Ultrasensitivity occurs because of sequestration of the substrate into one of two sinks (either fully phosphorylated and bound to kinase or fully dephosphorylated and bound to phosphatase) and is enhanced by the existence of an allosteric bias.

<p>(<b>A</b>) 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. Here we have , , s⁻¹, s⁻¹ (in units of the inverse total concentration of the substrate), s⁻¹, s⁻¹, . The Hill number is approximately 3.5. (<b>B</b>) Contour plot of the Hill number as a function of the allosteric bias and the relative dissociation rate obtained from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003175#pcbi.1003175.e141" target="_blank">Eq. (17)</a>. In this panel , the allosteric bias is given by and the relative dissociation rate is with and . <b>(C) An allosteric bias allows non-distributive systems to become ultrasensitive.</b> Contour plots of the Hill number as a function of the allosteric bias and the relative dissociation rate, obtained from solving <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003175#pcbi.1003175.e075" target="_blank">Eq. (12)</a> for . Left: purely distributive case (); centre: coexistence of distributivity and non-distributivity (); right: non-distributive case (). The relative dissociation rate is defined as in (B) and , except for the right panel where the relative dissociation rate is defined as and . In (B) and (C), the solid black line marks the boundary between subsensitivity (above the line) and ultrasensitivity (below the line).