Elimination Michaelis-Menten

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]. 

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

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).

For drugs that exhibit capacity-limited elimination (eg, phenytoin, ethanol), clearance will vary depending on the concentration of drug that is achieved (Table 3-1). Capacity-limited elimination is also known as saturable, dose- or concentration-dependent, nonlinear, and Michaelis-Menten elimination. 

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-... 

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-... 

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. 

The first model tested was a one-compartment model with Michaelis-Menten elimination, which served as a base against which to compare more complex models. A marked decrease in the objective function value (OFV) was obtained when a two-compartment model with Michaelis-Menten elimination was fitted to the data (5 = -743). The addition of a linear component to the elimination from the central compartment further reduced the OFV by an additional 245 points. The two-compartment models incorporating saturable elimination with and without the linear component were then further evaluated. Addition of the linear elimination pathway from the central compartment resulted in a decrease of 56 points in OFV compared to the model with saturable elimination only. 

The neutrophil-mediated clearance was expressed as a Michaelis-Menten function, because G-CSF receptor binding is subject to saturation. The product of kcat and the ratio of ANC and ANC at baseline is the maximum velocity of drug elimination from this pathway, km is the Michaelis constant, and C is the pegfilgrastim concentration. CL2 denotes the linear clearance pathway. 

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. 

Some fractional transfer functions of compartmental models may actually be functions, (i.e., the model may actually be nonlinear). The most common example is when a transfer or loss is saturable. Here a Michaelis-Menten type of transfer function can be defined, as was shown in Chapter 2 for the elimination of phenytoin. In this case, loss from compartment 1 is concentration dependent and saturable, and one can write... 

Last, population pharmacokinetics of sibrotuzumab, a humanized monoclonal antibody directed against fibroblast activation protein (FAP), which is expressed in the stromal fibroblasts in >90% of malignant epithelial tumors, were analzyed in patients with advanced or metastatic carcinoma after multiple IV infusions of doses ranging from 5 mg/m to a maximum of 100 mg (78). The PK model consisted of two distribution compartments with parallel first-order and Michaelis-Menten elimination pathways from the central compartment. Body weight was significantly correlated with both central and peripheral distribution volumes, the first-order elimination clearance, and ymax of the Michaelis-Menten pathway. Of interest was the observation that body surface area was inferior to body weight as a covariate in explaining interpatient variability. 

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

All metabolic processes are saturable at a certain concentration of the substrate/drug. Thus, rate of elimination of the drug by metabolism as described by Eq. (5) can also be described by a Michaelis-Menten equation ... 

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 ... 

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