Biomedical Engineering Reference
In-Depth Information
cell physiology under conditions of nutrient limitation is more easily studied in continuous
culture, as discussed later in Chapter 12.
Malthus growth model is valid only in the exponential growth phase. A modification of
the Malthus model by Verhulst in 1844 included an apparent biomass inhibition term:
r X ¼ kX 1
X
X N
(11.5)
where X
is the carrying capacity of the cells in the medium and k is the carrying capacity
coefficient. For a batch growth of constant culture volume, cell balance subjected to growth
rate given by Eqn (11.5) gives rise to
N
X 0 e kt
X ¼
(11.6)
X 0
X N ð
e kt
1
1
Þ
Equation (11.6) is also termed the logistic equation. The Verhulst model is able to describe the
exponential growth phase, the deceleration phase, and the stationary phase, via Eqn (11.6) .
Therefore, the Verhulst model (or logistic model) is a more accurate phenomenological model
than the Malthus model.
The stationary phase starts at the end of the deceleration phase, when the net growth rate is
zero (no cell division) or when the growth rate is equal to the death rate. Even though the net
growth rate is zero during the stationary phase, cells are still metabolically active and
produce secondary metabolites. Primary metabolites are growth-related products and
secondary metabolites are nongrowth related. In fact, the production of certain metabolites is
enhanced during the stationary phase (e.g. antibiotics, some hormones) due to metabolite
deregulation. During the course of the stationary phase, one or more of the following
phenomena may take place:
1. Total cell mass concentration may stay constant, but the number of viable cells may
decrease.
2. Cell lysis may occur, and viable cell mass may drop. A second growth phase may occur,
and cells may grow on lysis products of lysed cells (cryptic growth).
3. Cells may not be growing but may have active metabolism to produce secondary
metabolites. Cellular regulation changes when concentrations of certain metabolites
(carbon, nitrogen, phosphate) are low. Secondary metabolites are produced as a result of
metabolite deregulation.
During the stationary phase, the cell catabolizes cellular reserves for new building blocks and
for energy-producing monomers. This is called endogenous metabolism. The cell must always
expend energy to maintain an energized membrane (i.e. proton-motive force) and transport
of nutrients and for essential metabolic functions such as motility and repair of damage to
cellular structures. This energy expenditure is called maintenance energy. As such, mainte-
nance energy and endogenous metabolism are not limited to the stationary phase but become
dominant in the stationary phase. The maintenance or endogenous expenditure is just a small
fraction of the total cell needs during maximum growth. When the primary metabolism
diminishes as in the stationary phase, the endogenous metabolism becomes dominant.
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