Philip Greulich

Universal laws in stem cell biology from graph theory and population dynamics

Stem cells are the key players in tissue development and maintenance. The latter is achieved by (adult) stem cells' unlimited potential to divide ('self-renewal') and their ability to differentiate into all tissue-specific cell types, via a lineage hierarchy at whose apex the stem cells reside. But why has nature "invented" stem cells and such lineage hierarchies? Is it a coincidence of evolution or a (mathematical) necessity for maintaining a tissue in a healthy, homeostatic state? In this talk, I wish to address this question in a mathematically rigorous way, recognising that homeostasis means strict constraints on the population dynamics of tissue cells, which can be understood by dynamical systems and graph theory. As a consequence, the lineage architecture of homeostatic tissues is necessarily highly constrained and the two defining characteristics of stem cells, self-renewal and lineage potential, necessitate each other in homeostasis. Furthermore, we will see that any cell that can divide has the potential to become a stem cell if it is able to respond appropriately to the surrounding cell density, which could lead to "quasi-dedifferentiation". Finally, I will show how these findings can aid the inference of stem cell renewal strategies through modelling, as they reveal a small number of universality classes with respect to the clonal cell population dynamics.