Michaelis-Menten metabolic process

The amount of verapamil presented to the liver, and its effective concentration in the region of the hepatic er zymes soon after oral dosing, are related to the rate at which verapamO is absorbed from the gastrointestinal tract into the portal vein and to the flow rate of blood in the portal vein to the liver. For instance, by hypothesizing a Michaelis-Menten metabolic process, when the absorption rate is slow and concentrations in the portal vein and liver are low, the hepatic metabolism of both enantiomers will be approximately first-order. Under these conditions, the K S ratio of the umnetabolized enantiomers leaving the liver will be closely related to the ratio of the Michaelis-Menten saturation constants (K ) for the enantiomers. The observed more rapid metabolism of S-verapamil than R-verapamil (i.e., S-verapamil has the lower systemic concentrations) is consistent with the lower reported for S-verapamil (16). 

With more involved compartmental models, including, for example, Michaelis-Menten elimination kinetics, the model may be described more easily using differential equations. Thus, for a drug eliminated by a first-order excretion process and a Michaelis-Menten metabolic process, Eq. (4) holds ... 

This is known as Michaelis-Menten or saturation kinetics. The processes that involve specific interactions between chemicals and proteins such as plasma protein binding, active excretion from the kidney or liver via transporters, and metabolism catalyzed by enzymes can be saturated. This is because there are a specific number of binding sites that can be fully occupied at higher doses. In some cases, cofactors are required, and their concentration may be limiting (see chap. 7 for salicylate, paracetamol toxicity). These all lead to an increase in the free concentration of the chemical. Some drugs, such as phenytoin, exhibit saturation of metabolism and therefore nonlinear kinetics at therapeutic doses. Alcohol metabolism is also saturated at even normal levels of intake. Under these circumstances, the rate of... 

However, active uptake mechanisms have now been found in some bacteria for various xenobiotic organic anions. These include 4-chlorobenzoate (Groenewegen et al., 1990), 4-toluene sulfonate (Locher et al., 1993), 2,4-D (Leveau et al., 1998), mecoprop and dichlorprop (Zipper et al., 1998), and even aminopolycarboxylates (Egli, 2001). Such active uptake appears to be driven by the proton motive force (i.e., accumulation of protons in bacterial cytoplasm). These transport mechanisms exhibit saturation kinetics (e.g., Zipper et al., 1998), and so their quantitative treatment is the same as other enzyme-limited metabolic processes (discussed below as Michaelis-Menten cases). 

The factors that affect hepatic clearance include blood flow to the liver (Q), the fraction of drug not bound to plasma proteins (fu), and intrinsic clearance (CGjjf) (1, 2). Intrinsic clearance is simply the hepatic clearance that would be observed in the absence of blood flow and protein binding restrictions. As discussed in Chapter 2, hepatic clearance usually can be considered to be a first-order process. In those cases, intrinsic clearance represents the ratio of Vmax l m, and this relationship has been used as the basis for correlating in vitro studies of drug metabolism with in vivo results (3). However, for phenytoin and several other drugs, the Michaelis-Menten equation is needed to characterize intrinsic clearance. 

All metabolic processes are saturable at a certain concentration of the substrate/drug. Thus, rate of elimination of the drug by metabolism as described by Eq. (5) can also be described by a Michaelis-Menten equation ... 

The rate of the enzymatic process to metabolize a drug can be estunated using the Michaelis-Menten equation... 

The kinetics described so far have been based on first-order processes, yet often in toxicology, the situation after large doses are administered has to be considered when such processes do not apply. This situation may arise when excretion or metabolism is saturated and hence the rate of elimination decreases. This is known as Michaelis-Menten or saturation kinetics. Excretion by active transport (see below) and enzyme-mediated metabolism are saturable processes. In some cases cofactors are required and their concentration may be limiting (see Chapter 7, salicylate poisoning). When the concentration of foreign compound in the relevant tissue is lower than the km then linear, first-order... 

Nearly all enzymes follow what is known as Michaelis-Menten kinetics, which was encountered in Section 10.2.2 for carrier-mediated transport processes. The Michaelis-Menten equation for the rate of metabolism f mei) c.an be written as... 

Hydrolysis and fermentation models were developed using two hydrolysis datasets and two SSF datasets and by using modified Michaelis-Menten and Monod-type kinetics. Validation experiments made to represent typical kitchen waste correlated well with both models. The models were generated in Matlab Simulink and represent a simple method for implementing ODE system solvers and parameter estimation tools. These types of visual dynamic models may be useful for applying kinetic or linear-based metabolic engineering of bioconversion processes in the future. 

Compartmental models are not confined to linear systems. It is relatively easy to include nonlinear processes snch as satnrable metabolism or protein binding. For example, for some drngs one or more metabolism processes may follow Michae-lis-Menten kinetics, shown in Eqnation 12.20. Elimination is described in Equation 12.20 with a nonlinear metabolism process with the parameters V (maximum velocity) and (Michaelis constant). 

One apparent difference between drug discovery and development is the level of comprehension. Speed dictates the early discovery process, while in-depth understanding, which requires the synthetic standards of metabolites and/or the radiolabeled drug candidates, is emphasized in later discovery and particularly development. Therefore, metabolic stability is studied in the context of enzyme kinetics, that is, the determination of Am and Wnax, in later discovery and development. These parameters are derived from the Michaelis-Menten kinetics, and thus may not be directly applicable to atypical enzyme kinetics. 

Pharmacokinetic models describe the biological processes of absorption, distribution, metabolism, and excretion of exogenous compounds. With the exception of absorption into and across the skin, absorption, distribution, metabolism, and elimination are essential processes that also occur with nutrients and endogenous compounds. Many of these processes can become nonlinear with increasingly higher exposure concentrations. Pulmonary absorption can be limited by respiratory rates. Metabolism can often show Michaelis-Menten or saturable kinetics. Distribution can be limited by the affinity of the chemical for a specific tissue or by blood flow. 

Capacity-limited metabolism is also called saturable metabolism, Michaelis-Menten kinetics or mixed-order kinetics. The process of enzymatic metabolism of drugs may be explained by the relationship depicted below... 

Michaelis-Menten kinetics is often used to describe an enzymatic process and can be described mathematically by Eq. (6) [rate = ymaxC/(7r i- -C)]. In this case, C is the drug concentration in plasma, Fmax indicates the total amount of metabolizing enzyme, K n is the Michaelis constant, and l/K is a measure of the affinity between the drug and the enzyme. If C K a, Eq. (6) reduces to ... 

Fig. 8.5 Comparison between (a) the usual representations of catalysis and autocatalysis and (b) a more general version resulting from considering the cyclic architecture of reaction networks. The usual representation of enzyme catalysis deduced from Michaelis-Menten kinetics with two non-covalently bound complexes C S and C P fits the general description of a cycle by including the three states of the enzyme (free, bound to substrate, and bound to product). Genuine autocatalysis in its simplest version without covalent intermediate (up right) may be much more demanding than network autocatalysis because efficient autocatalysis requires that strong transient non-covalent interactions are present at the transition state whereas the reactant and product are stable in a monomer state. Moreover, the possibility that products or intermediates of downstream processes could be identical to intermediates of the metabolic cycle (M to M ) is statistically intaeased...

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