On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability

C. Russo, C. Giuraniuc, R. Blossey* (Corresponding Author), J. F. Bodart

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.

Original languageEnglish
Pages (from-to)5070-5080
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
Issue number24
Early online date19 Aug 2009
Publication statusPublished - 15 Dec 2009

Bibliographical note

CR gratefully acknowledges support through a grant from the French National Cancer Institute, INCa.


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