The Journal of Membrane Biology

, Volume 250, Issue 3, pp 285–299 | Cite as

Theoretical Study of Molecular Transport Through a Permeabilized Cell Membrane in a Microchannel

  • Masoumeh Mahboubi
  • Saeid Movahed
  • Reza Hosseini Abardeh
  • Vahid Hoshyargar
Article

Abstract

A two-dimensional model is developed to study the molecular transport into an immersed cell in a microchannel and to investigate the effects of finite boundary (a cell is suspended in a microchannel), amplitude of electric pulse, and geometrical parameter (microchannel height and size of electrodes) on cell uptake. Embedded electrodes on the walls of the microchannel generate the required electric pulse to permeabilize the cell membrane, pass the ions through the membrane, and transport them into the cell. The shape of electric pulses is square with the time span of 6 ms; their intensities are in the range of 2.2, 2.4, 2.6, 3 V. Numerical simulations have been performed to comprehensively investigate the molecular uptake into the cell. The obtained results of the current study demonstrate that calcium ions enter the cell from the anodic side (the side near positive electrode); after a while, the cell faces depletion of the calcium ions on a positive electrode-facing side within the microchannel; the duration of depletion depends on the amplitude of electric pulse and geometry that lasts from microseconds to milliseconds. By keeping geometrical parameters and time span constant, increment of a pulse intensity enhances molecular uptake and rate of propagation inside the cell. If a ratio of electrode size to cell diameter is larger than 1, the transported amount of Ca 2+ into the cell, as well as the rate of propagation, will be significantly increased. By increasing the height of the microchannel, the rate of uptake is decreased. In an infinite domain, the peak concentration becomes constant after reaching the maximum value; this value depends on the intra–extracellular conductivity and diffusion coefficient of interior and exterior domains of the cell. In comparison, the maximum concentration is changed by geometrical parameters in the microchannel. After reaching the maximum value, the peak concentration reduces due to the depletion of Ca 2+ ions within the microchannel. Electrophoretic velocity has a significant effect on the cell uptake.

Keywords

Electroporation Electropermeabilization Cell membrane Cell uptake Pore Electrokinetic 

References

  1. Abidor IG, Arakelyan VB, Chernomordik LV, Chizmadzhev Yu A, Pastushenko VF, Tarasevich MP (1979) Electric breakdown of bilayer lipid membranes: I. The main experimental facts and their qualitative discussion. J Electroanal Chem Interfacial Electrochem 104:37–52CrossRefGoogle Scholar
  2. Bürgel SC, Escobedo C, Haandbæk N, Hierlemann A (2015) On-chip electroporation and impedance spectroscopy of single-cells. Sens Actuators B 210:82–90. doi: 10.1016/j.snb.2014.12.016 CrossRefGoogle Scholar
  3. Cao Y et al (2008) Study of high-throughput cell electrofusion in a microelectrode-array chip. Microfluid Nanofluidics 5:669–675CrossRefGoogle Scholar
  4. Casciola M, Tarek M (2016) A molecular insight into the electro-transfer of small molecules through electropores driven by electric fields. Biochimica et Biophysica Acta (BBA) Biomembranes 1858:2278–2289CrossRefGoogle Scholar
  5. Cheng W, Klauke N, Smith G, Cooper JM (2010) Microfluidic cell arrays for metabolic monitoring of stimulated cardiomyocytes. Electrophoresis 31:1405–1413CrossRefPubMedGoogle Scholar
  6. Clarke M, McNEIL PL (1992) Syringe loading introduces macromolecules into living mammalian cell cytosol. J Cell Sci 102:533–541PubMedGoogle Scholar
  7. DeBruin KA, Krassowska W (1999a) Modeling electroporation in a single cell. I. Effects of field strength and rest potential. Biophys J 77:1213–1224CrossRefPubMedPubMedCentralGoogle Scholar
  8. DeBruin KA, Krassowska W (1999b) Modeling electroporation in a single cell. II. Effects of ionic concentrations. Biophys J 77:1225–1233CrossRefPubMedPubMedCentralGoogle Scholar
  9. Dill K, Bromberg S (2010) Molecular driving forces: statistical thermodynamics in biology, chemistry, physics, and nanoscience. Garland Science, New YorkGoogle Scholar
  10. Doherty GJ, McMahon HT (2009) Mechanisms of endocytosis. Annu Rev Biochem 78:857–902CrossRefPubMedGoogle Scholar
  11. Dupont E, Prochiantz A, Joliot A (2015) Penetratin story: an overview. In: Langel Ü (ed) Cell-penetrating peptides methods in molecular biology, 1324th edn. Springer, New York, pp 29–37. doi: 10.1007/978-1-4939-2806-4_2 CrossRefGoogle Scholar
  12. Gabriel B, Teissié J (1999) Time courses of mammalian cell electropermeabilization observed by millisecond imaging of membrane property changes during the pulse. Biophys J 76:2158–2165CrossRefPubMedPubMedCentralGoogle Scholar
  13. Gothelf A, Mir LM, Gehl J (2003) Electrochemotherapy: results of cancer treatment using enhanced delivery of bleomycin by electroporation. Cancer Treat Rev 29:371–387CrossRefPubMedGoogle Scholar
  14. Hapala I (1997) Breaking the barrier: methods for reversible permeabilization of cellular membranes. Crit Rev Biotechnol 17:105–122CrossRefPubMedGoogle Scholar
  15. Ho Y-P, Leong KW (2010) Quantum dot-based theranostics. Nanoscale 2:60–68CrossRefPubMedGoogle Scholar
  16. Ikeda N, Tanaka N, Yanagida Y, Hatsuzawa T (2007) On-chip single-cell lysis for extracting intracellular material. Jpn J Appl Phys 46:6410CrossRefGoogle Scholar
  17. Joshi RP, Nguyen A, Sridhara V, Hu Q, Nuccitelli R, Beebe SJ, Kolb J, Schoenbach KH (2007) Simulations of intracellular calcium release dynamics in response to a high-intensity, ultrashort electric pulse. Phys Rev E. doi: 10.1103/PhysRevE.75.041920
  18. Kaner A, Braslavsky I, Rubinsky B (2014) Model of pore formation in a single cell in a flow-through channel with micro-electrodes. Biomed Microdevice 16:181–189CrossRefGoogle Scholar
  19. Khine M, Ionescu-Zanetti C, Blatz A, Wang L-P, Lee LP (2007) Single-cell electroporation arrays with real-time monitoring and feedback control. Lab Chip 7:457–462CrossRefPubMedGoogle Scholar
  20. Krassowska W, Filev PD (2007) Modeling electroporation in a single cell. Biophys J 92:404–417CrossRefPubMedGoogle Scholar
  21. Lee WG, Demirci U, Khademhosseini A (2009) Microscale electroporation: challenges and perspectives for clinical applications. Integr Biol 1:242–251CrossRefGoogle Scholar
  22. Levine ZA, Vernier PT (2010) Life cycle of an electropore: field-dependent and field-independent steps in pore creation and annihilation. J Membr Biol 236:27–36CrossRefPubMedGoogle Scholar
  23. Li J, Lin H (2010) The current-voltage relation for electropores with conductivity gradients. Biomicrofluidics 4:013206CrossRefPubMedCentralGoogle Scholar
  24. Li J, Lin H (2011) Numerical simulation of molecular uptake via electroporation. Bioelectrochemistry 82:10–21CrossRefPubMedGoogle Scholar
  25. Li J, Tan W, Yu M, Lin H (2013) The effect of extracellular conductivity on electroporation-mediated molecular delivery. Biochimica et Biophysica Acta (BBA) -Biomembranes 1828:461–470CrossRefGoogle Scholar
  26. Lodish H (2008) Molecular cell biology. Macmillan, LondonGoogle Scholar
  27. Longsine-Parker W, Wang H, Koo C, Kim J, Kim B, Jayaraman A, Han A (2013) Microfluidic electro-sonoporation: a multi-modal cell poration methodology through simultaneous application of electric field and ultrasonic wave. Lab Chip 13:2144–2152CrossRefPubMedGoogle Scholar
  28. Mazari E, Zhao X, Migeotte I, Collignon J, Gosse C, Perea-Gomez A (2014) A microdevice to locally electroporate embryos with high efficiency and reduced cell damage. Development 141:2349–2359CrossRefPubMedGoogle Scholar
  29. Movahed S, Li D (2011) Microfluidics cell electroporation. Microfluid Nanofluidics 10:703–734CrossRefGoogle Scholar
  30. Movahed S, Li D (2012) Electrokinetic transport through the nanopores in cell membrane during electroporation. J Colloid Interface Sci 369:442–452CrossRefPubMedGoogle Scholar
  31. Movahed S, Li D (2013) A theoretical study of single-cell electroporation in a microchannel. J Membr Biol 246:151–160CrossRefPubMedGoogle Scholar
  32. Movahed S, Bazargan-Lari Y, Daneshmad F, Mashhoodi M (2014) Numerical modeling of bi-polar (AC) pulse electroporation of single cell in microchannel to create nanopores on its membrane. J Membr Biol 247:1229–1237CrossRefPubMedGoogle Scholar
  33. Neu JC, Krassowska W (1999) Asymptotic model of electroporation. Phys Rev E 59:3471CrossRefGoogle Scholar
  34. Neu WK, Neu JC (2009) Theory of electroporation. Cardiac Bioelectric Therapy. Springer, New York, pp 133–161CrossRefGoogle Scholar
  35. Neumann E, Schaefer-Ridder M, Wang Y, Hofschneider P (1982) Gene transfer into mouse lyoma cells by electroporation in high electric fields. EMBO J 1:841PubMedPubMedCentralGoogle Scholar
  36. Puc M, Kotnik T, Mir LM, Miklavčič D (2003) Quantitative model of small molecules uptake after in vitro cell electropermeabilization. Bioelectrochemistry 60:1–10CrossRefPubMedGoogle Scholar
  37. Sundararajan R (2008) Nanosecond electroporation: another look. Mol Biotechnol 41:69–82. doi: 10.1007/s12033-008-9107-y CrossRefPubMedGoogle Scholar
  38. Tarek M (2005) Membrane electroporation: a molecular dynamics simulation. Biophys J 88:4045–4053CrossRefPubMedPubMedCentralGoogle Scholar
  39. Tieleman DP, Leontiadou H, Mark AE, Marrink SJ (2003) Molecular dynamics simulation of pore formation in phospholipid bilayers by mechanical force and electric fields. J Am Chem Soc. doi: 10.1021/ja029504i PubMedGoogle Scholar
  40. Valero A, Post J, Van Nieuwkasteele J, Ter Braak P, Kruijer W, Van Den Berg A (2008) Gene transfer and protein dynamics in stem cells using single cell electroporation in a microfluidic device. Lab Chip 8:62–67CrossRefPubMedGoogle Scholar
  41. Wei Z, Li X, Zhao D, Yan H, Hu Z, Liang Z, Li Z (2014) Flow-through cell electroporation microchip integrating dielectrophoretic viable cell sorting. Anal Chem 86:10215–10222CrossRefPubMedGoogle Scholar
  42. Zaharoff DA, Henshaw JW, Mossop B, Yuan F (2008) Mechanistic analysis of electroporation-induced cellular uptake of macromolecules. Exp Biol Med 233:94–105CrossRefGoogle Scholar
  43. Zhang Y et al (2008) Zeta potential: a surface electrical characteristic to probe the interaction of nanoparticles with normal and cancer human breast epithelial cells. Biomed Microdevice 10:321–328CrossRefGoogle Scholar
  44. Saeid Movahed, Dongqing Li, (2011) Microfluidics cell electroporation. Microfluidics and Nanofluidics 10 (4):703-734CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Masoumeh Mahboubi
    • 1
  • Saeid Movahed
    • 1
  • Reza Hosseini Abardeh
    • 1
  • Vahid Hoshyargar
    • 2
  1. 1.Department of Mechanical EngineeringAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.Research Lab for Advanced Separation Processes, Department of Chemical EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations