Folding and Function as Two Sides of One Coin: Statistical Mechanics, Information Theory, and Deep Learning of Binding, Catalysis, and Allostery in an Exactly Enumerable Lattice Protein
Year: 2026
Type: preprint
Abstract: Folding and function depend on the same conformational ensemble, but they need not favor the same population distribution. We examine this relationship in a 27-residue lattice protein with 103,346 exactly enumerated compact conformations, combining statistical mechanics, information-theoretic analysis, and variational autoencoders. Exact identities separate binding into native-site recognition and population terms, distinguish transition-state complementarity from reorganization in catalysis, and express allosteric coupling as a conformational covariance. Under composition-conserving selection, binding and turnover optimization favor a dominant compact fold, whereas strong allostery can coexist with a distributed ensemble: pure coupling optimization gives a median native population of 0.47, compared with 0.85 when designs with additional stability rewards are pooled. Composition-free binding and catalytic selection provide further counterexamples to an unconditional function-to-folding implication. Rényi divergences quantify the shortfall from the best available binding or transition-state-recognition conformation; allosteric coupling instead depends on the magnitude and alignment of two ligand-induced responses. A sequence VAE generates target-fold-compatible sequences more frequently than an independent-site baseline and partially retains binding and catalytic properties, but not allosteric coupling. Time-lagged VAEs resolve additional basin information in selected allosteric trajectories, although incomplete interconversion prevents inference of equilibrium switching kinetics. Together, these results identify a conditional relationship between functional selection and fold specificity, and distinguish population concentration for recognition from population redistribution for allosteric communication.
Source: ChemRxiv
Author: Shubin Liu
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7224952622