Figure 1

The cell-sensor interface. (a) The coupling of the cell to the measurement system is shown. $V_M$ is the cell's potential in reference to extracellular space. $Z_{jm}$ describes the impedance of the cell membrane covering the aperture of the sensor, $R_j$ is the seal resistance, scaling the leakage current from the junction to the electrolyte. $Z_S$ is the impedance of the nanocavity sensor and $Z_M$ is the impedance of the measurement setup. $V_S$ is the voltage measured with the voltage amplifier. (b) The system is shown in more detail. The cell with Hodgkin-Huxley elements embedded in the membrane sits on the nanocavity electrode. $V_m^i$ is the Nernst voltage of the free membrane of the ion type $i$, $g_m^i$ is the membrane conductivity per unit area for this specific ion. $c_m$ is the capacitance per unit area of the cell membrane. Analogously, $V_{jm}^i$ is the Nernst voltage of the attached membrane, $g_{jm}^i$ the attached membrane's conductivity, and $c_{jm}$ the capacitance. Also shown is a voltage amplifier attached to the electrode. $Z_c$ is the impedance of the central spot of the microelectrode and $R_j$ is the leak resistance within the junction. $h$ is the height of the nanocavity. (c) A segment of the nanocavity in the radial direction is shown. $dR$ is the ohmic resistivity of the electrolyte and $dX$ the constant phase impedance of the electrode. Both $R\left(r\right)$ and $X\left(r\right)$ are functions of the distance $r$ to the center of the electrode.Reuse & Permissions

Figure 2

Shown is a Bode plot of experimental data (symbols) and model fits (solid lines). The absolute value and the phase of the impedance as a function of the frequency are shown. The squares are measured values of the impedance. The circles are measured values of the phase. The solid lines are the absolute value and phase of Eq. (7). The microelectrode used for this measurement has a central opening with radius $r_0=2.5$ $\mu \mathrm{m}$ and a total radius of $r=15$ $\mu \mathrm{m}$. The theory curves are calculated for $a=6\times {10}^5$ $\Omega$, $C_h=59$ $\mu {\mathrm{Fcm}}^{-2}$, and $\beta =0.89$.Reuse & Permissions

Figure 3

Shown is a plot of the phase as a function of the absolute value of the impedance. We compare experimental data (circles) with a fit from Eq. (7) (solid line). The parameters are the same as in Fig. 2.Reuse & Permissions

Figure 4

The electrical activity of HL-1 cells growing on the surface of a chip with nanocavity microelectrodes has been recorded. We show four different signals, which are not only qualitatively but quantitatively different. The used microelectrodes are geometrically identical. They have a central opening with radius $r_0=2.5$ $\mu \mathrm{m}$ and a total radius of $r=15$ $\mu \mathrm{m}$. The measurements have been performed in Claycomb's medium against a Ag–AgCl reference electrode.Reuse & Permissions

Figure 5

Simulated signals for the same type of electrode as in Figs. 2 and 4. The presented signals have been calculated from the circuitry in Fig. 1 and a model for human myocardial cells [46]. Free parameters to reproduce the experimental data are the scaling of the ion channels ${\chi }_i$ and the quality of the seal between the cell and sensor measured with $R_j$. Signal 1 has been calculated with $R_j=50\mathrm{M}\Omega$, ${\chi }_{\mathrm{Na}}=2.7$ and ${\chi }_{\mathrm{K}}=1.2$ ${\chi }_{\mathrm{Ca}}=1.0$. Signal 2 has been calculated with $R_j=30\mathrm{M}\Omega$, ${\chi }_{\mathrm{Na}}=2.1$, ${\chi }_{\mathrm{K}}=1.0$, and ${\chi }_{\mathrm{Ca}}=1.0$. Signal 3 shows a leaky cell with $R_j=20\mathrm{M}\Omega$, ${\chi }_{\mathrm{Na}}=1.35$, ${\chi }_{\mathrm{K}}=1$, and ${\chi }_{\mathrm{Ca}}^2=2.3$. The background calcium current is very strong ${\chi }_{\mathrm{Ca}}^1=14$. Signal 4 is calculated with $R_j=35\mathrm{M}\Omega$, ${\chi }_{\mathrm{Na}}=1.3$, and ${\chi }_{\mathrm{K}}={\chi }_{\mathrm{Ca}}=1$.Reuse & Permissions

Figure 6

Three response functions calculated for three different electrode radii. The graphs show the absolute values $\left|h\right(f\left)\right|$ and the phases $\arg \left(h\right(f\left)\right)$ as indicated by the arrows. All other parameters, $C_h=59$ $\mu {\mathrm{Fcm}}^{-2}$, $a=6\times {10}^5$ $\Omega$, $R_{\mathrm{load}}={10}^8$ $\Omega$, $C_{\mathrm{load}}=150\mathrm{pF}$, $R_j=15\mathrm{M}\Omega$, $\beta =0.89$, $R_{jm}=20\mathrm{G}\Omega$, and $C_{jm}=2.5\mathrm{pF}$ are kept constant.Reuse & Permissions

Figure 7

This figure shows the error measure Eq. (B7) for the approximations Eq. (B4) (dashed line) and Eq. (B5) (solid line). Since $\lambda$ depends on $\omega$, the quality of the approximation Eq. (B4) is deteriorating for greater frequencies. We can see that for the presented nanocavity sensors, Eq. (B5) is a good approximation.Reuse & Permissions