Substrate kinetic model

A kinetic model originally derived by Nyholm is distinguished from Monod s model by the fate of a hmiting substrate. Instead of immediate metabolism, the substrate in Nyholm s model is sequestered. The governing equations are ... 

Table 8.1 presents the results of the ICR retention time studies, sugar concentration (dual substrate) studies and cell density. The kinetic model for ICR was derived on the basis of a first order reaction, plug flow and steady-state behaviour. 

The corresponding reactions of transient Co(OEP)H with alkyl halides and epoxides in DMF has been proposed to proceed by an ionic rather than a radical mechanism, with loss of from Co(OEP)H to give [Co(TAP), and products arising from nucleophilic attack on the substrates. " " Overall, a general kinetic model for the reaction of cobalt porphyrins with alkenes under free radical conditions has been developed." Cobalt porphyrin hydride complexes are also important as intermediates in the cobalt porphyrin-catalyzed chain transfer polymerization of alkenes (see below). 

Although the major manifold is neglected dne to high enantioselectivity, the intermediate in the major manifold formed from the coordination of the substrate with the active catalyst Xq should be included in the kinetic model. This is because this intermediate is the resting station for bulk of the catalyst but in a rapid exchange with Xi in the minor manifold The intermediates in the kinetic model and the relationship among the intermediates are expressed in Figure 3.2B. 

As a third example let us consider the growth kinetics in a chemostat used by Kalogerakis (1984) to evaluate sequential design procedures for model discrimination in dynamic systems. We consider the following four kinetic models for biomass growth and substrate utilization in the continuous baker s yeast fermentation. 

Although not all facets of the reactions in which complexes function as catalysts are fully understood, some of the processes are formulated in terms of a sequence of steps that represent well-known reactions. The actual process may not be identical with the collection of proposed steps, but the steps represent chemistry that is well understood. It is interesting to note that developing kinetic models for reactions of substances that are adsorbed on the surface of a solid catalyst leads to rate laws that have exactly the same form as those that describe reactions of substrates bound to enzymes. In a very general way, some of the catalytic processes involving coordination compounds require the reactant(s) to be bound to the metal by coordinate bonds, so there is some similarity in kinetic behavior of all of these processes. Before the catalytic processes are considered, we will describe some of the types of reactions that constitute the individual steps of the reaction sequences. 

Liquid-liquid multiphasic catalysis with the catalyst present in the ionic liquid phase relies on the transfer of organic substrates into the ionic liquid or reactions must occur at the phase boundary. One important parameter for the development of kinetic models (which are crucial for up-scaling and proper economic evaluation) is the location of the reaction. Does the reaction take place in the bulk of the liquid, in the diffusion layer or immediately at the surface of the ionic liquid droplets ... 

We might take a purist s approach and attempt to use kinetic theory to describe the dissolution and precipitation of each mineral that might appear in the calculation. Such an approach, although appealing and conceptually correct, is seldom practical. The database required to support the calculation would have to include rate laws for every possible reaction mechanism for each of perhaps hundreds of minerals. Even unstable minerals that can be neglected in equilibrium models would have to be included in the database, since they might well form in a kinetic model (see Section 26.4, Ostwald s Step Rule). If we are to allow new minerals to form, furthermore, it will be necessary to describe how quickly each mineral can nucleate on each possible substrate. 

The autoxidation of 3,5-di-terf-butylcatechol (H2DTBC) was frequently used to test the catalytic activity of various metal complexes. Speier studied the reaction with [Cu(PY)Cl] (PY = pyridine) in CH2C12 and CHCI3, and reported second-, first- and zeroth-order dependence with respect to Cu(I), 02 and substrate concentrations, respectively (41). The results are consistent with a kinetic model in which the rate determining oxidation of Cu(I) is followed by fast reduction of Cu(II) by H2DTBC. 

The catalytic activities of Cu(II), Co(II) and Mn(II) are considerably enhanced by sodium dodecyl sulfate (SDS) in the autoxidation of H2DTBC (51). The maximum catalytic activity was found in the CMC region. It was assumed that the micelles incorporate the catalysts and the short metal-metal distances increase the activity in accordance with the kinetic model discussed above. The concentration of the micelles increases at higher SDS concentrations. Thus, the concentrations of the catalyst and the substrate decrease in the micellar region and, as a consequence, the catalytic reaction becomes slower again. 

The reaction with CoII(ACAC)2 was studied in more detail and the rate law was established. The reaction was found to be first-order with respect to the substrate and the catalyst concentrations, and the partial pressure of 02. The corresponding kinetic model postulates reversible formation of a H2DTBC-Con(ACAC)2 02 adduct which undergoes redox decomposition in the rate-determining step. Hydrogen peroxide is also a primary... 

The presence of ascorbic acid as a co-substrate enhanced the rate of the Ru(EDTA)-catalyzed autoxidation in the order cyclohexane < cyclohexanol < cyclohexene (148). The reactions were always first-order in [H2A]. It was concluded that these reactions occur via a Ru(EDTA)(H2A)(S)(02) adduct, in which ascorbic acid promotes the cleavage of the 02 unit and, as a consequence, O-transfer to the substrate. While the model seems to be consistent with the experimental observations, it leaves open some very intriguing questions. According to earlier results from the same laboratory (24,25), the Ru(EDTA) catalyzed autoxidation of ascorbic acid occurs at a comparable or even a faster rate than the reactions listed in Table III. It follows, that the interference from this side reaction should not be neglected in the detailed kinetic model, in particular because ascorbic acid may be completely consumed before the oxidation of the other substrate takes place. 

However, in some situations, it can be assumed that the particulate substrate is completely covered with bacteria that excrete the exoenzymes. As it is assumed that enzymes are excessively present, the hydrolysis rate is constant per unit area available for hydrolysis, i.e., a surface-based kinetics model ... 

The next step in formulating a kinetic model is to express the stoichiometric and regulatory interactions in quantitative terms. The dynamics of metabolic networks are predominated by the activity of enzymes proteins that have evolved to catalyze specific biochemical transformations. The activity and specificity of all enzymes determine the specific paths in which metabolites are broken down and utilized within a cell or compartment. Note that enzymes do not affect the position of equilibrium between substrates and products, rather they operate by lowering the activation energy that would otherwise prevent the reaction to proceed at a reasonable rate. 

In addition to bistability and hysteresis, the minimal model of glycolysis also allows nonstationary solutions. Indeed, as noted above, one of the main rationales for the construction of kinetic models of yeast glycolysis is to account for metabolic oscillations observed experimentally for several decades [297, 305] and probably the model system for metabolic rhythms. In the minimal model considered here, oscillations arise due to the inhibition of the first reaction by its substrate ATP (a negative feedback). Figure 24 shows the time courses of oscillatory solutions for the minimal model of glycolysis. Note that for a large... 

The dependence (1 TP of v, on ATP is modeled as in the previous section, using an interval C [—00,1] that reflects the dual role of the cofactor ATP as substrate and as inhibitor of the reaction. All other reactions are assumed to follow Michaelis Menten kinetics with ()rs E [0, 1], No further assumption about the detailed functional form of the rate equations is necessary. Given the stoichiometry, the metabolic state and the matrix of saturation parameter, the structural kinetic model is fully defined. An explicit implementation of the model is provided in Ref. [84],... 

To investigate these two questions, a parametric model of the Jacobian of human erythrocytes was constructed, based on the earlier explicit kinetic model of Schuster and Holzhiitter [119]. The model consists of 30 metabolites and 31 reactions, thus representing a metabolic network of reasonable complexity. Parameters and intervals were defined as described in Section VIII, with approximately 90 saturation parameters encoding the (unknown) dependencies on substrates and products and 10 additional saturation parameters encoding the (unknown) allosteric regulation. The metabolic state is described by the concentration and fluxes given in Ref. [119] for standard conditions and is consistent with thermodynamic constraints. 

The rate constants for micelle-catalyzed reactions, when plotted against surfactant concentration, yield approximately sigmoid-shaped curves. The kinetic model commonly used quantitatively to describe the relationship of rate constant to surfactant, D, concentration assumes that micelles, D , form a noncovalent complex (4a) with substrate, S, before catalysis may take place (Menger and Portnoy, 1967 Cordes and Dunlap, 1969). An alternative model... 

Continuous operation In flow-type reactors, e.g., loop reactors, the space velocity of the reaction is determined through the installed static mixing device that is used to generate the dispersion, together with the velocity of the circiflating medium (catalyst- and substrate/product phase). Knowledge of these parameters allows one to set up a kinetic model for the investigated reaction. 

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