Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification - Mathematical Methods and Models in Biomedicine - page 199

to be mutated in cancer [ 57 , 83 ]. Researchers have begun to seek ways of targeting
CSCs by blocking or modifying these pathways, with the aim of allowing specific
CSC therapy without affecting normal SCs [ 77 ].

4 Mathematical Modeling of Stem Cell Fate Decision

Understanding the mechanisms regulating SC fate decision is fundamental to
understanding homeostasis—a basic condition for life. Specifically, deciphering fate
decision in CSCs may be key to controlling and eliminating tumor growth. Although
more and more biological data have become available regarding multiple factors in
the microenvironment that affect SC fate decision [ 57 ], it is still not fully understood
what controls an SC's decision to replicate or to differentiate into self-amplifying
progenitors.
Over the last few years, mathematical models based on biological data have been
proposed to describe SC fate decision processes at the cellular and intracellular lev-
els. Some models have described the kinetics of molecular dynamical mechanisms,
such as signaling pathways (e.g., [ 2 , 44 ]). Systems biology approaches have been
employed to investigate intracellular signaling pathways and transcription factor
networks that play a role in determining SC fate (for a review see [ 70 ]).
In order to understand the dynamics of normal and cancerous tissues, which
might enable researchers to identify drug targets for controlling tumor cell popu-
lations, it is not sufficient to investigate intracellular molecular processes. Rather,
it is necessary to examine the tissue as a whole. Several mathematical models have
been proposed to describe the role of SCs and CSCs in tissue balance. Many of
these models used continuous ordinary differential equations (ODE) systems to
describe the dynamics of different cell subpopulations (e.g., SCs and DCs) [ 22 -
24 , 30 , 51 , 60 , 61 , 67 , 71 , 73 , 80 , 85 , 96 ]. Others are discrete cellular automata models,
where the behavior of individual cells is followed [ 3 - 5 , 8 , 28 , 59 , 64 , 91 ]. Most of
these studies did not focus on the regulation of fate decision and did not examine
the validity of the methods used to model this decision. SC control was either
considered stochastic, with fixed probabilities of differentiation and replication (e.g.,
[ 85 ]), or described by generic feedback from a homogeneous environment, with no
specified underlying mechanisms [ 22 - 24 , 30 , 61 , 67 , 73 , 80 ]. Some of the models
[ 51 , 71 , 96 ] introduce regulation by specific environmental signals (e.g., NF- B,

GDF11 or EGFR), but they did not consider cell-to-cell interactions. Many of the
models apply to specific systems and cannot be generalized [ 8 , 59 , 60 , 64 , 91 ].
In what follows we describe a series of models by Agur and colleagues, which
focus both on tissue-level cell-population dynamics and on intracellular molecular
signaling in order to describe SC and CSC behavior. The models rely on a
minimum of assumptions, all of which concern the SC fate decision mechanism.
This minimalism enables the models to provide generalizable conclusions and
concrete therapeutic recommendations that are not restricted to specific tissue or
disease types.

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