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Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade

Author

Listed:
  • Otto Hadač
  • František Muzika
  • Vladislav Nevoral
  • Michal Přibyl
  • Igor Schreiber

Abstract

Prompted by the recent growing evidence of oscillatory behavior involving MAPK cascades we present a systematic approach of analyzing models and elucidating the nature of biochemical oscillations based on reaction network theory. In particular, we formulate a minimal biochemically consistent mass action subnetwork of the Huang-Ferrell model of the MAPK signalling that provides an oscillatory response when a parameter controlling the activation of the top-tier kinase is varied. Such dynamics are either intertwined with or separated from the earlier found bistable/hysteretic behavior in this model. Using the theory of stability of stoichiometric networks, we reduce the original MAPK model, convert kinetic to convex parameters and examine those properties of the minimal subnetwork that underlie the oscillatory dynamics. We also use the methods of classification of chemical oscillatory networks to explain the rhythmic behavior in physicochemical terms, i.e., we identify of the role of individual biochemical species in positive and negative feedback loops and describe their coordinated action leading to oscillations. Our approach provides an insight into dynamics without the necessity of knowing rate coefficients and thus is useful prior the statistical evaluation of parameters.

Suggested Citation

  • Otto Hadač & František Muzika & Vladislav Nevoral & Michal Přibyl & Igor Schreiber, 2017. "Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-25, June.
  • Handle: RePEc:plo:pone00:0178457
    DOI: 10.1371/journal.pone.0178457
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    References listed on IDEAS

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    1. Liang Qiao & Robert B Nachbar & Ioannis G Kevrekidis & Stanislav Y Shvartsman, 2007. "Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling," PLOS Computational Biology, Public Library of Science, vol. 3(9), pages 1-8, September.
    2. Lufen Chang & Michael Karin, 2001. "Mammalian MAP kinase signalling cascades," Nature, Nature, vol. 410(6824), pages 37-40, March.
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