Two-component feedback loops and deformed mechanics

• Two-component molecular feedback loops are viewed as q-deformed Hamiltonian systems.
• Deformations are reversed using Jackson derivatives to take advantage of working in the Hamiltonian limit.
• New results are derived for the particular examples considered.
• General deformations are suggested to be associated with a broader class of biological processes.

It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed.