Biomedical Engineering Reference
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or some empirical formulae have been used when no equation is available. Some
complementary information about some of the assumptions made are given below.
3.2.4.1 Glucose Transport System
Prior the glucose pulse, the chemostat
culture is glucose-limited. Under these conditions, two different systems for glucose
transport across the cytoplasmic membrane are active in
E. coli
: the Mgl transport
systemwith a very high affinity for glucose (Km 0.2
M) and the PTS with a medium
affinity. There are two different PTSs, PTS G with a higher affinity and PTS M
with a lower affinity. Both affinities are in the range of 10
µ
M to 1mM. It has been
shown that the contribution of the PTS G for the glucose transport is greater even for
saturating glucose concentrations (for a complete review, cf. [28]). In our model, the
glucose uptake has been described only in terms of the PTS kinetics. We used the PTS
rate equation described by Liao et al. [6] with some modifications: a g6p inhibition
term was added to this equation according to Kaback [29] and Clark et al. [30]. In
the equation of Liao et al., the PTS rate (Eq. (3.1)) is assumed to be a function of
the pep/pyruvate ratio. Assuming a high pep/pyruvate ratio, it is possible to derive
a simple equation from this expression, where KPTS,a2 represents the Km value of
glucose. Since the PTS G system seems to be responsible for most of the uptake,
the KPTS,a2 parameter was fixed to its glucose Km value of 10
µ
M, according to
µ
Notley-McRobb et al. [31].
3.2.4.2 Glycolysis
Two glucose-6-phospho isomerase (PGI) isoenzymes are
present in
E. coli
, but in this model only one equation is used to describe the PGI
activity as the kinetic properties of both forms are identical [32]. Two forms of phos-
phofructokinase (PFK) are present in
E. coli
of which PFK-1 is the predominant form
accounting for 90 percent of the total activity. Thus, only this form was considered
in this model. The atp inhibition present in yeast was replaced by pep inhibition as
described for
E. coli
by Kotlarz et al. [33]. The pyruvate kinase activity is catalyzed
by two isoenzymes in
E. coli
: PKI, which is activated by fdp and inhibited by atp,
and the amp-activated PKII. These two enzymes seem to be of equal importance. As
the steady-state activity of these enzymes cannot be distinguished by flux analysis,
only one rate equation was used, including a combination of the different effectors.
This rate equation was based on the formula described by Johannes et al. [34] with
an additional term for amp activation.
3.2.4.3 Biosynthetic and Anaplerotic Reactions
The flux toward polysac-
charide synthesis was assessed based on the activity of G1PAT, the enzyme catalyzing
the initial reaction of this pathway. The biochemical pathways leading to the synthe-
sis of nucleotides and glycerol are represented in the model by the first reaction
of these pathways, ribose phosphate pyrophosphokinase, and glycerol-3-phosphate-
dehydrogenase, respectively. The anabolic fluxes from pep to mureine and chorismate
were lumped together in one empirical reaction (Eq. 3.1). A similar equation
(Eq. 3.2) represents the different anabolic fluxes from pyruvate to isoleucine, alanine,
alpha-ketoisovalarate, and diaminopimelate synthesis.
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