Multiexponential decays

Time Resolved Fluorescence Depolarization. In Equation 3, it is assumed that the polarization decays to zero as a single exponential function, which is equivalent to assuming that the molecular shape is spherical with isotropic rotational motion. Multiexponential decays arise from anisotropic rotational motion, which might indicate a nonspherical molecule, a molecule rotating in a nonuniform environment, a fluorophore bound to tbe molecule in a manner that binders its motion, or a mixture of fluorophores with different rotational rates. 

If the signal decay is a single-exponential curve, equations 16 and 17 result in values for X that are in agreement with each other. Dissimilar values indicate multiexponential decay, which usually means that the sample contains more than one fluorophore. Multiexponential decay can be resolved by using a phase fluorometer with phase sensitive detection. A time-independent, direct-current signal is produced that is proportional to the cosine of the difference between the phase angle of the detector ( D) and the phase angle of the fluorescence ( ) ... 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

Recently, Raluca Niesner et al. [14] have published a report in which they developed a noniterative method of fitting multiexponential decays which does not discard information and is nonre-strictive, thereby eliminating the difficulties with excess time being taken by computationally expensive iterative fitting routines. 

From the kinetic point of view SPR experiments have the advantage that both the association and dissociation processes can be measured from the two phases in one sensogram. However, it is possible for artifacts to arise from refractive index mismatch during the buffer change and, for this reason, in general the initial parts of the association and dissociation phases are excluded from the kinetic analysis.73 When multiexponential decays are observed it is important to distinguish between kinetics related to the chemistry and potential artifacts, such as conformational changes of the bound reactant or effects due to mass transport limitations.73,75 The upper limit of detectable association rate constants has been estimated to be on the order of... 

The multiexponential decay law of the emission from a mixture of fluorophores can be recovered from phase and modulation measurements over a range of multiple frequencies by... 

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... 

In the second region, relatively far from the particle, the refocusing pulses are effective, which corresponds to a weak magnetization condition. The relaxation rate can then be analyzed following Majumdar and Gore 26). The result of this calculation is in remarkable agreement with the slow rates, obtained from simulated multiexponential decays 27) ... 

In kinetic analysis of complex reactions, 210, 382 fluorescence decay rate distributions, 210, 357 implementation in Laplace de-convolution noniterative method, 210, 293 in multiexponential decays, 210, 296 partial global analysis by simulated annealing methods, 210, 365 spectral resolution, 210, 299. 

There have been major advances in the development of both methods in recent years and fluorescence lifetime measurements on the picosecond time scale are now quite feasible. Precise analysis of the fluorescence decay revealed that even in the case of a peptide containing a single fluorophore multiexponential decay rather than single-exponential decay is often observed, as described by eq 5... 

Caspar et al. have also observed multiexponential decay for naphthalene triplets in M + -X (M = K, Rb, and Cs) zeolites [238,239]. Interestingly at... 

Figure 11. Fluorescence transients of 7-(dimethylamino)couinarin-4-acetate ion in water recorded at 445 nm (upper), 483 nm (middle), and 509 nm (lower). The solid line through the points is a fit of the data to a multiexponential decay. The peak near zero time in the upper panel is instrument response function (280 fs fwhm). From Ref. 33 with permission, from J. Phys. Chem. 93, 7040 (1988). Copyright 1988, American Chemical Society.

If several nuclei could be observed in high-resolution NMR techniques to monitor similarities or differences in both chemical shifts or integrals, other parameters can be monitored by using LF 1H NMR. In this case, relaxation parameters are usually measured as intrinsic discriminating values. As pointed out in several studies, T2 relaxation decay has a multiexponential decay in both muscles and fish tissues. This suggests the presence of different "pools" in tissues and water distribution was assumed to be present in three distinct compartments, namely (a) "bound water," (b) "entrapped water," and (c) "free water." In those three pools, water acts with different relaxation times because it can be bound to proteins, involved in the conversion of muscle to meat and entrapped by weak surface forces, showing relaxation values in the range of 1-10,10-100, and 100-400 ms, respectively. 

This situation is illustrated in Fig. 11, where the relative statistical weights and, hence, the amplitudes contributing to the multiexponential decays, are plotted as a function of M. The curves are arbitrarily normalized to unity at M = 105 g/mol. The strong underestimation of components with low molar mass in PCS is obvious. The shaded area is accessible to TDFRS, and the two limiting cases correspond to short and long exposure times. 

The dilatational rheology of the poly(vinylacetate) monolayer onto an aqueous subphase has been studied between 1°C and 25°C by Monroy et al. [59], These authors have used the combination of several techniques. By this way, the exploration of a broad frequency range was possible. The relaxation experiments have shown multiexponential decay curves, whose complexity increases with decreasing the temperature. A regularization technique has been used to obtain the relaxation spectra from the relaxation curves and the dilatational viscoelastic parameters have been calculated from the spectra. The shapes of the relaxation spectra agree with the predictions of the theoretical model proposed by Noskov [100],... 

Complementary nanosecond experiments ratify the photosensitization of the triplet features in 5 and 6 (Fig. 8.15). In the absence of molecular oxygen multiexponential decay kinetics point to a fairly complex deactivation scheme. 

Often, experimentally measured fluorescence decays do not follow the simple single-exponential form predicted by Pquation 2. In many cases, the fluorescence decays are better described by a multiexponential decay ... 

Even proteins that contain only a single Trp residue generally exhibit multiexponential decays. Several hypotheses have been proposed to explain why. Pirst, multiple conformational states may exist for the single Trp such as different rotameric configurations (orientations about the Trp xi or X2 C-C bond) (18). Even in the absence of mnltiple rotamers, the electron-transfer qnenching rate is extremely sensitive to the local environment, so a distribntion of local microconformational states may cause a nonexponential flnorescence decay. Other possible sonrces of nonexponential flnorescence decay inclnde the response of the protein and surronnding solvent to the change in dipole moment of Trp on excitation ( solvation ) (19). 

Even in proteins containing a sin e tryptophan residue, multiexponential decay kinetics have been observed suggesting mobility of the protein structure during emission . However, recent time-resolved fluorescence studies of the tryptophan zwitterion and tryptophan peptides indicate that this fluorc hore does not decay... 

After encoding of the we observe two regimes of relaxation. an initial, very rapid decay, occurring just after stopping of the seeding process, and the second, much slower, multiexponential decay, comparable to the decay observed in polymers poled by the corona poling method. Orientation losses vary from 10% to 20% after 15 hours in the dark at ambient temperature. 

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