We determine membrane capacitance, $C$ as a function of dc voltage for the human embryonic kidney (HEK) cell. $C$ was calculated from the admittance, $Y$, obtained during a voltage ramp when the HEK cell was held in whole-cell patch-clamp configuration. $Y$ was determined at frequencies of 390.625 and $781.25\mathrm{Hz}$ from the measured current, $i$ obtained with a dual-sinusoidal stimulus. We find that the fractional increase in the capacitance, $C$ is small $(<1\%)$ and grows with the square of the voltage, $\Psi$. $C$ can be described by: $C=C\left(0\right)(1+\alpha {(\Psi +{\psi }_s)}^2)$ [where $C\left(0\right)$: Capacitance at $0\text{volts}$, ${\psi }_s$: Difference in surface potential between cytoplasmic and extracellular leaflets and $\alpha$: Proportionality constant]. We find that $\alpha$ and ${\psi }_s$ are 0.120 $(\pm 0.01){\mathrm{V}}^{-2}$ and $-0.073$ $(\pm 0.017)\mathrm{V}$ in solutions that contain ion channel blockers and 0.108 $(\pm 0.29){\mathrm{V}}^{-2}$ and $-0.023$ $(\pm 0.009)\mathrm{V}$ when $10\mathrm{mM}$ sodium salicylate was added to the extracellular solution. This suggests that salicylate does not affect the rate at which $C$ grows with $\Psi$, but reduces the charge asymmetry of the membrane. We also observe an additional linear differential capacitance of about $(-46{\mathrm{fFV}}^{-1})$ in about 60% of the cells, this additional component acts simultaneously with the quadratic component and was not observed when salicylate was added to the solution. We suggest that the voltage dependent capacitance originates from electromechanical coupling either by electrostriction and/or Maxwell stress effects and estimate that a small electromechanical force $(\approx 1\mathrm{pN})$ acts at physiological potentials. These results are relevant to understand the electromechanical coupling in outer hair cells (OHCs) of the mammalian cochlea, where an asymmetric bell-shaped $C$ versus $\Psi$ relationship is observed upon application of a similar field. Prestin, a membrane protein expressed in OHCs is required to observe this function. When we compare the total charge contributions from HEK cell membrane ($7\times {10}^4$ electrons, $10\mathrm{pF}$ cell) with that determined for prestin transfected cells (up to $5\times {10}^6$ electrons) we conclude that the charge contributions from the collective motion of membrane proteins and lipids in the field is dwarfed relative to that when prestin is present. We suggest that the capacitance-voltage relationships should be similar to that observed for HEK cells for OHCs that do not express prestin in their membranes.

• Received 21 October 2004
• Corrected 12 May 2006

DOI:https://doi.org/10.1103/PhysRevE.73.041930