A mathematical model of dielectrophoretic data to connect measurements with cell properties

  • Shannon Huey Hilton
  • Mark A. HayesEmail author
Research Paper


Dielectrophoresis (DEP) brings about the high-resolution separations of cells and other bioparticles arising from very subtle differences in their properties. However, an unanticipated limitation has arisen: difficulty in assignment of specific biological features which vary between two cell populations. This hampers the ability to interpret the significance of the variations. To realize the opportunities made possible by dielectrophoresis, the data and the diversity of structures found in cells and bioparticles must be linked. While the crossover frequency in DEP has been studied in-depth and exploited in applications using AC fields, less attention has been given when a DC field is present. Here, a new mathematical model of dielectrophoretic data is introduced which connects the physical properties of cells to specific elements of the data from potential- or time-varied DEP experiments. The slope of the data in either analysis is related to the electrokinetic mobility, while the potential at which capture initiates in potential-based analysis is related to both the electrokinetic and dielectrophoretic mobilities. These mobilities can be assigned to cellular properties for which values appear in the literature. Representative examples of high and low values of properties such as conductivity, zeta potential, and surface charge density for bacteria including Streptococcus mutans, Rhodococcus erythropolis, Pasteurella multocida, Escherichia coli, and Staphylococcus aureus are considered. While the many properties of a cell collapse into one or two features of data, for a well-vetted system the model can indicate the extent of dissimilarity. The influence of individual properties on the features of dielectrophoretic data is summarized, allowing for further interpretation of data.

Graphical abstract


Dielectrophoresis Electrophoresis Electrokinetic mobility Bacterial variations Biophysical properties Data modeling 



Capture onset potential


General Clausius-Mossotti factor






Electric unit charge


Electric field strength


Average electric field magnitude


Average electric field magnitude as a function of the applied potential


Electrode-based dielectrophoresis


Electric field local maximum magnitude


Electric field local maximum magnitude as a function of the applied potential


Dielectrophoretic force


Clausius-Mossotti factor


Fluorescence intensity


Observed fluorescence intensity




Identity tensor


Insulator-based dielectrophoresis


Average particle density


Number of particles


Surface charge density


nth-order multipolar moment




Stack factor






Applied potential


Dielectrophoretic velocity


Electrokinetic velocity


Electroosmotic velocity


Electrophoretic velocity


Average width


Valence of charged groups


Monopole moment


Quadrupole moment


Nominal integrated fluorescence signal for an average particle




Complex permittivity


Zeta potential




Debye-Huckel parameter


Surface softness


Dielectrophoretic mobility


Electrokinetic mobility


Electroosmotic mobility


Electrophoretic mobility

\( {\varPhi}_{r_{\mathrm{int}}} \)

Electric potential due to the particle


Potential at the boundary


Donnan potential



The authors acknowledge Claire Crowther for her assistance in this work.

Funding information

This work was supported by the National Institutes of Health grants 1R03AI094193-01, 1R03AI099740-01, 1R03AI111361-01, 1R21AI130855-01, and 1R03AI133397-01.

Compliance with ethical standards

Conflict of interest

Shannon Huey Hilton and Mark A. Hayes declare a conflict of interest with regard to Charlot Biosciences.


  1. 1.
    Pohl HA. The motion and precipitation of suspensoids in divergent electric fields. J Appl Phys. 1951;22:869–71.CrossRefGoogle Scholar
  2. 2.
    Pethig R. Where is dielectrophoresis (dep) going? J Electrochem Soc. 2016;164:B3049–B55.CrossRefGoogle Scholar
  3. 3.
    Asbury CL, Dierks AH, van den Engh G. Trapping of DNA by dielectrophoresis. Electrophoresis. 2002;23:2658–66.CrossRefGoogle Scholar
  4. 4.
    Chou C-F, Tegenfeldt JO, Bakajin O, Chan SS, Cox EC, Darnton N, et al. Electrodless dielectrophoresis of single- and double-stranded DNA. Biophys J. 2002;83:2170–9.CrossRefGoogle Scholar
  5. 5.
    Gascoyne PRC, Noshari J, Anderson TJ, Becker FF. Isolation of rare cells from cell mixtures by dielectrophoresis. Electrophoresis. 2009;30:1388–98.CrossRefGoogle Scholar
  6. 6.
    Jones PV, DeMichele AF, Kemp L, Hayes MA. Differentiation of Escherichia coli serotypes using dc gradient insulator dielectrophoresis. Anal Bioanal Chem. 2014;406:183–92.CrossRefGoogle Scholar
  7. 7.
    Lapizco-Encinas BH, Ozuna-Chacon S, Rito-Palomares M. Protein manipulation with insulator-based dielectrophoresis and direct current electric fields. J Chromatogr A. 2008;1206:45–51.CrossRefGoogle Scholar
  8. 8.
    Lapizco-Encinas BH, Simmons BA, Cummings EB, Fintschenko Y. Dielectrophoretic concentration and separation of live and dead bacteria in an array of insulators. Anal Chem. 2004;76:1571–9.CrossRefGoogle Scholar
  9. 9.
    Markx GH, Huang Y, Zhou X-F, Pethig R. Dielectrophoretic characterization and separation of micro-organisms. Microbiology. 1994;140:585–91.CrossRefGoogle Scholar
  10. 10.
    Otto S, Kaletta U, Bier FF, Wenger C, Holzel R. Dielectrophoretic immobilisation of antibodies on microelectrode arrays. Lab Chip. 2014;14:998–1004.CrossRefGoogle Scholar
  11. 11.
    Regtmeier J, Duong TT, Eichhorn R, Anselmetti D, Ros A. Dielectrophoretic manipulation of DNA: separation and polarizability. Anal Chem. 2007;79:3925–32.CrossRefGoogle Scholar
  12. 12.
    Staton SJR, Jones PV, Ku G, Gilman SD, Kheterpal I, Hayes MA. Manipulation and capture of abeta amyloid fibrils and monomers by dc insulator gradient dielectrophoresis (dc-igdep). Analyst. 2012;137:3227–9.CrossRefGoogle Scholar
  13. 13.
    Wang X-B, Huang Y, Burt JPH, Markx GH, Pethig R. Selective dielectrophoretic confinement of bioparticles in potential energy wells. J Phys D Appl Phys. 1993;26:1276–85.Google Scholar
  14. 14.
    Washizu M, Suzuki S, Kurosawa O, Nishizaka T, Shinohara T. Molecular dielectrophoresis of biopolymers. IEEE Trans Ind Appl. 1994;30:835–43.CrossRefGoogle Scholar
  15. 15.
    Adams TNG, Leonard KM, Minerick AR. Frequency sweep rate dependence on the dielectrophoretic response of polystyrene beads and red blood cells. Biomicrofluidics. 2013;7:64114.CrossRefGoogle Scholar
  16. 16.
    Jones PV, Staton SJR, Hayes MA. Blood cell capture in a sawtooth dielectrophoretic microchannel. Anal Bioanal Chem. 2011;401:2103–11.CrossRefGoogle Scholar
  17. 17.
    Huang Y, Holzel R, Pethig R, Wang X-B. Differences in the ac electrodynamics of viable and non-viable yeast cells determined through combined dielectrophoresis and electrorotation studies. Phys Med Biol. 1992;37:1499–517.CrossRefGoogle Scholar
  18. 18.
    Jones TB. Electromechanics of particles. New York: Cambridge University Press; 1995.CrossRefGoogle Scholar
  19. 19.
    Pethig R. Dielectrophoresis: status of the theory, technology, and applications. Biomicrofluidics. 2010;4:022811.CrossRefGoogle Scholar
  20. 20.
    Pohl HA. Dielectrophoresis the behavior of neutral matter in nonuniform electric fields. New York: Cambridge University Press; 1978.Google Scholar
  21. 21.
    Washizu M, Jones TB. Multipolar dielectrophoretic force calculation. J Electrost. 1994;33:187–98.CrossRefGoogle Scholar
  22. 22.
    Crane JS, Pohl HA. The dielectric properties of single yeast cells. J Electrost. 1978;5:11–9.CrossRefGoogle Scholar
  23. 23.
    Gagnon ZR. Cellular dielectrophoresis: applications to the characterization, manipulation, separation and patterning of cells. Electrophoresis. 2011;32:2466–87.CrossRefGoogle Scholar
  24. 24.
    Cummings EB, Singh AK. Dielectrophoresis in microchips containing arrays of insulating posts: theoretical and experimental results. Anal Chem. 2003;75:4724–31.CrossRefGoogle Scholar
  25. 25.
    Becker FF, Wang X-B, Huang Y, Pethig R, Vykoukal J, Gascoyne PRC. Separation of human breast cancer cells from blood by differential dielectric affinity. Proc Natl Acad Sci U S A. 1995;92:860–4.CrossRefGoogle Scholar
  26. 26.
    Rohani A, Moore JH, Kashatus JA, Sesaki H, Kashatus DF, Swami NS. Label-free quantification of intracellular mitochondrial dynamics using dielectrophoresis. Anal Chem. 2017;89:5757–64.CrossRefGoogle Scholar
  27. 27.
    Adams TNG, Jiang AYL, Vyas PD, Flanagan LA. Separation of neural stem cells by whole cell membrane capacitance using dielectrophoresis. Methods. 2018;133:91–103.CrossRefGoogle Scholar
  28. 28.
    Srivastava SK, Daggolu PR, Burgess SC, Minerick AR. Dielectrophoretic characterization of erythrocytes: positive abo blood types. Electrophoresis. 2008;29:5033–46.CrossRefGoogle Scholar
  29. 29.
    Jones PV, Huey S, Davis P, Yanashima R, McLemore R, McLaren A, et al. Biophysical separation of Staphylococcus epidermidis strains based on antibiotic resistance. Analyst. 2015;140:5152–61.CrossRefGoogle Scholar
  30. 30.
    Braff WA, Willner D, Hugenholtz P, Rabaey K, Buie CR. Dielectrophoresis-based discrimination of bacteria at the strain level based on their surface properties. PLoS One. 2013;8:e76751.CrossRefGoogle Scholar
  31. 31.
    Jones PV, Hayes MA. Development of the resolution theory for gradient insulator-based dielectrophoresis. Electrophoresis. 2015;36:1098–106.CrossRefGoogle Scholar
  32. 32.
    LaLonde A, Romero-Creel MF, Saucedo-Espinosa MA, Lapizco-Encinas BH. Isolation and enrichment of low abundant particles with insulator-based dielectrophoresis. Biomicrofluidics. 2015;9:064113.CrossRefGoogle Scholar
  33. 33.
    Minerick AR. The rapidly growing field of micro and nanotechnology to measure living cells. AICHE J. 2008;54:2230–7.CrossRefGoogle Scholar
  34. 34.
    Saucedo-Espinosa MA, Lapizco-Encinas BH. Experimental and theoretical study of dielectrophoretic particle trapping in arrays of insulating structures: effect of particle size and shape. Electrophoresis. 2015;36:1086–97.CrossRefGoogle Scholar
  35. 35.
    Staton SJR, Chen KP, Taylor TJ, Pacheco JR, Hayes MA. Characterization of particle capture in a sawtooth patterned insulating electrokinetic microfluidic device. Electrophoresis. 2010;31:3634–41.CrossRefGoogle Scholar
  36. 36.
    Davies JT, Rideal EK. Interfacial phenomena. New York: Academic Press; 1961.Google Scholar
  37. 37.
    Nguyen N-T, Wereley ST. Fundamentals and applications of microfluidics. 2nd ed. Boston: Artech House; 2006.Google Scholar
  38. 38.
    Tabeling P. Introduction to microfluidics. New York: Oxford University Press; 2005.Google Scholar
  39. 39.
    Clarke RW, Piper JD, Ying L, Klenerman D. Surface conductivity of biological macromolecules measured by nanopipette dielectrophoresis. Phys Rev Lett. 2007;98:198102.CrossRefGoogle Scholar
  40. 40.
    Nili H, Green NG. Higher-order dielectrophoresis of nonspherical particles. Phys Rev E Stat Nonlinear Soft Matter Phys. 2014;89:063302.CrossRefGoogle Scholar
  41. 41.
    Irimajiri A, Hanai T, Inoyue A. A dielectric theory of “multi-stratified shell” model with its application to a lymphoma cell. J Theor Biol. 1979;78:251–69.CrossRefGoogle Scholar
  42. 42.
    Bai W, Zhao K, Asami K. Effects of copper on dielectric properties of E. coli cells. Colloids Surf B. 2007;58:105–15.CrossRefGoogle Scholar
  43. 43.
    Kakutani T, Shibatani S, Sugai M. Electrorotation of non-spherical cells: theory for ellipsoidal cells with an arbitrary number of shells. Bioelectrochem Bioenerg. 1993;31:131–45.CrossRefGoogle Scholar
  44. 44.
    Ohshima H, Kondo T. Electrophoretic mobility and Donnan potential of a large colloidal particle with a surface charge layer. J Colloid Interface Sci. 1987;116:305–11.CrossRefGoogle Scholar
  45. 45.
    Ohshima H, Kondo T. Approximate analytic expression for the electrophoretic mobility of colloidal particles with surface-charge layers. J Colloid Interface Sci. 1989;130:281–2.CrossRefGoogle Scholar
  46. 46.
    Sonohara R, Muramatsu N, Ohshima H, Kondo T. Difference in surface properties between Escherichia coli and Staphylococcus aureus as revealed by electrophoretic mobility measurements. Biophys Chem. 1995;55:273–7.CrossRefGoogle Scholar
  47. 47.
    Daly E, Saunders BR. Temperature–dependent electrophoretic mobility and hydrodynamic radius measurements of poly(n-isopropylacrylamide) microgel particles: structural insights. Phys Chem Chem Phys. 2000;2:3187–93.CrossRefGoogle Scholar
  48. 48.
    Ortega-Vinuesa JL, Hidalgo-Alvarez R, de las Nieves FJ, Davey CL, Newman DJ, Price CP. Characterization of immunoglobulin g bound to latex particles using surface plasmon resonance and electrophoretic mobility. J Colloid Interface Sci. 1998;204:300–11.CrossRefGoogle Scholar
  49. 49.
    Takashima S, Morisaki H. Surface characteristics of the microbial cell of pseudomonas syringae and its relevance to cell attachment. Colloids Surf B. 1997;9:205–12.CrossRefGoogle Scholar
  50. 50.
    Torimura M, Ito S, Kano K, Ikeda T, Esaka Y, Ueda T. Surface characterization and on-line activity measurements of microorganism by capillary zone electrophoresis. J Chromatogr B. 1999;721:31–7.CrossRefGoogle Scholar
  51. 51.
    Anderson JL. Effect of nonuniform zeta potential on particle movement in electric fields. J Colloid Interface Sci. 1985;105:45–54.CrossRefGoogle Scholar
  52. 52.
    Fair MC, Anderson JL. Electrophoresis of nonuniformly charged ellipsoidal particles. J Colloid Interface Sci. 1989;127:388–400.CrossRefGoogle Scholar
  53. 53.
    Pysher MD, Hayes MA. Effects of deformability, uneven surface charge distributions, and multipole moments on biocolloid electrophoretic migration. Langmuir. 2005;21:3572–7.CrossRefGoogle Scholar
  54. 54.
    Dinpajooh M, Matyushov DV. Dielectric constant of water in the interface. J Chem Phys. 2016;145:014504.CrossRefGoogle Scholar
  55. 55.
    Dinpajooh M, Matyushov DV. Mobility of nanometer-size solutes in water driven by electric field. Phys A. 2016;463:366–75.CrossRefGoogle Scholar
  56. 56.
    Matyushov DV. Dipole solvation in dielectrics. J Chem Phys. 2004;120:1375–82.CrossRefGoogle Scholar
  57. 57.
    Matyushov DV. Dipolar response of hydrated proteins. J Chem Phys. 2012;136:085102.CrossRefGoogle Scholar
  58. 58.
    Matyushov DV. Electrophoretic mobility without charge driven by polarisation of the nanoparticle–water interface. Mol Phys. 2014;112:2029–39.CrossRefGoogle Scholar
  59. 59.
    Seyedi S, Matyushov DV. Dipolar susceptibility of protein hydration shells. Chem Phys Lett. 2018;712 accepted (preprint available from corresponding author).Google Scholar
  60. 60.
    Crowther CV, Hayes MA. Refinement of insulator-based dielectrophoresis. Analyst. 2017;142:1608–18.CrossRefGoogle Scholar
  61. 61.
    Braff WA, Pignier A, Buie CR. High sensitivity three-dimensional insulator-based dielectrophoresis. Lab Chip. 2012;12:1327–31.CrossRefGoogle Scholar
  62. 62.
    Camacho-Alanis F, Gan L, Ros A. Transitioning streaming to trapping in dc insulator-based dielectrophoresis for biomolecules. Sensors Actuators B Chem. 2012;173:668–75.CrossRefGoogle Scholar
  63. 63.
    Ding J, Lawrence RM, Jones PV, Hogue BG, Hayes MA. Concentration of sindbis virus with optimized gradient insulator-based dielectrophoresis. Analyst. 2016;141:1997–2008.CrossRefGoogle Scholar
  64. 64.
    Ding J, Woolley C, Hayes MA. Biofluid pretreatment using gradient insulator-based dielectrophoresis: separating cells from biomarkers. Anal Bioanal Chem. 2017;409:6405–14.CrossRefGoogle Scholar
  65. 65.
    Nakano A, Camacho-Alanis F, Ros A. Insulator-based dielectrophoresis with beta-galactosidase in nanostructured devices. Analyst. 2015;140:860–8.CrossRefGoogle Scholar
  66. 66.
    Polniak DV, Goodrich E, Hill N, Lapizco-Encinas BH. Separating large microscale particles by exploiting charge differences with dielectrophoresis. J Chromatogr A. 2018;1545:84–92.CrossRefGoogle Scholar
  67. 67.
    Rabbani MT, Schmidt CF, Ros A. Single-walled carbon nanotubes probed with insulator-based dielectrophoresis. Anal Chem. 2017;89:13235–44.CrossRefGoogle Scholar
  68. 68.
    Saucedo-Espinosa MA, LaLonde A, Gencoglu A, Romero-Creel MF, Dolas JR, Lapizco-Encinas BH. Dielectrophoretic manipulation of particle mixtures employing asymmetric insulating posts. Electrophoresis. 2016;37:282–90.CrossRefGoogle Scholar
  69. 69.
    Brazey B, Cottet J, Bolopion A, Van Lintel H, Renaud P, Gauthier M. Impedance-based real-time position sensor for lab-on-a-chip devices. Lab Chip. 2018;18:818–31.CrossRefGoogle Scholar
  70. 70.
    Chuang C-H, Huang Y-W. Condensation of fluorescent nanoparticles using a dep chip with a dot-electrode array. Microelectron Eng. 2012;97:317–23.CrossRefGoogle Scholar
  71. 71.
    Lapizco-Encinas BH, Simmons BA, Cummings EB, Fintschenko Y. Insulator-based dielectrophoresis for the selective concentration and separation of live bacteria in water. Electrophoresis. 2004;25:1695–704.CrossRefGoogle Scholar
  72. 72.
    Moncada-Hernandez H, Baylon-Cardiel JL, Perez-Gonzalez VH, Lapizco-Encinas BH. Insulator-based dielectrophoresis of microorganisms: theoretical and experimental results. Electrophoresis. 2011;32:2502–11.CrossRefGoogle Scholar
  73. 73.
    Ozuna-Chacon S, Lapizco-Encinas BH, Rito-Palomares M, Martinez-Chapa SO, Reyes-Betanzo C. Performance characterization of an insulator-based dielectrophoretic microdevice. Electrophoresis. 2008;29:3115–22.CrossRefGoogle Scholar
  74. 74.
    Wang Z, Han T, Jeon T-J, Park S, Kim SM. Rapid detection and quantification of bacteria using an integrated micro/nanofluidic device. Sensors Actuators B Chem. 2013;178:683–8.CrossRefGoogle Scholar
  75. 75.
    Tomizawa Y, Tamiya E, Takamura Y. Trapping probability analysis of a DNA trap using electric and hydrodrag force fields in tapered microchannels. Phys Rev E Stat Nonlinear Soft Matter Phys. 2009;79:051902.CrossRefGoogle Scholar
  76. 76.
    Pethig R. Dielectrophoresis : theory, methodology and biological applications. 1st ed. Hoboken: Wiley; 2017.CrossRefGoogle Scholar
  77. 77.
    Markx GH, Davey CL. The dielectric properties of biological cells at radiofrequencies: applications in biotechnology. Enzym Microb Technol. 1999;25:161–71.CrossRefGoogle Scholar
  78. 78.
    Pethig R, Markx GH. Applications of dielectrophoresis in biotechnology. Trends Biotechnol. 1997;15:426–32.CrossRefGoogle Scholar
  79. 79.
    Holzel R. Non-invasive determination of bacterial single cell properties by electrorotation. Biochim Biophys Acta. 1999;1450:53–60.CrossRefGoogle Scholar
  80. 80.
    Olsson J, Glantz P-O. Effect of ph and counter ions on the zeta-potential of oral streptococci. Arch Oral Biol. 1977;22:461–6.CrossRefGoogle Scholar
  81. 81.
    van der Wal A, Minor M, Norde W, Zehnder AJB, Lyklema J. Conductivity and dielectric dispersion of gram-positive bacterial cells. J Colloid Interface Sci. 1997;186:71–9.CrossRefGoogle Scholar
  82. 82.
    Wilson WW, Wade MM, Holman SC, Champlin FR. Status of methods for assessing bacterial cell surface charge properties based on zeta potential measurements. J Microbiol Methods. 2001;43:153–64.CrossRefGoogle Scholar
  83. 83.
    Kiers PJM, Bos R, van der Mei HC, Busscher HJ. The electrophoretic softness of the surface of Staphylococcus epidermidis cells grown in a liquid medium and on a solid agar. Microbiology. 2001;147:757–62.CrossRefGoogle Scholar
  84. 84.
    Schnelle T, Muller T, Fiedler S, Fuhr G. The influence of higher moments on particle behaviour in dielectrophoretic field cages. J Electrost. 1999;46:13–28.CrossRefGoogle Scholar
  85. 85.
    Liang E, Smith RL, Clague DS. Dielectrophoretic manipulation of finite sized species and the importance of the quadrupolar contribution. Phys Rev E Stat Nonlinear Soft Matter Phys. 2004;70:066617.CrossRefGoogle Scholar
  86. 86.
    Washizu M, Jones TB, Kaler KVIS. Higher-order dielectrophoretic effects: levitation at a field null. Biochim Biophys Acta. 1993;1158:40–6.CrossRefGoogle Scholar
  87. 87.
    Washizu M. Precise calculation of dielectrophoretic force in arbitrary field. J Electrost. 1992;29:177–88.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Molecular SciencesArizona State UniversityTempeUSA

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