Fundamental limits on performance of autocatalytic pathways with chain topologies

In this paper, we develop some basic principles to study dynamical networks and exploit their structural properties in order to characterize their existing hard limits and essential tradeoffs. Our main focus is on an important class of interconnected network of dynamical systems so called autocatalytic networks. In an interconnected dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. We study cascade interconnection of autocatalytic pathways with chain topologies. It is shown that whenever autocatalytic feedbacks are active in all pathways, some fundamental tradeoffs between transient behavior of the network and its net production emerges. We use glycolysis pathway as our motivating example and develop our network models around this canonical model.