Fluorescence depolarization correlation function

Figure 4.6 shows an apparatus for the fluorescence depolarization measurement. The linearly polarized excitation pulse from a mode-locked Ti-Sapphire laser illuminated a polymer brush sample through a microscope objective. The fluorescence from a specimen was collected by the same objective and input to a polarizing beam splitter to detect 7 and I by photomultipliers (PMTs). The photon signal from the PMT was fed to a time-correlated single photon counting electronics to obtain the time profiles of 7 and I simultaneously. The experimental data of the fluorescence anisotropy was fitted to a double exponential function. 

Another experimental method that has been used to determine orientational correlation functions in macromolecular systems is based on measurements of the time-dependence of the depolarization of fluorescence 26 From these measurements rotational diffusion coefficients and the shape of the rotating macromolecule have been determined.27... 

All of these methods yield information about the time evolution of the specific correlation functions. What is usually measured, except in the case of the depolarization of fluorescence, is the power or frequency spectrum of the respective correlation functions over a wide range of frequencies. 

Fluorescence depolarization measurements of aromatic residues and other probes in proteins can provide information on the amplitudes and time scales of motions in the picosecond-to-nanosecond range. As for NMR relaxation, the parameters of interest are related to time correlation functions whose decay is determined by reorientation of certain vectors associated with the probe (i.e., vectors between nuclei for NMR relaxation and transition moment vectors for fluorescence depolarization). Because the contributions of the various types of motions to the NMR relaxation rates depend on the Fourier transform of the appropriate correlation functions, it is difficult to obtain a unique result from the measurements. As described above, most experimental estimates of the time scales and magnitudes of the motions generally depend on the particular choice of model used for their interpretation. Fluorescence depolarization, although more limited in the sense that only a few protein residues (i.e., tryptophans and tyrosines) can be studied with present techniques, has the distinct advantage that the measured quantity is directly related to the decay of the correlation function. 

This same type of analysis is useful in connection with other experimental methods for determining orientational correlation functions. As an example we consider fluorescence depolarization experiments. In a fluorescence experiment, the following steps are followed ... 

Although the relation between fluorescence depolarisation and rotational Brownian motion was first identified by Perrin and the development of the theoretical background of the time-resolved fluorescence depolarization experiments was made by Jablonski use of the technique was limited until the advent of improved fluorescence decay time measurements some fifteen years i. An alternative, related technique, involving excitation using a continuous polarised light source, provides only the time average of the correlation function (Eq. 18) and as such, is less useful than the time resolved method. Other disadvantages are that the natural decay time of the chromophore must be determined from a sqrarate experiment and it is necessary to alter the viscosity, and/or temperature of the medium, often withun-... 

Thus, for fluorescence depolarization meaaiiements in wiiich the second order correlation function is desired... 

Whilst the equilibrium theory outlined above is well-known, the time-correlation function representation is not so well-known. Time-correlation functions have been used frequently in the recent literature for a variety of relaxation, spectroscopic and scattering phenomena for liquids and solids. The analysis of Kerr-effect relaxation (Beevers and co-workers, 1976), fluorescence depolarization (Valeur and... 

The analysis of fluorescence depolarization and NMR relaxation from simulations is the final topic of this review. Refs. 3 and 4 provide additional detail on the connection of time correlation functions to these and other spectroscopic methods. 

The time-dependent anisotropy, r(r), in a fluorescence depolarization experiment is directly related to the reorientational correlation function ... 

A useful and common way of describing the reorientation dynamics of molecules in the condensed phase is to use single molecule reorientation correlation functions. These will be described later when we discuss solute molecular reorientational dynamics. Indirect experimental probes of the reorientation dynamics of molecules in neat bulk liquids include techniques such as IR, Raman, and NMR spectroscopy. More direct probes involve a variety of time-resolved methods such as dielectric relaxation, time-resolved absorption and emission spectroscopy, and the optical Kerr effect. The basic idea of time-resolved spectroscopic techniques is that a short polarized laser pulse removes a subset of molecular orientations from the equifibrium orientational distribution. The relaxation of the perturbed distribution is monitored by the absorption of a second time-delayed pulse or by the time-dependent change in the fluorescence depolarization. 

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