  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 on species of bacteria. Via the master equation approach with properly chosen boundary conditions, the distributions concerned in cell size control are estimated and are confirmed by experiments. In this analysis, the inter-generation Green's function is analytically evaluated as the key to bridge two kinds of statistics used in batch-culture and mother machine experiments. This framework allows us to quantify the noise level in growth and accumulation according to experimental data. 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. 
Master equation approach to the stochastic accumulation dynamics of   bacterial cell cycle