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

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Abstract

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.

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Abbreviations

c :

Capture onset potential

CM(n) :

General Clausius-Mossotti factor

d :

Distance

DEP:

Dielectrophoresis

e :

Electric unit charge

E :

Electric field strength

E ave :

Average electric field magnitude

E ave(V):

Average electric field magnitude as a function of the applied potential

eDEP:

Electrode-based dielectrophoresis

E max :

Electric field local maximum magnitude

E max(V):

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

F :

Dielectrophoretic force

f CM :

Clausius-Mossotti factor

FI:

Fluorescence intensity

FIobs :

Observed fluorescence intensity

h :

Height

I :

Identity tensor

iDEP:

Insulator-based dielectrophoresis

n :

Average particle density

N :

Number of particles

N c :

Surface charge density

p n :

nth-order multipolar moment

r :

Radius

s :

Stack factor

t :

Time

v :

Velocity

V :

Applied potential

v DEP :

Dielectrophoretic velocity

v EK :

Electrokinetic velocity

v EOF :

Electroosmotic velocity

v EP :

Electrophoretic velocity

w :

Average width

z :

Valence of charged groups

β 0 :

Monopole moment

β 2 :

Quadrupole moment

γ :

Nominal integrated fluorescence signal for an average particle

ε :

Permittivity

ε ∗ :

Complex permittivity

ζ :

Zeta potential

η :

Viscosity

κ m :

Debye-Huckel parameter

λ −1 :

Surface softness

μ DEP :

Dielectrophoretic mobility

μ EK :

Electrokinetic mobility

μ EOF :

Electroosmotic mobility

μ EP :

Electrophoretic mobility

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

Electric potential due to the particle

ψ(0):

Potential at the boundary

ψ DON :

Donnan potential

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Acknowledgements

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

Funding

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

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  1. School of Molecular Sciences, Arizona State University, Mail Stop 1604, Tempe, AZ, 85281, USA

    Shannon Huey Hilton & Mark A. Hayes

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

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Hilton, S.H., Hayes, M.A. A mathematical model of dielectrophoretic data to connect measurements with cell properties. Anal Bioanal Chem 411, 2223–2237 (2019). https://doi.org/10.1007/s00216-019-01757-7

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