Fundamental Limits and Tradeoffs in Autocatalytic Pathways
For researchers studying autocatalytic networks (e.g., metabolic pathways), this work provides theoretical bounds and tradeoffs, though the results are derived for simplified models.
This paper derives hard limits on disturbance attenuation and output energy in autocatalytic pathways, revealing fundamental tradeoffs between transient and steady-state behavior and net production.
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.