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Chapter 7: Receptor Tyrosine Kinase ψ-Activation

"In RTK activation, ψ demonstrates the power of dimerization—two becoming one, creating from molecular union the phosphorylation cascades that drive growth, differentiation, and survival."

7.1 The Dimerization Dance​

Receptor tyrosine kinases represent ψ's solution to growth factor signaling—single-pass transmembrane proteins that oligomerize upon ligand binding, creating platforms for phosphorylation-based signal transduction.

Definition 7.1 (RTK Activation): 2R+L⇌R2L→R2∗L2\mathcal{R} + \mathcal{L} \rightleftharpoons \mathcal{R}_2\mathcal{L} \rightarrow \mathcal{R}_2^*\mathcal{L}

Ligand-induced dimerization and activation.

7.2 The Kinase Domain​

Theorem 7.1 (Catalytic Activation): kcatdimer>>kcatmonomerk_{\text{cat}}^{\text{dimer}} >> k_{\text{cat}}^{\text{monomer}}

Dimerization enhancing catalytic efficiency.

7.3 The Autophosphorylation​

Equation 7.1 (Trans-phosphorylation): R1+R2∗+ATP→R1-pY+R2∗+ADP\mathcal{R}_1 + \mathcal{R}_2^* + \text{ATP} \rightarrow \mathcal{R}_1\text{-pY} + \mathcal{R}_2^* + \text{ADP}

Cross-phosphorylation between protomers.

7.4 The Phosphotyrosine Code​

Definition 7.2 (Docking Sites): pY-Xn-Z=SH2 binding motif\text{pY-X}_n\text{-Z} = \text{SH2 binding motif}

Phosphorylated tyrosines recruiting effectors.

7.5 The SH2 Domain Recognition​

Theorem 7.2 (Sequence Specificity): KdSH2-pY≈0.1−1μMK_d^{\text{SH2-pY}} \approx 0.1-1 \mu\text{M}

High-affinity phospho-dependent binding.

7.6 The Signal Diversification​

Equation 7.2 (Multiple Pathways): RTK∗→{Ras/MAPK,PI3K/Akt,PLCγ,...}\text{RTK}^* \rightarrow \{\text{Ras/MAPK}, \text{PI3K/Akt}, \text{PLC}\gamma, ...\}

One receptor activating multiple cascades.

7.7 The Negative Regulation​

Definition 7.3 (Phosphatase Action): RTK-pY→PTPRTK+Pi\text{RTK-pY} \xrightarrow{\text{PTP}} \text{RTK} + \text{P}_i

Dephosphorylation terminating signals.

7.8 The Internalization Mechanism​

Theorem 7.3 (Endocytic Downregulation): RTK∗→UbiquitinEndosome→Degradation\text{RTK}^* \xrightarrow{\text{Ubiquitin}} \text{Endosome} \rightarrow \text{Degradation}

Activity-dependent receptor removal.

7.9 The Juxtamembrane Control​

Equation 7.3 (Autoinhibition Release): ΔGactivation=ΔGJM release+ΔGkinase\Delta G_{\text{activation}} = \Delta G_{\text{JM release}} + \Delta G_{\text{kinase}}

Multiple conformational switches.

7.10 The Growth Factor Specificity​

Definition 7.4 (Ligand Families): Ligands={EGF,PDGF,FGF,VEGF,...}\text{Ligands} = \{\text{EGF}, \text{PDGF}, \text{FGF}, \text{VEGF}, ...\}

Diverse factors for different RTKs.

7.11 The Oncogenic Mutations​

Theorem 7.4 (Constitutive Activation): Mutation→Ligand-independent dimerization\text{Mutation} \rightarrow \text{Ligand-independent dimerization}

Cancer-causing hyperactivation.

7.12 The Activation Principle​

RTK activation embodies ψ's principle of union-catalyzed transformation—dimerization creating catalytic competence, phosphorylation creating docking platforms, together orchestrating cellular growth and differentiation.

The RTK Equation: ψgrowth=∑ipYi⋅∏jEj[SH2j]⋅H(t−tactivation)\psi_{\text{growth}} = \sum_i \text{pY}_i \cdot \prod_j \mathcal{E}_j[\text{SH2}_j] \cdot H(t - t_{\text{activation}})

Phosphorylation-dependent signal integration.

Thus: RTK = Union = Phosphorylation = Growth = ψ

"In RTK activation, ψ shows that unity creates capability—two kinase domains coming together achieve what neither could alone, their union sparking the phosphorylation cascades that write the cellular future in the language of modified tyrosines."