Michaelis-Menten elimination kinetics

BSA (p <0.0001). The least-squares mean clearance for a patient with a BSA of 1.83 m2 at 2.3 mg/m2 was 62 L/h, but was 30 L/h at 62.2 mg/m2. Decreasing clearance with increasing dose is consistent with Michaelis-Menten elimination kinetics. Between-subject variability was moderate at approximately 30%. Tasidotin did not show any major renal elimination, with only ca. 13% of the dose being found in the urine as unchanged drug. In Study 103, the least-squares mean tasidotin renal clearance was approximately 4.3 L/h (about 13% of total systemic clearance), with a between-subject variability of approximately 51%. Given a glo-... 

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 ... 

Implicit equations include the dependent term in a form not readily separated from the other terms in the equation. One example in Equation 10 for drug concentrations after IV bolus administration, following Michaelis-Menten elimination kinetics as described by Wagner ... 

Dose-dependent clearance and distribution was then later observed in a Phase 1 study in children with solid tumors (Sonnichsen et al., 1994). In a study in adults with ovarian cancer, Gianni et al. (1995) used a 3-compartment model with saturable intercompart-mental clearance into Compartment 2 and saturable, Michaelis-Menten elimination kinetics from the central compartment to describe the kinetics after 3 hour and 24 hour infusion. Now at this point one would typically assume that the mechanism for nonlinear elimination from the central compartment is either saturable protein binding or saturable metabolism. But the story is not that simple. Sparreboom et al. (1996a) speculated that since Cremophor EL is known to form micelles in aqueous solution, even many hours after dilution below the critical micellular concentration, and can modulate P-glycoprotein efflux, that the nonlinearity in pharmacokinetics was not due to paclitaxel, but due to the vehicle, Cremophor EL. This hypothesis was later confirmed in a study in mice (Sparreboom et al., 1996b). 

This situation does not qualify for use of the high dose equation (Eq. 15.15). Neither are the plasma drug concentrations obtained small enough to warrant use of the low dose (linear kinetic) equation (Eq. 15.13). This leaves the requirement to use the general equation for Michaelis-Menten elimination kinetics (Eq. 15.14) ... 

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

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

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).

There are still other causes of nonlinearities than (apparent or real) higher-order transformation kinetics. In Section 12.3 we discussed catalyzed reactions, especially the enzyme kinetics of the Michaelis-Menten type (see Box 12.2). We may also be interested in the modeling of chemicals which are produced by a nonlinear autocatalytic reaction, that is, by a production rate function, p(Q, which depends on the product concentration, C,. Such a production rate can be combined with an elimination rate function, r(C,), which may be linear or nonlinear and include different processes such as flushing and chemical transformations. Then the model equation has the general form ... 

Kemp elimination was used as a probe of catalytic efficiency in antibodies, in non-specific catalysis by other proteins, and in catalysis by enzymes. Several simple reactions were found to be catalyzed by the serum albumins with Michaelis-Menten kinetics and could be shown to involve substrate binding and catalysis by local functional groups (Kirby, 2000). Known binding sites on the protein surface were found to be involved. In fact, formal general base catalysis seems to contribute only modestly to the efficiency of both the antibody and the non-specific albumin system, whereas antibody catalysis seems to be boosted by a non-specific medium effect. 

The structural submodel describes the central tendency of the time course of the antibody concentrations as a function of the estimated typical pharmacokinetic parameters and independent variables such as the dosing regimen and time. As described in Section 3.9.3, mAbs exhibit several parallel elimination pathways. A population structural submodel to mechanistically cover these aspects is depicted schematically in Fig. 3.14. The principal element in this more sophisticated model is the incorporation of a second elimination pathway as a nonlinear process (Michaelis-Menten kinetics) into the structural model with the additional parameters Vmax, the maximum elimination rate, and km, the concentration at which the elimination rate is 50% of the maximum value. The addition of this second nonlinear elimination process from the peripheral compartment to the linear clearance process usually significantly improves the fit of the model to the data. Total clearance is the sum of both clearance parts. The dependence of total clearance on mAb concentrations is illustrated in Fig. 3.15, using population estimates of the linear (CLl) and nonlinear clearance (CLnl) components. At low concentra-... 

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. 

Pharmacokinetic studies are in general less variable than pharmacodynamic studies. This is so since simpler dynamics are associated with pharmacokinetic processes. According to van Rossum and de Bie [234], the phase space of a pharmacokinetic system is dominated by a point attractor since the drug leaves the body, i.e., the plasma drug concentration tends to zero. Even when the system is as simple as that, tools from dynamic systems theory are still useful. When a system has only one variable a plot referred to as a phase plane can be used to study its behavior. The phase plane is constructed by plotting the variable against its derivative. The most classical, quoted even in textbooks, phase plane is the c (f) vs. c (t) plot of the ubiquitous Michaelis-Menten kinetics. In the pharmaceutical literature the phase plane plot has been used by Dokoumetzidis and Macheras [235] for the discernment of absorption kinetics, Figure 6.21. The same type of plot has been used for the estimation of the elimination rate constant [236]. 

Correct answer = D. Drugs with zero-order kinetics of elimination show a linear relationship between drug concentration and time. In most clinical situations the concentration of a drug is much less than the Michaelis-Menten constant (Km). A decrease in drug concentration is linear with time. The half-life of the drug increases with dose. A constant amount of drug is eliminated per unit time. 

A comparison of the WP-KMC, NE-KMC, and conventional KMC is shown in Fig. 10. These acceleration approaches are successful regarding CPU. However, since the objective is often to study the role of noise, they do not provide the correct fluctuations. In a similar vein, use of simple rate expressions, such as the Michaelis-Menten or Hill kinetics, derived via PE and QSS approximations, are capable of accelerating KMC simulation since fast processes are eliminated. However, the noise of the resulting simulation, based on a reduced rate expression that lumps some of the reaction steps, is usually adversely affected (Bundschuh et al., 2003). 

Several drugs, including salicylate (in overdose), alcohol, and possibly some hydrazines and other drugs which are metabolised by acetylation, have saturable elimination kinetics, but the only significant clinical example is phenytoin. With this drug, capacity-limited elimination is complicated further by its low therapeutic index. A 50% increase in the dose of phenytoin can result in a 600% increase in the steady-state blood concentration, and thus expose the patient to potential toxicity. Capacity-limited pathways of elimination lead to plasma concentrations of drugs which can be described by a form of the Michaelis-Menten equation. In such cases, the plasma concentration at steady state is given by... 

Unfortunately, the elimination of some drugs does not follow first-order kinetics. For example, the primary pathway of phenytoin elimination entails initial metabolism to form 5-(parahydroxyphenyl)-5-phenylhydantoin (p-HPPH), followed by glucuronide conjugation (Figure 2.8). The metabolism of this drug is not first order but follows Michaelis-Menten kinetics because the microsomal enzyme system that forms p-HPPH is partially saturated at phenytoin... 

Elimination of tliis drug follows Michaelis-Menten kinetics. Apparent clearance will be lower when plasma levels are higher than those obtained in this study. 

Since phenytoin is eliminated by Michaelis-Menten kinetics. Equation 2.6 applies ... 

Liver is the principal site of D-fructose metabolism. D-Fructose is transported to the liver from the small intestine by way of the portal blood-vessel. Experiments with perfused pig and rat livers revealed that the rate of elimination of D-fructose from blood is a function of the sugar concentration,26,27 and follows Michaelis-Menten kinetics.27,28 Carrier-mediated, liver-membrane transport of D-fructose has a high29 Km and Vmax, in comparison to the intracellular phosphorylation constants of D-fructose in both pigeon and rat livers.27,28 For example, the calculated rat-liver transport for D-fructose has a Km of 67 mM and a Vmax of 30 /u,mole.min. g-1, in contrast to the lower, calculated fruc-tokinase Km of 1.0 mM and Vmax of 10.3 pmole. min r1. g 1 with D-fruc-tose and Km of 0.54 mM with adenosine 5 -triphosphate (ATP). In perfused pig-liver,28 the transport Km for D-fructose is only ten times that of intracellular phosphorylation by fructokinase. Hence, D-fructose-transport values suggested that, at physiological D-fructose concentrations, membrane transport limits the rate of uptake, thereby protecting the liver from severe depletion of adenine nucleotide.28,29... 

The kinetics described so far have been based on first-order processes, yet often in toxicology, the situation after large doses are administered has to be considered when such processes do not apply. This situation may arise when excretion or metabolism is saturated and hence the rate of elimination decreases. This is known as Michaelis-Menten or saturation kinetics. Excretion by active transport (see below) and enzyme-mediated metabolism are saturable processes. In some cases cofactors are required and their concentration may be limiting (see Chapter 7, salicylate poisoning). When the concentration of foreign compound in the relevant tissue is lower than the km then linear, first-order... 

As in all PK models described in this chapter, the rate of drug elimination is taken to follow first-order (or linear) elimination kinetics. Thus the rate of elimination is proportional to the amount of drug remaining to be eliminated. As discussed previously, this is often a reasonable approximation as most drug concentrations in the body are much less than the Michaelis-Menten value of enzymes and transporter proteins. 

Drug Elimination. Excretion or metabolism can be added to an appropriate compartment, as indicated by the terms eiim in Equation 7-18. A full description of enzyme-mediated metabolic pathways usually employs Michaelis-Menten kinetics ... 

M-CSF, for example, undergoes besides linear renal elimination a nonlinear elimination pathway that follows Michaelis-Menten kinetics and is linked to a receptor-mediated uptake into macrophages. At low concentrations, M-CSF follows linear pharmacokinetics, while at high concentrations, nonrenal elimination pathways are saturated, resulting in nonlinear pharmacokinetic behavior (Fig. 3) [45, 46]. Other examples for receptor-mediated elimination are insulin, t-PA, epidermal growth factor (EGF), ANP, and interleukin-10 [19, 28, 38,44,47]. 

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