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

TL;DR

This paper uses dynamical mean-field theory to analyze how scale-free topologies in metabolic networks influence cellular dynamics, revealing that such structures can prevent starvation transitions and reflect in molecular abundance distributions.

Contribution

It provides an exact analytical solution for catalytic reaction networks with arbitrary degree distributions, linking network topology to metabolic behavior under nutrient scarcity.

Findings

Scale-free out-degree distribution eliminates starvation transition.

Biomolecular abundance distribution mirrors network degree distribution.

Numerical simulations confirm theoretical predictions.

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.