Gene expression analysis on biochemical networks with the potts spin model

Introduction. Gene expression profiling on a large scale has emerged from specialised groups to mainstream laboratories in modern medical and biological research within a few years time (Shoemaker and Linsley 2002). DNA microarrays allow to explore a major subset or all genes of an organism. In multi-conditional experiments, a variety of conditions such as samples of several treatments, mutants, developmental stages, or time points are examined. The technique allowed to support the classification and sub-classification of tumor samples (Golub et al., 1999; Van't Veer et al., 2002) and discoveries of regulatory mechanisms (Spellman et al., 1998, Gasch et al., 2000). The analysis for these studies based on supervised or unsupervised learning schemes without applying prior knowledge of further relationships between the genes under observation, such as biochemical pathways. Besides this, over the last 30 years, biochemical investigations discovered a more and more consistent image of the metabolism of a cell (see e.g. Stryer, 1995). Especially, for small organisms, like Echerichia coli, the metabolic network could be rather clarified (Karp et al., 2002). In our approach, we investigated the network to discover its fragmentations when the organism is treated, e.g. with drugs, starvation, or if it is mutated. As an example, we took gene expression data of E. coli, provided by Khodursky et al. (2000). They treated E. coli cells with tryptophan excess, starvation, and used tryptophan repressor mutants. We represented a metabolic network as a bipartite graph, consisting of alternating enzymes and metabolites. The network was clustered by a nearest neighbour based clustering algorithm. This algorithm uses the potts spin model, coming from statistical physics to describe magnetic behaviour of glassy systems (Blatt et al., 1997; Getz et al., 2000; Domany, 1999). The network showed fragmentation in the biosynthesis pathway of tryptophan, reflecting the expected regulatory response of the system.