Fig. 1

The dynamics of the covalent modification cycle. a The schematic of the covalent modification cycle. b The abstract chemical reaction representation of the covalent modification cycle. c The abstract chemical reaction can be described by ordinary differential equations (ODE’s) using mass action kinetics. d Depending on the choice of reaction rates, the set of ODE’s exhibits four distinct mapping regimes [25]: (I) Hyperbolic. (II) Signal-transducing. (III) Threshold-hyperbolic. (IV) Ultrasensitive