Performance limitations in autocatalytic networks in biology

Autocatalytic networks, where a member can stimulate its own production, can be unstable when not controlled by feedback. Even when such networks are stabilized by regulating control feedbacks, they tend to exhibit non-minimum phase behavior. In this paper, we study the hard limits of the ideal performance of such networks and the hard limit of their minimum output energy. We consider a simplified model of glycolysis as our motivating example. For the glycolysis model, we characterize hard limits on the minimum output energy by analyzing the limiting behavior of the optimal cheap control problem for two different interconnection topologies. We show that some network interconnection topologies result in zero hard limits. Then, we develop necessary tools and concepts to extend our results to a general class of autocatalytic networks.