Evolutionary dynamics of adult stem cells: Comparison of random and immortal-strand segregation mechanisms

This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes of chromosome segregation: (1) random segregation, where the daughter chromosomes of a given parent chromosome segregate randomly into the stem cell and its differentiating sister cell and (2) “immortal DNA strand” co-segregation, for which the stem cell retains the daughter chromosomes with the oldest parent strands. Immortal strand co-segregation is a mechanism, originally proposed by [Cairns Nature (London) 255, 197 (1975)], by which stem cells preserve the integrity of their genomes. For random segregation, we develop an ordered strand pair formulation of the dynamics, analogous to the ordered strand pair formalism developed for quasispecies dynamics involving semiconservative replication with imperfect lesion repair (in this context, lesion repair is taken to mean repair of postreplication base-pair mismatches). Interestingly, a similar formulation is possible with immortal strand co-segregation, despite the fact that this segregation mechanism is age dependent. From our model we are able to mathematically show that, when lesion repair is imperfect, then immortal strand co-segregation leads to better preservation of the stem cell lineage than random chromosome segregation. Furthermore, our model allows us to estimate the optimal lesion repair efficiency for preserving an adult stem cell population for a given period of time. For human stem cells, we obtain that mispaired bases still present after replication and cell division should be left untouched, to avoid potentially fixing a mutation in both DNA strands.

Figure 1

(Color online) Generation of differentiated tissue cells (green/lighter gray) from an adult stem cell (blue/darker gray).

Figure 2

(Color online) Illustration of immortal DNA strand chromosome segregation. The red/dark gray lines represent newer strands, while the brown/lighter gray line represents the oldest template strand.

Figure 3

A comparison of theory and simulation for a population of 10 000 stem cells with genomes of sequence length 20. We assume $k_{+}=10$, $k_{-}=1$, $\mu =0.1$, and $l=1$. We iterated in time steps of length 0.001 out to a time of 10.