Analysis of heat kernel highlights the strongly modular and heat-preserving structure of proteins

TL;DR

This study reveals that proteins exhibit a strongly modular, heat-preserving structure, with heat kernel analysis providing insights into their unique design constraints and subdiffusive behavior compared to other biological networks.

Contribution

The paper introduces heat kernel analysis as a novel approach to characterize protein structures and demonstrates its effectiveness in distinguishing proteins from other networks.

Findings

Proteins show high modularity and heat-preserving properties.

Heat kernel analysis effectively discriminates between network types.

Proteins exhibit subdiffusion in heat trace decay, indicating unique structural constraints.

Abstract

In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological descriptors, such as the modularity and statistics of the shortest paths, and different interpretations in terms of diffusion provided by the discrete heat kernel, which is elaborated from the normalized graph Laplacians. A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based vector characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among those two characterizations, providing thus an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered networks do not need to obey. Notably, the heat trace decay of an ensemble of varying-size proteins denotes subdiffusion, a peculiar property of proteins.