Michaelis constant kinetic metabolic modeling

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. 

Lion Biosciences is the supplier of the iDEA Metabolism software package as well as other ADME/T services (289). The iDEA software simulates metabolism and predicts a compound s metabolic behavior in humans. The Metabolism Module consists of a data expert module to perform data fitting and analysis of collected in vitro data and the physiological metabolism model. The physiological metabolism model is constructed from proprietary database of 64 clinically tested compounds. Additionally, the metabolism module automatically calculates the Michaelis-Menten constants Km and VjIiax for the kinetic analysis of metabolism turnover (289). 

Compartmental models are not confined to linear systems. It is relatively easy to include nonlinear processes snch as satnrable metabolism or protein binding. For example, for some drngs one or more metabolism processes may follow Michae-lis-Menten kinetics, shown in Eqnation 12.20. Elimination is described in Equation 12.20 with a nonlinear metabolism process with the parameters V (maximum velocity) and (Michaelis constant). 

Coe and Bessell and coworkers studied the metabolic fates of 2-deoxy-2-fluoro-D-glucose (2DFG) and related compounds by using yeast hexokinase (as a model for mammalian hexokinase), and determined the kinetic constants K and V ) of the Michaelis-Menten equation D-glucose 0.17 (K in mAf)> 1 00 (relative value, D-glucose taken as 1) 2DG 0.59 0.11, 0.85 2DFG 0.19 0.03, 0.50 2-deoxy-2-fluoro-D-mannose (2DFM) 0.41 0.05, 0.85 2-deoxy-2,2-difluoro-D-nraZ>//Jo-hexose... 

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

---