Local Entropy in Proteins

Abstract

Proteins populate dynamic ensembles, yet how temperature and mutations reshape these ensembles remains poorly understood. We introduce a local entropy metric that assigns each residue a Shannon entropy based on a graph-derived map of accessible substates, providing a continuous measure of structural complexity across folded, unfolded, and intrinsically disordered states. In molecular dynamics simulations of the fast-folding gpW protein, the average local entropy exhibits a sharp transition near the melting point. Residue-specific entropy curves cluster into distinct unfolding categories and reveal that the apparent unfolding transition depends on the spatial scale used to describe amino-acid environments. \rouge{We further show that local entropy captures features that differ markedly from other residue-level measures of structural fluctuations, such as the accessible volume (and the associated packing entropy), which is correlated with B-factors and primarily reflects the hydrophobic effect.} In simulations of $\alpha$-synuclein, an intrinsically disordered protein, local entropy varies strongly along the sequence at physiological temperature and resembles that of gpW near its melting point. Parkinson’s-disease mutations in $\alpha$-synuclein locally reduce entropy while also perturbing distant regions \rouge{including P1, P2 and NAC segments implicated in fibril formations}. These results highlight how temperature and subtle perturbations—such as single-residue changes—remodel conformational ensembles. Local entropy correlates with NMR observables and provides a generalizable framework for quantifying disorder, with broad potential applications beyond protein science.