A Contraction Theory-based Framework for the Design of Robustness to Global Perturbations in Biomolecular Circuits

It is challenging to design robustness against global perturbations that affect the plant as well as the controller. A particular instance of practical importance is the design of biomolecular circuits that are robust to global variables such as temperature. To address this, we developed a framework based on contraction theory and used mathematical models as case studies. We mathematically modelled the global effect on parameters as an additive state-dependent uncertainty. We quantified the difference between the perturbed and the nominal system trajectories for the global perturbations. For specific biomolecular circuit designs, we noted that as the contraction rate increased, the envelope between the nominal and the perturbed trajectory shrunk, resulting in robust behaviour. These results should help in the rational design of robustness in systems with global perturbations such as in biomolecular circuits.