{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T18:31:18Z","timestamp":1769020278158,"version":"3.49.0"},"reference-count":54,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,8]],"date-time":"2017-02-08T00:00:00Z","timestamp":1486512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010751","name":"FONDECYT","doi-asserted-by":"publisher","award":["1150229"],"award-info":[{"award-number":["1150229"]}],"id":[{"id":"10.13039\/501100010751","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010751","name":"FONDECYT","doi-asserted-by":"publisher","award":["3170122"],"award-info":[{"award-number":["3170122"]}],"id":[{"id":"10.13039\/501100010751","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>The basic processes that bring about living systems are conventionally represented in the framework of chemical reaction networks. Recently, it has been proposed that this framework can be exploited for studying various other phenomena. Reaction networks are specially suited for representing situations where different types of entities interact in contextual ways leading to the emergence of meta-structures. At an abstract level, a reaction network represents a universe whose evolution corresponds to the transformation of collections of entities into other collections of entities. Hence, we propose that systems correspond to the sub-networks that are stable enough to be observed. In this article, we discuss how to use reaction networks for representing systems. Namely, we introduce the different representational levels available (relational, stoichiometric, and kinetic), we show how to identify observable systems in the reaction network, discuss some relevant systemic notions such as context, emergence, and meta-system, and present some examples.<\/jats:p>","DOI":"10.3390\/systems5010011","type":"journal-article","created":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T05:27:09Z","timestamp":1486704429000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3014-8340","authenticated-orcid":false,"given":"Tomas","family":"Veloz","sequence":"first","affiliation":[{"name":"Center Leo Apostel for Interdisciplinary Studies, Brussels Free University, 1050 Brussels, Belgium"},{"name":"Insituto de Filosof\u00eda y Ciencias de la Complejidad, Los Alerces 3024, \u00d1u\u00f1oa, Santiago, Chile"}]},{"given":"Pablo","family":"Razeto-Barry","sequence":"additional","affiliation":[{"name":"Insituto de Filosof\u00eda y Ciencias de la Complejidad, Los Alerces 3024, \u00d1u\u00f1oa, Santiago, Chile"},{"name":"Universidad Diego Portales, Vicerrector\u00eda Acad\u00e9mica, Manuel Rodr\u00edguez Sur 415, Santiago, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,8]]},"reference":[{"key":"ref_1","unstructured":"Bogdanov, A. (1984). Essays in Tektology: The General Science of Organization, Intersystems Publications."},{"key":"ref_2","unstructured":"Von Bertalanffy, L. (1968). General Systems Theory, George Braziller."},{"key":"ref_3","unstructured":"Vemuri, V. (2014). Modeling of Complex Systems: An Introduction, Academic Press."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ashby, W.R. (1956). An Introduction to Cybernetics, Chapman & Hall.","DOI":"10.5962\/bhl.title.5851"},{"key":"ref_5","unstructured":"Laszlo, E., and Clark, J.W. (1972). Introduction to Systems Philosophy, Gordon and Breach."},{"key":"ref_6","unstructured":"Goertzel, B. (2013). Chaotic Logic: Language, Thought, and Reality from the Perspective of Complex Systems Science, Springer Science & Business Media."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1162\/106454601753238636","article-title":"Artificial chemistries\u2014A review","volume":"7","author":"Dittrich","year":"2001","journal-title":"Artif. Life"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1126\/science.1069492","article-title":"Systems biology: A brief overview","volume":"295","author":"Kitano","year":"2002","journal-title":"Science"},{"key":"ref_9","first-page":"105","article-title":"Computational models of metabolism: Stability and regulation in metabolic networks","volume":"142","author":"Steuer","year":"2009","journal-title":"Adv. Chem. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Albrecht, M., Kerren, A., Klein, K., Kohlbacher, O., Mutzel, P., Paul, W., Schreiber, F., and Wybrow, M. (2009). On Open Problems in Biological Network Visualization, Springer. International Symposium on Graph Drawing.","DOI":"10.1007\/978-3-642-11805-0_25"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2144","DOI":"10.1093\/bioinformatics\/btg271","article-title":"MetaFluxNet: The management of metabolic reaction information and quantitative metabolic flux analysis","volume":"19","author":"Lee","year":"2003","journal-title":"Bioinformatics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1038\/73786","article-title":"A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks","volume":"18","author":"Schuster","year":"2000","journal-title":"Nat. Biotechnol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1016\/0009-2509(74)80195-8","article-title":"Dynamics of open chemical systems and the algebraic structure of the underlying reaction network","volume":"29","author":"Feinberg","year":"1974","journal-title":"Chem. Eng. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1007\/s11538-006-9130-8","article-title":"Chemical organisation theory","volume":"69","author":"Dittrich","year":"2007","journal-title":"Bull. Math. Biol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1049\/ip-syb:20050035","article-title":"Algorithmic approaches for computing elementary modes in large biochemical reaction networks","volume":"152","author":"Klamt","year":"2005","journal-title":"IEE Proc. Syst. Biol."},{"key":"ref_16","first-page":"154","article-title":"Chemical organization theory applied to virus dynamics (Theorie chemischer organisationen angewendet auf infektionsmodelle)","volume":"48","author":"Matsumaru","year":"2006","journal-title":"IT Inf. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kreyssig, P., Escuela, G., Reynaert, B., Veloz, T., Ibrahim, B., and Dittrich, P. (2012). Cycles and the qualitative evolution of chemical systems. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0045772"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.pss.2006.08.002","article-title":"Chemical organizations in atmospheric photochemistries\u2014A new method to analyze chemical reaction networks","volume":"55","author":"Centler","year":"2007","journal-title":"Planet. Space Sci."},{"key":"ref_19","unstructured":"Matsumaru, N., Centler, F., di Fenizio, P.S., and Dittrich, P. (2005). Proceedings of the 2005 Workshop on Unconventional Computing: From Cellular Automata to Wetware, Luniver Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1093\/bioinformatics\/btp332","article-title":"Using chemical organization theory for model checking","volume":"25","author":"Kaleta","year":"2009","journal-title":"Bioinformatics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0022-0000(69)80011-5","article-title":"Parallel program schemata","volume":"3","author":"Karp","year":"1969","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1109\/5.24143","article-title":"Petri nets: Properties, analysis and applications","volume":"77","author":"Murata","year":"1989","journal-title":"IEEE Proc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF02575679","article-title":"Commutative grammars","volume":"13","author":"Mandrioli","year":"1976","journal-title":"Calcolo"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Heiner, M., Koch, I., and Voss, K. (2001, January 29\u201331). Analysis and simulation of steady states in metabolic pathways with Petri nets. Proceedings of the Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools (CPN\u201901), Aarhus, Denmark.","DOI":"10.7146\/dpb.v31i560.7117"},{"key":"ref_25","unstructured":"Veloz Gonz\u00e1lez, T.I. (2010). A Computational Study of Algebraic Chemistry. [Master Thesis, Universidad de Chile]."},{"key":"ref_26","unstructured":"Heiner, M., Gilbert, D., and Donaldson, R. (2008). International School on Formal Methods for the Design of Computer, Communication and Software Systems, Springer."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Pascual, M., and Dunne, J.A. (2006). Ecological Networks: Linking Structure to Dynamics in Food Webs, Oxford University Press.","DOI":"10.1093\/oso\/9780195188165.001.0001"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1126\/science.1165821","article-title":"Network analysis in the social sciences","volume":"323","author":"Borgatti","year":"2009","journal-title":"Science"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/s11084-012-9297-y","article-title":"Autopoiesis 40 years later. A review and a reformulation","volume":"42","year":"2012","journal-title":"Orig. Life Evol. Biosph."},{"key":"ref_30","unstructured":"Veloz, T. (2014). Autopoiesis: Un Concepto Vivo, Universitas Nueva Civilizaci\u00f3n. (In Chile)."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1142\/S0219525908001878","article-title":"Chemical organizations in a toy model of the political system","volume":"11","author":"Dittrich","year":"2008","journal-title":"Adv. Complex Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00285-012-0626-6","article-title":"Reaction networks and evolutionary game theory","volume":"68","author":"Veloz","year":"2014","journal-title":"J. Math. Biol."},{"key":"ref_33","unstructured":"Dittrich, P., and Winter, L. (2005, January 9\u201313). Reaction networks as a formal mechanism to explain social phenomena. Proceedings of the 4th Iternational Workshop on Agent-Based Approaches in Economics and Social Complex Systems (AESCS 2005), Tokyo, Japan."},{"key":"ref_34","unstructured":"Feinberg, M. (1979). Lectures on Chemical Reaction Networks, University of Wisconsin. Notes of lectures given at the Mathematics Research Center."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"i475","DOI":"10.1093\/bioinformatics\/btu453","article-title":"Effects of small particle numbers on long-term behaviour in discrete biochemical systems","volume":"30","author":"Kreyssig","year":"2014","journal-title":"Bioinformatics"},{"key":"ref_36","unstructured":"Veloz, T., and Razeto-Barry, P. (2016). Studying Structural Changes of a System using Reaction Networks. Systems, submitted for publication."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF00251225","article-title":"General mass action kinetics","volume":"47","author":"Horn","year":"1972","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_38","unstructured":"Strogatz, S.H. (2014). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1142\/S0219525911002895","article-title":"On the relation between organizations and limit sets in chemical reaction systems","volume":"14","author":"Peter","year":"2011","journal-title":"Adv. Complex Syst."},{"key":"ref_40","unstructured":"Peter, S., Veloz, T., and Dittrich, P. (2010, January 24\u201327). Feasibility of Organizations\u2014A Refinement of Chemical Organization Theory with Application to P Systems. Proceedings of the 11th International Conference on Membrane Computing (CMC11), Jena, Germany."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1093\/bioinformatics\/btn228","article-title":"Computing chemical organizations in biological networks","volume":"24","author":"Centler","year":"2008","journal-title":"Bioinformatics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1093\/bioinformatics\/btq263","article-title":"A parallel algorithm to compute chemical organizations in biological networks","volume":"26","author":"Centler","year":"2010","journal-title":"Bioinformatics"},{"key":"ref_43","unstructured":"Veloz, T., Reynaert, B., Rojas, D., and Dittrich, P. (2011, January 8\u201312). A decomposition theorem in chemical organizations. Proceedings of the European Conference in Artificial Life, Paris, France."},{"key":"ref_44","unstructured":"Maturana, H., and Varela, F. (1985). Autopoiesis and Cognition: The Realization of the Living, Springer."},{"key":"ref_45","unstructured":"Mesarovic, M.D., Macko, D., and Takahara, Y. (2000). Theory of Hierarchical, Multilevel, Systems, Elsevier."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1006\/jcss.1999.1693","article-title":"Computing with membranes","volume":"61","year":"2000","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.gloenvcha.2006.04.002","article-title":"Resilience: The emergence of a perspective for social\u2013ecological systems analyses","volume":"16","author":"Folke","year":"2006","journal-title":"Glob. Environ. Chang."},{"key":"ref_48","unstructured":"Luhmann, N. (1983). The Differentiation of Society, Columbia University Press."},{"key":"ref_49","first-page":"13","article-title":"La paradoja de la probabilidad de lo improbable y el pensamiento evolutivo de Niklas Luhmann","volume":"18","author":"Cienfuegos","year":"2011","journal-title":"Convergencia"},{"key":"ref_50","unstructured":"Axelrod, R. (1997). The Complexity of Cooperation, Princeton University Press."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Axelrod, R.M. (2006). The Evolution of Cooperation, Basic Books.","DOI":"10.1073\/pnas.0606053103"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1126\/science.1133755","article-title":"Five rules for the evolution of cooperation","volume":"314","author":"Nowak","year":"2006","journal-title":"Science"},{"key":"ref_53","unstructured":"Harley, J.L. (1959). The Biology of Mycorrhiza, Leonard Hill (Books) Ltd."},{"key":"ref_54","unstructured":"Birkhoff, G., Birkhoff, G., Birkhoff, G., Math\u00e9maticien, E.U., and Birkhoff, G. (1948). Lattice Theory, American Mathematical Society."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/5\/1\/11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:27:40Z","timestamp":1760207260000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/5\/1\/11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,8]]},"references-count":54,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["systems5010011"],"URL":"https:\/\/doi.org\/10.3390\/systems5010011","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,8]]}}}