TBI-Preprint 06-05-003

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**Titel:**

**
A Topological Approach to Chemical Organizations
**

**Author(s):**

Gil Benkö,
Florian Centler,
Peter Dittrich,
Christoph Flamm,
Bärbel M. R. Stadler,
Peter F. Stadler

**Submitted to:**

Artifical Life Special Issue on Artificial Chemistry 2006

**Abstract:**

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.

**Keywords:**

chemical reaction networks,
hypergraphs,
stoichiometric matrix,
flux analysis,
generalized topology,
closure functions,
organization theory,
connectedness

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Last modified: 2006-08-09 15:22:42 xtof