Michaelis-Menten metabolism

Due to the Michaelis-Menten metabolism of phenytoin, alterations in its protein binding will result in increased severity of dose-related adverse effects. In patients with suspected changes in protein binding, it is useful to measure unbound phenytoin concentrations. 

When valproate protein binding is altered, the risk for severe dose-related adverse effects is much less compared to phenytoin. Michaelis-Menten metabolism is not a factor with valproate, so hepatic enzymes are able to efficiently metabolize the additional unbound portion. 

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 ... 

Nonhnear (Michaelis-Menten) metabolism is observed with the PHT doses that are used clinically. 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

Log-concave kinetics can be due to saturable Michaelis-Menten elimination depending on the maximal metabolism capacity (Umax) and the Michaelis constant (Km). 

Coe and Bessell and coworkers studied the metabolic fates of 2-deoxy-2-fluoro-D-glucose (2DFG) and related compounds by using yeast hexokinase (as a model for mammalian hexokinase), and determined the kinetic constants K and V ) of the Michaelis-Menten equation D-glucose 0.17 (K in mAf)> 1 00 (relative value, D-glucose taken as 1) 2DG 0.59 0.11, 0.85 2DFG 0.19 0.03, 0.50 2-deoxy-2-fluoro-D-mannose (2DFM) 0.41 0.05, 0.85 2-deoxy-2,2-difluoro-D-nraZ>//Jo-hexose... 

Sato et al. (1991) expanded their earlier PBPK model to account for differences in body weight, body fat content, and sex and applied it to predicting the effect of these factors on trichloroethylene metabolism and excretion. Their model consisted of seven compartments (lung, vessel rich tissue, vessel poor tissue, muscle, fat tissue, gastrointestinal system, and hepatic system) and made various assumptions about the metabolic pathways considered. First-order Michaelis-Menten kinetics were assumed for simplicity, and the first metabolic product was assumed to be chloral hydrate, which was then converted to TCA and trichloroethanol. Further assumptions were that metabolism was limited to the hepatic compartment and that tissue and organ volumes were related to body weight. The metabolic parameters, (the scaling constant for the maximum rate of metabolism) and (the Michaelis constant), were those determined for trichloroethylene in a study by Koizumi (1989) and are presented in Table 2-3. 

The first-order transfer and exit rate constants can be replaced by nonlinear terms dependent on the amount or concentration of drug in a particular compartment. For instance, saturable metabolism of drug in compartment 1 (the central compartment) would result in the Michaelis-Menten equation... 

Yu, XZ, Gu J-D (2006) Uptake, metabolism, and toxicity of methyl ter/-butyl ether (MTBE) in weeping willows. J Hardz Mat B137 1417-1423 Yu, XZ, Gu J-D (2007a) Differences in Michaelis-Menten kinetics for different cultivars of maize during cyanide removal. Ecotoxicol Environ Saf 67 254-259... 

Aiming at a computer-based description of cellular metabolism, we briefly summarize some characteristic rate equations associated with competitive and allosteric regulation. Starting with irreversible Michaelis Menten kinetics, the most common types of feedback inhibition are depicted in Fig. 9. Allowing all possible associations between the enzyme and the inhibitor shown in Fig. 9, the total enzyme concentration Er can be expressed as... 

Similar to Eq. (67), the first reaction (incorporating the enzyme phosphofructo-kinase) exhibits a Hill-type inhibition by its substrate ATP [126]. The overall ATP utilization v3 (ATP) is modeled by a saturable Michaelis Menten function. The system is specified by five kinetic parameters (with Gx lumped into Vm ), the Hill coefficient n, and the total concentration, 4 / = [ATP] + [ADP]. Note that the model is not intended to capture biological realism, rather it serves as a paradigmatic example to identify dynamic behavior in metabolic pathways. 

Most problems associated with approximate kinetics are avoided when Michaelis Menten-type rate equations are utilized. Though this choice sacrifices the possibility of analytical treatment, reversible Michaelis Menten-type equations are straightforwardly consistent with fundamental thermodynamic constraints, have intuitively interpretable parameters, are computationally no more demanding than logarithmic functions, and are well known to give an excellent account of biochemical kinetics. Consequently, Michaelis Menten-type kinetics are an obvious choice to translate large-scale metabolic networks into (approximate) dynamic models. It should also be emphasized that simplified Michaelis Menten kinetics are common in biochemical practice almost all rate equations discussed in Section III.C are simplified instances of more complicated rate functions. 

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],... 

For any arbitrary metabolic network, the Jacobian matrix can be decomposed into a sum of three fundamental contributions A term M eg that relates to allosteric regulation. A term M in that relates to the kinetic properties of the network, as specified by the dissociation and Michaelis Menten parameters. And, finally, a term that relates to the displacement from thermodynamic equilibrium. We briefly evaluate each contribution separately. 

Figure 40. A simple example Cellular metabolism is modeled as a linear chain of reactions, with long range interactions mimicking the cellular environment and interactions within the metabolic network. The parameters are the number of metabolites m, the number of regulatory interactions, the probability p of positive versus negative interaction, as well as the maximal displacement ymax from equilibrium for each reaction. Each reaction is modeled as a reversible Michaelis Menten equation according to the methodology described in Section VIII.

The gas-uptake data for rats were well described using a single Michaelis-Menten equation to describe metabolism. For the mouse inhalation studies, a simple Michaelis-Menten equation failed to adequately describe the chloroform-metabolizing capacity based on the data collected and model constants. The authors suspected that, following the administration of chloroform (particularly at higher concentrations), destmction of microsomal enzymes and subsequent resynthesis of microsomal enzymes was important in the mouse. This phenomenon has been documented in phenobarbital-induced but not naive rats. To account for this phenomenon, a first-order rate constant for the loss and subsequent regeneration of metabolic capacity was incorporated into the model for mice only. 

Lion Biosciences is the supplier of the iDEA Metabolism software package as well as other ADME/T services (289). The iDEA software simulates metabolism and predicts a compound s metabolic behavior in humans. The Metabolism Module consists of a data expert module to perform data fitting and analysis of collected in vitro data and the physiological metabolism model. The physiological metabolism model is constructed from proprietary database of 64 clinically tested compounds. Additionally, the metabolism module automatically calculates the Michaelis-Menten constants Km and VjIiax for the kinetic analysis of metabolism turnover (289). 

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... 

The rate of butadiene metabolism in diverse cell fractions has been investigated in various species and is characterized by the Michaelis-Menten parameters and apparent Three methods have been used to determine these parameters ... 

Physiological toxicokinetic models have been presented describing the behaviour of inhaled butadiene in the human body. Partition coefficients for tissue air and tissue blood, respectively, had been measured directly using human tissue samples or were calculated based on theoretical considerations. Parameters of butadiene metabolism were obtained from in-vitro studies in human liver and lung cell constituents and by extrapolation of parameters from experiments with rats and mice in vivo (see above). In these models, metabolism of butadiene is assumed to follow Michaelis-Menten kinetics. 

Male Fischer 344/N rats were exposed via the nose only for 6 h to concentrations of vinylidene fluoride ranging from 27 to 16 000 ppm [71-42 000 mg/m. Tidal volume (mean, 1.51 mL/brcath) and respiratory frequency (mean, 132 breaths/min) were not influenced by exposure concentration. Steady-state blood levels of vinylidene fluoride increased linearly with increasing exposure concentration up to 16 000 ppm. Vinylidene fluoride tissue/air partition coefficients were determined experimentally to be 0.07, 0.18, 0.8,10, and 0.29 for water, blood, liver, fat and muscle, respectively. Previously published detenninations (Filser Bolt, 1979) for the maximum velocity of metabolism in mg/li/kg) and Michaelis Menten constant (K in mg/L) are 0.07 and 0.13, respectively. Time to reach steady-state blood levels of vinylidene fluoride was less than 15 min for all concentrations. After cessation of exposure, blood levels of vinylidene fluoride decreased to 10% of steady-state levels within 1 h. Simulation of the metabolism of vinylidene fluoride mdicated that although blood levels of vinylidene fluoride increased linearly with increasing exposure concentration, the amount of vinylidene fluoride metabolized per 6-h exposure period approached a maximum at about 2000 ppm [5240 mg/m vinylidene fluoride (Medinsky et al., 1988). 

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