Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification - Mathematical Methods and Models in Biomedicine - page 215

experimental protocol, i.e., duration of treatment with Dkk1 before and during
the mammosphere-forming assay (see Fig. 4 in [ 5 ]) or before the flow cytometry
of CD 44 + CD 24 −/ low cells. The latter result lends support to the prediction that
the CSC proliferation rate under low Dkk1 levels may vary in different tissues,
depending on parameters such as pathway activity levels and DCs' mortality.
In addition, the effect of Notch pathway activation and inhibition was examined.
For this purpose, Agur and colleagues investigated the response of MCF-7 cells
to a recombinant human Notch-receptor ligand DLL4, and to exposure to DAPT,
an inhibitor that blocks Notch receptor activity, as well as to knocking out Notch4
expression by siRNA. The experimental results confirm the role of Notch activation
in increasing proliferation rate in BCSCs, as predicted by the model.

7 Conclusion and Discussion

7.1 Establishment of the Quorum Sensing Theory in Healthy

Stem Cells and in Cancer

The series of mathematical models reviewed in this chapter was aimed at revealing
what determines homeostasis in developing tissues. The fundamental question
of homeostasis of tissue composition can, actually, be narrowed down to the
question of how SC fate is decided, between continued replication and commitment
to maturation. The understanding of this important control function might also
illuminate the possible derangements of SC fate decision in cancer, thus leading
to improved ways of controlling cancer progression.
The first SC model formulated by Agur and colleagues aimed to decipher the
basic regulation of SC fate decision that yields homeostasis in developing tissues.
Using a simple mathematical model, Agur et al. [ 4 ] showed that an extrinsic
control—QS, or negative feedback on SC replication—is sufficient for maintaining
homeostasis in a developing tissue, given the existence of an intrinsic control—a
cell-cycle clock.
The developed CA model was general, describing only basic universal properties
of SCs. No specific assumptions were made about tissue spatial structure, growth
rate, duration of cell cycle, or DC population characteristics, such as their life span.
This underlines the generality of the model's conclusion, regarding the significance
of the feedback of cell densities in the SC's environment on its fate decision. In other
words, the SC's ability to “count” its stem neighbors lies at the core of homeostasis.
The QS concept in the context of oncogenesis was established experimentally in
BCSCs as described above [ 3 ].
A more realistic model [ 90 ], implemented as a probabilistic CA, shed new
light on the role of QS-regulated fate decision in CSC-based tumor progression.
Simulations showed that the model yielded a quasi-steady-state of the proportion
of CSCs in the tumor cell population, which is comparable to the homeostatic