Fluorescence Lifetime Distributions

The conventional analysis of fluorescence decay is described in terms of a sum of one or more exponential terms, each with a characteristic lifetime 

The mathematical basis of the distributional approach can be understood by reference to the equations used for multiexponential decay. Integrals replace finite sums of terms, while the discrete parameters inside the sums are replaced by continuous functions of these parameters. The equation 

Equation (5.2) is often modified by introducing terms which relate to the normalization of the distribution function or by its reexpression in terms of a rate variable which is the reciprocal of the lifetime. Normalization can be understood by reference to Eq. (5.1), where the preexponential a, are usually subject to the normalization condition that their sum equal 1. The analogous condition for distribution functions once again replaces this sum with an integral over all positive values. Also by analogy to the preexponential a,the distribution functions are usually positively valued. Negative preexponential terms or distribution function values can arise, however, in cases such as excited-state reactions.(17) 

Although satisfactory criteria for deciding whether data are better analyzed by distributions or multiexponential sums have yet to established, several methods for determining distributions have been developed. For pulse fluorometry, James and Ware(n) have introduced an exponential series method. Here, data are first analyzed as a sum of up to four exponential terms with variable lifetimes and preexponential weights. This analysis serves to establish estimates for the range of the preexponential and lifetime parameters used in the next step. Next, a probe function is developed with fixed lifetime values and equal preexponential factors. An iterative Marquardt(18) least-squares analysis is undertaken with the lifetimes remaining fixed and the preexponential constrained to remain positive. When the preexponential 

The mathematical basis for the exponential series method is Eq. (5.3), the use of which has recently been criticized by Phillips and Lyke.(19) Based on their analysis of the one-sided Laplace transform of model excited-state distribution functions, it is concluded that a small, finite series of decay constants cannot be used to represent a continuous distribution. Livesey and Brouchon(20) described a method of analysis using pulse fluorometry which determines a distribution using a maximum entropy method. Similarly to Phillips and Lyke, they viewed the determination of the distribution function as a problem related to the inversion of the Laplace transform of the distribution function convoluted with the excitation pulse. Since Laplace transform inversion is very sensitive to errors in experimental data,(21) physically and nonphysically realistic distributions can result from the same data. The latter technique provides for the exclusion of nonrealistic trial solutions and the determination of a physically realistic solution. These authors noted that this technique should be easily extendable to data from phase-modulation fluorometry. 

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Siemiarczuk A, Ware WR (1987) Complex excited-state relaxation in p-(9-Anthryl)-N, N-dimethylaniline derivatives evidenced by fluorescence lifetime distributions. J Phys Chem 91 3677-3682... 

Vincent M, Gallay J, Demchenko AP (1995) Solvent relaxation around the excited-state of indole - analysis of fluorescence lifetime distributions and time-dependence spectral shifts. J Phys Chem 99 14931-14941... 

A. Seimiarczuk and W. R. Ware, Temperature dependence of fluorescence lifetime distributions in l,3-di(l-pyrenyl)propane with maximum entropy method, J. Phys. Chem, 93, 7609-7618 (1989). 

J. R. Alcala, E. Gratton, and F. Prendergast, Resolvability of fluorescence lifetime distributions using phase fluorometry, Biophys. J. 51, 587-596 (1987). 

Table 14.2. Fluorescence Lifetime Distributions of Some Fluorophore-Protein Conjugates...

R. Fiorini, M. Valentino, S. Wang, M. Glaser, and E. Gratton, Fluorescence lifetime distributions of l,6-diphenyl-l,3,5-hexatriene in phospholipid vesicles, Biochemistry 26, 3864-3870 (1987). 

Photochemistry can be used to demonstrate solvent effects in supercritical fluids. The analysis revealed trimodal fluorescence lifetime distributions near the critical temperature, which can be explained by the presence of solvent-solute and solute-solute clustering. This local aggregation causes an increase in nonradiative relaxations and, therefore, a decrease in the observed fluorescence lifetimes. Concentration and density gradients are responsible for these three unique lifetimes (trimodal) in the supercritical fluid, as contrasted with the single lifetime observed in a typical organic solvent. The... 

Fig. 2 Normalized fluorescence lifetime distributions (ELDs) for (a) the cGMP-imprinted and (b) non-imprinted thin-layer polymer film obtained from the fluorescence microscopy measurements (adapted from [47, 66])...

Fig. 4. Fluorescence lifetime distributions of /f2AR labeled at Cys265627 with fluorescein maleimide (Ghanouni et al., 2001a). (A) Single lifetime distributions are observed for unliganded receptor and receptor bound to the neutral antagonist alprenolol (ALP). (B and G) Two lifetime distributions are observed for /J2AR bound to the full agonist isoproterenol (ISO) and the partial agonist salbutamol (SAL). The short lifetime distribution for ISO is different from that for SAL, consistent with a different active conformation.

To determine the shape of the hydrophobic barrier of bilayer membranes, fatty acids and PC molecules spin labeled with nitroxides at various positions along the lipid chains were diffused into vesicles and their solvent-sensitive isotropic coupling constants were measured [54]. Results are plotted in Figure 5 in terms of distance of the probe from the bilayer center. Also shown is the profile of the dielectric constant along the membrane normal evaluated from the fluorescence lifetime distribution of fluorescence probes in PC liposomes [55]. These data correlate well with results from neutron diffraction studies that map the positional distribution of water and lipid moieties along the bilayer normal [56]. 

Fluorescence lifetime distribution of OPH reveal the effects of cholesterol on the microheterogeneity of erythrocyte membr a nes 2 1. ... 

The field-induced morphological change is clearly observed in the fluorescence intensity image, but the peak position of the fluorescence lifetime distribution remains constant at around 2.4ns at 100min after exposure (see Figure 31.8). This result indicates that the halobacteria mostly exhibit a fluorescence lifetime of 2.4 ns, regardless of exposure time the pH in the halobacteria is essentially the same, irrespective of aggregate formation. 

A particularly useful paper by Wagner and Ware applies the maximum entropy method for the recovery of fluorescence lifetime distributions to Forster transfer in rigid and viscous media. As shown by treatment of specific examples it is evident that this constitutes a powerful treatment for determining the distribution of rate constants in this type of system. 

Gilmore AM, Shinkarev V, Hazlett TL and Govindjee (1998) Quantitative analysis of the effects of intrathylakoid pH and xanthophyll cycle pigments on chlorophyll a fluorescence lifetime distributions and intensity in thylakoids. Biochemistry 37 13582- 13593... 

Brochon JC, Livesey AK (1990) Data analysis in frequency-domain fluorometry by the maximum entropy method - recovery of fluorescence lifetime distributions. Chem Phys Lett 174 517-522... 

Liu YS, Ware WR (1993) Photophysics of polycyclic aromatic hydrocarbons adsorbed on silica gel surfaces. 1. Fluorescence lifetime distribution analysis an ill-conditioned problem. J Phys Chem 97 5980-5986... 

Lee, M. Tang, L Hoshstrasser, R.M., Fluorescence Lifetime Distribution of Single Molecules Undergoing Forster Energy Transfer, Chem. Phys. Lett. (2001) 344, 501-508. 

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