Basic Features of a Cell Electroporation Model: Illustrative Behavior for Two Very Different Pulses

Science increasingly involves complex modeling. Here we describe a model for cell electroporation in which membrane properties are dynamically modified by poration. Spatial scales range from cell membrane thickness (5 nm) to a typical mammalian cell radius (10 $$\upmu$$μm), and can be used with idealized and experimental pulse waveforms. The model consists of traditional passive components and additional active components representing nonequilibrium processes. Model responses include measurable quantities: transmembrane voltage, membrane electrical conductance, and solute transport rates and amounts for the representative “long” and “short” pulses. The long pulse—1.5 kV/cm, 100 $$\upmu$$μs—evolves two pore subpopulations with a valley at $${\sim}$$∼5 nm, which separates the subpopulations that have peaks at $${\sim}$$∼1.5 and $${\sim}$$∼12 nm radius. Such pulses are widely used in biological research, biotechnology, and medicine, including cancer therapy by drug delivery and nonthermal physical tumor ablation by causing necrosis. The short pulse—40 kV/cm, 10 ns—creates 80-fold more pores, all small ($$<$$<3 nm; $$\sim$$∼1 nm peak). These nanosecond pulses ablate tumors by apoptosis. We demonstrate the model’s responses by illustrative electrical and poration behavior, and transport of calcein and propidium. We then identify extensions for expanding modeling capability. Structure-function results from MD can allow extrapolations that bring response specificity to cell membranes based on their lipid composition. After a pulse, changes in pore energy landscape can be included over seconds to minutes, by mechanisms such as cell swelling and pulse-induced chemical reactions that slowly alter pore behavior.

[1]  M. R. Tarasevich,et al.  246 - Electric breakdown of bilayer lipid membranes I. The main experimental facts and their qualitative discussion , 1979 .

[2]  Wanda Krassowska,et al.  Model of creation and evolution of stable electropores for DNA delivery. , 2004, Biophysical journal.

[3]  T. L. Ellis,et al.  Non-Thermal Irreversible Electroporation (N-TIRE) and Adjuvant Fractionated Radiotherapeutic Multimodal Therapy for Intracranial Malignant Glioma in a Canine Patient , 2011, Technology in cancer research & treatment.

[4]  Julie Gehl,et al.  Electrochemotherapy: results of cancer treatment using enhanced delivery of bleomycin by electroporation. , 2003, Cancer treatment reviews.

[5]  A. T. Esser,et al.  Microdosimetry for conventional and supra-electroporation in cells with organelles. , 2006, Biochemical and biophysical research communications.

[6]  Paul Gaynor,et al.  Modelling single cell electroporation with bipolar pulse parameters and dynamic pore radii , 2010 .

[7]  D Peter Tieleman,et al.  BMC Biochemistry BioMed Central Research article The molecular basis of electroporation , 2004 .

[8]  M. Risk,et al.  Size-controlled nanopores in lipid membranes with stabilizing electric fields. , 2012, Biochemical and biophysical research communications.

[9]  James C. Weaver,et al.  Electrodiffusion of Molecules in Aqueous Media: A Robust, Discretized Description for Electroporation and Other Transport Phenomena , 2012, IEEE Transactions on Biomedical Engineering.

[10]  L. Mir,et al.  Introduction of definite amounts of nonpermeant molecules into living cells after electropermeabilization: direct access to the cytosol. , 1988, Experimental cell research.

[11]  I. Sugár The effects of external fields on the structure of lipid bilayers. , 1981, Journal de physiologie.

[12]  G. Narayanan,et al.  Irreversible Electroporation , 2015, Seminars in Interventional Radiology.

[13]  H. Pauly,et al.  Über die Impedanz einer Suspension von kugelförmigen Teilchen mit einer Schale , 1959 .

[14]  J. Weaver,et al.  Transport lattice approach to describing cell electroporation: use of a local asymptotic model , 2004, IEEE Transactions on Plasma Science.

[15]  J. Litster,et al.  Stability of lipid bilayers and red blood cell membranes , 1975 .

[16]  A. T. Esser,et al.  Towards Solid Tumor Treatment by Nanosecond Pulsed Electric Fields , 2009, Technology in cancer research & treatment.

[17]  G. A. Hofmann,et al.  Medical applications of electroporation , 2000 .

[18]  R. Keynes,et al.  ELECTROGENIC ION PUMPS , 1974, Annals of the New York Academy of Sciences.

[19]  R A Knight,et al.  Molecular definitions of cell death subroutines: recommendations of the Nomenclature Committee on Cell Death 2012 , 2011, Cell Death and Differentiation.

[20]  Soichi Watanabe,et al.  Proportion-corrected scaled voxel models for Japanese children and their application to the numerical dosimetry of specific absorption rate for frequencies from 30 MHz to 3 GHz. , 2008, Physics in medicine and biology.

[21]  R. O. Price,et al.  Plasma membrane voltage changes during nanosecond pulsed electric field exposure. , 2006, Biophysical journal.

[22]  L. Chernomordik,et al.  The electrical breakdown of cell and lipid membranes: the similarity of phenomenologies. , 1987, Biochimica et biophysica acta.

[23]  Lucie Delemotte,et al.  Molecular Dynamics Simulations of Lipid Membrane Electroporation , 2012, The Journal of Membrane Biology.

[24]  Boris Rubinsky,et al.  Cancer Cells Ablation with Irreversible Electroporation , 2005, Technology in cancer research & treatment.

[25]  Kyle C. Smith,et al.  A unified model of electroporation and molecular transport , 2011 .

[26]  Wanda Krassowska,et al.  Asymptotic model of electroporation , 1999 .

[27]  P. Thomas Vernier,et al.  Life Cycle of an Electropore: Field-Dependent and Field-Independent Steps in Pore Creation and Annihilation , 2010, The Journal of Membrane Biology.

[28]  James C. Weaver,et al.  Determination of the electric field and anomalous heating caused by exponential pulses with aluminum electrodes in electroporation experiments , 1996 .

[29]  V A Parsegian,et al.  ION‐MEMBRANE INTERACTIONS AS STRUCTURAL FORCES , 1975, Annals of the New York Academy of Sciences.

[30]  Daniela O. H. Suzuki,et al.  Theoretical and Experimental Analysis of Electroporated Membrane Conductance in Cell Suspension , 2011, IEEE Transactions on Biomedical Engineering.

[31]  W. Krassowska,et al.  Electrical energy required to form large conducting pores. , 2003, Bioelectrochemistry.

[32]  Caterina Merla,et al.  Novel Passive Element Circuits for Microdosimetry of Nanosecond Pulsed Electric Fields , 2012, IEEE Transactions on Biomedical Engineering.

[33]  Uwe Pliquett,et al.  Nonlinear current-voltage relationship of the plasma membrane of single CHO cells. , 2007, Bioelectrochemistry.

[34]  Stefania Romeo,et al.  Water influx and cell swelling after nanosecond electropermeabilization. , 2013, Biochimica et biophysica acta.

[35]  James C. Weaver,et al.  Emergence of a large pore subpopulation during electroporating pulses. , 2014, Bioelectrochemistry.

[36]  Caterina Merla,et al.  Microdosimetry for Nanosecond Pulsed Electric Field Applications: A Parametric Study for a Single Cell , 2011, IEEE Transactions on Biomedical Engineering.

[37]  Martin A Gundersen,et al.  Nanoelectropulse-driven membrane perturbation and small molecule permeabilization , 2006, BMC Cell Biology.

[38]  L. Loew,et al.  Quantitative cell biology with the Virtual Cell. , 2003, Trends in cell biology.

[39]  Damijan Miklavcic,et al.  Second-order model of membrane electric field induced by alternating external electric fields , 2000, IEEE Transactions on Biomedical Engineering.

[40]  Mounir Tarek,et al.  Membrane electroporation: a molecular dynamics simulation. , 2005, Biophysical journal.

[41]  I. Vattulainen,et al.  Ion leakage through transient water pores in protein-free lipid membranes driven by transmembrane ionic charge imbalance. , 2007, Biophysical journal.

[42]  Julie Gehl,et al.  Direct therapeutic applications of calcium electroporation to effectively induce tumor necrosis. , 2012, Cancer research.

[43]  Damijan Miklavcic,et al.  Electroporation of Intracellular Liposomes Using Nanosecond Electric Pulses—A Theoretical Study , 2013, IEEE Transactions on Biomedical Engineering.

[44]  Boris Rubinsky,et al.  Optimal parameters for the destruction of prostate cancer using irreversible electroporation. , 2008, The Journal of urology.

[45]  H. Itoh,et al.  Electroporation of cell membrane visualized under a pulsed-laser fluorescence microscope. , 1988, Biophysical journal.

[46]  D. Tieleman,et al.  Atomistic simulations of pore formation and closure in lipid bilayers. , 2014, Biophysical journal.

[47]  Damijan Miklavcic,et al.  Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields. , 2006, Biophysical journal.

[48]  Martin A Gundersen,et al.  Nanopore formation and phosphatidylserine externalization in a phospholipid bilayer at high transmembrane potential. , 2006, Journal of the American Chemical Society.

[49]  Helmut Grubmüller,et al.  Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations. , 2008, Biophysical journal.

[50]  Sugár Ip The effects of external fields on the structure of lipid bilayers. , 1981 .

[51]  James C. Weaver,et al.  Electroporation: a unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes☆ , 1991 .

[52]  C Sauterey,et al.  Osmotic pressure induced pores in phospholipid vesicles. , 1975, Biochemistry.

[53]  A. T. Esser,et al.  Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Y. Chizmadzhev,et al.  251 - Electric breakdown of bilayer lipid membranes VI. A stochastic theory taking into account the processes of defect formation and death: Membrane lifetime distribution function , 1979 .

[55]  Juergen F Kolb,et al.  Membrane permeabilization and cell damage by ultrashort electric field shocks. , 2007, Archives of biochemistry and biophysics.

[56]  I. Chatterjee,et al.  Modulation of intracellular Ca2+ levels in chromaffin cells by nanoelectropulses. , 2012, Bioelectrochemistry.

[57]  M. Prausnitz,et al.  Quantitative study of electroporation-mediated molecular uptake and cell viability. , 2001, Biophysical journal.

[58]  Juergen F Kolb,et al.  Long‐lasting plasma membrane permeabilization in mammalian cells by nanosecond pulsed electric field (nsPEF) , 2007, Bioelectromagnetics.

[59]  Boris Rubinsky,et al.  Model of pore formation in a single cell in a flow-through channel with micro-electrodes , 2014, Biomedical microdevices.

[60]  R. Benz,et al.  Reversible electrical breakdown of lipid bilayer membranes: A charge-pulse relaxation study , 1979, The Journal of Membrane Biology.

[61]  Martin L. Yarmush,et al.  Nonthermal Irreversible Electroporation: Fundamentals, Applications, and Challenges , 2013, IEEE Transactions on Biomedical Engineering.

[62]  Alan E Mark,et al.  Simulation of pore formation in lipid bilayers by mechanical stress and electric fields. , 2003, Journal of the American Chemical Society.

[63]  Joseph A. Bank,et al.  Supporting Online Material Materials and Methods Figs. S1 to S10 Table S1 References Movies S1 to S3 Atomic-level Characterization of the Structural Dynamics of Proteins , 2022 .

[64]  Damijan Miklavčič,et al.  Nanosecond electric pulses cause mitochondrial membrane permeabilization in Jurkat cells , 2012, Bioelectromagnetics.

[65]  James C Weaver,et al.  Transmembrane molecular transport during versus after extremely large, nanosecond electric pulses. , 2011, Biochemical and biophysical research communications.

[66]  J. Weaver,et al.  Theory of electroporation: A review , 1996 .

[67]  L. Chernomordik,et al.  Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer. , 2001, Biophysical journal.

[68]  James C Weaver,et al.  An approach to electrical modeling of single and multiple cells , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[69]  Michael P. Eastwood,et al.  Atomic-level simulation of current–voltage relationships in single-file ion channels , 2013, The Journal of general physiology.

[70]  Hao Lin,et al.  Numerical simulation of molecular uptake via electroporation. , 2011, Bioelectrochemistry.

[71]  Damijan Miklavcic,et al.  The effect of high frequency electric pulses on muscle contractions and antitumor efficiency in vivo for a potential use in clinical electrochemotherapy. , 2005, Bioelectrochemistry.

[72]  L. Chernomordik,et al.  Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. , 1988, Biochimica et biophysica acta.

[73]  K. Schoenbach,et al.  Nanosecond, high‐intensity pulsed electric fields induce apoptosis in human cells , 2003, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[74]  W Krassowska,et al.  Modeling electroporation in a single cell. II. Effects Of ionic concentrations. , 1999, Biophysical journal.

[75]  Richard Nuccitelli,et al.  First‐in‐human trial of nanoelectroablation therapy for basal cell carcinoma: proof of method , 2014, Experimental dermatology.

[76]  Kenneth R. Foster,et al.  Thermal and nonthermal mechanisms of interaction of radio-frequency energy with biological systems , 2000 .

[77]  D. Miklavčič,et al.  Cell electrofusion using nanosecond electric pulses , 2013, Scientific Reports.

[78]  A. Parsegian,et al.  Energy of an Ion crossing a Low Dielectric Membrane: Solutions to Four Relevant Electrostatic Problems , 1969, Nature.

[79]  M. Breton,et al.  Microsecond and nanosecond electric pulses in cancer treatments , 2012, Bioelectromagnetics.

[80]  K. Schoenbach,et al.  Nanosecond pulsed electric field (nsPEF) effects on cells and tissues: apoptosis induction and tumor growth inhibition , 2001, PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference. Digest of Papers (Cat. No.01CH37251).

[81]  James C. Weaver,et al.  Intracellular electroporation site distributions: Modeling examples for nsPEF and IRE pulse waveforms , 2011, 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[82]  James C. Weaver,et al.  Decreased bilayer stability due to transmembrane potentials , 1981 .

[83]  Laura Marcu,et al.  In vitro and in vivo evaluation and a case report of intense nanosecond pulsed electric field as a local therapy for human malignancies , 2007, International journal of cancer.

[84]  A. T. Esser,et al.  Mechanisms for the intracellular manipulation of organelles by conventional electroporation. , 2010, Biophysical journal.

[85]  A. T. Esser,et al.  Towards Solid Tumor Treatment by Irreversible Electroporation: Intrinsic Redistribution of Fields and Currents in Tissue , 2007, Technology in cancer research & treatment.

[86]  U. Pliquett,et al.  Nanosecond pulsed electric fields cause melanomas to self-destruct , 2006, Conference Record of the 2006 Twenty-Seventh International Power Modulator Symposium.

[87]  James C Weaver,et al.  Electrical behavior and pore accumulation in a multicellular model for conventional and supra-electroporation. , 2006, Biochemical and biophysical research communications.

[88]  Caixin Sun,et al.  Analysis of Transmembrane Potentials Induced by Pulsed Electric Field with Different Durations Based on Five-shelled Dielectric Model of Cell , 2005, 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference.

[89]  A. T. Esser,et al.  A brief overview of electroporation pulse strength-duration space: a region where additional intracellular effects are expected. , 2012, Bioelectrochemistry.

[90]  Damijan Miklavcic,et al.  Quantitative model of small molecules uptake after in vitro cell electropermeabilization. , 2003, Bioelectrochemistry.

[91]  James C Weaver,et al.  Active mechanisms are needed to describe cell responses to submicrosecond, megavolt-per-meter pulses: cell models for ultrashort pulses. , 2008, Biophysical journal.

[92]  W. Krassowska,et al.  Modeling electroporation in a single cell. , 2007, Biophysical journal.

[93]  K. Schoenbach,et al.  Bioelectric effects of intense ultrashort pulses. , 2010, Critical reviews in biomedical engineering.

[94]  W. Krassowska,et al.  Modeling electroporation in a single cell. I. Effects Of field strength and rest potential. , 1999, Biophysical journal.

[95]  Thomas Berghöfer,et al.  Transmembrane potential measurements on plant cells using the voltage-sensitive dye ANNINE-6 , 2010, 2008 IEEE 35th International Conference on Plasma Science.

[96]  P. Vernier,et al.  Nanosecond field alignment of head group and water dipoles in electroporating phospholipid bilayers. , 2007, The journal of physical chemistry. B.

[97]  U. Zimmermann,et al.  Reversible Electropermeabilization of Mammalian Cells by High-Intensity, Ultra-Short Pulses of Submicrosecond Duration , 2001, The Journal of Membrane Biology.

[98]  K. Schoenbach,et al.  Intracellular effect of ultrashort electrical pulses , 2001, Bioelectromagnetics.

[99]  L. Mir,et al.  Very high cytotoxicity of bleomycin introduced into the cytosol of cells in culture. , 1991, Biochemical pharmacology.

[100]  Hao Lin,et al.  Quantification of propidium iodide delivery using millisecond electric pulses: experiments. , 2013, Biochimica et biophysica acta.

[101]  E. Neumann,et al.  Ionic conductivity of electroporated lipid bilayer membranes. , 2002, Bioelectrochemistry.

[102]  P. Lamberti,et al.  Influence of Uncertain Electrical Properties on the Conditions for the Onset of Electroporation in an Eukaryotic Cell , 2010, IEEE Transactions on NanoBioscience.

[103]  S. Hagness,et al.  Cationic Peptide Exposure Enhances Pulsed-Electric-Field-Mediated Membrane Disruption , 2014, PloS one.

[104]  N. Chavannes,et al.  Mastering Conformal Meshing for Complex CAD-Based C-FDTD Simulations , 2008, IEEE Antennas and Propagation Magazine.

[105]  Isabelle Leray,et al.  Demonstration of cell membrane permeabilization to medium-sized molecules caused by a single 10 ns electric pulse. , 2012, Bioelectrochemistry.

[106]  Boris Rubinsky,et al.  Electrical impedance tomography for imaging tissue electroporation , 2004, IEEE Transactions on Biomedical Engineering.