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

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 a power-law in-degree distribution of the underlying catalytic reaction network gives rise to a power-law distribution of biomolecular abundances with the same exponent. Large-scale numerical simulations validate these predictions. Our results provide a theoretical framework linking network topology and metabolic dynamics.