  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.
