Apparent kinetic parameters

Table 5.1 presents the intrinsic kinetic parameters (Km and Vln lx) for the free lipase system and apparent kinetic parameters (K and V ) for the immobilised lipase in the EMR using fixed 2g-l 1 lipase concentration. The immobilised lipase showed higher maximum apparent reaction rate and greater enzyme-substrate (ES) affinity compared with free lipase. 

The decomposition of dolomite shows many points of similarity with the reactions of calcite and of other single carbonates of Group IIA metals (Sects. 3.1.1 and 3.1.2) the reaction is reversible, occurs at an interface, and both apparent kinetic parameters and reactivity are influenced by the prevailing C02 pressure. 

The apparent kinetic parameters are expressed as the summation of the terms corresponding to amorphous and crystalline fractions. 

J. Yang, R. Mirand and C. Roy, Using the DTG cnrve fitting method to determine the apparent kinetic parameters of thermal decomposition of polymers. Polymer Degradation and Stability, 73, 455-461 (2001). 

Two apparent kinetic parameters are usually introduced, namely the apparent standard rate constant k% sX the equilibrium potential E = E defined by Eq. (23) and the apparent charge transfer coefficient a (cf. Eq. (24)) ... 

ABSTRACT Experimental results frombirchwood and pinewood pyrolysis in a new single particle reactor are presented. Apparent kinetic parameters for the mass-loss of wood particles (5-800 mg) at tenyeratures from 300 to 860 C are determined. Kinetic parameters for the evolution of CO, COj, H O, Hj and CH4 are also established. The drying process was examined and it was found that drying and pyrolysis increasingly overlap in time as temperature rises and that the overlap is substantial above 4S0 C. 

Apparent kinetic parameters have been obtained for mass-loss and noncondensable gas evolution. The activation energy, above an ambient temperature of 370 "C, was found to be about 30 kJmol under the present circumstances. The activation energy for the imss-loss below 370 C agrees with those found in the literature for the kinetics of the main wood constituents. 

In this paper, the cracking of n-hexane, n-dodecane and n-hexadecane on ZSM-5 zeolites at about atmosphere and temperatures of 260-400°C were studied. The results showed that both mono-molecular cracking and bimolecular reaction (disproportionation) for n-hexane cracking took place. A network for initial reactions was proposed, and the apparent kinetic parameters of the reactions were estimated. An examination for the factors affecting the product destribu-tion of n-hexadecane indicated that hydrogen transfer on the surface of HZSM-5 zeolites plays an important role in cracking reaction. 

A recent detailed study of the kinetic mechanism of the E. coli enzyme using steady-state kinetics and ITC shows that the enzyme has a random bi-bi mechanism in which a ternary complex of enzyme, ATP, and phosphopantetheine are formed. The following apparent kinetic parameters for the forward reaction were determined 220 10 pmoll and cat 1.59 0.01 s (for ATP), and 4.7 0.5 pmolP and ifcat... 

Figure 24. Apparent kinetic parameters obtained as a function of pipette radius for ET between TCNQ and the EDTA complex of Fe(II). (Reprinted with permission from Ref. 179 copyright 2006, American Chemical Society.)...

The biocatalysts obtained were evaluated with respect to the composition, morphology, activity and stability of the immobilised enzyme in the starch hydrolysis reaction. In general, two alternative methods can be used, considering the bioartificial matrix as a substrate for the enzyme (this method is used for example to drive drug release into erosion control devices), or alternatively, as in the case of this work, after blending the enzyme with a polymer, and investigating its activity against an external substrate. The apparent kinetic parameters of the reaction catalyzed by the immobilised and native enzymes were determined and compared. 

Table I. Molecular weight of PBA by the polymerization of cyclic oligomer and apparent kinetic parameters for ring-opening reaction.

Cyclic oligomer Apparent kinetic parameters of lipase CA for ring-opening reaction A4 of the polymer produced by the ring-opening polymerization... 

The experiments described above produce accurate decay constants only when sir is negligible. The apparent kinetic parameters that are obtained when this is not the case involve all of the k and W values simultaneously. It is not possible under these circumstances to obtain the actual decay constants from these experiments. Experimental methods have been developed, however, that allow extraction of the individual k and W values in the presence of slr. One method applies to the regime where sir is dominant, that is, W > k, whereas the other is applicable when W < k. The latter method has been applied to biopolymer ODMR and involves deconvolution of phosphorescence decays measured during continuous microwave saturation of pairs of triplet sublevels. Microwave saturation creates a pseudo-two-level system whose decays are easily deconvoluted and are amenable to analysis. The analytical development of the microwave-saturated phosphorescence decay method is rather lengthy, so it is not discussed in this chapter. Detailed descriptions of the method may be found elsewhere. 

Table 1 [53] shows the apparent kinetic parameters of HK in three kinds of reversed micellar solutions based on concentrations of substrates in the water pools and in the aqueous bulk solution. The apparent V aax in the AOT, HTAC, and C Eg reversed micelles, and in the aqueous bulk solution increased in that order. HK may become fairly denatured in the AOT and HTAC reversed micelles because the ionic surfactants in the aqueous bulk solution are usually known as strong denaturants for protein. 

TABLE 1 Apparent Kinetic Parameters of HK in Three Kinds of Reversed Micellar Solution... 

The kinetic study for the reaction outlined in Scheme 3.17 has demonstrated that the isomerization from cis to trans is signihcantly retarded hy the addition of a small amount of PPhs, implying prior dissociation of the coordinated PPhs, but the rate constant reaches a constant value at a certain concentration of PPhs, suggesting involvement of a concomitant process independent of PPha concentration. Although this isomerization proceeds via several different routes, Eyring plot of the total isomerization rate constants gives apparent kinetic parameters with negative entropy of activation = —21 J mol ), in which a mecha-... 

Table 3.4 Values of Apparent Kinetic Parameters for Different Kinetic Models...

Once the mechanism of inhibition has been identified, expressions for the apparent kinetic parameters for each mechanism of inhibition are obtained from Eq. 3.41 and Table 3.2, as indicated in Table 3.4. Their values are experimentally determined from the intercepts of the double reciprocal plots, as shown in Fig. 3.5 and then, by using secondary linear plots, the corresponding kinetic constants can be determined as shown in Fig. 3.6. 

By plotting 1/v versus 1/a at constant b (columns in Table 3.6) values of apparent kinetic parameters Vap and Kap are obtained from the intercepts in the Y and X-axis respectively, as shown in Fig. 3.8 for ordered (I) and random (II) mechanisms. By plotting 1/v versus 1/b at constant a (rows in Table 3.6) values of apparent kinetic parameters Vap and Kap are obtained from the intercepts in the Y and X-axis respectively, as shown in Fig. 3.8 for ordered (I) and random (II) mechanisms. Ordered sequential mechanism can be easily distinguished from random sequential in Lineweaver-Burke plots in the case of ordered mechanism, intercept in the Y-axis (1/Vap ) is a constant (1/V) independent of a (the substrate who binds to the enzyme first), while in the case or random mechanism it depends on a (see Table 3.5). 

Ishikawa H, Tanaka T, Kuro K et al. (1987) Evaluation of tme kinetic parameters for reversible immobihzed enzyme reactions. Biotechnol Bioeng 29 924-933 Jeison D, Ruiz G, Acevedo F et al. (2003) Simulation of the effect of intrinsic reaction kinetics and particle size on the behavior of immobihzed enzymes under internal diffusional restrictions and steady state operation. Proc Biochem 39(3) 393-399 Katchalski-Katzir E, Kraemer DM (2000) Eupergit C, a carrier for immobDization of enzymes of industrial potential. J Mol Catal B Enzym 10 157-176 Kheirolomoom A, Khorasheh F, Fazehnia H (2002) Influence of external mass transfer limitation on apparent kinetic parameters of peniciUin G acylase immobihzed on nonporous ultrafine silica particles. J Biosci Bioeng 93 125-129... 

If it is known that this hypothesis is an oversimpMfication, then why is it made so often Mostly, because the additional effort required to integrate micro-, meso- and macroscale phenomena in a single model does not necessarily lead to better quantitative predictions when it comes to industrial reactors. Uncertainties on model parameter values are, most often, too high to try to decouple true polymerization kinetic parameters from mass and heat transfer effects often apparent kinetic parameters will do an equally good job from an engineering perspective [86]. 

Table 7. Apparent Kinetic Parameters of Isocyanurate and Oxazolidone Formation Derived by Analysis of DSC Peak Areas... 

Here, and Cp are sets of reactant and product concentrations ki are apparent kinetic parameters of the steady-state kinetic description, ki (= kjk ) are modified kinetic parameters, and pii is a positive integer. The numerator in these equations is often referred to as the driving force, while the denominator may he termed the kinetic resistance. ... 

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