{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:08:37Z","timestamp":1761487717099},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Background<\/jats:title>\n            <jats:p>Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Methods<\/jats:title>\n            <jats:p>We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in <jats:italic>Saccharomyces cerevisiae<\/jats:italic> serves as case study.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of <jats:italic>feasible<\/jats:italic> t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define <jats:italic>maximal common transition sets<\/jats:italic> (<jats:italic>MCT-sets<\/jats:italic>), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1471-2105-7-482","type":"journal-article","created":{"date-parts":[[2006,11,3]],"date-time":"2006-11-03T02:04:00Z","timestamp":1162519440000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":139,"title":["Application of Petri net based analysis techniques to signal transduction pathways"],"prefix":"10.1186","volume":"7","author":[{"given":"Andrea","family":"Sackmann","sequence":"first","affiliation":[]},{"given":"Monika","family":"Heiner","sequence":"additional","affiliation":[]},{"given":"Ina","family":"Koch","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,11,2]]},"reference":[{"key":"1221_CR1","first-page":"355","volume-title":"Nature","author":"P Blume-Jensen","year":"2001","unstructured":"Blume-Jensen P, Hunter T: Oncogenic kinase signalling. Nature 2001, 355\u2013365. 10.1038\/35077225"},{"issue":"5701","key":"1221_CR2","doi-asserted-by":"publisher","first-page":"1508","DOI":"10.1126\/science.1104568","volume":"306","author":"Y Wang","year":"2004","unstructured":"Wang Y, Dohlman HG: Pheromone signaling mechanisms in yeast: a prototypical sex machine. Science 2004, 306(5701):1508\u20131509. 10.1126\/science.1104568","journal-title":"Science"},{"issue":"2","key":"1221_CR3","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/j.peptides.2004.10.002","volume":"26","author":"L Bardwell","year":"2004","unstructured":"Bardwell L: A walk-through of the yeast mating pheromone response pathway. Peptides 2004, 26(2):339\u2013350. 10.1016\/j.peptides.2004.10.002","journal-title":"Peptides"},{"issue":"4","key":"1221_CR4","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1128\/MMBR.62.4.1264-1300.1998","volume":"62","author":"MC Gustin","year":"1998","unstructured":"Gustin MC, Albertyn J, Alexander M, Davenport K: MAP kinase pathways in the yeast Saccharomyces cerevisiae. Microbiol Mol Biol Rev 1998, 62(4):1264\u20131300.","journal-title":"Microbiol Mol Biol Rev"},{"issue":"6","key":"1221_CR5","doi-asserted-by":"publisher","first-page":"1243","DOI":"10.1083\/jcb.200306139","volume":"163","author":"A Ciliberto","year":"2003","unstructured":"Ciliberto A, Novak B, Tyson JJ: Mathematical model of the morphogenesis checkpoint in budding yeast. J Cell Biol 2003, 163(6):1243\u20131254. 10.1083\/jcb.200306139","journal-title":"J Cell Biol"},{"issue":"10","key":"1221_CR6","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1002\/yea.1122","volume":"21","author":"B Kofahl","year":"2004","unstructured":"Kofahl B, Klipp E: Modelling the dynamics of the yeast pheromone pathway. Yeast 2004, 21(10):831\u2013850. 10.1002\/yea.1122","journal-title":"Yeast"},{"issue":"18","key":"1221_CR7","doi-asserted-by":"publisher","first-page":"4199","DOI":"10.1242\/jcs.01294","volume":"117","author":"Z Qu","year":"2004","unstructured":"Qu Z, Weiss JN, MacLellan WR: Coordination of cell growth and cell division: a mathematical modeling study. J Cell Sci 2004, 117(18):4199\u20134207. 10.1242\/jcs.01294","journal-title":"J Cell Sci"},{"issue":"19","key":"1221_CR8","doi-asserted-by":"publisher","first-page":"10764","DOI":"10.1073\/pnas.1834247100","volume":"100","author":"TM Yi","year":"2003","unstructured":"Yi TM, Kitano H, Simon MI: A quantitative characterization of the yeast heterotrimeric G protein cycle. Proc Natl Acad Sci 2003, 100(19):10764\u201310769. 10.1073\/pnas.1834247100","journal-title":"Proc Natl Acad Sci"},{"key":"1221_CR9","first-page":"101","volume":"1996","author":"S Schuster","year":"1993","unstructured":"Schuster S, Hilgetag C, Schuster R: Determining elementary modes of functioning in biochemical reaction networks at steady state. Proc Second Gauss Symposium 1993, 1996: 101\u2013114.","journal-title":"Proc Second Gauss Symposium"},{"key":"1221_CR10","volume-title":"BMC Bioinformatics","author":"S Klamt","year":"2006","unstructured":"Klamt S, Saez-Rodriguez J, Lindquist JA, Simeoni L, D GE: A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics 2006., 7(56):"},{"issue":"Suppl 2","key":"1221_CR11","doi-asserted-by":"publisher","first-page":"ii 190","DOI":"10.1093\/bioinformatics\/bti1130","volume":"21","author":"E Simao","year":"2005","unstructured":"Simao E, Remy E, Thieffry D, Chaouiya C: Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E. Coli. Bioinformatics 2005, 21(Suppl 2):ii 190-ii 196.","journal-title":"Bioinformatics"},{"key":"1221_CR12","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1016\/j.compchemeng.2004.08.026","volume":"29","author":"I Zevedei-Oancea","year":"2005","unstructured":"Zevedei-Oancea I, Schuster S: A theoretical framework for detecting signal transfer routes in signalling networks. Computers and Chemical Engineering 2005, 29: 597\u2013617. 10.1016\/j.compchemeng.2004.08.026","journal-title":"Computers and Chemical Engineering"},{"key":"1221_CR13","first-page":"173","volume-title":"Proc First Int Workshop on Computational Methods in Systems Biology, (CMSB 2003) Rovereto, LCNS 2602","author":"M Heiner","year":"2003","unstructured":"Heiner M, Koch I, Will J: Model validation of biological pathways using Petri nets \u2013 demonstrated for apoptosis. Proc First Int Workshop on Computational Methods in Systems Biology, (CMSB 2003) Rovereto, LCNS 2602 2003, 173."},{"issue":"1\u20133","key":"1221_CR14","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.biosystems.2004.03.003","volume":"75","author":"M Heiner","year":"2004","unstructured":"Heiner M, Koch I, Will J: Model validation of biological pathways using Petri nets \u2013 demonstrated for apoptosis. Biosystems 2004, 75(1\u20133):15\u201328. 10.1016\/j.biosystems.2004.03.003","journal-title":"Biosystems"},{"key":"1221_CR15","first-page":"216","volume-title":"Proceedings of the 25th International Conference on Applications and Theory of Petri Nets, Bologna, LCNS 3099","author":"M Heiner","year":"2004","unstructured":"Heiner M, Koch I: Petri net based model validation in systems biology. Proceedings of the 25th International Conference on Applications and Theory of Petri Nets, Bologna, LCNS 3099 2004, 216\u2013237."},{"key":"1221_CR16","volume-title":"Communication with automata (in German)","author":"CA Petri","year":"1962","unstructured":"Petri CA: Communication with automata (in German). Institut f\u00fcr instrumentelle Mathematik, Bonn: Schriften des IIM Nr. 3; 1962."},{"key":"1221_CR17","first-page":"541","volume-title":"Proceedings of the IEEE","author":"T Murata","year":"1989","unstructured":"Murata T: Petri nets: Properties, analysis and applications. Proceedings of the IEEE 1989, 541\u2013580. 10.1109\/5.24143"},{"key":"1221_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-09262-9","volume-title":"Analysis of Petri net models (in German)","author":"PH Starke","year":"1990","unstructured":"Starke PH: Analysis of Petri net models (in German). Stuttgart: Teubner Verlag; 1990."},{"key":"1221_CR19","first-page":"328","volume-title":"Proc Int Conf Intell Syst Mol Biol","author":"VN Reddy","year":"1993","unstructured":"Reddy VN, Mavrovouniotis ML, Liebman MN: Petri net representation in metabolic pathways. Proc Int Conf Intell Syst Mol Biol 1993, 328\u2013336."},{"key":"1221_CR20","first-page":"113","volume":"16","author":"R Hofest\u00e4dt","year":"1994","unstructured":"Hofest\u00e4dt R: A Petri net application of metabolic processes. Journal of Systems Analysis, Modelling and Simulation 1994, 16: 113\u2013122.","journal-title":"Journal of Systems Analysis, Modelling and Simulation"},{"issue":"2","key":"1221_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0010-4825(95)00042-9","volume":"26","author":"VN Reddy","year":"1996","unstructured":"Reddy VN, Liebman MN, Mavrovouniotis ML: Qualitative analysis of biochemical reaction systems. Comput Biol Med 1996, 26(2):9\u201324. 10.1016\/0010-4825(95)00042-9","journal-title":"Comput Biol Med"},{"issue":"7","key":"1221_CR22","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1093\/bioinformatics\/bti145","volume":"21","author":"I Koch","year":"2005","unstructured":"Koch I, Junker BH, Heiner M: Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 2005, 21(7):1219\u20131226. 10.1093\/bioinformatics\/bti145","journal-title":"Bioinformatics"},{"issue":"3","key":"1221_CR23","first-page":"367","volume":"3","author":"K Voss","year":"2003","unstructured":"Voss K, Heiner M, Koch I: Steady state analysis of metabolic pathways using Petri nets. In Silico Biol 2003, 3(3):367\u2013387.","journal-title":"In Silico Biol"},{"issue":"3","key":"1221_CR24","first-page":"389","volume":"3","author":"H Matsuno","year":"2003","unstructured":"Matsuno H, Tanaka Y, Aoshima H, Doi A, Matsui M, Miyano S: Biopathways representation and simulation on hybrid functional Petri net. In Silico Biol 2003, 3(3):389\u2013404.","journal-title":"In Silico Biol"},{"key":"1221_CR25","volume-title":"J Biomed Inform","author":"M Chen","year":"2005","unstructured":"Chen M, Hofest\u00e4dt R: A medical bioinformatics approach for metabolic disorders: Biomedical data prediction, modeling, and systematic analysis. J Biomed Inform 2005."},{"issue":"23","key":"1221_CR26","first-page":"271","volume":"4","author":"A Doi","year":"2004","unstructured":"Doi A, Fujita S, Matsuno H, Nagasaki M, Miyano S: Constructing biological pathway models with hybrid functional Petri nets. In Silico Biol 2004, 4(23):271\u2013291.","journal-title":"In Silico Biol"},{"issue":"4","key":"1221_CR27","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1142\/S0219720004000752","volume":"2","author":"S Hardy","year":"2004","unstructured":"Hardy S, Robillard PN: Modelling and simulation of molecular biology systems using Petri nets: modelling goals of various approaches. J Bioinform Comput Biol 2004, 2(4):595\u2013613. 10.1142\/S0219720004000764","journal-title":"J Bioinform Comput Biol"},{"issue":"6","key":"1221_CR28","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1042\/bst0311513","volume":"31","author":"JW Pinney","year":"2003","unstructured":"Pinney JW, Westhead DR, McConkey GA: Petri net representations in systems biology. Biochem Soc Trans 2003, 31(6):1513\u20131515.","journal-title":"Biochem Soc Trans"},{"key":"1221_CR29","volume-title":"Computer Science Reports 04\/2002","author":"J Will","year":"2002","unstructured":"Will J, Heiner M: Petri Nets in biology, chemistry, and medicine \u2013 bibliography. In Computer Science Reports 04\/2002. Brandenburg University of Technology at Cottbus; 2002."},{"key":"1221_CR30","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1146\/annurev.biochem.70.1.703","volume":"70","author":"HG Dohlman","year":"2001","unstructured":"Dohlman HG, Thorner JW: Regulation of G protein-initiated signal transduction in yeast: paradigms and principles. Annu Rev Biochem 2001, 70: 703\u2013754. 10.1146\/annurev.biochem.70.1.703","journal-title":"Annu Rev Biochem"},{"issue":"5710","key":"1221_CR31","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1126\/science.1109500","volume":"307","author":"EA Elion","year":"2005","unstructured":"Elion EA, Qi M, Chen W: Signal transduction. Signaling specificity in yeast. Science 2005, 307(5710):687\u2013688. 10.1126\/science.1109500","journal-title":"Science"},{"issue":"18","key":"1221_CR32","doi-asserted-by":"publisher","first-page":"2887","DOI":"10.1101\/gad.12.18.2887","volume":"12","author":"L Bardwell","year":"1998","unstructured":"Bardwell L, Cook JG, Voora D, Baggott DM, Martinez AR, Thorner J: Repression of yeast Ste12 transcription factor by direct binding of unphosphorylated Kss1 MAPK and its regulation by the Ste7 MEK. Genes Dev 1998, 12(18):2887\u20132898.","journal-title":"Genes Dev"},{"issue":"2","key":"1221_CR33","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1083\/jcb.141.2.349","volume":"141","author":"L Hicke","year":"1998","unstructured":"Hicke L, Zanolari B, Riezman H: Cytoplasmic tail phosphorylation of the alpha-factor receptor is required for its ubiquitination and internalization. J Cell Biol 1998, 141(2):349\u2013358. 10.1083\/jcb.141.2.349","journal-title":"J Cell Biol"},{"issue":"14","key":"1221_CR34","doi-asserted-by":"publisher","first-page":"9160","DOI":"10.1073\/pnas.142034399","volume":"99","author":"RK Esch","year":"2002","unstructured":"Esch RK, Errede B: Pheromone induction promotes Ste11 degradation through a MAPK feedback and ubiquitin-dependent mechanism. Proc Natl Acad Sci 2002, 99(14):9160\u20139165. 10.1073\/pnas.142034399","journal-title":"Proc Natl Acad Sci"},{"key":"1221_CR35","volume-title":"Petri nets basics and applications (in German)","author":"B Baumgarten","year":"1996","unstructured":"Baumgarten B: Petri nets basics and applications (in German). Heidelberg, Berlin, Oxford: Spektrum Akademischer Verlag; 1996."},{"key":"1221_CR36","volume-title":"Exact liveness conditions of a Petri Net class (in German)","author":"K Lautenbach","year":"1973","unstructured":"Lautenbach K: Exact liveness conditions of a Petri Net class (in German). Bonn: GMD Report 82; 1973."},{"issue":"3","key":"1221_CR37","first-page":"323","volume":"3","author":"I Zevedei-Oancea","year":"2003","unstructured":"Zevedei-Oancea I, Schuster S: Topological analysis of metabolic networks based on Petri net theory. In Silico Biol 2003, 3(3):323\u2013345.","journal-title":"In Silico Biol"},{"key":"1221_CR38","volume-title":"Discrete, continuous, and hybrid Petri nets","author":"R David","year":"2005","unstructured":"David R, Alla H: Discrete, continuous, and hybrid Petri nets. Berlin: Springer Verlag; 2005."},{"key":"1221_CR39","volume-title":"Hybrid systems modelling in engineering and life sciences","author":"K Lonitz","year":"2005","unstructured":"Lonitz K: Hybrid systems modelling in engineering and life sciences. Master's Thesis, Universit\u00e4t Koblenz-Landau; 2005."},{"key":"1221_CR40","first-page":"181","volume-title":"Proceedings of the 27th International Conference on Applications and Theory of Petri Nets, Turku, LCNS 4024","author":"D Gilbert","year":"2006","unstructured":"Gilbert D, Heiner M: From Petri nets to differential equations \u2013 an integrative approach for biochemical network analysis. Proceedings of the 27th International Conference on Applications and Theory of Petri Nets, Turku, LCNS 4024 2006, 181\u2013200."},{"issue":"4","key":"1221_CR41","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1038\/nbt0402-370","volume":"20","author":"B Schoeberl","year":"2002","unstructured":"Schoeberl B, Eichler-Jonsson C, Gilles ED, Muller G: Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol 2002, 20(4):370\u2013375. 10.1038\/nbt0402-370","journal-title":"Nat Biotechnol"},{"key":"1221_CR42","volume-title":"Mol Syst Biol","author":"K Oda","year":"2005","unstructured":"Oda K, Matsuoka Y, Funahashi A, Kitano H: A comprehensive pathway map of epidermal growth factor receptor signaling. Mol Syst Biol 2005., 1:"},{"key":"1221_CR43","unstructured":"Snoopy \u2013 Petri net editor and animator[http:\/\/www-dssz.informatik.tu-cottbus.de\/]"},{"key":"1221_CR44","volume-title":"Design and implementation of a generic and adaptive tool for graph manipulation (in German)","author":"M Fieber","year":"2004","unstructured":"Fieber M: Design and implementation of a generic and adaptive tool for graph manipulation (in German). Master's Thesis, Brandenburg University of Technology at Cottbus; 2004."},{"key":"1221_CR45","unstructured":"INA \u2013 The Integrated Net Analyzer[http:\/\/www2.informatik.hu-berlin.de\/~starke\/ina.html]"},{"key":"1221_CR46","unstructured":"Supplementary material[http:\/\/www.tfh-berlin.de\/bi\/pheromone\/]"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-7-482.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T03:14:29Z","timestamp":1630466069000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-7-482"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11,2]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["1221"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-7-482","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,11,2]]},"assertion":[{"value":"5 May 2006","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2006","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2006","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"482"}}