190
Chapter 6
The main theme o f our textbook is the cellular reaction for which the kinetics is treated in
Chapter 7. It is impossible to treat the kinetics of cellular reactions solely on the assumption of
known kinetics for all the enzyme reactions in the cell
- in itself a never to be satisfied
assumption. The cell is much more “than a bag of enzymes”, and
in vitro
studies of enzyme
kinetics tell nothing about the influence of the control structure of the cell which is destroyed
when the enzymes are investigated outside their natural habitat.
Still, the apparent analogies between enzyme kinetics and cell kinetics have often been used to
home in on the right structure o f a kinetic expression for the conversion of substrates by a living
cell. This alone is a good reason for giving a short treatment of enzyme kinetics. Furthermore,
enzyme-based assays are used routinely to study the state of the cell at a certain set of
environmental conditions. Some of these assays are not easily understood without prior
knowledge of the behavior of the enzymatic reaction on which the assay is based.
Finally, when taking the step from analysis of the steady state flux distribution in a metabolic
network to an analysis of the rate of production that can be supported by the network, one needs
to include a kinetic analysis of the different enzymatic reactions in the network. The outcome of
this analysis is a prediction of how genetic manipulations of the network can lead to a change in
the flux distribution and perhaps to a higher yield and a higher production rate of the desired
product in a given branch of the network.
Consequently, enzyme kinetics will be treated with a view of analyzing the rates of production in
different branches of a metabolic network. The analysis is based on the sensitivity of each
enzymatic reaction in a particular branch to changes in the activity of each of the enzymes in the
pathway, and to changes in the metabolite levels at the different steps.
The activity of enzymes is a function of a number of environmental factors, e.g. temperature and
pH. Many enzyme preparations are sold as particles of immobilized enzymes in a support. Here
mass transport and chemical reaction both play a role for the overall reaction rate as is well
known for normal chemical reactions. It therefore becomes important to analyze when mass
transport is likely to influence the bio-reaction mediated by the enzyme. Both of these topics
will, however, be treated in the context of cellular reactions (Chapters 7 and 10) which are
modeled by expressions similar to the mechanistic models of enzyme reactions, but with an extra
factor, the biomass concentration
x,
which is responsible for the autocatalytic nature of the
cellular kinetics. When yeast cells are embedded in an alginate matrix and the biomass
concentration is assumed to be constant there is in fact no difference between the behavior of this
system
and
an
immobilized
glucose
isomerase
or penicillin
deacylase
embedded
in
a
glutaraldehyde matrix.
6.1 Michaelis-Menten and Analogous Enzyme Kinetics
Very often the rate of an enzymatic reaction when pictured as a function of the substrate
concentration s takes the form of Fig. 6.1.
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