Each round of DNA replication cannot fully copy the very end of a linear chromosome (the end-replication problem), so the double-stranded telomeric repeat tract shortens by roughly 50–200 bp per division while a short single-stranded 3′ overhang remains. The shelterin complex folds that overhang back to invade the duplex, forming a T-loop that physically hides the chromosome end from the cell's DNA-repair machinery.
T-loop probability: P = 1 / (1 + exp(-(D - Dc) / k))
scaled by shelterin: P_eff = P · (0.4 + 0.6·S)
DNA-damage signal: DDR → (1 - P_eff) · 100% (relaxes toward this target)
Replication loss: ΔL ≈ -(100 to 150) bp per division (+telomerase gain if active)
Expected divisions: E[N] = Σ_{n=0..∞} S_n , S_n = Π_{i=1..n} P_eff(D_i)
D is the double-stranded telomere length, Dc ≈ 1,500 bp is the critical length below which there usually isn't enough duplex left for stable strand invasion, k sets how sharply the transition happens, and S ∈ [0,1] is the shelterin level. When the T-loop can't be maintained, the exposed end is read by the cell as a double-strand break and the cell exits the cycle — replicative senescence, the cellular basis of the Hayflick limit. The population panel runs thousands of independent lineages through the same probabilistic rule and compares the measured average division-count-to-senescence against the closed-form expectation E[N] above.
- Telomere length / Shelterin level — set the starting duplex length and how much protective complex is available.
- Divide Cell / Auto-divide — runs replication cycles one at a time or continuously; each shortens the duplex via the end-replication problem (and regrows it if telomerase is active).
- Run lineages — simulates thousands of independent cells from the current settings and reports how many divisions each survived before its T-loop first failed to form, cross-checked against the formula.