Determination of Metabolic Rates and Enzyme Kinetics

Kinetics is the branch of science concerned with the rates of chemical reactions. The study of enzyme kinetics addresses the biological roles of enzymatic catalysts and how they accomplish their remarkable feats. In enzyme kinetics, we seek to determine the maximum reaction velocity that the enzyme can attain and its binding affinities for substrates and inhibitors. Coupled with studies on the structure and chemistry of the enzyme, analysis of the enzymatic rate under different reaction conditions yields insights regarding the enzyme s mechanism of catalytic action. Such information is essential to an overall understanding of metabolism. 

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. 

Predictive models can be better produced when recombinant cytochrome data are available, an experimental technique which may increase the probability of obtaining consistent and predictive models, since one protein is involved in the metabolic reaction. The most accurate data to describe the rate and affinity of the ligand towards an enzyme are the kinetic parameters Vmax and Km. Nevertheless, the calculation of these parameters is time consuming. A less precise parameter is the determination of the compound percentage remaining in a cytochrome incubation after a certain period of time. These metabolic data are less accurate and can only be used to classify the compounds in a metabolic system as stable or unstable. This type of data was the basis for a predictive model of metabolic stability towards CYP3A4 [35]. 

For in vitro assays, it is extremely difficult to determine the relevant intracellular concentrations of substrates due to compartmentalization of particular reactions, competing reactions that produce and consume common substrates, and metabolic channeling (Albe et al, 1990 Srere, 1987). Consequently, in vitro kinetic measurements may not be very useful for assessing in situ or in vivo reaction rates. However, provided assays conditions are carefully controlled, kinetic parameters may be very useful for characterizing enzyme isoforms and enzymes from different metabolic pools, different organisms, or from organisms collected from different environments. 

Figure 30.6 shows a prediction of the plasma concentration of ARA-C and total radioactivity (ARA-C plus ARA-U) following administration of two separate bolus intravenous injections of 1.2 mg/kg to a 70-kg woman. All compartment sizes and blood flow rates were estimated a -priori, and all enzyme kinetic parameters were determined from published in vitro studies. None of the parameters was selected specifically for this patient only the dose per body weight was used in the simulation. The prediction has the correct general shape and magnitude. It can be made quantitative by relatively minor changes in model parameters with no requirement to adjust the parameters describing metabolism. 

When ascorbate acts as an antioxidant or enzyme cofactor, it becomes oxidized to DHAA. Ascorbate and DHAA possess roughly equivalent bioavailability. Bioavailability is determined by the rates of absorption, distribution, and metabolism within the body, and by excretion. Ascorbate and DHAA are absorbed along the entire length of the human intestine (Malo and Wilson, 2000). For both the DHAA and ascorbate transport systems, initial rates of uptake saturate with increasing external substrate concentration, reflecting high-affinity interactions that can be described by Michaelis-Menten kinetics. 

FIGURE 3.1 Basic principles of metabolism. The unit of metabolism is the chemical reaction, catalyzed by an enzyme (upper left). Each reaction can be studied individually in vitro to determine its mechanism and kinetics parameters. In a linear metabolic pathway (e.g., glycolysis), the reactions are coupied in series (lower left). The rate of the first reaction of the chain (A + B C) reaction is controlled by the fluxes of A and B. The flux through the whole metabolic pathway is determined by the rate of production of E. The same rules apply for a cyclic metabolic pathway such as Krebs cycle (right panel). 

They showed how varying the rate of equilibration of a reaction, by increasing the concentration of the relevant enzyme, allows the determination of the equilibriiun constant independently from the subsequent hydrolysis of the lactone to gluconic acid. They found that the latter reaction had a time constant of about 25 min at pH 6.4, but at pH above neutrality the increased rate required the use of stopped-flow techniques. Many other metabolic intermediates occur as different isomers, anomers and conformers (see for instance Rose, 1975 Middleford, Gupta Rose, 1976 Benkovic, 1979). In many cases kinetic techniques have to be used to determine which are the correct substrates and products before thermody-... 

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