The exceptions to this observation have a tendency to include the exclusively UPUC set UPUC∩SAc∩MCc where Xc denotes the absolute complement. On the other hand, the majority of combinatorial sets is significantly enriched for essential reactions (Figure 5c). More importantly, more than half of the combinatorial sets exhibit a clear separation of essential from conditional lethal and non-essential classes. Comparing Figure 5a and Figure 5c reveals that the sequence of combinatorial sets in the

sorted non-essential enrichment resembles the essential sequence in reverse order (e.g., the Inhibitors,research,lifescience,medical exclusive UPUC set being visually absent for high essential reaction enrichment). This observation provides evidence for a strong negative association between these two essentiality

classes in the context of the UPUC, SA and MC categories. Figure 5 Enrichment of combinatorial reaction category sets for essentiality classes. Combinatorial Inhibitors,research,lifescience,medical sets sorted on the basis of (a) non-essential, (b) conditional lethal and (c) essential class enrichment. Venn diagrams [34] on the abscissa indicate each of the … Unfortunately, no clear separation of conditional lethal from non-essential and essential reactions is achieved by this combinatorial approach (Figure 5b). These results indicate that UPUC, SA and MC, albeit good Inhibitors,research,lifescience,medical essentiality predictors, do not provide the means for a topological characterization of medium-dependent Inhibitors,research,lifescience,medical essentiality. 2.3. Distribution of Essentiality Classes Across Three-Node Subgraphs In the following we will now quantify whether the established topological categories or the three-node subgraphs contain more information about medium-dependent essential reactions. Figure 6 shows the statistical over-

and under-representation of the three established topological categories (Figure 6a) and the three essentiality classes (Figure 6b) across all possible three-node subgraphs of the reaction-centric metabolic network (Figure 3). The striking result is that the three established topological categories display very similar subgraph associations, while the three essentiality classes show strong differences in their Inhibitors,research,lifescience,medical subgraph associations. Counter-intuitively, subgraphs thus perform better in distinguishing essentiality classes than in distinguishing secondly the established topological categories discussed above. Figure 6 Enrichment on three-node subgraphs. The statistical over- and under-representation of (a) reaction categories and (b) essentiality classes on all occurring three-node subgraphs (two motifs have been omitted as they were not detected in any effective network). … Conditional lethal reactions have a fundamentally check details different “footprint” when mapped onto subgraphs. The most important building block is the bidirectional V-in (i.e., the V-in with one of the links being bi-directional). Non-essential reactions, on the other hand, are suppressed in chains, but elevated in V-in and V-out subgraphs.