1.

Introduction

Electricity is a fundamental driving force in biological systems.¹ It often acts in terms of a mechanical response.^2–5 Important examples include electrically regulated beating of heart cells,^6,7 auditory sensing of hair cells,^7–9 and conformational changes in voltage-gated ion channels.^10,11 This electromechanical coupling effect is anticipated from thermodynamics, e.g., the Lippmann equation, which relates electrical potential-induced surface tension to surface charge density. However, the underlying molecular scale mechanism, especially in biological systems, is still largely unknown. An experimental challenge in studying this effect is that the electromechanical deformation at the single cell level is on the subnanometer to nanometer scale.^4,12,13 Biologically, the cell tension is subject to many factors, such as the change of cell cycles,^14–17 cell migration status,¹⁸ cell types,^19–21 pharmaceutical environment,²² and the number may vary for more than 10 times. Atomic force microscopy (AFM) can probe the mechanical deformation,^{12,13,23–25} but it involves the contact of the AFM tip to the cells. AFM is also limited to the study of the top surface of cells and is unable to directly measure the bottom surface of cells, as well as the cell–substrate interactions. Newly developed technologies, including the piezoelectric nanoribbon transducer,²⁶ and optical methods, such as spectral-domain optical coherence phase microscopy (SD-OCT),²⁷ have been applied to mechanical deformation measurement. They either measure one location at a given time or the whole cell, which is insufficient to resolve subcellular responses. Quantitative phase microscopy provides subcellular imaging resolution, but the subtle potential-induced mechanical deformation at subcellular level has not been studied.²⁸

Here we have shown a plasmonic imaging method to quantify the subnanometer cell deformation at cell–substrate interface. We studied the cell electromechanical responses and quantified the subcellular mechanical deformation at various membrane potential polarization levels and frequencies. We further modeled the cell electromechanical responses and investigated the effect of mechanical perturbations on cytoskeletons.

2.

Experiments

3.

Results and Discussion

We quantify the cell deformation using plasmonic imaging. The imaging system was built on top of an inverted optical microscope. Incident light was coupled into the microscope via a high numerical aperture objective. Reflection light from a gold-coated cover glass is imaged by a CMOS camera [Fig. 1(a)].^29–31 We manually tuned the incident angle close to the surface plasmon resonance angle to generate an evanescent field near the gold surface ( Supplementary Material—supporting note 4). Since the evanescent field decays exponentially into the solution from the surface with a decay length of only about 100 nm, the plasmonic imaging is extremely sensitive to the mechanical deformation perpendicular to the surface ($z$-direction) (for detailed theoretical calculations, please refer to previous studies^32–34). The deformation can be quantified according to the following equation:

Fig. 1

Plasmonic imaging of cellular mechanical deformation. (a) Schematic diagram of experimental setup. Cells are plated on the gold-coated coverslip and are imaged with plasmonic microscopy via a fast camera. Membrane potential modulation waveform was applied to the cell with a micropipette in a whole-cell patch clamp configuration. (b) Membrane potential change induces mechanical deformation on the membrane. (c) Plasmonic images were analyzed by applying FFT along time, and the amplitude and phase-shift images at the modulation frequency were obtained, to quantify the deformation amplitude and direction.

We cultured HEK293T cells on top of the gold sensing surface. The evanescent field interacts with the bottom part of the cell, and the deformation of the cell is recorded in the plasmonic images. To study the membrane potential-induced deformation, we controlled the potential across the cell membrane with a patch-clamp micropipette and simultaneously recorded the plasmonic images when the membrane potential was polarized. The corresponding polarization current was also recorded electrically. Since the deformation was extremely small, we applied a sinusoidal waveform to repeatedly measure this electromechanical response [Fig. 1(b)]. FFT was performed on the recorded images over time [Fig. 1(c)] and the noise at frequencies other than the one at the applied alternating potential was removed ( Supplementary Material—supporting note 5). The FFT amplitude represents the magnitude of the intensity change to the applied potential. From the FFT amplitude, we further determined local cell deformation using Eq. (1), and from the FFT phase, we obtained the deformation direction with respect to the polarity of the applied potential.

Figures 2(a) and 2(b) show the bright field and plasmonic images of a cell. A glass micropipette was pressed onto the cell membrane, and the membrane patch inside the micropipette tip was ruptured after a tight glass-membrane seal was established at the contact area. In this configuration, the electrode in the micropipette is in direct contact with the intracellular fluid, allowing precise and flexible control of the potential across the cell membrane. Since micropipette is beyond the penetration depth of the surface evanescent field, it is invisible on the plasmonic images. We then applied an alternating depolarization potential from $-60$ to 140 mV at 37 Hz to the cell [Fig. 2(c)]. Depolarization causes a 1-nA injection of current. Correspondingly, plasmonic images also show a pronounced response at the applied frequency [Figs. 2(d) and 2(e)]. We extracted the intensity profile from the cell area, as well as from the background region without cells. A sharp peak was observed at the frequency of applied potential in the whole cell region after FFT, indicating the mechanical deformation generated from the cell by the applied potential [Fig. 2(f)]. In contrast, no obvious response was detected in the background region. From the FFT amplitude image, we observed a much bigger response at the cell edge than that from the center, suggesting a heterogeneous electromechanical deformation at different subcellular regions [Fig. 2(d)].

Fig. 2

Membrane potential-induced mechanical deformation in cells. (a) Transmitted and (b) plasmonic images of a cell whose membrane potential is modulated at 37 Hz using a glass micropipette. (c) Membrane potential and current associated with the potential modulation. (d) Amplitude images of the cell at the frequency of the applied potential modulation (37 Hz). (e) Phase image of the cell. (f) Spectral response of the plasmonic image intensity of the whole cell and a background region (without the cell), where the peak at the modulation frequency from the whole cell region is the mechanical deformation of the cell. Scale bar: $10\mu \mathrm{m}$.

To quantify the time delay of the electromechanical deformation, we analyzed the phase shift of the recorded images with respect to the applied potential. Only in-phase (0 deg) and antiphase (180 deg) responses were observed in the FFT phase image at 37 Hz [Fig. 2(e)]. The cell center mainly displayed an in-phase (0 deg) response (colored as cyan), whereas the edge area was antiphase (180 deg, red). This result shows that the cell bottom deforms along with the applied potential, but cell center and edge deform in opposite directions. When the cell is depolarized, the center portion of the cell moves closer to the gold surface (intensity increase) while the edge moves away from the surface (intensity decrease) [Fig. 1(b)]. This bidirectional response rules out the possibilities that the observed plasmonic signal was from other mechanisms ( Supplementary Material—supporting note 2).

To further study the relationship between mechanical deformation and membrane potential changes, we measured the mechanical responses at different potential polarization levels. The cells were electrically hyperpolarized or depolarized in potential steps from $-80$ to 100 mV at an interval of 60 mV per step [Fig. 3(c)]. Plasmonic images were simultaneously captured at the same sampling rate as 10,000 fps (see Supplementary Material—experiments and supporting note 5, for more details) [Fig. 3(a)]. This sequence was repeated and the plasmonic images were averaged over the repeated measurement for denoising (see methods). Figure 3(b) shows a differential image of cellular response of potential depolarization from $-60$ to 100 mV after averaging over 94 cycles of repeated measurements. The cell center showed an increased plasmonic intensity, whereas the cell edge showed an opposite response, which is consistent with the result presented in the previous section. The similar intensity outside the cell contour region was due to the noise from the background. To accurately quantify the dynamic response of the cell deformation, we plotted the deformation responses over the cell center and over the cell edge, respectively [Fig. 3(d)]. Both regions deformed slowly after a sudden potential polarization. However, the exact response speed is biased due to the moving average used in the denoising scheme. At the steady state, deformation magnitude showed a linear dependency on the membrane polarization for both regions [Fig. 3(e)], with an average displacement of about 0.02 nm per 100 mV at the cell edge and 0.005 nm per 100 mV at the cell center, respectively. These numbers are about one order of magnitude smaller than that of the mechanical motions tracked at the cell edge using digital microscopy.⁴ This is probably due to the impeded motions at the cell–substrate interface of the adherent cells. The thermal energy-induced fluctuation is typically at the same level. However, these fluctuations were random, spanning across the whole spectrum. In our current detection scheme, we externally drive the motion. Different subcellular regions deform in a synchronous manner. Thus, the thermal fluctuation is suppressed by either averaging (as in Fig. 3) or limiting the detection bandwidth (as in Fig. 2).

Fig. 3

Cell deformation and its dependence on the membrane potential. (a) Raw plasmonic and (b) differential plasmonic images of a depolarized cell from $-600$ to 100 mV, where the white line marks the edge of the cell, the green and blue dashed lines indicate a cell edge and center regions selected for quantification, respectively. (c) Stepwise change of the membrane potential polarization. (d) Time profiles of the mechanical deformation in the cell edge (top) and center (bottom) regions in response to the stepwise membrane potential polarization. (e) Relationship of the mechanical deformation in the cell edge and center regions at the steady state of each potential steps, where the error bars indicate the temporal standard deviation of the deformation for each potential step (averaged over 94 cycles). Scale bar: $10\mu \mathrm{m}$.

Thermodynamics predicts that potential changes across the cell membrane will lead to a mechanical deformation.¹² The relationship between surface tension and potentials for a single interface is described as Lippmann equation:

To explain the observed electromechanical response, as well as to accurately evaluate the response speed, we performed a spectral analysis on the deformation of single cells. We measured the cellular mechanical response over a wide frequency range from 7 to 312.5 Hz with a constant potential change (200 mV of depolarization from $-60\mathrm{mV}$ resting potential) for each frequency. Figures 4(a)–4(e) show the responses at different modulation frequencies after FFT from the recorded plasmonic images. The amplitude is shown as the brightness and the phase-shift is encoded in color. We observed a near-in-phase and antiphase mechanical responses with respect to the applied potential modulation (0 deg and 180 deg only) over the frequencies. No other intermediate phases were detected.

Fig. 4

Cell deformation and its dependence on the membrane potential modulation frequency. (a)–(e) FFT image of cellular mechanical deformation in response to membrane potential modulation frequencies, where the brightness and color indicate the amplitude and phase of the FFT images. (f) Mechanical model of cell deformation. (g), (h) Mechanical deformation in the cell edge and center regions versus modulation frequency, where the data are plotted in log-log scale and fitted with a linear equation. Scale bar: $20\mu \mathrm{m}$.

The mechanical property of a cell can be modeled as

Electromechanical properties of the cell can be extracted by analyzing the relation between the displacement and the applied potential. We calculated the averaged deformation magnitude from both the cell center and the edge at different frequencies. Figures 4(g) and 4(h) show the spectral response of deformations with 200 mV depolarization at both regions. Fitted with a linear equation in log-log scale, the deformation magnitude followed a negative power-law form, $|x(f)|\sim f^{-\beta }$, with exponent $\beta$ equal to 0.15 and 0.3 in edge and center regions, respectively. The storage modulus, the inverse of displacement with the same modulation potential, is given as $|G^{\prime }(f)|\sim f^{\beta }$. This result is in good agreement with previous rheological measurements using intracellular microbead- or cytoskeleton-attached magnetic nanoparticle conducted on cells.^38,39

We anticipate that mechanical perturbation to the cellular structure will remarkably affect the electromechanical response and can be observed with plasmonic imaging (see Supplementary Material—supporting note 3, for full electromechanical model). To confirm this, we treated the cells with an actin polymerization inhibitor, cytochalasin D, and examined the corresponding electromechanical responses.⁴⁰ Actin fibers are the main component of the cytoskeleton and determine the cell mechanics.^20,41–43 After depolymerizing the actin frame structure, cell centers show an expanded anti-phase area (red) compared with those in the normal condition [Figs. 5(a) and 5(b), white dash lines]. The boundaries between the in-phase and the antiphase regions disappeared, and the in-phase regions appeared to be more random at different subcellular locations. To quantitatively examine the subcellular phase change, we quantified the average phase-shift over the whole cell area. A significant phase shift toward antiphase (180 deg) after cytochalasin D treatment was observed [Fig. 5(c), $p<0.01$, $t$-test]. This result suggests that a larger portion of the cell bottom membrane moved inward synchronously after depolarization [Figs. 5(d) and 5(e)].

Fig. 5

Modification of the mechanical properties of the cell with cytochalasin D. (a), (b) Potential-induced cell deformation of (a) cytochalasin D-treated cells and (b) normal cells, where the white lines indicate the phase boundary. (c) Averaged phase shift of the whole cell; $p<0.01$, $t$-test. (d), (e) Model illustration of the potential-induced cell mechanical deformation of the cytochalasin D-treated cells and normal cells. Scale bar: $10\mu \mathrm{m}$.

4.

Conclusion

We have demonstrated a plasmonic method for detecting subnanometer deformation from cell electromechanical coupling. This capability allows us to visualize membrane-potential-induced cell mechanical deformation. At frequencies below hundreds of hertz, the deformation is mainly elastic. Deconstructing the actin structure revealed an important role of cytoskeleton in the observed potential-induced cell mechanical deformation. Our work shows that membrane potential-induced cell mechanical deformation can be imaged with the plasmonic method with subcellular spatial resolution and subnanometer resolution. We anticipate that the method can contribute to mechanobiological studies and shed light on the understanding of important biological functions, including mechanosensitive ion channels and protein configuration changes in voltage-gated ion channels.