Modulation of cell function by electric field: a high-resolution analysis

Abstract

Regulation of cell function by a non-thermal, physiological-level electromagnetic field has potential for vascular tissue healing therapies and advancing hybrid bioelectronic technology. We have recently demonstrated that a physiological electric field (EF) applied wirelessly can regulate intracellular signalling and cell function in a frequency-dependent manner. However, the mechanism for such regulation is not well understood. Here, we present a systematic numerical study of a cell-field interaction following cell exposure to the external EF. We use a realistic experimental environment that also recapitulates the absence of a direct electric contact between the field-sourcing electrodes and the cells or the culture medium. We identify characteristic regimes and present their classification with respect to frequency, location, and the electrical properties of the model components. The results show a striking difference in the frequency dependence of EF penetration and cell response between cells suspended in an electrolyte and cells attached to a substrate. The EF structure in the cell is strongly inhomogeneous and is sensitive to the physical properties of the cell and its environment. These findings provide insight into the mechanisms for frequency-dependent cell responses to EF that regulate cell function, which may have important implications for EF-based therapies and biotechnology development.

Keywords: cell transmembrane potential; cell-substrate interaction; electrical cell stimulation; frequency-dependent response; surface charge.

Figure 1.

(a) Non-contact electrical stimulation of live cells. The electrodes are isolated from the culture medium by the substrate layer (bottom) and the coating layer (top). Electrodes are oriented to ensure that the resulting electric field, EF_induced, is perpendicular to the cell substrate. Cells are placed on the substrate surface which is in contact with the stimulation apparatus. (b) Equivalent electric circuit with no cell present. C_coating and C_substrate represent the capacitance of the dielectric insulating layers; C_medium and R_medium are the capacitance and resistance associated with the electrolyte (culture medium), respectively. The oscillating voltage V is applied to the top and bottom electrodes. (Online version in colour.)

Figure 2.

Induced electric field in the culture medium as a function of the applied field frequency in the non-contact model. At low frequency of the applied field, EF_induced is excluded from the culture medium. By contrast, EF_induced in the culture medium rises dramatically as the frequency approaches 100 MHz and reaches a constant value above 10 GHz. Electrode separation is 50 µm and V = 10 V. (Online version in colour.)

Figure 3.

(a) Schematic of a cell attached to the substrate. (b) Hemispherical cell model used for simulations. Cell radius is 5 µm and membrane thickness is 5 nm (not drawn to scale). Polar coordinate system (r, θ) is used to characterize the magnitude of the induced EF in the cell membrane.

Figure 4.

Frequency dependence of EF_induced in the cell cytoplasm and the culture medium (a) and the cell membrane at the apex and substrate side (b). The response to the applied electric field can be divided into three regions. In region I, the electric field is induced in the cell membrane and is excluded from the cytoplasm and culture medium. In region II, EF_induced in the cell membrane increases at the cell apex up to the maximum value (E_max ∼ 12 × 10⁵ V m⁻¹) and starts to penetrate into the cytoplasm and culture medium, while it does not change significantly at the cell membrane facing the substrate. In region III, the magnitudes of EF_induced at the cell apex and the substrate side both decrease and eventually reach the same plateau, while EF_induced in the cytoplasm and culture medium both increase and also reach plateau values at high frequencies.

Figure 5.

(a) Spatial distribution of the induced electric field in a single cell attached to a substrate and exposed to the external electric field that is perpendicular to the substrate. The scale applies to all colour plots, with the maximum value of E_max ∼ 12 × 10⁵ V m⁻¹. At low frequency of the applied field, the induced electric field is present only in the cell membrane and is excluded from the cell cytoplasm and culture medium (i). As the frequency increases, the electric field starts penetrating into the cell cytoplasm and culture medium (ii). At high frequencies, a strong electric field is induced in all cell compartments and culture medium (iii), with the significant spatial variation in the values for EF_induced along the cell membrane. (b) Distribution of EF_induced is shown for the cell membrane facing the medium (solid line) and for the cell membrane facing the substrate (dashed line) for the same frequency ranges, demonstrating significant frequency dependence of the magnitude of the EF_induced in the membrane at either side of the membrane.

Figure 6.

EF_induced as a function of frequency of the applied field at different positions along the cell membrane. Within the 10⁶–10⁷ Hz range, EF_induced increases near the apex but decreases near the substrate-facing side of the membrane.

Figure 7.

Effect of cytoplasm conductivity on the induced electric field in different cell compartments. (a) The increase in the EF_induced at the cell apex disappears with decreasing the cytoplasmic conductivity, while EF_induced in the membrane facing the substrate side does not depend on σ_cytoplasm. (b) Lower values of the cytoplasmic conductivity lead to a weakened cytoplasm EF screening and a shift of the EF penetration to a lower frequency.

Figure 8.

Effect of the geometrical and electrical parameters of the stimulation system on EF_induced in the culture medium. (a) The thinner substrate allows EF penetration into the medium at lower frequencies of the applied field. (b) Decreasing the conductivity of the medium or increasing the permittivity of the substrate shifts the penetration frequency to lower frequencies.