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.