Skip to main content
SpringerLink
Log in

Modeling the measurements of cellular fluxes in microbioreactor devices using thin enzyme electrodes

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

An analytic approach to the modeling of stop-flow amperometric measurements of cellular metabolism with thin glucose oxidase and lactate oxidase electrodes would provide a mechanistic understanding of the various factors that affect the measured signals. We divide the problem into two parts: (1) analytic formulas that provide the boundary conditions for the substrate and the hydrogen peroxide at the outer surface of the enzyme electrode layers and the electrode current expressed through these boundary conditions, and (2) a simple diffusion problem in the liquid compartment with the provided boundary conditions, which can be solved analytically or numerically, depending on the geometry of the compartment. The current in an amperometric stop-flow measurement of cellular glucose or lactate consumption/excretion is obtained analytically for two geometries, corresponding to devices developed at the Vanderbilt Institute for Integrative Biosystems Research and Education: a multianalyte nanophysiometer with effective one-dimensional diffusion and a multianalyte microphysiometer, for which plentiful data for metabolic changes in cells are available. The data are calibrated and fitted with the obtained time dependences to extract several cellular fluxes. We conclude that the analytical approach is applicable to a wide variety of measurement geometries and flow protocols.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N.A. N’Dri, M. Stremler, S. Eluvathingal, D. Cliffel, R. Snider, M. Velkovsky, J.P. Wikswo, In preparation (2006)

  2. Eklund S.E., Cliffel D.E., Kozlov E., Prokop A., Wikswo J.P. Jr., Baudenbacher F.J.: Anal. Chim. Acta 496, 93 (2003)

    Article  CAS  Google Scholar 

  3. Eklund S.E., Taylor D., Kozlov E., Prokop A., Cliffel D.E.: Anal. Chem. 76, 519 (2004)

    Article  CAS  Google Scholar 

  4. Eklund S.E., Snider R.M., Wikswo J., Baudenbacher F., Prokop A., Cliffel D.E.: J. Electroanal. Chem. 587, 333 (2006)

    Article  CAS  Google Scholar 

  5. Wikswo J.P., Prokop A., Baudenbacher F., Cliffel D., Csukas B., Velkovsky M.: IEE Proc. Nanobiotechnol. 153, 81 (2006)

    Article  CAS  Google Scholar 

  6. Prokop A., Prokop Z., Schaffer D., Kozlov E., Wikswo J.P., Cliffel D., Baudenbacher F.: Biomed. Microdevices 6, 325 (2004)

    Article  CAS  Google Scholar 

  7. Ges I.A., Ivanov B.L., Werdich A.A., Baudenbacher F.J.: Biosens. Bioelectron. 22, 1303 (2007)

    Article  CAS  Google Scholar 

  8. Ges I.A., Ivanov B.L., Schaffer D.K., Lima E.A., Werdich A.A., Baudenbacher F.J.: Biosens. Bioelectron. 21, 248 (2005)

    Article  CAS  Google Scholar 

  9. Werdich A., Lima E.A., Ivanov B., Ges I., Wikswo J.P., Baudenbacher F.J.: Lab Chip 4, 357 (2004)

    Article  CAS  Google Scholar 

  10. Ges I.A., Baudenbacher F.: J. Exp. Nanosci. 3, 63 (2008)

    Article  CAS  Google Scholar 

  11. R. Baronas, F. Ivanauskas, J.Kulys, in Mathematical Modeling of Biosensors, (Springer, New York, 2010)

  12. Baronas R., Kulys J., Ivanauskas F.: Biosens. Bioelectron. 19, 915 (2004)

    Article  CAS  Google Scholar 

  13. Leegsma-Vogt G., Venema K., Brouwer N., Gramsbergen J.B., Copray S., Korf J.: Anal. Chem. 76, 5431 (2004)

    Article  CAS  Google Scholar 

  14. S.J. Farlow, in Partial Differential Equations for Scientists and Engineers, (Dover Publications, New York, 1993)

  15. Snider R.M., Ciobanu M., Rue A.E., Cliffel D.E.: Anal. Chimi. Acta 609, 44 (2008)

    Article  CAS  Google Scholar 

  16. Bartlett P.N., Pratt K.F.E.: J. Electroanal. Chem. 397, 61 (1995)

    Article  Google Scholar 

  17. Gooding J.J.: Electrochem. Commun. 1, 119 (1999)

    Article  CAS  Google Scholar 

  18. Tatsuma T., Watanabe T.: Anal. Chem. 64, 625 (1992)

    Article  CAS  Google Scholar 

  19. Lemke K.: Biomed. Biochim. Acta 48, 867 (1989)

    CAS  Google Scholar 

  20. Memoli A., Annesini M.C., Mascini M., Papale S., Petralito S.: J. Pharm. Biomed. Anal. 29, 1045 (2002)

    Article  CAS  Google Scholar 

  21. Tammeveski K., Tenno T.T., Mashirin A.A., Hillhouse E.W., Manning P., Mcneil C.J.: Free Radic. Biol. Med. 25, 973 (1998)

    Article  CAS  Google Scholar 

  22. E. Eklund, E. Kozlov, D.E. Taylor, F. Baudenbacher, D.E. Chiffel, in NanoBiotechnology Protocols, ed. by S. Rosenthal, vol. 303, ch. Chapter 16 (Humana Press, Totawa, 2005), pp. 209–223

  23. Ohara T.J., Rajagopalan R., Heller A.: Anal. Chem. 66, 2451 (1994)

    Article  CAS  Google Scholar 

  24. van Leeuwen H.P., Puy J., Galceran J., Cecilia J.: J. Electroanal. Chem. 526, 10 (2002)

    Article  Google Scholar 

  25. Buffle J., Startchev K., Galceran J.: Phys. Chem. Chem. Phys. 9, 2844 (2007)

    Article  CAS  Google Scholar 

  26. I.A. Ges, F.J. Baudenbacher, Biosensors and Bioelectronics, (2008)

  27. Phanthong C., Somasundrum M.: J. Electroanal. Chem. 558, 1 (2003)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, 37235, USA

    Momchil Velkovsky & John P. Wikswo

  2. Vanderbilt Institute for Integrative Biosystems Research and Education, Vanderbilt University, Nashville, TN, 37235, USA

    Momchil Velkovsky, David E. Cliffel & John P. Wikswo

  3. Department of Chemistry, Vanderbilt University, Nashville, TN, 37235, USA

    Rachel Snider & David E. Cliffel

  4. Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, 37235, USA

    John P. Wikswo

  5. Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, TN, 37235, USA

    John P. Wikswo

Authors
  1. Momchil Velkovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rachel Snider
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David E. Cliffel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. John P. Wikswo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David E. Cliffel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Velkovsky, M., Snider, R., Cliffel, D.E. et al. Modeling the measurements of cellular fluxes in microbioreactor devices using thin enzyme electrodes. J Math Chem 49, 251–275 (2011). https://doi.org/10.1007/s10910-010-9744-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-010-9744-9

Keywords

Search

Navigation