Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification - Mathematical Methods and Models in Biomedicine - page 195

SCs do not proliferate or differentiate at a constant rate. Rather, their behavior
is highly complex and closely regulated, attuned to the exact needs of the tissue at
any given time. For example, under normal conditions SCs might produce only a
few differentiated tissue cells (DCs) at a continuous rate, but if a tissue is injured,
the SCs may suddenly be required to produce larger quantities of DCs to repair
it. It is crucial that SC proliferation and differentiation correspond precisely to the
requirements of the tissue. Insufficiently rapid proliferation and differentiation may
impair tissue function, whereas overproliferation may result in uncontrolled growth
and increase the occurrence of mutations, which might be cancerous [ 7 ]. The need
to maintain the delicate balance between proliferation and differentiation implies the
existence of a dynamic regulatory mechanism that, at each point in time, determines
the fate of each SC in the tissue: according to the requirements of the tissue, the SC
either proliferates, differentiates, or is quiescent.
The SC fate decision mechanism is a key component of homeostasis ,orthe
maintenance of a stable internal environment, which is a fundamental condition
for life. The fate decision mechanism is responsible, for example, for ensuring
that the blood continuously contains enough red blood cells to carry oxygen to
remote corners of the body, while at the same time triggering immune responses to
unexpected, immediate threats. An understanding of SC fate decision can shed light
on the very essence of homeostasis. Correspondingly, if we examine what happens
when the fate decision mechanism malfunctions, we might be able to understand
what happens in diseases in which homeostasis is interrupted—such as cancer.
One approach to investigating the role of SC fate decision in cancer relates to
the theory of cancer stem cells. This theory suggests that, like healthy tissues,
cancers are characterized by a hierarchical structure, in which a small minority
of cancer cells (called cancer stem cells, or CSCs) have stem cell-like properties
[ 6 , 18 , 75 ]. CSCs can proliferate indefinitely and are responsible for tumor growth,
whereas the majority of (differentiated) cancer cells have only a limited ability
to proliferate [ 57 ]. Even a few CSCs can regenerate a depleted tumor following
treatment, and therefore, according to the CSC theory, the only way of effectively
curing disease is to eliminate the CSC population [ 39 ]. Therapeutic approaches
that target CSCs may entail simply killing these cells (elimination therapy) or,
alternatively, inhibiting their proliferation (inhibition therapy), or driving them to
differentiation (differentiation therapy), which eliminates their unlimited replication
capacity [ 78 ]. The latter two kinds of therapy involve interfering with CSC fate
decision mechanisms. A deeper understanding of SC and CSC fate decision could
be instrumental in the development of such treatments.
Herein we review a series of mathematical models formulated by Agur and col-
leagues, aimed at elucidating fate decision mechanisms in SC and CSC populations.
These models are, then, used to gain insight into cancer therapy.
The first SC model by Agur et al. is aimed to decipher homeostasis in developing
systems, using as few assumptions as possible [ 4 ]. This model is a cellular
automaton, general enough to represent any normally functioning tissue. The model
assumes that SC fate decision is determined by negative feedback, depending on