Bilayer Lipid Membrane as Memcapacitance: Capacitance-Voltage Pinched Hysteresis and Negative Insertion Conductance

Inelastic (dissipative) effects of different natures in lipid bilayer membranes can lead to hysteresis phenomena. Early, it was shown that lipid bilayer membranes, under the action of a periodic sinusoidal voltage, demonstrate pinched-hysteresis loops in the experimental capacitance-voltage dependences and are almost the only example of the physical implementation of memcapacitance. Here, we propose an equivalent circuit and mathematical framework for analyzing the dynamic nonlinear current response of a lipid bilayer membrane as an externally controlled memcapacitance. Solving a nonlinear differential equation for the equivalent circuit of a membrane in the form of a parallel connection of a nonlinear viscoelastic capacitor and an active resistance using the small parameter method, we obtain explicit analytical dependences for the current response of the membrane and pinched-hysteresis loops. The explicit solutions and their comparison with experimental data allow us to identify the lumped equivalent circuit parameters that govern the memcapacitor behavior of the membrane and hence the magnitude of the hysteresis. We quantify the memcapacitance hysteresis in terms of negative work done by the control signal. An analysis of the formulas leads to the conclusion that the determining factor for the appearance of pinched hysteresis is the type of nonlinear dependence of the device capacitance on voltage.