7
Modeling of Growth Kinetics
In chapters 3 and 5 we have discussed how the two important design parameters
yield
and
productivity
can be derived from experimental data,
e.g.
from measurements of the substrate
consumption and the product formation. Furthermore, we have shown how measured steady state
rates (or fluxes) in and out of the cell can be used to calculate the fluxes through the different
branches of the metabolic network functioning in a given cell. However, we have not yet
established a quantitative relation between the fluxes and the variables (concentrations etc.) that
characterize the environment of the cell, and we have also not considered how the fluxes change
with changes in the operating conditions,
e.g.
the response to a change in medium composition or
temperature. In order to do this it is necessary to define kinetic expressions for the key reactions
and processes considered in the model - or in other terms to set up a mathematical model that
can simulate the studied process (see Note 7.1). Setting up kinetic expressions is normally
referred to as
kinetic modeling
, and this involves defining verbally or mathematically expressed
correlations between rates and reactant/product concentrations that, inserted in mass balances,
permits a prediction of the degree of conversion of substrates and the yield of individual products at
other operating conditions. Conceptually this is a great step forward compared to the methodology
applied in chapters 3 and 5. Thus, if the rate expressions are correctly set up, it is possible to
express the course of a fermentation experiment based on initial values (or input) for the
components of the state vector, e.g., concentration of substrates. This leads to simulations that
finally may result in an optimal design of the equipment or an optimal mode of operation for a
given system. Independent of the model structure, the process of defining a quantitative
description of a fermentation process often involves an iterative process where the model is
continuously revised when new process information is obtained. However, it is always
important
to clearly define the aim o f the model,
i.e., what the model is going to be used for. The model
structure and complexity should relate to this.
Models are used by all researchers in life sciences when results from individual experiments are
interpreted and when results from several different experiments are compared with the aim of
setting up a model that may lead to deeper insight into the biological system. Biologists
constantly use models
e.g.
when experiments on gene regulation and expression are to be
interpreted, and these models are very important when the inherent message from often quite
complicated experiments is to be extracted. Most of these biological models are qualitative
only
,
and they do not allow quantitative analysis. Often these
verbal models
can be quite easily
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