Table 5 Network with PBK+EI from [1]

Network with PBK and EI the NB model [3] assumes that the activation (inactivation) of β-catenin-based transcription complex is equivalent to the fact that the sample is cancerous (normal). This assumption needs to be tested and in this research work, the two newly improvised models based on prior biological knowledge regarding the signaling pathway assume that sample prediction may not always mean that the β-catenin-based transcription complex is activated. These assumptions are incorporated by inserting another node of Sample for which gene expression measurements were available. This is separate from the TRCMPLX node that influences a particular set of known genes in the human colorectal cancer. For those genes whose relation with the TRCMPLX is currently not known or biologically affirmed, indirect paths through the Sample node to the TRCMPLX exist, technical aspect of which will be described shortly. Since all gene expressions have been measured from a sample of subjects, the expression of genes is conditional on the state of the Sample. Here, both tumorous and normal cases are present in equal amounts. The transcription factor TRCMPLX under investigation is known to operate with the help of interaction between β-catenin with T C F4 and L E F1 [9, 33]. It is also known that the regions in the TSS of MYC [34], C C N D1 [35], C D44 [36], S F R P1 [37], W I F1 [38], D K K1 [39], and D K K4 [40, 41] contain factors that have affinity to β-catenin-based TRCMPLX. Thus, expression of these genes are shown to be influenced by TRCMPLX, in Fig. 2.

Roles of D K K2 [42] and D K K3 [43, 44] have been observed in colorectal cancer but their transcriptional relation with β-catenin-based TRCMPLX is not known. Similarly, S F R P2 is known to be a target of P a x2 transcription factor and yet it affects the β-catenin Wnt signaling pathway [45]. Similarly, S F R P4 [46, 47] and S F R P5 [27] are known to have an effect on the Wnt pathway but their role with TRCMPLX is not well studied. S F R P3 is known to have a different structure and function with respect to the remaining SFRPx gene family [48]. Also, the role of D A C T2 is found to be conflicting in the Wnt pathway [49]. Thus, for all these genes whose expression mostly have an extracellular effect on the pathway and information regarding their influence on β-catenin-based TRCMPLX node is not available, an indirect connection has been made through the Sample node. This connection will be explained at the end of this section.