Fundamental Limits and Tradeoffs in Autocatalytic Pathways

• Published in: arXiv.org 2017-06
• Main Authors: Siami, Milad, Nader Motee, Buzi, Gentian, Bamieh, Bassam, Khammash, Mustafa, Doyle, John C
• Format: Article
• Language: English
• Subjects: Attenuation; Chemical reactions; Glycolysis; Lumping; Tradeoffs
• ISSN: 2331-8422

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.