Chemical Organisation Theory |
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Authors: | Peter Dittrich Pietro Speroni di Fenizio |
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Institution: | (1) Bio Systems Analysis Group, Jena Centre for Bioinformatics and Department of Mathematics and Computer Science, Friedrich Schiller University Jena, D-07743 Jena, Germany |
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Abstract: | 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.
Both authors contributed equally. |
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Keywords: | Reaction networks Constraint based network analysis Hierarchical decomposition Constructive dynamical systems |
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