Estimation of the physical properties of neurons and glial cells using dielectrophoresis crossover frequency

Abstract

We successfully determine the ranges of dielectric permittivity, cytoplasm conductivity, and specific membrane capacitance of mouse hippocampal neuronal and glial cells using dielectrophoresis (DEP) crossover frequency (CF). This methodology is based on the simulation of CF directly from the governing equation of a dielectric model of mammalian cells, as well as the measurements of DEP CFs of mammalian cells in different suspension media with different conductivities, based on a simple experimental setup. Relationships between the properties of cells and DEP CF, as demonstrated by theoretical analysis, enable the simultaneous estimation of three properties by a straightforward fitting procedure based on experimentally measured CFs. We verify the effectiveness and accuracy of this approach for primary mouse hippocampal neurons and glial cells, whose dielectric properties, previously, have not been accurately determined. The estimated neuronal properties significantly narrow the value ranges available from the literature. Additionally, the estimated glial cell properties are a valuable addition to the scarce information currently available about this type of cell. This methodology is applicable to any type of cultured cell that can be subjected to both positive and negative dielectrophoresis.

Keywords: Crossover frequency; Dielectrophoresis (DEP); Electric properties; Fitting procedure; Hippocampal neurons and glial cells.

Fig. 1

Quadrupole electrode array for cell crossover frequency measurement. Cells are initially positioned in the area indicated by the dashed square

Fig. 2

a Experimental setup for DEP crossover measurement on a probe station. A glass cover slide above the Petri dish is used to stabilize the fluidic surface for better visualization under a microscope. The scale bar is applied towards the surface of the microscope station. b Video frame showing a cell under DEP manipulation

Fig. 3

Comparison of theoretical CFs calculated with a ‘+’ sign (red) and a ‘–’ sign (blue) from expression (7). Black data points represent the measured CFs (stars). The property values of hippocampal neurons used in this calculation are: ɛ _c/ɛ ₀ = 60, σ _c = 0.7 Sm⁻¹, c _m = 0.010 Fm⁻², r = 4.3 μm

Fig. 4

Dielectric property values for mouse hippocampal neurons based on values shown in Table 2 are evaluated, according to experimentally measured CFs. The theoretical CFs in 50% cell media are also calculated in each figure. One property is fit to the experimental values, whereas the other two values are fixed to the values described in each situation. a Cytoplasm dielectric constant values ɛ _c/ɛ ₀ = 40, 60, 75, 85, and 95 are fitted. Smaller values (40, 60) give a slightly better fit. (σ _c = 0.65 Sm⁻¹, c _m = 0.010 Fm⁻²). b Cytoplasm conductivity values σ _c = 0.35, 0.45, 0.55, 0.65, 0.75, 0.85 and 0.95 Sm⁻¹ are fitted. Larger values (0.75–0.95) have a closer fit. (ɛ _c/ɛ ₀ = 60, c _m = 0.010 Fm⁻²). c Membrane effective capacitance values c _m = 0.006, 0.008, 0.01 and 0.012 Fm⁻² are fitted. Larger values (0.01–0.012) provide a closer fit to measured CFs. (ɛ _c/ɛ ₀ = 60, σ _c = 0.75 Sm⁻¹)

Fig. 5

Dielectric property values for mouse hippocampal glial cells given in Table 2 are evaluated according to experimentally measured CFs. One property is fit to the experimental values, whereas the other two values are fixed to the values described in each situation. a Cytoplasm conductivity values σ _c = 0.2, 0.3, 0.4, 0.5 and 0.6 Sm⁻¹ are fitted. Only values σ _c ≥ 0.3 will generate CFs in 20% cell media solution. (ɛ _c/ɛ ₀ = 60, c _m = 0.0106 Fm⁻²). b Cytoplasm dielectric constant values ɛ _c/ɛ ₀ = 40, 60, 75, 85 and 95 are fitted. Smaller values have a slightly closer fit. (σ _c = 0.3 Sm⁻¹, c _m = 0.0106 Fm⁻²). c Membrane effective capacitance values c _m = 0.006, 0.008, 0.01, and 0.012 Fm⁻² are fitted. Larger values (0.01–0.012) give a closer fit to measured data. (ɛ _c/ɛ ₀ = 60, σ _c =0.3 Sm⁻¹)

Fig. 6

Linear fitting of (f ⋅ r) against σ _m, based on data from Fig. 4c and the formula in [26], predicts cell membrane effective capacitance well within our suggested range, verifying the accuracy of our fitting procedure

Fig. 7

Maple simulation of DEP spectra for glial cells. Different cytoplasm conductivity σ _c fit in 30% cell media solution