Starvation suppression in scale-free metabolic networks: Dynamical mean-field analysis of dense catalytic reaction networks

Abstract

Cellular metabolic networks exhibit scale-free topologies with power-law degree distributions across diverse organisms. Although such topologies are often linked to mutational robustness and evolutionary advantage, their role in metabolic dynamics remains unclear. Using dynamical mean-field theory, we derive an exact solution for an intracellular catalytic reaction model on dense random networks with arbitrary degree distributions. We show that the metabolic-starvation transition observed under nutrient-poor conditions for homogeneous degree distributions disappears when the out-degree distribution is scale-free. We also show that the power-law distribution of biomolecular abundances observed in real cells reflects the power-law in-degree distribution of the underlying catalytic reaction network. Large-scale numerical simulations validate these predictions. Our results provide a theoretical framework linking network topology and metabolic dynamics, and identify a dynamical advantage of scale-free topology under nutrient limitation.