Michaelis-Menten kinetics limitations

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. 

An additional problem arises when the exchange processes are rate-limited. This may be caused by enzymes that become saturated when all their active sites are occupied by the drug, or it may be due to adsorbing proteins that have a limited binding capacity. In such cases, one obtains a type of Michaelis-Menten kinetics of the form ... 

There are two limiting cases of Michaelis-Menten kinetics. Beginning from Eq. (1) at high substrate excesses (or very small Michaelis constants) Eq. (4 a) results. This corresponds to a zero-order reaction with respect to the substrate, the rate of product formation being independent of the substrate concentration. In contrast, very low substrate concentrations [26] (or large Michaelis constants) give the limiting case of first-order reactions with respect to the substrate, Eq. (4b) ... 

As explained earlier, the pre-equilibria are characterized by the limiting values of Michaelis-Menten kinetics. In the case of first-order reactions with respect to the substrate, we have Kfvl [S]0. Since the pre-equilibria are shifted to the side of educts during hydrogenation, only the solvent complex is detectable. In contrast, in the case of zero-order reactions only catalyst-substrate complexes are expected under stationary hydrogenation conditions in solution. These consequences resulting from Michaelis-Menten kinetics can easily be proven by var-... 

Characteristically, within certain concentration limits, if a chemical is absorbed by passive diffusion, then the concentration of toxicant in the gut and the rate of absorption are linearly related. However, if absorption is mediated by active transport, the relationship between concentration and rate of absorption conforms to Michaelis-Menten kinetics and a Lineweaver-Burk plot (i.e., reciprocal of rate of absorption plotted against reciprocal of concentration), which graphs as a straight line. 

Equation (4) corresponds to saturation-type (Michaelis-Menten) kinetics and rate constants obtained over a suitable range of [CD], sufficient to reflect the hyperbolic curvature, can be analysed to provide the limiting rate constant, kc, and the dissociation constant, Ks (VanEtten et al., 1967a Bender and Komiyama, 1978 Szejtli, 1982 Sirlin, 1984 Tee and Takasaki, 1985). The rate constant ku is normally determined directly (at zero [CD]), and sometimes Ks can be corroborated by other means (Connors, 1987). 

The quantity of any given solute being presented to the reabsorptive mechanisms is determined by the product of the GFR and the solute concentration in plasma. One of the features of any carrier-mediated process is its limited capacity. Binding of a substance to its transport protein follows the same principles as substrate binding to an enzyme or hormone binding to its receptor so we may appropriately liken the dynamics to Michaelis-Menten kinetics. 

A term (also referred to as prior equilibrium ) denoting any reversible step that precedes an irreversible step or the rate-limiting step in a multistage reaction mechanism. The so-described reaction step must rapidly establish an equilibrium between its reactants and products. The first association/dissociation equilibrium leading to the formation of EX complex from E and S in the Michaelis-Menten treatment is an example of a preequilibrium. See Michaelis-Menten Kinetics... 

Furthermore, it can be shown that, in the limiting cases of first-order kinetics [Equation (11.35) also holds for this case] and zero-order kinetics, the equal and optimal sizes are exactly the same. As shown, the optimal holding times can be calculated very simply by means of Equation (11.40) and the sum of these can thus be used as a good approximation for the total holding time of equal-sized CSTRs. This makes Equation (11.31) an even more valuable tool for design equations. The restrictions are imposed by the assumption that the biocatalytic activity is constant in the reactors. Especially in the case of soluble enzymes, for which ordinary Michaelis-Menten kinetics in particular apply, special measures have to be taken. Continuous supply of relatively stable enzyme to the first tank in the series is a possibility, though in general expensive. A more attractive alternative is the application of a series of membrane reactors. 

We conclude that the neutral substrate enters 1 to form a host-guest complex, leading to the observed substrate saturation. The encapsulated substrate then undergoes encapsulation-driven protonation, presumably by deprotonation of water, followed by acid-catalyzed hydrolysis inside 1, during which two equivalents of the corresponding alcohol are released. Finally, the protonated formate ester is ejected from 1 and further hydrolyzed by base in solution. The reaction mechanism (Scheme 7.7) shows direct parallels to enzymes that obey Michaelis-Menten kinetics due to the initial pre-equilibrium followed by a first-order rate-limiting step. 

It was pointed out in Chapter 3, section A3, that when kcJKM is at the diffusion-controlled limit, Briggs-Haldane rather than Michaelis-Menten kinetics are obeyed. Thus, the more advanced an enzyme is toward the evolution of maximum rate, the more important are Briggs-Haldane kinetics. 

From the point of view of this book, the most important experimental observation is that most reactions obey Michaelis-Menten kinetics when the concentration of one substrate is held constant and the other is varied. Furthermore, in practice, only a limited range of mechanisms is commonly observed. 

Fig. S.51. Eadie-Hofstee type plot showing departure from Michaelis-Menten kinetics due to external diffusion limitation...

Mean clearance (CL) values for cetuximab are displayed as a function of dose in Fig. 14.3. Mean CL values decreased from 0.079 to 0.018 L/h/m2 after single cetuximab doses of 20 to 500 mg/m2, respectively. In the dose range 20 to 200 mg/m2, CL values decreased with dose. At doses of 200 mg/m2 and greater, CL values leveled off at a value of approximately 0.02 L/h/m2. This biphasic behavior suggests the existence of two elimination pathways. The elimination of cetuximab apparently involves a specific, capacity-limited elimination process that is saturable at therapeutic concentrations, in parallel with a nonspecific first-order elimination process that is non-saturable at therapeutic concentrations. Increasing doses of cetuximab will therefore ultimately lead to the saturation of the elimination process that is capacity-limited and that follows Michaelis-Menten kinetics, whereas the first-order process will become the dominant mechanism of elimination beyond a particular dose range. 

Figure 14.6 (a) Concentration vs. membrane thickness applying the Michaelis-Menten kinetics (continuous lines) and its limiting... 

Equation (5.18) is the general equation for a phosphorylation-dephosphorylation switch with Michaelis-Menten kinetics [163], Two limiting cases are particularly worth mentioning. First, if the kinase and the phosphatase are not saturated with respect to the substrate, i.e., S0 << K. K.%, then we have... 

Michaelis-Menten kinetics and empirical kinetic parameters can be joined to give pieces of information on optimum (diffusion-controlled) catalytic kinetics, just assuming that optimum turnover means use of the best catalytic center species and half substrate saturation. This holds for small substrate concentrations, probably subject to intracellular control or limited take-up. Then ... 

Another parameter often referred to when discussing Michaelis-Menten kinetics is kcaJ Ky. This is an apparent second-order rate constant that relates the reaction rate to the free (not total) enzyme concentration. As described above, at very low substrate concentrations when the enzyme is predominantly unbound, the velocity (f) is equal to [El Ky. The value of Is JKy sets a lower limit on the rate constant for the association of enzyme and substrate. It is sometimes referred to as the specificity constant because it determines the specificity of the enzyme for competing substrates. 

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