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

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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.

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References

  1. Huang CP, Chen XM, Chen ZQ. Osteocyte: the impresario in the electrical stimulation for bone fracture healing. Med Hypotheses. 2008;70:287–90.

    Article  Google Scholar 

  2. Zhao M, Forrester JV, McCaig CD. A small, physiological electric field orients cell division. Proc Natl Acad Sci. 1999;96:4942–6.

    Article  Google Scholar 

  3. Robinson KR. The responses of cells to electrical fields: a review. J Cell Biol. 1985;101:2023–7.

    Article  Google Scholar 

  4. Tsong TY. Electroporation of cell membranes. Biophys J. 1991;60:297–306.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  6. Zimmermann U, Vienken J. Electric field-induced cell-to-cell fusion. J Membr Biol. 1982;67:165–82.

    Article  Google Scholar 

  7. Wong T-K, Neumann E. Electric field mediated gene transfer. Biochem Biophys Res Commun. 1982;107:584–7.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  15. Miller L, Leor J, Rubinsky B. Cancer cells ablation with irreversible electroporation. Technol Cancer Res Treat. 2005;4:699–705.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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;39

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  23. Basu B. Biomaterials science and tissue engineering: principles and methods: Cambridge University Press; 2017.

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  29. Pethig R, Menachery A, Pells S, De Sousa P. Dielectrophoresis: a review of applications for stem cell research. Biomed Res Int. 2010;2010

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  39. Ellappan P, Sundararajan R. A simulation study of the electrical model of a biological cell. J Electrost. 2005;63:297–307.

    Article  Google Scholar 

  40. Grosse C, Schwan HP. Cellular membrane potentials induced by alternating fields. Biophys J. 1992;63:1632–42.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  42. Dubey A, Banerjee M, Basu B. Biological cell–electrical field interaction: stochastic approach. J Biol Phys. 2011;37:39–50.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  44. Kotnik T, Miklavčič D. Analytical description of transmembrane voltage induced by electric fields on spheroidal cells. Biophys J. 2000;79:670–9.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  46. Ly JD, Grubb D, Lawen A. The mitochondrial membrane potential (Δψm) in apoptosis; an update. Apoptosis. 2003;8:115–28.

    Article  Google Scholar 

  47. Gowrishankar TR, Weaver JC. An approach to electrical modeling of single and multiple cells. Proc Natl Acad Sci. 2003;100:3203–8.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  53. Gehl J. Electroporation: theory and methods, perspectives for drug delivery, gene therapy and research. Acta Physiol. 2003;177:437–47.

    Article  Google Scholar 

  54. Weaver JC. Electroporation: a general phenomenon for manipulating cells and tissues. J Cell Biochem. 1993;51:426–35.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  59. Foster KR, Schwan HP. Dielectric properties of tissues. Handbook of biological effects of electromagnetic fields. 1995;2:25–102.

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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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.

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Authors and Affiliations

  1. Materials Research Centre, Indian Institute of Science, Bangalore, 560012, India

    K. Ravikumar & Bikramjit Basu

  2. Department of Ceramic Engineering, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, 221005, India

    Ashutosh Kumar Dubey

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  1. K. Ravikumar
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Correspondence to Bikramjit Basu or Ashutosh Kumar Dubey.

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Future Work

The present analysis is limited to a single cell, but cell biology experiments in general are carried out on cell populations. Hence, a natural continuation of this work will be to apply similar analytical techniques and simulation tools to study how a group of cells respond to electrical stimulus.

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Ravikumar, K., Basu, B. & Dubey, A.K. Analysis of Electrical Analogue of a Biological Cell and Its Response to External Electric Field. Regen. Eng. Transl. Med. 5, 10–21 (2019). https://doi.org/10.1007/s40883-018-0073-z

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