Cell size scaling laws: a unified theory

Abstract

The dimensions and compositions of cells are tightly regulated by active processes. This exquisite control is embodied in the robust scaling laws relating cell size, dry mass, and nuclear size. Despite accumulating experimental evidence, a unified theoretical framework is still lacking. Here, we show that these laws and their breakdown can be explained quantitatively by three simple, yet generic, physical constraints defining altogether the Pump and Leak model (PLM). Based on estimations, we clearly map the PLM coarse-grained parameters with the dominant cellular events they stem from. We propose that dry mass density homeostasis arises from the scaling between proteins and small osmolytes, mainly amino-acids and ions. Our theory predicts this scaling to naturally fail, both at senescence when DNA and RNAs are saturated by RNA polymerases and ribosomes respectively, and at mitotic entry due to the counterion release following histone tail modifications. We further show that nuclear scaling result from osmotic balance at the nuclear envelope (NE) and a large pool of metabolites, which dilutes chromatin counterions that do not scale during growth.