Electrodeformation and Electroporation of Membranes in the Fluid Phase

Vesicles exposed to electric fields deform. The response of GUVs to electric fields has been the subject of extensive i rives tiga tion. When exposed to AC electric fields, as a stationary state they attain elhpsoidal shapes-prolate or oblate-depending on the field frequency and media conduchvity [42, 64]. Initiated by tlie seminal work of Winterhalter and Helfrich ]65], this effect has been considered theoretically [66-74] and experimentally ]42, 64, 67, 75-77], whereby intereshng dynamics and flows in the membrane and in the surrounding medium were observed 

While vesicle deformation in AC fields concerns stationary shapes, DC pulses induce short-lived shape deformations. In different studies, the pulse duration has been typically varied from several microseconds to milliseconds, while studies on cells have investigated a much wider range of pulse durations-from tens of nanoseconds to milliseconds and even seconds [80], as discussed in other chapters of this book. Various pulse profiles, unipolar or bipolar, as well as trains of pulses have been also employed (e.g., [81, 82]). Because the application of both AC flelds and DC pulses creates a transmembrane potential, vesicle deformations of similar nature are to be expected in both cases. However, the working fleld strength for DC pulses is usually higher by several orders of magnitude. Thus, the degree of deformation can be different. 

The typical decay hme for the relaxahon of nonporated vesicles, t, is of the order of 100 ps. It is set by the relaxahon of the membrane tension achieved at the end of the pulse. The membrane tension, acquired during the pulse, also referred to as electric tension, arises from the transmembrane potenhal, ( , built across the membrane during the pulse. Lipid membranes are impermeable to ions and, in the presence of an electric field, charges accumulate on both sides of the bilayer, which gives rise to this transmembrane potential [91]  

Ai and Aex are the conductivities of the solutions inside and outside the vesicle, respectively. Equations (7.1) and (7.2) are valid only for a nonconductive membrane. 

The effective electrical tension, Ja, induced by the transmembrane potential, Pja, is defined by the Maxwell stress tensor [59, 89, 92] 

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