Figure 1

Complex Overlap Decomposition. A simplified illustration of the Complex Overlap Decomposition (COD) method. An edge, (3, 4), connecting a pair of weak siblings is added to the graph. A fill-in edge between proteins 5 and 8 is added to eliminate all five 4-cycles in the graph: {5, 6, 8, 7}, {1, 5, 7, 8}, {2, 5, 7, 8}, {1, 5, 6, 8}, and {2, 5, 6, 8}. If the modified graph is chordal, all clique tree representations are computed (cf. Methods). Each clique tree representation results in a Tree of Complexes representation, where the Tree of Complexes is constructed by projecting each maximal clique in the modified graph, G*, to a functional group in the original graph G. For example, a four node maximal clique, {1, 2, 5, 8}, in G* is projected to a four node functional group in G, by removing a fill-in edge (5, 8). Each functional group is represented by a Boolean expression, such as (1 ∧ 2) ∧ (5 ∨ 8), which means that the functional group contains two variants of a complex, {1, 2, 5} and {1, 2, 8}.