Retroactivity as a Criterion to Define Modules in Signaling Networks

  • Julio Saez-Rodriguez
  • Holger Conzelmann
  • Michael Ederer
  • Ernst Dieter Gilles


The concept of modularity has been widely studied in the context of molecular biology. Since engineering sciences are used to work in a modular manner, it is tempting to approach the definition of biological modules from an engineering perspective. From a system-theoretical point of view an interesting criterion might be the definition of modules where both the input signals and the output signals are unidirectional, that is, there is no retroactivity. In this chapter, we review the applicability of this concept to biological networks. We start describing which biochemical situations can lead to absence of retroactivity. Then, we show how this concept can be automatized into an algorithm to decompose biochemical networks into modules so that the retroactivity among the modules is minimized. This decomposition facilitates the analysis of complex models because the modules can, to some degree, be studied separately. We complement this analysis with a consideration of retroactivity in signal transduction processes using a domain-oriented description. Finally, we explore the interplay between retroactivity and thermodynamics in the domain-oriented description, and show how the binding site phosphorylation is a mechanism that is able to realize unidirectional signal transduction.


Retroactivity Modularity Wegscheider condition Domain-oriented modeling Signaling Thermodynamics Systems-theory Network theory Unidirectionality Futily cycles Phosphorylation MAPK Michaelis-Menten 



We thank Eduardo Sontag for useful discussions. The work described here was supported by DFG (FOR521) and the German Ministry of Research and Education BMBF (SysTec Initative, HepatoSys, DYNAMO Consortium).


  1. 1.
    Alon U (2007) An introduction to systems biology: design principles of biological circuits. Chapman&Hall/CRC, London, UKGoogle Scholar
  2. 2.
    Blüthgen N, Bruggeman FJ, Legewie S, Herzel H, Westerhoff HV, Kholodenko BN (2006) Effects of sequestration on signal transduction cascades. FEBS J 273(5):895–906CrossRefGoogle Scholar
  3. 3.
    Borisov NM, Markevich NI, Hoek JB, Kholodenko BN (2005) Signaling through receptors and scaffolds: independent interactions reduce combinatorial complexity. Biophys J 89(2):951–966. doi:10.1529/biophysj.105.060533, Google Scholar
  4. 4.
    Borisov NM, Markevich NI, Hoek JB, Kholodenko BN (2006) Trading the micro-world of combinatorial complexity for the macro-world of protein interaction domains. Biosystems 83(2–3):152–166. doi:10.1016/j.biosystems.2005.03.006, Google Scholar
  5. 5.
    Conzelmann H (2009) Mathematical modeling of biochemical signal transduction pathways in mammalian cells: a domain-oriented approach to reduce combinatorial complexity. PhD thesis, University of Stuttgart, GermanyGoogle Scholar
  6. 6.
    Conzelmann H, Gilles ED (2008) Functional proteomics: methods and protocols. In: Thompson JD et al. (ed) Dynamic pathway modeling of signal transduction networks – A domain-oriented approach. Humana Press, NYC, US, pp 557–576Google Scholar
  7. 7.
    Conzelmann H, Saez-Rodriguez J, Sauter T, Bullinger E, Allgoewer F, Gilles ED (2004) Reduction of mathematical models of signal transduction networks: simulation-based approach applied to egf receptor signaling. Syst Biol 1(1):159–169. doi:10.1049/sb:20045011CrossRefGoogle Scholar
  8. 8.
    Conzelmann H, Saez-Rodriguez J, Sauter T, Kholodenko BN, Gilles ED (2006) A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks. BMC Bioinformatics 7:34. doi:10.1186/1471-2105-7-34,
  9. 9.
    Famili I, Palsson BO (2003) The convex basis of the left null space of the stoichiometric matrix leads to the definition of metabolically meaningful pools. Biophys J 85:16–26CrossRefGoogle Scholar
  10. 10.
    Feret J, Danos V, Krivine J, Harmer R, Fontana W (2009) Internal coarse-graining of molecular systems. Proc Natl Acad Sci U S A 106(16):6453–6458. doi:10.1073/pnas.0809908106CrossRefGoogle Scholar
  11. 11.
    Gilles ED (1998) Network theory for chemical processes. Chem Eng Technol 21(2):121–132MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hartwell L, Hopfield J, Leibler S, Murray A (1999) From molecular to modular cell biology. Nature 402(6761-supp):C47–C52Google Scholar
  13. 13.
    Heinrich R, Schuster S (1996) The regulation of cellular systems. Chapman & Hall, NYC, USAMATHGoogle Scholar
  14. 14.
    Klamt S, Saez-Rodriguez J, Lindquist J, Simeoni L, Gilles ED (2006) A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics 7:56. doi:10.1186/1471-2105-7-34CrossRefGoogle Scholar
  15. 15.
    Koschorreck M, Conzelmann H, Ebert S, Ederer M, Gilles ED (2007) Reduced modeling of signal transduction – A modular approach. BMC Bioinformatics 8(1):336. doi:10.1186/1471-2105-8-336, Google Scholar
  16. 16.
    Lauffenburger DA (2000) Cell signaling pathways as control modules: complexity for simplicity? Proc Natl Acad Sci U S A 97(10):5031–5033CrossRefGoogle Scholar
  17. 17.
    Mathworks (2006) Matlab.
  18. 18.
    Mirschel S, Steinmetz K, Rempel M, Ginkel M, Gilles ED (2009) Promot: modular modeling for systems biology. Bioinformatics 25(5):687–689. doi:10.1093/bioinformatics/btp029CrossRefGoogle Scholar
  19. 19.
    Newman MEJ (2006) Modularity and community structure in networks. Proc Natl Acad Sci U S A 103(23):8577–8582. doi:10.1073/pnas.0601602103,
  20. 20.
    Oda K, Matsuoka Y, Funahashi A, Kitano H (2005) A comprehensive pathway map of epidermal growth factor receptor signaling. Mol Syst Biol 1:2005.0010Google Scholar
  21. 21.
    Pawson T, Nash P (2003) Assembly of cell regulatory systems through protein interaction domains. Science 300(5618):445–452. doi:10.1126/science.1083653, Google Scholar
  22. 22.
    Saez-Rodriguez J, Kremling A, Conzelmann H, Bettenbrock K, Gilles ED (2004) Modular analysis of signal transduction networks. IEEE Contr Syst Mag 24(4):35–52. doi:10.1109/MCS.2004.1316652MathSciNetCrossRefGoogle Scholar
  23. 23.
    Saez-Rodriguez J, Kremling A, Gilles ED (2005) Dissecting the puzzle of life: modularization of signal transduction networks. Comput Chem Eng 29(3):619–629. doi:10.1016/j.compchemeng.2004.08.035CrossRefGoogle Scholar
  24. 24.
    Saez-Rodriguez J, Gayer S, Ginkel M, Gilles ED (2008) Automatic decomposition of kinetic models of signaling networks minimizing the retroactivity among modules. Bioinformatics 24(16):i213–i219. doi:10.1093/bioinformatics/btn289, Google Scholar
  25. 25.
    Sauro HM (2008) Modularity defined. Mol Syst Biol 4:166. doi:10.1038/msb.2008.3Google Scholar
  26. 26.
    Sauro HM, Kholodenko BN (2004) Quantitative analysis of signaling networks. Prog Biophys Mol Biol 86(1):5–43, doi:10.1016/j.pbiomolbio.2004.03.002CrossRefGoogle Scholar
  27. 27.
    Schoeberl B, Eichler-Jonsson C, Gilles E, Müller G (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol 20(4):370–375CrossRefGoogle Scholar
  28. 28.
    Schuster S, Schuster R (1989) A generalization of Wegscheider’s condition. Implications for properties of steady states and for quasi-steady-state approximation. J Math Chem 3(1):25–42. doi:10.1007/BF01171883, Google Scholar
  29. 29.
    Segel IH (1993) Enzyme kinetics. Behavior and analysis of rapid equilibrium and steady-State enzyme systems. Wiley, Berlin, GermanyGoogle Scholar
  30. 30.
    Segel LA (1988) On the validity of the steady state assumption of enzyme kinetics. Bull Math Biol 50(6):579–593MathSciNetMATHGoogle Scholar
  31. 31.
    Smith LP, Bergmann FT, Chandran D, Sauro HM (2009) Antimony: a modular model definition language. Bioinformatics 25(18):2452–2454. doi:10.1093/bioinformatics/btp401CrossRefGoogle Scholar
  32. 32.
    Sontag ED (1998) Mathematical control theory, 2nd edn. Springer, Berlin and Heidelberg, GermanyMATHGoogle Scholar
  33. 33.
    Vecchio DD, Ninfa AJ, Sontag ED (2008) Modular cell biology: retroactivity and insulation. Mol Syst Biol 4:161. doi:10.1038/msb4100204Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Julio Saez-Rodriguez
    • 1
  • Holger Conzelmann
  • Michael Ederer
  • Ernst Dieter Gilles
  1. 1.Genome Biology UnitEuropean Bioinformatics Institute (EMBL-EBI) and EMBL-HeidelbergCambridgeUK

Personalised recommendations