Figure 1

A graphical example that illustrates the motivations. This figure illustrates the concept of an MDS. Specially, an MDS is an optimized subset of proteins (black nodes) from which each remaining (i.e., non-MDS) protein (white nodes) can be immediately reached by one step. According to the standard MDS model, there exists four different MDSs for the given the toy network: (A) {1, 6}; (B) {5, 10}; (C) {1, 10}; (D) {5, 6}. Different optimization methods would generate different MDS configurations, and it is difficult to determine which one is reasonable in practice. For example, “lp_solve” produces result (A); while “intlinprog” produces result (B). To overcome this problem, we introduce a CC-MDS model of which the objective function takes variation in degree and betweenness centralities of proteins into consideration. In (E), we compute the degree, betweenness and weight (with γ=0.05) defined in Equation (3) for the four proteins which seems to be driver proteins. In (F), the objective functions of the original MDS model (Equation (1)) and the centrality-corrected model (Equation (2)) are computed. The objective function of the MDS model can not distinguish the four sets of proteins. According to the corrected model, (D) has the lowest value of objective function since the degree and betweenness of proteins 5 and 6 are highest. Both “lp_solve” and “intlinprog” determine proteins 5 and 6 as driver proteins.