Mathematical modeling of the loss of telomere sequences

Shortening of telomeres is one of the supposed mechanisms of cellular aging and death. An important question related to this so-called “end-replication” hypothesis is whether it can explain in quantitative detail the dynamic of cell sensescencein vitroandin vivo.A natural way to answer this question is to use mathematical modeling. In this paper, the models were successfully fitted to data on cultured fibroblasts from two different sources assuming that after reaching the Hayflick checkpoint on a single chromosome cells cease to proliferate. The main conclusion is that the end-replication hypothesis provides an explanation for the cell aging process which is quantitatively consistent with the data. As a secondary outcome, estimates were obtained of the rate of shortening of telomeres and several interesting mathematical results for branching processes with infinite type spaces arise.