Understanding the organization of reaction fluxes in cellular metabolism from the stoichiometry and the topology of the underlying biochemical network is a central issue in systems biology. In this task, it is important to devise reasonable approximation schemes that rely on the stoichiometric data only, because full-scale kinetic approaches are computationally affordable only for small networks (e.g. red blood cells, about 50 reactions). Methods commonly employed are based on finding the stationary flux configurations that satisfy mass-balance conditions for metabolites, often coupling them to local optimization rules (e.g. maximization of biomass production) to reduce the size of the solution space to a single point. Such methods have been widely applied and have proven able to reproduce experimental findings for relatively simple organisms in specific conditions. Here we define and study a constraint-based model of cellular metabolism where neither mass balance nor flux stationarity are postulated, and where the relevant flux configurations optimize the global growth of the system. In the case of E. coli, steady flux states are recovered as solutions, though mass-balance conditions are violated for some metabolites, implying a non-zero net production of the latter. Such solutions furthermore turn out to provide the correct statistics of fluxes for the bacterium E. coli in different environments and compare well with the available experimental evidence on individual fluxes. Conserved metabolic pools play a key role in determining growth rate and flux variability. Finally, we are able to connect phenomenological gene essentiality with `frozen fluxes (i.e. fluxes with smaller allowed variability) in E. coli metabolism.
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