GenPath-PPH: Integrating gene expression and pathway networks via persistent path homology enhances detection of...

Identifying disease-relevant biological pathways is critical for understanding the molecular mechanisms underlying specific disease phenotypes. Traditional techniques, such as gene set analysis, often neglect topological interactions among genes within actual biological pathways. To address this limitation, we introduce GenPath-PPH, a novel framework that integrates gene expression data with directed biological pathway networks using persistent path homology (PPH), a topological tool for analyzing directional relationships. GenPath-PPH tracks changes in correlation strength between interacting genes across two conditions (e.g., disease and control) and interprets these differences as topological, disease-related alterations in the pathway network. Within pathways, it identifies changes in connected components (co-expression clusters) as well as in higher-order structures (directed cycles), which are not detectable by conventional homology methods. By combining connectivity and cyclic features, GenPath-PPH highlights significantly altered pathways, using permutation testing to assess statistical significance. When applied to peripheral blood mononuclear cell (PBMC) samples from hepatocellular carcinoma (HCC) patients, GenPath-PPH not only identifies well-known cancer-associated pathways (e.g., JAK-STAT signaling, p53 signaling and the pentose phosphate pathway) in accordance with other techniques, but also reveals additional pathways (e.g., NF- $\kappa$ B signaling, sphingolipid signaling and aminoacyl-tRNA biosynthesis) that are either missed by other techniques, despite their known relevance to HCC, or represent novel candidate pathways for experimental evaluation. Our work bridges network topology and biological function, offering a new analytical approach capable of uncovering previously overlooked connections between topological structure and functional activity.