  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. We
consider a simplified model of Glycolysis pathway as our motivating
application. First, the properties of these class of pathways are investigated
through a simplified two-state model, which is obtained by lumping all the
intermediate reactions into a single intermediate reaction. Then, we generalize
our results to autocatalytic pathways that are composed of a chain of
enzymatically catalyzed intermediate reactions. 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. Finally, 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.
