Three level signal transduction cascades lead to reliably timed switches

Hans Armbruster, John Nagy, Jon Young

Research output: Contribution to journalArticlepeer-review


Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades.

Original languageEnglish (US)
Pages (from-to)69-80
Number of pages12
JournalJournal of Theoretical Biology
StatePublished - Nov 21 2014


  • MAP-kinase network
  • Michaelis-Menten equations
  • Time-dependent ODEs

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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