Sensing cellular growth rate facilitates its robust optimal adaptation to changing conditions

AO_SCPLOWBSTRACTC_SCPLOWThe determinants of growth rate and the associated metabolism has been at center stage in microbial physiology for over seventy years. In this paper we show that a cell sensing its own growth rate is in principle capable of maximising it using a gene regulatory circuit responsible for adapting metabolic enzyme concentrations in dynamic conditions. This is remarkable, since any state of (close-to) optimal growth depends on nutrient conditions, and is thus not a fixed target. We derive the properties of such gene regulatory networks, and prove that such circuits allow the growth rate to be a Lyapunov function. We derive this from a general stoichiometric and kinetic description of cellular metabolism. Interestingly, our finding is in agreement with our current understanding of how E. coli controls its growth rate. It uses ppGpp to tune the growth rate by balancing metabolic and ribosomal protein expression. Since ppGpp covaries 1-to-1 with the protein translation rate, an excellent proxy for growth rate, on a timescale of seconds, this suggests that direct sensing of the growth rate underlies growth rate optimisation in E. coli.