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Stem cells have the potential to produce lineages of non-stem cellpopulations (differentiated cells) via a ubiquitous hierarchal division scheme.Differentiation of a stem cell into (partially) differentiated cells can happeneither symmetrically or asymmetrically. The selection dynamics of a mutantcancer stem cell should be investigated in the light of a stem cellproliferation hierarchy and presence of a non-stem cell population. Byconstructing a three-compartment Moran-type model composed of normal stemcells, mutant (cancer) stem cells and differentiated cells, we derive thereplicator dynamics of stem cell frequencies where asymmetric differentiationand differentiated cell death rates are included in the model. We determine howthese new factors change the conditions for a successful mutant invasion anddiscuss the variation on the steady state fraction of the population asdifferent model parameters are changed. By including the phenotypicplasticity/dedifferentiation, in which a progenitor/differentiated cell cantransform back into a cancer stem cell, we show that the effective fitness ofmutant stem cells is not only determined by their proliferation and death ratesbut also according to their dedifferentiation potential. By numerically solvingthe model we derive the phase diagram of the advantageous and disadvantageousphases of cancer stem cells in the space of proliferation and dedifferentiationpotentials. The result shows that at high enough dedifferentiation rates even apreviously disadvantageous mutant can take over the population of normal stemcells. This observation has implications in different areas of cancer researchincluding experimental observations that imply metastatic cancer stem celltypes might have lower proliferation potential than other stem cell phenotypeswhile showing much more phenotypic plasticity and can undergo clonal expansion.

Replicator Dynamics of of Cancer Stem Cell; Selection in the Presence of Differentiation and Plasticity