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

2014/09/30 by Lorenzo Livi, Enrico Maiorino, Andréa Pinna +4 · 14 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Bioinformatics and Genomic Networks #Biological system #Biology #Combinatorics #Computational Drug Discovery Methods #Computer science #Graph #Heat kernel #Interpretability #Kernel (algebra) #Kernel method #Kernel principal component analysis #Mathematical analysis #Mathematics #Modular design #Modularity (biology) #Physics #Principal component analysis #Protein Structure and Dynamics #Pure mathematics #Statistical physics #Support vector machine #Theoretical computer science #Topology (electrical circuits) #physics.bio-ph #physics.data-an #q-bio.BM

paper · pdf · doi:10.1016/j.physa.2015.08.059

published in Physica A Statistical Mechanics and its Applications 441, 199-214 (Elsevier BV)

arxiv created 2015/03/16 · arxiv updated 2015/09/04 · openalex publication_date 2015/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Residue network in protein native structure belongs to the universality class of a three-dimensional critical percolation cluster
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• The large-scale organization of metabolic networks
• Power laws, Pareto distributions and Zipf's law
• Temporal networks