Huntingtin exon-1 fragments carrying an expanded CAG-repeat tract misfold into a polyglutamine (polyQ) β-sheet and self-assemble by nucleated polymerization — the same two-step kinetic scheme used for amyloid-β and other amyloidogenic proteins. This 2D twin drives the identical kinetics as an explicit size-dependent addition-rate function rather than a fitted curve:
k_add(s, Q) = k_slow(Q) if s < n*(Q) (nucleation regime — slow)
k_add(s, Q) = k_fast if s ≥ n*(Q) (elongation regime — fast)
k_slow(Q) = k0 · exp[ α (Q − Qc) ], Qc ≈ 36
n*(Q) decreases as Q grows (disease-severity correlation)
Every tick, the probability that the aggregate captures one more free monomer is 1 − exp(−freeCount · k_add(s,Q) · D · dt) — a Bernoulli approximation of a Gillespie stochastic-simulation step. While the aggregate is smaller than the critical nucleus, captures are rare (k_slow is tiny), producing the lag phase. The moment the aggregate crosses n*(Q), the rate jumps to k_fast and growth accelerates sharply — rapid elongation — until the free-monomer pool is depleted and the curve plateaus. No sigmoid formula is written anywhere; the S-shape is an emergent result of this two-regime rate.
- CAG repeat length Q — sets both n*(Q) (smaller nucleus needed at higher Q) and k_slow(Q) (nucleation accelerates steeply above the ~36-repeat pathogenic threshold), matching the length-dependence measured for huntingtin exon-1 in vitro.
- Monomer pool size — starting free-monomer count; more monomers raise the encounter rate driving both regimes.
- Diffusion rate D — Brownian-motion speed (temperature/viscosity proxy); it scales the encounter-limited capture rate directly, as in real diffusion-limited kinetics.
Use Run repeat-length sweep to fast-simulate several Q values back-to-back (averaged over replicates) and read off the measured lag time t₅₀ (time to reach 50% of the pool aggregated) for each — it comes out shorter as Q grows, exactly the disease-severity trend.