How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 600

However, if the substrate limiting the growth is also the one being converted to the extra-
cellular product, the specific endogenous metabolic rate can be expressed as

m e m max m G
K e m þ m G

m e ¼ (11.36)

Cells die (physiological development) due to harsh environment (high temperature, pH,
or harmful chemicals) or simply due to aging. The death rate is usually modeled by
a first-order relation:

m d ¼ k d (11.23)

In single-celled microorganisms, cell death is the point at which reinitiation of division is no
longer possible. Dead cells cease nutrients uptake. Cell functions stop even other cells
continue to function normally.
The net specific cell growth rate is the growth rate subtracted cell death rate, that is

m net ¼ m G k d (11.24)

To this end, we have the necessary simple growth model equations to characterize cell
growth and product formation.
During batch cultivation, a population of cells typically exhibits several different growth
phases. During the lag phase, the cell builds the biosynthetic pathways necessary for
maximal growth rates in the fresh medium. The lag phase is a period when cells attempt
to establish pseudosteady-state metabolic functions. Once pseudosteady state (balanced
growth) is established, cell growth is the fastest. During maximum growth, cell replication
rate is maximal, and the chemical composition of the cell population is nearly constant
(e.g. balanced growth). Total cell mass increases exponentially with time, which is the
reason this phase also termed exponential growth. Because of the exponential increase of
cell biomass with time, experimental data can be presented on semi-log plot to better illus-
trate the various phases of growth. When substrate is nearly exhausted or when toxic meta-
bolic by-products have built to a critical level, the growth rate begins to drop rapidly,
causing significant changes in biosynthetic pathways. In the stationary phase, there is no
net growth; cells now reorient their metabolic machinery to increase the probability of
long-term survival. At some point, some cells can no longer obtain enough energy from
their reserves or enough of another critical resource, and the culture enters the death phase.
Dead cells do not have an energized membrane and often lyse (or break apart). Nutrients
released by lysed cells can be utilized by survivors, allowing cryptic growth. Products
formed by cells can be related to this batch-culture growth cycle. Primary products are
growth associated. Secondary products are nongrowth associated and are made in the
stationary phase and/or death phase. Some products have both growth- and nongrowth-
associated components.
Batch cultivations are commonly applied in pharmaceutical and food productions. Strict
quality control up to the detailed process flow sheet by Food and Drug Administration
and the commonly low production rate are the main reasons for batch operations, among
others.