How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 586

a large number of parameters and intercellular components. Full kinetic description can be
extremely demanding. While on the first instances mathematical description via simplifica-
tion of metabolic pathway by approximation is desirable, sometimes we resort to phenome-
nological models that may or may not reflect directly the metabolic pathway. Models that can
describe wide range of growth behaviors involve recognition of the structured nature of each
cell and the segregation of the culture into individual units (cells) that may differ from each
other.
A compositionally structured phenomenological model divides the cell mass into compo-
nents. A fully structured model would be the one able to mimic the complete metabolism and
cell generation and physiology. If the ratio of the individual cell components can change in
response to perturbations in the extracellular environment, then the structured model is
behaving analogously to a cell changing its composition in response to environmental
changes. Consider in Chapter 10 our discussion of cellular regulation, particularly the induc-
tion of whole pathways. Any of these metabolic responses results in changes in intracellular
structure. Furthermore, if a model of a culture is constructed from discrete units, it begins to
mimic the segregation observed in real cultures whereby cell physiology can be modeled. As
shown in Fig. 11.11 , models may be structured and segregated, structured and nonsegre-
gated, unstructured and segregated, and unstructured and nonsegregated. Models contain-
ing both structure and segregation can be the most realistic, but they are also computationally
complex.
The degree of realism and complexity required in a phenomenological model depends on
what is being described; the modeler should always choose the simplest model that can
adequately describe the desired system. An unstructured model assumes fixed cell compo-
sition, which is equivalent to assuming pseudosteady state or balanced growth. The balanced
growth assumption is valid primarily in single-stage, steady-state continuous culture and the
exponential phase of batch culture; it fails during any transient conditions. How fast the cell
responds to perturbations in its environment and how fast these perturbations occur deter-
mine whether pseudobalanced growth can be assumed. If cell response is fast compared to
external changes and if the magnitude of these changes is not too large (e.g. a 10% or 20%
variation from initial conditions), then the use of unstructured models can be justified, since
the deviation from balanced growth may be small. Culture response to large or rapid pertur-
bations cannot be described satisfactorily by unstructured models.

FIGURE 11.11 Classification
of phenomenological microbial
kinetic models.

Nonsegregated
Structured

Segregated
Structured

Nonsegregated
Nonstructured

Segregated
Nonstructured

Differentiation from cell to cell (population distribution): Segregartion of cells