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

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  • Russo, C.
  • Giuraniuc, C.
  • Blossey, R.
  • Bodart, J.-F.

Abstract

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.

Suggested Citation

  • Russo, C. & Giuraniuc, C. & Blossey, R. & Bodart, J.-F., 2009. "On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(24), pages 5070-5080.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:24:p:5070-5080
    DOI: 10.1016/j.physa.2009.08.018
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