  The solution space of genome-scale models of cellular metabolism provides a
map between physically viable flux configurations and cellular metabolic
phenotypes described, at the most basic level, by the corresponding growth
rates. By sampling the solution space of E. coli's metabolic network, we show
that empirical growth rate distributions recently obtained in experiments at
single-cell resolution can be explained in terms of a trade-off between the
higher fitness of fast-growing phenotypes and the higher entropy of
slow-growing ones. Based on this, we propose a minimal model for the evolution
of a large bacterial population that captures this trade-off. The scaling
relationships observed in experiments encode, in such frameworks, for the same
distance from the maximum achievable growth rate, the same degree of growth
rate maximization, and/or the same rate of phenotypic change. Being grounded on
genome-scale metabolic network reconstructions, these results allow for
multiple implications and extensions in spite of the underlying conceptual
simplicity.
