Figure 4. Ultrasensitivity in covalent modification cycles with a bifunctional converter enzyme.

(A) Reaction scheme: A substrate molecule () undergoes reversible phosphorylation by a bifunctional converter enzyme which can exist in two activity states. Binding of the allosteric effector inhibits the kinase activity () and, concomitantly, activates the phosphatase activity () of the enzyme. (B) As the value of the dissociation constant is lowered from to (from right to left) the steady state curve becomes ultrasensitive near the transition point , as defined in Eq. (21). The solid lines were computed from the full model using Eqs. (4)–(7). Dashed lines were computed from the reduced models using Eq. (14) (right curve) and Eq. (18) (left curve). Parameters: , , so that , and (for ) or (for ).