Fig 3. A two-state model of PhoPQ TCS can explain biphasic response.

A -Schematic of the two-state model. PhoQ exists in phosphatase (PhoQ) or kinase (PhoQ*) form, PhoQ* assumed to bind Mg²⁺ and switch to PhoQ. Concentration of Mg²⁺ in medium assumed constant, and absorbed into a pseudo-first order kinetic rate, k₋₁ (blue arrow). MgrB reversibly binds PhoQ/PhoQ*. B—Simulated output (normalized YFP:CFP; Methods) from the ODE model representing schematic in A with two rate constants suppressed in MgrB bound PhoQ. The pre-factor $k_{-1}^0(s^{-1}m{M}^{-1})$ converts Mg²⁺ concentration (mM) to rate constant k₋₁(s⁻¹). The affected rates are denoted by red arrows: switching rate from phosphatase to kinase (i.e. k₁, PhoQ-Mg²⁺ dissociation), and autophosphorylation. Detailed balance condition is satisfied by assuming PhoQ-MgrB dissociation is suppressed by the same factor as k₁. Simulated steady state output shows biphasic response to increasing signal.