Von Neumann's expanding model on random graphs

Abstract

Within the framework of Von Neumann's expanding model, we study the maximum growth rate r achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating) number D of reagents. r is calculated numerically using a variant of the Minover algorithm, and analytically via the cavity method for disordered systems. As the ratio between the number of reactions and that of reagents increases the system passes from a contracting (r<1) to an expanding regime (r>1). These results extend the scenario derived in the fully connected model ($D\to\infinity$), with the important difference that, generically, larger growth rates are achievable in the expanding phase for finite D and in more diluted networks. Moreover, the range of attainable values of r shrinks as the connectivity increases.

20 pages

References in corpus (4)

• The large-scale organization of metabolic networks
• The random K-satisfiability problem: from an analytic solution to an efficient algorithm
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices

Cited by in corpus (10)

• Energy metabolism and glutamate-glutamine cycle in the brain: a stoichiometric modeling perspective
• Identifying essential genes in E. coli from a metabolic optimization principle
• A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks
• The solution space of metabolic networks: producibility, robustness and fluctuations
• Statistics of optimal information flow in ensembles of regulatory motifs
• Boolean constraint satisfaction problems for reaction networks
• Von Neumann's growth model: statistical mechanics and biological applications
• Optimal flux states, reaction replaceability and response to knockouts in the human red blood cell
• Stock-flow consistent macroeconomic model with nonuniform distributional constraint
• Identifying all irreducible conserved metabolite pools in genome-scale metabolic networks: a general method and the case of Escherichia coli