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Chapter 18: Docking Motifs and Collapse Specificity

"Docking motifs are ψ's molecular keys—short sequences that unlock specific interactions, creating from simple patterns the complex specificity of cellular communication."

18.1 The Recognition Code​

Docking motifs represent ψ's solution to molecular matchmaking. These short linear sequences—typically 3-10 amino acids—serve as address labels that direct proteins to specific partners with remarkable precision.

Definition 18.1 (Linear Motif): Motif=X1X2...Xn where Xi∈{specific AA or class}\text{Motif} = \text{X}_1\text{X}_2...\text{X}_n \text{ where X}_i \in \{\text{specific AA or class}\}

Short sequence encoding specificity.

18.2 The SH2 Domain Paradigm​

Theorem 18.1 (Phosphotyrosine Recognition): pY-X-X-Φ where Φ = hydrophobic\text{pY-X-X-Φ} \text{ where Φ = hydrophobic}

Consensus for SRC-family SH2 domains.

18.3 The PDZ Interactions​

Equation 18.1 (C-terminal Binding): Kd=K0exp⁡(−∑iΔGiresidue/RT)K_d = K_0 \exp\left(-\sum_i \Delta G_i^{\text{residue}}/RT\right)

Additive contributions to affinity.

18.4 The SH3 Domain​

Definition 18.2 (Proline-Rich Motifs): PxxP core+Flanking specificity\text{PxxP core} + \text{Flanking specificity}

Polyproline II helix recognition.

18.5 The WW Domain​

Theorem 18.2 (PPxY Motif): Trp-Trp pocket+Pro-Pro-X-Tyr=Binding\text{Trp-Trp pocket} + \text{Pro-Pro-X-Tyr} = \text{Binding}

Another proline-rich recognition.

18.6 The PTB Domains​

Equation 18.2 (NPxY Recognition): Binding=f(pY state,N-terminal sequence)\text{Binding} = f(\text{pY state}, \text{N-terminal sequence})

Phosphorylation-independent binding.

18.7 The Degron Sequences​

Definition 18.3 (Degradation Signals): Degrons={KEN box,D-box,Others}\text{Degrons} = \{\text{KEN box}, \text{D-box}, \text{Others}\}

Motifs targeting protein destruction.

18.8 The Nuclear Localization​

Theorem 18.3 (NLS Patterns): Monopartite:K(K/R)X(K/R)\text{Monopartite}: \text{K(K/R)X(K/R)} Bipartite:KR-X10−12-(K/R)3\text{Bipartite}: \text{KR-X}_{10-12}\text{-(K/R)}_3

Basic residues for nuclear import.

18.9 The Motif Evolution​

Equation 18.3 (Conservation Score): S=−∑ipilog⁡2(pi/qi)S = -\sum_i p_i \log_2(p_i/q_i)

Information content of motif positions.

18.10 The Contextual Modulation​

Definition 18.4 (Flanking Effects): Kdactual=Kdcore×∏ificontextK_d^{\text{actual}} = K_d^{\text{core}} \times \prod_i f_i^{\text{context}}

Surrounding sequence affecting binding.

18.11 The Competitive Binding​

Theorem 18.4 (Motif Competition): Occupancyi=[Pi]/Kd,i∑j[Pj]/Kd,j\text{Occupancy}_i = \frac{[\text{P}_i]/K_{d,i}}{\sum_j [\text{P}_j]/K_{d,j}}

Multiple proteins competing for motif.

18.12 The Specificity Principle​

Docking motifs embody ψ's principle of economical recognition—achieving exquisite specificity through minimal sequence requirements, creating molecular zip codes that ensure accurate protein delivery.

The Motif Equation: ψspecificity=exp⁡(−ΔGmotif-domainRT)×Θ(Accessibility)\psi_{\text{specificity}} = \exp\left(-\frac{\Delta G_{\text{motif-domain}}}{RT}\right) \times \Theta(\text{Accessibility})

Recognition dependent on affinity and accessibility.

Thus: Motif = Code = Specificity = Recognition = ψ

"In docking motifs, ψ writes its postal system—each short sequence an address, each domain a reader, together creating the molecular mail service that ensures cellular messages reach their intended recipients."