Fluorescence correlation spectroscopy

The fluorescence correlation spectroscopy ( English fluorescence correlation spectroscopy , FCS) is a highly sensitive optical measuring method that resulting from fluctuations in the fluorescence intensity gaining information. With FCS diffusion constants , concentrations and bonds between different diffusing species are usually measured. The method was developed in the 1970s by Douglas Magde , Elliot Elson and Watt W. Webb .

construction

Schematic structure for FCS

The basis for FCS is usually a confocal microscope (see figure). The excitation light is focused into the sample with the help of an objective so that the smallest possible excitation volume is created. If fluorescent particles (e.g. fluorescence-labeled proteins ) now diffuse into the excitation volume, they are excited there to fluoresce. In doing so, these particles absorb the photons of the excitation light and in turn emit photons of greater wavelength , i.e. lower energy. The emitted photons can now pass the beam splitter (which is impermeable to the excitation light) and are then detected with a photodetector . It is important that the readout rate of the detector is several orders of magnitude higher than the typical residence time of a particle in focus. For FCS, avalanche photodiodes are mainly used today, which can detect individual photons ( SPAD ). But there are also variants that z. B. based on EMCCD cameras. In connection with cameras, other lighting modalities are often used, such as internal total reflection fluorescence microscopy (TIR-FCS) or light disk microscopy (SPIM-FCS), which also allow spatially resolved measurement of mobility.

(Auto) correlation function

Fluorescence time track (above) and the correlation function calculated from it (below, circles) as well as its adaptation with the equation opposite (below, red line)

The actual measured variable in FCS is the fluorescence intensity as a function of time , usually called a time track. The figure (above) shows the time track of a highly diluted sample. Each peak in the time track represents a fluorescent particle that is just diffusing through the excitation volume. Each of these particles takes a certain amount of time to cross the focus. Therefore there is a high probability that photons will be detected by one and the same particle at successive sampling times. It is said that the measured intensities are correlated over time. In order to evaluate the time traces, they are correlated with themselves (autocorrelated). The autocorrelation function is defined as follows: ${\displaystyle F(t)}$ ${\displaystyle G(\tau )}$

${\displaystyle G(\tau ):={\frac {\langle \delta F(t)\delta F(t+\tau )\rangle }{\langle F(t)\rangle ^{2}}}={\frac {\langle F(t)F(t+\tau )\rangle }{\langle F(t)\rangle ^{2}}}-1}$.

The angle brackets mean an average over time, and . ${\displaystyle \delta F(t)=F(t)-\langle F(t)\rangle }$

The figure (below) shows the autocorrelation of the fluorescence time track, whereby the logarithmic scale of the time axis must be observed. The decrease in the autocorrelation function to half its starting value is a measure of the diffusion time . This indicates how long a particle needs on average to traverse the excitation volume. For free three-dimensional diffusion it can be shown that the autocorrelation function can be expressed as follows: ${\displaystyle \tau _{D}}$

${\displaystyle G(\tau )={\frac {1}{\langle N\rangle }}{\frac {1}{1+{\frac {\tau }{\tau _{D}}}}}{\frac {1}{\sqrt {1+{\frac {\omega ^{2}}{z^{2}}}\cdot {\frac {\tau }{\tau _{D}}}}}}}$

${\displaystyle \langle N\rangle }$is the mean number of particles in the excitation volume (focus), the lateral focus diameter and the axial focus diameter. The intensity distribution of the excitation light is assumed here as a three-dimensional Gaussian function , which is a good approximation for many microscope objectives. ${\displaystyle \omega }$ ${\displaystyle z}$

From the concentration can be the fluorescent-active particles in the solution state, if the excitation volume knows: . The diffusion constant results from . ${\displaystyle \langle N\rangle }$ ${\displaystyle C}$ ${\displaystyle V}$ ${\displaystyle \langle C\rangle ={\frac {\langle N\rangle }{V}}}$ ${\displaystyle D={\frac {\omega ^{2}}{4\tau _{D}}}}$

The root term is omitted for two-dimensional diffusion (e.g. in cell membranes ).

Applications

• In molecular biophysics , the dependence of the diffusion coefficient on the hydrodynamic radius allows conclusions to be drawn about the size of a protein and thus, especially in combination with the Förster resonance energy transfer (FRET), its folding state.
• In the research area of cell biology there are more and more working groups that carry out FCS in living cells. It is now possible to carry out fluorescence correlation measurements with appropriately equipped commercial confocal microscopes , with FCS extensions for existing older systems also being offered.
• In the field of biotechnology , a. Screening robots based on autocorrelation measurements are offered.

See also

• Fluorescence lifetime correlation spectroscopy (engl. Fluorescence lifetime correlation spectroscopy , FLCS)

literature

• Douglas Magde, Elliot Elson, WW Webb: Thermodynamic Fluctuations in a Reacting System — Measurement by Fluorescence Correlation Spectroscopy . In: Physical Review Letters . tape 29 , no. 11 , 1972, p. 705-708 , doi : 10.1103 / PhysRevLett.29.705 .
• Elliot L. Elson, Douglas Magde: Fluorescence correlation spectroscopy. I. Conceptual basis and theory . In: Biopolymers . tape 13 , no. 1 , 1974, p. 1–27 , doi : 10.1002 / gdp . 1974.360130102 .
• Douglas Magde, Elliot L. Elson, Watt W. Webb: Fluorescence correlation spectroscopy. II. An experimental realization . In: Biopolymers . tape 13 , no. 1 , 1974, p. 29-61 , doi : 10.1002 / gdp . 1974.360130103 .
• M. Ehrenberg, R. Rigler: Rotational brownian motion and fluorescence intensify fluctuations . In: Chemical Physics . tape 4 , no. 3 , 1974, p. 390-401 , doi : 10.1016 / 0301-0104 (74) 85005-6 .
• R. Rigler, E. Elson: Fluorescence correlation spectroscopy: theory and applications . Springer, 2001, ISBN 3-540-67433-0 .
• P. Schwille, E. Haustein: Fluorescence correlation spectroscopy. An introduction to its concepts and applications . In: Biophysics Textbook Online . tape 1 , no. 3 , 2001 ( PDF ; 1.10 MB).

Individual evidence

1. ^ Douglas Magde, Elliot Elson, WW Webb: Thermodynamic Fluctuations in a Reacting System — Measurement by Fluorescence Correlation Spectroscopy . In: Physical Review Letters . tape 29 , no. 11 , 1972, p. 705-708 , doi : 10.1103 / PhysRevLett.29.705 .
2. ↑ Balakrishnan Kannan, Lin Guo, Thankiah Sudhaharan, Sohail Ahmed, Ichiro Maruyama, Thorsten Wohland: Spatially Resolved Total Internal Reflection Fluorescence Correlation Microscopy Using an Electron Multiplying Charge-Coupled Device Camera. In Analytical Chemistry . 79, 2007, pp. 4463-4470, doi : 10.1021 / ac0624546
3. ↑ T. Wohland, X. Shi, J. Sankaran, EH Stelzer: Single plane illumination fluorescence correlation spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments. In Optics express , Volume 18, No. 10, 2010, ISSN  1094-4087 , pp. 10627-10641, PMID 20588915
4. ↑ J. Capoulade, M. Wachsmuth, L. Hufnagel, M. Knop: Quantitative fluorescence imaging of protein diffusion and interaction in living cells . In Nature Biotechnology . Volume 29, No. 9, 2011, ISSN  1087-0156 , pp. 835-839. doi : 10.1038 / nbt.1928 , PMID 21822256