Correlation spectroscopy fluorescence

In general, the deviations of the fluorescence amplitude around the mean follow a binomial distribution. The binomial distribution function describes the probability, P(x,n,p), of having x successes in n trials if the probability of a success in any individual trial is p and the probability of a failure is I —p. This is given by the expression 

There are several useful approximations for the binomial distribution that apply in certain limits of n and p (Box 5.4). However, neither of these limits is generally applicable to the situation we are considering here. 

The limit of a binomial distribution (Eq. 5.76) when the probability of success on an individual trial is very small (p 1) is the Poisson distribution, 

As in the underlying binomial distribution, There is the mean value of x and is equal to np where n is the number of trials. The variance of a Poisson distribution also is np, as you can see by letting the factor (1 — p) in Eq. (5.78) go to 1. The standard deviation from the mean of a Poisson distribution (rr) thus is the square root of the mean. 

Binomial distributions have another important approximation in the limit that n is infinitely large andp also is large enough so that np l. This is the 

Fluorescence correlation spectroscopy (FCS) is based on exciting a small number of molecules in a femtoliter volume and correlating the fluctuations of the fluorescence intensity. The fluctuations are caused by diffusion, rotation, intersystem crossing, conformational changes, or other random effects. The technique dates back to a work of Magde, Elson and Webb published in 1972 [335]. Theory and applications of FCS are described in [51, 429, 430, 431, 456, 457, 497, 537, 556]. 

An FCS system with two-photon excitation is shown in Fig. 5.108, right [51, 457]. A femtosecond Ti Sapphire laser of high repetition rate is used to excite the sample. Because there is no appreciable excitation outside the focal plane of the microscope lens a small sample volume is achieved without a confocal pinhole. This makes the optical setup very simple. In terms of signal recording there is no difference between one-photon and two-photon FCS. 

FCS and fluorescence lifetime experiments are often used in eombination to explore the fluorescence dynamics of dye-protein complexes. The traditional approach is to acquire FSC and lifetime data in separate experiments [226, 458]. 

However, almost all advanced TCPCS devices are able to reeord lifetime data and PCS data simultaneously [25, 65]. The advantage compared to the traditional approach is that PCS and lifetime data originate from the same sample, from the same spot of a sample, or even from the same molecules. TCSPC data can therefore be used to distinguish between different types of molecules, different quenching states, or different binding or conformation states of dye-protein eomplexes it is also possible to include lifetime variations in the correlation [498, 548]. The principle of TCSPC-based PCS is shown in Pig. 5.109. 

The single-photon pulses of the detectors are fed into a router (see Sect. 3.1, page 29). Por each photon detected in any of the detectors, the router delivers a single-photon pulse and the number of the detector that detected the photon. The TCSPC module determines the time of the photon in the laser pulse sequence ( micro time ) and the time from the start of the experiment ( macro time ). The detector number, the micro time, and the macro time are written into a first-in-first-out (PlPO) buffer (see Sect. 3.6, page 43). The output of the PlPO is continuously read by the computer, and the photon data are written in the main memory of the computer or on the hard disc. 

In fluorescence correlation spectroscopy (FCS), the temporal fluctuations of the fluorescence intensity are recorded and analyzed in order to determine physical or chemical parameters such as translational diffusion coefficients, flow rates, chemical kinetic rate constants, rotational diffusion coefficients, molecular weights and aggregation. The principles of FCS for the determination of translational and rotational diffusion and chemical reactions were first described in the early 1970s. But it is only in the early 1990s that progress in instrumentation (confocal excitation, photon detection and correlation) generated renewed interest in FCS. 

The theoretical treatment of PCS considers the persistence of temporal information in a fluctuation trace through the construction of a temporal autocorrelation function, which can then be fit using models based on physical processes which may be present in the sample and which cause the fluctuations. Por a more detailed review the reader is referred elsewhere [28-34 ]. 

Time domain autocorrelation analysis provides a measure of the self-similarity of a time series signal and the decay of the autocorrelation function describes the temporal persistence of information carried by it. The normalized fluorescence correlation function of a fluctuating signal F t) can be written as [29], 

Autocorrelation is often applied to any signal or data set and used to show up trends that may exist For example, autocorrelation of residuals from fitting can give information on trends in a fit to data, which may reflect systematic errors in the experiment or inappropriateness of the model fit 

Combining equations 2.15, 2.17, and 2.19 yields the fluorescence fluctuation autocorrelation function [34], 

The particular case of G(0) represents the correlation of a molecule at r with a molecule at r at the same instant. In a sample in which there are no long-range interactions, no spatial correlations such as this exist and therefore fluctuations are only correlated at the same instant at the same position (and all positions are equivalent). In this limit it can then be shown that equation 2.20 reduces to [34], 

Variations in the diffusion time of the fluorescent molecules can therefore be detected and used to probe molecular interactions in FCS. Such variations are induced by a large increase in the molecular mass of the fluorescence molecules ( 10 fold) upon their binding to a specific partner e.g. a large protein like a receptor).  

Due to the use of a confocal volume, FCS is particularly suited for miniaturization in HTS and relatively insensitive to auto fluorescent test compounds. Moreover, in compound testing, the small path length of the confocal volume greatly limits any filter effects on fluorescence intensity. As in FP, the requirement for large differences in mass in the assay design is a limitation to the applicability of FCS. However, it can be overcome by methods like Fluorescence Intensity Distribution Analysis (FIDA) or two-colour cross correlation derived from the original FCS concept. 

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Application of Fluorescence Correlation Spectroscopy to the Measurement of Local Temperature at a Small Area in Solution... 

Fluorescence intensity detected with a confocal microscope for the small area of diluted solution temporally fluctuates in sync with (i) motions of solute molecules going in/out of the confocal volume, (ii) intersystem crossing in the solute, and (hi) quenching by molecular interactions. The degree of fluctuation is also dependent on the number of dye molecules in the confocal area (concentration) with an increase in the concentration of the dye, the degree of fluctuation decreases. The autocorrelation function (ACF) of the time profile of the fluorescence fluctuation provides quantitative information on the dynamics of molecules. This method of measurement is well known as fluorescence correlation spectroscopy (FCS) [8, 9]. 

Application of Fluorescence Correlation Spectroscopy 145 Table 8.1 Local temperature deviation, extinction coefficient, thermal conductivity. 

Rigler, R. and Elson, E. S. (eds) (2001) Fluorescence Correlation Spectroscopy, Springer Series in Chemical Physics, 65, Springer, Berlin. 

Krichevsky, O. and Bonnet, G. (2002) Fluorescence correlation spectroscopy the technique and its applications. Rep. Prog. Phys., 65, 251-297. 

Elson, E. L. and Magde, D. (1974) Fluorescence correlation spectroscopy. 1. Conceptual basis and theory. Biopolymers, 13, 1-27 Elson, E. L. and Webb, W. W. (1974) Fluorescence correlation spectroscopy. 11. An experimental realization. Biopolymers, 13, 29-61. 

Masuda, A., Ushdia, K and Okamoto, T. (2005) New fluorescence correlation spectroscopy enabbng direct observation of spatiotemporal dependence of diffusion constants as an evidence of anomalous transport in extracellular matrices. Biophys.J., 88, 3584—3591. 

Doose, S., Tsay, J. M., Pinaud, F. and Weiss, S. (2005) Comparison of photophysical and colloidal properties of biocompatible semiconductor nanocrystals using fluorescence correlation spectroscopy. Anal. Chem., 77, 2235-2242. 

Application of fluorescence correlation spectroscopy to the measurement of local temperature in solutions under optical trapping condition./. Phys. Chem. B, 111, 2365-2371. 

Gregor, 1., Patra, D. and Enderlein, J. (2005) Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation. 

Hosokawa, C., Yoshikawa, H. and Masuhara, H. (2004) Optical assembling dynamics of individual polymer nanospheres investigated by singleparticle fluorescence detection. Phys. Rev. E, 70, 061410-1-061410-7 (2005) Cluster formation of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy. Phys. Rev. E, 72, 021408-1-021408-7. 

Schwille, P., Korkach, J. and Webb, W. W. (1999) Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes. Cytometry, 36, 176-182. 

Burns, A. R., Frankel, D. J. and Buranda, T. (2005) Local mobility in hpid domains of supported bilayers characterized by atomic force microscopy and fluorescence correlation spectroscopy. Biophys. J., 89, 1081-1093. 

Fluorescence Correlation Spectroscopy on Molecular Diffusion Inside and Outside a Single Living Cell 645... 

WHAT FLUORESCENCE CORRELATION SPECTROSCOPY CAN TELL US ABOUT UNFOLDED PROTEINS... 

Fluorescence correlation spectroscopy (FCS) measures rates of diffusion, chemical reaction, and other dynamic processes of fluorescent molecules. These rates are deduced from measurements of fluorescence fluctuations that arise as molecules with specific fluorescence properties enter or leave an open sample volume by diffusion, by undergoing a chemical reaction, or by other transport or reaction processes. Studies of unfolded proteins benefit from the fact that FCS can provide information about rates of protein conformational change both by a direct readout from conformation-dependent fluorescence changes and by changes in diffusion coefficient. 

IV. Advantages and Disadvantages of Using Fluorescence Correlation Spectroscopy to Study Protein Conformational Changes... 

The material presented in this chapter demonstrates the utility of fluorescence correlation spectroscopy in the study of unfolded proteins. 

Czemey P, Lehmann F, Wenzel M, Buschmann V, Dietrich A, Mohr GJ (2001) Tailor-made dyes for fluorescence correlation spectroscopy (FCS). Biol Chem 382 495-498... 

Haupts U, Maiti S, Schwille P, Webb WW (1998) Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy. Proc Natl Acad Sci USA 95 13573-13578... 

Schwille P, Kummer S, Heikal AA, Moemer WE, Webb WW (2000) Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins. Proc Natl Acad Sci USA 97 151-156... 

Elson, E. and Magde, D. (1974). Fluorescence correlation spectroscopy I Conceptual basis and theory. Biopolymers 13, 1-28. 

Schwille, P., Bieschke, J. and Oehlenschlager, F. (1997). Kinetic investigations by fluorescence correlation spectroscopy The analytical and diagnostic potential of diffusion studies. Biophys. Chem. 66, 211-28. 

Webb, W. (2001). Fluorescence correlation spectroscopy Inception, biophysical experimentations, and prospectus. Appl. Opt. 40, 3969-83. 

Bjemeld E.J., Foldes-Papp Z., Kail M., Rigler R., Single-molecule surface-enhanced Raman and fluorescence correlation spectroscopy of horseradish peroxidase, J. Phys. Chem. B 2002 106 1213-1218. 

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