(

**A**) 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**) Contour plot of the Hill number as a function of the allosteric bias and the relative dissociation rate obtained from . In this panel

, the allosteric bias is given by

and the relative dissociation rate is

with

and

.

**(C) An allosteric bias allows non-distributive systems to become ultrasensitive.** Contour plots of the Hill number as a function of the allosteric bias and the relative dissociation rate, obtained from solving 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).

## PubMed Commons