In the electrical representation of biological membranes, the lipid bilayer is often considered as a simple insulator mostly impermeable to the passage of ions or small molecules. This view is included in the electrical equivalent of the membrane of excitable cells, that models the bilayer as a planar capacitor whose capacitance is independent of the applied electric field. This has been shown not to be true, especially close to the lipid phase transition, where the compressibility of the membrane is maximum and electrostrictive forces can change the membrane dimensions significantly. Moreover, membrane dimensions change significantly at the transition, and this, in turn, can change the value of the capacitance. Furthermore, lipid bilayers show finite permeability to ions, which is also maximum at the transition due to the enhanced area fluctuation. Biological membranes display lipid melting close to physiological conditions, making these effects biologically relevant.

In this work, we consider the case of asymmetric membranes which can display spontaneous polarization in the absence of a field. Close to the phase transition, we find that the membrane displays piezoelectric, flexoelectric and thermoelectric behaviour. In particular, the membrane capacitance is a nonlinear function of the applied voltage. Furthermore, in the presence of spontaneous polarization, our thermodynamical description is able to explain the outward rectified current-voltage relationship measured on synthetic lipid bilayers.

Due to the nonlinear dependence of the membrane capacitance and conductance on voltage and the presence of spontaneous polarization, the traditional equivalent circuit of the membrane is not an accurate description in physiological conditions. An updated equivalent circuit of the lipid bilayer is here proposed, which takes into account the nonlinearities of the membrane and their time dependence. Using our updated equivalent model, we predict the response of the bilayer to common voltage experiments, e.g. voltage jumps and impedance spectroscopy. Our results show that the lipid bilayer alone can display several electrical behaviours similar to those measured for biological membranes and considered to be distinctive features of protein channels, like outward rectification and gating currents. Finally, our proposed equivalent model is suggested by the structure and physical properties of the system, and not from empirical analysis of the the data. Therefore, it has predictive power.

In the experimental part of this work, we find qualitative similarities between the melting enthalpy and the temperature dependence of the membrane capacitance, as expected from our theory. Measurements of I-V curves on different geometries point in the direction of a flexoelectric mechanism behind current rectification in lipid bilayers. Finally, we suggest that our updated equivalent circuit should be included in the interpretation of elctrophysiological data.