Transient and steady-state deformations of a vesicle with an insulating membrane in response to step-function or alternating electric fields

Deformation of a vesicle with an insulating membrane under an external electric field is considered. Application of a step-function field, under which the eventual form is prolate, is shown to transiently induce an oblate deformation, provided that the conditions of the surrounding medium are chosen properly. It is further demonstrated that alternating electric fields induce deformation in a frequency-dependent manner; the deformation at low frequencies is always a prolate one, whereas the steady-state deformation at high frequencies is either prolate or oblate depending on the medium conditions. If this frequency dependence is experimentally observable, the capacitance and curvature elastic modulus of the membrane as well as the intravesicular conductance can be estimated directly from the data. The field-induced deformation may serve as a novel experimental method in cell biology.