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 journalArticle

31 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages591-601
Number of pages11
JournalBiosystems
Volume90
Issue number3
Early online date14 Jan 2007
DOIs
Publication statusPublished - 2007

Fingerprint

Bistability
Protease
Model structures
Peptide Hydrolases
Theoretical Models
Mathematical models
Signal transduction
Complex networks
Evaluation
Blood Coagulation
Systems Analysis
Signal Transduction
Blood
Systems analysis
Inhibitor
Mathematical Model
Phase Plane Analysis
Signaling Pathways
Zero
Bifurcation Analysis

Keywords

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

Cite this

Eissing, T., Waldherr, S., Allgöwer, F., Scheurich, P., & Bullinger, E. (2007). Steady state and (bi-) stability evaluation of simple protease signalling networks. Biosystems, 90(3), 591-601. https://doi.org/10.1016/j.biosystems.2007.01.003
Eissing, T. ; Waldherr, S. ; Allgöwer, F. ; Scheurich, P. ; Bullinger, Eric. / Steady state and (bi-) stability evaluation of simple protease signalling networks. In: Biosystems. 2007 ; Vol. 90, No. 3. pp. 591-601.
@article{6aae497e4691448caf00595f1fd2b55a,
title = "Steady state and (bi-) stability evaluation of simple protease signalling networks",
abstract = "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.",
keywords = "bistability, switch, threshold, signalling, proteases, caspases, apoptosis",
author = "T. Eissing and S. Waldherr and F. Allg{\"o}wer and P. Scheurich and Eric Bullinger",
year = "2007",
doi = "10.1016/j.biosystems.2007.01.003",
language = "English",
volume = "90",
pages = "591--601",
journal = "Biosystems",
issn = "0303-2647",
number = "3",

}

Eissing, T, Waldherr, S, Allgöwer, F, Scheurich, P & Bullinger, E 2007, 'Steady state and (bi-) stability evaluation of simple protease signalling networks' Biosystems, vol. 90, no. 3, pp. 591-601. https://doi.org/10.1016/j.biosystems.2007.01.003

Steady state and (bi-) stability evaluation of simple protease signalling networks. / Eissing, T.; Waldherr, S.; Allgöwer, F.; Scheurich, P.; Bullinger, Eric.

In: Biosystems, Vol. 90, No. 3, 2007, p. 591-601.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Steady state and (bi-) stability evaluation of simple protease signalling networks

AU - Eissing, T.

AU - Waldherr, S.

AU - Allgöwer, F.

AU - Scheurich, P.

AU - Bullinger, Eric

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - bistability

KW - switch

KW - threshold

KW - signalling

KW - proteases

KW - caspases

KW - apoptosis

U2 - 10.1016/j.biosystems.2007.01.003

DO - 10.1016/j.biosystems.2007.01.003

M3 - Article

VL - 90

SP - 591

EP - 601

JO - Biosystems

T2 - Biosystems

JF - Biosystems

SN - 0303-2647

IS - 3

ER -