Lifetimes distributions

Figure A3,12.2(a) illnstrates the lifetime distribution of RRKM theory and shows random transitions among all states at some energy high enongh for eventual reaction (toward the right). In reality, transitions between quantum states (though coupled) are not equally probable some are more likely than others. Therefore, transitions between states mnst be snfficiently rapid and disorderly for the RRKM assumption to be mimicked, as qualitatively depicted in figure A3.12.2(b). The situation depicted in these figures, where a microcanonical ensemble exists at t = 0 and rapid IVR maintains its existence during the decomposition, is called intrinsic RRKM behaviour [9].

Figure A3.12.2. Relation of state oeeupation (sehematieally shown at eonstant energy) to lifetime distribution for the RRKM theory and for various aetiial situations. Dashed eiirves in lifetime distributions for (d) and (e) indieate RRKM behaviour, (a) RRKM model, (b) Physieal eounterpart of RRKM model, (e) Collisional state seleetion. (d) Chemieal aetivation. (e) Intrinsieally non-RRKM. (Adapted from [9].)...

In the above discussion it was assumed that the barriers are low for transitions between the different confonnations of the fluxional molecule, as depicted in figure A3.12.5 and therefore the transitions occur on a timescale much shorter than the RRKM lifetime. This is the rapid IVR assumption of RRKM theory discussed in section A3.12.2. Accordingly, an initial microcanonical ensemble over all the confonnations decays exponentially. However, for some fluxional molecules, transitions between the different confonnations may be slower than the RRKM rate, giving rise to bottlenecks in the unimolecular dissociation [4, ]. The ensuing lifetime distribution, equation (A3.12.7), will be non-exponential, as is the case for intrinsic non-RRKM dynamics, for an mitial microcanonical ensemble of molecular states. 

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

By means of Laplace transforms of the foregoing three equations mating use of the convolution theorem and the assumptions Pf(t) — Pt a constant which is the ratio of the in use time (t the total operating time of the 4th component), Gt(t) si — exp ( — t/dj (note that a double transform is applied to Ff(t,x)), we obtain an expression in terms of the lifetime distribution, i.e.,... 

F. Gabern, W. S. Koon, J. E. Marsden, and S. D. Ross, Theory and computation of non-RRKM lifetime distributions and rates in chemical systems with three or more degrees of freedom, Physica D 211, 391 (2005). 

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... 

Fig. 3.11. FRET FLIM experiment to study colocalization of two lipid raft markers, GPI-GFP and CTB-Alexa594. The rows of images show intensity and lifetime images of donor-labeled and donor + acceptor-labeled cells. The histogram shows the lifetime distribution of the whole cells. The FRET...

A closer look at the data shows the lifetime distributions are comparatively broad, about 0.25 ns for both distributions. This is in fact much broader than what one would expect from photon statistics alone. Based on realistic / -values (1.2-1.5) lifetime images recorded with this many counts are expected to yield distributions with widths on the order of 0.1 ns. The broadening is therefore not because of photon statistics. Variations in the microenvironment of the GFP are the most likely source of the lifetime heterogeneities. Importantly, such sensitivity for local microenvironment may be the source of apparent FRET signals. In this particular FRET-FLIM experiment, we found that the presence of CTB itself without the acceptor dye already introduced a noticeable shift of the donor lifetime. Therefore, in this experiment the donor-only lifetime image was recorded after unlabeled CTB was added to the cells. The low FRET efficiency and broadened lifetime distribution call for careful control experiments and repeatability checks. 

Rzad et al. (1970) obtained the relative lifetime distribution of electron-ion recombination in cyclohexane by 1LT of Eq. (7.26). Denoting the probability that the lifetime would be between t and t + dt as f(t) dt, the thusly defined scavenging function at scavenger concentration c% is given by... 

Rzad et al.( 1970) compared the consequences of the lifetime distribution obtained by ILT method (Eq. 7.27) with the experiment of Thomas et al. (1968) for the decay of biphenylide ion (10-800 ns) after a 10-ns pulse-irradiation of 0.1 M biphenyl solution of cyclohexane. It was necessary to correct for the finite pulse width also, a factor rwas introduced to account for the increase of lifetime on converting the electron to a negative ion. Taking r = 17 and Gfi = 0.12 in consistence with free-ion yield measurement, they obtained rather good agreement between calculated and experimental results. The agreement actually depends on A /r, rather than separately on A or r. 

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... 

In some circumstances, it can be anticipated that continuous lifetime distributions would best account for the observed phenomena. Examples can be found in biological systems such as proteins, micellar systems and vesicles or membranes. If an a priori choice of the shape of the distribution (i.e. Gaussian, sum of two Gaussians, Lorentzian, sum of two Lorentzians, etc.) is made, a satisfactory fit of the experimental data will only indicate that the assumed distribution is compatible with the experimental data, but it will not demonstrate that this distribution is the only possible one, and that a sum of a few distinct exponentials should be rejected. 

To answer the question as to whether the fluorescence decay consists of a few distinct exponentials or should be interpreted in terms of a continuous distribution, it is advantageous to use an approach without a priori assumption of the shape of the distribution. In particular, the maximum entropy method (MEM) is capable of handling both continuous and discrete lifetime distributions in a single analysis of data obtained from pulse fluorometry or phase-modulation fluorometry (Brochon, 1994) (see Box 6.1). 

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). 

Figure 5.11. Decay time distribution for different temperatures recovered by fitting Gaussian lifetime distributions to the observed nonexponential decays of TB9ACN in PMMA.(26)x, 261 K , 243 K , 224 K +, 203 K O. 175 K , 146 K,...

The temporal luminescence of a highly heterogeneous sensor-carrier mixtures cannot be uniquely represented by sums of exponentials (Eq. (9.23)) due to the lack of orthogonality of the exponential function. In this case it becomes appropriate to express equations (9.17) or (9.23) in terms of probability density functions or lifetime distribution functions 5t(8 14)... 

Even though the temporal luminescence of a sensor cannot be uniquely represented in terms of lifetime distribution functions, the use of lifetime distributions provides a more convenient way to characterize the transient luminescence of sensors than the use of few discrete exponentials. Lifetime distribution functions require less parameters to describe the sensor luminescence response which is an advantage in the implementation of data analysis for real-time applications. 

Nonexponential luminescence decays are not well understood. However, regardless of the lack of understanding, it is a tradition to fit complex decays to sums of exponential functions either discrete or continuous (lifetime distributions). An important limitation of this approach is introduced by the nonorthogonal nature of the exponential function. The practice of fitting nonexponential luminescence decays to... 

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...

A solution of a pure fluorophore may reasonably be expected to display a single exponential decay time. The emission from fluorophore-protein conjugates, on the other hand, may be best characterized by two or three exponential decay times (Table 14.2). In labeling proteins with fluorophores, a heterogeneity of labeled sites results in fluorophore populations that have different environments, and hence different lifetimes. The lifetime distribution of a fluorophore-protein conjugate in bulk solution may vary further when immobilized on a solid support (Table 14.2). 

E. Amler, L. Mazzanti, E. Bertoli, and A. Kotyk, Lifetime distribution of low sample concentrations A new cuvette for highly accurate and sensitive fluorescence measurements, Biochem. Int. 27, 771-776 (1992). 

One would expect that lowering the temperature or increasing the viscosity of the solvent would increase the width of the lifetime distribution, since both factors may affect the rate of transitions between microstates. If this rate is high as compared with the mean value of the fluorescence lifetime, the distribution should be very narrow, as for tryptophan in solution. When the rate of transitions between microstates is low, a wide distribution would be expected. 

The measurement of fluorescence lifetimes is an integral part of the anisotropy, energy transfer, and quenching experiment. Also, the fluorescence lifetime provides potentially useful information on the fluorophore environment and therefore provides useful information on membrane properties. An example is the investigation of lateral phase separations. Recently, interest in the fluorescence lifetime itself has increased due to the introduction of the lifetime distribution model as an alternative to the discrete multiexponential approach which has been prevalent in the past. 

An increase indicates a broadening lifetime distribution. Gel-liquid-crystalline phase transition. 

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