Scale invariance during bacterial reductive division observed by an extensive microperfusion system.

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.