In stable environments, statistics of cell size fluctuations is thought to be governed by simple physical principles . Past studies suggested that bacterial cell sizes exhibit a universal distribution irrespective of growth conditions, and for eukaryotes, a single distribution may describe size fluctuations of various cell species. The distinguished feature of those distributions is scale invariance; i.e., the distribution function is determined solely by the mean cell size. Here we show, using E. coli, that such a simple distribution law also persists under time-dependent environments, which then involve regulations of cell cycle kinetics. By developing a membrane-based microfluidic device suitable for culturing a large cell population under uniform and controllable growth conditions, we study how the cell size distribution changes after the supplied medium is switched from a nutritious to non-nutritious one, triggering the bacterial reductive division . The mean cell size then gradually decreases, but we find that the size distribution is kept unchanged if the cell sizes are normalized by their time-dependent mean value ; in other words the scale invariance holds as it is. We also study a model considering intracellular replication and cell volume growth and successfully reproduce our experimental results. Furthermore, we give a theoretical expression for the time-dependent cell size distribution and  propose a sufficient condition for the scale invariance. Our findings emphasize that, compared with environmental factors, the intrinsic cellular replication processes have stronger impact on the cell size distribution, and consequently bacteria and eukaryotes are ruled by different, yet possibly universal distributions .
In stable environments, cell size fluctuations are thought to be governed by simple physical principles , as suggested by recent finding of scaling properties. Here we show, using E. coli, that the scaling concept also rules cell size fluctuations under time-dependent conditions, even though the distribution changes with time. We develop a microfluidic device for observing dense and large bacterial populations, under uniform and switchable conditions. Triggering bacterial reductive division by switching to non-nutritious medium, we find evidence that the cell size distribution changes in a specific manner that keeps its normalized form unchanged ; in other words , scale invariance holds . This finding is underpinned by simulations of a model based on cell growth and intracellular replication. We also formulate the problem theoretically and propose a sufficient condition for the scale invariance. Our results emphasize the importance of intrinsic cellular replication processes in this problem, suggesting different distribution trends for bacteria and eukaryotes .
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