Date Published: June 29, 2017
Publisher: Public Library of Science
Author(s): Edgar Altszyler, Alejandra C. Ventura, Alejandro Colman-Lerner, Ariel Chernomoretz, Ferenc Gallyas.
Ultrasensitive response motifs, capable of converting graded stimuli into binary responses, are well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive modules can enhance the system’s ultrasensitivity, how a given combination of layers affects a cascade’s ultrasensitivity remains an open question for the general case. Here, we introduce a methodology that allows 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 it is particularly well-suited to characterize and understand mathematical models used to study real biological systems. As a case study, we have considered three mathematical models introduced by O’Shaughnessy et al. to study a tunable synthetic MAPK cascade, and we show how our methodology can help modelers better understand alternative models.
Sigmoidal input-output response modules are well-conserved in cell signaling networks. They might be used to implement binary responses, a key element in cellular decision-making processes. Additionally, sigmoidal modules might be part of more complex structures, where they can provide the nonlinearities which are needed in a broad spectrum of biological processes [1, 2], such as multistability [3, 4], adaptation , and oscillations . There are several molecular mechanisms that are able to produce sigmoidal responses, such as inhibition by titration [7, 8], zero-order ultrasensitivity in covalent cycles [9, 10], and multistep activation processes such as multisite phosphorylation [11–15] or ligand binding to multimeric receptors .
The study of signal transmission and information processing inside the cell has been, and still is, an active field of research. In particular, the analysis of signaling cascades has received a lot of attention as they are well-conserved motifs that can be found in many cell fate decision systems. The aim of this paper was to propose a framework to characterize and better understand mathematical models used to study real biological systems. For a given mathematical model, the methodology we described, allowed us to disentangle the origin of the predicted ultrasensitivity behavior in terms of HWR repositioning and/or sequestration effects acting on the modular cascade architecture of interest. In this respect, even though we have not addressed the general and important problem of resolving the working principles acting on a given real cascade, we did provide a useful tool for modelers to better understand and perform educated choices between modeling alternatives.
In this article we provided a framework for characterizing mathematical models used to describe real biological systems of ultrasensitive character. We presented a mathematical link between global and local ultrasensitivity estimators for a sigmoidal unit and generalized these results for a cascade of such units. Using the introduced concept of HWR, the overall system’s ultrasensitivity could be defined in terms of effective contributions of each cascade layer. Moreover, we were able to explain the origin of the ultrasensitivity in a given mathematical model in terms of HWR repositioning and/or sequestration effects.