Table 2 The size distribution of perfect clusters in the E. coli metabolic network and their explanation in terms of UP-UC clusters. The third column lists the number of perfect clusters that are explained by UP-UC clusters calculated using the reduced network. The fourth column gives the breakup of the explained perfect clusters in terms of UP-UC clusters of various sizes. E.g. in the second row the entry 7 × (3) + 2 × (2) implies that 7 UP-UC clusters of size 3 are identical to 7 perfect clusters of size 3 and furthermore, two UP-UC clusters of size 2 are subsets of two size 3 perfect clusters. In the fourth row the term 1 × (3+2) means that one of perfect clusters of size 5 contained two distinct UP-UC clusters of sizes 3 and 2. There are 26 UP-UC clusters that are part of the largest perfect cluster of 148 reactions accounting for 125 reactions in it. This largest perfect cluster is a subset of reactions that are active for all input conditions and is located near the output end of the metabolic network.
From: Low degree metabolites explain essential reactions and enhance modularity in biological networks
Size of perfect clusters | Number of perfect clusters | Number of perfect clusters explained | Breakup of explained clusters into UP-UC clusters in the reduced network |
|---|---|---|---|
2 | 48 | 22 | 22 × (2) |
3 | 19 | 9 | 7 × (3) + 2 × (2) |
4 | 11 | 10 | 8 × (4) + 1 × (3) + 1 × (2) |
5 | 4 | 3 | 1 × (4) + 1 × (3+2) + 1 × (2+2) |
6 | 1 | 1 | 1 × (6) |
7 | 1 | 1 | 1 × (7) |
8 | 2 | 2 | 1 × (6+2) + 1 × (5+2) |
148 | 1 | 1 | (14+12+10+9+7+6+6+6+5+5+4+4+4+4+4+3+3+3+2+2+2+2+2+2+2+2) |