Steady state and (bi-) stability evaluation of simple protease signalling networks

T. Eissing, S. Waldherr, F. Allgöwer, P. Scheurich, Eric Bullinger

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)
73 Downloads (Pure)


Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis.

The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is.

Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation.
Original languageEnglish
Pages (from-to)591-601
Number of pages11
Issue number3
Early online date14 Jan 2007
Publication statusPublished - 2007


  • bistability
  • switch
  • threshold
  • signalling
  • proteases
  • caspases
  • apoptosis

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