Engineering insulation from retroactivity of the frequency response of covalent modification cycles

A bottom-up approach to designing biomolecular circuits in living cells is based on composing simple working modules to create larger circuits with more complicated functions. For this approach to work, the behavior of the modules should be, to some extent, isolated from that of the surrounding modules. Unfortunately, impedance effects in biomolecular systems, called retroactivity, alter the behavior of a module upon interconnection with other systems. In this paper, we perform a mathematical analysis of a Goldbeter-Koshland covalent modification cycle, a recurrent circuit structure in natural signal transduction networks, and demonstrate that it can be tuned to function as an insulating amplifier, hence buffering systems from retroactivity.