We study a statistical model describing the steady state distribution of thefluxes in a metabolic network. The resulting model on continuous variables canbe solved by the cavity method. In particular analytical tractability ispossible solving the cavity equation over an ensemble of networks with the samedegree distribution of the real metabolic network. The flux distribution thatoptimizes production of biomass has a fat tail with a power-law exponentindependent on the structural properties of the underling network. Theseresults are in complete agreement with the Flux-Balance-Analysis outcome of thesame system and in qualitative agreement with the experimental results.
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