The mechanism of bacterial cell size control has been a mystery for decades, which involves the well-coordinated growth and division in  cell cycle. The revolutionary modern techniques of microfluidicsand the advanced imaging analysis techniques allow long term single cell observation and has promoted a new wave of quantitative investigations on this puzzle. Taking the opportunity, this theoretical study aims to clarify the stochastic nature of bacterial cell size control under the assumption of the accumulation mechanism, which is favored by recent experiments. Via the master equation approach to the stochastic birth process combined with proper chosen boundary conditions, the cell size distribution of an exponentially growing colony is revisited. In the context of mother machine experiments, the inter-generation dynamics is derived for the stochastic accumulation model, of which the propagator is analytically obtained. Given a growth condition, the added size distribution is found independent of the birth size, the reason of which is shown in the picture of subortinated random walk. The distributions of the division size and inter-division time are obtained for the long time statistics of mother machine, which are well confirmed by experiments. As a consequence of non-Gaussian noises of the added sizes, the non-equilibrium nature of bacterial cell size homeostasis is revealed , of which the biological meaning requires further investigation.
The mechanism of bacterial cell size control has been a mystery for decades, which involves the well-coordinated growth and division in the cell cycle. The revolutionary modern techniques of microfluidics and the advanced live imaging analysis techniques allow long term observations and high-throughput analysis of bacterial growth on single cell level, promoting a new wave of quantitative investigations on this puzzle. Taking the opportunity, this theoretical study aims to clarify the stochastic nature of bacterial cell size control under the assumption of the accumulation mechanism, which is favoured by recent experiments. Via the master equation approach to the stochastic birth process combined with properly chosen boundary conditions, the cell size distribution of an exponentially growing population is revisited. In the context of mother machine experiments, the inter-generation dynamics is derived for the stochastic accumulation model, of which the propagator is analytically obtained. Given a growth condition, the added size distribution is found independent of the birth size, the reason for which is shown in the picture of the subordinated random walk. The distributions of the division size and inter-division time are obtained for the long time statistics of mother machine, which are well confirmed by experiments. As a consequence of non-Gaussian noises of the added sizes, the non-equilibrium nature of bacterial cell size homeostasis is predicted , of which the biological meaning requires further investigation.
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