Kinetics Michaelis-Menton

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. 

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. 

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). 

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. 

Accordingly, Michaelis-Menton kinetics were examined in relation to the accumulation of pesticide. The pertinent mathematical expressions are shown below (I). 

Figure 3. Accumulated residue in soil. Calculated for Michaelis-Menton kinetics limiting half life. 1 year, single annual addition of one concentration unit.

Table IV. Limiting Maximum Accumulated Residues in Soil as Calculated for Michaelis-Menton Kinetics and a Single Annual Addition of One Concentration Unit...

Do the following data conform to the Michaelis-Menton kinetic model ... 

Allosteric enzymes constitute an important class of enzymes whose catalytic activity can be regulated. These enzymes, which do not conform to Michaelis-Menton kinetics, have multiple active sites. These active sites display cooperativity, as evidenced by a sigmoidal depen-dence of reaction velocity on substrate concentration. 

Salicylate and its metabolites are rapidly and almost completely excreted in the urine by glomerular filtration and by renal tubular secretion. Passive reabsorption of salicylate occurs in the distal tubules. Salicylate elimination is saturable and characterized by Michaelis-Menton kinetics where the elimination half-life is dependent on the dose. Since the pRa of salicylic acid is 3, its renal clearance is greatly influenced by changes in urinary pH. Increasing urinary pH can significantly increase the overall salicylate elimination rate via ion trapping. 

Activation at high substrate concentrations not only explains the failure of butyrylcholinesterase to follow simple Michaelis-Menton kinetics, but also explains the enigma of substrate inhibition of the enzyme using either benzoylcholine (A21, T7) or acetyl- or butyryl-salicylcholine as substrates. The proposal made by Hastings is analogous to that of Myers (M24, M25) for the inhibition of acetylcholinesterase by excess substrate, in this case acetylcholine. 

Main (M4), in an excellent review article on cholinesterase inhibitors, discussed the additional complication of substrate inhibition in the above general mechanism. However, in many inhibition studies Michaelis-Menton kinetics are obeyed quite closely. One simple reaction scheme which leads to such kinetics is as follows ... 

Morrow and Trogler (109) have studied the hydrolysis of two phosphate diesters by [Cu(bipy)] (bipy = 2,2 -bipyridine) in aqueous solution at 75°C in the pH range 5.8-8.3. For both bis(4-nitrophenyl)phosphate and ethyl-4-nitrophenylphosphate the reaction was proposed to proceed via coordination of the diester to the [Cu(bipy)] moiety followed by attack of a cis coordinated OH ion at the P center. Maximal rate enhancements of 1(P- to- 10 -fold were reported. The reaction was accompanied by incorporation of a single label in the product ethylphosphate when the reaction was conducted in labeled water. Saturation kinetics were observed for the hydrolysis of ENPP (ethyl-4-nitrophenylphosphate). The reaction obeyed Michaelis-Menton kinetics with a for the ENPP ion of... 

The importance of the changes in quaternary structure in determining the sigmoidal curve is illustrated nicely by studies of the isolated catalytic trimer, freed by p-hydroxymercuribenzoate treatment. The catalytic subunit shows Michaelis-Menton kinetics with kinetic parameters that are indistinguishable from those deduced for the R state. Thus, the term tense is apt in the T state, the regulatory dimers hold the two catalytic trimers sufficiently close to one other that key loops on their surfaces collide and interfere with conformational adjustments necessary for high-affinity substrate binding and catalysis. 

Figure 3.11 Typical form of Michaelis-Menton kinetic results.

In interior wetland areas, the source of nitrate is primarily nitrification, and denitrification rates in these areas are limited by nitrate availability. Several studies have shown that denitrification rates increase with an increase in nitrate concentration. Half-saturation constants (one of the Michaelis-Menton kinetics parameter) reported for denitrification range from 27 to 344 pM for lake and marine sediments (Seitzinger, 1988) and 130 to 1,200 pM for soils (Firestone, 1982). Low half-saturation constants probably reflect carbon limitation in soil or diffusion of nitrate from aerobic sites to anaerobic sites. 

Evaluation of the polymer s catalytic activity involved monitoring hydrolysis reactions using 50-fold molar excess of 23 with respect to the theoretical amount of functional groups present in each polymer. Figure 4 shows a plot of percent hydrolysis vs. time. Curves a, b, and c correspond to polymers P-12, P-13, and P-11, respectively. It is clear that curves a and b do not display a typical pseudo first-order kinetics. Only curve c displays Michaelis-Menton kinetics, indicating P-11 contains an active site that may bear some features of saturation kinetics (Table 5) wherein cooperative effects from juxtaposed ligands help to enhance the nucleophilicity of the serine-hydroxyl group (Scheme 12). 

Verify if the given data confirm to the Michaelis-Menton kinetic rate equation... 

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