Fig. 4. Schematic of the mathematical model.

The model considers an extracellular stimulus triggering the autophosphorylation of HK and activating a TCS pathway. The phosphorylated HK can transfer the phosphoryl group to its cognate RR, which can bind DNA and trigger a response including the synthesis of the HK and RR proteins, marking positive autoregulation. The phosphorylated HK could bind non-cognate RRs (red) preferentially, when the latter have higher affinity for the HK than its cognate RR, resulting in HK sequestration and the suppression of cognate signaling. Only with a sufficiently strong stimulus does sufficient HK autophosphorylation result leading to cognate RR binding despite sequestration and the mounting of a response through the cognate pathway. Equations (1–19) list the reaction events in this model. The rate equations are in “Methods” section.