  Biological membranes are capacitors that can be charged by applying a field
across the membrane. The charges on the capacitor exert a force on the membrane
that leads to electrostriction, i.e. a thinning of the membrane. Since the
force is quadratic in voltage, negative and positive voltage have an identical
influence on the physics of symmetric membranes. However, this is not the case
for a membrane with an asymmetry leading to a permanent electric polarization.
Positive and negative voltages of identical magnitude lead to different
properties. Such an asymmetry can originate from a lipid composition that is
different on the two monolayers of the membrane, or from membrane curvature.
The latter effect is called 'flexoelectricity'. As a consequence of permanent
polarization, the membrane capacitor is discharged at a voltage different from
zero. This leads to interesting electrical phenomena such as outward or inward
rectification of membrane permeability.
  Here, we introduce a generalized theoretical framework, that treats
capacitance, polarization, flexoelectricity and piezoelectricity in the same
language.
