TOMOC: a topology-driven multi-objective evolutionary framework for robust overlapping protein complex detection in noisy PPI networks

Abstract Background Protein complexes constitute fundamental functional modules within cells and play a crucial role in regulating many biological processes. Detecting protein complexes from protein-protein interaction (PPI) networks has therefore become a central problem in computational systems biology. However, many existing computational approaches struggle to accurately identify overlapping complexes where proteins participate in multiple functional modules simultaneously. In addition, large-scale PPI networks are inherently noisy and incomplete due to experimental limitations, which significantly affects the reliability of complex detection methods. Results In this work, we propose TOMOC, a topology-driven multi-objective evolutionary framework for robust detection of overlapping protein complexes in noisy PPI networks. The novelty of TOMOC lies in the integration of a topology-driven bi-objective formulation, an edge-based evolutionary representation that naturally supports overlapping memberships, and a topology-aware structural refinement mechanism within a unified framework for protein complex detection in noisy PPI networks. The proposed framework introduces an edge-based evolutionary representation that models candidate solutions at the interaction level, allowing overlapping memberships to emerge naturally during decoding. It further optimizes two complementary structural objectives by minimizing average conductance and triangle-density loss, enabling the algorithm to balance boundary quality and internal structural density. In addition, a topology-aware structural overlap refinement (SOR) operator is designed to improve structural coherence and robustness against noisy interactions through boundary-aware repair, triangle-closure expansion, and triangle-support pruning. Extensive experiments conducted on three benchmark PPI networks (Yeast-D1, Yeast-D2, and Collins) demonstrate that TOMOC achieves competitive performance compared with several state-of-the-art methods in terms of precision, recall, and F1-score. Conclusions The proposed TOMOC framework provides an effective and scalable topology-driven approach for detecting overlapping protein complexes directly from PPI network topology. By integrating multi-objective evolutionary optimization with topology-aware refinement mechanisms, TOMOC effectively captures the structural characteristics of protein complexes and demonstrates strong robustness when applied to large and noisy biological interaction networks.