Michael Mislan

Attracting oscillations in sequential distributive multisite phosphorylation

The sequential distributive n-site phosphorylation cycle with one kinase and one phosphatase admits attracting positive periodic orbits under mass-action kinetics for every n≥3. An explicit three-site family has a fixed positive equilibrium, a transversal imaginary-eigenvalue cro...

Endotactic permanence and quantitative recovery with vanishing reverse rates

For a finite ordinary endotactic reaction network, measurable reaction rates in a fixed positive compact box admit a compact convex invariant absorbing set in every positive stoichiometric class. Global positive Carathéodory solutions are unique, and entry times are uniform over...

Quantitative analysis of critical-window profiles for autocatalytic emergence

The critical-window profiles for RAF emergence in reversible binary-polymer networks are studied in the split-position and commuting-factor quotient catalogues, with monomer/dimer food. Total algorithms enclose survival probabilities at every rational openness to arbitrary prescr...

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≥1. The stable-state ceiling includes nonhyperbo...