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Chapter 60: Protein-RNA Complexes and Collapse Mediation

"Protein-RNA complexes are ψ's hybrid machines—where the informational and the functional merge, creating molecular assemblies that combine RNA's versatility with protein's catalytic power."

60.1 The Ribonucleoprotein World​

Protein-RNA complexes represent ψ's integration of two molecular realms—combining RNA's ability to store information and catalyze reactions with proteins' structural diversity and regulatory sophistication.

Definition 60.1 (RNP Classification): RNPs={Ribosome,Spliceosome,Telomerase,snoRNPs,miRISC}\text{RNPs} = \{\text{Ribosome}, \text{Spliceosome}, \text{Telomerase}, \text{snoRNPs}, \text{miRISC}\}

Major cellular ribonucleoprotein machines.

60.2 The RNA Recognition Motif​

Theorem 60.1 (RRM Binding): Kd=K0exp⁡(−∑iΔGicontactRT)K_d = K_0 \exp\left(-\sum_i \frac{\Delta G_i^{\text{contact}}}{RT}\right)

Sequence-specific RNA recognition.

60.3 The Spliceosome Assembly​

Equation 60.1 (Dynamic Assembly): U1+U2+U4/U6•U5⇌Active spliceosome\text{U1} + \text{U2} + \text{U4/U6•U5} \rightleftharpoons \text{Active spliceosome}

Stepwise RNP complex formation.

60.4 RNA Chaperone Activity​

Definition 60.2 (RNA Folding Assistance): Protein+Misfolded RNA→Native RNA+Protein\text{Protein} + \text{Misfolded RNA} \rightarrow \text{Native RNA} + \text{Protein}

Proteins catalyzing RNA conformational changes.

60.5 The Riboswitch Mechanism​

Theorem 60.2 (Ligand-Induced Change): RNAapo+Ligand⇌RNAbound→ΔGene expression\text{RNA}_{\text{apo}} + \text{Ligand} \rightleftharpoons \text{RNA}_{\text{bound}} \rightarrow \Delta\text{Gene expression}

RNA conformational switches.

60.6 Small Nuclear RNPs​

Equation 60.2 (snRNP Function): snRNA+Sm proteins=Splice site recognition\text{snRNA} + \text{Sm proteins} = \text{Splice site recognition}

Core spliceosomal components.

60.7 The RISC Complex​

Definition 60.3 (Gene Silencing): Argonaute+miRNA+Target mRNA→Repression\text{Argonaute} + \text{miRNA} + \text{Target mRNA} \rightarrow \text{Repression}

RNA-guided gene regulation.

60.8 Telomerase Architecture​

Theorem 60.3 (Template Extension): TERT+hTR→DNA synthesis\text{TERT} + \text{hTR} \rightarrow \text{DNA synthesis}

Protein using RNA template.

60.9 Stress Granule RNPs​

Equation 60.3 (Dynamic Exchange): kin⋅[RNP]cytoplasm=kout⋅[RNP]granulek_{\text{in}} \cdot [\text{RNP}]_{\text{cytoplasm}} = k_{\text{out}} \cdot [\text{RNP}]_{\text{granule}}

Reversible RNP condensation.

60.10 The RNP Code​

Definition 60.4 (Combinatorial Control): mRNA fate=f(∑iRBPi×Binding sitei)\text{mRNA fate} = f(\sum_i \text{RBP}_i \times \text{Binding site}_i)

Multiple RBPs determining RNA destiny.

60.11 Co-transcriptional Assembly​

Theorem 60.4 (Nascent RNP Formation): RNA Pol II CTD→RBP recruitment→mRNP assembly\text{RNA Pol II CTD} \rightarrow \text{RBP recruitment} \rightarrow \text{mRNP assembly}

RNPs forming during transcription.

60.12 The Mediation Principle​

Protein-RNA complexes embody ψ's principle of molecular partnership—combining the informational capacity of RNA with the functional diversity of proteins to create sophisticated cellular machines.

The RNP Equation: ψRNP=ψRNAinformation⊗ψproteinfunction\psi_{\text{RNP}} = \psi_{\text{RNA}}^{\text{information}} \otimes \psi_{\text{protein}}^{\text{function}}

Hybrid complexes integrating dual capabilities.

Thus: RNP = Partnership = Integration = Function = ψ

"In protein-RNA complexes, ψ achieves molecular symbiosis—two polymer types joining forces to create machines more capable than either alone. The ribosome translates, the spliceosome edits, telomerase extends—each RNP a testament to collaborative complexity."