Topological tradeoffs in autocatalytic metabolic pathways

Metabolic pathways in cells convert external food and resources into useful cell components and energy. In many cases the cell employs product inhibition to regulate and control these pathways. We investigate the performance of such regulation and control on certain autocatalytic pathways. Specifically, we examine how well the pathways can maintain the desired output concentrations in the presence of disturbances, such as perturbations in resources, enzyme concentrations and product demand. Using control theoretic tools, we show the effects of the pathway size, the reversibility of the intermediate reactions and the coupling of pathways through the consumption of intermediate metabolites on performance. In addition, we establish some necessary conditions on the existence of fixed points and their stability for such pathways.