Effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor cells in mathematical models with feedback regulation

Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here.