240
Chapter 7
Note 7.2 Model complexity
A simple illustration of difference in model complexity is the quantitative description of the fractional
saturation y of a protein at a ligand concentration
C\.
This may be described either by the Hill equation
(see Chapter 6):
y = ~T T l?
C,
+
A.
where
h
and
K
are empirical parameters, or by the equation of Monod
et al.
(1963):
LaU+2
)
H
i+k.
î\
y =
L
1 +
acl
Y
(
1
)
(
2
)
where
L, a,
and
KR
are parameters. Both equations address the same experimental problem, but whereas
eq. (1) is completely empirical with
h
and
K
as fitted parameters eq. (2) is taken from a truly mechanistic
model for enzymatic reactions where the parameters have a direct physical interpretation. If the aim of
the modeling is to understand the underlying mechanism of the process eq. (1) can obviously not be
applied since the kinetic parameters are completely empirical and give no (or little) information about the
ligand binding to the protein. In this case eq. (2) should be applied, since by estimating the kinetic
parameter one obtains valuable information about the system, and the parameters can be directly
interpreted. If, on the other hand, the aim of the modeling is to simulate the ligand binding to the protein
eq. (1) may be as good as eq. (2) - one may even prefer eq. (1) since it is more simple in structure and has
fewer parameters, and it actually often gives a better fit to experimental data than eq. (2). Thus, the
answer to which model one should prefer depends on the aim of the modeling exercise. In the list of
unstructured models (Table 7.2) the expression (I) appears as the Moser kinetics, but here the
mechanistic foundation is completely absent.___________________________________________________
7.2 A General Structure for Kinetic Models
In order to describe kinetic growth models it is useful to apply a general framework that allows
uniform presentation of the models. Hereby the model construction process is facilitated and it is
also easy to compare different model structures. In this section we will present such a general
framework. Although it may look like a rather theoretical presentation of cellular growth, it will
facilitate our subsequent discussion significantly.
7.2.1 Specification of Reaction Stoichiometries
As shown in Fig. 7.1 model construction start with defining the stoichiometry of the reactions to
be considered in the model. In order to start this process we consider the general model