Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification - Mathematical Methods and Models in Biomedicine - page 217

of an external, well-defined niche structure is not necessary for controlling the
replication-differentiation balance. The niche could be formed spontaneously, with
required conditions for SC proliferation and differentiation being supplied by the
SC population itself. This proposition is supported by mathematical analysis [ 44 ]of
the model for intra- and intercellular feedback mechanisms.

7.2 Implications of Model Analysis for Cancer Therapy

Theoretical analysis and simulations of these mathematical models have already
yielded some conclusions that may help open new directions for cancer therapy.
First, the intensity of SC-to-SC signaling was found to be a critical factor in the
maintenance of tissue balance. Insufficient signal intensity, either due to environ-
mental factors, or due to insufficient signal receipt, as a result of mutations inherent
in the SCs themselves, was shown to lead to excessive SC proliferation until they
completely deplete the DC population from the tissue [ 3 ]. This implies that cancer
initiation may be stimulated by changes in the microenvironment, affecting the
magnitude of the signals transduced to SCs, and that this process can be reversible
under environmental changes that modify the signal intensity. If cancer initiation is
caused by increased mutagenesis [ 58 ], no epigenetic process can prevent it.
Exploring the system behavior under various possible manipulations, changing
factors that influence proliferation and differentiation rates, suggested that only
combinational therapy that targets both CSC proliferation and differentiation can
be effective [ 90 ]. This is in line with clinical experience, since drugs targeting CSCs
were found to be clinically more effective when combined with each other, or with
conventional therapy that mainly targets DCs [ 27 , 68 ].
The implementation of a molecular model of processes on the intracellular scale
pointed to Dkk1 as a key factor in SC fate decision regulation [ 5 ]. Dkk1 can be
used for differentiation therapy and is expected to be more effective than other
agents stimulating SC differentiation, since it also reduces proliferation. According
to the model, Dkk1 therapy challenges the QS-regulated fate decision, which is a
general cellular homeostasis mechanism; hence, it should be more robust than other
methods. However, the generality of the model does not allow parameter estimation
that would be accurate enough to estimate the optimal Dkk1 dosage. Optimizing
the dosage of Dkk1 administration is crucial to effectiveness of therapy, since both
simulations and experimental results showed that too low administration of Dkk1
may stimulate CSC proliferation. This may not only be ineffective in eliminating
the tumor, but also lead to the opposite result.
The simulation results also provide new insights into the tumor growth rate.
Simulation results imply that tumor radius grows linearly with time, i.e., the growth
of tumor volume is cubic in time [ 90 ]. This finding is corroborated by experimental
results [ 48 ]. Yet only a few previous studies have related to the possibility of
a power-law tumor growth rate [ 26 , 31 , 36 ], whereas it is widely accepted to
model tumor growth as exponential or Gompertzian (e.g., [ 49 ]). This could have