluctuations are, e.g. how long a molecule stayed in the confocal volume). It extracts the average behavior of ensembles from the random behavior of individual molecules.

To calculate the auto-correlation function, one compares the measured data with a time-shifted version (the lag time τ) of itself. If there is no time-shift, both data traces are identical - the correlation is high. If the shift is large, the two traces are very different - the correlation is low (this is true as long as the signal has no periodicity). Mathematically this comparison is done by integration over the measurement time t from start of the experiment (t = 0) to it's end (t = T, T = total measurement time). The result is the auto-correlation function for one given lag time τ:

The second term is an alternative spelling of the integral often used in FCS literature. The measured intensity can be described as a constant term plus fluctuations, resulting in an alternative form of the auto-correlation function:

It is common to normalize the auto-correlation function:

The information about the measured fluctuations is contained in δI(t). The constant term I reduces the signal. Thus it is important to increase δI(t) (e.g. reducing measurement volume) and decrease I (e.g. reducing background fluorescence). The term "+1" is sometimes omitted.

Stowers Links:
Stowers Institute Home Page
Stowers Institute Core Facilities

Web Links:
Wikipedia: Autocorrelation
Mathworld: Autocorrelation