Dynamic proteome trade-offs regulate cell size and growth in fluctuating nutrient conditions*

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.