Journal of Mathematical Chemistry

, Volume 49, Issue 1, pp 251–275 | Cite as

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

  • Momchil Velkovsky
  • Rachel Snider
  • David E. Cliffel
  • John P. Wikswo
Original Paper


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.


Biosensor Analytical model Enzyme electrode Bioreactor Microphysiometry Electrochemistry 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Momchil Velkovsky
    • 1
    • 2
  • Rachel Snider
    • 3
  • David E. Cliffel
    • 2
    • 3
  • John P. Wikswo
    • 1
    • 2
    • 4
    • 5
  1. 1.Department of Physics and AstronomyVanderbilt UniversityNashvilleUSA
  2. 2.Vanderbilt Institute for Integrative Biosystems Research and EducationVanderbilt UniversityNashvilleUSA
  3. 3.Department of ChemistryVanderbilt UniversityNashvilleUSA
  4. 4.Department of Biomedical EngineeringVanderbilt UniversityNashvilleUSA
  5. 5.Department of Molecular Physiology and BiophysicsVanderbilt UniversityNashvilleUSA

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