Fig. 4
From: ELIMINATOR: essentiality analysis using multisystem networks and integer programming
Toy example solution. Possible scenarios when FZD7 and FZD1 are expressed. W5F7C represents the WNT5A/FZD7 complex, W3F1C represents the WNT3A/FZD1 complex, and ABSTR represents the Wnt receptor signaling pathway, planar cell polarity pathway. Dark and light nodes represent inactive and active nodes in the final solution respectively, namely Ei = 0 and Ei = 1. The dashed edge in a gene g represents highly expressed genes (g ∈ G) whereas continuous edges represent lowly expressed genes (g ∈ L). A WNT5A and WNT3A are lowly expressed. For the abstract to be active we need to activate one lowly expressed gene (WNT3A in the example). A knockout of FZD1 requires the activation of one lowly expressed gene (WNT5A in the example) thus providing an equivalent solution (Swild = SFZD1, FZD1 is not essential). B WNT5A is lowly expressed and WNT3A is highly expressed. For the abstract to be active we do not need to activate any lowly expressed gene. A knock-out of FZD7 does not require the activation of any lowly expressed gene for the abstract to be active (Swild = SFZD7, FZD7 is not essential). C WNT5A is highly expressed and WNT3A is lowly expressed. For the abstract to be active we do not need to activate any lowly expressed gene. A knock-out of FZD7 requires the activation of one lowly expressed gene (WNT3A) for the abstract to be active (Swild < SFZD7, FZD7 is essential)