Modularization of biochemical networks based on classification of Petri net t-invariants

• Published in: BMC bioinformatics 2008-02, Vol.9 (1), p.90-90, Article 90
• Main Authors: Grafahrend-Belau, Eva, Schreiber, Falk, Heiner, Monika, Sackmann, Andrea, Junker, Björn H, Grunwald, Stefanie, Speer, Astrid, Winder, Katja, Koch, Ina
• Format: Article
• Language: English
• Subjects: Algorithms; Computational biology; Computer Simulation; Genes; Models, Biological; Multigene Family - physiology; Proteome - metabolism; Saccharomyces cerevisiae; Signal Transduction - physiology; Transduction
• ISSN: 1471-2105; 1471-2105
• DOI: 10.1186/1471-2105-9-90

Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find the optimal number of t-clusters to consider for interpretation, the cluster validity measure, Silhouette Width, is applied. We considered two different case studies as examples: a small signal transduction pathway (pheromone response pathway in Saccharomyces cerevisiae) and a medium-sized gene regulatory network (gene regulation of Duchenne muscular dystrophy). We automatically classified the t-invariants into functionally distinct t-clusters, which could be interpreted biologically as functiona