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.