Monotonicity of Kinetic Proofreading

This manuscript studies the monotonicity of multi-step ligand-receptor signalling motifs. Monotonicity with respect to parameters and state perturbations allow not only to exclude periodic solutions, but also to easily bound the responses in cases of bounded perturbations. In classical coordinates, multi-step ligand-receptor signalling motifs are known not to be monotone. However, a generic coordinate transform allows for deriving conditions on the kinetic rate constants such that the signal is monotonously affected by perturbations to any one of the kinetic rate constants. The result is illustrated at the hand of a model of kinetic proofreading.