A Granularity-related Network Refinement Method Based on Module Division and Biological Information for Identifying Essential Proteins

Essential proteins play a pivotal role in biological systems, and their identification is critical for elucidating complex life mechanisms and disease pathogenesis. While most existing identification methods rely on protein-protein interaction networks (PINs), the inherent noise in raw PINs frequently compromises identification efficiency. To address this limitation, researchers often employ network refinement strategies to improve PIN quality, with modularity-based approaches demonstrating particularly strong efficacy in enhancing the predictive performance of essential protein identification. Emerging evidence reveals that protein complexes exhibit distinct fine-grained modular architectures. This observation suggests that systematically incorporating modular granularity considerations during refined PIN construction could significantly improve the accuracy of essential protein identification. Building on this premise, we propose a novel granularity-aware network refinement framework that integrates hierarchical module division and multi-source biological evidence for essential protein discovery. Our methodology comprises three key phases: (1) Weighted PIN construction through integration of gene expression profiles and Gene Ontology (GO) biological process annotations; (2) Hierarchical module division using the Louvain algorithm to optimize granularity resolution; (3) Critical module detection via synthesis of evolutionary conservation scores and nuclear localization enrichment metrics, ultimately generating a Granularity-Modulated PIN (GM-PIN). To validate our approach, we performed comparative evaluations against four baseline networks (S-PIN, D-PIN, RD-PIN and CM-PIN) using ten state-of-the-art essential protein identification methods (DC, LAC, NC, EC, BC, CC, SC, PR, PeC and WDC) across two species (yeast and human). Experimental results demonstrate that GM-PIN achieves superior performance across multiple metrics, including essential proteins identified in top K, Jackknifing, PRAUC, sensitivity, F-measure and accuracy. These findings confirm that our granularity-modulated refinement method effectively constructs high-quality PINs that substantially enhance essential protein discovery.