A mathematical model of cellular apoptosis and senescence through the dynamics of telomere loss

The shortening of telomeric repeats as a cell replicates has long been implicated as a determinant of cell viability. However, recent studies have indicated that it is not telomere length, but rather whether telomeres have bound a telomere-related protein, which in mammals is TTAGGG repeat binding factor-2 (TRF2), that determines whether a cell undergoes apoptosis (programmed cell death), enters senescence (a quiescent, non-replicative state), or continues to proliferate. When bound to a telomere, TRF2 allows a cell to recognize the telomere as the point where a chromosome ends rather than a break in DNA. When telomeres are not bound by TRF2, the cell can either immediately trigger senescence or apoptosis via the DNA damage response pathway, or indirectly trigger it by attempting to repair the chromosome, which results in chromosomal end joining. We model the ability of telomeres to bind TRF2 as a function of telomere length and apply the resulting binding probability to a model of cellular replication that assumes a homogeneous cell population. The model fits data from cultured human fibroblasts and human embryonic kidney cells for two free parameters well. We extract values for the percent of telomere loss at which cell proliferation ceases. We show, in agreement with previous experiments, that overexpression of TRF2 allows a cell to delay the senescence setpoint. We explore the effect of oxidative stress, which increases the rate of telomere loss, on cell viability and show that cells in the presence of oxidative stress have reduced lifespans. We also show that the addition of telomerase, an enzyme that maintains telomere length, is sufficient to result in cell immortality. We conclude that the increasing inability of TRF2 to bind telomeres as they shorten is a quantitatively reasonable model for a cause of either cellular apoptosis or senescence.