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March 29, 2026Open Access

The Funneled Void: Protein Folding as Péclet-Number Minimization and the Thermodynamic Resolution of the Levinthal Paradox

Key Points

The research aims to formalize protein folding as a Péclet-number minimization process and resolve the Levinthal paradox.
Formalization of protein folding using Péclet-number concepts.
Application of AlphaFold2's Evoformer for co-evolutionary weight computation.
Empirical testing across 35 proteins from three classes.
Statistical correlation analysis to assess aggregation propensity.
Strong correlation (ρ = 0.972) between Péclet-number and aggregation propensity across all proteins.
Class 1 shows perfect correlation (ρ = 1.000), indicating high predictability for prion variants.
Class 2 and Class 3 display strong correlations with values of 0.909 and 0.936, respectively.
Falsification test indicates that the non-amyloidogenic rat IAPP shows a negative Péclet aggregation value.

Abstract

Formalizes protein folding as a Péclet-number minimization process. The Levinthal paradox (3¹00 conformational states) is resolved by showing the funneled energy landscape is the physical implementation of the prohibition-ritual pair: the funnel IS the constraint specification. AlphaFold2's Evoformer computes pair-residue coevolutionary weights equivalent to BG (native contact probability matrix), making it an implicit Pe minimizer. Empirical test: ρ (Peₐgg, aggregationₚropensity) > 0. 85 across 35 proteins in 3 classes (prion variants, amyloid-forming sequences, IDPs). Results: Class 1 ρ=1. 000, Class 2 ρ=0. 909, Class 3 ρ=0. 936, Pooled ρ=0. 972. Falsification test: rat IAPP (non-amyloidogenic) has Peₐgg < 0, human IAPP Peₐgg = 16. 0.

The Funneled Void: Protein Folding as Péclet-Number Minimization and the Thermodynamic Resolution of the Levinthal Paradox

Key Points

Abstract

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