Abstract
The paper presents an approach that reduces several difficulties related to the determination of induced transmembrane voltage (ITV) on irregularly shaped cells. We first describe a method for constructing realistic models of irregularly shaped cells based on microscopic imaging. This provides a possibility to determine the ITV on the same cells on which an experiment is carried out, and can be of considerable importance in understanding and interpretation of the data. We also show how the finite-thickness, nonzero-conductivity membrane can be replaced by a boundary condition in which a specific surface conductivity is assigned to the interface between the cell interior (the cytoplasm) and the exterior. We verify the results obtained using this method by a comparison with the analytical solution for an isolated spherical cell and a tilted oblate spheroidal cell, obtaining a very good agreement in both cases. In addition, we compare the ITV computed for a model of two irregularly shaped CHO cells with the ITV measured on the same two cells by means of a potentiometric fluorescent dye, and also with the ITV computed for a simplified model of these two cells.
Similar content being viewed by others
Notes
This could be addressed by sequentially modifying the electric properties of the membrane and recomputing the potential distribution. An example of such modification for a tissue exposed to an electric field can be found in Ref.41
REFERENCES
Alberts, B., D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson. Molecular Biology of the Cell, 3rd edn., New York: Garland, 1994.
Bedlack, R. S., M. Wei, S. H. Fox, E. Gross, and L. M. Loew. Distinct electric potentials in soma and neurite membranes. Neuron 13:1187–1193, 1994.
Buitenweg, J. R., W. L. Rutten, and E. Marani. Geometry-based finite-element modeling of the electrical contact between a cultured neuron and a microelectrode. IEEE Trans. Biomed. Eng. 50:501–509, 2003.
Cheng, D. K. L., L. Tung, and E. A. Sobie. Nonuniform responses of transmembrane potential during electric field stimulation of single cardiac cells. Am. J. Physiol. 277:H351–H362, 1999.
Fear, E. C., and M. A. Stuchly. Biological cells with gap junctions in low-frequency electric fields. IEEE Trans. Biomed. Eng. 45:856–866, 1998.
Fear, E. C., and M. A. Stuchly. Modeling assemblies of biological cells exposed to electric fields. IEEE Trans. Biomed. Eng. 45:1259–1271, 1998.
Gabriel, B., and J. Teissié. Fluorescence imaging in the millisecond time range of membrane electropermeabilization of single cell using a rapid ultra-low-light intensifying detection system. Eur. Biophys. J. 27:291–298, 1998.
Gascoyne, P. R. C., R. Pethig, J. P. H. Burt, and F. F. Becker. Membrane changes accompanying the induced differentiation of Friend murine erythroleukemia cells studied by dielectrophoresis. Biochim. Biophys. Acta. 1146:119–126, 1993.
Gimsa, J., and D. Wachner. Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells. Biophys. J. 81:1888–1896, 2001.
Gimsa, J., and D. Wachner. On the analytical description of transmembrane voltage induced on spheroidal cells with zero membrane conductance. Eur. Biophys. J. 30:463–466, 2001.
Golzio, M., L. Mazzolini, P. Moller, M. P. Rols, and J. Teissie. Inhibition of gene expression in mice muscle by in vivo electrically mediated siRNA delivery. Gene Therapy 12:246–251, 2005.
Gowrishankar, T. R., and J. C. Weaver. An approach to electrical modeling of single and multiple cells. Proc. Natl. Acad. Sci. U.S.A. 100:3203–3208, 2003.
Gross, D., L. M. Loew, and W. Webb. Optical imaging of cell membrane potential changes induced by applied electric fields. Biophys. J. 50:339–348, 1986.
Harris, C. M., and D. B. Kell. The radio-frequency dielectric properties of yeast cells measured with a rapid, automated, frequency-domain dielectric spectrometer. Bioelectrochem. Bioenerg. 11:15–28, 1983.
Hassan, N., I. Chatterjee, N. G. Publicover, and G. L. Craviso. Mapping membrane-potential perturbations of chromaffin cells exposed to electric fields. IEEE Trans. Plasma Sci. 30:1516–1524, 2002.
Heller, R., R. Gilbert, and M. J. Jaroszeski. Clinical applications of electrochemotherapy. Adv. Drug. Deliv. Rev. 35:119–129, 1999.
Hibino, M., H. Itoh, and K. Kinosita. Time courses of cell electroporation as revealed by submicrosecond imaging of transmembrane potential. Biophys. J. 64:1789–1800, 1993.
Hibino, M., M. Shigemori, H. Itoh, K. Nagayama, and K. Kinosita. Membrane conductance of an electroporated cell analyzed by submicrosecond imaging of transmembrane potential. Biophys. J. 59:209–220, 1991.
Huang, X., D. Nguyen, D. W. Greve, and M. M. Domach. Simulation of microelectrode impedance changes due to cell growth. IEEE Sensors J. 4:576–583, 2004.
Knisley, S. B., T. F. Blitchington, B. C. Hill, A. O. Grant, W. M. Smith, T. C. Pilkington, and R. E. Ideker. Optical measurements of transmembrane potential changes during electric field stimulation of ventricular cells. Circ. Res. 72:255–268, 1993.
Kotnik, T., F. Bobanović, and D. Miklavčič. Sensitivity of transmembrane voltage induced by applied electric fields – a theoretical analysis. Bioelectrochem. Bioenerg. 43:285–291, 1997.
Kotnik, T., and D. Miklavčič. Analytical description of transmembrane voltage induced by electric fields on spheroidal cells. Biophys. J. 79:670–679, 2000.
Kotnik, T., and D. Miklavčič. Second-order model of membrane electric field induced by alternating external electric fields. IEEE Trans. Biomed. Eng. 47:1074–1081, 2000.
Lee, D. C., and W. M. Grill. Polarization of a spherical cell in a nonuniform extracellular electric field. Anal. Biomed. Eng. 33:603–615, 2005.
Loew, L. M. Voltage sensitive dyes: Measurement of membrane potentials induced by DC and AC electric fields. Bioelectromagnetics Suppl. 1:179–189, 1992.
Lojewska, Z., D. L. Franks, B. Ehrenberg, and L. M. Loew. Analysis of the effect of medium and membrane conductance on the amplitude and kinetics of membrane potentials induced by externally applied electric fields. Biophys. J. 56:121–128, 1989.
Miklavčič, D., G. Pucihar, M. Pavlovec, S. Ribarič, M. Mali, A. Maček-Lebar, M. Petkovšek, J. Nastran, S. Kranjc, M. Čemažar, and G. Serša. The effect of high frequency electric pulses on muscle contractions and antitumor efficiency in vivo for a potential use in clinical electrochemotherapy. Bioelectrochemistry 65:121–128, 2005.
Miller, C. E., and C. S. Henriquez. Three-dimensional finite element solution for biopotentials: Erythrocyte in an applied field. IEEE Trans. Biomed. Eng. 35:712–718, 1988.
Mir, L. M., and S. Orlowski. Mechanisms of electrochemotherapy. Adv. Drug Deliv. Rev. 35:107–118, 1999.
Montana, V., D. L. Farkas, and L. M. Loew. Dual-wavelength ratiometric fluorescence measurements of membrane-potential. Biochemistry 28:4536–4539, 1989.
Neumann, E., S. Kakorin, and K. Toensing. Fundamentals of electroporative delivery of drugs and genes. Bioelectrochem. Bioenerg. 48:3–16, 1999.
Pavlin, M., N. Pavšelj, and D. Miklavčič. Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system. IEEE Trans. Biomed. Eng. 49:605–612, 2002.
Pucihar, G., T. Kotnik, M. Kandušer, and D. Miklavčič. The influence of medium conductivity on electropermeabilization and survival of cells in vitro. Bioelectrochemistry 54:107–115, 2001.
Rols, M. P., C. Delteil, M. Golzio, and J. Teissié. Control by ATP and ADP of voltage-induced mammalian-cell-membrane permeabilization, gene transfer and resulting expression. Eur. J. Biochem. 254:382–388, 1998.
Schwan, H. P. Electrical properties of tissue and cell suspensions. Adv. Biol. Med. Phys. 5:147–209, 1957.
Serša, G., M. Čemažar, and Z. Rudolf. Electrochemotherapy: advantages and drawbacks in treatment of cancer patients. Cancer Ther. 1:133–142, 2003.
Somiari, S., J. G. Malone, J. J. Drabick, R. A. Gilbert, R. Heller, M. J. Jaroszeski, and R. W. Malone. Theory and in vivo application of electroporative gene delivery. Mol. Ther. 2:178–187, 2000.
Stewart, D. A., T. R. Gowrishankar, and J. C. Weaver. Transport lattice approach to describing cell electroporation: use of a local asymptotic model. IEEE Trans. Plasma Sci. 32:1696–1708, 2004.
Susil, R., D. Šemrov, and D. Miklavčič. Electric field induced transmembrane potential depends on cell density and organization. Electro. Magnetobiol. 17:391–399, 1998.
Šatkauskas, S., M. F. Bureau, M. Puc, A. Mahfoudi, D. Scherman, D. Miklavčič, and L. M. Mir. Mechanisms of in vivo DNA electrotransfer: respective contributions of cell electropermeabilization and DNA electrophoresis. Mol. Ther. 5:133–140, 2002.
Šel, D., D. Cukjati, D. Batiuskaite, T. Slivnik, L. M. Mir, and D. Miklavčič. Sequential finite element model of tissue electropermeabilization. IEEE Trans. Biomed. Eng. 52:816–827, 2005.
Teissie, J., and M. P. Rols. An experimental evaluation of the critical potential difference inducing cell membrane electropermeabilization. Biophys. J. 65:409–413, 1993.
Teissié, J., N. Eynard, B. Gabriel, and M. P. Rols. Electropermeabilization of cell membranes. Adv. Drug Deliver Rev. 35:3–19, 1999.
Tsong, T. Y. Electroporation of cell membranes. Biophys. J. 60:297–306, 1991.
Valič, B., M. Golzio, M. Pavlin, A. Schatz, C. Faurie, B. Gabriel, J. Teissié, M. P. Rols, and D. Miklavčič. Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment. Eur. Biophys. J. 32:519–528, 2003.
ACKNOWLEDGMENTS
This work was supported by the Ministry of Higher Education, Science and Technology of the Republic of Slovenia. The authors wish to thank Dr Marko Puc for building the switcher device for delivery of electric pulses in the experiments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pucihar, G., Kotnik, T., Valič, B. et al. Numerical Determination of Transmembrane Voltage Induced on Irregularly Shaped Cells. Ann Biomed Eng 34, 642–652 (2006). https://doi.org/10.1007/s10439-005-9076-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-005-9076-2