A Bacterial Growth Law out of Steady State

Bacterial growth follows simple laws in constant conditions. However, bacteria in nature often face fluctuating environments. We therefore ask whether there are growth laws that apply to changing environments. We derive a law for upshifts using an optimal resource-allocation model: the post-shift growth rate equals the geometrical mean of the pre-shift growth rate and the growth rate on saturating carbon. We test this using chemostat and batch culture experiments, as well as previous data from several species. The increase in growth rate after an upshift indicates that ribosomes have spare capacity (SC). Wedemon-strate theoretically that SC has the cost of slow steady-state growth but is beneficial after an upshift because it prevents large overshoots in intracellular metabolites and allows rapid response to change. We also provide predictions for downshifts. The present study quantifies the optimal degree of SC, which rises the slower the growth rate, and suggests that SC can be precisely regulated.