Emergent lag phase in flux-regulation models of diauxie

Lag phase is observed in bacterial growth during a sudden change in conditions: growth is inhibited whilst cells adapt to the environment. Bi-phasic, or diauxic growth is commonly exhibited by many species. In the presence of two sugars, cells initially grow by consuming the preferred sugar then undergo a lag phase before resuming growth on the second. Biomass increase is characterised by a diauxic growth curve: exponential growth followed by a period of no growth before a second exponential growth. Recent literature lacks a complete dynamic description, artificially modelling lag phase and employing non-physical representations of precursor pools. Here, we focus on glucoselactose diauxie of Escherichia coli formulating a rational mechanistic model based on flux-regulation/proteome partitioning with a finite precursor pool that reveals core mechanisms in a compact form. Unlike earlier systems, the characteristic dynamics emerge as part of the solution, including the lag phase, and results accurately reproduce experiments. We show that for a single strain of E. coli, diauxic growth yields mathematically optimised growth rates. However, intriguingly, for two competing strains diauxic growth is not always the best strategy. Our description can be generalised to model multiple different microorganisms and investigate competition between species/strains.