Sharp equilibrium and stable-state capacities of multisite phosphorylation
For the sequential distributive $n$-site phosphorylation cycle with one kinase and one phosphatase, the maximal number of positive equilibria is $2n-1$ and the maximal number of locally asymptotically stable equilibria is $n$, for every $n\ge1$. The stable-state ceiling includes nonhyperbolic attractors. Both bounds are attained simultaneously at common conserved totals by rational positive rate constants and rational hyperbolic equilibria: $n$ sinks alternate with $n-1$ saddles, each with one unstable direction. This configuration persists on a nonempty open subset of the full parameter…
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