{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:27:19Z","timestamp":1787171239432,"version":"build-2736575974"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T00:00:00Z","timestamp":1787011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T00:00:00Z","timestamp":1787097600000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100012320","name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012320","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>\n                      <jats:bold>Background<\/jats:bold>\n                    <\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>\n                      <jats:bold>Results<\/jats:bold>\n                    <\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>\n                      <jats:bold>Conclusions<\/jats:bold>\n                    <\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12859-026-06603-z","type":"journal-article","created":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T15:04:50Z","timestamp":1787065490000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["TOMOC: a topology-driven multi-objective evolutionary framework for robust overlapping protein complex detection in noisy PPI networks"],"prefix":"10.1186","volume":"27","author":[{"given":"Mustafa","family":"Abbas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Broneske","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gunter","family":"Saake","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,18]]},"reference":[{"issue":"5","key":"6603_CR1","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1145\/2160718.2160738","volume":"55","author":"N Atias","year":"2012","unstructured":"Atias N, Sharan R. Comparative analysis of protein networks: hard problems, practical solutions. Commun ACM. 2012;55(5):88\u201397.","journal-title":"Commun ACM"},{"issue":"1","key":"6603_CR2","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1038\/msb4100129","volume":"3","author":"R Sharan","year":"2007","unstructured":"Sharan R, Ulitsky I, Shamir R. Network-based prediction of protein function. Mol Syst Biol. 2007;3(1):88.","journal-title":"Mol Syst Biol"},{"issue":"15\u201316","key":"6603_CR3","doi-asserted-by":"publisher","first-page":"2100190","DOI":"10.1002\/pmic.202100190","volume":"22","author":"S Wang","year":"2022","unstructured":"Wang S, Wu R, Lu J, Jiang Y, Huang T, Cai Y-D. Protein-protein interaction networks as miners of biological discovery. Proteomics. 2022;22(15\u201316):2100190.","journal-title":"Proteomics"},{"issue":"7084","key":"6603_CR4","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1038\/nature04670","volume":"440","author":"NJ Krogan","year":"2006","unstructured":"Krogan NJ, Cagney G, Yu H, Zhong G, Guo X, Ignatchenko A, et al. Global landscape of protein complexes in the yeast saccharomyces cerevisiae. Nature. 2006;440(7084):637\u201343.","journal-title":"Nature"},{"issue":"6887","key":"6603_CR5","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1038\/nature750","volume":"417","author":"C Von Mering","year":"2002","unstructured":"Von Mering C, Krause R, Snel B, Cornell M, Oliver SG, Fields S, et al. Comparative assessment of large-scale data sets of protein-protein interactions. Nature. 2002;417(6887):399\u2013403.","journal-title":"Nature"},{"key":"6603_CR6","doi-asserted-by":"crossref","unstructured":"Luo X, Wang L, Hu P, Hu L. Predicting protein-protein interactions using sequence and network information via variational graph autoencoder. IEEE\/ACM Transactions on Computational Biology and Bioinformatics. 2023.","DOI":"10.1109\/TCBB.2023.3273567"},{"issue":"2","key":"6603_CR7","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1109\/TCBB.2015.2407393","volume":"14","author":"L Zhu","year":"2015","unstructured":"Zhu L, Deng S-P, You Z-H, Huang D-S. Identifying spurious interactions in the protein-protein interaction networks using local similarity preserving embedding. IEEE\/ACM Trans Comput Biol Bioinf. 2015;14(2):345\u201352.","journal-title":"IEEE\/ACM Trans Comput Biol Bioinf"},{"issue":"17","key":"6603_CR8","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1093\/bioinformatics\/bty573","volume":"34","author":"S Hashemifar","year":"2018","unstructured":"Hashemifar S, Neyshabur B, Khan AA, Xu J. Predicting protein-protein interactions through sequence-based deep learning. Bioinformatics. 2018;34(17):802\u201310.","journal-title":"Bioinformatics"},{"issue":"2","key":"6603_CR9","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1038\/nrg1272","volume":"5","author":"A-L Barabasi","year":"2004","unstructured":"Barabasi A-L, Oltvai ZN. Network biology: understanding the cell\u2019s functional organization. Nat Rev Genet. 2004;5(2):101\u201313.","journal-title":"Nat Rev Genet"},{"issue":"8","key":"6603_CR10","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1136\/jmg.2006.041376","volume":"43","author":"M Oti","year":"2006","unstructured":"Oti M, Snel B, Huynen MA, Brunner HG. Predicting disease genes using protein-protein interactions. J Med Genet. 2006;43(8):691\u20138.","journal-title":"J Med Genet"},{"key":"6603_CR11","unstructured":"Dongen S. A Cluster Algorithm for Graphs. CWI (Centre for Mathematics and Computer Science). 2000."},{"issue":"1","key":"6603_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-4-2","volume":"4","author":"GD Bader","year":"2003","unstructured":"Bader GD, Hogue CW. An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics. 2003;4(1):1\u201327.","journal-title":"BMC Bioinformatics"},{"issue":"7043","key":"6603_CR13","doi-asserted-by":"publisher","first-page":"814","DOI":"10.1038\/nature03607","volume":"435","author":"G Palla","year":"2005","unstructured":"Palla G, Der\u00e9nyi I, Farkas I, Vicsek T. Uncovering the overlapping community structure of complex networks in nature and society. Nature. 2005;435(7043):814\u20138.","journal-title":"Nature"},{"issue":"8","key":"6603_CR14","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1093\/bioinformatics\/btl039","volume":"22","author":"B Adamcsek","year":"2006","unstructured":"Adamcsek B, Palla G, Farkas IJ, Der\u00e9nyi I, Vicsek T. Cfinder: locating cliques and overlapping modules in biological networks. Bioinformatics. 2006;22(8):1021\u20133.","journal-title":"Bioinformatics"},{"issue":"5","key":"6603_CR15","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1038\/nmeth.1938","volume":"9","author":"T Nepusz","year":"2012","unstructured":"Nepusz T, Yu H, Paccanaro A. Detecting overlapping protein complexes in protein-protein interaction networks. Nat Methods. 2012;9(5):471\u20132.","journal-title":"Nat Methods"},{"issue":"1","key":"6603_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-14-163","volume":"14","author":"N Zaki","year":"2013","unstructured":"Zaki N, Efimov D, Berengueres J. Protein complex detection using interaction reliability assessment and weighted clustering coefficient. BMC Bioinformatics. 2013;14(1):1\u20139.","journal-title":"BMC Bioinformatics"},{"issue":"3","key":"6603_CR17","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1109\/TCBB.2016.2642107","volume":"15","author":"T He","year":"2016","unstructured":"He T, Chan KC. Evolutionary graph clustering for protein complex identification. IEEE\/ACM Trans Comput Biol Bioinf. 2016;15(3):892\u2013904.","journal-title":"IEEE\/ACM Trans Comput Biol Bioinf"},{"issue":"1","key":"6603_CR18","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1186\/1471-2105-15-186","volume":"15","author":"X-F Zhang","year":"2014","unstructured":"Zhang X-F, Dai D-Q, Ou-Yang L, Yan H. Detecting overlapping protein complexes based on a generative model with functional and topological properties. BMC Bioinformatics. 2014;15(1):186.","journal-title":"BMC Bioinformatics"},{"issue":"4","key":"6603_CR19","doi-asserted-by":"publisher","first-page":"3275","DOI":"10.1109\/TNSE.2021.3109880","volume":"8","author":"L Hu","year":"2021","unstructured":"Hu L, Zhang J, Pan X, Luo X, Yuan H. An effective link-based clustering algorithm for detecting overlapping protein complexes in protein-protein interaction networks. IEEE Trans Netw Sci Eng. 2021;8(4):3275\u201389.","journal-title":"IEEE Trans Netw Sci Eng"},{"issue":"9","key":"6603_CR20","doi-asserted-by":"publisher","first-page":"4569","DOI":"10.1109\/JBHI.2023.3289490","volume":"27","author":"W Wang","year":"2023","unstructured":"Wang W, Meng X, Xiang J, Shuai Y, Bedru HD, Li M. Caco: a core-attachment method with cross-species functional ortholog information to detect human protein complexes. IEEE J Biomed Health Inform. 2023;27(9):4569\u201378.","journal-title":"IEEE J Biomed Health Inform"},{"issue":"1","key":"6603_CR21","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1093\/bib\/bbac523","volume":"24","author":"H Chen","year":"2023","unstructured":"Chen H, Cai Y, Ji C, Selvaraj G, Wei D, Wu H. Adappi: identification of novel protein functional modules via adaptive graph convolution networks in a protein-protein interaction network. Brief Bioinform. 2023;24(1):523.","journal-title":"Brief Bioinform"},{"key":"6603_CR22","doi-asserted-by":"crossref","unstructured":"Yang Y, Hu L, Li G, Li D, Hu P, Luo X. Fmvpci: a multiview fusion neural network for identifying protein complex via fuzzy clustering. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2025.","DOI":"10.1109\/TSMC.2025.3578348"},{"issue":"1","key":"6603_CR23","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1186\/s12859-018-2309-9","volume":"19","author":"R Wang","year":"2018","unstructured":"Wang R, Liu G, Wang C, Su L, Sun L. Predicting overlapping protein complexes based on core-attachment and a local modularity structure. BMC Bioinformatics. 2018;19(1):305.","journal-title":"BMC Bioinformatics"},{"issue":"10","key":"6603_CR24","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.3390\/e23101271","volume":"23","author":"H Jeong","year":"2021","unstructured":"Jeong H, Kim Y, Jung Y-S, Kang DR, Cho Y-R. Entropy-based graph clustering of ppi networks for predicting overlapping functional modules of proteins. Entropy. 2021;23(10):1271.","journal-title":"Entropy"},{"issue":"6","key":"6603_CR25","doi-asserted-by":"publisher","first-page":"2000","DOI":"10.1109\/TCBB.2024.3429546","volume":"21","author":"W Wang","year":"2024","unstructured":"Wang W, Meng X, Xiang J, Bedru HD, Li M. Dopcc: detecting overlapping protein complexes via multi-metrics and co-core attachment method. IEEE\/ACM Trans Comput Biol Bioinf. 2024;21(6):2000\u201310.","journal-title":"IEEE\/ACM Trans Comput Biol Bioinf"},{"key":"6603_CR26","doi-asserted-by":"crossref","unstructured":"Pizzuti C, Rombo S. Experimental evaluation of topological-based fitness functions to detect complexes in ppi networks. In: Proceedings of the 14th annual conference on genetic and evolutionary computation. 2012. p. 193\u2013200.","DOI":"10.1145\/2330163.2330191"},{"issue":"10","key":"6603_CR27","doi-asserted-by":"publisher","first-page":"1343","DOI":"10.1093\/bioinformatics\/btu034","volume":"30","author":"C Pizzuti","year":"2014","unstructured":"Pizzuti C, Rombo SE. Algorithms and tools for protein-protein interaction networks clustering, with a special focus on population-based stochastic methods. Bioinformatics. 2014;30(10):1343\u201352.","journal-title":"Bioinformatics"},{"issue":"1","key":"6603_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13015-015-0056-2","volume":"10","author":"S Bandyopadhyay","year":"2015","unstructured":"Bandyopadhyay S, Ray S, Mukhopadhyay A, Maulik U. A multiobjective approach for identifying protein complexes and studying their association in multiple disorders. Algorithms Mol Biol. 2015;10(1):1\u201315.","journal-title":"Algorithms Mol Biol"},{"issue":"11","key":"6603_CR29","doi-asserted-by":"publisher","first-page":"3721","DOI":"10.1007\/s00500-017-2593-8","volume":"22","author":"BA Attea","year":"2018","unstructured":"Attea BA, Abdullah QZ. Improving the performance of evolutionary-based complex detection models in protein-protein interaction networks. Soft Comput. 2018;22(11):3721\u201344.","journal-title":"Soft Comput"},{"issue":"1","key":"6603_CR30","doi-asserted-by":"publisher","first-page":"2132516","DOI":"10.1155\/2021\/2132516","volume":"2021","author":"N Shirmohammady","year":"2021","unstructured":"Shirmohammady N, Izadkhah H, Isazadeh A. Ppi-ga: a novel clustering algorithm to identify protein complexes within protein-protein interaction networks using genetic algorithm. Complexity. 2021;2021(1):2132516.","journal-title":"Complexity"},{"key":"6603_CR31","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.compbiolchem.2015.06.006","volume":"58","author":"B Cao","year":"2015","unstructured":"Cao B, Luo J, Liang C, Wang S, Song D. Moepga: a novel method to detect protein complexes in yeast protein-protein interaction networks based on multiobjective evolutionary programming genetic algorithm. Comput Biol Chem. 2015;58:173\u201381.","journal-title":"Comput Biol Chem"},{"issue":"6","key":"6603_CR32","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","volume":"11","author":"Q Zhang","year":"2007","unstructured":"Zhang Q, Li H. Moea\/d: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput. 2007;11(6):712\u201331.","journal-title":"IEEE Trans Evol Comput"},{"issue":"7084","key":"6603_CR33","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1038\/nature04532","volume":"440","author":"A-C Gavin","year":"2006","unstructured":"Gavin A-C, Aloy P, Grandi P, Krause R, Boesche M, Marzioch M, et al. Proteome survey reveals modularity of the yeast cell machinery. Nature. 2006;440(7084):631\u20136.","journal-title":"Nature"},{"issue":"10","key":"6603_CR34","doi-asserted-by":"publisher","first-page":"2459","DOI":"10.1002\/prot.24130","volume":"80","author":"N Zaki","year":"2012","unstructured":"Zaki N, Berengueres J, Efimov D. Detection of protein complexes using a protein ranking algorithm. Proteins: Struct, Funct, Bioinf. 2012;80(10):2459\u201368.","journal-title":"Proteins: Struct, Funct, Bioinf"},{"key":"6603_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/jbiol36","volume":"5","author":"T Reguly","year":"2006","unstructured":"Reguly T, Breitkreutz A, Boucher L, Breitkreutz B-J, Hon GC, Myers CL, et al. Comprehensive curation and analysis of global interaction networks in saccharomyces cerevisiae. J Biol. 2006;5:1\u201328.","journal-title":"J Biol"},{"issue":"1","key":"6603_CR36","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1093\/nar\/30.1.31","volume":"30","author":"H-W Mewes","year":"2002","unstructured":"Mewes H-W, Frishman D, G\u00fcldener U, Mannhaupt G, Mayer K, Mokrejs M, et al. Mips: a database for genomes and protein sequences. Nucleic Acids Res. 2002;30(1):31\u20134.","journal-title":"Nucleic Acids Res"},{"issue":"3","key":"6603_CR37","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1093\/nar\/gkn1005","volume":"37","author":"S Pu","year":"2009","unstructured":"Pu S, Wong J, Turner B, Cho E, Wodak SJ. Up-to-date catalogues of yeast protein complexes. Nucleic Acids Res. 2009;37(3):825\u201331.","journal-title":"Nucleic Acids Res"},{"issue":"D1","key":"6603_CR38","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1093\/nar\/gkr1029","volume":"40","author":"JM Cherry","year":"2012","unstructured":"Cherry JM, Hong EL, Amundsen C, Balakrishnan R, Binkley G, Chan ET, et al. Saccharomyces genome database: the genomics resource of budding yeast. Nucleic Acids Res. 2012;40(D1):700\u20135.","journal-title":"Nucleic Acids Res"},{"issue":"10","key":"6603_CR39","doi-asserted-by":"publisher","first-page":"1274","DOI":"10.1093\/bioinformatics\/btm087","volume":"23","author":"JZ Wang","year":"2007","unstructured":"Wang JZ, Du Z, Payattakool R, Yu PS, Chen C-F. A new method to measure the semantic similarity of go terms. Bioinformatics. 2007;23(10):1274\u201381.","journal-title":"Bioinformatics"},{"issue":"1","key":"6603_CR40","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","volume":"57","author":"Y Benjamini","year":"1995","unstructured":"Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J Roy Stat Soc: Ser B (Methodol). 1995;57(1):289\u2013300.","journal-title":"J Roy Stat Soc: Ser B (Methodol)"},{"key":"6603_CR41","doi-asserted-by":"crossref","unstructured":"Abbas MN, Bara\u2019a AA, Broneske D, Saake G. An evolutionary algorithm with heuristic operator for detecting protein complexes in protein interaction networks with negative controls. IEEE Access; 2024.","DOI":"10.1109\/ACCESS.2024.3367746"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12859-026-06603-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-026-06603-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-026-06603-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:02:15Z","timestamp":1787169735000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s12859-026-06603-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,18]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["6603"],"URL":"https:\/\/doi.org\/10.1186\/s12859-026-06603-z","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,18]]},"assertion":[{"value":"5 March 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 August 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 August 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Not applicable.","order":1,"name":"Ethics","label":"Ethics approval and consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing of interests.","order":3,"name":"Ethics","label":"Competing of interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"189"}}