Authors: Peter Dittrich Pietro Speroni di Fenizio
Publish Date: 2007/04/06
Volume: 69, Issue: 4, Pages: 1199-1231
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 selfmaintaining 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 HIVimmune 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
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