Fig. 1: Minimal generic model of hierarchically differentiating tissues and corresponding cell lineage trees.
a cells are organized into n + 1 hierarchical levels based on their differentiation state. The bottom level (level 0) corresponds to tissue-specific stem cells, higher levels represent progressively differentiated progenitor cells, and the top level (level n) is comprised of terminally differentiated cells. Four microscopic events can occur with a cell: (i) asymmetric cell division, (ii) symmetric cell division with differentiation, (iv) symmetric cell division without differentiation and (iv) cell death. The number of cells on level k under normal homeostatic conditions is denoted by Nk. Under homeostatic conditions each level (except for the terminally differentiated one at the top) provides the next level with newly differentiated cells at a rate δk. Terminally differentiated cells at the top of the hierarchy cannot divide and are destined to wear away (i.e., leave the tissue). b At progenitor levels k > 0 in fully developed tissues under homeostatic conditions self-renewal replenishes only a fraction of the cells lost as cells arrive by differentiation from lower levels and, as a result, progenitor cells always have an inherent proliferative disadvantage. c Cell lineage trees in “wild type” tissues are shown for two different values of a uniform amplification factor γk = γ. Given the same rate of production of terminally differentiated cells (terminal tips of the cell lineage tree) larger values of γ correspond to a steeper decline in cell division rates towards lower levels, and slower dividing stem cells with longer progenitor sublineages (cf. the two sublineages highlighted with bold arrows). Longer sublineages for larger values of γ are the result of increased self-renewal (i.e., more symmetric cell division events shown in blue) and, equivalently, decreasing proliferative disadvantage of progenitor cells (cf. Eq. (8)).
