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Dielectric characterization of erythrocytes by electrostatic force microscopy

The method of determination of the dielectric constant of individual erythrocytes, based on a quantitative analysis of the profiles of their images obtained by electrostatic force microscopy, is presented. A model of electrostatic interaction between the atomic force microscope probe and the biological cell is proposed. The obtained values of the permittivity of individual erythrocytes agree well with known literature data.


Introduction
The human cells have unique biophysical and biochemical properties that ensure interaction with the surrounding physiological environment to realize the specific functions. The study of mechanical, electrical, and optical parameters of cells is important for clinical diagnostics.
The electrical properties of cells are investigated generally by measuring their response on the external electric field [1], which depends on the shape, size, internal structure, and conductivity of the cell, as well as susceptibility of the cellular components. It should be noted that the response registration is usually performed on large cell populations that leads to averaging the measured parameters. In this case, the properties of individual cells are not taken into evaluation that leads to limited measurement accuracy. The study of individual cells allows determining the heterogeneity of their characteristics within cells population and measuring the samples containing various cell types without their separation [2]. Using the electrostatic force microscopy (EFM) to determine the dielectric response of individual bacterial cells with high precision and reproducibility was demonstrated in [3]. The method of determining the dielectric constant of individual hemoglobin molecules based on the modelling of EFM profiles was presented in [4]. This technique can be adapted to determine the dielectric constant of individual erythrocytes, also called red blood cells (RBC) that perform a fundamental physiological function of living organisms -transport of respiratory gasses. The purpose of this work is application of EFM method for dielectric characterization of individual RBC.

Materials and methods
RBC were separated by centrifugation of whole blood, and then washed three times with isotonic solution. In the next step, RBC were fixed of a 2%-paraformaldehyde solution for 2 h, then transferred to deionized water to achieve concentration equal to 10 8 cells/ml. Aqueous suspension of RBC (15 μl) was deposited on a freshly cleaved surface of highly oriented pyrolytic graphite (HOPG) and incubated for 30 min. Then the samples were washed in deionized water to remove non-adsorbed cells and airdried at room temperature.  Figure 1a shows an example of topography and corresponding EFM-contrast (Fig. 1b) for the individual RBC on HOPG surface at + 3 V at the probe. From topography profiles analysis, the shape of the cells was determined as an almost symmetrical disk with average height of about 80 nm. Figure 1c presents the phase shift (ΔΦ) between RBC and HOPG surface on EFM-profile. Figure 2 demonstrates the EFM measurements for quantitative analysis of experimental data. RBC modelled as a disc with the height H and dielectric constant ε is located on the HOPG. The probe tip is assumed to be a hemisphere with the curvature radius R that is at a fixed height h above the sample.

Results and discussion
The dependence of the phase shift tangent on the square of the applied voltage for studied samples is linear. This indicates that the contrast of EFM-images for RBC is determined only by the probesample capacitive coupling.
The EFM-profiles modelling was performed according to the method described in [4]. To calculate the phase shift between RBC and the probe, the second derivative of the probe-RBC-HOPG capacitance was calculated using the equation: where ε0 -vacuum permittivity, ε -permittivity of individual RBC, y1 =  By fitting the model phase shift to the experimental one, the mean value and the permittivity range of individual RBC were determined to be equal to 2.6 ± 0.8. Since the volume of the RBC is filled with proteins, which, according to the literature, have dielectric permittivity values of 2-4 [3], the obtained value of ε is adequate.
For comparison, RBC permittivity ε was estimated using an effective medium approximation for multilayer dielectric systems [5]. The model of cross profile of RBC has a three-layer structure: a cytoplasmic layer (cytoskeleton filled with hemoglobin), which is located between two membrane layers consisting from lipids (Fig. 3). The fraction of integral membrane proteins is approximately 0.5; however, their dielectric constant is not known; therefore, they were not taken into account in the permittivity calculations.
According to effective medium model, the effective permittivity of two-component medium, in this case, an RBC is written as: where εRBC, εHb, εm -permittivity of RBC, hemoglobin and membrane, fHb and fm -volume fractions of hemoglobin and membrane, respectively.
The measured values of the RBC height from the topography images and the known thickness of the membrane layer (dm ≈ 8 nm [6]) were used for estimation of the volume fractions. As a result, the calculated data were fHb ≈ 0.8 and fm ≈ 0.1, respectively. The necessary permittivity was taken from the literature: εHb ≈ 2.9 [4], εm ≈ 2.0 (permittivity of the membrane was taken for lipids [3]). As a result, permittivity of RBC determined by the relationship (2) was equal to 2.7. This value agrees well with the mean value for permittivity of RBC obtained by EFM. Calculations by effective medium approximation for RBC show that the cytoplasmic membrane provides the lower permittivity for the RBC (equal to 2.7) compared with the permittivity of its main component -hemoglobin (equal to 2.9).

Conclusion
The technique described in [4] is adapted to determine the permittivity of individual erythrocytes taking into account the features of electrostatic interaction between an atomic force microscope probe and a biological cell on the substrate surface. This method allows determining the values of the permittivity of individual erythrocytes, which is in good agreement with the known literature data and corresponds to the value obtained by the effective medium approximation. The mentioned technique can be applied to study the dielectric characteristics of other individual cells.