Michaelis-Menten kinetics modeling

The Michaelis-Menten kinetic model explains several aspects of the behavior of many enzymes. Each enzyme has a Km value characteristic of that enzyme under specified conditions. 

There has been a substantial effort to model the kinetics of enzymatic hydrolysis of cellulose and (pretreated) lignocellulosic substrates. Bansal et al. (2009) provide a comprehensive review of many of the models that have been developed. Most of these models are strictly empirical or based on highly simplified Michaelis-Menten concepts. Unfortunately, the assumptions commonly used with Michaelis-Menten kinetics models, namely, that reaction takes place in solution and there is a single... 

The simplest model for any catalytic reaction is the one most commonly used for enzymes—the Michaelis-Menten kinetic model. As previously shown in Figure 9.3, the sub-... 

There are many ways in which catalysts can become reduced in activity, a general phenomenon known as inhibition. The inhibition of an enzyme is a common way to create a pharmaceutical that impedes a chemical reaction required in a bacterial or viral life cycle. In the following three examples, use the Michaelis-Menten kinetics model, and derive the kinetic expression for the rate of product formation when the inhibitor acts as shown 1 = inhibitor, S = substrate, P = product, and E = enzyme (catalyst)]. Use your rate equations to explain how each form of inhibition cau.ses the rate to move further from Vn,. 

The Michaelis-Menten kinetics model, illustrated for a lake in Example 2.20, may also be applied to a flowing stream in which the microorganisms are attached to the surfaces of the charmel, have a relatively steady cell density, and are exposed to the full chemical concentration in the stream (Cohen et al., 1995 Kim et al., 1995). Microorganisms attached to solid surfaces form biofilms, as populations of attached microbes accumulate on top of one another, building up a layer of microbes embedded in an extracellular matrix which they secrete. Within biofilms, the microbial cell density X corresponds to the number of attached microorganisms divided by the volume of the biofilm. In wastewater treatment engineering, a biofilm is often referred to as attached growth. A biofilm may also be called a bacterial... 

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. 

Quite often the asymptotic behavior of the model can aid us in determining sufficiently good initial guesses. For example, let us consider the Michaelis-Menten kinetics for enzyme catalyzed reactions,... 

Use of a N. globerula R-9 strain was demonstrated for desulfurization of straight run diesel oils. Sulfur reduction from 1807 to 741 mg/dm3 was reported at a desulfurization rate of 5.1 mmol/Kgdcw/h. The desulfurization of model oils containing DBT and 4,6 dimethyl DBT was studied and Michaelis-Menten kinetic parameters were reported. 

This relationship corresponds to the simplest Michaelis-Menten kinetics (Eq. (3)). In addition to the equation derived earlier by Halpern et al. for the simplest model case of a C2-symmetric ligand without intramolecular exchange [21b], every other possibility of reaction sequence corresponding to Scheme 10.3 can be reduced to Eq. (13). Only the physical content of the values of kobs and Km, which must be determined macroscopically, differs depending upon the approach (see [59] for details). Nonetheless, the constants k0bs and KM allow conclusions to be made about the catalyses ... 

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 the irreversible reactions, we assume Michaelis Menten kinetics, giving rise to 15 saturation parameters O1. C [0, 1] for substrates and products, respectively. In addition, the triosephospate translocator is modeled with four saturation parameters, corresponding to the model of Petterson and Ryde-Petterson [113]. Furthermore, allosteric regulation gives rise to 10 additional parameters 7 parameters 9" e [0, — n for inhibitory interactions and 3 parameters 0" [0, n] for the activation of starch synthesis by the metabolites PGA, F6P, and FBP. We assume n = 4 as an upper bound for the Hill coefficient. 

An example of the use of Michaelis-Menten kinetics in a compartmental model is given in the model of Stella and Himmelstein [5], depicted in Figure 13.3. 

Figure 13.3. Model of Stella and Himmelstein, adapted from reference [5] (Section 13.3.1). The drug-carrier conjugate (DC) is administered at a rate i c(DC) into the central compartment of DC, which is characterized by a volume of distribution Fc(DC). DC is transported with an inter-compartmental clearance CLcr(DC) to and from the response (target) compartment with volume Fr(DC), and is eliminated from the central compartment with a clearance CZ.c(DC). The active drug (D) is released from DC in the central and response compartments via saturable processes obeying Michaelis-Menten kinetics defined by Fmax and Km values. D is distributed over the volumes Fc(D) and Fr(D) of the central and response compartment, respectively. D is transported with an inter-compartmental clearance CLcr(D) between the central compartment and response compartment, and is eliminated from the central compartment with a clearance CLc(D).

In order to predict the effect of a mixture of chemicals with the same target receptor, but with different nonlinear dose-effect relationships, either physiological or mathematical modeling can be applied. For interactions between chemicals and a target receptor or enzyme, the Michaelis-Menten kinetics (first order kinetics but with saturation) are often applicable. This kind of action can then be considered a special case of similar combined action (dose addition). 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

MICHAELIS-MENTEN EQUATION MICHAELIS-MENTEN KINETICS MONOD-WYMAN-CHANGEUX MODEL NEGATIVE COOPERATIVITY POSITIVE COOPERATIVITY Cooperativity index. 

Tewis DL, Holm HW, Hodson RE. 1984. Application of single and multiphasic Michaelis-Menten kinetics to predictive modeling for aquatic ecosystems. Env Tox Chem 3 563-574. 

The design of real reactors, taking into account the diffusion, axial dispersion and enzyme inactivation effects, is described in the following sections, considering Michaelis-Menten kinetics as a model. These models are veiy important in predicting and simulating bioreactor performance and in modeling future processes. Also, for control purposes they are indispensable. 

Substituting this model in the reactor-performance equations for Michaelis-Menten kinetics, the following equations can be obtained for the three main types of reactions Batch reactor ... 

It would be distinctly arrogant to say that we understand how enzymes work. At best we catch glimpses of their action. One model involves the key-and-lock concept—an attempt to rationalize their specificity. A much simplified presentation is shown in Fig. 7.115. The idea is that certain shapes in the enzyme structure are precise fits for a part of the reactant molecule. A famous formulation of this is the Michaelis-Menten kinetics. If E is the enzyme and R is some part of a reactant (a complex biomolecule),... 

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. 

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