Cell size regulation and proliferation fluctuations in single-cell derived colonies

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. Analyzing colony-to-colony fluctuations in the number of cells, we report an intriguing find: the extent of fluctuations first increases with time and then decreases to approach zero at large numbers of cells. In contrast, in classical size-independent proliferation models, where cell division occurs based on a pure timing mechanism, fluctuations in cell number increase monotonically over time to approach a nonzero value. We systematically study these differences and the convergence speed using different size control strategies.