Michaelis Menton

The kinetic expressions arehighlynonlinearbecause they include a Michaelis-Menton rate term ... 

In this scheme, EOH is the enzyme, IX is the inhibitor (either a carbamate or an organophosphate). EOH(IX) is analogous to the Michaelis Menton comploc seen with the substrate reaction. EOI is the acyl-enzyme intermediate for carbamates or a phosphoro-enzyme intermediate for the organophosphates. The equilibrium constant for this reaction (K ) is defined as k /k and the phosphorylation or carbamylation constant is defined as k2- In this study 42)y ANTX-A(S) was found to be more specific for AChE than BUChE. The double reciprocal and Dixon plot of the inhibition of electric eel AChE indicated that the toxin is a non-competitive inhibitor decreases, k remains unchanged) (Figure 2). 

The cytochrome P-450-dependent metabolism of trichloroethylene was studied in hepatic microsomal fractions from 23 different humans (Lipscomb et al. 1997). CYP2E1 was the predominant form of P-450 responsible for the metabolism of trichloroethylene in humans. Incubations of trichloroethylene with the microsomal preparations resulted in hyperbolic plots consistent with Michaelis-Menton kinetics. The values ranged from 12 to 55.7 pM, and were not normally distributed, and the values range from 490 to 3,455 pmol/min/mg protein and were normally distributed. The study authors concluded that the human variability in metabolism of trichloroethylene via P-450-dependent pathways was within a 10-fold range. 

Estimated based on published protein expression (19) and converted to total number of subunit active sites per g of liver tissue. The Michaelis-Menton parameters for ethanol oxidation at pH 7.5 were utilized to calculate individual isozyme activities as a total activity per g of tissue and then normalized as a percent of total activity per pg of tissue following summation of all isozyme activities... 

Fig. 14.7 (a) Measured resonant mode spectral shift for increasing concentrations of target oligonucleotides. The line fit is a Michaelis Menton curve with a Kd of 2.9 nM and a maximum resonant wavelength shift of 5.1 pm. (b) Measured resonant mode shift for oligonucleotides of increasing number of base pair mismatches with the capture probe. Reprinted from Ref. 32 with permission. 2008 Elsevier... 

A model of such structures has been proposed that captures transport phenomena of both substrates and redox cosubstrate species within a composite biocatalytic electrode.The model is based on macrohomo-geneous and thin-film theories for porous electrodes and accounts for Michaelis—Menton enzyme kinetics and one-dimensional diffusion of multiple species through a porous structure defined as a mesh of tubular fibers. In addition to the solid and aqueous phases, the model also allows for the presence of a gas phase (of uniformly contiguous morphology), as shown in Figure 11, allowing the treatment of high-rate gas-phase reactant transport into the electrode. 

If a detailed theoretical knowledge of the system is available, it is often possible to construct a mechanistic model which will describe the general behavior of the system. For example, if a biochemist is dealing with an enzyme system and is interested in the rate of the enzyme catalyzed reaction as a function of substrate concentration (see Figure 1.15), the Michaelis-Menton equation might be expected to provide a general description of the system s behavior. 

The Michaelis-Menton equation represents a mechanistic model because it is based on an assumed chemical reaction mechanism of how the system behaves. If the system does indeed behave in the assumed manner, then the mechanistic model is adequate for describing the system. If, however, the system does not behave in the assumed manner, then the mechanistic model is inadequate. The only way to determine the adequacy of a model is to carry out experiments to see if the system does behave as the model predicts it will. (The design of such experiments will be discussed in later chapters.) In the present example, if substrate inhibition occurs, the Michaelis-Menton model would probably be found to be inadequate a different mechanistic model would better describe the behavior of the system. 

Non-linear pharmacokinetics are much less common than linear kinetics. They occur when drug concentrations are sufficiently high to saturate the ability of the liver enzymes to metabolise the drug. This occurs with ethanol, therapeutic concentrations of phenytoin and salicylates, or when high doses of barbiturates are used for cerebral protection. The kinetics of conventional doses of thiopentone are linear. With non-linear pharmacokinetics, the amount of drug eliminated per unit time is constant rather than a constant fraction of the amount in the body, as is the case for the linear situation. Non-linear kinetics are also referred to as zero order or saturation kinetics. The rate of drug decline is governed by the Michaelis-Menton equation ... 

The Michaelis-Menton equation is an important biochemical rate law. It relates the rate of the reaction v to a substrate concentration [5] in terms of two constants vmax and KM ... 

Enzymes and micelles resemble each other with respect to both structure (e.g., globular proteins and spherical aggregates) and catalytic activity. Probably the most common form of enzyme catalysis follows the mechanism known in biochemistry as Michaelis-Menton kinetics. In this the rate of the reaction increases with increasing substrate concentration, eventually leveling off. According to this mechanism, enzyme E and substrate A first react reversibly to form a complex EA, which then dissociates to form product P and regenerate the enzyme ... 

The enhancement of rate qualitatively follows Michaelis-Menton kinetics, with both the initial slope and the final plateau increasing with increasing length of the alkyl tails of the surfactant. 

The membrane containing the immobilized enzyme is handled by partitioning it into a specified number of volume elements so that Equations 20.23 and 20.24 are valid in this model. While the concentration of each species may vary from element to element, the steady-state assumption (d[ES]/dt = 0) may be invoked independently for each volume element. This results in the definition of the Michaelis-Menton constant, KM ... 

This mechanism is important for compounds that lack sufficient lipid solubility to move rapidly across the membrane by simple diffusion. A membrane-associated protein is usually involved, specificity, competitive inhibition, and the saturation phenomenon and their kinetics are best described by Michaelis-Menton enzyme kinetic models. Membrane penetration by this mechanism is more rapid than simple diffusion and, in the case of active transport, may proceed beyond the point where concentrations are equal on both... 

Kinetic studies of this reaction have shown that it obeys Michaelis-Menton kinetics as expressed by the Lineweaver-Burk plot, the Michaelis constant (KJ for this reaction at pH 7.0 and 37.5 °C being 2.86 x 10 4 M 24). Free lysine, Leuehs Poly-L-lysine, total hydrolyzates of thermal polylysine, and amino group-modified thermal polylysine are completely inactive. The activity of thermal polylysine depends on the degree of polymerization 24). 

Here k is the rate constant for the irreversible reaction, Ceo is the total enzyme concentration, Cs is the substrate concentration, and is the Michaelis-Menton constant. Both k and KM may be functions of pH, temperature, and other properties of the fermentation medium. From this kinetic expression, we see that at high substrate concentrations the rate of product formation is independent of Cs and is approximately equal to kCm-This is due to the presence of a limited amount of enzyme, which is required for the reaction to proceed, and adding more substrate under these conditions will not cause the reaction rate to increase further. At low substrate concentrations, the rate of product formation becomes first-order with respect to Cs- Under these conditions the substrate concentration becomes the determinant for product formation, and increasing Cs produces a proportional increase in rate. The rate is also proportional to the total enzyme concentration under all conditions of substrate concentration. 

Relates IC50 to Kt under conditions of competitive inhibition Kt equilibrium enzyme inhibitor dissociation constant Km Michaelis-Menton constant, [S] substrate concentration. 

A physiologically based pharmacokinetics (PBPK) model based on the ventilation rate, cardiac output, tissue blood flow rates, and volumes as well as measured tissue/air and blood/air partition coefficients has been developed (Medinsky et al. 1989a Travis et al. 1990). Experimentally determined data and model simulations indicated that during and after 6 hours of inhalation exposure to benzene, mice metabolized benzene more efficiently than rats (Medinsky et al. 1989a). After oral exposure, mice and rats appeared to metabolize benzene similarly up to oral doses of 50 mg/kg, above which rats metabolized more benzene than did mice on a per kg body weight basis (Medinsky et al. 1989b). This model may be able to predict the human response based on animal data. Benzene metabolism followed Michaelis-Menton kinetics in vivo primarily in the liver, and to a lesser extent in the bone marrow. Additional information on PBPK modeling is presented in Section 2.3.5. 

---