Stability and Control of Biomolecular Circuits through Structure

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building feedback control through such structures. In this work, we develop the tool of log derivatives to capture structures in how the production and degradation rates of molecules depend on concentrations of reactants. We show that log derivatives could establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through the structures captured. Due to the methods simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations.