Fluorescence correlation spectroscopy autocorrelation function

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]. 

Fig. 11.10. Schematic illustration of fluorescence correlation spectroscopy. The autocorrelation function characterises the fluctuations of the fluorescence intensity its decay time expresses the average duration of a...

In fluorescence correlation spectroscopy (FCS) a small volume element or a small area) of a sample is illuminated by a laser beam and the autocorrelation function of fluctuations in the fluorescence is determined by photon counting. From this autocorrelation function the mean number densities of the fluorophores and their diffusion coefficients can be extracted. Measurement and analysis of higher order correlation functions of the fluorescence has been shown to yield information concerning aggregation states of fluorophores ). 

Fluorescence correlation spectroscopy analyses the temporal fluctuations of the fluorescence intensity by means of an autocorrelation function from which translational and rotational diffusion coefficients, flow rates and rate constants of chemical processes of single molecules can be determined. For example, the dynamics of complex formation between /3-cyclodextrin as a host for guest molecules was investigated with singlemolecule sensitivity, which revealed that the formation of an encounter complex is followed by a unimolecular inclusion reaction as the rate-limiting step.263... 

Figure 5.18 shows autocorrelation functions calculated fi om several time courses similar to those in Fig. 5.17C but averaged over longer periods of time (2 X 10 time steps). The autocorrelation functions are normalized relative to x as in Fq. (5.81). As Fq. (5.81) predicts, the normalized values at zero time are inversely proportional to N (Fig. 5.18A) and K q (Fig. 5.18B). Fluorescence correlation spectroscopy thus provides a way to determine the number of fluorescent molecules in a small region of a sample, along with the equilibrium constant between states that have different fluorescence yields.

Inspection of Fig. 5.18 shows that the autocorrelation functions for this particular model decay exponentially with time, and that the rate constant for this decay is the sum of the rate constants for forward and backward transitions between the two states (kon + The upper curve in Fig. 5.18B, for example, decays to He (0.368) of its initial value in 16.61 At, which is the reciprocal of (0.05 -t 0.01 )Mt. In classical kinetics, if a system with first-order reactions in the forward and backward directions is perturbed by an abrupt change in the concentration of one of the components, a change in temperature, or some other disturbance, it will relax to equilibrium with a rate constant given by the sum of the rate constants for the forward and backward reactions. The fact that the autocorrelation functions in Fig. 5.18 decay with the relaxation rate constant of the system is a general property of classical time-correlation functions [259-262]. One of the potential strengths of fluorescence correlation spectroscopy is that the relaxation dynamics can be obtained with the system at equilibrium no perturbation is required. 

Fluorescence correlation spectroscopy thus provides a way to study processes that change the translational diffusion coefficient, such as binding of a small, fluorescent ligand to a macromolecule. However, the spatial dependence of the light intensity in the focal region can be more complex than Eq. (5.83) assumes and this can add spurious components to the autocorrelation function [263]. 

The arrival times of fluorescence photons contain information about correlations in fluorescence signals. Eluorescence correlation spectroscopy (FCS) (26) exploits these correlations to measure the magnitude and time scales of fluctuations in fluorescence. These fluctuations contain information about the dynamic time scales of the system and the concentration of fluorescing molecules. Correlations may span time ranges from nanoseconds to milliseconds, which extends the dynamic time window for fluorescence measurements far beyond what is achievable in fluorescence lifetime measurements. The autocorrelation function is calculated as ... 

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