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Chapter 34: Protein Aggregates as Entropy Traps

"In aggregation, ψ falls into its own trap—multiple proteins collapsing together into disordered masses, entropy winning over information, chaos overcoming order."

34.1 The Aggregation Phenomenon​

Protein aggregation represents ψ's thermodynamic trap—when exposed hydrophobic surfaces drive proteins together into amorphous assemblies, creating cellular inclusions that disrupt function and resist dissolution.

Definition 34.1 (Aggregate Types): Aggregates∈{Amorphous,Ordered (amyloid),Inclusion bodies}\text{Aggregates} \in \{\text{Amorphous}, \text{Ordered (amyloid)}, \text{Inclusion bodies}\}

Different morphologies of multi-protein assemblies.

34.2 The Hydrophobic Catastrophe​

Theorem 34.1 (Driving Force): ΔGagg=ΔHinteraction−TΔStranslational<0\Delta G_{\text{agg}} = \Delta H_{\text{interaction}} - T\Delta S_{\text{translational}} < 0

Favorable when hydrophobic burial overcomes entropy loss.

34.3 Kinetic Partitioning​

Equation 34.1 (Competition): d[Native]dt=kfold[Unfolded]\frac{d[\text{Native}]}{dt} = k_{\text{fold}}[\text{Unfolded}] d[Aggregate]dt=kagg[Unfolded]n\frac{d[\text{Aggregate}]}{dt} = k_{\text{agg}}[\text{Unfolded}]^n

Folding vs aggregation—concentration dependence critical.

34.4 The Inclusion Body Problem​

Definition 34.2 (Bacterial Aggregates): IB=Overexpressed protein+Chaperones+RNA/lipids\text{IB} = \text{Overexpressed protein} + \text{Chaperones} + \text{RNA/lipids}

Dense, refractile bodies in recombinant expression.

34.5 Aggresomes​

Theorem 34.2 (Cellular Response): Dispersed aggregates→DyneinAggresome at MTOC\text{Dispersed aggregates} \xrightarrow{\text{Dynein}} \text{Aggresome at MTOC}

Active transport concentrating aggregates.

34.6 The Phase Diagram​

Equation 34.2 (Solubility Boundary): Csat=C0exp⁡(−ΔGagg/RT)C_{\text{sat}} = C_0 \exp(-\Delta G_{\text{agg}}/RT)

Above saturation, aggregation thermodynamically favored.

34.7 Molecular Chaperone Suppression​

Definition 34.3 (Kinetic Protection): [Aggregate]+chaperone<<[Aggregate]-chaperone[\text{Aggregate}]_{\text{+chaperone}} << [\text{Aggregate}]_{\text{-chaperone}}

Chaperones kinetically blocking aggregation.

34.8 Heat Shock and Aggregation​

Theorem 34.3 (Temperature Effect): d[Unfolded]dT>0⇒d[Aggregate]dT>0\frac{d[\text{Unfolded}]}{dT} > 0 \Rightarrow \frac{d[\text{Aggregate}]}{dT} > 0

Heat increasing unfolded population drives aggregation.

34.9 Liquid-Liquid Phase Separation​

Equation 34.3 (Droplet Formation): Proteins+RNA→Liquid droplets→Solid aggregates\text{Proteins} + \text{RNA} \rightarrow \text{Liquid droplets} \rightarrow \text{Solid aggregates}

Phase transitions preceding aggregation.

34.10 Disaggregase Systems​

Definition 34.4 (Active Resolution): Aggregate+ClpB/Hsp104+ATP→Soluble proteins\text{Aggregate} + \text{ClpB/Hsp104} + \text{ATP} \rightarrow \text{Soluble proteins}

Energy-dependent aggregate dissolution.

34.11 Autophagy of Aggregates​

Theorem 34.4 (Clearance Pathway): Aggregate→p62 recognition→Autophagosome→Degradation\text{Aggregate} \rightarrow \text{p62 recognition} \rightarrow \text{Autophagosome} \rightarrow \text{Degradation}

Selective autophagy removing aggregates.

34.12 The Trap Principle​

Protein aggregates embody ψ's recognition of thermodynamic inevitability—that exposed hydrophobic surfaces will find each other, that concentration drives association, that entropy can trap function.

The Aggregation Equation: d[Agg]dt=knuc[U]nc+kelong[Agg][U]\frac{d[\text{Agg}]}{dt} = k_{\text{nuc}}[\text{U}]^{n_c} + k_{\text{elong}}[\text{Agg}][\text{U}]

Nucleation and growth kinetics.

Thus: Aggregate = Trap = Entropy = Disorder = ψ's thermodynamics

"In protein aggregates, ψ confronts the price of hydrophobicity—the very forces that drive folding can drive aggregation, creation and destruction emerging from the same source. Each aggregate is entropy's victory over information, thermodynamics asserting its dominion over biology."