Packing and Gatekeeping
A human cell holds about 2 m of DNA in a nucleus roughly 6 µm across, a packing ratio of over 300,000 to 1. The packing is hierarchical, and crucially it is reversible, because DNA that cannot be reached cannot be read.
The first level wraps 147 base pairs around a histone octamer to form a nucleosome, the "beads on a string" arrangement. Nucleosomes coil into a 30 nm fibre, which loops onto a protein scaffold, and in mitosis condenses further into the visible chromosome.
Packing state is functional, and the two states are visibly different: euchromatin is loosely packed and transcriptionally active; heterochromatin is densely packed and silent. A cell regulates genes partly by moving regions between the two.
The nuclear envelope is a double membrane continuous with the endoplasmic reticulum, perforated by nuclear pore complexes: large assemblies of around 30 different proteins. Small molecules diffuse through freely; anything above roughly 40 kDa needs a nuclear localisation signal and active, energy-dependent transport. Traffic is heavy: a typical pore handles hundreds of molecules a second, in both directions at once.
The nucleolus is not a membrane-bound organelle but a dense region where ribosomal RNA is transcribed and ribosomal subunits are assembled before export. Its size tracks how much protein synthesis a cell is doing, so a rapidly growing cell has a conspicuously large nucleolus.
The envelope is also structural: the nuclear lamina, a mesh of intermediate filaments, lines its inner face, gives the nucleus its shape and anchors chromatin. Mutations in lamins cause a striking set of diseases including progeria, evidence of how much depends on the nucleus being mechanically sound.
Common pitfall: thinking chromosomes are always the X-shaped objects of textbook diagrams. That form exists only during division. For most of a cell's life the DNA is decondensed chromatin, and it has to be, because condensed DNA cannot be transcribed.