Complex decay

Luminescence reaction (Viviani et al., 2002a) The luciferin-luciferase luminescence reaction was carried out in 0.1 M Tris-HCl, pH 8.0, containing 2mM ATP and 4mM Mg2+. Mixing luciferase with luciferin and ATP resulted in an emission of light with rapid onset and a kinetically complex decay. Further additions of fresh luciferase, after the luminescence has decayed to about 10% of its maximum value, resulted in additional luminescence responses similar to the initial one (Fig. 1.15). According to the authors, the repetitive light emission occurred in consequence of the inhibition of luciferase by a reaction product, as seen in the case of the firefly system (McElroy et al., 1953). The luminescence spectrum showed a peak at 487nm (Fig. 1.16). 

The complex decays with first-order kinetics, releasing the enzyme to act again ... 

It is generally understood that the reactive intermediates are generated in a random distribution of different microenvironments, each with its own energy barrier. The complex decay of this dispersion of rates leads to the nonexponential kinetics. Thus, disappearance plots are dominated at early times by reaction of those species in fast sites , which have lower energy barriers. As these sites are cleared, the distribution of rates over time becomes more reflective of sites with higher barriers. Finally, at longer times, the decay curves are dominated by the slowest sites. It is often observed that plots of In [intensity] versus or are approximately linear. It... 

The reaction dynamics are quite different for Y + propene. The wide angle scattering in the Y atom angular distribution (Fig. 22) indicates that a substantial fraction of initially-formed complexes decay back to reactants, rather than forming chemical products.122,123 Recent calculations on... 

One of the issues which have impeded the study of tissue AF is the complex decay profile that it exhibits. It is often assumed that fluorescence decay is necessarily a simple exponential. This assumption is not necessarily valid, as is explained in Chapter 4. 

Figure 4.7 shows the best fits to the experimental data using Eq. (4.11). Although the data are fit within experimental error, the two-state model is certainly just an approximation. More complex distributions of sites with different quenching constants could fit the data. The success of the two-state model is not surprising given the well-known ability of two exponentials to accurately mimic complex decay curves (see above). Further, r data indicate that a more complex model is needed for a full description. 

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... 

In the case of a single lifetime with no interference from ambient or backscattered light only a single frequency is necessary to determine the lifetime of the luminescence. Determination of the phase and modulation at multiple frequencies is necessary to characterize complex decays in fiberoptic sensors. 

We note that a variety of factors can be responsible for a complex multiexponential or nonexponential decays. Depending on the molecular origin of the complex decay... 

The fluorescence decay parameters of tyrosine and several tyrosine analogues at neutral pH are listed in Table 1.2. Tyrosine zwitterion and analogues with an ionized a-carboxyl group exhibit monoexponential decay kinetics. Conversion of the a-carboxyl group to the corresponding amide results in a fluorescence intensity decay that requires at least a double exponential to fit the data. While not shown in Table 1.2, protonation of the carboxyl group also results in complex decay kinetics.(38)... 

The lowest excited states of paramagnetic metal complexes are described by configuration interactions of the porphyrin (7T,tt ) excited singlet and triplet states and the "porphyrin-to-metal" or metal-to-porphyrin charge-transfer excited states (35,36). Thus T (phosphorescence) emission of paramagnetic metal complexes decays... 

In contrast, at [H+] > 0.1 M, the same reaction results in two or three new EPR signals (glso 1.974, 1.971, and 1.966) in addition to the one already mentioned feso= 1.979).68,75 These EPR signals turn out to be consistent with six-coordinated oxo-Cr(V) species. In this situation, the relative intensity of the EPR signal is pH dependent but is independent of the aldohexose/Cr(VI) ratio. In fact, six-coordinated species are dominant at [H+] > 0.75 M. In addition, both species [six- and five-coordinated oxo-Cr(V) complexes] decay at the same rate, meaning that they are in a rapid equilibrium. Scheme 5 shows the complexation chemistry and the observed Cr(V)-sugar redox processes. 

A number of studies on the fluorescence decay of tyrosine, tyrosine derivatives, and small tyrosyl peptides have been carried out. 36-38 Whereas the tyrosine zwitterion and tyrosine derivatives with an ionized a-carboxy group exhibited monoexponential fluorescence decay (x = 3.26-3.76 ns), double- or triple-exponential decay was observed in most other cases. As in the case of the tryptophan model compounds, the complex decay kinetics were again interpreted in terms of rotamer populations resulting from rotation around the C —Cp bond. There is evidence to indicate that the shorter fluorescence lifetimes may arise from rotamers in which the phenol ring is in close contact with a hydrated carbonyl group 36 37 and that a charge-transfer mechanism may be implicated in this quenching process. 39 ... 

A. The calculated values of the equilibrium constant appeared to be very close to those estimated from the kinetic data. The values of the equilibrium constants are given Co(II) + Me2PhCOOH 44- Complex at =318 and rate constants (kd) of this complex decay to free radicals [71]. 

As a new subject we have considered the effect of the frequency-dependence of the elastic moduli on dynamic light scattering. The resultant nonexponential decay of the time-correlation function seems to be observable ubiquitously if gels are sufficiently compliant. Furthermore, even if the frequency-dependent parts of the moduli are very small, the effect can be important near the spinodal point. The origin of the complex decay is ascribed to the dynamic coupling between the diffusion and the network stress relaxation [76], Further scattering experiments based on the general formula (6.34) should be very informative. 

Scheme 1 predicts a complex decay for the singlet-oxygen phosphorescence. However, there are three simple, limiting situations. For simplicity, let us assume only two pseudophases, the lipidic and the aqueous pseudophases. The three above-mentioned situations are as follows ... 

In Fig. 10, the transients exhibit quite different behavior from opal A to opal CT. In particular, a bi-exponential decay (Eq. 2) failed to reproduce the kinetics of opal CT. In this material, the emission is red-shifted towards 2.6 eV and the PL is strongly quenched at shorter time delays, with an unusual, non-linear kinetics in semi-log scale, indicating a complex decay channel either involving multi-exponential relaxation or exciton-exciton annihilations. Runge-Kutta integration of Eq. 5 seems to confirm the latter assumption with satisfactory reproduction of the observed decays. The lifetimes and annihilation rates are Tct = 9.3 ns, ta = 13.5 ns, 7ct o = 650 ps-1 and 7 0 = 241 ps-1, for opal CT and opal A, respectively. 

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