Time-resolved fluorescence data analysis

Figure 8.9 Time-resolved fluorescent lifetime analysis of Cy3 attached to double-stranded DNA (Iqbal et al., 2008b). Fluorescent decay curve for Cy3 attached to a 16 bp DNA duplex, showing the experimental data and the instrument response function (IRF), and the fit to three exponential functions (line). The decay curve was generated using time-correlated single-photon counting, after excitation by 200 fs pulses from a titanium sapphire laser at 4.7 MHz.

A map of the photoisomerization potential energy surface for tetraphenylethylene in alkane solvents was prepared using a fluorescence and picosecond optical calorimetry (Figure 3.4) [21]. Line shapes of the vertical and relaxed exdted-state emissions at 294 K in methylcyclohexane were obtained from the steady-state emission spec-tmm, the wavelength dependence of the time-resolved fluorescence decays, the temperature dependences of the vertical and relaxed state emission quantum yields, and of the time-resolved fluorescence decays. Analysis of these data in conjunction with values of the twisted exdted-state energy provided values for the energies of the vertical, conformationally relaxed, and twisted exdted states on the photoisomerization surface, as well as the barriers to their interconversion. The energy difference between the last two states is found to be 1.76 0.15 kcal/mol in methylcyclohexane. 

Extensions of the analysis of time-resolved fluorescence anisotropy decay data in terms of two order parameters have also been developed (see, e.g., Refs. 51-54). Thus, the corresponding higher order parameter term is <7%) given by(53)... 

Figure 8 shows a pair of typical time-resolved fluorescence decay traces for 100 / M pyrene in supercritical CO2 (Tr = 1.02 pr = 1.17). Note that the ordinate is logarithmic. The upper and lower panels show results for selective observation in the monomer (400 +. 10 nm) and excimer (460 + 10 nm) regions of the pyrene emission spectrum. Several interesting features are apparent from these traces. First, both decay processes are not single exponential. Second, the excimer emission has a significant contribution from a species that "grows in" between 30 - 75 ns this is a result of the excimer taking time to form (i.e., k in Figure 1). Third, the fits between the experimental data and the model shown in Figure 1 are good. Detailed analysis of these decay traces (10,11,21-26) yields the entire ensemble of photophysical kinetic parameters for the pyrene excimer in supercritical C02.

Time-resolved fluorescence depolarization studies have, over the past decade, provided an interesting method for monitoring molecular reorientational motions in solution. The technique has been applied to investigations of both nthetic polymers and macromolecules of biological interest, and a selection of the results of these are discussed here. However, until recently, the relatively pc r quality of much of the data available from these measurements has precluded detafled quantitative interpretations of the results. With the advent of improved experimental techniques for fluorescence decay time determinations due in part to the availability of pulsed lasers for sample excitation and more accurate data analysis procedures, it is envisaged that interest in the technique may be revived. We will present here a short recapitulation of the background to these experiments, following from Sect. A. V. 

As an example of excitation energy transfer studied by time-resolved fluorescence, let us take again the case of the inclusion complex of the multichromophoric cyclodextrin CD-St with oxazine 725 described in Section 7.2.4.2 [15]. Figure 7.9 shows the fluorescence decay of CD-St the very first part of the decay is due to energy transfer [13] from the steroidic naphthalene fluorophores to oxazine 725. Data analysis led to an average decay time for transfer of about 25 ps, which is quite fast, as expected from the short average distance between donor and acceptor ( 9-10 A). 

An analysis of the time-resolved fluorescence in excimer-forming polymer systems can also prove informative in elucidating the conformations of macromo-lecular chains in solution these data are particularly relevant in terms of the structures adopted by polyelectrolytes in aqueous media. In this latter context, it is useful at this stage to briefly overview the development of the kinetic schemes to describe excited state interactions in fluorescent polymer solutions. 

A general discussion of the use of least-squares fitting in fluorescence measurements may be found in (28). The global analysis of fluorescence data is discussed in (29). Commercially available time-resolved fluorimeters are typically sold with data analysis software included. Available stand-alone packages include the Globals Unlimited suite, which is capable of analysing both time- and frequency-domain data, stopped-flow kinetics, etc. The Center for Fluorescence Spectroscopy at the University of Maryland (USA) also offers software for frequency- and time-domain fluorescence lifetime analysis. 

The analysis of time-resolved fluorescence decay curves, using a sum of discrete exponential functions to fit the experimental data, is based on a simple assumption the number of different exponential terms used has to be equal to the number of kinetically different excited state species present in the molecular system. While this assumption has the advantage of providing a clear physical meaning for the fitting parameters, decay times and pre-exponential coefficients, the identification of the different kinetic species is frequently not evident, particularly in more complex systems like polymers and proteins, and this approach has been questioned [85]. 

Time-resolved fluorescence anisotropy measurements [47] can provide detailed information on the reorientation dynamics of molecules in solution. Until recently, however, this information has b n limited to single rotational correlation times, which are only strictly appropriate for the diffusion of spherically symmetric molecules. Improvements in instrumentation and data analysis techniques during the last decade have led to increasingly accurate measurements of fluorescence lifetimes, with parallel improvements in determinations of fluorescence anisotropies. 

Polymers are not homogeneous in a microscopic scale and a number of perturbed states for a dye molecule are expected. As a matter of fact, non-exponential decay of luminescence in polymer systems is a common phenomenon. For some reaction processes (e.g, excimer and exciplex formation), one tries to fit the decay curve to sums of two or three exponential terms, since this kind of functional form is predicted by kinetic models. Here one has to worry about the uniqueness of the fit and the reliability of the parameters. Other processes can not be analyzed in this way. Examples include transient effects in diffusion-controlled processes, energy transfer in rigid matrices, and processes which occur in a distribution of different environments, each with its own characteristic rate. This third example is quite common when solvent relaxation about polar excited states occurs on the same time scale as emission from those states. Careful measurement of time-resolved fluorescence spectra is an approach to this problem. These problems and many others are treated in detail in recent books (9,11), including various aspects of data analysis. 

Time-resolved IR spectra of similar peptides following a laser-excited temperature jump showed two relaxation times, unfolding 160 ns and faster components <10 ns (Williams et al., 1996). These times are very sensitive to the length, sequence, and environment of these peptides, but do show that the fundamental helix unfolding process is quite fast. These fast IR data have been contrasted with Raman and fluorescence-based T-jump experiments (Thompson et al., 1997). Raman experiments at various temperatures have suggested a folding in 1 /xs, based on an equilibrium analysis (Lednev et al., 2001). But all agree that the mechanism of helix formation is very fast. 

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