Generic properties of chemical networks: Artificial chemistry based on graph rewriting

We use a Toy Model of chemistry that represents molecules in terms of usual structural formulae to generate large chemical reaction networks. An extremely simplified quantum mechanical energy calculation and a straightforward implementation of reactions as graph rewritings ensure both transparency and closeness to chemical reality, both conditions that are necessary for the analysis of generic properties of large reaction networks. We show that some chemical networks graphs, e.g., repetitive Diels-Alder reactions, have the small-world property and exhibit a scale-free degree distribution. On the other hand, the Formose reaction does not fit well to this paradigm

Petri net based model validation in systems biology

Abstract. This paper describes the thriving application of Petri net theory for model validation of different types of molecular biological systems. After a short introduction into systems biology we demonstrate how to develop and validate qualitative models of biological pathways in a systematic manner using the well-established Petri net analysis technique of place and transition invariants. We discuss special properties, which are characteristic ones for biological pathways, and give three representative case studies, which we model and analyse in more detail. The examples used in this paper cover signal transduction pathways as well as metabolic pathways.