Ultrasensitivity in Phosphorylation-Dephosphorylation Cycles with Little Substrate
Figure 2
A model of a phosphorylation-dephosphorylation cycle for an allosteric substrate with multiple phosphorylation sites has two “sink” states and multiple competitions between the modifying enzymes for the substrate.
For each level of phosphorylation, the free substrate switches conformations allosterically between (inactive, in grey) and
(active, in yellow). The rate of allosteric transitions from active states to inactive states is
and the reverse rate of allosteric transitions from inactive states to active states is
. The kinase (in red) binds to the active forms of the substrate; the phosphatase (in blue) binds to the inactive forms. The two sinks
and
, are shown with shadows. The rate of association of the kinase to the substrate is
; the rate of dissociation of the kinase-substrate complex is
. Phosphorylation of a phosphosite resulting in dissociation of the kinase from the substrate has rate
per phosphosite (distributive catalytic rate represented by the diagonal black arrows). Phosphorylation of a phosphosite whereby the enzyme remains bound to the substrate has a rate
(non-distributive catalytic rate represented by the straight grey arrows). The rate of association of the phosphatase to the substrate is
and its rate of dissociation is
. De-phosphorylation of a phosphosite resulting in dissociation of the phosphatase from the substrate has a distributive rate
per phosphosite. Dephosphorylation of a phosphosite whereby the enzyme remains bound to the substrate has a non-distributive rate
.