Fluorescence correlation spectroscopy
Encyclopedia
Fluorescence correlation spectroscopy (FCS) is a correlation analysis of fluctuation of the fluorescence intensity. The analysis provides parameters of the physics under the fluctuations. One of the interesting applications of this is an analysis of the concentration fluctuations of fluorescent particles (molecules) in solution. In this application, the fluorescence emitted from a very tiny space in solution containing a small number of fluorescent particles (molecules) is observed. The fluorescence intensity is fluctuating due to Brownian motion of the particles. In other words, the number of the particles in the sub-space defined by the optical system is randomly changing around the average number. The analysis gives the average number of fluorescent particles and average diffusion time, when the particle is passing through the space. Eventually, both the concentration and size of the particle (molecule) are determined. Both parameters are important in biochemical research, biophysics, and chemistry.
FCS is such a sensitive analytical tool because it observes a small number of molecules (nanomolar to picomolar concentrations) in a small volume (~1μm). In contrast to other methods (such as HPLC analysis) FCS has no physical separation process; instead, it achieves its spatial resolution though its optics. Furthermore, FCS enables observation of fluorescence-tagged molecules in the biochemical pathway in intact living cells. This opens a new area, "in situ or in vivo biochemistry": tracing the biochemical pathway in intact cells and organs.
Commonly, FCS is employed in the context of optical microscopy, in particular confocal or two-photon excitation microscopy
. In these techniques light is focused on a sample and the measured fluorescence
intensity fluctuations (due to diffusion
, physical or chemical reactions, aggregation, etc.) are analyzed using the temporal autocorrelation. Because the measured property is essentially related to the magnitude and/or the amount of fluctuations, there is an optimum measurement regime at the level when individual species enter or exit the observation volume (or turn on and off in the volume). When too many entities are measured at the same time the overall fluctuations are small in comparison to the total signal and may not be resolvable – in the other direction, if the individual fluctuation-events are too sparse in time, one measurement may take prohibitively too long. FCS is in a way the fluorescent counterpart to dynamic light scattering
, which uses coherent light scattering, instead of (incoherent) fluorescence.
When an appropriate model is known, FCS can be used to obtain quantitative information such as
Because fluorescent markers come in a variety of colors and can be specifically bound to a particular molecule (e.g. proteins, polymers, metal-complexes, etc.), it is possible to study the behavior of individual molecules (in rapid succession in composite solutions). With the development of sensitive detectors such as avalanche photodiode
s the detection of the fluorescence signal coming from individual molecules in highly dilute samples has become practical. With this emerged the possibility to conduct FCS experiments in a wide variety of specimens, ranging from materials science to biology. The advent of engineered cells with genetically tagged proteins (like green fluorescent protein
) has made FCS a common tool for studying molecular dynamics in living cells.
Beginning in 1993, a number of improvements in the measurement techniques—notably using confocal microscopy, and then two-photon microscopy—to better define the measurement volume and reject background—greatly improved the signal-to-noise ratio and allowed single molecule sensitivity. Since then, there has been a renewed interest in FCS, and as of August 2007 there have been over 3,000 papers using FCS found in Web of Science. See Krichevsky and Bonnet for a recent review. In addition, there has been a flurry of activity extending FCS in various ways, for instance to laser scanning and spinning-disk confocal microscopy (from a stationary, single point measurement), in using cross-correlation (FCCS) between two fluorescent channels instead of autocorrelation, and in using Förster Resonance Energy Transfer
(FRET) instead of fluorescence.
), and from 690–1100 nm (pulsed)), which is reflected into a microscope objective by a dichroic mirror. The laser beam is focused in the sample, which contains fluorescent particles (molecules) in such high dilution, that only a few are within the focal spot (usually 1–100 molecules in one fL). When the particles cross the focal volume, they fluoresce. This light is collected by the same objective and, because it is red-shifted with respect to the excitation light it passes the dichroic mirror reaching a detector, typically a photomultiplier
tube or avalanche photodiode
detector. The resulting electronic signal can be stored either directly as an intensity versus time trace to be analyzed at a later point, or computed to generate the autocorrelation directly (which requires special acquisition cards). The FCS curve by itself only represents a time-spectrum. Conclusions on physical phenomena have to be extracted from there with appropriate models. The parameters of interest are found after fitting the autocorrelation curve to modeled functional forms.
(or PSF), it is essentially the image of a point source. The PSF is often described as an ellipsoid (with unsharp boundaries) of few hundred nanometers in focus diameter, and almost one micrometre along the optical axis. The shape varies significantly (and has a large impact on the resulting FCS curves) depending on the quality of the optical elements (it is crucial to avoid astigmatism and to check the real shape of the PSF on the instrument). In the case of confocal microscopy, and for small pinholes (around one Airy unit), the PSF is well approximated by Gaussians:
where
is the peak intensity, r and z are radial and axial position, and 
and 
are the radial and axial radii, and 
. This Gaussian form is assumed in deriving the functional form of the autocorrelation.
Typically
is 200–300 nm, and 
is 2–6 times larger. One common way of calibrating the measurement volume parameters is to perform FCS on a species with known diffusion coefficient and concentration (see below). Diffusion coefficients for common fluorophores in water are given in a later section.
The Gaussian approximation works to varying degrees depending on the optical details, and corrections can sometimes be applied to offset the errors in approximation.
, as a function of 
:
where
is the deviation from the mean intensity. The normalization (denominator) here is the most commonly used for FCS, because then the correlation at 
, G(0), is related to the average number of particles in the measurement volume.
where
is the ratio of axial to radial 
radii of the measurement volume, and 
is the characteristic residence time. This form was derived assuming a Gaussian measurement volume. Typically, the fit would have three free parameters—G(0), 
, and 
--from which the diffusion coefficient and fluorophore concentration can be obtained.
With the normalization used in the previous section, G(0) gives the mean number of diffusers in the volume, or equivalently—with knowledge of the observation volume size—the mean concentration:
where the effective volume is found from integrating the Gaussian form of the measurement volume and is given by:
, where the temporal dependenc of the MSD is non-linear as in the power-law:
where
is an anomalous diffusion coefficient. "Anomalous diffusion" commonly refers only to this very generic model, and not the many other possibilities that might be described as anomalous. Also, a power law is, in a strict sense, the expected form only for a narrow range of rigorously defined systems, for instance when the distribution of obstacles is fractal
. Nonetheless a power law can be a useful approximation for a wider range of systems.
The FCS autocorrelation function for anomalous diffusion is:
where the anomalous exponent
is the same as above, and becomes a free parameter in the fitting.
Using FCS, the anomalous exponent has been shown to be an indication of the degree of molecular crowding (it is less than one and smaller for greater degrees of crowding).
where the sum is over the number different sizes of particle, indexed by i, and
gives the weighting, which is related to the quantum yield and concentration of each type. This introduces new parameters, which makes the fitting more difficult as a higher dimensional space must be searched. Nonlinear least square fitting typically becomes unstable with even a small number of 
s. A more robust fitting scheme, especially useful for polydisperse samples, is the Maximum Entropy Method.
in the lateral direction, the autocorrelation is:
where
is the average residence time if there is only a flow (no diffusion).
where
is the relaxation time and depends on the reaction kinetics (on and off rates), and:
is related to the equilibrium constant K.
Most systems with chemical relaxation also show measureable diffusion as well, and the autocorrelation function will depend on the details of the system. If the diffusion and chemical reaction are decoupled, the combined autocorrelation is the product of the chemical and diffusive autocorrelations.
, rhodamine, Cy3 and Alexa Fluor dyes—some fraction of illuminated particles are excited to a triplet state
(or other non-radiative decaying states) and then do not emit photons for a characteristic relaxation time
. Typically 
is on the order of microseconds, which is usually smaller than the dynamics of interest (e.g. 
) but large enough to be measured. A multiplicative term is added to the autocorrelation to account for the triplet state. For normal diffusion:
where
is the fraction of particles that have entered the triplet state and 
is the corresponding triplet state relaxation time. If the dynamics of interest are much slower than the triplet state relaxation, the short time component of the autocorrelation can simply be truncated and the triplet term is unnecessary.
for instance), or is a naked fluorophore that is used to probe some environment of interest (e.g. the cytoskeleton of a cell). The following table gives diffusion coefficients of some common fluorophores in water at room temperature, and their excitation wavelengths.
where
is the viscosity of the sample and 
is the molecular mass of the fluorescent species. In practice, the diffusion times need to be sufficiently different—a factor of at least 1.6--which means the molecular masses must differ by a factor of 4. Dual color fluorescence cross-correlation spectroscopy
(FCCS) measures interactions by cross-correlating two or more fluorescent channels (one channel for each reactant), which distinguishes interactions more sensitively than FCS, particularly when the mass change in the reaction is small.
) is related to the variance (
) and the average intensity (
) as follows:
Here
and 
are the fractional intensity and molecular brightness, respectively, of species 
.
(FRET) instead of fluorescence, and is called FRET-FCS. With FRET, there are two types of probes, as with FCCS; however, there is only one channel and light is only detected when the two probes are very close—close enough to ensure an interaction. The FRET signal is weaker than with fluorescence, but has the advantage that there is only signal during a reaction (aside from autofluorescence
).
Some variations of FCS are only applicable to serial scanning laser microscopes. Image Correlation Spectroscopy and its variations all were implemented on a scanning confocal or scanning two photon microscope, but transfer to other microscopes, like a spinning disk confocal microscope. Raster ICS (RICS), and position sensitive FCS (PSFCS) incorporate the time delay between parts of the image scan into the analysis. Also, low dimensional scans (e.g. a circular ring)—only possible on a scanning system—can access time scales between single point and full image measurements. Scanning path has also been made to adaptively follow particles.
Another variation of ICS performs a spatial autocorrelation on images, which gives information about the concentration of particles. The correlation is then averaged in time.
A natural extension of the temporal and spatial correlation versions is spatio-temporal ICS (STICS). In STICS there is no explicit averaging in space or time (only the averaging inherent in correlation). In systems with non-isotropic motion (e.g. directed flow, asymmetric diffusion), STICS can extract the directional information. A variation that is closely related to STICS (by the Fourier transform) is k-space Image Correlation Spectroscopy (kICS).
There are cross-correlation versions of ICS as well.
(TIRF) is a microscopy approach that is only sensitive to a thin layer near the surface of a coverslip, which greatly minimizes background fluorscence. FCS has been extended to that type of microscope, and is called TIR-FCS. Because the fluorescence intensity in TIRF falls off exponentially with distance from the coverslip (instead of as a Gaussian with a confocal), the autocorrelation function is different.
, a region is briefly exposed to intense light, irrecoverably photobleaching fluorophores, and the fluorescence recovery due to diffusion of nearby (non-bleached) fluorophores is imaged. A primary advantage of FRAP over FCS is the ease of interpreting qualitative experiments common in cell biology. Differences between cell lines, or regions of a cell, or before and after application of drug, can often be characterized by simple inspection of movies. FCS experiments require a level of processing and are more sensitive to potentially confounding influences like: rotational diffusion, vibrations, photobleaching, dependence on illumination and fluorescence color, inadequate statistics, etc. It is much easier to change the measurement volume in FRAP, which allows greater control. In practice, the volumes are typically larger than in FCS. While FRAP experiments are typically more qualitative, some researchers are studying FRAP quantitatively and including binding dynamics. A disadvantage of FRAP in cell biology is the free radical perturbation of the cell caused by the photobleaching. It is also less versatile, as it cannot measure concentration or rotational diffusion, or co-localization. FRAP requires a significantly higher concentration of fluorophores than FCS.
FCS is such a sensitive analytical tool because it observes a small number of molecules (nanomolar to picomolar concentrations) in a small volume (~1μm). In contrast to other methods (such as HPLC analysis) FCS has no physical separation process; instead, it achieves its spatial resolution though its optics. Furthermore, FCS enables observation of fluorescence-tagged molecules in the biochemical pathway in intact living cells. This opens a new area, "in situ or in vivo biochemistry": tracing the biochemical pathway in intact cells and organs.
Commonly, FCS is employed in the context of optical microscopy, in particular confocal or two-photon excitation microscopy
Two-photon excitation microscopy
Two-photon excitation microscopy is a fluorescence imaging technique that allows imaging of living tissue up to a very high depth, that is up to about one millimeter. Being a special variant of the multiphoton fluorescence microscope, it uses red-shifted excitation light which can also excite...
. In these techniques light is focused on a sample and the measured fluorescence
Fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation of a different wavelength. It is a form of luminescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation...
intensity fluctuations (due to diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
, physical or chemical reactions, aggregation, etc.) are analyzed using the temporal autocorrelation. Because the measured property is essentially related to the magnitude and/or the amount of fluctuations, there is an optimum measurement regime at the level when individual species enter or exit the observation volume (or turn on and off in the volume). When too many entities are measured at the same time the overall fluctuations are small in comparison to the total signal and may not be resolvable – in the other direction, if the individual fluctuation-events are too sparse in time, one measurement may take prohibitively too long. FCS is in a way the fluorescent counterpart to dynamic light scattering
Dynamic light scattering
thumb|right|350px|Hypothetical Dynamic light scattering of two samples: Larger particles on the top and smaller particle on the bottomDynamic light scattering is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers...
, which uses coherent light scattering, instead of (incoherent) fluorescence.
When an appropriate model is known, FCS can be used to obtain quantitative information such as
- diffusion coefficients
- hydrodynamic radii
- average concentrations
- kinetic chemical reaction rates
- singlet-triplet dynamics
Because fluorescent markers come in a variety of colors and can be specifically bound to a particular molecule (e.g. proteins, polymers, metal-complexes, etc.), it is possible to study the behavior of individual molecules (in rapid succession in composite solutions). With the development of sensitive detectors such as avalanche photodiode
Avalanche photodiode
An avalanche photodiode is a highly sensitive semiconductor electronic device that exploits the photoelectric effect to convert light to electricity. APDs can be thought of as photodetectors that provide a built-in first stage of gain through avalanche multiplication. From a functional standpoint,...
s the detection of the fluorescence signal coming from individual molecules in highly dilute samples has become practical. With this emerged the possibility to conduct FCS experiments in a wide variety of specimens, ranging from materials science to biology. The advent of engineered cells with genetically tagged proteins (like green fluorescent protein
Green fluorescent protein
The green fluorescent protein is a protein composed of 238 amino acid residues that exhibits bright green fluorescence when exposed to blue light. Although many other marine organisms have similar green fluorescent proteins, GFP traditionally refers to the protein first isolated from the...
) has made FCS a common tool for studying molecular dynamics in living cells.
History
Signal-correlation techniques were first experimentally applied to fluorescence in 1972 by Magde, Elson, and Webb, who are therefore commonly credited as the "inventors" of FCS. The technique was further developed in a group of papers by these and other authors soon after, establishing the theoretical foundations and types of applications. See Thompson (1991) for a review of that period.Beginning in 1993, a number of improvements in the measurement techniques—notably using confocal microscopy, and then two-photon microscopy—to better define the measurement volume and reject background—greatly improved the signal-to-noise ratio and allowed single molecule sensitivity. Since then, there has been a renewed interest in FCS, and as of August 2007 there have been over 3,000 papers using FCS found in Web of Science. See Krichevsky and Bonnet for a recent review. In addition, there has been a flurry of activity extending FCS in various ways, for instance to laser scanning and spinning-disk confocal microscopy (from a stationary, single point measurement), in using cross-correlation (FCCS) between two fluorescent channels instead of autocorrelation, and in using Förster Resonance Energy Transfer
Fluorescence resonance energy transfer
Förster resonance energy transfer , also known as fluorescence resonance energy transfer, resonance energy transfer or electronic energy transfer , is a mechanism describing energy transfer between two chromophores.A donor chromophore, initially in its electronic excited state, may transfer energy...
(FRET) instead of fluorescence.
Typical FCS setup
The typical FCS setup consists of a laser line (wavelengths ranging typically from 405–633 nm (cwContinuous wave
A continuous wave or continuous waveform is an electromagnetic wave of constant amplitude and frequency; and in mathematical analysis, of infinite duration. Continuous wave is also the name given to an early method of radio transmission, in which a carrier wave is switched on and off...
), and from 690–1100 nm (pulsed)), which is reflected into a microscope objective by a dichroic mirror. The laser beam is focused in the sample, which contains fluorescent particles (molecules) in such high dilution, that only a few are within the focal spot (usually 1–100 molecules in one fL). When the particles cross the focal volume, they fluoresce. This light is collected by the same objective and, because it is red-shifted with respect to the excitation light it passes the dichroic mirror reaching a detector, typically a photomultiplier
Photomultiplier
Photomultiplier tubes , members of the class of vacuum tubes, and more specifically phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum...
tube or avalanche photodiode
Avalanche photodiode
An avalanche photodiode is a highly sensitive semiconductor electronic device that exploits the photoelectric effect to convert light to electricity. APDs can be thought of as photodetectors that provide a built-in first stage of gain through avalanche multiplication. From a functional standpoint,...
detector. The resulting electronic signal can be stored either directly as an intensity versus time trace to be analyzed at a later point, or computed to generate the autocorrelation directly (which requires special acquisition cards). The FCS curve by itself only represents a time-spectrum. Conclusions on physical phenomena have to be extracted from there with appropriate models. The parameters of interest are found after fitting the autocorrelation curve to modeled functional forms.
The measurement volume
The measurement volume is a convolution of illumination (excitation) and detection geometries, which result from the optical elements involved. The resulting volume is described mathematically by the point spread functionPoint spread function
The point spread function describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse response, the PSF being the impulse response of a focused optical system. The PSF in many contexts can be thought of as the extended blob...
(or PSF), it is essentially the image of a point source. The PSF is often described as an ellipsoid (with unsharp boundaries) of few hundred nanometers in focus diameter, and almost one micrometre along the optical axis. The shape varies significantly (and has a large impact on the resulting FCS curves) depending on the quality of the optical elements (it is crucial to avoid astigmatism and to check the real shape of the PSF on the instrument). In the case of confocal microscopy, and for small pinholes (around one Airy unit), the PSF is well approximated by Gaussians:
where
is the peak intensity, r and z are radial and axial position, and and are the radial and axial radii, and . This Gaussian form is assumed in deriving the functional form of the autocorrelation.Typically
is 200–300 nm, and is 2–6 times larger. One common way of calibrating the measurement volume parameters is to perform FCS on a species with known diffusion coefficient and concentration (see below). Diffusion coefficients for common fluorophores in water are given in a later section.The Gaussian approximation works to varying degrees depending on the optical details, and corrections can sometimes be applied to offset the errors in approximation.
Autocorrelation function
The (temporal) autocorrelation function is the correlation of a time series with itself shifted by time, as a function of :where
is the deviation from the mean intensity. The normalization (denominator) here is the most commonly used for FCS, because then the correlation at , G(0), is related to the average number of particles in the measurement volume.Interpreting the autocorrelation function
To extract quantities of interest, the autocorrelation data can be fitted, typically using a nonlinear least squares algorithm. The fit's functional form depends on the type of dynamics (and the optical geometry in question).Normal diffusion
The fluorescent particles used in FCS are small and thus experience thermal motions in solution. The simplest FCS experiment is thus normal 3D diffusion, for which the autocorrelation is:
where
is the ratio of axial to radial radii of the measurement volume, and is the characteristic residence time. This form was derived assuming a Gaussian measurement volume. Typically, the fit would have three free parameters—G(0), , and --from which the diffusion coefficient and fluorophore concentration can be obtained.With the normalization used in the previous section, G(0) gives the mean number of diffusers in the volume
where the effective volume is found from integrating the Gaussian form of the measurement volume and is given by:
-
gives the diffusion coefficient: -
Anomalous diffusion
If the diffusing particles are hindered by obstacles or pushed by a force (molecular motors, flow, etc.) the dynamics is often not sufficiently well-described by the normal diffusion model, where the mean squared displacement (MSD) grows linearly with time. Instead the diffusion may be better described as anomalous diffusionAnomalous Diffusion
Anomalous diffusion is a term used to describe a diffusion process with a non-linear relationship to time, in contrast to a typical diffusion process, in which the mean squared displacement , σr2, of a particle is a linear function of time....
, where the temporal dependenc of the MSD is non-linear as in the power-law:
where
is an anomalous diffusion coefficient. "Anomalous diffusion" commonly refers only to this very generic model, and not the many other possibilities that might be described as anomalous. Also, a power law is, in a strict sense, the expected form only for a narrow range of rigorously defined systems, for instance when the distribution of obstacles is fractalFractal
A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...
. Nonetheless a power law can be a useful approximation for a wider range of systems.
The FCS autocorrelation function for anomalous diffusion is:
where the anomalous exponent
is the same as above, and becomes a free parameter in the fitting.Using FCS, the anomalous exponent has been shown to be an indication of the degree of molecular crowding (it is less than one and smaller for greater degrees of crowding).
Polydisperse diffusion
If there are diffusing particles with different sizes (diffusion coefficients), it is common to fit to a function that is the sum of single component forms:
where the sum is over the number different sizes of particle, indexed by i, and
gives the weighting, which is related to the quantum yield and concentration of each type. This introduces new parameters, which makes the fitting more difficult as a higher dimensional space must be searched. Nonlinear least square fitting typically becomes unstable with even a small number of s. A more robust fitting scheme, especially useful for polydisperse samples, is the Maximum Entropy Method.Diffusion with flow
With diffusion together with a uniform flow with velocity in the lateral direction, the autocorrelation is:
where
is the average residence time if there is only a flow (no diffusion).Chemical relaxation
A wide range of possible FCS experiments involve chemical reactions that continually fluctuate from equilibrium because of thermal motions (and then "relax"). In contrast to diffusion, which is also a relaxation process, the fluctuations cause changes between states of different energies. One very simple system showing chemical relaxation would be a stationary binding site in the measurement volume, where particles only produce signal when bound (e.g. by FRET, or if the diffusion time is much faster than the sampling interval). In this case the autocorrelation is:
where
is the relaxation time and depends on the reaction kinetics (on and off rates), and:
is related to the equilibrium constant K.
Most systems with chemical relaxation also show measureable diffusion as well, and the autocorrelation function will depend on the details of the system. If the diffusion and chemical reaction are decoupled, the combined autocorrelation is the product of the chemical and diffusive autocorrelations.
Triplet state correction
The autocorrelations above assume that the fluctuations are not due to changes in the fluorescent properties of the particles. However, for the majority of (bio)organic fluorophores—e.g. green fluorescent proteinGreen fluorescent protein
The green fluorescent protein is a protein composed of 238 amino acid residues that exhibits bright green fluorescence when exposed to blue light. Although many other marine organisms have similar green fluorescent proteins, GFP traditionally refers to the protein first isolated from the...
, rhodamine, Cy3 and Alexa Fluor dyes—some fraction of illuminated particles are excited to a triplet state
Triplet state
A spin triplet is a set of three quantum states of a system, each with total spin S = 1 . The system could consist of a single elementary massive spin 1 particle such as a W or Z boson, or be some multiparticle state with total spin angular momentum of one.In physics, spin is the angular momentum...
(or other non-radiative decaying states) and then do not emit photons for a characteristic relaxation time
. Typically is on the order of microseconds, which is usually smaller than the dynamics of interest (e.g. ) but large enough to be measured. A multiplicative term is added to the autocorrelation to account for the triplet state. For normal diffusion:
where
is the fraction of particles that have entered the triplet state and is the corresponding triplet state relaxation time. If the dynamics of interest are much slower than the triplet state relaxation, the short time component of the autocorrelation can simply be truncated and the triplet term is unnecessary.Common fluorescent probes
The fluorescent species used in FCS is typically a biomolecule of interest that has been tagged with a fluorophore (using immunohistochemistryImmunohistochemistry
Immunohistochemistry or IHC refers to the process of detecting antigens in cells of a tissue section by exploiting the principle of antibodies binding specifically to antigens in biological tissues. IHC takes its name from the roots "immuno," in reference to antibodies used in the procedure, and...
for instance), or is a naked fluorophore that is used to probe some environment of interest (e.g. the cytoskeleton of a cell). The following table gives diffusion coefficients of some common fluorophores in water at room temperature, and their excitation wavelengths.
| Fluorescent dye |  (×10−10 m2 s−1) |
Excitation wavelength (nm) | Reference | |
|---|---|---|---|---|
| Rhodamine 6G | 2.8, 3.0, 4.14 ± 0.05 @ 25.00 °C | 514 | , | |
| Rhodamine 110 | 2.7 | 488 | ||
| Tetramethyl rhodamine | 2.6 | 543 | ||
| Cy3 | 2.8 | 543 | ||
| Cy5 | 2.5, 3.7 ± 0.15 @ 25.00 °C | 633 | , | |
| carboxyfluorescein | 3.2 | 488 | ||
| Alexa-488 | 1.96,4.35 @ 22.5±0.5 °C | 488 | ||
| Atto655-maleimide | 4.07 ± 0.1 @ 25.00 °C | 663 | ||
| Atto655-carboxylicacid | 4.26 ± 0.08 @ 25.00 °C | 663 | ||
| 2′, 7′-difluorofluorescein (Oregon Green488) | 4.11 ± 0.06 @ 25.00 °C | 498 |
Variations of FCS
FCS almost always refers to the single point, single channel, temporal autocorrelation measurement, although the term "fluorescence correlation spectroscopy" out of its historical scientific context implies no such restriction. FCS has been extended in a number of variations by different researchers, with each extension generating another name (usually an acronym).Fluorescence cross-correlation spectroscopy (FCCS)
FCS is sometimes used to study molecular interactions using differences in diffusion times (e.g. the product of an association reaction will be larger and thus have larger diffusion times than the reactants individually); however, FCS is relatively insensitive to molecular mass as can be seen from the following equation relating molecular mass to the diffusion time of globular particles (e.g. proteins):
where
is the viscosity of the sample and is the molecular mass of the fluorescent species. In practice, the diffusion times need to be sufficiently different—a factor of at least 1.6--which means the molecular masses must differ by a factor of 4. Dual color fluorescence cross-correlation spectroscopyFluorescence cross-correlation spectroscopy
Fluorescence cross-correlation spectroscopy was introduced by Eigen and Rigler in 1994 and experimentally realized by Schwille in 1997...
(FCCS) measures interactions by cross-correlating two or more fluorescent channels (one channel for each reactant), which distinguishes interactions more sensitively than FCS, particularly when the mass change in the reaction is small.
Brightness analysis methods (N&B, PCH, FIDA, Cumulant Analysis)
Fluorescence cross correlation spectroscopy overcomes the weak dependence of diffusion rate on molecular mass by looking at multicolor coincidence. What about homo-interactions? The solution lies in brightness analysis. These methods use the heterogeneity in the intensity distribution of fluorescence to measure the molecular brightness of different species in a sample. Since dimers will contain twice the number of fluorescent labels as monomers, their molecular brightness will be approximately double that of monomers. As a result, the relative brightness is sensitive a measure of oligomerization. The average molecular brightness () is related to the variance () and the average intensity () as follows:
Here
and are the fractional intensity and molecular brightness, respectively, of species .Two- and three- photon FCS excitation
Several advantages in both spatial resolution and minimizing photodamage/photobleaching in organic and/or biological samples are obtained by two-photon or three-photon excitation FCS.FRET-FCS
Another FCS based approach to studying molecular interactions uses fluorescence resonance energy transferFluorescence resonance energy transfer
Förster resonance energy transfer , also known as fluorescence resonance energy transfer, resonance energy transfer or electronic energy transfer , is a mechanism describing energy transfer between two chromophores.A donor chromophore, initially in its electronic excited state, may transfer energy...
(FRET) instead of fluorescence, and is called FRET-FCS. With FRET, there are two types of probes, as with FCCS; however, there is only one channel and light is only detected when the two probes are very close—close enough to ensure an interaction. The FRET signal is weaker than with fluorescence, but has the advantage that there is only signal during a reaction (aside from autofluorescence
Autofluorescence
Autofluorescence is the natural emission of light by biological entities such as mitochondria and lysosomes, and is used to distinguish the light originating from artificially added fluorescent markers...
).
Scanning FCS
In Scanning fluorescence correlation spectroscopy (sFCS) the measurement volume is moved across the sample in a defined way. The introduction of scanning is motivated by its ability to alleviate or remove several distinct problems often encountered in standard FCS, and thus, to extend the range of applicability of fluorescence correlation methods in biological systems.Some variations of FCS are only applicable to serial scanning laser microscopes. Image Correlation Spectroscopy and its variations all were implemented on a scanning confocal or scanning two photon microscope, but transfer to other microscopes, like a spinning disk confocal microscope. Raster ICS (RICS), and position sensitive FCS (PSFCS) incorporate the time delay between parts of the image scan into the analysis. Also, low dimensional scans (e.g. a circular ring)—only possible on a scanning system—can access time scales between single point and full image measurements. Scanning path has also been made to adaptively follow particles.
Spinning disk FCS, and spatial mapping
Any of the image correlation spectroscopy methods can also be performed on a spinning disk confocal microscope, which in practice can obtain faster imaging speeds compared to a laser scanning confocal microscope. This approach has recently been applied to diffusion in a spatially varying complex environment, producing a pixel resolution map of a diffusion coefficient. The spatial mapping of diffusion with FCS has subsequently been extended to the TIRF system. Spatial mapping of dynamics using correlation techniques had been applied before, but only at sparse points or at coarse resolution.Image correlation spectroscopy (ICS)
When the motion is slow (in biology, for example, diffusion in a membrane), getting adequate statistics from a single-point FCS experiment may take a prohibitively long time. More data can be obtained by performing the experiment in multiple spatial points in parallel, using a laser scanning confocal microscope. This approach has been called Image Correlation Spectroscopy (ICS). The measurements can then be averaged together.Another variation of ICS performs a spatial autocorrelation on images, which gives information about the concentration of particles. The correlation is then averaged in time.
A natural extension of the temporal and spatial correlation versions is spatio-temporal ICS (STICS). In STICS there is no explicit averaging in space or time (only the averaging inherent in correlation). In systems with non-isotropic motion (e.g. directed flow, asymmetric diffusion), STICS can extract the directional information. A variation that is closely related to STICS (by the Fourier transform) is k-space Image Correlation Spectroscopy (kICS).
There are cross-correlation versions of ICS as well.
Total internal reflection FCS
Total internal reflection fluorescenceTotal internal reflection fluorescence microscope
A total internal reflection fluorescence microscope is a type of microscope with which a thin region of a specimen, usually less than 200 nm, can be observed.-Background:...
(TIRF) is a microscopy approach that is only sensitive to a thin layer near the surface of a coverslip, which greatly minimizes background fluorscence. FCS has been extended to that type of microscope, and is called TIR-FCS. Because the fluorescence intensity in TIRF falls off exponentially with distance from the coverslip (instead of as a Gaussian with a confocal), the autocorrelation function is different.
Other fluorescent dynamical approaches
There are two main non-correlation alternatives to FCS that are widely used to study the dynamics of fluorescent species.Fluorescence recovery after photobleaching (FRAP)
In FRAPFluorescence recovery after photobleaching
Fluorescence recovery after photobleaching denotes an optical technique capable of quantifying the two dimensional lateral diffusion of a molecularly thin film containing fluorescently labeled probes, or to examine single cells. This technique is very useful in biological studies of cell membrane...
, a region is briefly exposed to intense light, irrecoverably photobleaching fluorophores, and the fluorescence recovery due to diffusion of nearby (non-bleached) fluorophores is imaged. A primary advantage of FRAP over FCS is the ease of interpreting qualitative experiments common in cell biology. Differences between cell lines, or regions of a cell, or before and after application of drug, can often be characterized by simple inspection of movies. FCS experiments require a level of processing and are more sensitive to potentially confounding influences like: rotational diffusion, vibrations, photobleaching, dependence on illumination and fluorescence color, inadequate statistics, etc. It is much easier to change the measurement volume in FRAP, which allows greater control. In practice, the volumes are typically larger than in FCS. While FRAP experiments are typically more qualitative, some researchers are studying FRAP quantitatively and including binding dynamics. A disadvantage of FRAP in cell biology is the free radical perturbation of the cell caused by the photobleaching. It is also less versatile, as it cannot measure concentration or rotational diffusion, or co-localization. FRAP requires a significantly higher concentration of fluorophores than FCS.
Particle tracking
In particle tracking, the trajectories of a set of particles are measured, typically by applying particle tracking algorithms to movies.http://www.physics.emory.edu/~weeks/idl/ Particle tracking has the advantage that all the dynamical information is maintained in the measurement, unlike FCS where correlation averages the dynamics to a single smooth curve. The advantage is apparent in systems showing complex diffusion, where directly computing the mean squared displacement allows straightforward comparison to normal or power law diffusion. To apply particle tracking, the particles have to be distinguishable and thus at lower concentration than required of FCS. Also, particle tracking is more sensitive to noise, which can sometimes affect the results unpredictably.See also
- Confocal microscopyConfocal microscopyConfocal microscopy is an optical imaging technique used to increase optical resolution and contrast of a micrograph by using point illumination and a spatial pinhole to eliminate out-of-focus light in specimens that are thicker than the focal plane. It enables the reconstruction of...
- Fluorescence cross-correlation spectroscopyFluorescence cross-correlation spectroscopyFluorescence cross-correlation spectroscopy was introduced by Eigen and Rigler in 1994 and experimentally realized by Schwille in 1997...
,FCCS - FRETFretA fret is a raised portion on the neck of a stringed instrument, that extends generally across the full width of the neck. On most modern western instruments, frets are metal strips inserted into the fingerboard...
- Dynamic light scatteringDynamic light scatteringthumb|right|350px|Hypothetical Dynamic light scattering of two samples: Larger particles on the top and smaller particle on the bottomDynamic light scattering is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers...
- Diffusion coefficient
Further reading
- Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, BioScience (Ed. Klinge & Owman) p. 180
- Oehlenschläger F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.