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Solution of the Poisson-Nernst-Planck equations in the cell-substrate interface

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Abstract.

Electrogenic cells are able to generate electrical signals which can be measured by various invasive electrophysiological methods such as patch-clamp or sharp microelectrode recordings. Growing cells on the surfaces of e.g. metal microelectrodes or field-effect transistors allows the recording of an extracellular component of these signals. For an understanding of such extracellular signals it is mandatory to get detailed topographical as well as electrical information about the cell-sensor interface. In a first approximation, this interface can be described by a flat disk between cell membrane and sensor surface. For a correct description of the signals, the electrodiffusion of ions in this interface is modeled by using the stationary Poisson-Nernst-Planck equations. We solve the equations analytically, and derive expressions for the potential, the ionic charge densities, and the seal resistance. The results provide a method for determining the distance h between sensor surface and cell membrane. For human embryonic kidney cells, we receive h ≈ 70 nm. Comparison with literature shows good agreement.

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References

  1. J. Pine, J. Neurosci. Methods 2, 19 (1980).

    Article  Google Scholar 

  2. G.W. Gross, W.Y. Wen, J.W. Lin, J. Neurosci. Methods 15, 243 (1985).

    Article  Google Scholar 

  3. P. Fromherz, A. Offenhäusser, T. Vetter, J. Weis, Science 252, 1290 (1991).

    Article  ADS  Google Scholar 

  4. P. Bergveld, J. Wiersma, H. Meertens, IEEE Trans. Biomed. Eng. 23, 136 (1976).

    Article  Google Scholar 

  5. A. Offenhäusser, J. Rühe, W. Knoll, J. Vac. Sci. Technol. A. 13, 2606 (1995).

    Article  ADS  Google Scholar 

  6. A. Cohen, M.E. Spira, S. Yitshaik, G. Borghs, O. Shwartzglass, J. Shappir, Biosens. Bioelectron. 19, 1703 (2004).

    Article  Google Scholar 

  7. W.G. Regehr, J. Pine, C.S. Cohan, M.D. Mischke, D.W. Tank, J. Neurosci. Methods. 30, 91 (1989).

    Article  ADS  Google Scholar 

  8. R. Weis, P. Fromherz, Phys. Rev. E. 55, 877 (1997).

    Article  ADS  Google Scholar 

  9. M. Brittinger, P. Fromherz, Appl. Phys. A-Mater. Sci. Process. 81, 439 (2005).

    Article  ADS  Google Scholar 

  10. G. Wrobel, R. Seifert, S. Ingebrandt, J. Enderlein, H. Ecken, A. Baumann, U.B. Kaupp, A. Offenhäusser, Biophys. J. 89, 3628 (2005).

    Article  ADS  Google Scholar 

  11. E. Mason, E. McDaniel, Transport Properties of Ions in Gases (John Wiley and Sons, New York, 1988)

  12. J.W. Jerome, Analysis of Charge Transport - A Mathematical Study of Semiconductor Devices (Springer-Verlag, New York, 1996)

  13. S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer-Verlag, Wien, 1984)

  14. N. Qian, T.J. Sejnowski, Biol. Cybern. 62, 1 (1989).

    Article  MATH  Google Scholar 

  15. D.G. Levitt, Biophys. J. 22, 209 (1978).

    Article  ADS  Google Scholar 

  16. D.G. Levitt, Biophys. J. 22, 221 (1978).

    ADS  Google Scholar 

  17. D.P. Chen, R. Eisenberg, Biophys. J. 64, 1405 (1993).

    ADS  Google Scholar 

  18. D. Chen, J. Lear, B. Eisenberg, Biophys. J. 72, 97 (1997).

    ADS  Google Scholar 

  19. M.G. Kurnikova, R.D. Coalson, P. Graf, A. Nitzan, Biophys. J. 76, 642 (1999).

    ADS  Google Scholar 

  20. B. Corry, S. Kuyucak, S.H. Chung, J. Gen. Physiol. 114, 597 (1999).

    Article  Google Scholar 

  21. S.H. Chung, M. Hoyles, T. Allen, S. Kuyucak, Biophys. J. 75, 793 (1998).

    ADS  Google Scholar 

  22. E. Jakobsson, S.W. Chiu, Biophys. J. 52, 33 (1987).

    ADS  Google Scholar 

  23. B. Roux, B. Prodhom, M. Karplus, Biophys. J. 68, 876 (1995).

    ADS  Google Scholar 

  24. W. Im, S. Seefeld, B. Roux, Biophys. J. 79, 788 (2000).

    ADS  Google Scholar 

  25. R.S. Eisenberg, J. Membr. Biol. 150, 1 (1996).

    Article  Google Scholar 

  26. R.D. Coalson, M.G. Kurnikova, IEEE Trans. Nanobiosci. 4, 81 (2005).

    Article  Google Scholar 

  27. A. Peskoff, D.M. Bers, Biophys. J. 53, 863 (1988).

    ADS  Google Scholar 

  28. P. Debye, E. Hückel, Physi. Zeit. 24, 185 (1923).

    Google Scholar 

  29. G. Wrobel, M. Höller, S. Ingebrandt, S. Dieluweit, F. Sommerhage, H.P. Bochem, A. Offenhäusser, to be published in J. R. Soc. Interface, doi:10.1098/rsif.2007.1094.

  30. D. Braun, P. Fromherz, Biophys. J. 87, 1351 (2004).

    Article  ADS  Google Scholar 

  31. R. Gleixner, P. Fromherz, Biophys. J. 90, 2600 (2006).

    Article  ADS  Google Scholar 

  32. C. Sprössler, D. Richter, M. Denyer, A. Offenhäusser, Biosens. Bioelectron. 13, 613 (1998).

    Article  Google Scholar 

  33. H. Terlau, J. Ludwig, R. Steffan, O. Pongs, W. Stühmer, S.H. Heinemann, Pflugers Arch. 432, 301 (1996).

    Article  Google Scholar 

  34. R. Schönherr, L.M. Mannuzzu, E.Y. Isacoff, S.H. Heinemann, Neuron 35, 935 (2002).

    Article  Google Scholar 

  35. S. Frings, N. Brüll, C. Dzeja, A. Angele, V. Hagen, U.B. Kaupp, A. Baumann, J. Gen. Physiol. 111, 583 (1998).

    Article  Google Scholar 

  36. B. Straub, E. Meyer, P. Fromherz, Nat. Biotechnol. 19, 121 (2001).

    Article  Google Scholar 

  37. P. Fromherz, Ann. N.Y. Acad. Sci. 1093, 143 (2006).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Bio- and Nanosystems (IBN-2) and CNI - Center of Nanoelectronic Systems for Information Technology, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany

    M. Pabst, G. Wrobel, S. Ingebrandt, F. Sommerhage & A. Offenhäusser

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  1. M. Pabst
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  2. G. Wrobel
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  3. S. Ingebrandt
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  4. F. Sommerhage
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  5. A. Offenhäusser
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Correspondence to M. Pabst.

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Pabst, M., Wrobel, G., Ingebrandt, S. et al. Solution of the Poisson-Nernst-Planck equations in the cell-substrate interface. Eur. Phys. J. E 24, 1–8 (2007). https://doi.org/10.1140/epje/i2007-10204-6

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  • DOI: https://doi.org/10.1140/epje/i2007-10204-6

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