Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002

A Toy Model of Chemical Reaction Networks

Gil Benkoe

Theoretical Biochemistry Group, Institute for Theoretical Chemistry and Structural Biology, University of Vienna, Austria, Währingerstrasse 17, A-1090 Vienna, Austria

Chemical reactions networks (CRN) occur in our metabolism, in planetary atmospheres, they are used in combinatorial chemistry, and in the study of chemical decay processes. Simulations of CRNs range from chemically accurate QM/MM simulations to artificial chemistries like the lambda-calculus, with transparent dynamics. The one extreme is slow and difficult to analyze, while the other extreme does not include thermodynamics and other important features of chemistry. Our model represents an intermediate level of abstraction. In analogy to the tree representation of the secondary structure of RNA, three-dimensional molecules are reduced to the topology of their graph representation. Using a parameterized Extended Hückel Theory, the graphs can then be submitted to a simple quantum mechanical wavefunction analysis. This yields for every graph an energy, its charge distribution, and molecular orbitals. Additionally, reaction mechanisms are abstracted by graph rewriting rules. The set of these rules thus specifies the chemistry of a CRN, i.e. its combinatorics. Directed by the energy and wavefunction shape of the reactants for every reaction, rewriting rules may be repeatedly applied. Thus a reaction network is generated from an initial set of molecules. The aim of this model is to provide a consistent framework in which generic properties of a chemical reaction network can be explored.