Uniform Sampling of Steady States in Genome Scale Metabolic Networks and Some Applications

We show that it is possible to perform an exact uniform sampling of steady states in genome scale metabolic network models in feasible times by means of ellipsoidal rounding techniques,
and then consider two applications to the metabolism of E Coli: a genome scale estimate of the metabolic turnover and the modeling of empirical  growth rate distributions.
1)We argue that an estimate of the metabolic turnover should be performed from total fluxes,
that in turn can be inferred from net fluxes (uniform sampling)
and free energies (energy balance analysis) upon assuming a simplified form of the fluctuation theorem.
Our analysis on E.Coli show a faster-than-expected turnover with respect to an estimate from net fluxes
that still does not affect the well mixing hypothesis. We confirm the time hierarchy hypothesis.  
2)FBA predicts a single optimal value for the growth rate of batch cultures in a stationary growing phase
whereas experimental observations on single cells display  possibly broad growth rate distributions.
We show that max-entropy distributions with fixed average growth rate (partial optimization)
well reproduce experimental distributions leading to an estimate of the maximum growth rate and of the level of optimization.