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

Abstract

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.

Fig. 1

Gene network topology in ARPKD patients. This figure illustrates the gene network in ARPKD patients, where each node represents a gene, and each edge indicates a gene pair with a correlation coefficient of 0.6 or higher. To emphasize the distribution of nodes, edges are rendered fully transparent. Node size is proportional to its degree, reflecting the number of connections with other genes. Larger nodes represent highly connected hub genes, which may play key roles in network stability. Clusters were detected using the Louvain method, with each color representing a distinct community: Community 0 (dark purple), Community 1 (green), and Community 2 (yellow). Genes within each community exhibit higher intra-cluster connectivity, visually delineating the structure of correlated gene groups.

Fig. 2

Gene network topology in healthy control individuals. This figure shows the gene network in healthy control individuals, with each node representing a gene and each edge representing a gene pair with a correlation of 0.6 or higher. The edges are fully transparent to focus on the structure and prominence of individual nodes. The size of each node is proportional to the number of other genes and is strongly correlated with, emphasizing the hub genes that are central to the network. Different colors indicate clusters detected by the Louvain method, with each color representing a distinct community of genes: Community 3 is shown in purple, Community 4 in green, and Community 5 in yellow. Genes within each community exhibit strong mutual interactions, illustrating the structure of gene relationships based on correlations in healthy kidney function. These clusters highlight potential functional groupings of genes, with central genes in each community likely playing key roles in maintaining normal cellular processes in the kidneys.