Bacteria dynamically regulate cell size and growth to thrive in changing environments. While previous studies have characterized bacterial growth physiology at steady-state, a quantitative understanding of bacterial physiology in time-varying environments is lacking. Here we develop a quantitative theory connecting bacterial growth and division rates to proteome allocation in time-varying nutrient environments. In such environments, cell size and growth are regulated by trade-offs between prioritization of biomass accumulation or division, resulting in decoupling of single-cell growth rate from population growth rate. Specifically, bacteria transiently prioritize biomass accumulation over production of division machinery during nutrient upshifts, while prioritizing division over growth during downshifts. When subjected to pulsatile nutrient concentration, we find that bacteria exhibit a transient memory of previous metabolic states due to the slow dynamics of proteome reallocation. This allows for faster adaptation to previously seen environments and results in division control which is dependent on the time-profile of fluctuations.

Bacteria dynamically regulate cell size and growth rate to thrive in changing environments. While much work has been done to characterize bacterial growth physiology and cell size control during steady-state exponential growth, a quantitative understanding of how bacteria dynamically regulate cell size and growth in time-varying nutrient environments is lacking. Here we develop a dynamic coarse-grained proteome sector model which connects growth rate and division control to proteome allocation in time-varying environments in both exponential and stationary phase. In such environments, growth rate and size control is governed by trade-offs between prioritization of biomass accumulation or division, and results in the uncoupling of single-cell growth rate from population growth rate out of steady-state. Specifically, our model predicts that cells transiently prioritize ribosome production, and thus biomass accumulation, over production of division machinery during nutrient upshift, explaining experimentally observed size control behaviors. Strikingly, our model predicts the opposite behavior during downshift, namely that bacteria temporarily prioritize division over growth, despite needing to upregulate costly division machinery and increasing population size when nutrients are scarce. Importantly, when bacteria are subjected to pulsatile nutrient concentration, we find that cells exhibit a transient memory of the previous metabolic state due to the slow dynamics of proteome reallocation. This phenotypic memory allows for faster adaptation back to previously-seen environments when nutrient fluctuations are short-lived.