Characterization of hard limits on performance of autocatalytic pathways

In this paper, we develop some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their existing hard limits and essential tradeoffs. In a dynamical system with autocatalytic structure, the system´s output is necessary to catalyze its own production. We consider a simplified model of glycolysis as our motivating example. We study the hard limits of the ideal performance of such pathways. First, for a simple two-state model of glycolysis we explicitly derive the hard limit on the minimum L₂-gain disturbance attenuation and the hard limit of its minimum output energy. Then, we generalize our results to higher dimensional model of autocatalytic pathways. Finally, we show that how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production.