Single-cell mechanical analysis and tension quantification via electrodeformation relaxation

Abstract

The mechanical behavior and cortical tension of single cells are analyzed using electrodeformation relaxation. Four types of cells, namely, MCF-10A, MCF-7, MDA-MB-231, and GBM, are studied, with pulse durations ranging from 0.01 to 10 s. Mechanical response in the long-pulse regime is characterized by a power-law behavior, consistent with soft glassy rheology resulting from unbinding events within the cortex network. In the subsecond short-pulse regime, a single timescale well describes the process and indicates the naive tensioned (prestressed) state of the cortex with minimal force-induced alteration. A mathematical model is employed and the simple ellipsoidal geometry allows for use of an analytical solution to extract the cortical tension. At the shortest pulse of 0.01 s, tensions for all four cell types are on the order of 10^{-2} N/m.

FIG. 11.

(a) Shape factor changes of four different MDA-MB-231 cells under consecutively increasing pulsing, each 0.5 s at 7 MHz. (b) The maximum deformation achieved at the end of pulsation ${\delta }_{max}$ shows approximately a linear correlation with $V_{pp}^2$.

FIG. 12.

(a) Model geometry. (b) Exemplary electric field distribution. (c) Exemplary heat map due to Joule heating; the ambient temperature is assumed to be 20 °C. The cross section is taken perpendicular to the electrode edges and at the cell equator. The simulation parameters are $a_0=7.5\mu \mathrm{m},V_{pp}=50\mathrm{V}$, and $f=5\mathrm{M}\mathrm{H}\mathrm{z}$.

FIG. 13.

Dependence of $F_0$ on (a) frequency, (b) cell radius, and (c) applied voltage. The reference case is $a_0=7.5\mu \mathrm{m},V_{pp}=100\mathrm{V}$, and $f=5\mathrm{M}\mathrm{H}\mathrm{z}$.

FIG. 14.

The RMSE for the two analytical approaches. The number of repeats is provided in Table III.

FIG. 1.

(a) Exemplary image of the etched ITO slide where the conductive coating is separated by a 35-μm gap. (b) Schematic of the experimental setup.

FIG. 2.

Exemplary images of the cell deformation-relaxation process. (a) An MDA-MB-231 cell at rest prior to the deformation pulse ($t=0\mathrm{s}$ and $\delta =0$); the horizontal line is one of the electrode edges. (b) The same cell is deformed with a high-amplitude, high-frequency pulse ($t=0.5\mathrm{s},\delta =0.12,V_{pp}=40\mathrm{V}$, and $f=5\mathrm{M}\mathrm{H}\mathrm{z}$). Here $a$ and $b$ denote the long and short axes of the ellipse, respectively. (c) The cell begins to relax once the pulse ceases ($t=0.6\mathrm{s}$ and $\delta =0.05$). (d) The cell eventually recovers its shape at the end of relaxation ($t=2\mathrm{s}$ and $\delta =0$).

FIG. 3.

Evolution of the shape factor for two different pulse durations for a single MDA-MB-231 cell. Here $\delta =a/a_0-1$ (see Fig. 2) and (a) $t_p=0.01\mathrm{s},V_{pp}=40\mathrm{V}$, and $f=5\mathrm{M}\mathrm{H}\mathrm{z}$ and (b) $t_p=0.5\mathrm{s},V_{pp}=25\mathrm{V}$, and $f=7\mathrm{M}\mathrm{H}\mathrm{z}$. For both cases, two analytical strategies are attempted: a power-law model (black dashed line) and a single-exponential model (red dashed line). The coefficients of determination R² are provided for both cases.

FIG. 4.

(a) Power-law exponent $\alpha$ versus pulse duration $t_p$. Error bars indicate standard deviation. The number of cells examined in each data point is tabulated in Table III. (b) Error quantification [rms error (RMSE)] for MCF-7. Results for other cell types are found in Fig. 14.

FIG. 5.

(a) Extracted timescale $t_r$, (b) surface tension ${\gamma }_s$, and (c) surface viscosity ${\eta }_s$. Error bars indicate standard deviation. The number of repeats is provided in Table III.

FIG. 6.

Extracted $E_0$ for $t_p⩾0.1\mathrm{s}$. Error bars indicate standard deviation. The number of repeats is provided in Table III.

FIG. 7.

Pooled results for all cell types and pulse durations: (a) ${\gamma }_s$ and ${\eta }_s$ from the surface tension model and (b) $\alpha$ and $E_0$ from the power-law damping model. Error bars indicate standard error. The number of repeats is provided in Table III.

FIG. 8.

Direct property comparison between the two models. Error bars indicate standard error. The number of repeats is provided in Table III.

FIG. 9.

Model schematic. The cell is simplified as an infinitesimally thin, viscoelastic cortex with cortical tension ${\gamma }_s$ and surface viscosity ${\eta }_s$.

FIG. 10.

(a) Extracted timescale $t_r$, (b) surface tension ${\gamma }_s$, and (c) surface viscosity ${\eta }_s$ for $t_p>0.1$. Error bars indicate standard deviation. The number of repeats is provided in Table III.