Balance of osmotic pressures determines the volume of the cell nucleus

The volume of the cell nucleus varies across cell-types and species, and is commonly thought to be determined by the size of the genome and degree of chromatin compaction. However, this notion has been challenged over the years by multiple experimental evidence. Here, we consider the physical condition of mechanical force balance as a determining condition of the nuclear volume and use quantitative, order-of-magnitude analysis to estimate the forces from different sources of nuclear and cellular pressure. Our estimates suggest that the dominant pressure within the nucleus and cytoplasm originates from the osmotic pressure of proteins and RNA molecules that are localized to the nucleus or cytoplasm by out-of-equilibrium, active nucleocytoplasmic transport rather than from chromatin or its associated ions. This motivates us to formulate a physical model for the ratio of the cell and nuclear volumes in which osmotic pressures of localized proteins determine the relative volumes. In accordance with unexplained observations that are century-old, our model predicts that the ratio of the cell and nuclear volumes is a constant, robust to a wide variety of biochemical and biophysical manipulations, and is changed only if gene expression or nucleocytoplasmic transport are modulated.