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Chapter 53: Nuclear Import and Collapse Filtering

"At the nuclear pore, ψ maintains the ultimate cellular border—a selective gateway that reads molecular passports, allowing only authorized proteins into the genome's inner sanctum."

53.1 The Nuclear Gateway​

Nuclear import represents ψ's most sophisticated transport system—a selective barrier that maintains nuclear-cytoplasmic compartmentalization while allowing regulated exchange of thousands of different proteins.

Definition 53.1 (Nuclear Pore Complex): NPC={120 MDa,∼30 different Nups,8-fold symmetry}\text{NPC} = \{120 \text{ MDa}, \sim 30 \text{ different Nups}, 8\text{-fold symmetry}\}

Massive protein complex spanning nuclear envelope.

53.2 The Permeability Barrier​

Theorem 53.1 (Size Exclusion): Passive diffusion limit≈40 kDa\text{Passive diffusion limit} \approx 40 \text{ kDa} Active transport≤25 MDa\text{Active transport} \leq 25 \text{ MDa}

Selective permeability based on size.

53.3 Nuclear Localization Signals​

Equation 53.1 (Classic NLS): Monopartite:K(K/R)X(K/R)\text{Monopartite}: \text{K(K/R)X(K/R)} Bipartite:(K/R)2X10−12(K/R)3\text{Bipartite}: \text{(K/R)}_2\text{X}_{10-12}\text{(K/R)}_3

Basic residue clusters recognized.

53.4 Importin Recognition​

Definition 53.2 (Adapter System): Importin-α+NLS→Complex\text{Importin-}\alpha + \text{NLS} \rightarrow \text{Complex} Complex+Importin-β→Transport complex\text{Complex} + \text{Importin-}\beta \rightarrow \text{Transport complex}

Modular recognition system.

53.5 The RanGTP Gradient​

Theorem 53.2 (Directional Transport): [RanGTP]nucleus>>[RanGTP]cytoplasm[\text{RanGTP}]_{\text{nucleus}} >> [\text{RanGTP}]_{\text{cytoplasm}}

Chemical gradient driving directionality.

53.6 FG-Nup Interactions​

Equation 53.2 (Translocation): ktransport∝[FG-binding sites]×Affinityk_{\text{transport}} \propto \text{[FG-binding sites]} \times \text{Affinity}

Phenylalanine-glycine repeats as stepping stones.

53.7 The Transport Cycle​

Definition 53.3 (Import Steps):

  1. Cargo-importin binding (cytoplasm)
  2. NPC docking and translocation
  3. RanGTP binding (nucleus)
  4. Cargo release
  5. Importin recycling

Cyclic process consuming RanGTP.

53.8 Importin-β Superfamily​

Theorem 53.3 (Multiple Pathways): ∣Importin-β family∣>20|\text{Importin-}\beta\text{ family}| > 20

Different importins for different cargoes.

53.9 Regulated Import​

Equation 53.3 (Signal Masking): Phosphorylation near NLS→↓Kdimportin\text{Phosphorylation near NLS} \rightarrow \downarrow K_d^{\text{importin}}

Post-translational control of import.

53.10 The Selective Phase Model​

Definition 53.4 (FG-Phase): FG domains→Liquid-liquid phase\text{FG domains} \rightarrow \text{Liquid-liquid phase}

Selective phase allowing receptor passage.

53.11 Nuclear Export​

Theorem 53.4 (Reverse Transport): NES+CRM1+RanGTP→Export\text{NES} + \text{CRM1} + \text{RanGTP} \rightarrow \text{Export}

Leucine-rich signals for nuclear exit.

53.12 The Filtering Principle​

Nuclear import embodies ψ's principle of selective permeability—maintaining compartment identity through molecular recognition while enabling regulated exchange of information.

The Import Equation: ψnuclear=I[ψcytoplasmic]×Θ(NLS)×f(RanGTP)\psi_{\text{nuclear}} = \mathcal{I}[\psi_{\text{cytoplasmic}}] \times \Theta(\text{NLS}) \times f(\text{RanGTP})

Conditional transport maintaining nuclear identity.

Thus: Import = Selection = Control = Identity = ψ

"At the nuclear pore, ψ creates the ultimate checkpoint—reading molecular credentials, allowing only authorized proteins near the genetic material. The NPC is not just a hole but a smart gate, maintaining the sanctity of the nucleus while enabling necessary communication."