Skip to main content
SpringerLink
Log in
Book cover

Bioelectrochemistry: General Introduction pp 49–131Cite as

Methods of mathematical modelling

  • Chapter

Part of the book series: Bioelectrochemistry: Principles and Practice ((BPP,volume 1))

Abstract

Nonequilibrium thermodynamics and kinetics as presented in chapter 1 are adequate and sufficient for the analysis of systems or processes in the steady state. On the other hand, they only provide necessary tools for the analysis of a system on its way to a steady state, but not the actual means of performing the analysis. To carry out such an analysis one must invoke mathematical modelling. Moreover, even in the steady state modelling proves to be a valuable means of exploring the behavior of complex systems. Thus mathematical modelling is an important subject in bioelectrochemistry and hence is dealt with in this chapter. Furthermore, this chapter includes a number of carefully-chosen worked examples. These examples are not only illustrative and designed to cover most features of modelling, but they are also biologically realistic, and in an important sense extend the treatment given in chapter 1. In addition, they present novel aspects of bioelectrochemistry which are difficult to display without the aid of simulation.

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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D Walz, Biochim. Biophys. Acta 1019 (1990) 171–224.

    Article  CAS  Google Scholar 

  2. J Horno, F González-Caballero and CF González-Fernández, Eur. Biophys. J. 17 (1990) 307–313.

    Article  CAS  Google Scholar 

  3. EL King and C Altman, J. Phys. Chem. 60 (1956) 1375–1378.

    Article  CAS  Google Scholar 

  4. SJ Mason and HJ Zimmerman, Electronic Circuits, Signals, and Systems, M.I.T. Press, Cambridge, MA, 1970.

    Google Scholar 

  5. TL Hill, Free Energy Transduction in Biology, Academic Press, New York, 1977.

    Google Scholar 

  6. GF Oster, A Perelson and A Katchalsky, Q. Rev. Biophys. 6 (1973) 1–134.

    Article  CAS  Google Scholar 

  7. L Peusner, Studies in Network Thermodynamics, Elsevier, Amsterdam, 1986.

    Google Scholar 

  8. DC Mikulecky, Biophys. J. 25 (1979) 323–339.

    Article  CAS  Google Scholar 

  9. DC Mikulecky, in Membrane Biophysics II: Physical Methods in the Study of Epithelia, M Dinno, AB Calahan and TC Rozzell (eds), Alan R. Liss, New York, 1983, pp. 257–282.

    Google Scholar 

  10. DC Mikulecky, EG Huf and SR Thomas, Biophys. J. 25 (1979) 87–105.

    Article  CAS  Google Scholar 

  11. JC White and DC Mikulecky, Pharmacol. Ther. 15 (1981) 251–291.

    Article  CAS  Google Scholar 

  12. PW Tuinenga, SPICE: A Guide to Circuit Simulation and Analysis Using PSpice, Prentice Hall, Englewood Cliffs, NJ, 1988.

    Google Scholar 

  13. D Walz, Biochim. Biophys. Acta 505 (1979) 279–353.

    CAS  Google Scholar 

  14. A Vladimirescu, K Zhang, AR Newton, DO Pederson and A Sangiovanni-Vincentelli, SPICE Version 2G.6 User’s Guide, University of California, Berkeley, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Biozentrum, University of Basel, Basel, Switzerland

    Dieter Walz

  2. Department of Membrane Research and Biophysics, The Weizmann Institute of Science, Rehovot, Israel

    S. Roy Caplan

  3. Department of Physiology, University of the Witwatersrand Medical School, Parktown, Johannesburg, South Africa

    David R. L. Scriven

  4. Department of Physiology and Biophysics, Medical College of Virginia, Virginia Commonwealth University, Richmond, VA, USA

    Donald C. Mikulecky

Authors
  1. Dieter Walz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Roy Caplan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David R. L. Scriven
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Donald C. Mikulecky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Membrane Research and Biophysics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    S. Roy Caplan Ph.D. (Professor Emeritus) & Israel R. Miller Ph.D. (Professor Emeritus) (Professor Emeritus) &  (Professor Emeritus)

  2. Istituto Superiore di Santià, Rome, Italy

    Giulio Milazzo (Professor) (Professor)

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Brikhäuser Verlag Basel/Switzerland

About this chapter

Cite this chapter

Walz, D., Caplan, S.R., Scriven, D.R.L., Mikulecky, D.C. (1995). Methods of mathematical modelling. In: Caplan, S.R., Miller, I.R., Milazzo, G. (eds) Bioelectrochemistry: General Introduction. Bioelectrochemistry: Principles and Practice, vol 1. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7318-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7318-5_2

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7320-8

  • Online ISBN: 978-3-0348-7318-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation