Skip to main content
SpringerLink
Log in

Using Chemical Kinetics to Model Neuronal Signalling Pathways

  • Chapter
  • First Online:
Computational Systems Neurobiology

Abstract

Understanding the physical principles and mechanisms underlying biochemical reactions allows to create mechanistic mathematical models of complex biological processes, such as those occurring during neuronal signal transduction. In this chapter we introduce basic concepts of chemical and enzyme kinetics, and reaction thermodynamics. Furthermore we show, how the temporal evolution of a reaction system can be described by ordinary differential equations, that can numerically solved on a computer. Finally we give a short overview of different approaches to modelling cooperative binding to, and allosteric control of, receptors and ion channels.

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

Access this chapter

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

Institutional subscriptions

Notes

  1. 1.

    Under non-ideal conditions, as found in biology, activities instead of concentrations should actually be used both for describing rate equations and equilibria. As this is not common practise in biological modelling, we do not distinguish between activities and concentrations in the following. It should be noted, though, that activities can differ significantly from concentrations in cellular environments.

  2. 2.

    The term mass-action stems from the proportionality of the so called reaction “force” to the mass of a substance in a fixed volume, which is proportional to the molar concentration of a substance.

References

  • Adair GS (1925) The hemoglobin system. IV. The oxygen dissociation curve of hemoglobin. J Biol Chem 63:529–545

    CAS  Google Scholar 

  • Allen JP (ed) (2008) Biophysical chemistry. Wiley-Blackwell, Oxford

    Google Scholar 

  • Bhalla U, Iyengar R (1999) Emergent properties of networks of biological signaling pathways. Science 283(5400):381–387

    Article  PubMed  CAS  Google Scholar 

  • Borghans JM, Dupont G, Goldbeter A (1997) Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms. Biophys Chem 66(1):25–41

    CAS  Google Scholar 

  • Briggs GE, Haldane JB (1925) A note on the kinetics of enzyme action. Biochem J 19(2):338–339

    PubMed  CAS  Google Scholar 

  • Colquhoun D, Dowsland KA, Beato M, Plested AJR (2004) How to impose microscopic reversibility in complex reaction mechanisms. Biophys J 86(6):3510–3518

    Article  PubMed  CAS  Google Scholar 

  • Cornish-Bowden A (2004) Fundamentals of enzyme kinetics. Portland Press, London

    Google Scholar 

  • Duke TA, Novère NL, Bray D (2001) Conformational spread in a ring of proteins: a stochastic approach to allostery. J Mol Biol 308(3):541–553

    Article  PubMed  CAS  Google Scholar 

  • Edelstein SJ, Schaad O, Henry E, Bertrand D, Changeux JP (1996) A kinetic mechanism for nicotinic acetylcholine receptors based on multiple allosteric transitions. Biol Cybern 75(5):361–379

    Article  PubMed  CAS  Google Scholar 

  • Edelstein SJ, Stefan MI, Le Novère N (2010) Ligand depletion in vivo modulates the dynamic range and cooperativity of signal transduction. PLoS One 5(1):e8449

    Article  PubMed  Google Scholar 

  • Fall C, Marland E, Wagner J, Tyson J (eds) (2002) Computational cell biology. Springer, New York

    Google Scholar 

  • Funahashi A, Matsuoka Y, Jouraku A, Morohashi M, Kikuchi N, Kitano H (2008) CellDesigner 3.5: a versatile modeling tool for biochemical networks. Proc IEEE 96:1254–1265

    Article  Google Scholar 

  • Hairer E, Wanner G (1996) Solving ordinary differential equation II: stiff and differential-algebraic problems. Springer, Berlin

    Google Scholar 

  • Hairer E, Nrsett SP, Wanner G (1993) Solving ordinary differential equations: nonstiff problems. Springer, Berlin

    Google Scholar 

  • Heinrich R, Schuster S (1996) The regulation of cellular systems. Springer, New York

    Book  Google Scholar 

  • Henri V (1902) Theorie generale de l’action de quelques diastases. C R Acad Sci. Paris 135:916–919

    CAS  Google Scholar 

  • Hill AV (1910) The possible effects of the aggregation of the molecules of hmoglobin on its dissociation curves. J Physiol 40:i–vii

    Google Scholar 

  • Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI–a complex pathway simulator. Bioinformatics 22(24):3067–3074

    Article  PubMed  CAS  Google Scholar 

  • Klotz IM (1946) The application of the law of mass action to binding by proteins. Interactions with calcium. Arch Biochem 9:109–117

    CAS  Google Scholar 

  • Klotz IM (2004) Ligand-receptor complexes: origin and development of the concept. J Biol Chem 279(1):1–12

    Article  PubMed  CAS  Google Scholar 

  • Koshland DE (1958) Application of a theory of enzyme specificity to protein synthesis. Proc Natl Acad Sci USA 44(2):98–104

    Article  PubMed  CAS  Google Scholar 

  • Koshland DJ, Nmethy G, Filmer D (1966) Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry 5(1):365–385

    Article  PubMed  CAS  Google Scholar 

  • Kotyk A (1967) Mobility of the free and of the loaded monosaccharide carrier in saccharomyces cerevisiae. Biochim Biophys Acta 135(1):112–119

    Article  PubMed  CAS  Google Scholar 

  • Land BR, Salpeter EE, Salpeter MM (1981) Kinetic parameters for acetylcholine interaction in intact neuromuscular junction. Proc Natl Acad Sci USA 78(11):7200–7204

    Article  PubMed  CAS  Google Scholar 

  • LeMasson G, Maex R (2001) Computational neuroscience, CRC press, London. Chapter Introduction to equation solving and parameter fitting, pp 1–23

    Google Scholar 

  • Mello BA, Tu Y (2005) An allosteric model for heterogeneous receptor complexes: understanding bacterial chemotaxis responses to multiple stimuli. Proc Natl Acad Sci USA 102(48):17354–17359

    Article  PubMed  CAS  Google Scholar 

  • Michaelis L, Menten M (1913) Die kinetik der invertinwirkung. Biochem Z 49:333–369

    CAS  Google Scholar 

  • Monod J, Wyman J, Changeux JP (1965) On the nature of allosteric transitions: a plausible model. J Mol Biol 12:88–118

    Article  PubMed  CAS  Google Scholar 

  • Najdi TS, Yang CR, Shapiro BE, Hatfield GW, Mjolsness ED (2006) Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes. J Bioinform Comput Biol 4(2):335–355

    Article  PubMed  CAS  Google Scholar 

  • Parthimos D, Haddock RE, Hill CE, Griffith TM (2007) Dynamics of a three-variable nonlinear model of vasomotion: comparison of theory and experiment. Biophys J 93(5):1534–1556

    Article  PubMed  CAS  Google Scholar 

  • Rubin MM, Changeux JP (1966) On the nature of allosteric transitions: implications of non-exclusive ligand binding. J Mol Biol 21(2):265–274

    Article  PubMed  CAS  Google Scholar 

  • Sauro H (2000) Jarnac: a system for interactive metabolic analysis. In: Hofmeyr JHS, Rohwer JM, Snoep JL (eds) Animating the cellular map 9th international BioThermoKinetics meeting,chap. 33.Stellenbosch University Press, Stellenbosch, pp 221–228

    Google Scholar 

  • Segel IH (ed) (1993) Enzyme kinetics. Wiley, New York

    Google Scholar 

  • Stefan MI, Edelstein SJ, Le Novère N (2008) An allosteric model of calmodulin explains differential activation of PP2B and CaMKII. Proc Natl Acad Sci USA 105(31):10768–10773

    Article  PubMed  CAS  Google Scholar 

  • Stefan MI, Edelstein SJ, Le Novère N (2009) Computing phenomenologic Adair-Klotz constants from microscopic MWC parameters. BMC Syst Biol 3:68

    Article  PubMed  Google Scholar 

  • Takahashi K, Ishikawa N, Sadamoto Y, Sasamoto H, Ohta S, Shiozawa A, Miyoshi F, Naito Y, Nakayama Y, Tomita M (2003) E-cell 2: multi-platform E-cell simulation system. Bioinformatics 19(13):1727–1729

    Article  PubMed  CAS  Google Scholar 

  • Waage P, Guldberg C (1864) Studies concerning affinity. Forhandlinger: Videnskabs-Selskabet i Christiana 35

    Google Scholar 

  • Yonetani T, Park SI, Tsuneshige A, Imai K, Kanaori K (2002) Global allostery model of hemoglobin. Modulation of O(2) affinity, cooperativity, and Bohr effect by heterotropic allosteric effectors. J Biol Chem 277(37):34508–34520

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EMBL-EBI, Hinxton, UK

    Lukas Endler, Melanie I. Stefan, Stuart J. Edelstein & Nicolas Le Novère

Authors
  1. Lukas Endler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Melanie I. Stefan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stuart J. Edelstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicolas Le Novère
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicolas Le Novère .

Editor information

Editors and Affiliations

  1. European Bioinformatics Institute, EMBL-Outstation-Hinxton, Wellcome Trust Genome Campus, Welcome-Trust Genome Campus, Hinxton, Cambridge, CB10 1SD, United Kingdom

    N. Le Novère

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Endler, L., Stefan, M.I., Edelstein, S.J., Novère, N.L. (2012). Using Chemical Kinetics to Model Neuronal Signalling Pathways. In: Le Novère, N. (eds) Computational Systems Neurobiology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3858-4_3

Download citation

Publish with us

Policies and ethics

Search

Navigation