Module 2 · The Information Core
The Nucleus as a Transport Organelle
The nucleus is habitually described as “where the DNA lives,” but the statement obscures the organelle’s more interesting property: it is the only compartment in the cell whose boundary must pass macromolecules in both directions at rates compatible with gene expression. A mammalian nucleus exports ~104 ribosomal subunits per minute and imports transcription factors on timescales of seconds. The machinery that makes this possible — the nuclear pore complex (NPC) — is the largest stable protein assembly in the cell, some 120 MDa of approximately 30 nucleoporins in 8-fold symmetry.
1. The Double Membrane & Its Continuity with the ER
The nuclear envelope is a double bilayer. Its outer membrane is continuous with the rough endoplasmic reticulum; its inner membrane is separate, coupled to the nuclear lamina (a meshwork of intermediate filaments: lamin A/C, lamin B). The perinuclear space — the 20–40 nm gap between the two leaflets — is continuous with the ER lumen.
During mitosis the envelope dissolves (in open mitosis, typical of metazoans), lamins depolymerise, and NPCs disassemble. Reassembly at telophase is one of the most dramatic topological events the cell performs: a sheet membrane must reassemble around segregated chromosomes, re-fuse with itself, and insert ~2000 new NPCs in fewer than 15 minutes. Yeasts do it differently (closed mitosis, intact envelope), which is why their NPC biology is simpler.
2. The Selectivity Paradox
The NPC must do two contradictory things. It must let a 60S ribosomal subunit — a 2.8 MDa, 25 nm object — pass through its 40 nm central channel, and simultaneously exclude globular proteins > 40 kDa that lack a nuclear localisation signal. A static filter cannot do both: a mesh with a 25 nm cutoff would leak every moderately sized protein in the cytosol, while a 5 nm cutoff would never let a ribosome through.
What the NPC does instead is to fill its channel with intrinsically disordered, phenylalanine–glycine-rich nucleoporins (FG-Nups) that form a selective phase. Cargo bound to an import receptor (importin-β, transportin) dissolves into the FG phase; naked cargo does not. This is membraneless-organelle physics (anticipating Module 6) operating inside a membrane-bounded organelle.
The selectivity ratio between bound and free cargo obeys Flory–Huggins partitioning:
\[ \dfrac{[C]_{\mathrm{in\,phase}}}{[C]_{\mathrm{out}}} \approx \exp\!\left(-\dfrac{\Delta G_{\mathrm{FG}}}{k_B T}\right) \]
with ΔGFG ≈ −5 kBTper binding receptor, so a protein decorated with a handful of import receptors enriches by > 103 in the pore.
Simulation: FG-Phase Partitioning & Size Cutoff
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Code will be executed with Python 3 on the server
3. The Ran-GTP Gradient
Partitioning into the FG phase gets cargo into the pore. What enforces directionality? The Ran-GTP/GDP gradient: Ran bound to GTP is enriched in the nucleus; Ran-GDP is enriched in the cytoplasm. Ran’s GAP (RanGAP1) is cytoplasmic (bound to Nup358 filaments), Ran’s GEF (RCC1) is nuclear (bound to chromatin). Geography sets the gradient.
Upon the cargo–importin complex entering the nucleus, RanGTP binds importin-β and dissociates the cargo. Importin-β-RanGTP then returns to the cytoplasm, where RanGAP catalyses hydrolysis, releasing free importin for another round. Export uses the mirror-image logic: CRM1/exportin binds cargo+RanGTP in the nucleus, transits to the cytoplasm, hydrolyses GTP via RanGAP, releases cargo.
The Ran cycle is the cell’s proof that gates alone are not enough: directional transport requires a free-energy-dissipating carrier cycle. Each imported cargo costs one GTP hydrolysis, ~20 kBT. Gene expression is not free.
4. Chromatin as a Polymer
Interior to the envelope, the ~2 m of DNA is organised into a hierarchical polymer. Most of its current theoretical treatment follows the fractal globule model of Grosberg, and its elaboration by Mirny and Dekker: chromatin behaves as an unknotted, compact polymer with contact probability P(s) ~ s−1over 0.5–7 Mb, distinct from the s−3/2 of an equilibrium globule.
The physical mechanism is loop extrusionby cohesin (interphase) and condensin (mitosis): SMC complexes load onto chromatin and reel DNA through their ring, forming progressively larger loops until halted by CTCF boundary elements. This is one of the best examples we have of a biological machine whose outputs are topological invariants: the set of chromatin loops is a knot diagram, and the cell builds it deterministically from boundary-element rules.
The hierarchical organisation proceeds: loops (10–106 bp) assemble into topologically-associating domains (TADs, ~1 Mb), which partition into A/B compartments (active/inactive, ~10 Mb), which finally occupy chromosome territories. Each level is polymer physics with one added ingredient (boundary elements, chromatin marks, nuclear lamina attachment), and at each level the biology is legible to a well-trained polymer theorist.
Simulation: Chromatin Contact Probability
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Code will be executed with Python 3 on the server
5. The Nucleolus: A Compartment Within a Compartment
Inside the nucleus, one encounters the nucleolus — the largest membraneless organelle in the cell, site of rRNA transcription and the first stages of ribosome assembly. It is the archetypal liquid-liquid phase-separated compartment: a dense, multi-layered droplet (FC / DFC / GC in classical EM, now understood as coexisting phases) stabilised by multivalent interactions among rRNA, NPM1, fibrillarin, and nucleolin. We return to nucleoli in detail in Module 6.