Skip to main content
SpringerLink
Log in
Book cover

New Frontiers of Network Analysis in Systems Biology pp 59–75Cite as

Generalised Modelling in Systems Biology

  • Chapter
  • First Online:

  • 1117 Accesses

Abstract

A major challenge in biology is to study the functioning and failure of large networks, such as metabolic pathways, gene regulatory nets, or signalling cascades. This challenge is complicated by the nonlinearity of interactions and uncertainties in the kinetic rate laws. In a generalised model, the system under consideration is restricted to a specific structure of interactions, but the rate-laws of processes need not be specified. Thus a single generalised model can describe a whole class of plausible model systems. Despite their generality, generalised models can be investigated efficiently by methods from dynamical systems theory. They can thereby provide highly robust insights into the dynamics of the system. This chapter provides a gentle introduction to generalised modelling that is geared toward applications in systems biology.

Open any issue of Nature and you will find a diagram illustrating the molecular interactions purported to underlie some behaviour of a living cell. The accompanying text explains how the link between molecules and behaviour is thought to be made. For the simplest connections, such stories may be convincing, but as the mechanisms become more complex, intuitive explanations become more error prone and harder to believe.

– John J.Tyson, Nature 445, 823, 2007

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Fell DA, Sauro HM (1985) Metabolic control and its analysis. Eur J Biochem 148:555–561

    Article  PubMed  CAS  Google Scholar 

  2. Gehrmann E, Drossel B (2010) Boolean versus continuous dynamics on simple two-gene modules. Phy Rev E 82:046120–046129

    Article  Google Scholar 

  3. Gehrmann E, Gläßer C, Jin Y, Sendhoff B, Drossel B, Hamacher K (2011) Robustness of glycolysis in yeast to internal and external noise. Phys Rev E 84:021913

    Article  Google Scholar 

  4. González JV, Balsa-Canto E, Wellstead P et al (2007) Power-law models of signal transduction pathways. Cell Signal 19:1531–1541

    Article  Google Scholar 

  5. Gross T (2001) Population dynamics. Der Andere Verlag, Tönning

    Google Scholar 

  6. Gross T, Feudel U (2004) Analytical search for bifurcation surfaces in parameter space. Phys D 195:292–302

    Article  Google Scholar 

  7. Gross T, Feudel U (2005) Long food chains are in general chaotic. Oikos 109:135–155

    Article  Google Scholar 

  8. Gross T, Feudel U (2006) Generalized models as an universal approach to the analysis of nonlinear dynamical systems. Phys Rev E 73:016205–016214

    Article  Google Scholar 

  9. Gross T, Ebenhöh W, Feudel U (2004) Enrichment and foodchain stability. J Theor Biol 227:349–358

    Article  PubMed  Google Scholar 

  10. Gross T, Rudolf L, Levin SA et al (2009) Generalized models reveal stabilizing factors in food webs. Science 325:747–750

    Article  PubMed  CAS  Google Scholar 

  11. Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer, Heidelberg

    Google Scholar 

  12. Guckenheimer J, Myers M (1996) Computing Hopf bifurcations II. SIAM J Sci Comput 17:1275–1301

    Article  Google Scholar 

  13. Jamshidi N, Palsson BØ(2008) Formulating genome-scale kinetic models in the post-genome era. Mol Syst Biol 4:1–10

    Article  Google Scholar 

  14. Huang C, Ferrell J (1996) Ultrasensitivity in the mitogenactivated protein kinase cascade. PNAS 93:10078–10083

    Article  PubMed  CAS  Google Scholar 

  15. Guhr T, Müller–Groeling A, Weidenmüller HA(1998) Random-matrix theories in quantum physics. Phys Rep 299:189–425

    Google Scholar 

  16. Kholodenko B (2000) Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur J Biochem 267:1583–1588

    Article  PubMed  CAS  Google Scholar 

  17. Komarova S, Smith R, Dixon S et al (2003) Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. Bone 33:206–215

    Article  PubMed  CAS  Google Scholar 

  18. Kuehn C, Siegmund S, Gross T (2010) On the dynamical analysis of evolution equations via generalized models. arXiv:1012.4340

    Google Scholar 

  19. Kuznetsov Yu A (2004) Elements of applied bifurcation theory. Springer, Heidelberg

    Google Scholar 

  20. Lemaire V, Tobin F, Greller L et al (2004) Modeling the interactions between osteoblast and osteoclast activities in bone remodeling. J Theor Biol 229:293–309

    Article  PubMed  CAS  Google Scholar 

  21. Markevich N, Hoek J, Kholodenko B (2004) Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J Cell Biol 164:353–359

    Article  PubMed  CAS  Google Scholar 

  22. May RM (1972) Will a large complex system be stable? Nature 238:413–414

    Article  PubMed  CAS  Google Scholar 

  23. Pivonka P, Zimak J, Smith D W et al (2008) Model structure and control of bone remodeling. Bone 43:249–263

    Article  PubMed  CAS  Google Scholar 

  24. Qiao L, Nachbar R, Kevrekidis IG et al (2007) Bistability and oscillations in the Huang-Ferrell model of MAPK signaling. PLoS Comput Biol 3:1819–1826

    Article  PubMed  CAS  Google Scholar 

  25. Reznik Ed, Segrè D (2010) On the stability of metabolic cycles. J Theor Biol 266:536–549

    Article  Google Scholar 

  26. Rodriguez A, Infante D (2009) Network models in the study of metabolism. Electron J Biotechnol 12:1–12

    Google Scholar 

  27. Savageau MA, Voit EO (1987) Recasting nonlinear differential equations as S-systems. Math Biosci 87:83–115

    Article  Google Scholar 

  28. Schallau K, Junker BH (2010) Simulating plant metabolic pathways with enzyme-kinetic models. Plant Physiol 152:1763–1771

    Article  PubMed  CAS  Google Scholar 

  29. Steuer R (2007) Computational approaches to the topology, stability and dynamics of metabolic networks. Phytochemistry 68:16–18

    Article  Google Scholar 

  30. Steuer R, Junker BH (2009) Computational models of metabolism. Adv Chem Phys 142:105–251

    Article  CAS  Google Scholar 

  31. Steuer R, Gross T, Selbig J et al (2006) Structural kinetic modeling of metabolic networks. PNAS 103:11868–11873

    Article  PubMed  CAS  Google Scholar 

  32. Steuer R, Nunes Nesi A, Fernie AR et al (2007) From structure to dynamics of metabolic pathways. Bioinformatics 23:1378–1385

    Article  PubMed  CAS  Google Scholar 

  33. Stiefs D, Gross T, Steuer R et al (2008) Computation and visualization of bifurcation surfaces. Int J Bifurc Chaos 18:2191–2206

    Article  Google Scholar 

  34. Stiefs D, van Voorn GAK, Kooi BW et al (2010) Food quality in producer-grazer models. Am Nat 176:367–380

    Article  PubMed  Google Scholar 

  35. Sweetlove LJ, Fell D, Fernie AR (2008) Getting to grips with the plant metabolic network. Biochem J 409:27–41

    Article  PubMed  CAS  Google Scholar 

  36. Tyson JJ (2007) Bringing cartoons to life. Nature 445:823–823

    Article  PubMed  CAS  Google Scholar 

  37. Yeakel JA, Stiefs D, Novak M et al (2011) Generalized modeling of ecological population dynamics. Theoretical Ecology 4(2): 179–194.

    Google Scholar 

  38. Zumsande M, Gross T (2010) Bifurcations and chaos in the MAPK signalling cascade. J Theor Biol 265:481–491

    Article  PubMed  CAS  Google Scholar 

  39. Zumsande M, Stiefs D, Siegmund S et al (2011) General analysis for mathematical models in bone remodeling. Bone 48(4): 910–917.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS81UB, UK

    Thilo Gross

Authors
  1. Thilo Gross
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thilo Gross .

Editor information

Editors and Affiliations

  1. Pharmacology & Systems Therapeutics, Systems Biology Center New York, Mount Sinai School of Medicine, New York, 10029, New York, USA

    Avi Ma'ayan

  2. Institute For Life Sciences, Southampton University, Highfield Campus, Southampton, SO17 1BJ, United Kingdom

    Ben D. MacArthur

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Gross, T. (2012). Generalised Modelling in Systems Biology. In: Ma'ayan, A., MacArthur, B. (eds) New Frontiers of Network Analysis in Systems Biology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4330-4_4

Download citation

Publish with us

Policies and ethics

Search

Navigation