Topological Analysis of Metabolic Networks Based on Petri Net Theory - Biological Petri Nets - page 17

Topological Analysis of Metabolic Networks
Based on Petri Net Theory
Ionela Zevedei-Oancea and Stefan Schuster ∗
Max Delbr uck Center for Molecular Medicine, Department of Bioinformatics, Berlin-Buch, Germany
ABSTRACT: Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between
the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix
of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have
the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the
Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of
the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for
illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the
role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All
Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.
KEYWORDS: Petri nets, elementary flux mode, metabolic networks, P -invariant, T -invariant, incidence matrix
INTRODUCTION
The aim of theoretical approaches is to build models, which should facilitate the study of real systems.
A huge variety of models has been developed in theoretical biology. For example, biochemical reaction
networks are the subject of extensive modelling studies [Fell and Wagner, 2000; Heinrich and Schuster,
1996; Jeong et al. , 2000; Peleg et al. , 2002; Schuster et al. , 2002a, 2002b; Teusink et al. , 1998]. This
modelling has important applications in biotechnology [Klamt and Stelling, 2003; Liao et al. , 1996;
Schuster et al. , 2000; Van Dien and Lidstrom, 2002] and genome research [Dandekar et al. , 1999; Price
et al. , 2002; F orster et al. , 2002]. Specific features of biochemical systems are that most reactions are
catalyzed by enzymes and that many reactions utilize more than one substrate (reactant) and/or generate
more than one product. Reaction systems that only involve isomerizations (that is, reactions with one
substrate and one product) can be depicted as graphs and their properties can be studied from the point
of view of graph theory. However, real biochemical networks cannot be represented as graphs due to bi-
or multimolecular reactions. These cases would require that arcs linking three or more nodes exist. One,
quite complicated, approach to coping with this situation is to consider the groups of substances on each
side of reaction arrows as nodes (so-called complexes) [Clarke, 1980; Horn and Jackson, 1972].
∗ Corresponding author: Stefan Schuster, Max Delbruck Center for Molecular Medicine, Department of Bioinformatics,
Robert-Rossle-Str 10, 13092 Berlin-Buch, Germany. Tel.: [phone]; Fax: [phone]; E-mail: stschust@mdc-
berlin.de.