Biomedical Engineering Reference
In-Depth Information
is such that the time duration of the S, G
2
, and M phases is relatively fixed. Once a cell
determines it needs to and can divide, it initiates DNA synthesis and subsequent cell divi-
sion. This process has the overall characteristics of a zero-order kinetic process. Once
initiated, it proceeds at a certain rate. The minimal cycling time of human cells is about
12 hours. Progenitor cells can cycle at this rate, whereas more differentiated cell types tend
to have longer cycle times.
DESCRIBING THE CELL CYCLE DYNAMICS
The dynamics of growth can be described in different ways.
1.
Exponential growth
. If growth is unconstrained, the rate of formation of new cells is
simply proportional to the number of cells present
dX
dt
¼
m
X
,
)
X
ð
t
Þ¼
X
o
exp
ð
m
t
Þ
ð
6
:
7
Þ
and exponential growth results. The growth rate
m
is equal to ln(2)/t
d
, where t
d
is the
doubling time.
2.
Age-time structured descriptions.
If the phases of the cell cycle are to be described, then
the status of the cell in the cycle needs to be incorporated in the dynamic description.
This leads to first-order partial differential equations in time and cell cycle status:
dX
dt
þ
v
dX
da
¼
a
ð
a
Þ
x
ð
6
:
8
Þ
where
v
is the rate at which the cell moves through the cell cycle,
a
is a variable that
describes the cell cycle status (
a
¼
0 newborn cell,
a
¼
1 cell completing mitosis), and
a
is the death rate of the cell that can be cell cycle dependent. This population balance
equation can be solved under the appropriate initial and boundary conditions.
3.
Molecular mechanisms.
The cascade of cyclin-dependent kinases that constitute themolecular
mechanism for cell cycling has largely been unraveled. Based on this knowledge, it is
possible to describe the cell cycle in terms of the underlying molecular determinants. Such
models have many components and typically need to be solved using computational
methods.
Interacting Cellular Fate Processes Determine Overall Tissue Dynamics
The differentiation process involves a series of changes in cell phenotype and morphol-
ogy that typically become more pronounced at the latter stages of the process. The key
event is milieu-dependent differentiation (or differential gene expression), which encom-
passes the organogenic process that yields mature cells of a certain type and function. Simi-
larly, embryonic induction can be described as a series of such events. This process is
schematically presented in Eq. (6.1).
This progression of changes is typically coupled to fundamental “driving forces”—for
example, cell cycling (
mitosis)
and cell death (apoptosis). Thus, the basic cellular processes
can be accounted for in a population balance on each stage of differentiation:
D
's in cell#
¼
exit by input
differentiation
exit by apoptosis
þ
entry by cell division
