Every cell has a nucleus, where the DNA is stored. The nucleus is like a fluid-filled pouch, and its size depends on how much protein is inside. Proteins can't slip out through the pores in the envelope, so they push against it from within, the way air pushes on the walls of a balloon.
When the nucleus changes size, genes start working differently. As it swells, genes that are usually silent switch on, and as it shrinks, the most active genes get a boost. This helps explain why cells age and how we might influence their fate.
The concentration of osmotically active macromolecules in the cell is only about 0.24–0.68 mM, hundreds of times lower than the concentration of small molecules, yet it is enough to determine nuclear size.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.