3 problems

For each $m\geq 2$, consider the weakly and strongly irreversible $m$-site phosphorylation networks and their parameter regions of multistationarity. Connectedness conjecture. The…

For a fixed $m\in\mathbb{N}$, consider the $m$-site phosphorylation cycle with Michaelis–Menten phosphorylation steps, reaction-rate constants $\kappa$, and parameters $c$. The ful…

Sharpness conjecture. The upper bound $2n-1$ can be attained for suitable parameter values.