Optimal design of phosphorylation-based insulation devices

We seek to minimize both the retroactivity to the output and the retroactivity to the input of a phosphorylation-based insulation device by finding an optimal substrate concentration. Characterizing and improving the performance of insulation devices brings us a step closer to their successful implementation in biological circuits, and thus to modularity. Previous works have mainly focused on attenuating retroactivity effects to the output using high substrate concentrations. This, however, worsens the retroactivity to the input, creating an error that propagates back to the output. Employing singular perturbation and contraction theory tools, this work provides a framework to determine an optimal substrate concentration to reach a tradeoff between the retroactivity to the input and the retroactivity to the output.