Code for EEC propotion simulation

Computer simulation of EEC production under probabilistic symmetric ISC divisionsTo assess whether the experimentally observed EEC clonal distribution remains consistent with a fixed-number division model when symmetric ISC divisions occur at a biologically plausible rate, we performed stochastic lineage simulations. The simulations incorporated the regionally fitted symmetric division probability (r = 3.87%) (i.e., probability of an ISC symmetric division event is 2r), with the complementary probability (λ = 1 - 2r = 92.26%) for ISC asymmetric divisions.Simulation frameworkEach simulation started from a single ISC (cell type A). Two alternative fate‑specification rules were tested:1. Fixed-number (k=9) division model: The ISC undergoes 8 consecutive divisions under Rule 1 (outcomes: ISC+ISC with probability r, EB+EB with probability r, or ISC+EB with probability λ). At the 9th division, the ISC switches to Rule 2, producing one ISC and one EEC (cell type C). After this event, the division counter resets, and the ISC resumes Rule 1 for the next 8 divisions.2. Fixed-probability (P=10%) model: At every division, the ISC has a fixed probability P = 0.1 of generating an EEC. The division outcomes are: ISC+ISC (r), EB+EB (r), ISC+EB (λ- P), or ISC+EEC (P).Differentiated cells (EBs and EECs) do not divide further. Each lineage simulation continued until either the total cell count reached 15 or no ISC remained. For each model, 100,000 independent lineage simulations were performed.Data extraction and comparison with experimentFrom each simulated lineage, we recorded the total clone size t and the number of ISCs present. Only lineages containing exactly one ISC were selected for analysis, mirroring the experimental filtering step. For each clone size t, we calculated the percentage of such one‑ISC clones that contained at least one EEC.