Fig. 6

The robustness analysis of the sequential mutation accumulations. A network is in general expected to be robust against the external signal when the number of attractors decreases or the average basin size of the five major attractors increases. Thus, the network becomes robust when the dot moves toward the left or upper part of the coordinate plane. The results of the sequential accumulation of mutations in colorectal cancer tumorigenesis have revealed that the robustness of the network against the external signals gradually increases in each step of mutation accumulation (top left). However, reversing the sequence of mutations accumulated in colorectal cancer tumorigenesis caused the increase of the robustness near the last step of the sequence (top right). Moreover, when we considered randomly selected mutation sequences (n = 30) and determined each mutation type to decrease the normal-like score, it also caused the increase of the robustness near the last step of the sequences (bottom left). A representative trajectory of random mutation sequences is shown in the figure. Furthermore, most of the random mutation accumulation sequences have not shown any significant increase of the robustness along with the accumulations of mutations (bottom right)