Fluorescence correlation spectroscopy

4886:, 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. 165:, 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 237: 4843:(SOFI) is a super-resolution technique that achieves spatial resolutions below the diffraction limit by post-processing analysis with correlation equations, similar to FCS. While original reports of SOFI used fluctuations from stationary, blinking of fluorophores, FCS has been combined with SOFI where fluctuations are produced from diffusing probes to produce super-resolution spatial maps of diffusion coefficients. This has been applied to understand diffusion and spatial properties of porous and confined materials. This includes agarose and temperature-responsive PNIPAM hydrogels, liquid crystals, and phase-separated polymers and RNA/protein condensates. 4491:

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 (

277:(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 micrometer 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: 248:), 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 630: 224:

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 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

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if multiple particle trajectories intersect, this method works in principle for arbitrarily large molecule densities and dynamical parameters (e.g. diffusion coefficients, velocities) as long as individual molecules can be identified. It is computationally cheap and robust and allows one to identify and quantify motions (e.g. diffusion, active transport, confined diffusion) within an ensemble of particles, without any a priori knowledge about the dynamics.

133:. The analysis provides kinetic parameters of the physical processes underlying 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 1573: 22: 4854:(TIRF) is a microscopy approach that is only sensitive to a thin layer near the surface of a coverslip, which greatly minimizes background fluorescence. 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. 4766:(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 4783:(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. 1218: 863: 4800:

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

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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,

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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

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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

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There are cross-correlation versions of ICS as well, which can yield the concentration, distribution and dynamics of co-localized fluorescent molecules. Molecules are considered co-localized when individual fluorescence contributions are indistinguishable due to overlapping point-spread functions of

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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

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analysis) FCS has no physical separation process; instead, it achieves its spatial resolution through 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

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PICS is a powerful analysis tool that resolves correlations on the nanometer length and millisecond timescale. Adapted from methods of spatio-temporal image correlation spectroscopy, it exploits the high positional accuracy of single-particle tracking. While conventional tracking methods break down

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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.

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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

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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. While camera white noise does not autocorrelate over time, it does over space - this creates a white noise amplitude in the

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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

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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

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Most systems with chemical relaxation also show measurable 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.

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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

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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,

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or selective plane imaging microscopy (SPIM) uses illumination that is done perpendicularly to the direction of observation, by using a thin sheet of (laser) light. Under certain conditions, this illumination principle can be combined with fluorescence correlation spectroscopy, to allow spatially

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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

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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.

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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

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This set of methods include number and brightness (N&B), photon counting histogram (PCH), fluorescence intensity distribution analysis (FIDA), and Cumulant Analysis. and Spatial Intensity Distribution Analysis. Combination of multiple methods is also reported. Fluorescence cross correlation

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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

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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.

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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

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Whereas FCS is a point measurement providing diffusion time at a given observation volume, svFCS is a technique where the observation spot is varied in order to measure diffusion times at different spot sizes. The relationship between the diffusion time and the spot area is linear and could be

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for freely diffusing Rhodamine 6G are shown in the figure to the right. The plot on top shows the fluorescent intensity versus time. The intensity fluctuates as Rhodamine 6G moves in and out of the focal volume. In the bottom plot is the autocorrelation on the same data. Information about the

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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

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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

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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

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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:

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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.

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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.

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foundations and types of applications. Around 1990, with the ability of detecting sufficiently small number of fluorescence particles, two issues emerged: A non-Gaussian distribution of the fluorescence intensity and the three-dimensional confocal

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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.

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of fluorophores in the focal volume is low and if dark states, etc., of the fluorophore can be ignored. In particular, no assumption was made on the type of diffusive motion under investigation. The formula allows for an interpretation of

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Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In

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Roy, Prithu; Claude, Jean-Benoît; Tiwari, Sunny; Barulin, Aleksandr; Wenger, Jérôme (5 January 2023). "Ultraviolet Nanophotonics Enables Autofluorescence Correlation Spectroscopy on Label-Free Proteins with a Single Tryptophan".

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Kwapiszewska, Karina; Kalwarczyk, Tomasz; Michalska, Bernadeta; Szczepański, Krzysztof; Szymański, Jędrzej; Patalas-Krawczyk, Paulina; Andryszewski, Tomasz; Iwan, Michalina; Duszyński, Jerzy; Hołyst, Robert (2019).

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of a laser-microscopy system. The former led to an analysis of distributions and moments of the fluorescent signals for extracting molecular information, which eventually became a collection of methods known as

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plotted in order to decipher the major contribution of confinement. The resulting curve is called the diffusion law. This technique is used in Biology to study the plasma membrane organization on living cells.

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Barulin, Aleksandr; Claude, Jean-Benoît; Patra, Satyajit; Bonod, Nicolas; Wenger, Jérôme (9 October 2019). "Deep Ultraviolet Plasmonic Enhancement of Single Protein Autofluorescence in Zero-Mode Waveguides".

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Müller, C.B.; Loman, A.; Pacheco, V.; Koberling, F.; Willbold, D.; Richtering, W.; Enderlein, J. (2008). "Precise measurement of diffusion by multi-color dual-focus fluorescence correlation spectroscopy".

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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.

1213:{\displaystyle G(\tau )={\frac {1}{\langle N\rangle }}\left\langle \exp \left(-{\frac {\Delta X(\tau )^{2}+\Delta Y(\tau )^{2}}{w_{xy}^{2}}}-{\frac {\Delta Z(\tau )^{2}}{w_{z}^{2}}}\right)\right\rangle ,} 2527: 2194:

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

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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

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FCS is such a sensitive analytical tool because it observes a small number of molecules (nanomolar to picomolar concentrations) in a small volume (~1 μm). In contrast to other methods (such as

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Recent advances in ultraviolet nanophotonics has led to development of single molecule study on label-free protein by exciting them with deep ultraviolet light and studying the dynamic processes.

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Wachsmuth, M.; Waldeck, W.; Langowski, J. (2000). "Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially resolved fluorescence correlation spectroscopy".

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Remaut, K.; Lucas, B.; Braeckmans, K.; Sanders, N.N.; Smedt, S.C. De; Demeester, J. (2005). "FRET-FCS as a tool to evaluate the stability of oligonucleotide drugs after intracellular delivery".

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Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

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A particle image cross-correlation spectroscopy (PICCS) extension is available for biological processes that involve multiple interaction partners, as can observed by two-color microscopy.

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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:

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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.

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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.

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Loman, A.; Dertinger, T.; Koberling, F.; Enderlein, J. (2008). "Comparison of optical saturation effects in conventional and dual-focus fluorescence correlation spectroscopy (2008)".

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Widengren, J.; Schwille, P. (2000). "Characterization of photoinduced isomerization and back-isomerization of the cyanine dye Cy5 by fluorescence correlation spectroscopy. (2000)".

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Wiseman, P. W.; Squier, J. A.; Ellisman, M. H.; Wilson, K. R. (2000). "Two-photon video rate image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS)".

1586: 130: 6068:"Conformation transition of Poly(N-isopropylacrylamide) Single Chains in Its Cononsolvency Process: A Study by Fluorescence Correlation Spectroscopy and Scaling Analysis. (2012)" 3323: 4964:

Chen, H., Farkas, E., & Webb, W. (2008). In vivo applications of fluorescence correlation spectroscopy. Biophysical Tools for Biologists, Vol 2: In Vivo Techniques, 89, 3-+.

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Kohler, R.H.; Schwille, P.; Webb, W.W.; Hanson, M.R. (2000). "Active protein transport through plastid tubules: velocity quantified by fluorescence correlation spectroscopy".

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Mayboroda, O. A.; van Remoortere, A.; Tanke, H. J.; Hokke, C. H.; Deelder, A. M. (2003). "A new approach for fluorescence correlation spectroscopy (FCS) based immunoassays".

858:{\displaystyle G(\tau )={\frac {\langle \delta I(t)\delta I(t+\tau )\rangle }{\langle I(t)\rangle ^{2}}}={\frac {\langle I(t)I(t+\tau )\rangle }{\langle I(t)\rangle ^{2}}}-1} 4732: 2513:

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).

1550: 1445: 584: 481: 4542: 3859: 2786: 2752: 611: 508: 6116:

Pristinski, D.; Kozlovskaya, V.; Sukhishvili, S. A. (2005). "Fluorescence correlation spectroscopy studies of diffusion of a weak polyelectrolyte in aqueous solutions".

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Eventually, both the concentration and size of the particle (molecule) are determined. Both parameters are important in biochemical research, biophysics, and chemistry.

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The Gaussian approximation works to varying degrees depending on the optical details, and corrections can sometimes be applied to offset the errors in approximation.

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Kwapiszewska, K.; Szczepański, K.; Kalwarczyk, T.; Michalska, B.; Patalas-Krawczyk, P.; Szymański, J.; Andryszewski, T.; Iwan, M.; Duszyński, J.; Hołyst, R. (2020).

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spatial autocorrelation function which must be accounted for when fitting the autocorrelation amplitude in order to find the concentration of fluorescent molecules.

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Rigler, R, Ü. Mets1, J. Widengren and P. Kask. "Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion.

4705: 4197: 2289: 1342: 675: 655: 451: 4479: 3904: 3829: 1928:(0) gives the mean number of diffusers in the volume <N>, or equivalently—with knowledge of the observation volume size—the mean concentration: 7839:

Capoulade, J.; Wachsmuth, M.; Hufnagel, L.; Knop, M. (September 2011). "Quantitative fluorescence imaging of protein diffusion and interaction in living cells".

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Shayegan, M.; Michnick, S. W.; Leslie, S. L. (2019). "Probing Inhomogeneous Diffusion in the Microenvironments of Phase-Separated Polymers under Confinement".

260:. 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 1865:

is the characteristic residence time. This form was derived assuming a Gaussian measurement volume. Typically, the fit would have three free parameters—G(0),

3798:{\displaystyle \ G(\tau )=G(0){\frac {(1-F+Fe^{-\tau /\tau _{F}})}{(1-F)}}{\frac {1}{(1+(\tau /\tau _{D,i}))(1+a^{-2}(\tau /\tau _{D,i}))^{1/2}}}+G(\infty )} 2521:

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:

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Magde, D.; Elson, E. L.; Webb, W. W. (1972). "Thermodynamic fluctuations in a reacting system: Measurement by fluorescence correlation spectroscopy".

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Widengren, J.; Mets; Rigler, R. (1995). "Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study".

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Höfling, F.; Bamberg, K.-U. & Franosch, T. (2011). "Anomalous transport resolved in space and time by fluorescence correlation spectroscopy".

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is the deviation from the mean intensity. The normalization (denominator) here is the most commonly used for FCS, because then the correlation at

58: 3547:) but large enough to be measured. A multiplicative term is added to the autocorrelation to account for the triplet state. For normal diffusion: 257: 2027: 7309:"Spatio-temporal image correlation spectroscopy (STICS): theory, verification and application to protein velocity mapping in living CHO cells" 7222:"Spatially resolved total internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera" 65: 4866:

resolved imaging of the mobility and interactions of fluorescing particles such as GFP labelled proteins inside living biological samples.

4840: 7530:"Particle Image Correlation Spectroscopy (PICS): Retrieving Nanometer-Scale Correlations from High-Density Single-Molecule Position Data" 4938: 4322: 5616:

Medina, M. A.; Schwille, P. (2002). "Fluorescence correlation spectroscopy for the detection and study of single molecules in biology".

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In particle tracking, the trajectories of a set of particles are measured, typically by applying particle tracking algorithms to movies.

4670:{\displaystyle \ \langle \varepsilon \rangle ={\frac {\sigma ^{2}-\langle I\rangle }{\langle I\rangle }}=\sum _{i}f_{i}\varepsilon _{i}} 4883: 72: 3144: 3245: 5538:

Rigler, M (1995). "Fluorescence correlations, single molecule detection and large number screening. Applications in biotechnology".

2717:{\displaystyle \ G(\tau )=G(0)\sum _{i}{\frac {\alpha _{i}}{(1+(\tau /\tau _{D,i}))(1+a^{-2}(\tau /\tau _{D,i}))^{1/2}}}+G(\infty )} 7696:

Dutta, C.; Bishop, L. D. C.; Landes, C.F. (2020). "Imaging Switchable Protein Interactions with an Active Porous Polymer Support".

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Berland, K. M. (2004). "Detection of specific DNA sequences using dual-color two-photon fluorescence correlation spectroscopy".

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microscope. This approach has been called Image Correlation Spectroscopy (ICS). The measurements can then be averaged together.

2480:{\displaystyle G(\tau )=G(0){\frac {1}{(1+(\tau /\tau _{D})^{\alpha })(1+a^{-2}(\tau /\tau _{D})^{\alpha })^{1/2}}}+G(\infty ),} 4763: 225: 142: 8129:"Two-photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of binary phospholipid mixtures" 5296:

Qian, H.; Elson, E. L. (1991). "Analysis of confocal laser-microscope optics for 3-D fluorescence correlation spectroscopy".

7649:"Characterization of Porous Materials by Fluorescence Correlation Spectroscopy Super-resolution Optical Fluctuation Imaging" 7473:-Space Image Correlation Spectroscopy: A Method for Accurate Transport Measurements Independent of Fluorophore Photophysics" 8186:"Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two- photon excitation" 871: 8270:

Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy,

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There are two main non-correlation alternatives to FCS that are widely used to study the dynamics of fluorescent species.

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The fluorescent species used in FCS is typically a biomolecule of interest that has been tagged with a fluorophore (using

8280:"Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with fluorescence correlation spectroscopy" 4862: 3068:{\displaystyle \ G(\tau )=G(0){\frac {1}{(1+(\tau /\tau _{D}))(1+a^{-2}(\tau /\tau _{D}))^{1/2}}}\times \exp+G(\infty )} 2116: 5253:

Magde, D.; Elson, E. L.; Webb, W. W. (1974). "Fluorescence correlation spectroscopy II. An experimental realization".

1561: 105: 6885:"Characterization of Protein Dynamics in Asymmetric Cell Division by Scanning Fluorescence Correlation Spectroscopy" 5456:

Thompson N L 1991 Topics in Fluorescence Spectroscopy Techniques vol 1, ed J R Lakowicz (New York: Plenum) pp 337–78

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where the effective volume is found from integrating the Gaussian form of the measurement volume and is given by:

513: 5573:

Krichevsky, O.; Bonnet, G. (2002). "Fluorescence correlation spectroscopy: the technique and its applications".

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extract the directional information. A variation that is closely related to STICS (by the Fourier transform) is

1760: 161:. In these techniques light is focused on a sample and the measured fluorescence intensity fluctuations (due to 4494: 2208: 6743:"Determination of G-protein–coupled receptor oligomerization by molecular brightness analyses in single cells" 3081: 6942:"Fluctuation Correlation Spectroscopy with a Laser-Scanning Microscope: Exploiting the Hidden Time Structure" 1747:{\displaystyle \ G(\tau )=G(0){\frac {1}{(1+(\tau /\tau _{D}))(1+a^{-2}(\tau /\tau _{D}))^{1/2}}}+G(\infty )} 7412:"Quantitation of membrane receptor distributions by image correlation spectroscopy: concept and application" 4328:

the following equation relating molecular mass to the diffusion time of globular particles (e.g. proteins):

3420:{\displaystyle G(0)={\frac {1}{\langle N\rangle }}{\frac {k_{on}}{k_{off}}}={\frac {1}{\langle N\rangle }}K} 2788:

s. A more robust fitting scheme, especially useful for polydisperse samples, is the Maximum Entropy Method.

236: 8414: 5863:"Measuring Size Distribution in Highly Heterogeneous Systems with Fluorescence Correlation Spectroscopy" 5215:

Elson, E. L.; Magde, D. "Fluorescence correlation spectroscopy I. Conceptual basis and theory, (1974)".

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Ehrenberg, M.; Rigler, R. (1974). "Rotational brownian motion and fluorescence intensity fluctuations".

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The (temporal) autocorrelation function is the correlation of a time series with itself shifted by time

6684:"Revealing protein oligomerization and densities in situ using spatial intensity distribution analysis" 6568:"Fluorescence-intensity distribution analysis and its application in biomolecular detection technology" 4547: 1448: 1347: 7587:"Quantification of Biological Interactions with Particle Image Cross-Correlation Spectroscopy (PICCS)" 7056:"Spatial-temporal studies of membrane dynamics: scanning fluorescence correlation spectroscopy (SFCS)" 3447: 2195: 199: 7165:"Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope" 6231:"Precise Measurement of Diffusion Coefficients using Scanning Fluorescence Correlation Spectroscopy" 5088:"Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations" 5028:"Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations" 1564:. The fit's functional form depends on the type of dynamics (and the optical geometry in question). 244:

The typical FCS setup consists of a laser line (wavelengths ranging typically from 405–633 nm (

4933: 4710: 2011:{\displaystyle \ G(0)={\frac {1}{\langle N\rangle }}={\frac {1}{V_{\text{eff}}\langle C\rangle }},} 166: 7784:"Total Internal Reflection with Fluorescence Correlation Spectroscopy: Nonfluorescent Competitors" 5696:"Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy" 1512: 1407: 559: 456: 4520: 3834: 2758: 2730: 589: 486: 32: 4268: 4235: 1868: 172:

When an appropriate model is known, FCS can be used to obtain quantitative information such as

3523: 3496: 3469: 1897: 1841: 3520:

is on the order of microseconds, which is usually smaller than the dynamics of interest (e.g.

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To extract quantities of interest, the autocorrelation data can be fitted, typically using a

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Diaspro, A.; Robello, M. (1999). "Multi-photon Excitation Microscopy to Study Biosystems".

8066: 8002: 7937: 7795: 7598: 7541: 7484: 7423: 7320: 7176: 7127: 7067: 7010: 6953: 6940:

Digman, M.A.; Sengupta, P.; Wiseman, P.W.; Brown, C.M.; Horwitz, A.R.; Gratton, E. (2005).

6896: 6804: 6695: 6638: 6579: 6522: 6465: 6408: 6242: 6203: 6168: 6125: 6079: 6032: 5874: 5817: 5770: 5707: 5582: 5492: 5411: 5352: 5305: 5189: 5154: 5099: 5039: 4683: 4175: 3871: 2267: 1327: 660: 640: 429: 253: 194: 8360: 1317:{\displaystyle \Delta {\vec {R}}(\tau )=(\Delta X(\tau ),\Delta Y(\tau ),\Delta Z(\tau ))} 974:

diffusion rate and concentration can be obtained using one of the models described below.

8: 8429: 4923: 4461: 3886: 3811: 2199: 2189: 154: 8295: 8201: 8144: 8070: 8006: 7941: 7799: 7673: 7602: 7545: 7488: 7427: 7324: 7180: 7131: 7112: 7071: 7014: 6957: 6900: 6808: 6699: 6642: 6583: 6526: 6469: 6412: 6246: 6207: 6172: 6129: 6083: 6036: 5878: 5821: 5774: 5711: 5586: 5496: 5415: 5356: 5309: 5193: 5158: 5103: 5043: 553:. This Gaussian form is assumed in deriving the functional form of the autocorrelation. 8218: 8185: 8161: 8128: 8090: 8056: 8023: 7992: 7980: 7961: 7927: 7864: 7816: 7783: 7764: 7721: 7619: 7586: 7562: 7529: 7505: 7468: 7444: 7411: 7392: 7341: 7308: 7284: 7197: 7164: 7088: 7055: 7031: 6998: 6974: 6941: 6917: 6884: 6825: 6792: 6773: 6718: 6683: 6659: 6626: 6543: 6510: 6486: 6453: 6429: 6396: 6263: 6230: 6095: 6048: 5895: 5862: 5838: 5805: 5786: 5760: 5728: 5695: 5641: 5598: 5278: 5232: 5122: 5087: 5062: 5027: 5002: 4975: 4737: 2799: 150: 8209: 8152: 7435: 6816: 6534: 6420: 5886: 5719: 5375: 5340: 2296:. Nonetheless a power law can be a useful approximation for a wider range of systems. 8365: 8319: 8314: 8279: 8223: 8166: 8094: 8082: 8028: 7979:

Barulin, Aleksandr; Roy, Prithu; Claude, Jean-Benoît; Wenger, Jérôme (5 April 2022).

7965: 7953: 7899: 7882:

Sprague, B.L.; McNally, J.G. (2005). "FRAP analysis of binding: proper and fitting".

7856: 7821: 7768: 7756: 7725: 7713: 7678: 7624: 7567: 7510: 7449: 7384: 7380: 7346: 7276: 7241: 7202: 7145: 7093: 7036: 6979: 6922: 6865: 6830: 6777: 6765: 6723: 6664: 6607: 6602: 6567: 6548: 6491: 6434: 6268: 6141: 6052: 5997: 5935: 5900: 5843: 5733: 5676: 5633: 5594: 5555: 5551: 5520: 5515: 5481:"Sorting single molecules: application to diagnostics and evolutionary biotechnology" 5480: 5439: 5434: 5399: 5380: 5321: 5270: 5201: 5127: 5067: 5007: 3317:

is the relaxation time and depends on the reaction kinetics (on and off rates), and:

1921:—from which the diffusion coefficient and fluorophore concentration can be obtained. 416:{\displaystyle PSF(r,z)=I_{0}e^{-2r^{2}/\omega _{xy}^{2}}e^{-2z^{2}/\omega _{z}^{2}}} 125:) is a statistical analysis, via time correlation, of stationary fluctuations of the 7868: 7288: 6099: 5790: 5602: 5236: 8355: 8347: 8309: 8299: 8213: 8205: 8156: 8148: 8074: 8018: 8010: 7945: 7891: 7848: 7811: 7803: 7748: 7705: 7668: 7660: 7614: 7606: 7557: 7549: 7500: 7492: 7439: 7431: 7396: 7376: 7336: 7328: 7268: 7233: 7192: 7184: 7135: 7083: 7075: 7026: 7018: 6969: 6961: 6912: 6904: 6857: 6820: 6812: 6757: 6713: 6703: 6654: 6646: 6597: 6587: 6538: 6530: 6481: 6473: 6424: 6416: 6258: 6250: 6211: 6176: 6133: 6087: 6044: 6040: 5989: 5962: 5927: 5890: 5882: 5833: 5825: 5778: 5723: 5715: 5668: 5645: 5625: 5590: 5547: 5510: 5500: 5429: 5419: 5370: 5360: 5313: 5282: 5262: 5224: 5197: 5162: 5117: 5107: 5057: 5047: 4997: 4987: 4767: 7220:

Kannan, B.; Guo, L.; Sudhaharan, T.; Ahmed, S.; Maruyama, I.; Wohland, T. (2007).

6861: 5993: 5672: 8398: 8393: 8338:

Haustein, Elke; Schwille, Petra (2004). "Single-molecule spectroscopic methods".

8078: 7949: 6454:"Mapping the number of molecules and brightness in the laser scanning microscope" 6215: 2198:(MSD) grows linearly with time. Instead the diffusion may be better described as 970: 629: 261: 249: 245: 134: 7807: 7553: 7496: 7332: 7188: 7079: 7022: 6965: 6908: 6742: 6650: 6477: 6254: 5829: 4992: 4734:

are the fractional intensity and molecular brightness, respectively, of species

2727:

where the sum is over the number different sizes of particle, indexed by i, and

8014: 7981:"Ultraviolet optical horn antennas for label-free detection of single proteins" 7648: 7610: 6761: 5266: 5228: 5166: 5112: 5052: 4090: 8351: 7895: 4425:{\displaystyle \ \tau _{D}={\frac {3\pi \omega _{xy}^{2}\eta }{2kT}}(M)^{1/3}} 2202:, where the temporal dependence of the MSD is non-linear as in the power-law: 966:(0), is related to the average number of particles in the measurement volume. 202:) has made FCS a common tool for studying molecular dynamics in living cells. 169:, which uses coherent light scattering, instead of (incoherent) fluorescence. 8408: 8304: 7709: 7113:"Tracking-FCS: Fluorescence correlation spectroscopy of individual particles" 6592: 4835: 3459: 7664: 6708: 5931: 5505: 5424: 5365: 4304:

Sampling-Volume-Controlled Fluorescence Correlation Spectroscopy (SVC-FCS):

8369: 8227: 8170: 8086: 8032: 7957: 7903: 7860: 7825: 7760: 7717: 7682: 7628: 7571: 7514: 7388: 7350: 7280: 7272: 7245: 7206: 7163:

Sisan, D.R.; Arevalo, R.; Graves, C.; McAllister, R.; Urbach, J.S. (2006).

7149: 7140: 7097: 7040: 6983: 6926: 6869: 6769: 6727: 6668: 6611: 6552: 6495: 6438: 6272: 6145: 6001: 5939: 5904: 5847: 5737: 5680: 5637: 5325: 5131: 5071: 5011: 4895: 126: 8323: 7453: 6834: 5559: 5524: 5443: 5400:"Distribution of molecular aggregation by analysis of fluctuation moments" 5384: 5274: 5084: 5024: 4973: 7752: 5317: 4779:

applicability of fluorescence correlation methods in biological systems.

3455: 2100:{\displaystyle \ V_{\text{eff}}=\pi ^{3/2}\omega _{xy}^{2}\omega _{z}.\,} 1324:

denotes the stochastic displacement in space of a fluorophore after time

6511:"The photon counting histogram in fluorescence fluctuation spectroscopy" 5966: 5341:"High-order fluorescence fluctuation analysis of model protein clusters" 4857: 5782: 5629: 8255: 7237: 6180: 6137: 6091: 5861:

Sengupta, P.; Garai, K.; Balaji, J.; Periasamy, N.; Maiti, S. (2003).

3129:

is the average residence time if there is only a flow (no diffusion).

1018:, the autocorrelation function is given by the general master formula 240:

A basic diagram of a fluorescence correlation spectroscopy instrument.

7852: 7410:

Petersen, N. O.; Wiseman, P. W.; Seger, O.; Magnusson, K. E. (1993).

7054:

Ruan, Q.; Cheng, M.A.; Levi, M.; Gratton, E.; Mantulin, W.W. (2004).

5750: 4316: 3831:

is the fraction of particles that have entered the triplet state and

162: 8376: 6793:"On the analysis of high order moments of fluorescence fluctuations" 4877: 21: 8061: 7997: 7932: 7584: 6999:"Position-Sensitive Scanning Fluorescence Correlation Spectroscopy" 4976:"Nanoscale Viscosity of Cytoplasm Is Conserved in Human Cell Lines" 4762:

Another FCS based approach to studying molecular interactions uses

2510:

is the same as above, and becomes a free parameter in the fitting.

1572: 7585:

Semrau, S.; Holtzer, L.; Gonzalez-Gaitan, M.; Schmidt, T. (2011).

5765: 4087:

with each extension generating another name (usually an acronym).

453:

is the peak intensity, r and z are radial and axial position, and

5658: 4820: 3463: 2293: 6193: 6115: 3229:{\displaystyle \ G(\tau )=G(0)\exp(-\tau /\tau _{B})+G(\infty )} 3307:{\displaystyle \ \tau _{B}=(k_{\text{on}}+k_{\text{off}})^{-1}} 7838: 6452:

Digman, M. A.; Dalal, R.; Horwitz, A. F.; Gratton, E. (2008).

3462:(or other non-radiative decaying states) and then do not emit 7409: 6397:"Resolution of fluorescence correlation measurements. (1999)" 4901: 3458:

dyes—some fraction of illuminated particles are excited to a

2299:

The FCS autocorrelation function for anomalous diffusion is:

8245:, D. Luthria, Editor pp.241–273, AOCS Press., Champaign, IL. 7162: 6847: 6627:"Cumulant analysis in fluorescence fluctuation spectroscopy" 5860: 4091:

Spot variation fluorescence correlation spectroscopy (svFCS)

1555: 8277: 7366: 6509:

Chen, Y.; Müller, J. D.; So, P. T. C.; Gratton, E. (1999).

6021: 5806:"Anomalous diffusion of proteins due to molecular crowding" 6939: 4836:

FCS Super-resolution Optical Fluctuation Imaging (fcsSOFI)

4310:

FCS with Nano-apertures: breaking the diffraction barrier

2796:

With diffusion together with a uniform flow with velocity

7647:

Kisley, L.; Higgins, D.; Weiss, S.; Landes, C.F. (2015).

7258: 6451: 4869: 3451: 129:

intensity. Its theoretical underpinning originated from

7646: 7306: 7219: 6394: 5917: 4786: 4199:

is the y axis intercept. In case of Brownian diffusion,

8183: 7916: 6395:

Meseth, U.; Wohland, T.; Rigler, R.; Vogel, H. (1999).

6066:

Wang, F.; Shi, Y.; Luo, S.; Chen, Y.; Zhao, J. (2012).

4909: 4795: 8184:

Schwille, P.; Haupts, U.; Maiti, S.; Webb, W. (1999).

8045: 7978: 7738: 6111: 6109: 4858:

FCS imaging using Light sheet fluorescence microscopy

4740: 4713: 4686: 4579: 4550: 4523: 4497: 4464: 4441: 4337: 4271: 4238: 4205: 4178: 4105: 3889: 3837: 3814: 3556: 3526: 3499: 3472: 3326: 3248: 3147: 3084: 2825: 2802: 2761: 2733: 2530: 2496: 2308: 2270: 2211: 2119: 2030: 1937: 1924:

With the normalization used in the previous section,

1900: 1871: 1844: 1814: 1763: 1589: 1515: 1457: 1410: 1377: 1350: 1330: 1229: 1027: 983: 942: 929:{\displaystyle \delta I(t)=I(t)-\langle I(t)\rangle } 874: 686: 663: 643: 592: 562: 516: 489: 459: 432: 286: 8278:

Oehlenschläger, F.; Schwille, P.; Eigen, M. (1996).

7307:

Hebert, B.; Constantino, S.; Wiseman, P. W. (2005).

7053: 6017: 6015: 6013: 6011: 4301:

svFCS studies on living cells and simulation papers

4232:. In case of a confinement due to isolated domains, 4162:{\displaystyle \ \omega _{xy}^{2}=4D\tau _{D}+t_{0}} 146:

the biochemical pathway in intact cells and organs.

6565: 6508: 6106: 5952: 2292:for instance when the distribution of obstacles is 220:. See Thompson (1991) for a review of that period. 6996: 6566:Kask, P.; Palo, K.; Ullmann, D.; Gall, K. (1999). 4746: 4726: 4699: 4669: 4562: 4536: 4509: 4473: 4450: 4424: 4317:Fluorescence cross-correlation spectroscopy (FCCS) 4290: 4257: 4224: 4191: 4161: 3898: 3853: 3823: 3797: 3539: 3512: 3485: 3419: 3306: 3228: 3121: 3067: 2816:in the lateral direction, the autocorrelation is: 2808: 2780: 2746: 2716: 2502: 2479: 2283: 2253: 2173:{\displaystyle \ D=\omega _{xy}^{2}/{4\tau _{D}}.} 2172: 2099: 2010: 1913: 1886: 1857: 1830: 1800: 1746: 1544: 1501: 1439: 1392: 1362: 1336: 1316: 1212: 1010: 954: 928: 857: 669: 649: 605: 578: 545: 502: 475: 445: 415: 7695: 7466: 6158: 6008: 4878:Fluorescence recovery after photobleaching (FRAP) 8406: 8337: 8126: 7832: 6228: 5572: 4846: 1344:. The expression is valid if the average number 217: 7110: 6997:Skinner, J.P.; Chen, Y.; Mueller, J.D. (2005). 5179: 258:superconducting nanowire single-photon detector 8107: 7881: 7467:Kolin, D.L.; Ronis, D.; Wiseman, P.W. (2006). 6065: 5615: 5338: 5252: 5144: 4821:Particle image correlation spectroscopy (PICS) 4813:-space Image Correlation Spectroscopy (kICS). 4485: 1502:{\displaystyle |\Delta {\vec {R}}(\tau )|^{2}} 7781: 7527: 5248: 5246: 4841:Super-resolution optical fluctuation imaging 4628: 4622: 4617: 4611: 4589: 4583: 4557: 4551: 4504: 4498: 3865: 3408: 3402: 3354: 3348: 1999: 1993: 1968: 1962: 1357: 1351: 1055: 1049: 923: 908: 837: 821: 816: 783: 765: 749: 744: 705: 149:Commonly, FCS is employed in the context of 8399:Fluorescence Correlation Spectroscopy (FCS) 7362: 7360: 5803: 5478: 4939:Fluorescence cross-correlation spectroscopy 4323:Fluorescence cross-correlation spectroscopy 3441: 624: 546:{\displaystyle \omega _{z}>\omega _{xy}} 7642: 7640: 7638: 4902:Auto-fluorescence correlation spectroscopy 1801:{\displaystyle a=\omega _{z}/\omega _{xy}} 1576:Correlated data and normal diffusion model 8359: 8313: 8303: 8217: 8160: 8060: 8022: 7996: 7931: 7815: 7672: 7618: 7561: 7504: 7443: 7340: 7196: 7139: 7087: 7030: 6973: 6916: 6824: 6790: 6717: 6707: 6658: 6601: 6591: 6542: 6485: 6428: 6262: 5894: 5837: 5764: 5727: 5514: 5504: 5433: 5423: 5397: 5374: 5364: 5295: 5243: 5121: 5111: 5061: 5051: 5001: 4991: 4510:{\displaystyle \langle \epsilon \rangle } 2516: 2254:{\displaystyle \ MSD=6D_{a}t^{\alpha }\,} 2250: 2096: 1556:Interpreting the autocorrelation function 106:Learn how and when to remove this message 7357: 7302: 7300: 7298: 6882: 5693: 3122:{\displaystyle \tau _{v}=\omega _{xy}/v} 1571: 628: 235: 7635: 6740: 5979: 5339:Palmer, A. G.; Thompson, N. L. (1989). 3430:is related to the equilibrium constant 212: 55:"Fluorescence correlation spectroscopy" 8407: 8387:Cell Migration Consortium FCS Tutorial 6624: 5537: 5214: 4870:Other fluorescent dynamical approaches 4852:Total internal reflection fluorescence 4764:fluorescence resonance energy transfer 3132: 2791: 2183: 42:Please improve this article by adding 8340:Current Opinion in Structural Biology 8127:Bagatolli, L.A.; Gratton, E. (2000). 7295: 6681: 4787:Spinning disk FCS and spatial mapping 4265:whereas in case of isolated domains, 3466:for a characteristic relaxation time 1838:radii of the measurement volume, and 268: 119:Fluorescence correlation spectroscopy 8274:(Ed. Klinge & Owman) p. 180 7782:Lieto, A.M.; Thompson, N.L. (2004). 4910:Two- and three-photon FCS excitation 4889: 4796:Image correlation spectroscopy (ICS) 977:For a Gaussian illumination profile 969:As an example, raw FCS data and its 510:are the radial and axial radii, and 15: 8401:(Becker & Hickl GmbH, web page) 4863:Light sheet fluorescence microscopy 4458:is the viscosity of the sample and 3925:2.8, 3.0, 4.14 ± 0.05, 4.20 ± 0.06 1567: 13: 8264: 7111:Berglund, A.; Mabuchi, H. (2005). 6883:Mashaghi, A.; et al. (2008). 3789: 3220: 3059: 2708: 2468: 2111:D gives the diffusion coefficient: 1878: 1738: 1463: 1296: 1278: 1260: 1230: 1157: 1108: 1083: 198:genetically tagged proteins (like 131:L. Onsager's regression hypothesis 14: 8441: 8331: 6682:Godin, Antoine (April 26, 2011). 5804:Banks, D. S.; Fradin, C. (2005). 4945:Förster resonance energy transfer 4563:{\displaystyle \langle I\rangle } 1562:nonlinear least squares algorithm 1363:{\displaystyle \langle N\rangle } 633:FCS raw data and correlated data. 226:Förster Resonance Energy Transfer 8110:European Microscopy and Analysis 7528:Semrau, S.; Schmidt, T. (2007). 7381:10.1046/j.1365-2818.2000.00736.x 1808:is the ratio of axial to radial 231: 228:(FRET) instead of fluorescence. 159:two-photon excitation microscopy 20: 8248: 8234: 8177: 8120: 8101: 8039: 7972: 7910: 7875: 7775: 7732: 7689: 7578: 7521: 7460: 7403: 7252: 7213: 7156: 7104: 7047: 6990: 6933: 6876: 6841: 6784: 6734: 6675: 6618: 6559: 6502: 6445: 6388: 6379: 6363: 6351: 6339: 6327: 6315: 6303: 6291: 6279: 6229:Petráaek; Schwille, P. (2008). 6222: 6187: 6152: 6059: 5973: 5946: 5911: 5854: 5797: 5744: 5694:Hess, S.T.; Webb, W.W. (2002). 5687: 5652: 5609: 5566: 5531: 5472: 5459: 5450: 5398:Qian, H.; Elson, E. L. (1990). 5391: 5332: 4773: 185:kinetic chemical reaction rates 8382:Stowers Institute FCS Tutorial 8361:11858/00-001M-0000-0029-D76C-C 6791:Qian, H.; Elson, E.L. (1990). 5479:Eigen, M.; Rigler, M. (1994). 5289: 5208: 5173: 5138: 5078: 5018: 4967: 4958: 4517:) is related to the variance ( 4405: 4398: 3792: 3786: 3760: 3756: 3729: 3707: 3704: 3701: 3674: 3665: 3653: 3641: 3636: 3590: 3584: 3578: 3569: 3563: 3336: 3330: 3292: 3265: 3223: 3217: 3208: 3184: 3175: 3169: 3160: 3154: 3062: 3056: 3047: 3002: 2980: 2974: 2945: 2941: 2920: 2898: 2895: 2892: 2871: 2862: 2853: 2847: 2838: 2832: 2711: 2705: 2679: 2675: 2648: 2626: 2623: 2620: 2593: 2584: 2558: 2552: 2543: 2537: 2471: 2465: 2439: 2429: 2407: 2385: 2382: 2373: 2351: 2342: 2333: 2327: 2318: 2312: 1950: 1944: 1881: 1875: 1741: 1735: 1709: 1705: 1684: 1662: 1659: 1656: 1635: 1626: 1617: 1611: 1602: 1596: 1489: 1484: 1478: 1472: 1459: 1387: 1381: 1311: 1308: 1302: 1290: 1284: 1272: 1266: 1257: 1251: 1245: 1239: 1170: 1163: 1121: 1114: 1096: 1089: 1037: 1031: 1005: 993: 920: 914: 902: 896: 887: 881: 833: 827: 813: 801: 795: 789: 761: 755: 741: 729: 720: 714: 696: 690: 308: 296: 1: 8210:10.1016/S0006-3495(99)77065-7 8153:10.1016/s0006-3495(00)76592-1 7436:10.1016/S0006-3495(93)81173-1 6862:10.1016/j.jconrel.2004.11.019 6817:10.1016/s0006-3495(90)82539-x 6535:10.1016/s0006-3495(99)76912-2 6421:10.1016/s0006-3495(99)77321-2 6385:Eggeling et al. (2009) Nature 5994:10.1016/j.jbiotec.2003.11.006 5887:10.1016/s0006-3495(03)75006-1 5720:10.1016/s0006-3495(02)73990-8 5673:10.1016/j.jbiotec.2003.10.007 4951: 4847:Total internal reflection FCS 4727:{\displaystyle \epsilon _{i}} 4544:) and the average intensity ( 4081: 2490:where the anomalous exponent 44:secondary or tertiary sources 8243:Oil Extraction and Analysis. 8079:10.1021/acs.nanolett.2c03797 7950:10.1021/acs.nanolett.9b03137 6572:Proc. Natl. Acad. Sci. U.S.A 6216:10.1016/j.cplett.2008.05.018 5552:10.1016/0168-1656(95)00054-t 5202:10.1016/0301-0104(74)85005-6 1545:{\displaystyle w_{xy},w_{z}} 1440:{\displaystyle w_{xy},w_{z}} 579:{\displaystyle \omega _{xy}} 476:{\displaystyle \omega _{xy}} 7: 7808:10.1529/biophysj.103.035030 7554:10.1529/biophysj.106.092577 7497:10.1529/biophysj.106.082768 7333:10.1529/biophysj.104.054874 7189:10.1529/biophysj.106.084251 7080:10.1529/biophysj.103.036483 7023:10.1529/biophysj.105.060749 6966:10.1529/biophysj.105.061788 6909:10.1529/biophysj.108.135152 6651:10.1529/biophysj.103.037887 6478:10.1529/biophysj.107.114645 6357:Humpolıckova et al. (2006) 6285:Wawrezinieck et al. (2005) 6255:10.1529/biophysj.107.108811 5830:10.1529/biophysj.104.051078 5467:European Biophysics Journal 4993:10.1021/acs.jpclett.0c01748 4917: 4757: 4537:{\displaystyle \sigma ^{2}} 4486:Brightness analysis methods 3854:{\displaystyle \ \tau _{F}} 2781:{\displaystyle \tau _{D,i}} 2747:{\displaystyle \alpha _{i}} 606:{\displaystyle \omega _{z}} 503:{\displaystyle \omega _{z}} 10: 8448: 8284:Proc. Natl. Acad. Sci. USA 8015:10.1038/s41467-022-29546-4 7611:10.1016/j.bpj.2010.12.3746 6762:10.1038/s41596-020-00458-1 6045:10.1209/0295-5075/83/46001 5595:10.1088/0034-4885/65/2/203 5485:Proc. Natl. Acad. Sci. USA 5267:10.1002/bip.1974.360130103 5229:10.1002/bip.1974.360130102 5167:10.1103/physrevlett.29.705 5113:10.1038/s41598-019-42418-0 5053:10.1038/s41598-019-42418-0 4817:fluorescence intensities. 4320: 4291:{\displaystyle t_{0}<0} 4258:{\displaystyle t_{0}>0} 4062:2′, 7′-difluorofluorescein 2187: 1887:{\displaystyle G(\infty )} 1449:moment-generating function 1404:for small beam parameters 205: 8352:10.1016/j.sbi.2004.09.004 8256:q-bio/0407006 (July 2004) 7896:10.1016/j.tcb.2004.12.001 6333:Billaudeau et al. (2013) 3866:Common fluorescent probes 3540:{\displaystyle \tau _{D}} 3513:{\displaystyle \tau _{F}} 3486:{\displaystyle \tau _{F}} 3448:green fluorescent protein 2196:mean squared displacement 1914:{\displaystyle \tau _{D}} 1858:{\displaystyle \tau _{D}} 200:green fluorescent protein 8305:10.1073/pnas.93.23.12811 7710:10.1021/acs.jpcb.0c01807 6593:10.1073/pnas.96.24.13756 5404:Proc Natl Acad Sci U S A 5345:Proc Natl Acad Sci U S A 4934:Dynamic light scattering 4046:Atto 655-carboxylicacid 3442:Triplet state correction 1393:{\displaystyle G(\tau )} 1011:{\displaystyle PSF(r,z)} 625:Autocorrelation function 586:is 200–300 nm, and 188:singlet-triplet dynamics 167:dynamic light scattering 8425:Fluorescence techniques 7665:10.1021/acsnano.5b03430 6709:10.1073/pnas.1018658108 6321:Ruprecht et al. (2011) 5932:10.1242/jcs.113.22.3921 5506:10.1073/pnas.91.13.5740 5425:10.1073/pnas.87.14.5479 5366:10.1073/pnas.86.16.6148 4451:{\displaystyle \ \eta } 4225:{\displaystyle t_{0}=0} 2503:{\displaystyle \alpha } 955:{\displaystyle \tau =0} 7884:Trends in Cell Biology 7273:10.1006/jmbi.2000.3692 7141:10.1364/opex.13.008069 6625:Müller, J. D. (2004). 4748: 4728: 4701: 4671: 4564: 4538: 4511: 4475: 4452: 4426: 4292: 4259: 4226: 4193: 4163: 3953:Tetramethyl rhodamine 3900: 3855: 3825: 3799: 3541: 3514: 3487: 3421: 3308: 3230: 3123: 3069: 2810: 2782: 2748: 2718: 2517:Polydisperse diffusion 2504: 2481: 2285: 2255: 2174: 2101: 2012: 1915: 1888: 1859: 1832: 1831:{\displaystyle e^{-2}} 1802: 1748: 1577: 1546: 1503: 1441: 1394: 1364: 1338: 1318: 1214: 1012: 956: 930: 859: 671: 651: 634: 607: 580: 547: 504: 477: 447: 417: 241: 182:average concentrations 176:diffusion coefficients 31:relies excessively on 7985:Nature Communications 6741:Içbilir, Ali (2021). 6345:Masuda et al. (2005) 6335:Methods In Enzymology 4929:Diffusion coefficient 4749: 4729: 4702: 4700:{\displaystyle f_{i}} 4672: 4565: 4539: 4512: 4476: 4453: 4427: 4293: 4260: 4227: 4194: 4192:{\displaystyle t_{0}} 4164: 3901: 3856: 3826: 3800: 3542: 3515: 3488: 3422: 3309: 3231: 3124: 3070: 2811: 2783: 2749: 2719: 2505: 2482: 2286: 2284:{\displaystyle D_{a}} 2256: 2175: 2102: 2013: 1916: 1889: 1860: 1833: 1803: 1749: 1575: 1547: 1504: 1442: 1395: 1365: 1339: 1337:{\displaystyle \tau } 1319: 1215: 1013: 957: 931: 860: 672: 670:{\displaystyle \tau } 652: 650:{\displaystyle \tau } 632: 608: 581: 548: 505: 478: 448: 446:{\displaystyle I_{0}} 418: 275:point spread function 239: 195:avalanche photodiodes 7841:Nature Biotechnology 7753:10.1021/jacs.8b13349 7226:Analytical Chemistry 6297:Lenne et al. (2006) 5318:10.1364/AO.30.001185 4738: 4711: 4684: 4577: 4548: 4521: 4495: 4462: 4439: 4335: 4269: 4236: 4203: 4176: 4103: 3887: 3872:immunohistochemistry 3835: 3812: 3554: 3524: 3497: 3470: 3324: 3246: 3145: 3082: 2823: 2800: 2759: 2731: 2528: 2494: 2306: 2268: 2209: 2117: 2028: 1935: 1898: 1869: 1842: 1812: 1761: 1587: 1513: 1455: 1408: 1375: 1348: 1328: 1227: 1025: 981: 940: 872: 684: 661: 641: 590: 560: 514: 487: 457: 430: 284: 254:avalanche photodiode 8296:1996PNAS...9312811O 8290:(23): 12811–12816. 8202:1999BpJ....77.2251S 8190:Biophysical Journal 8145:2000BpJ....78..290B 8071:2023NanoL..23..497R 8007:2022NatCo..13.1842B 7942:2019NanoL..19.7434B 7800:2004BpJ....87.1268L 7603:2011BpJ...100.1810S 7546:2007BpJ....92..613S 7489:2006BpJ....91.3061K 7428:1993BpJ....65.1135P 7325:2005BpJ....88.3601H 7181:2006BpJ....91.4241S 7169:Biophysical Journal 7132:2005OExpr..13.8069B 7072:2004BpJ....87.1260R 7015:2005BpJ....89.1288S 6958:2005BpJ....88L..33D 6901:2008BpJ....95.5476P 6889:Biophysical Journal 6809:1990BpJ....57..375Q 6700:2011PNAS..108.7010G 6643:2004BpJ....86.3981M 6584:1999PNAS...9613756K 6578:(24): 13756–13761. 6527:1999BpJ....77..553C 6470:2008BpJ....94.2320D 6413:1999BpJ....76.1619M 6309:Guia et al. (2011) 6247:2008BpJ....94.1437P 6208:2008CPL...459...18L 6173:2000JPCA..104.6416W 6130:2005JChPh.122a4907P 6084:2012MaMol..45.9196W 6037:2008EL.....8346001M 5967:10.1021/j100036a009 5961:(36): 13368–13379. 5879:2003BpJ....84.1977S 5822:2005BpJ....89.2960B 5775:2011SMat....7.1358H 5712:2002BpJ....83.2300H 5587:2002RPPh...65..251K 5497:1994PNAS...91.5740E 5416:1990PNAS...87.5479Q 5357:1989PNAS...86.6148P 5310:1991ApOpt..30.1185Q 5194:1974CP......4..390E 5159:1972PhRvL..29..705M 5104:2019NatSR...9.5906K 5044:2019NatSR...9.5906K 4980:J. Phys. Chem. Lett 4924:Confocal microscopy 4474:{\displaystyle \ M} 4380: 4126: 4064:(Oregon Green 488) 4030:Atto 655-maleimide 3999:carboxyfluorescein 3899:{\displaystyle \ D} 3824:{\displaystyle \ F} 3133:Chemical relaxation 2792:Diffusion with flow 2200:anomalous diffusion 2190:Anomalous diffusion 2184:Anomalous diffusion 2146: 2082: 1194: 1148: 657:, as a function of 410: 367: 218:Brightness Analyses 155:confocal microscopy 8415:Physical chemistry 8392:2010-09-24 at the 5783:10.1039/C0SM00718H 5630:10.1002/bies.10118 5469:(1993) 22(3), 159. 5092:Scientific Reports 5032:Scientific Reports 4744: 4724: 4697: 4667: 4646: 4560: 4534: 4507: 4471: 4448: 4422: 4363: 4288: 4255: 4222: 4189: 4159: 4109: 3896: 3851: 3821: 3795: 3537: 3510: 3483: 3417: 3304: 3226: 3119: 3065: 2806: 2778: 2744: 2714: 2570: 2500: 2477: 2281: 2251: 2170: 2129: 2097: 2065: 2008: 1911: 1884: 1855: 1828: 1798: 1744: 1578: 1542: 1499: 1437: 1402:return probability 1390: 1360: 1334: 1314: 1210: 1180: 1131: 1008: 952: 926: 855: 667: 647: 635: 603: 576: 543: 500: 473: 443: 413: 396: 350: 269:Measurement volume 242: 213:Measurement Volume 193:detectors such as 179:hydrodynamic radii 151:optical microscopy 8196:(10): 2251–2265. 7926:(10): 7434–7442. 7747:(19): 7751–7757. 7704:(22): 4412–4420. 7238:10.1021/ac0624546 7232:(12): 4463–4470. 7175:(11): 4241–4252. 7126:(20): 8069–8082. 6895:(11): 5476–5486. 6694:(17): 7010–7015. 6181:10.1021/jp000059s 6167:(27): 6416–6428. 6138:10.1063/1.1829255 6092:10.1021/ma301780f 6078:(22): 9196–9204. 5926:(22): 3921–3930. 5491:(13): 5740–5747. 5410:(14): 5479–5483. 5351:(16): 6148–6152. 5304:(10): 1185–1195. 4986:(16): 6914–6920. 4890:Particle tracking 4747:{\displaystyle i} 4637: 4632: 4582: 4467: 4444: 4396: 4340: 4108: 4079: 4078: 3892: 3840: 3817: 3778: 3657: 3559: 3412: 3391: 3358: 3288: 3275: 3251: 3150: 3045: 2963: 2828: 2809:{\displaystyle v} 2697: 2561: 2533: 2457: 2214: 2122: 2041: 2033: 2003: 1990: 1972: 1940: 1727: 1592: 1475: 1242: 1223:where the vector 1195: 1149: 1059: 847: 775: 116: 115: 108: 90: 8437: 8373: 8363: 8327: 8317: 8307: 8258: 8252: 8246: 8238: 8232: 8231: 8221: 8181: 8175: 8174: 8164: 8124: 8118: 8117: 8105: 8099: 8098: 8064: 8043: 8037: 8036: 8026: 8000: 7976: 7970: 7969: 7935: 7914: 7908: 7907: 7879: 7873: 7872: 7853:10.1038/nbt.1928 7836: 7830: 7829: 7819: 7794:(2): 1268–1278. 7779: 7773: 7772: 7741:J. Am. Chem. Soc 7736: 7730: 7729: 7698:J. Phys. Chem. B 7693: 7687: 7686: 7676: 7659:(9): 9158–9166. 7644: 7633: 7632: 7622: 7597:(7): 1810–1818. 7582: 7576: 7575: 7565: 7525: 7519: 7518: 7508: 7483:(8): 3061–3075. 7464: 7458: 7457: 7447: 7422:(3): 1135–1146. 7407: 7401: 7400: 7364: 7355: 7354: 7344: 7319:(5): 3601–3614. 7304: 7293: 7292: 7256: 7250: 7249: 7217: 7211: 7210: 7200: 7160: 7154: 7153: 7143: 7117: 7108: 7102: 7101: 7091: 7066:(2): 1260–1267. 7051: 7045: 7044: 7034: 7009:(2): 1288–1301. 6994: 6988: 6987: 6977: 6937: 6931: 6930: 6920: 6880: 6874: 6873: 6845: 6839: 6838: 6828: 6788: 6782: 6781: 6756:(3): 1419–1451. 6750:Nature Protocols 6747: 6738: 6732: 6731: 6721: 6711: 6679: 6673: 6672: 6662: 6637:(6): 3981–3992. 6622: 6616: 6615: 6605: 6595: 6563: 6557: 6556: 6546: 6506: 6500: 6499: 6489: 6464:(6): 2320–2332. 6449: 6443: 6442: 6432: 6407:(3): 1619–1631. 6392: 6386: 6383: 6377: 6367: 6361: 6355: 6349: 6343: 6337: 6331: 6325: 6319: 6313: 6307: 6301: 6295: 6289: 6283: 6277: 6276: 6266: 6241:(4): 1437–1448. 6226: 6220: 6219: 6196:Chem. Phys. Lett 6191: 6185: 6184: 6161:J. Phys. Chem. A 6156: 6150: 6149: 6113: 6104: 6103: 6063: 6057: 6056: 6019: 6006: 6005: 5977: 5971: 5970: 5950: 5944: 5943: 5915: 5909: 5908: 5898: 5873:(3): 1977–1984. 5858: 5852: 5851: 5841: 5816:(5): 2960–2971. 5801: 5795: 5794: 5768: 5759:(4): 1358–1363. 5748: 5742: 5741: 5731: 5706:(4): 2300–2317. 5691: 5685: 5684: 5656: 5650: 5649: 5613: 5607: 5606: 5570: 5564: 5563: 5546:(2–3): 177–186. 5535: 5529: 5528: 5518: 5508: 5476: 5470: 5463: 5457: 5454: 5448: 5447: 5437: 5427: 5395: 5389: 5388: 5378: 5368: 5336: 5330: 5329: 5293: 5287: 5286: 5250: 5241: 5240: 5212: 5206: 5205: 5177: 5171: 5170: 5142: 5136: 5135: 5125: 5115: 5082: 5076: 5075: 5065: 5055: 5022: 5016: 5015: 5005: 4995: 4971: 4965: 4962: 4768:autofluorescence 4753: 4751: 4750: 4745: 4733: 4731: 4730: 4725: 4723: 4722: 4706: 4704: 4703: 4698: 4696: 4695: 4676: 4674: 4673: 4668: 4666: 4665: 4656: 4655: 4645: 4633: 4631: 4620: 4607: 4606: 4596: 4580: 4569: 4567: 4566: 4561: 4543: 4541: 4540: 4535: 4533: 4532: 4516: 4514: 4513: 4508: 4480: 4478: 4477: 4472: 4465: 4457: 4455: 4454: 4449: 4442: 4431: 4429: 4428: 4423: 4421: 4420: 4416: 4397: 4395: 4384: 4379: 4374: 4355: 4350: 4349: 4338: 4297: 4295: 4294: 4289: 4281: 4280: 4264: 4262: 4261: 4256: 4248: 4247: 4231: 4229: 4228: 4223: 4215: 4214: 4198: 4196: 4195: 4190: 4188: 4187: 4168: 4166: 4165: 4160: 4158: 4157: 4145: 4144: 4125: 4120: 4106: 3986:2.5, 3.7 ± 0.15 3905: 3903: 3902: 3897: 3890: 3881:Fluorescent dye 3878: 3877: 3860: 3858: 3857: 3852: 3850: 3849: 3838: 3830: 3828: 3827: 3822: 3815: 3804: 3802: 3801: 3796: 3779: 3777: 3776: 3775: 3771: 3755: 3754: 3739: 3728: 3727: 3700: 3699: 3684: 3660: 3658: 3656: 3639: 3635: 3634: 3633: 3632: 3623: 3588: 3557: 3546: 3544: 3543: 3538: 3536: 3535: 3519: 3517: 3516: 3511: 3509: 3508: 3492: 3490: 3489: 3484: 3482: 3481: 3426: 3424: 3423: 3418: 3413: 3411: 3397: 3392: 3390: 3389: 3374: 3373: 3361: 3359: 3357: 3343: 3313: 3311: 3310: 3305: 3303: 3302: 3290: 3289: 3286: 3277: 3276: 3273: 3261: 3260: 3249: 3235: 3233: 3232: 3227: 3207: 3206: 3197: 3148: 3128: 3126: 3125: 3120: 3115: 3110: 3109: 3094: 3093: 3074: 3072: 3071: 3066: 3046: 3044: 3043: 3042: 3033: 3015: 3010: 3009: 3000: 2999: 2990: 2964: 2962: 2961: 2960: 2956: 2940: 2939: 2930: 2919: 2918: 2891: 2890: 2881: 2857: 2826: 2815: 2813: 2812: 2807: 2787: 2785: 2784: 2779: 2777: 2776: 2753: 2751: 2750: 2745: 2743: 2742: 2723: 2721: 2720: 2715: 2698: 2696: 2695: 2694: 2690: 2674: 2673: 2658: 2647: 2646: 2619: 2618: 2603: 2582: 2581: 2572: 2569: 2531: 2509: 2507: 2506: 2501: 2486: 2484: 2483: 2478: 2458: 2456: 2455: 2454: 2450: 2437: 2436: 2427: 2426: 2417: 2406: 2405: 2381: 2380: 2371: 2370: 2361: 2337: 2290: 2288: 2287: 2282: 2280: 2279: 2260: 2258: 2257: 2252: 2249: 2248: 2239: 2238: 2212: 2179: 2177: 2176: 2171: 2166: 2165: 2164: 2151: 2145: 2140: 2120: 2106: 2104: 2103: 2098: 2092: 2091: 2081: 2076: 2064: 2063: 2059: 2043: 2042: 2039: 2031: 2017: 2015: 2014: 2009: 2004: 2002: 1992: 1991: 1988: 1978: 1973: 1971: 1957: 1938: 1920: 1918: 1917: 1912: 1910: 1909: 1893: 1891: 1890: 1885: 1864: 1862: 1861: 1856: 1854: 1853: 1837: 1835: 1834: 1829: 1827: 1826: 1807: 1805: 1804: 1799: 1797: 1796: 1784: 1779: 1778: 1753: 1751: 1750: 1745: 1728: 1726: 1725: 1724: 1720: 1704: 1703: 1694: 1683: 1682: 1655: 1654: 1645: 1621: 1590: 1568:Normal diffusion 1551: 1549: 1548: 1543: 1541: 1540: 1528: 1527: 1508: 1506: 1505: 1500: 1498: 1497: 1492: 1477: 1476: 1468: 1462: 1446: 1444: 1443: 1438: 1436: 1435: 1423: 1422: 1399: 1397: 1396: 1391: 1369: 1367: 1366: 1361: 1343: 1341: 1340: 1335: 1323: 1321: 1320: 1315: 1244: 1243: 1235: 1219: 1217: 1216: 1211: 1206: 1202: 1201: 1197: 1196: 1193: 1188: 1179: 1178: 1177: 1155: 1150: 1147: 1142: 1130: 1129: 1128: 1104: 1103: 1081: 1060: 1058: 1044: 1017: 1015: 1014: 1009: 961: 959: 958: 953: 935: 933: 932: 927: 864: 862: 861: 856: 848: 846: 845: 844: 819: 781: 776: 774: 773: 772: 747: 703: 676: 674: 673: 668: 656: 654: 653: 648: 612: 610: 609: 604: 602: 601: 585: 583: 582: 577: 575: 574: 552: 550: 549: 544: 542: 541: 526: 525: 509: 507: 506: 501: 499: 498: 482: 480: 479: 474: 472: 471: 452: 450: 449: 444: 442: 441: 422: 420: 419: 414: 412: 411: 409: 404: 395: 390: 389: 369: 368: 366: 361: 349: 344: 343: 323: 322: 153:, in particular 111: 104: 100: 97: 91: 89: 48: 24: 16: 8447: 8446: 8440: 8439: 8438: 8436: 8435: 8434: 8405: 8404: 8394:Wayback Machine 8334: 8267: 8265:Further reading 8262: 8261: 8253: 8249: 8239: 8235: 8182: 8178: 8125: 8121: 8106: 8102: 8044: 8040: 7977: 7973: 7915: 7911: 7880: 7876: 7837: 7833: 7780: 7776: 7737: 7733: 7694: 7690: 7645: 7636: 7583: 7579: 7526: 7522: 7465: 7461: 7408: 7404: 7375:(Pt 1): 14–25. 7365: 7358: 7305: 7296: 7257: 7253: 7218: 7214: 7161: 7157: 7115: 7109: 7105: 7052: 7048: 6995: 6991: 6938: 6934: 6881: 6877: 6846: 6842: 6789: 6785: 6745: 6739: 6735: 6680: 6676: 6623: 6619: 6564: 6560: 6507: 6503: 6450: 6446: 6393: 6389: 6384: 6380: 6368: 6364: 6356: 6352: 6344: 6340: 6332: 6328: 6320: 6316: 6308: 6304: 6296: 6292: 6284: 6280: 6227: 6223: 6192: 6188: 6157: 6153: 6114: 6107: 6064: 6060: 6020: 6009: 5978: 5974: 5951: 5947: 5916: 5912: 5859: 5855: 5802: 5798: 5749: 5745: 5692: 5688: 5657: 5653: 5614: 5610: 5575:Rep. Prog. Phys 5571: 5567: 5536: 5532: 5477: 5473: 5464: 5460: 5455: 5451: 5396: 5392: 5337: 5333: 5294: 5290: 5251: 5244: 5213: 5209: 5178: 5174: 5153:(11): 705–708. 5143: 5139: 5083: 5079: 5023: 5019: 4972: 4968: 4963: 4959: 4954: 4920: 4912: 4904: 4892: 4880: 4872: 4860: 4849: 4838: 4823: 4798: 4789: 4776: 4760: 4739: 4736: 4735: 4718: 4714: 4712: 4709: 4708: 4691: 4687: 4685: 4682: 4681: 4661: 4657: 4651: 4647: 4641: 4621: 4602: 4598: 4597: 4595: 4578: 4575: 4574: 4549: 4546: 4545: 4528: 4524: 4522: 4519: 4518: 4496: 4493: 4492: 4488: 4463: 4460: 4459: 4440: 4437: 4436: 4412: 4408: 4404: 4385: 4375: 4367: 4356: 4354: 4345: 4341: 4336: 4333: 4332: 4325: 4319: 4276: 4272: 4270: 4267: 4266: 4243: 4239: 4237: 4234: 4233: 4210: 4206: 4204: 4201: 4200: 4183: 4179: 4177: 4174: 4173: 4153: 4149: 4140: 4136: 4121: 4113: 4104: 4101: 4100: 4093: 4084: 4063: 3913: 3906: 3888: 3885: 3884: 3868: 3845: 3841: 3836: 3833: 3832: 3813: 3810: 3809: 3767: 3763: 3759: 3744: 3740: 3735: 3720: 3716: 3689: 3685: 3680: 3664: 3659: 3640: 3628: 3624: 3619: 3612: 3608: 3589: 3587: 3555: 3552: 3551: 3531: 3527: 3525: 3522: 3521: 3504: 3500: 3498: 3495: 3494: 3477: 3473: 3471: 3468: 3467: 3444: 3401: 3396: 3379: 3375: 3366: 3362: 3360: 3347: 3342: 3325: 3322: 3321: 3295: 3291: 3285: 3281: 3272: 3268: 3256: 3252: 3247: 3244: 3243: 3202: 3198: 3193: 3146: 3143: 3142: 3135: 3111: 3102: 3098: 3089: 3085: 3083: 3080: 3079: 3038: 3034: 3029: 3019: 3014: 3005: 3001: 2995: 2991: 2986: 2952: 2948: 2944: 2935: 2931: 2926: 2911: 2907: 2886: 2882: 2877: 2861: 2856: 2824: 2821: 2820: 2801: 2798: 2797: 2794: 2766: 2762: 2760: 2757: 2756: 2738: 2734: 2732: 2729: 2728: 2686: 2682: 2678: 2663: 2659: 2654: 2639: 2635: 2608: 2604: 2599: 2583: 2577: 2573: 2571: 2565: 2529: 2526: 2525: 2519: 2495: 2492: 2491: 2446: 2442: 2438: 2432: 2428: 2422: 2418: 2413: 2398: 2394: 2376: 2372: 2366: 2362: 2357: 2341: 2336: 2307: 2304: 2303: 2275: 2271: 2269: 2266: 2265: 2244: 2240: 2234: 2230: 2210: 2207: 2206: 2192: 2186: 2160: 2156: 2152: 2147: 2141: 2133: 2118: 2115: 2114: 2087: 2083: 2077: 2069: 2055: 2051: 2047: 2038: 2034: 2029: 2026: 2025: 1987: 1983: 1982: 1977: 1961: 1956: 1936: 1933: 1932: 1905: 1901: 1899: 1896: 1895: 1870: 1867: 1866: 1849: 1845: 1843: 1840: 1839: 1819: 1815: 1813: 1810: 1809: 1789: 1785: 1780: 1774: 1770: 1762: 1759: 1758: 1716: 1712: 1708: 1699: 1695: 1690: 1675: 1671: 1650: 1646: 1641: 1625: 1620: 1588: 1585: 1584: 1570: 1558: 1536: 1532: 1520: 1516: 1514: 1511: 1510: 1493: 1488: 1487: 1467: 1466: 1458: 1456: 1453: 1452: 1431: 1427: 1415: 1411: 1409: 1406: 1405: 1376: 1373: 1372: 1349: 1346: 1345: 1329: 1326: 1325: 1234: 1233: 1228: 1225: 1224: 1189: 1184: 1173: 1169: 1156: 1154: 1143: 1135: 1124: 1120: 1099: 1095: 1082: 1080: 1076: 1072: 1065: 1061: 1048: 1043: 1026: 1023: 1022: 982: 979: 978: 971:autocorrelation 941: 938: 937: 873: 870: 869: 840: 836: 820: 782: 780: 768: 764: 748: 704: 702: 685: 682: 681: 662: 659: 658: 642: 639: 638: 627: 597: 593: 591: 588: 587: 567: 563: 561: 558: 557: 534: 530: 521: 517: 515: 512: 511: 494: 490: 488: 485: 484: 464: 460: 458: 455: 454: 437: 433: 431: 428: 427: 405: 400: 391: 385: 381: 374: 370: 362: 354: 345: 339: 335: 328: 324: 318: 314: 285: 282: 281: 271: 262:autocorrelation 250:photomultiplier 234: 208: 135:Brownian motion 112: 101: 95: 92: 49: 47: 41: 37:primary sources 25: 12: 11: 5: 8445: 8444: 8433: 8432: 8427: 8422: 8417: 8403: 8402: 8396: 8384: 8379: 8374: 8346:(5): 531–540. 8333: 8332:External links 8330: 8329: 8328: 8275: 8266: 8263: 8260: 8259: 8247: 8233: 8176: 8139:(1): 290–305. 8119: 8100: 8055:(2): 497–504. 8038: 7971: 7909: 7874: 7847:(9): 835–839. 7831: 7774: 7731: 7688: 7634: 7577: 7540:(2): 613–621. 7520: 7459: 7402: 7356: 7294: 7267:(4): 677–689. 7251: 7212: 7155: 7103: 7046: 6989: 6932: 6875: 6856:(1): 259–271. 6840: 6803:(2): 375–380. 6783: 6733: 6674: 6617: 6558: 6521:(1): 553–567. 6501: 6444: 6387: 6378: 6362: 6350: 6338: 6326: 6314: 6302: 6290: 6278: 6221: 6186: 6151: 6105: 6072:Macromolecules 6058: 6007: 5988:(2): 127–136. 5972: 5945: 5910: 5853: 5796: 5743: 5686: 5667:(2): 185–192. 5651: 5624:(8): 758–764. 5608: 5581:(2): 251–297. 5565: 5530: 5471: 5458: 5449: 5390: 5331: 5298:Applied Optics 5288: 5242: 5207: 5188:(3): 390–401. 5172: 5137: 5077: 5017: 4966: 4956: 4955: 4953: 4950: 4949: 4948: 4942: 4936: 4931: 4926: 4919: 4916: 4911: 4908: 4903: 4900: 4891: 4888: 4879: 4876: 4871: 4868: 4859: 4856: 4848: 4845: 4837: 4834: 4822: 4819: 4797: 4794: 4788: 4785: 4775: 4772: 4759: 4756: 4743: 4721: 4717: 4694: 4690: 4678: 4677: 4664: 4660: 4654: 4650: 4644: 4640: 4636: 4630: 4627: 4624: 4619: 4616: 4613: 4610: 4605: 4601: 4594: 4591: 4588: 4585: 4570:) as follows: 4559: 4556: 4553: 4531: 4527: 4506: 4503: 4500: 4487: 4484: 4470: 4447: 4433: 4432: 4419: 4415: 4411: 4407: 4403: 4400: 4394: 4391: 4388: 4383: 4378: 4373: 4370: 4366: 4362: 4359: 4353: 4348: 4344: 4321:Main article: 4318: 4315: 4287: 4284: 4279: 4275: 4254: 4251: 4246: 4242: 4221: 4218: 4213: 4209: 4186: 4182: 4170: 4169: 4156: 4152: 4148: 4143: 4139: 4135: 4132: 4129: 4124: 4119: 4116: 4112: 4092: 4089: 4083: 4080: 4077: 4076: 4074: 4071: 4068: 4065: 4059: 4058: 4056: 4053: 4050: 4047: 4043: 4042: 4040: 4037: 4034: 4031: 4027: 4026: 4024: 4021: 4018: 4015: 4011: 4010: 4008: 4005: 4003: 4000: 3996: 3995: 3993: 3990: 3987: 3984: 3980: 3979: 3977: 3974: 3972: 3969: 3965: 3964: 3962: 3959: 3957: 3954: 3950: 3949: 3947: 3944: 3942: 3939: 3938:Rhodamine 110 3935: 3934: 3932: 3929: 3926: 3923: 3919: 3918: 3915: 3910: 3907: 3895: 3882: 3867: 3864: 3848: 3844: 3820: 3806: 3805: 3794: 3791: 3788: 3785: 3782: 3774: 3770: 3766: 3762: 3758: 3753: 3750: 3747: 3743: 3738: 3734: 3731: 3726: 3723: 3719: 3715: 3712: 3709: 3706: 3703: 3698: 3695: 3692: 3688: 3683: 3679: 3676: 3673: 3670: 3667: 3663: 3655: 3652: 3649: 3646: 3643: 3638: 3631: 3627: 3622: 3618: 3615: 3611: 3607: 3604: 3601: 3598: 3595: 3592: 3586: 3583: 3580: 3577: 3574: 3571: 3568: 3565: 3562: 3534: 3530: 3507: 3503: 3480: 3476: 3443: 3440: 3428: 3427: 3416: 3410: 3407: 3404: 3400: 3395: 3388: 3385: 3382: 3378: 3372: 3369: 3365: 3356: 3353: 3350: 3346: 3341: 3338: 3335: 3332: 3329: 3315: 3314: 3301: 3298: 3294: 3284: 3280: 3271: 3267: 3264: 3259: 3255: 3237: 3236: 3225: 3222: 3219: 3216: 3213: 3210: 3205: 3201: 3196: 3192: 3189: 3186: 3183: 3180: 3177: 3174: 3171: 3168: 3165: 3162: 3159: 3156: 3153: 3134: 3131: 3118: 3114: 3108: 3105: 3101: 3097: 3092: 3088: 3076: 3075: 3064: 3061: 3058: 3055: 3052: 3049: 3041: 3037: 3032: 3028: 3025: 3022: 3018: 3013: 3008: 3004: 2998: 2994: 2989: 2985: 2982: 2979: 2976: 2973: 2970: 2967: 2959: 2955: 2951: 2947: 2943: 2938: 2934: 2929: 2925: 2922: 2917: 2914: 2910: 2906: 2903: 2900: 2897: 2894: 2889: 2885: 2880: 2876: 2873: 2870: 2867: 2864: 2860: 2855: 2852: 2849: 2846: 2843: 2840: 2837: 2834: 2831: 2805: 2793: 2790: 2775: 2772: 2769: 2765: 2741: 2737: 2725: 2724: 2713: 2710: 2707: 2704: 2701: 2693: 2689: 2685: 2681: 2677: 2672: 2669: 2666: 2662: 2657: 2653: 2650: 2645: 2642: 2638: 2634: 2631: 2628: 2625: 2622: 2617: 2614: 2611: 2607: 2602: 2598: 2595: 2592: 2589: 2586: 2580: 2576: 2568: 2564: 2560: 2557: 2554: 2551: 2548: 2545: 2542: 2539: 2536: 2518: 2515: 2499: 2488: 2487: 2476: 2473: 2470: 2467: 2464: 2461: 2453: 2449: 2445: 2441: 2435: 2431: 2425: 2421: 2416: 2412: 2409: 2404: 2401: 2397: 2393: 2390: 2387: 2384: 2379: 2375: 2369: 2365: 2360: 2356: 2353: 2350: 2347: 2344: 2340: 2335: 2332: 2329: 2326: 2323: 2320: 2317: 2314: 2311: 2278: 2274: 2262: 2261: 2247: 2243: 2237: 2233: 2229: 2226: 2223: 2220: 2217: 2185: 2182: 2181: 2180: 2169: 2163: 2159: 2155: 2150: 2144: 2139: 2136: 2132: 2128: 2125: 2112: 2108: 2107: 2095: 2090: 2086: 2080: 2075: 2072: 2068: 2062: 2058: 2054: 2050: 2046: 2037: 2019: 2018: 2007: 2001: 1998: 1995: 1986: 1981: 1976: 1970: 1967: 1964: 1960: 1955: 1952: 1949: 1946: 1943: 1908: 1904: 1883: 1880: 1877: 1874: 1852: 1848: 1825: 1822: 1818: 1795: 1792: 1788: 1783: 1777: 1773: 1769: 1766: 1755: 1754: 1743: 1740: 1737: 1734: 1731: 1723: 1719: 1715: 1711: 1707: 1702: 1698: 1693: 1689: 1686: 1681: 1678: 1674: 1670: 1667: 1664: 1661: 1658: 1653: 1649: 1644: 1640: 1637: 1634: 1631: 1628: 1624: 1619: 1616: 1613: 1610: 1607: 1604: 1601: 1598: 1595: 1569: 1566: 1557: 1554: 1539: 1535: 1531: 1526: 1523: 1519: 1496: 1491: 1486: 1483: 1480: 1474: 1471: 1465: 1461: 1434: 1430: 1426: 1421: 1418: 1414: 1389: 1386: 1383: 1380: 1359: 1356: 1353: 1333: 1313: 1310: 1307: 1304: 1301: 1298: 1295: 1292: 1289: 1286: 1283: 1280: 1277: 1274: 1271: 1268: 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1241: 1238: 1232: 1221: 1220: 1209: 1205: 1200: 1192: 1187: 1183: 1176: 1172: 1168: 1165: 1162: 1159: 1153: 1146: 1141: 1138: 1134: 1127: 1123: 1119: 1116: 1113: 1110: 1107: 1102: 1098: 1094: 1091: 1088: 1085: 1079: 1075: 1071: 1068: 1064: 1057: 1054: 1051: 1047: 1042: 1039: 1036: 1033: 1030: 1007: 1004: 1001: 998: 995: 992: 989: 986: 951: 948: 945: 925: 922: 919: 916: 913: 910: 907: 904: 901: 898: 895: 892: 889: 886: 883: 880: 877: 866: 865: 854: 851: 843: 839: 835: 832: 829: 826: 823: 818: 815: 812: 809: 806: 803: 800: 797: 794: 791: 788: 785: 779: 771: 767: 763: 760: 757: 754: 751: 746: 743: 740: 737: 734: 731: 728: 725: 722: 719: 716: 713: 710: 707: 701: 698: 695: 692: 689: 666: 646: 626: 623: 600: 596: 573: 570: 566: 540: 537: 533: 529: 524: 520: 497: 493: 470: 467: 463: 440: 436: 424: 423: 408: 403: 399: 394: 388: 384: 380: 377: 373: 365: 360: 357: 353: 348: 342: 338: 334: 331: 327: 321: 317: 313: 310: 307: 304: 301: 298: 295: 292: 289: 270: 267: 256:detector or a 233: 230: 207: 204: 190: 189: 186: 183: 180: 177: 114: 113: 28: 26: 19: 9: 6: 4: 3: 2: 8443: 8442: 8431: 8428: 8426: 8423: 8421: 8418: 8416: 8413: 8412: 8410: 8400: 8397: 8395: 8391: 8388: 8385: 8383: 8380: 8378: 8377:FCS Classroom 8375: 8371: 8367: 8362: 8357: 8353: 8349: 8345: 8341: 8336: 8335: 8325: 8321: 8316: 8311: 8306: 8301: 8297: 8293: 8289: 8285: 8281: 8276: 8273: 8269: 8268: 8257: 8251: 8244: 8237: 8229: 8225: 8220: 8215: 8211: 8207: 8203: 8199: 8195: 8191: 8187: 8180: 8172: 8168: 8163: 8158: 8154: 8150: 8146: 8142: 8138: 8134: 8130: 8123: 8115: 8111: 8104: 8096: 8092: 8088: 8084: 8080: 8076: 8072: 8068: 8063: 8058: 8054: 8050: 8042: 8034: 8030: 8025: 8020: 8016: 8012: 8008: 8004: 7999: 7994: 7990: 7986: 7982: 7975: 7967: 7963: 7959: 7955: 7951: 7947: 7943: 7939: 7934: 7929: 7925: 7921: 7913: 7905: 7901: 7897: 7893: 7889: 7885: 7878: 7870: 7866: 7862: 7858: 7854: 7850: 7846: 7842: 7835: 7827: 7823: 7818: 7813: 7809: 7805: 7801: 7797: 7793: 7789: 7785: 7778: 7770: 7766: 7762: 7758: 7754: 7750: 7746: 7742: 7735: 7727: 7723: 7719: 7715: 7711: 7707: 7703: 7699: 7692: 7684: 7680: 7675: 7670: 7666: 7662: 7658: 7654: 7650: 7643: 7641: 7639: 7630: 7626: 7621: 7616: 7612: 7608: 7604: 7600: 7596: 7592: 7588: 7581: 7573: 7569: 7564: 7559: 7555: 7551: 7547: 7543: 7539: 7535: 7531: 7524: 7516: 7512: 7507: 7502: 7498: 7494: 7490: 7486: 7482: 7478: 7474: 7472: 7463: 7455: 7451: 7446: 7441: 7437: 7433: 7429: 7425: 7421: 7417: 7413: 7406: 7398: 7394: 7390: 7386: 7382: 7378: 7374: 7370: 7363: 7361: 7352: 7348: 7343: 7338: 7334: 7330: 7326: 7322: 7318: 7314: 7310: 7303: 7301: 7299: 7290: 7286: 7282: 7278: 7274: 7270: 7266: 7262: 7255: 7247: 7243: 7239: 7235: 7231: 7227: 7223: 7216: 7208: 7204: 7199: 7194: 7190: 7186: 7182: 7178: 7174: 7170: 7166: 7159: 7151: 7147: 7142: 7137: 7133: 7129: 7125: 7121: 7114: 7107: 7099: 7095: 7090: 7085: 7081: 7077: 7073: 7069: 7065: 7061: 7057: 7050: 7042: 7038: 7033: 7028: 7024: 7020: 7016: 7012: 7008: 7004: 7000: 6993: 6985: 6981: 6976: 6971: 6967: 6963: 6959: 6955: 6952:(5): L33–36. 6951: 6947: 6943: 6936: 6928: 6924: 6919: 6914: 6910: 6906: 6902: 6898: 6894: 6890: 6886: 6879: 6871: 6867: 6863: 6859: 6855: 6851: 6850:J Control Rel 6844: 6836: 6832: 6827: 6822: 6818: 6814: 6810: 6806: 6802: 6798: 6794: 6787: 6779: 6775: 6771: 6767: 6763: 6759: 6755: 6751: 6744: 6737: 6729: 6725: 6720: 6715: 6710: 6705: 6701: 6697: 6693: 6689: 6685: 6678: 6670: 6666: 6661: 6656: 6652: 6648: 6644: 6640: 6636: 6632: 6628: 6621: 6613: 6609: 6604: 6599: 6594: 6589: 6585: 6581: 6577: 6573: 6569: 6562: 6554: 6550: 6545: 6540: 6536: 6532: 6528: 6524: 6520: 6516: 6512: 6505: 6497: 6493: 6488: 6483: 6479: 6475: 6471: 6467: 6463: 6459: 6455: 6448: 6440: 6436: 6431: 6426: 6422: 6418: 6414: 6410: 6406: 6402: 6398: 6391: 6382: 6376: 6372: 6366: 6360: 6354: 6348: 6342: 6336: 6330: 6324: 6318: 6312: 6306: 6300: 6294: 6288: 6282: 6274: 6270: 6265: 6260: 6256: 6252: 6248: 6244: 6240: 6236: 6232: 6225: 6217: 6213: 6209: 6205: 6201: 6197: 6190: 6182: 6178: 6174: 6170: 6166: 6162: 6155: 6147: 6143: 6139: 6135: 6131: 6127: 6124:(1): 014907. 6123: 6119: 6118:J. Chem. Phys 6112: 6110: 6101: 6097: 6093: 6089: 6085: 6081: 6077: 6073: 6069: 6062: 6054: 6050: 6046: 6042: 6038: 6034: 6030: 6026: 6018: 6016: 6014: 6012: 6003: 5999: 5995: 5991: 5987: 5983: 5982:J. Biotechnol 5976: 5968: 5964: 5960: 5956: 5955:J. Chem. Phys 5949: 5941: 5937: 5933: 5929: 5925: 5921: 5914: 5906: 5902: 5897: 5892: 5888: 5884: 5880: 5876: 5872: 5868: 5864: 5857: 5849: 5845: 5840: 5835: 5831: 5827: 5823: 5819: 5815: 5811: 5807: 5800: 5792: 5788: 5784: 5780: 5776: 5772: 5767: 5762: 5758: 5754: 5747: 5739: 5735: 5730: 5725: 5721: 5717: 5713: 5709: 5705: 5701: 5697: 5690: 5682: 5678: 5674: 5670: 5666: 5662: 5661:J. Biotechnol 5655: 5647: 5643: 5639: 5635: 5631: 5627: 5623: 5619: 5612: 5604: 5600: 5596: 5592: 5588: 5584: 5580: 5576: 5569: 5561: 5557: 5553: 5549: 5545: 5541: 5540:J. Biotechnol 5534: 5526: 5522: 5517: 5512: 5507: 5502: 5498: 5494: 5490: 5486: 5482: 5475: 5468: 5462: 5453: 5445: 5441: 5436: 5431: 5426: 5421: 5417: 5413: 5409: 5405: 5401: 5394: 5386: 5382: 5377: 5372: 5367: 5362: 5358: 5354: 5350: 5346: 5342: 5335: 5327: 5323: 5319: 5315: 5311: 5307: 5303: 5299: 5292: 5284: 5280: 5276: 5272: 5268: 5264: 5260: 5256: 5249: 5247: 5238: 5234: 5230: 5226: 5222: 5218: 5211: 5203: 5199: 5195: 5191: 5187: 5183: 5176: 5168: 5164: 5160: 5156: 5152: 5148: 5147:Phys Rev Lett 5141: 5133: 5129: 5124: 5119: 5114: 5109: 5105: 5101: 5097: 5093: 5089: 5081: 5073: 5069: 5064: 5059: 5054: 5049: 5045: 5041: 5037: 5033: 5029: 5021: 5013: 5009: 5004: 4999: 4994: 4989: 4985: 4981: 4977: 4970: 4961: 4957: 4946: 4943: 4940: 4937: 4935: 4932: 4930: 4927: 4925: 4922: 4921: 4915: 4907: 4899: 4896: 4887: 4885: 4875: 4867: 4864: 4855: 4853: 4844: 4842: 4833: 4830: 4826: 4818: 4814: 4812: 4806: 4802: 4793: 4784: 4780: 4771: 4769: 4765: 4755: 4741: 4719: 4715: 4692: 4688: 4662: 4658: 4652: 4648: 4642: 4638: 4634: 4625: 4614: 4608: 4603: 4599: 4592: 4586: 4573: 4572: 4571: 4554: 4529: 4525: 4501: 4483: 4468: 4445: 4417: 4413: 4409: 4401: 4392: 4389: 4386: 4381: 4376: 4371: 4368: 4364: 4360: 4357: 4351: 4346: 4342: 4331: 4330: 4329: 4324: 4314: 4311: 4308: 4305: 4302: 4299: 4285: 4282: 4277: 4273: 4252: 4249: 4244: 4240: 4219: 4216: 4211: 4207: 4184: 4180: 4154: 4150: 4146: 4141: 4137: 4133: 4130: 4127: 4122: 4117: 4114: 4110: 4099: 4098: 4097: 4088: 4075: 4072: 4069: 4066: 4061: 4060: 4057: 4054: 4051: 4048: 4045: 4044: 4041: 4038: 4035: 4032: 4029: 4028: 4025: 4022: 4019: 4016: 4013: 4012: 4009: 4006: 4004: 4001: 3998: 3997: 3994: 3991: 3988: 3985: 3982: 3981: 3978: 3975: 3973: 3970: 3967: 3966: 3963: 3960: 3958: 3955: 3952: 3951: 3948: 3945: 3943: 3940: 3937: 3936: 3933: 3930: 3927: 3924: 3922:Rhodamine 6G 3921: 3920: 3916: 3911: 3908: 3893: 3883: 3880: 3879: 3876: 3873: 3863: 3846: 3842: 3818: 3783: 3780: 3772: 3768: 3764: 3751: 3748: 3745: 3741: 3736: 3732: 3724: 3721: 3717: 3713: 3710: 3696: 3693: 3690: 3686: 3681: 3677: 3671: 3668: 3661: 3650: 3647: 3644: 3629: 3625: 3620: 3616: 3613: 3609: 3605: 3602: 3599: 3596: 3593: 3581: 3575: 3572: 3566: 3560: 3550: 3549: 3548: 3532: 3528: 3505: 3501: 3478: 3474: 3465: 3461: 3460:triplet state 3457: 3453: 3450:, rhodamine, 3449: 3439: 3435: 3433: 3414: 3405: 3398: 3393: 3386: 3383: 3380: 3376: 3370: 3367: 3363: 3351: 3344: 3339: 3333: 3327: 3320: 3319: 3318: 3299: 3296: 3282: 3278: 3269: 3262: 3257: 3253: 3242: 3241: 3240: 3214: 3211: 3203: 3199: 3194: 3190: 3187: 3181: 3178: 3172: 3166: 3163: 3157: 3151: 3141: 3140: 3139: 3130: 3116: 3112: 3106: 3103: 3099: 3095: 3090: 3086: 3053: 3050: 3039: 3035: 3030: 3026: 3023: 3020: 3016: 3011: 3006: 2996: 2992: 2987: 2983: 2977: 2971: 2968: 2965: 2957: 2953: 2949: 2936: 2932: 2927: 2923: 2915: 2912: 2908: 2904: 2901: 2887: 2883: 2878: 2874: 2868: 2865: 2858: 2850: 2844: 2841: 2835: 2829: 2819: 2818: 2817: 2803: 2789: 2773: 2770: 2767: 2763: 2739: 2735: 2702: 2699: 2691: 2687: 2683: 2670: 2667: 2664: 2660: 2655: 2651: 2643: 2640: 2636: 2632: 2629: 2615: 2612: 2609: 2605: 2600: 2596: 2590: 2587: 2578: 2574: 2566: 2562: 2555: 2549: 2546: 2540: 2534: 2524: 2523: 2522: 2514: 2511: 2497: 2474: 2462: 2459: 2451: 2447: 2443: 2433: 2423: 2419: 2414: 2410: 2402: 2399: 2395: 2391: 2388: 2377: 2367: 2363: 2358: 2354: 2348: 2345: 2338: 2330: 2324: 2321: 2315: 2309: 2302: 2301: 2300: 2297: 2295: 2276: 2272: 2245: 2241: 2235: 2231: 2227: 2224: 2221: 2218: 2215: 2205: 2204: 2203: 2201: 2197: 2191: 2167: 2161: 2157: 2153: 2148: 2142: 2137: 2134: 2130: 2126: 2123: 2113: 2110: 2109: 2093: 2088: 2084: 2078: 2073: 2070: 2066: 2060: 2056: 2052: 2048: 2044: 2035: 2024: 2023: 2022: 2005: 1996: 1984: 1979: 1974: 1965: 1958: 1953: 1947: 1941: 1931: 1930: 1929: 1927: 1922: 1906: 1902: 1872: 1850: 1846: 1823: 1820: 1816: 1793: 1790: 1786: 1781: 1775: 1771: 1767: 1764: 1732: 1729: 1721: 1717: 1713: 1700: 1696: 1691: 1687: 1679: 1676: 1672: 1668: 1665: 1651: 1647: 1642: 1638: 1632: 1629: 1622: 1614: 1608: 1605: 1599: 1593: 1583: 1582: 1581: 1574: 1565: 1563: 1553: 1537: 1533: 1529: 1524: 1521: 1517: 1494: 1481: 1469: 1450: 1447:and (ii) the 1432: 1428: 1424: 1419: 1416: 1412: 1403: 1384: 1378: 1354: 1331: 1305: 1299: 1293: 1287: 1281: 1275: 1269: 1263: 1254: 1248: 1236: 1207: 1203: 1198: 1190: 1185: 1181: 1174: 1166: 1160: 1151: 1144: 1139: 1136: 1132: 1125: 1117: 1111: 1105: 1100: 1092: 1086: 1077: 1073: 1069: 1066: 1062: 1052: 1045: 1040: 1034: 1028: 1021: 1020: 1019: 1002: 999: 996: 990: 987: 984: 975: 972: 967: 965: 949: 946: 943: 917: 911: 905: 899: 893: 890: 884: 878: 875: 852: 849: 841: 830: 824: 810: 807: 804: 798: 792: 786: 777: 769: 758: 752: 738: 735: 732: 726: 723: 717: 711: 708: 699: 693: 687: 680: 679: 678: 664: 644: 631: 622: 619: 616: 598: 594: 571: 568: 564: 554: 538: 535: 531: 527: 522: 518: 495: 491: 468: 465: 461: 438: 434: 406: 401: 397: 392: 386: 382: 378: 375: 371: 363: 358: 355: 351: 346: 340: 336: 332: 329: 325: 319: 315: 311: 305: 302: 299: 293: 290: 287: 280: 279: 278: 276: 266: 263: 259: 255: 251: 247: 238: 232:Typical setup 229: 227: 221: 219: 214: 203: 201: 196: 187: 184: 181: 178: 175: 174: 173: 170: 168: 164: 160: 156: 152: 147: 144: 139: 136: 132: 128: 124: 120: 110: 107: 99: 88: 85: 81: 78: 74: 71: 67: 64: 60: 57: – 56: 52: 51:Find sources: 45: 39: 38: 34: 29:This article 27: 23: 18: 17: 8420:Spectroscopy 8343: 8339: 8287: 8283: 8271: 8250: 8242: 8236: 8193: 8189: 8179: 8136: 8132: 8122: 8113: 8109: 8103: 8052: 8049:Nano Letters 8048: 8041: 7988: 7984: 7974: 7923: 7920:Nano Letters 7919: 7912: 7890:(2): 84–91. 7887: 7883: 7877: 7844: 7840: 7834: 7791: 7787: 7777: 7744: 7740: 7734: 7701: 7697: 7691: 7656: 7652: 7594: 7590: 7580: 7537: 7533: 7523: 7480: 7476: 7470: 7462: 7419: 7415: 7405: 7372: 7368: 7316: 7312: 7264: 7261:J. Mol. Biol 7260: 7254: 7229: 7225: 7215: 7172: 7168: 7158: 7123: 7120:Opt. 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3570:) 3564:( 3561:G 3533:D 3506:F 3479:F 3432:K 3415:K 3406:N 3399:1 3394:= 3387:f 3384:f 3381:o 3377:k 3371:n 3368:o 3364:k 3352:N 3345:1 3340:= 3337:) 3334:0 3331:( 3328:G 3300:1 3293:) 3283:k 3279:+ 3270:k 3266:( 3263:= 3258:B 3224:) 3218:( 3215:G 3212:+ 3209:) 3204:B 3195:/ 3185:( 3176:) 3173:0 3170:( 3167:G 3164:= 3161:) 3155:( 3152:G 3117:v 3113:/ 3107:y 3104:x 3096:= 3091:v 3063:) 3057:( 3054:G 3051:+ 3048:] 3040:D 3031:/ 3024:+ 3021:1 3017:1 3007:2 3003:) 2997:v 2988:/ 2981:( 2975:[ 2958:2 2954:/ 2950:1 2946:) 2942:) 2937:D 2928:/ 2921:( 2916:2 2909:a 2905:+ 2902:1 2899:( 2896:) 2893:) 2888:D 2879:/ 2872:( 2869:+ 2866:1 2863:( 2859:1 2854:) 2851:0 2848:( 2845:G 2842:= 2839:) 2833:( 2830:G 2804:v 2774:i 2771:, 2768:D 2740:i 2712:) 2706:( 2703:G 2700:+ 2692:2 2688:/ 2684:1 2680:) 2676:) 2671:i 2668:, 2665:D 2656:/ 2649:( 2644:2 2637:a 2633:+ 2630:1 2627:( 2624:) 2621:) 2616:i 2613:, 2610:D 2601:/ 2594:( 2591:+ 2588:1 2585:( 2579:i 2567:i 2559:) 2556:0 2553:( 2550:G 2547:= 2544:) 2538:( 2535:G 2475:, 2472:) 2466:( 2463:G 2460:+ 2452:2 2448:/ 2444:1 2440:) 2430:) 2424:D 2415:/ 2408:( 2403:2 2396:a 2392:+ 2389:1 2386:( 2383:) 2374:) 2368:D 2359:/ 2352:( 2349:+ 2346:1 2343:( 2339:1 2334:) 2331:0 2328:( 2325:G 2322:= 2319:) 2313:( 2310:G 2277:a 2273:D 2242:t 2236:a 2232:D 2228:6 2225:= 2222:D 2219:S 2216:M 2168:. 2162:D 2154:4 2149:/ 2143:2 2138:y 2135:x 2127:= 2124:D 2094:. 2089:z 2079:2 2074:y 2071:x 2061:2 2057:/ 2053:3 2045:= 2036:V 2006:, 1997:C 1985:V 1980:1 1975:= 1966:N 1959:1 1954:= 1951:) 1948:0 1945:( 1942:G 1926:G 1907:D 1882:) 1876:( 1873:G 1851:D 1824:2 1817:e 1794:y 1791:x 1782:/ 1776:z 1768:= 1765:a 1742:) 1736:( 1733:G 1730:+ 1722:2 1718:/ 1714:1 1710:) 1706:) 1701:D 1692:/ 1685:( 1680:2 1673:a 1669:+ 1666:1 1663:( 1660:) 1657:) 1652:D 1643:/ 1636:( 1633:+ 1630:1 1627:( 1623:1 1618:) 1615:0 1612:( 1609:G 1606:= 1603:) 1597:( 1594:G 1538:z 1534:w 1530:, 1525:y 1522:x 1518:w 1495:2 1490:| 1485:) 1479:( 1470:R 1460:| 1433:z 1429:w 1425:, 1420:y 1417:x 1413:w 1388:) 1382:( 1379:G 1355:N 1312:) 1309:) 1303:( 1300:Z 1294:, 1291:) 1285:( 1282:Y 1276:, 1273:) 1267:( 1264:X 1258:( 1255:= 1252:) 1246:( 1237:R 1208:, 1199:) 1191:2 1186:z 1182:w 1175:2 1171:) 1164:( 1161:Z 1145:2 1140:y 1137:x 1133:w 1126:2 1122:) 1115:( 1112:Y 1106:+ 1101:2 1097:) 1090:( 1087:X 1074:( 1053:N 1046:1 1041:= 1038:) 1032:( 1029:G 1006:) 1003:z 1000:, 997:r 994:( 991:F 988:S 985:P 964:G 950:0 947:= 921:) 918:t 915:( 912:I 903:) 900:t 897:( 894:I 891:= 888:) 885:t 882:( 879:I 853:1 842:2 834:) 831:t 828:( 825:I 814:) 808:+ 805:t 802:( 799:I 796:) 793:t 790:( 787:I 778:= 770:2 762:) 759:t 756:( 753:I 742:) 736:+ 733:t 730:( 727:I 721:) 718:t 715:( 712:I 700:= 697:) 691:( 688:G 599:z 572:y 569:x 539:y 536:x 523:z 496:z 469:y 466:x 439:0 435:I 407:2 402:z 393:/ 387:2 383:z 379:2 372:e 364:2 359:y 356:x 347:/ 341:2 337:r 333:2 326:e 320:0 316:I 312:= 309:) 306:z 303:, 300:r 297:( 294:F 291:S 288:P 121:( 109:) 103:( 98:) 94:( 84:· 77:· 70:· 63:· 40:.

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Knowledge

Fluorescence correlation spectroscopy

Index