Generation of capacitance current harmonics during electrostriction of inhomogeneous bilayers

The mechanisms of generation of capacitance current harmonics arising from bilayer electrostriction are investigated theoretically in the case when fixed charges or dipoles are located inside the bilayer. If the elastic properties of the bilayer are inhomogeneous in a transversal direction, these charges or dipoles affect substantially the amplitude A2 of the second current harmonic and accordingly the magnitude of compensatory constant voltage VC, which shold be applied to the membrane to reduce A2 to zero. In membranes whose Young's modulus is minimum at the center of bilayer, the dependence of VC on depth of immersion of the charge xA into the bilayer represents a function with alternating signs, which is reduced to zero at the center of bilayer. In the case of a dipole source immersed into the bilayer, the appropriate dependence is oscillating as well, and its shape is a derivative of the corresponding dependence of VC for fixed charges with respect to a coordinate. Possible applications of the results are discussed.