Minimal requirements for robust cell size control in eukaryotic cells

Abstract

Most cell types living in a stable environment tend to keep a constant characteristic size over successive generations. Size homeostasis requires that cells exert a tight control over the size at which they divide. Cell size control is not only robust against various noises, but also highly flexible since cell sizes can vary tremendously, notably as a function of nutrient levels. We formulated a minimal mathematical model of the eukaryotic cell cycle in which the cell size control operates through a cell growth-dependent bifurcation in the cell cycle dynamics. Such a bifurcation mechanism can readily explain the occurrence of a minimum critical size at division under limiting growth conditions. However, it also predicts that cells should become progressively larger and larger under prolific growth conditions. We argue that the cell size control can be reinforced at fast growth rates by adding a new cell cycle inhibitory activity whose strength would increase with the cell growth rate. We further show that various sources of noise may also generate a large variability in cell size at division and interdivision time that exhibit characteristic exponential tail distributions, without compromising the robustness of the cell size control.