Each division of a somatic cell replicates its DNA, but the replication machinery cannot fully copy the very end of a linear chromosome — the end-replication problem. Every cycle the protective telomere cap shortens by a small amount ΔL:
L(n+1) = L(n) − ΔL·(1 − a)
a = telomerase activity, 0 ≤ a ≤ 1
if L(n) ≤ L_senescent → cell exits the cycle (Hayflick limit)
With telomerase inactive (a = 0), as in almost all normal somatic tissue, telomeres shorten a fixed amount per division. After roughly 40–60 divisions a cell reaches the Hayflick limit and becomes senescent: it stops dividing but stays metabolically alive, exactly as modelled here (orange cells).
Germline, stem and ~90% of cancer cells re-activate the enzyme telomerase, which rebuilds the telomere cap after each division. Raise the telomerase activity slider toward 100% and ΔL effectively drops to zero — the population keeps dividing indefinitely instead of aging out, the same escape from replicative senescence that makes a cell line "immortal" in culture (e.g. HeLa cells) or drives unchecked tumour growth.
The background apoptosis slider is a constant per-cell hazard of programmed cell death, independent of telomere state — it represents normal tissue turnover and immune clearance, and is what keeps an immortalized (high-telomerase) colony from growing forever even though its cells never senesce.
- Division interval — mean time between replication attempts for a cycling cell.
- Telomere loss / division — ΔL, the base erosion per replication before telomerase compensation.
- Telomerase activity — fraction of ΔL that is repaired each division; 100% ≈ immortalized cell line.
- Background apoptosis — probability per second that any single cell (dividing or senescent) is cleared.