Cell volume distributions in exponentially growing populations

Stochastic effects in cell growth and division drive variability in cellular volumes both at the single-cell level and at the level of growing cell populations. Here we consider a simple and tractable model in which cell volumes grow exponentially, cell division is symmetric, and its rate is volume-dependent. Consistently with previous observations, the model is shown to sustain oscillatory behaviour with alternating phases of slow and fast growth. Exact simulation algorithms and large-time asymptotics are developed and cross-validated for the single-cell and whole-population formulations of the model. The two formulations are shown to provide similar results during the phases of slow growth, but differ during the fast-growth phases. Specifically, the single-cell formulation systematically underestimates the proportion of small cells. More generally, our results suggest that measurable characteristics of cells may follow different distributions depending on whether a single-cell lineage or an entire population is considered.