Signaling Cascades: Consequences of Varying Substrate and Phosphatase Levels

Conference paper
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 736)


We study signaling cascades with an arbitrary number of layers of one-site phosphorylation cycles. Such cascades are abundant in nature and integrated parts of many pathways. Based on the Michaelis–Menten model of enzyme kinetics and the law of mass-action, we derive explicit analytic expressions for how the steady state concentrations and the total amounts of substrates, kinase, and phosphatates depend on each other. In particular, we use these to study how the responses (the activated substrates) vary as a function of the available amounts of substrates, kinase, and phosphatases. Our results provide insight into how the cascade response is affected by crosstalk and external regulation.



EF has received support from a postdoctoral grant of the “Ministerio de Educación” of Spain and the project MTM2009-14163-C02-01 from the “Ministerio de Ciencia e Innovación”. CW is supported by the Lundbeck Foundation, Denmark.


  1. 1.
    Blume-Jensen P, Hunter T (2001) Oncogenic kinase signalling. Nature 411:355–365Google Scholar
  2. 2.
    Sesti G, Federici M, Hribal ML, Lauro D, Sbraccia P, Lauro R (2001) Defects of the insulin receptor substrate (IRS) system in human metabolic disorders. FASEB J 15:2099–2111Google Scholar
  3. 3.
    Chaves, M, Sontag ED, Dinerstein RJ (2004) Optimal length and signal amplification in weakly activated signal transduction cascades. J Phys Chem B 108(39):15311–15320Google Scholar
  4. 4.
    Ferrell JE, Xiong W (2001) Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible. Chaos 11:227–236Google Scholar
  5. 5.
    Goldbeter A, Koshland DE (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci USA 78:6840–6844Google Scholar
  6. 6.
    Qiao L, Nachbar RB, Kevrekidis IG, Shvartsman SY (2007) Bistability and oscillations in the Huang–Ferrell model of MAPK signaling. PLoS Comput Biol 3:1819–1826Google Scholar
  7. 7.
    Ventura AC, Sepulchre JA, Merajver SD (2008) A hidden feedback in signaling cascades is revealed. PLoS Comput Biol 4:e1000041Google Scholar
  8. 8.
    Cooper GM, Hausman RE (2009) The cell. 5th edn. ASM Press, WashingtonGoogle Scholar
  9. 9.
    MacFarlane RG (1964) An enzyme cascade in the blood clotting mechanism, and its function as a biochemical amplifier. Nature 202:498–499Google Scholar
  10. 10.
    Waters CM, Bassler BL (2005) Quorum sensing: cell-to-cell communication in bacteria. Ann Rev Cell Dev Biol 21:319–346Google Scholar
  11. 11.
    Bluthgen N, Bruggeman FJ, Legewie S, Herzel H, Westerhoff HV, Kholodenko BN (2006) Effects of sequestration on signal transduction cascades. FEBS J 273:895–906Google Scholar
  12. 12.
    Salazar C, Höfer T (2006) Kinetic models of phosphorylation cycles: a systematic approach using the rapid-equilibrium approximation for protein–protein interactions. Biosystems 83:195–206Google Scholar
  13. 13.
    Goldbeter A, Koshland DE (1984) Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects. J Biol Chem 259:14441–14447Google Scholar
  14. 14.
    Legewie S, Bluthgen N, Schafer R, Herzel H (2005) Ultrasensitization: switch-like regulation of cellular signaling by transcriptional induction. PLoS Comput Biol 1:e54Google Scholar
  15. 15.
    Kholodenko BN, Hoek JB, Westerhoff HV, Brown GC (1997) Quantification of information transfer via cellular signal transduction pathways. FEBS Lett 414:430–434Google Scholar
  16. 16.
    Qu Z, Vondriska TM (2009) The effects of cascade length, kinetics and feedback loops on biological signal transduction dynamics in a simplified cascade model. Phys Biol 6:016007Google Scholar
  17. 17.
    Feliu E, Knudsen M, Andersen LN, Wiuf C (2011) An algebraic approach to signaling cascade with n layers. Bull Math Biol, DOI 10.1007/s11538-011-9658-0,
  18. 18.
    Gunawardena J (2005) Multisite protein phosphorylation makes a good threshold but can be a poor switch. Proc Natl Acad Sci USA 102:14617–14622Google Scholar
  19. 19.
    Salazar C, Höfer T (2009) Multisite protein phosphorylation – From molecular mechanisms to kinetic models. FEBS J 276:3177–3198Google Scholar
  20. 20.
    Thomson M, Gunawardena J (2009) The rational parameterization theorem for multisite post-translational modification systems. J Theor Biol 261:626–636Google Scholar
  21. 21.
    Heinrich R, Neel BG, Rapoport TA (2002) Mathematical models of protein kinase signal transduction. Mol Cell 9:957–970Google Scholar
  22. 22.
    Markevich NI, Hoek JB, Kholodenko BN (2004) Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J Cell Biol 164:353–359Google Scholar
  23. 23.
    Huang CY, Ferrell JE (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc Natl Acad Sci USA 93:10078–10083Google Scholar
  24. 24.
    Gunawardena J (2010) Biological systems theory. Science 328:581–582Google Scholar
  25. 25.
    Shinar G, Feinberg M (2010) Structural sources of robustness in biochemical reaction networks. Science 327:1389–1391Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Elisenda Feliu
    • 1
  • Michael Knudsen
    • 1
    • 2
  • Carsten Wiuf
    • 1
    • 2
  1. 1.Bioinformatics Research CentreAarhus UniversityAarhusDenmark
  2. 2.Centre for Membrane Pumps in Cells and Disease (PUMPKIN)Aarhus UniversityAarhusDenmark

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