Biomedical Engineering Reference
In-Depth Information
taken for a mammalian cell to complete S [Figure 7.8(b)] phase is about 8 hours.
Another gap (
G
2
) follows when the newly duplicated chromosomes condense. In
the M period, the chromosomes divide into two sets, and the cell forms two nuclei
and then divides into two daughter cells. The length of the M phase is about 1 hour
and is also normally invariant. When normal cells differentiate, typically with a
gain in the properties required for organ or tissue functions, they generally lose the
capacity to continue cell division.
G
1
and
G
2
phases are required for the synthesis
of cellular constituents needed to support the following phase and ultimately to
complete cell division. The length of
G
2
phase is about 2 hours. The length of
G
1
phase is highly variable and can range from about 6 hours to several days or longer.
Nondividing cells are not considered to be in the cell cycle.
7.3.2.1 Calculating Cell Proliferation
Cells cultured in vitro undergo four major phases of growth [Figure 7.8(c)]. In the
lag phase or induction phase, cell division does not occur. The length of the lag
phase is mostly attributed to the type and age of the cell, cell density, and culture
parameters such as nutrient concentration. In the growth phase, the cell number
follows an exponential trend as division takes place. The growth rate increases with
the cell density. Lack of nutrients and overpopulation push the micro-organism into
a stationary phase where no further increase in cell density is to be expected. This
stage is followed by a decrease in the number of viable cells as a result of toxic waste
buildup and a depletion of nutrients.
Growth-phase classification is very important for control or optimization pur-
poses. Hence, it is commonly assumed that all cells are in the growth phase and
cells double with every cell cycle (i.e., the daughter cells themselves divide upon
completion of the next cell cycle). The most prominent parameter for analyzing cell
proliferation is the measurement of DNA content or synthesis as a specific marker
for replication. In measuring DNA synthesis, labeled DNA precursors ([3H]-Thy-
midine or 5-bromo-2
-deoxyuridine [BrdU]) are added to cells (or animals), and
their incorporation into genomic DNA is quantified following incubation and sam-
ple preparation. Incorporation of the labeled precursor into DNA is directly pro-
portional to the rate of cell division occurring in the sample. Exponential growth
is expressed as
′
XX
=
0
exp(
μ
t
)
(7.23)
where
X
is the number of cells (or number of cells per unit volume) at time
t
,
C
0
is
the initial number of cells seeded, and
is called the specific growth rate constant
with day
−1
units. While utilizing bioreactors for large-scale production, (7.23) is
rewritten in the differential form as
μ
dX
(7.24)
=
μ
X
dt
