The Goldbeter–Koshland kinetics   describe a steady-state solution for a 2-state biological system. In this system, the interconversion between these two states is performed by two enzymes with opposing effect. One example would be a protein Z that exists in a phosphorylated form Z and in an unphosphorylated form Z; the corresponding kinase Y and phosphatase X interconvert the two forms. In this case we would be interested in the equilibrium concentration of the protein Z (Goldbeter–Koshland kinetics only describe equilibrium properties, thus no dynamics can be modeled). It has many applications in the description of biological systems.
The Goldbeter–Koshland kinetics is described by the Goldbeter–Koshland function:
with the constants
Graphically the function takes values between 0 and 1 and has a sigmoid behavior. The smaller the parameters J and J the steeper the function gets and the more of a switch-like behavior is observed. Goldbeter–Koshland kinetics is an example of ultrasensitivity.