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Chapter 23: Allosteric Collapse Communication

"Allostery is ψ's action at a distance—binding events at one site creating earthquakes at another, proving that in proteins, as in quantum mechanics, everything is connected."

23.1 The Non-Local Effects​

Allosteric regulation represents ψ's solution to long-range communication within proteins. Through networks of coupled residues, binding at one site propagates conformational changes to distant regions, enabling sophisticated regulation.

Definition 23.1 (Allostery): ΔGbindingsite 2=f(Occupancysite 1)\Delta G_{\text{binding}}^{\text{site 2}} = f(\text{Occupancy}_{\text{site 1}})

Binding at one site affecting another.

23.2 The Conformational Selection​

Theorem 23.1 (Pre-existing States): Protein⇌T state⇌R state\text{Protein} \rightleftharpoons \text{T state} \rightleftharpoons \text{R state}

Ligands stabilizing existing conformations.

23.3 The Induced Fit Model​

Equation 23.1 (Sequential Changes): E+S⇌ES→ES∗\text{E} + \text{S} \rightleftharpoons \text{ES} \rightarrow \text{ES}^*

Binding inducing new conformations.

23.4 The Hemoglobin Paradigm​

Definition 23.2 (Cooperative Binding): Y=[O2]nKdn+[O2]nY = \frac{[\text{O}_2]^n}{K_d^n + [\text{O}_2]^n}

Oxygen binding enhancing further binding.

23.5 The Communication Networks​

Theorem 23.2 (Residue Coupling): Correlationij=⟨ΔxiΔxj⟩\text{Correlation}_{ij} = \langle \Delta x_i \Delta x_j \rangle

Correlated motions revealing pathways.

23.6 The Entropic Effects​

Equation 23.2 (Dynamic Allostery): ΔSallosteric=−R∑ipiln⁡pi\Delta S_{\text{allosteric}} = -R\sum_i p_i \ln p_i

Changes in conformational entropy.

23.7 The Symmetric Complexes​

Definition 23.3 (Concerted Model): All subunits switch together\text{All subunits switch together}

Quaternary structure transitions.

23.8 The Sequential Model​

Theorem 23.3 (Independent Transitions): Each subunit changes individually\text{Each subunit changes individually}

Progressive conformational changes.

23.9 The Allosteric Drugs​

Equation 23.3 (Modulator Binding): Activity=Activity0×(1+α[M]/KM)\text{Activity} = \text{Activity}_0 \times (1 + \alpha[\text{M}]/K_M)

Drugs binding away from active site.

23.10 The Evolution of Allostery​

Definition 23.4 (Functional Advantage): Fitness∝Regulatory capacity\text{Fitness} \propto \text{Regulatory capacity}

Selection for controllable proteins.

23.11 The Allosteric Hotspots​

Theorem 23.4 (Key Residues): ΔΔGmutation>Threshold⇒Loss of allostery\Delta\Delta G_{\text{mutation}} > \text{Threshold} \Rightarrow \text{Loss of allostery}

Critical positions for communication.

23.12 The Communication Principle​

Allostery embodies ψ's principle of molecular holism—proteins as integrated wholes where local perturbations create global responses, enabling sophisticated regulation through conformational coupling.

The Allosteric Equation: ψresponse=∫proteinC[ψperturbation]⋅exp⁡(−r/ξ) dV\psi_{\text{response}} = \int_{\text{protein}} \mathcal{C}[\psi_{\text{perturbation}}] \cdot \exp(-r/\xi) \, dV

Conformational waves propagating through structure.

Thus: Allostery = Communication = Integration = Regulation = ψ

"In allostery, ψ reveals proteins as resonant structures—binding events creating vibrations that propagate through molecular space, distant sites feeling the tremors, the whole protein participating in the dance of regulation."