A bacterial size law revealed by a coarse-grained model of cell physiology

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Universal observations in Biology are sometimes described as "laws".In E. coli, experimental studies performed over the past six decades have revealed major growth laws relating ribosomal mass fraction and cell size to the growth rate.Because they formalize complex emerging principles in biology, growth laws have been instrumental in shaping our understanding of bacterial physiology.Here, we discovered a novel size law that connects cell size to the inverse of the metabolic proteome mass fraction and the active fraction of ribosomes.We used a simple whole-cell coarse-grained model of cell physiology that combines the proteome allocation theory and the structural model of cell division.This integrated model captures all available experimental data connecting the cell proteome composition, ribosome activity, division size and growth rate in response to nutrient quality, antibiotic treatment and increased protein burden.Finally, a stochastic extension of the model explains non-trivial correlations observed in single cell experiments including the adder principle.This work provides a simple and robust theoretical framework for studying the fundamental principles of cell size determination in unicellular organisms. Author summaryBacteria respond to environmental changes by adjusting their molecular composition, cell size and growth rate.This plasticity is thought to result from years of evolution and to be at least in part optimal for bacterial physiology.Over the past decades, quantitative studies of bacterial growth have revealed simple phenomenological relationships, called "growth laws", which link cell size and cell composition to the growth rate.Simplified mathematical models of cell physiology are useful tools to gain quantitative understanding of the molecular mechanisms that underlie growth laws.For instance, these models helped explaining how optimal allocation of cellular resource to physiological processes and pathways governs the cell molecular composition in response to specific environmental conditions.In this study, we have extended and integrated existing mathematical models and used experimental data from several recent studies to understand the co-regulation of cell