  Despite major environmental and genetic differences, microbial metabolic
networks are known to generate consistent physiological outcomes across vastly
different organisms. This remarkable robustness suggests that, at least in
bacteria, metabolic activity may be guided by universal principles. The
constrained optimization of evolutionarily-motivated objective functions like
the growth rate has emerged as the key theoretical assumption for the study of
bacterial metabolism. While conceptually and practically useful in many
situations, the idea that certain functions are optimized is hard to validate
in data. Moreover, it is not always clear how optimality can be reconciled with
the high degree of single-cell variability observed in experiments within
microbial populations. To shed light on these issues, we develop an inverse
modeling framework that connects the fitness of a population of cells
(represented by the mean single-cell growth rate) to the underlying metabolic
variability through the Maximum-Entropy inference of the distribution of
metabolic phenotypes from data. While no clear objective function emerges, we
find that, as the medium gets richer, the fitness and inferred variability for
Escherichia coli populations follow and slowly approach the theoretically
optimal bound defined by minimal reduction of variability at given fitness.
These results suggest that bacterial metabolism may be crucially shaped by a
population-level trade-off between growth and heterogeneity.
