Ultrasensitivity on signaling cascades revisited: Linking local and global ultrasensitivity estimations

Ultrasensitive response motifs, which are capable of converting graded stimulus in binary responses, are very well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive modules can produce an enhancement of the system's ultrasensitivity, how the combination of layers affects the cascade's ultrasensitivity remains an open question for the general case. Here we introduced a methodology that allowed us to determine the presence of sequestration effects and to quantify the relative contribution of each module to the overall cascade's ultrasensitivity. The proposed analysis framework provides a natural link between global and local ultrasensitivity descriptors and is particularly well-suited to characterize and better understand mathematical models used to study real biological systems. As a case study we considered three mathematical models introduced by O'Shaughnessy et al. to study a tunable synthetic MAPK cascade, and showed how our methodology might help modelers to better understand modeling alternatives.