A bacterial growth law out of steady-state
Bacterial growth depends on numerous reactions, and yet follows surprisingly simple laws that inspired biologists for decades. Growth laws until now primarily dealt with steady-state exponential growth in constant conditions. However, bacteria in nature often face fluctuating environments, with nutritional upshifts and downshifts. We therefore ask whether there are growth laws that apply to changing environments. We derive a law for strong upshifts using an optimal resource-allocation model that was previously calibrated at steady-state growth: 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 robotic batch culture experiments, as well as previous data from several species, and find good agreement with the model predictions. The increase in growth rate after an upshift indicates that ribosomes have spare capacity. We demonstrate theoretically that spare ribosomal capacity has the cost of slow steady-state growth, but is beneficial in fluctuating environments because it prevents large overshoots in intracellular metabolites after an upshift and allows rapid response to change. We also provide predictions for downshifts for future experimental tests. Spare capacity appears in diverse biological systems, and the present study quantifies the optimal degree of spare capacity, which rises the slower the growth rate, and suggests that it can be precisely regulated.