Normalized Laplacian Diffusion for Robust Cancer Pathway Extension and Critical Gene Identification from Limited Data

Cancer progression is primarily driven by disruptions in critical biological pathways, including ErbB signaling, p53-mediated apoptosis, and GSK3 signaling. However, experimental and clinical studies typically identify only limited disease-associated genes, challenging traditional pathway analysis methods that require larger gene sets. To overcome this limitation, reliably expanded gene sets are required to align with cancer-related pathways. Although various propagation methods are available, the key challenge is to select techniques that can effectively propagate signals from limited seed gene sets through protein interaction networks, thereby generating robust, expanded sets capable of revealing pathway disruptions in cancer. In this study, the number of seed genes was systematically varied to evaluate the alignment of pathways obtained from different propagation methods with known pathways using Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) annotations. Among the evaluated propagation methods, normalized Laplacian diffusion (NLD) demonstrated the strongest alignment with reference pathways, with an average area under the ROC curve (AUC) of 95.11% and an area under precision–recall (AUPR) of 71.20%. Focusing specifically on well-established cancer pathways, we summarized the enriched pathways and discussed their biological relevance with limited gene input. Results from multiple runs were aggregated to identify genes consistently prioritized but absent from core pathway annotations, representing potential pathway extensions. Notable examples include RAC2 (ErbB pathway), FOXO3 and ESR1 (GSK3 signaling), and XIAP and BRD4 (p53 pathway), which were significantly associated with patient survival. Literature validation confirmed their biological relevance, underscoring their potential as prognostic markers and therapeutic targets. In summary, NLD-based diffusion proves effective for pathway discovery from limited input, extending beyond annotated members to reveal clinically relevant genes with therapeutic and biomarker potential.