Advertisement

Analysis of Electrical Analogue of a Biological Cell and Its Response to External Electric Field

  • K. Ravikumar
  • Bikramjit BasuEmail author
  • Ashutosh Kumar DubeyEmail author
Article
  • 100 Downloads

Abstract

The use of electric field stimulation to elicit a desired cell/tissue response has become a versatile strategy in regenerative medicine. Using an array of cell types and biomaterial substrates, our group has experimentally investigated the influence of external electric field parameters on the modulation of cellular functionality in vitro. However, the mechanism of action of electric field is not clearly understood, especially in cases where cell fate processes such as differentiation and proliferation are significantly enhanced due to electric field stimulation. In order to understand these important phenomena, it is necessary to first examine the response on a single cell. In this direction, we analyze the response of an electrical analogue of a single biological cell, wherein an electrical equivalent resistor-capacitor (R-C) network has been constructed by considering membranes as capacitive and surrounding biological media (cytoplasm and nucleoplasm) as resistive components. The response of this electrical analogue of a biological cell to external electric field (E-field) is determined using analytical techniques and SPICE-based simulations. The solutions for the network provide a time constant of ≈ 30 μs, which is higher compared to the case when membranes were considered to be purely capacitive. The above model formulation has been further extended to determine the steady-state current response under various input signals, like sinusoidal, square, and triangular pulses using SPICE simulation package. In the context of regenerative engineering, the results of the present work are perceived to be important to design electric field-based stimulation strategies to obtain desired responses of electroactive tissues.

Lay Summary

The importance of the effect of electric field on cells and tissues has become evident over the last two decades. Prior studies indicate that based on the electric field parameters, it is possible to get various cellular responses. The current study is an attempt to investigate why this is the case by approximating a single cell into an equivalent electrical network with resistors and capacitors. The network response is studied using simulation tools to get current waveforms and analytical techniques to obtain time constants, which provide vital insights into the observed cell behaviors reported in the literature.

Keywords

Electrical analogue of cell RC model Time constant SPICE simulation Electric field effects 

Notes

Acknowledgements

We would like to thank SERB, Department of Science and Technology (DST), Government of India, and National Network for Mathematical and Computational Biology (NNMCB) for their support in carrying out this work.

References

  1. 1.
    Huang CP, Chen XM, Chen ZQ. Osteocyte: the impresario in the electrical stimulation for bone fracture healing. Med Hypotheses. 2008;70:287–90.CrossRefGoogle Scholar
  2. 2.
    Zhao M, Forrester JV, McCaig CD. A small, physiological electric field orients cell division. Proc Natl Acad Sci. 1999;96:4942–6.CrossRefGoogle Scholar
  3. 3.
    Robinson KR. The responses of cells to electrical fields: a review. J Cell Biol. 1985;101:2023–7.CrossRefGoogle Scholar
  4. 4.
    Tsong TY. Electroporation of cell membranes. Biophys J. 1991;60:297–306.CrossRefGoogle Scholar
  5. 5.
    Beebe SJ, Fox P, Rec L, Somers K, Stark RH, Schoenbach KH. Nanosecond pulsed electric field (ns PEF) effects on cells and tissues: apoptosis induction and tumor growth inhibition. IEEE Trans Plasma Sci. 2002;30:286–92.CrossRefGoogle Scholar
  6. 6.
    Zimmermann U, Vienken J. Electric field-induced cell-to-cell fusion. J Membr Biol. 1982;67:165–82.CrossRefGoogle Scholar
  7. 7.
    Wong T-K, Neumann E. Electric field mediated gene transfer. Biochem Biophys Res Commun. 1982;107:584–7.CrossRefGoogle Scholar
  8. 8.
    Ghasemi-Mobarakeh L, Prabhakaran MP, Morshed M, Nasr-Esfahani MH, Baharvand H, Kiani S, et al. Application of conductive polymers, scaffolds and electrical stimulation for nerve tissue engineering. J Tissue Eng Regen Med. 2011;5:e17–35.CrossRefGoogle Scholar
  9. 9.
    Hronik-Tupaj M, Rice WL, Cronin-Golomb M, Kaplan DL, Georgakoudi I. Osteoblastic differentiation and stress response of human mesenchymal stem cells exposed to alternating current electric fields. Biomed Eng Online. 2011;10:9.CrossRefGoogle Scholar
  10. 10.
    Thrivikraman G, Madras G, Basu B. Electrically driven intracellular and extracellular nanomanipulators evoke neurogenic/cardiomyogenic differentiation in human mesenchymal stem cells. Biomaterials. 2016;77:26–43.CrossRefGoogle Scholar
  11. 11.
    Thrivikraman G, Madras G, Basu B. Intermittent electrical stimuli for guidance of human mesenchymal stem cell lineage commitment towards neural-like cells on electroconductive substrates. Biomaterials. 2014;35:6219–35.CrossRefGoogle Scholar
  12. 12.
    Hammerick KE, Longaker MT, Prinz FB. In vitro effects of direct current electric fields on adipose-derived stromal cells. Biochem Biophys Res Commun. 2010;397:12–7.CrossRefGoogle Scholar
  13. 13.
    Onuma EK, Hui S-W. Electric field-directed cell shape changes, displacement, and cytoskeletal reorganization are calcium dependent. J Cell Biol. 1988;106:2067–75.CrossRefGoogle Scholar
  14. 14.
    Dubey AK, Kumar R, Banerjee M, Basu B. Analytical computation of electric field for onset of electroporation. J Comput Theor Nanosci. 2012;9:137–43.CrossRefGoogle Scholar
  15. 15.
    Miller L, Leor J, Rubinsky B. Cancer cells ablation with irreversible electroporation. Technol Cancer Res Treat. 2005;4:699–705.CrossRefGoogle Scholar
  16. 16.
    Dubey AK, Agrawal P, Misra RDK, Basu B. Pulsed electric field mediated in vitro cellular response of fibroblast and osteoblast-like cells on conducting austenitic stainless steel substrate. J Mater Sci Mater Med. 2013;24:1789–98.CrossRefGoogle Scholar
  17. 17.
    Dubey AK, Gupta SD, Basu B. Optimization of electrical stimulation parameters for enhanced cell proliferation on biomaterial surfaces. J Biomed Mater Res B Appl Biomater. 2011;98:18–29.CrossRefGoogle Scholar
  18. 18.
    Panagopoulos DJ, Messini N, Karabarbounis A, Philippetis AL, Margaritis LH. A mechanism for action of oscillating electric fields on cells. Biochem Biophys Res Commun. 2000;272:634–40.CrossRefGoogle Scholar
  19. 19.
    Naderi-Meshkin H, Bahrami AR, Bidkhori HR, Mirahmadi M, Ahmadiankia N. Strategies to improve homing of mesenchymal stem cells for greater efficacy in stem cell therapy. Cell Biol Int. 2015;39Google Scholar
  20. 20.
    Stewart E, Kobayashi NR, Higgins MJ, Quigley AF, Jamali S, Moulton SE, et al. Electrical stimulation using conductive polymer polypyrrole promotes differentiation of human neural stem cells: a biocompatible platform for translational neural tissue engineering. Tissue Eng Part C Methods. 2014;21:385–93.CrossRefGoogle Scholar
  21. 21.
    Thrivikraman G, Boda SK, Basu B. Unraveling the mechanistic effects of electric field stimulation towards directing stem cell fate and function: a tissue engineering perspective. Biomaterials. 2018;150:60–86.CrossRefGoogle Scholar
  22. 22.
    Sauer H, Rahimi G, Hescheler J, Wartenberg M. Effects of electrical fields on cardiomyocyte differentiation of embryonic stem cells. J Cell Biochem. 1999;75:710–23.CrossRefGoogle Scholar
  23. 23.
    Basu B. Biomaterials science and tissue engineering: principles and methods: Cambridge University Press; 2017.Google Scholar
  24. 24.
    Thrivikraman G, Lee PS, Hess R, Haenchen V, Basu B, Scharnweber D. Interplay of substrate conductivity, cellular microenvironment, and pulsatile electrical stimulation toward osteogenesis of human mesenchymal stem cells in vitro. ACS Appl Mater Interfaces. 2015;7:23015–28.CrossRefGoogle Scholar
  25. 25.
    Akhavan O, Ghaderi E, Shirazian SA, Rahighi R. Rolled graphene oxide foams as three-dimensional scaffolds for growth of neural fibers using electrical stimulation of stem cells. Carbon. 2016;97:71–7.CrossRefGoogle Scholar
  26. 26.
    Sun LY, Hsieh DK, Yu TC, Chiu HT, Lu SF, Luo GH, et al. Effect of pulsed electromagnetic field on the proliferation and differentiation potential of human bone marrow mesenchymal stem cells. Bioelectromagnetics. 2009;30:251–60.CrossRefGoogle Scholar
  27. 27.
    Ravikumar K, Boda SK, Basu B. Synergy of substrate conductivity and intermittent electrical stimulation towards osteogenic differentiation of human mesenchymal stem cells. Bioelectrochemistry. 2017;116:52–64.CrossRefGoogle Scholar
  28. 28.
    Boda SK, Thrivikraman G, Basu B. Magnetic field assisted stem cell differentiation—role of substrate magnetization in osteogenesis. J Mater Chem B. 2015;3:3150–68.CrossRefGoogle Scholar
  29. 29.
    Pethig R, Menachery A, Pells S, De Sousa P. Dielectrophoresis: a review of applications for stem cell research. Biomed Res Int. 2010;2010Google Scholar
  30. 30.
    Yamada M, Tanemura K, Okada S, Iwanami A, Nakamura M, Mizuno H, et al. Electrical stimulation modulates fate determination of differentiating embryonic stem cells. Stem Cells. 2007;25:562–70.CrossRefGoogle Scholar
  31. 31.
    Maziarz A, Kocan B, Bester M, Budzik S, Cholewa M, Ochiya T, et al. How electromagnetic fields can influence adult stem cells: positive and negative impacts. Stem Cell Res Ther. 2016;7:54.CrossRefGoogle Scholar
  32. 32.
    Weaver JC, Smith KC, Esser AT, Son RS, Gowrishankar T. A brief overview of electroporation pulse strength–duration space: a region where additional intracellular effects are expected. Bioelectrochemistry. 2012;87:236–43.CrossRefGoogle Scholar
  33. 33.
    Neumann E, Schaefer-Ridder M, Wang Y, Hofschneider P. Gene transfer into mouse lyoma cells by electroporation in high electric fields. EMBO J. 1982;1:841.CrossRefGoogle Scholar
  34. 34.
    Nuccitelli R, Pliquett U, Chen X, Ford W, Swanson RJ, Beebe SJ, et al. Nanosecond pulsed electric fields cause melanomas to self-destruct. Biochem Biophys Res Commun. 2006;343:351–60.CrossRefGoogle Scholar
  35. 35.
    Gothelf A, Mir LM, Gehl J. Electrochemotherapy: results of cancer treatment using enhanced delivery of bleomycin by electroporation. Cancer Treat Rev. 2003;29:371–87.CrossRefGoogle Scholar
  36. 36.
    Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952;117:500–44.CrossRefGoogle Scholar
  37. 37.
    Schoenbach KH, Peterkin FE, Alden RW, Beebe SJ. The effect of pulsed electric fields on biological cells: experiments and applications. IEEE Trans Plasma Sci. 1997;25:284–92.CrossRefGoogle Scholar
  38. 38.
    Deng J, Schoenbach KH, Buescher ES, Hair PS, Fox PM, Beebe SJ. The effects of intense submicrosecond electrical pulses on cells. Biophys J. 2003;84:2709–14.CrossRefGoogle Scholar
  39. 39.
    Ellappan P, Sundararajan R. A simulation study of the electrical model of a biological cell. J Electrost. 2005;63:297–307.CrossRefGoogle Scholar
  40. 40.
    Grosse C, Schwan HP. Cellular membrane potentials induced by alternating fields. Biophys J. 1992;63:1632–42.CrossRefGoogle Scholar
  41. 41.
    Kotnik T, Miklavčič D. Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields. Biophys J. 2006;90:480–91.CrossRefGoogle Scholar
  42. 42.
    Dubey A, Banerjee M, Basu B. Biological cell–electrical field interaction: stochastic approach. J Biol Phys. 2011;37:39–50.CrossRefGoogle Scholar
  43. 43.
    Dubey AK, Dutta-Gupta S, Kumar R, Tewari A, Basu B. Time constant determination for electrical equivalent of biological cells. J Appl Phys. 2009;105:084705.CrossRefGoogle Scholar
  44. 44.
    Kotnik T, Miklavčič D. Analytical description of transmembrane voltage induced by electric fields on spheroidal cells. Biophys J. 2000;79:670–9.CrossRefGoogle Scholar
  45. 45.
    Sundelacruz S, Levin M, Kaplan DL. Role of membrane potential in the regulation of cell proliferation and differentiation. Stem Cell Rev Rep. 2009;5:231–46.CrossRefGoogle Scholar
  46. 46.
    Ly JD, Grubb D, Lawen A. The mitochondrial membrane potential (Δψm) in apoptosis; an update. Apoptosis. 2003;8:115–28.CrossRefGoogle Scholar
  47. 47.
    Gowrishankar TR, Weaver JC. An approach to electrical modeling of single and multiple cells. Proc Natl Acad Sci. 2003;100:3203–8.CrossRefGoogle Scholar
  48. 48.
    Joshi RP, Schoenbach KH. Electroporation dynamics in biological cells subjected to ultrafast electrical pulses: a numerical simulation study. Phys Rev E. 2000;62:1025–33.CrossRefGoogle Scholar
  49. 49.
    Reynolds CR, Tedeschi H. Permeability properties of mammalian cell nuclei in living cells and in vitro. J Cell Sci. 1984;70:197–207.Google Scholar
  50. 50.
    Kinosita K, Ashikawa I, Saita N, Yoshimura H, Itoh H, Nagayama K, et al. Electroporation of cell membrane visualized under a pulsed-laser fluorescence microscope. Biophys J. 1988;53:1015–9.CrossRefGoogle Scholar
  51. 51.
    Kotnik T, Kramar P, Pucihar G, Miklavcic D, Tarek M. Cell membrane electroporation—part 1: the phenomenon. IEEE Electr Insul Mag. 2012;28:14–23.CrossRefGoogle Scholar
  52. 52.
    Schoenbach KH, Hargrave SJ, Joshi RP, Kolb JF, Nuccitelli R, Osgood C, et al. Bioelectric effects of intense nanosecond pulses. IEEE Trans Dielectr Electr Insul. 2007;14:1088–109.CrossRefGoogle Scholar
  53. 53.
    Gehl J. Electroporation: theory and methods, perspectives for drug delivery, gene therapy and research. Acta Physiol. 2003;177:437–47.CrossRefGoogle Scholar
  54. 54.
    Weaver JC. Electroporation: a general phenomenon for manipulating cells and tissues. J Cell Biochem. 1993;51:426–35.CrossRefGoogle Scholar
  55. 55.
    Hibino M, Itoh H, Kinosita K. Time courses of cell electroporation as revealed by submicrosecond imaging of transmembrane potential. Biophys J. 1993;64:1789–800.CrossRefGoogle Scholar
  56. 56.
    Kotnik T, Miklavčič D, Slivnik T. Time course of transmembrane voltage induced by time-varying electric fields—a method for theoretical analysis and its application. Bioelectrochem Bioenerg. 1998;45:3–16.CrossRefGoogle Scholar
  57. 57.
    Pucihar G, Kotnik T, Valič B, Miklavčič D. Numerical determination of transmembrane voltage induced on irregularly shaped cells. Ann Biomed Eng. 2006;34:642.CrossRefGoogle Scholar
  58. 58.
    Matthews BD, Overby DR, Mannix R, Ingber DE. Cellular adaptation to mechanical stress: role of integrins, Rho, cytoskeletal tension and mechanosensitive ion channels. J Cell Sci. 2006;119:508–18.CrossRefGoogle Scholar
  59. 59.
    Foster KR, Schwan HP. Dielectric properties of tissues. Handbook of biological effects of electromagnetic fields. 1995;2:25–102.Google Scholar
  60. 60.
    Mossop BJ, Barr RC, Zaharoff DA, Yuan F. Electric fields within cells as a function of membrane resistivity—a model study. IEEE Trans Nanobioscience. 2004;3:225–31.CrossRefGoogle Scholar
  61. 61.
    Kirson ED, Dbalý V, Tovaryš F, Vymazal J, Soustiel JF, Itzhaki A, et al. Alternating electric fields arrest cell proliferation in animal tumor models and human brain tumors. Proc Natl Acad Sci. 2007;104:10152–7.CrossRefGoogle Scholar
  62. 62.
    Wolf FI, Torsello A, Tedesco B, Fasanella S, Boninsegna A, D'Ascenzo M, et al. 50-Hz extremely low frequency electromagnetic fields enhance cell proliferation and DNA damage: possible involvement of a redox mechanism. Biochim et Biophys Acta. 2005;1743:120–9.CrossRefGoogle Scholar
  63. 63.
    Hartig M, Joos U, Wiesmann H-P. Capacitively coupled electric fields accelerate proliferation of osteoblast-like primary cells and increase bone extracellular matrix formation in vitro. Eur Biophys J. 2000;29:499–506.CrossRefGoogle Scholar
  64. 64.
    Piacentini R, Ripoli C, Mezzogori D, Azzena GB, Grassi C. Extremely low-frequency electromagnetic fields promote in vitro neurogenesis via upregulation of Cav1-channel activity. J Cell Physiol. 2008;215:129–39.CrossRefGoogle Scholar
  65. 65.
    Zhao M, Song B, Pu J, Wada T, Reid B, Tai G, et al. Electrical signals control wound healing through phosphatidylinositol-3-OH kinase-γ and PTEN. Nature. 2006;442:457–60.CrossRefGoogle Scholar
  66. 66.
    Li L, El-Hayek YH, Liu B, Chen Y, Gomez E, Wu X, et al. Direct-current electrical field guides neuronal stem/progenitor cell migration. Stem Cells. 2008;26:2193–200.CrossRefGoogle Scholar

Copyright information

© The Regenerative Engineering Society 2018

Authors and Affiliations

  1. 1.Materials Research CentreIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Ceramic EngineeringIndian Institute of Technology (BHU)VaranasiIndia

Personalised recommendations