Pilot study using a discrete mathematical approach for topological analysis and ssGSEA of gene expression in autosomal recessive polycystic kidney disease.

Autosomal recessive polycystic kidney disease (ARPKD) is a severe genetic disorder characterized by renal cystogenesis and hepatic fibrosis, primarily associated with PKHD1 mutations. While differential expression analysis (DEG) has identified key genes involved in ARPKD, their network-level interactions remain unclear. Recent studies have implicated WNT signaling in ARPKD pathogenesis, but a topological framework may provide additional insights into gene community structures. This study applied a network-based approach integrating single-sample gene set enrichment analysis (ssGSEA) and topological centrality analysis to investigate gene communities in ARPKD. We identified three key communities: Community 2, centered on IFT22, exhibited stable activation in both ARPKD and healthy samples, suggesting its role in ciliary function. Community 5, predominantly activated in ARPKD, included genes linked to tissue repair and immune regulation. In contrast, Community 3 was suppressed in ARPKD, indicating potential structural instability. Notably, PKHD1 was mathematically isolated, suggesting limited direct involvement in ARPKD-specific transcriptional networks, while the absence of WNT5A, CDH1, and FZD10 from defined communities in ARPKD may indicate potential alterations in their network associations compared to healthy individuals. These findings highlight the advantages of network topology over conventional DEG analysis in elucidating ARPKD pathophysiology. By identifying gene communities and regulatory hubs, this approach offers novel insights into disease mechanisms and potential therapeutic targets.