Voltage dependence of bilayer membrane capacitance: Harmonic response to ac excitation with dc bias

Abstract

The capacitive current is calculated for a nonlinear element ( C = C 0 + αu 2), when an ac voltage together with a dc voltage is applied. Three frequency ranges have to be distinguished for each effect which contributes to the capacitance change. They are classified as low frequency range, dispersion range and high frequency range. In the low frequency range the increase in capacitance due to the dc voltage is twice the amount of the increase due to ac voltage (rms). In the high frequency range, dc voltage and ac voltage (rms) have the same effect. The second and third harmonics of the fundamental frequency are generated in the low frequency and dispersion range. In the low frequency range amplitudes and phases of the harmonics are related to the “fast capacitance increase.” The change in capacitance and the Fourier-coefficients of the second and third harmonics were measured at bilayer membranes made from oxidized cholesterol + decane. Agreement was obtained between the measured voltage dependence of these quantities and the calculated one.