The metabolism of a pollutant due to microbial degradation is modeled
according to Monod kinetics. Note that the Michaelis-Menten kinetics,
widely used to model enzymatic reactions affecting the
concentration of pollutants in different body tissues and organs,
are completely analogous to the Monod kinetics, and we will therefore
use the corresponding terms interchangeably.
In a situation governed by Michaelis-Menten kinetics,
the rate of change of the mass of pollutant in the compartment no. k
() is additionally affected by a term of the form
where is the maximal induction level of the enzyme connecting to the pollutant and is the dissociation constant of the enzyme. These two parameters have to be specified by the modeler. As a consequence, the system of ordinary differential equations that has to be solved is not (3.3), but
Of course, this additional nonlinearity destroys any mass-conservation properties that the model might had beforehand. Nevertheless, mass conservation with respect to the kinetics is an important feature of any model and code trying to analyze quantitatively the effects of pollutants on individuals, and we believe that software whose kinetic model is not mass conservative will have serious difficulties in predicting the aforementioned effects. In any case, metabolism and degradation will usually take place only in a few selected compartments, such that most of the nonlinear terms just introduced will vanish.