Kinetic deconvolution

Possibly less obvious than the foregoing is a procedure we refer to as "kinetic deconvolution." We have examined this method carefully in the situation where heterogeneous charge transfer kinetics represent the kinetic problem. Other classes of "kinetic problems," such as coupled chemical reactions, also could be addressed by a more complicated procedure, but this has not yet been attempted. The... 

M Cd at DME-aqueous 1.0 M Na2S04 interface, 25 C peak admittance, 5 replicates. (B) l.OxlO" M Cr(CN)53-at HMDE-aqueous 1.0 M KCN interface, 25 C peak a it-tance, one pass. (C) 1.0 x 10"3 M pyrene at DME-0.1 M TBAP, acetonitrile interface, 25 C peak admittance, 2 replicates. (D) 1.0 x 10"3, IMPD" " at Pt-0.1 M TBAP, acetonitrile interface, 25 C crossover point admittance, one pass. Applied Same as Figure 27. Measured Same as Figure 27B. = raw data, a= kinetically deconvoluted data. 

In our hands it appears that the heterogeneous charge transfer kinetic deconvolution is completely successful in both aqueous and aprotic solvents with both Hg and Pt working electrodes. 

Kinetic deconvolution of spectral components was achieved using the matrix algebra procedure suggested by Rich et al. (4-6). 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

In the range of linearity, Eq. (29) correctly represents the heat transfer within the calorimeter. It should be possible, then, by means of this equation to achieve the deconvolution of the thermogram, i.e., knowing g(l) (the thermogram) and the parameters in Eq. (29), to define f(t) (the input). This is evidently the final objective of the analysis of the calorimeter data, since the determination of the input f(t) not only yields the total amount of heat produced, but also defines completely the kinetics of the thermal phenomenon under investigation. 

If the width of the excitation flash (nowadays typically from a pulsed LED or laser diode) is not shorter than approximately 1/3 of the fluorescence lifetime to be measured, signal deconvolution should be used to extract meaningful values from the kinetic data fit. 

An extensive mutagenesis protocol was used to probe the contribution of these observed changes in the STS fold towards cyclization specificity in CHS. Initially, an 18X mutant of alfalfa CHS was created to probe the mechanistic relevance of the structural differences observed in STS. Introduction of the pine STS primary sequence, consisting of 18 amino acid changes in areas 1-3, into alfalfa CHS results in an enzyme with similar kinetic efficiency to wild-type CHS. However, the mutant now produces resveratrol as the major product by using coumaroyl-CoA and malonyl-CoA in assays (Fig. 12.9B). Further deconvolution of the necessary... 

Proteins having one chromophore per molecule are the simplest and most convenient in studies of fluorescence decay kinetics as well as in other spectroscopic studies of proteins. These were historically the first proteins for which the tryptophan fluorescence decay was analyzed. It was natural to expect that, for these proteins at least, the decay curves would be singleexponential. However, a more complex time dependence of the emission was observed. To describe the experimental data for almost all of the proteins studied, it was necessary to use a set of two or more exponents.(2) The decay is single-exponential only in the case of apoazurin.(41) Several authors(41,42) explained the biexponentiality of the decay by the existence of two protein conformers in equilibrium. Such an explanation is difficult to accept without additional analysis, since there are many other mechanisms leading to nonexponential decay and in view of the fact that deconvolution into exponential components is no more than a formal procedure for treatment of nonexponential curves. 

Astonishingly, the study of the mechanism of formaldehyde loss from anisole revealed two different pathways for this process, one involving a four- and one a five-membered cyclic transition state (Fig. 6.37). [129] The four-membered transition state conserves aromaticity in the ionic product, which therefore has the lower heat of formation. Prompted by the observation of a composite metastable peak, this rather unusual behavior could be uncovered by deconvolution of two different values of kinetic energy release with the help of metastable peak shape analysis (Chap. 2.8). 

Any advanced absorbance/fluorescence spectrophotometer designed for routine acquistion of absorption or emission on the subsecond time scale. The basic goal is to obtain a series of complete UV/visible or fluorescence spectra as a function of time, usually after samples are mixed in a stopped-flow device. Such data help the investigator to infer the most likely structures of transient intermediates whose electronic spectra or fluorescence spectra can be determined by deconvoluting the spectra with appropriate reaction kinetic simulation software or by some other global analysis method (Fig. 1). 

The first two sections of Chapter 5 give a practical introduction to dynamic models and their numerical solution. In addition to some classical methods, an efficient procedure is presented for solving systems of stiff differential equations frequently encountered in chemistry and biology. Sensitivity analysis of dynamic models and their reduction based on quasy-steady-state approximation are discussed. The second central problem of this chapter is estimating parameters in ordinary differential equations. An efficient short-cut method designed specifically for PC s is presented and applied to parameter estimation, numerical deconvolution and input determination. Application examples concern enzyme kinetics and pharmacokinetic compartmental modelling. 

Another approach is to conduct competitive experiments with binary mixtures in which the complete reaction pathway is developed according to a reaction scheme like that of Scheme 1 described in the beginning of this review or like those shown in Figs. 12-15. Much of the confusion found in past reports of the kinetics of dibenzothiophene and its alkylated derivatives has come from incomplete deconvolution of the reaction network. Selectivity is often reported as the ratio of the yields of biphenyls (direct sulfur extraction) to the yields of cyclohexylbenzenes (hydrogenative route). As discussed in Section IV, cyclohexylbenzenes are produced via two different routes and, unfortunately, even low-conversion studies do not circumvent this confusion. To illustrate how conclusions can often be confused if the wrong model is used, some examples of reported competitive inhibition experiments will be discussed. 

Although the simple rate expressions, Eqs. (2-6) and (2-9), may serve as first approximations they are inadequate for the complete description of the kinetics of many epoxy resin curing reactions. Complex parallel or sequential reactions requiring more than one rate constant may be involved. For example these reactions are often auto-catalytic in nature and the rate may become diffusion-controlled as the viscosity of the system increases. If processes of differing heat of reaction are involved, then the deconvolution of the DSC data is difficult and may require information from other analytical techniques. Some approaches to the interpretation of data using more complex kinetic models are discussed in Chapter 4. 

Deconvolution. When the luminescence lifetime is close to the laser pulse duration, the kinetics can still be obtained by a process known as deconvolution, so long as the luminescence decay is exponential. The deconvolution program is a computer simulation of the shape of the laser pulse modified for various luminescence lifetimes. An example is given in Figure 7.33. The kinetics of fluorescence decay could not be resolved directly, but it is clear that the emission pulse shape differs from the laser pulse shape... 

Furthermore, the short scan times of EPR (usually 500 ms or less) and the ability to measure species in diamagnetic matrices, for example, aqueous solutions, enable the time-resolved monitoring of chemical reactions involving radical reactants or intermediates. In this way, kinetics of such reactions can be studied even if multiple magnetic species are involved, as their characteristic signals typically differ sufficiently to deconvolute the resulting EPR spectra. Commercial pulsed EPR spectrometers are also available, enabling the study of spin dynamics, that is, the relaxation of the excited system via spin-spin and spin-lattice mechanisms. 

These kinetics studies required development of reproducible criteria of subtraction of foe H-O-H bending band of water, which completely overlaps foe Amide I (1650 cm 1) and Amide II (1550 cm"1) bands (98). In addition, correction of foe kinetic spectra of adsorbed protein layers for foe presence of "bulk" unadsorbed protein was described (99). Examination of kinetic spectra from an experiment involving a mixture of fibrinogen and albumin showed that a stable protein layer was formed on foe IRE surface, based on foe intensity of the Amide II band. Subsequent replacement of adsorbed albumin by fibrinogen followed, as monitored by foe intensity ratio of bands near 1300 cm"1 (albumin) and 1250 cm"1 (fibrinogen) (93). In addition to foe total amount of protein present at an interface, foe possible perturbation of foe secondary structure of foe protein upon adsorption is of interest. Deconvolution of foe broad Amide I,II, and m bands can provide information about foe relative amounts of a helices and f) sheet contents of aqueous protein solutions. Perturbation of foe secondary structures of several well characterized proteins were correlated with foe changes in foe deconvoluted spectra. Combining information from foe Amide I and m (1250 cm"1) bands is necessary for evaluation of protein secondary structure in solution (100). 

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