Open Research Index

Attracting oscillations in sequential distributive phosphorylation

Michael Mislan

Palomar Registrypalomar/PALOMAR-2026-09-30-000009Sep 30, 2026math.DSscore 0

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…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-30-000009
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-30-000009/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-30-000009/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'