Topological thermal instability and the length of proteins

TL;DR

This paper investigates how the global topology of proteins influences their thermal stability, revealing a strong correlation between spectral dimension and protein length, and suggesting that proteins adopt the least compact stable fold.

Contribution

It introduces the spectral dimension as a key topological parameter linked to protein stability and provides a novel analysis connecting topology with thermodynamic properties.

Findings

Spectral dimension correlates strongly with protein length.

Larger spectral dimension indicates more topologically compact structures.

Proteins tend to fold into the least compact stable configuration.

Abstract

We present an analysis of the role of global topology on the structural stability of folded proteins in thermal equilibrium with a heat bath. For a large class of single domain proteins, we compute the harmonic spectrum within the Gaussian Network Model (GNM) and we determine the spectral dimension, a parameter describing the low frequency behaviour of the density of modes. We find a surprisingly strong correlation between the spectral dimension and the number of aminoacids of the protein. Considering that the larger the spectral dimension, the more topologically compact is the folded state, our results indicate that for a given temperature and length of the protein, the folded structure corresponds to the less compact folding compatible with thermodynamic stability.