Phosphorylation-dephosphorylation cycles can generate non-monotonic input-output relationships.

<p>Here the allostery of the substrate inhibits further modifying reactions by disfavouring binding of the kinase when the substrate is phosphorylated and disfavouring binding of the phosphatase when the substrate is dephosphorylated. Simulation of the response curve (in black) and the concentration of the states of the system (coloured bars) as a function of the signal, i.e., the ratio of phosphatase to kinase, for a system where , , s⁻¹, s⁻¹, s⁻¹ (in units of the inverse total concentration of the substrate), s⁻¹, s⁻¹, .