Topological Analysis of Age-Related Proteins in Protein-Protein Interaction Networks via Local Persistent Homology

Ageing is a complex biological process that gradually alters cellular function and patterns of protein interaction. Standard network-based measures such as degree, betweenness and clustering coefficient are widely used in protein–protein interaction networks (PPINs), but these metrics may overlook subtle changes within local neighbourhoods. This study applies Local Persistent Homology (LPH) to characterise age-related differences in the local topology of PPINs, providing structural information that is not captured through global or node-level analyses. For each protein, a level 2 ego network is constructed and its and features are summarised using persistence diagrams (PDs). The Wasserstein distance between PDs from adult and elderly networks is then computed to quantify topological variation across age groups. The Wasserstein distance for each protein was compared with its degree, betweenness, and local clustering coefficient to examine how local topological structure relates to standard centrality measures. Proteins with many topological components tend to exhibit higher degree and betweenness but lower clustering, while proteins in simpler neighbourhoods show longer average persistence and more stable structural patterns. By integrating LPH results with gene-disease association data, 25 proteins with notable age-related topological differences are identified, including several associated with neurodegenerative diseases. Overall, LPH deepens the analysis of PPIN architecture by exposing subtle, age-linked structural patterns that remain undetected using network centralities.