A Topological Approach to Chemical Organizations
Gil Benkö, Florian Centler, Peter Dittrich, Christoph Flamm, Bärbel M. R. Stadler, Peter F. Stadler
Artifical Life Special Issue on Artificial Chemistry 2006
Large chemical reaction networks often exhibit distinctive features which can be interpreted as higher-level structures. Prime examples are metabolic pathways in a biochemical context. In this contribution we review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of set-valued set-functions the encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organization-theoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggest to explore the chemical meaning of well-established topological concepts. As an example, we consider connectedness in some details.
chemical reaction networks, hypergraphs, stoichiometric matrix, flux analysis, generalized topology, closure functions, organization theory, connectedness
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