Description
The ends of linear chromosomes, called telomeres, shorten at each cell replication, eventually driving the cells to a senescent state when they become too short. The enzyme telomerase, present in cancerous cells and some unicellular organisms, elongates the telomeres and allows cells to continue replicating. Recent experiments show that if this enzyme is inactivated some rare survivors (ALT), which elongate their telomeres without telomerase, will appear and will eventually invade the cultures.
To model the emergence and invasion of the ALT cells we study the large population limit of a simple stochastic particle system under appropriate scaling assumptions corresponding to rare mutations and different division rates depending on the cell type. This limit involves classical results on density-dependent Markov processes together with a sharp control of the mutant process, which starts with a single individual.