  Microbial metabolic networks perform the basic function of harvesting energy
from nutrients to generate the work and free energy required for survival,
growth and replication. The robust physiological outcomes they generate across
vastly different organisms in spite of major environmental and genetic
differences represent an especially remarkable trait. Most notably, it suggests
that metabolic activity in bacteria may follow universal principles, the search
for which is a long-standing issue. Most theoretical approaches to modeling
metabolism assume that cells optimize specific evolutionarily-motivated
objective functions (like their growth rate) under general physico-chemical or
regulatory constraints. While conceptually and practically useful in many
situations, the idea that certain objectives are optimized is hard to validate
in data. Moreover, it is not clear how optimality can be reconciled with the
degree of single-cell variability observed within microbial populations. To
shed light on these issues, we propose here an inverse modeling framework that
connects fitness to variability through the Maximum-Entropy guided inference of
metabolic flux distributions from data. While no clear optimization emerges, we
find that, as the medium gets richer, Escherichia coli populations slowly
approach the theoretically optimal performance defined by minimal reduction of
phenotypic variability at given mean growth rate. Inferred flux distributions
provide multiple biological insights, including on metabolic reactions that are
experimentally inaccessible. These results suggest that bacterial metabolism is
crucially shaped by a population-level trade-off between fitness and
cell-to-cell heterogeneity.
