{"id":"palomar/PALOMAR-2026-09-30-000009","url":"https://github.com/mmislan/palomar-p064-multisite-phosphorylation-oscillations/tree/99597afe8632cbd41f0ffec6c04f73a554ba9881","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000009-v1.json","repo":"https://github.com/mmislan/palomar-p064-multisite-phosphorylation-oscillations","tags":["math.DS","q-bio.MN","msc:34C23","msc:37G15","msc:34D20","msc:92C45","dynamical-systems","hopf-bifurcation","phosphorylation","mass-action"],"score":0,"title":"Attracting oscillations in sequential distributive phosphorylation","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"Vassena (arXiv:2608.27081v2, Section 8) left open whether sequential distributive phosphorylation cycles with three or more sites admit Hopf bifurcation under mass-action kinetics. For every n >= 3, a componentwise-affine family of positive rate constants is constructed for the n-site cycle with one kinase and one phosphatase and a fixed positive equilibrium. A family of strictly positive, nonconstant periodic orbits bifurcates from this equilibrium, with amplitudes tending to zero and periods tending to a finite positive limit. Each orbit is orbitally asymptotically stable within its…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true,"formalizes":[{"title":"Attracting oscillations in sequential distributive multisite phosphorylation: dynamic enzyme sequestration and what static elimination cannot see","identifier":"","relationship":"formalizes"}]}