Bulletin of Mathematical Biology

, Volume 69, Issue 4, pp 1199–1231 | Cite as

Chemical Organisation Theory

  • Peter DittrichEmail author
  • Pietro Speroni di Fenizio
Original Article


Complex dynamical reaction networks consisting of many components that interact and produce each other are difficult to understand, especially, when new component types may appear and present component types may vanish completely. Inspired by Fontana and Buss (Bull. Math. Biol., 56, 1–64) we outline a theory to deal with such systems. The theory consists of two parts. The first part introduces the concept of a chemical organisation as a closed and self-maintaining set of components. This concept allows to map a complex (reaction) network to the set of organisations, providing a new view on the system’s structure. The second part connects dynamics with the set of organisations, which allows to map a movement of the system in state space to a movement in the set of organisations. The relevancy of our theory is underlined by a theorem that says that given a differential equation describing the chemical dynamics of the network, then every stationary state is an instance of an organisation. For demonstration, the theory is applied to a small model of HIV-immune system interaction by Wodarz and Nowak (Proc. Natl. Acad. USA, 96, 14464–14469) and to a large model of the sugar metabolism of E. Coli by Puchalka and Kierzek (Biophys. J., 86, 1357–1372). In both cases organisations where uncovered, which could be related to functions.


Reaction networks Constraint based network analysis Hierarchical decomposition Constructive dynamical systems 


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Copyright information

© Springer Science + Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Bio Systems Analysis Group, Jena Centre for Bioinformatics and Department of Mathematics and Computer ScienceFriedrich Schiller University JenaJenaGermany

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