Fundamental Limits and Tradeoffs in Autocatalytic Pathways

Abstract

This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. Our study has been motivated by a simplified model of a glycolysis pathway. First, the properties of this class of pathways are investigated through a network model, which consists of a chain of enzymatically catalyzed intermediate reactions coupled with an autocatalytic component. We explicitly derive a hard limit on the minimum achievable $\mathcal L_2$ -gain disturbance attenuation and a hard limit on its minimum required output energy. Then, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production.