  In this work maximum entropy distributions in the space of steady states of
metabolic networks are defined upon constraining the first and second moment of
the growth rate. Inherent bistability of fast and slow phenotypes, akin to a
Van-Der Waals picture, emerges upon considering control on the average growth
(optimization/repression) and its fluctuations (heterogeneity). This is applied
to the carbon catabolic core of E.coli where it agrees with some stylized facts
on the persisters phenotype and it provides a quantitative map with metabolic
fluxes, opening for the possibility to detect coexistence from flux data.
Preliminary analysis on data for E.Coli cultures in standard conditions shows,
on the other hand, degeneracy for the inferred parameters that extend in the
coexistence region.
