Population balancing with species switching

Abstract

Biological organisms are composed of cells differentiated from stem cells. Emerging evidence suggests phenotypic switches of differentiated cells, called transdifferentiation, during development and under pathophysiological conditions. To examine the role of transdifferentiation for population balances, we construct a stochastic model mapped into urn problems. When a colored ball is drawn from an urn, one additional ball with the same color is put into the urn in Polya’s urn scheme while the drawn ball is replaced by another ball with different color in Ehrenfest’s urn scheme. Our population balance model is a mixture of the two classic urn problems corresponding to cell replication and transdifferentiation. Because a dominant population is more likely to be drawn, the preferential replication and transdifferentiation of the dominant population contribute to increasing and decreasing the gap between the two populations, respectively. Therefore, their competition determines population balancing. We analyze the dependence of population dynamics on the replication and the transdifferentiation rates of each population. Finally, experimentally probing the event of transdifferentiation is a challenging problem because it is indistinguishable from death of one cell type and concurrent replication of another cell type. Our analysis suggests that transdifferentiation generates fewer fluctuations in population dynamics than the combined events of cell death and replication do.