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-ended question for the general case. Here we have developed a methodology that allowed us to quantify the effective contribution of each module to the overall cascade's ultrasensitivity and to determine the impact of sequestration effects in the overall system's ultrasensitivity . The proposed analysis framework provided a natural link between global and local ultrasensitivity descriptors and was particularly well-suited to study the ultrasensitivity in MAP kinase cascades. We used our methodology to revisit O'Shaughnessy et al.  tunable synthetic MAPK cascade, in which they claim to have found a new source of ultrasensitivity: ultrasensitivity generated de novo, which arises due to cascade structure itself. In this respect, we showed that the system's ultrasensitivity in its single-step cascade did not come from a cascading effect but from a hidden first-order ultrasensitivity process in one of the cascade's layer. Our analysis also highlighted the impact of the detailed functional form of a module's response curve on the overall system's ultrasensitivity in cascade architectures. Local sensitivity features of the involved transfer functions were found to be of the uttermost importance in this kind of setting and could be at the core of non-trivial phenomenology associated to ultrasensitive motifs .
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 .
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in which they claim to have found a new source of ultrasensitivity: ultrasensitivity generated de novo, which arises due to cascade structure itself. In this respect, we showed that the system's ultrasensitivity in its single-step cascade did not come from a cascading effect but from a hidden first-order ultrasensitivity process in one of the cascade's layer. Our analysis also highlighted the impact of the detailed functional form of a module's response curve on the overall system's ultrasensitivity in cascade architectures. Local sensitivity features of the involved transfer functions were found to be of the uttermost importance in this kind of setting and could be at the core of non-trivial phenomenology associated to ultrasensitive motifs
and showed how our methodology might help modelers to better understand modeling alternatives