A Population-Based Approach to Study the Effects of Growth and Division Rates on the Dynamics of Cell Size Statistics

The dynamics of the size distribution in growing and dividing rod-shaped bacteria can change depending on the perspective through which the cell population is observed. From the perspective of single-cell lineages, only one descendant is followed after each division, while in population snapshots all of the offspring is considered. In this letter, we propose an analytical derivation of Population Balance Equations (PBEs) that can be used to compute the dynamics of the main statistics of the cell size distribution. We then explore how the dynamics are affected by different division strategies and by the two different perspectives of observation. To assess the accuracy of our derivations, we compare the analytical results with those obtained numerically and through stochastic simulations. The comparison allows us to establish mathematical relationships between the two perspectives of observation, thus improving our knowledge of how cells control their growth and proliferation.