Cell size control shapes fluctuations in colony population

Exponentially growing cells regulate their size by controlling their timing of division. Since two daughter cells are born as a result of this cell splitting, cell size regulation has a direct connection with cell proliferation dynamics. Recent models found more clues about this connection by suggesting that division occurs at a size-dependent rate. In this article, we propose a framework that couples the stochastic transient dynamics of both the cell size and the number of cells in the initial expansion of a single-cell-derived colony. We describe the population from the two most common perspectives. The first is known as Single Lineage: where only one cell is followed in each colony, and the second is Population Snapshots: where all cells in different colonies are followed. At a low number of cells, we propose a third perspective; Single Colony, where one tracks only cells with a common ancestor. We observe how the statistics of these three approaches are different at low numbers and how the Single Colony perspective tends to Population Snapshots at high numbers. We analyze random fluctuations from colony to colony in the number of cells. If cell division occurs at a size-dependent rate, the extent of this variability first increases with time and then decreases to near zero when the population is high. In contrast, in classical proliferation models, where cell division occurs based not on cell size but on a pure timing mechanism, fluctuations in cell number increase monotonically over time to approach a non-zero value. We systematically study these differences and the convergence speed using different size control strategies.