Modeling of Growth Kinetics
241
Figure 7.3 A general representation of reactions involved in cellular growth.
N
substrates enter the cell
and are converted into
M
metabolic products and
Q
biomass constituents. The conversions involves
J
cellular reactions for which the rates are given by V|.
..Vj. Rates of substrate uptake
and
product formation
are also shown. In addition to Fig. 5.3 intracellular structure in the
biomass is considered.
illustrated in Fig. 7.3, where
N
substrates are taken up by the cells and converted into
M
metabolic products and
Q
biomass constituents. The conversions are carried out in
J
reactions.
The number of reactions and processes involved in cellular growth is very large, and as
mentioned above the reactions are therefore typically lumped reactions, e.g., conversion of
glucose into cellular protein. Often the lumped reactions are completely empirical, e.g.,
conversion of glucose into “active biomass”.
In order to describe the stoichiometry of the reactions we introduce stoichiometric coefficients
for all the components in the system. Thus, stoichiometric coefficients for the substrates are
termed a , the stoichiometric coefficients for the metabolic products are termed
P
and the
stoichiometric coefficients for the biomass constituents are termed 7. The numerical value of
these stoichiometric coefficients are analogous to the yield coefficients o f the black box model
introduced in Chapter 3, but since we will use the yield coefficients to specify overall conversion
yields it is necessary to distinguish between the stoichiometric coefficients that appear in
independent reactions and the yield coefficients. Clearly the stoichiometric coefficients are
identical to the yield coefficients if all the reactions are lumped into a single reaction, as is done
in the black box kinetic models to be described in Section 7.3.1.
Since there are many different compounds involved in many different reactions it is necessary to
use two indices on the stoichiometric coefficients to indicate the reaction number and the
compound,
e.g.,
aj7 is the stoichiometric coefficient for the /th substrate in theyth reaction. Thus,
in the general framework for growth models, we introduce stoichiometric coefficients for all
substrates, metabolic products and biomass constituents in each of the
J
reactions, but many of
the stoichiometric coefficients will be zero, since only a few compounds participate in any given
reactions.