Bioelectrorheological model of the cell. 2. Analysis of creep and its experimental verification

Permeabilizing Cell Membranes with Electric Fields

The biological impact of exogenous, alternating electric fields (AEFs) and direct-current electric fields has a long history of study, ranging from effects on embryonic development to influences on wound healing. In this article, we focus on the application of electric fields for the treatment of cancers. In particular, we outline the clinical impact of tumor treating fields (TTFields), a form of AEFs, on the treatment of cancers such as glioblastoma and mesothelioma. We provide an overview of the standard mechanism of action of TTFields, namely, the capability for AEFs (e.g., TTFields) to disrupt the formation and segregation of the mitotic spindle in actively dividing cells. Though this standard mechanism explains a large part of TTFields' action, it is by no means complete. The standard theory does not account for exogenously applied AEFs' influence directly upon DNA nor upon their capacity to alter the functionality and permeability of cancer cell membranes. This review summarizes the current literature to provide a more comprehensive understanding of AEFs' actions on cell membranes. It gives an overview of three mechanistic models that may explain the more recent observations into AEFs' effects: the voltage-gated ion channel, bioelectrorheological, and electroporation models. Inconsistencies were noted in both effective frequency range and field strength between TTFields versus all three proposed models. We addressed these discrepancies through theoretical investigations into the inhomogeneities of electric fields on cellular membranes as a function of disease state, external microenvironment, and tissue or cellular organization. Lastly, future experimental strategies to validate these findings are outlined. Clinical benefits are inevitably forthcoming.

Actuation of flexoelectric membranes in viscoelastic fluids with applications to outer hair cells

Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, and it is used by the outer hair cells (OHCs) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHCs is to find the relations and impact of the electromechanical properties of the membrane, the rheological properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular membrane attached to the inner surface of a circular capillary and (ii) the coupled capillary flow of contacting viscoelastic phases, such that the membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equation, analytical expressions for the transfer function associated with the curvature and electrical field and for the power dissipation of elastic storage energy were found.

Bioelectrorheological model of the cell. 4. Analysis of the extensil deformation of cellular membrane in alternating electric field

Analysis of the angular distribution of extensil mechanical stress, sigma e, generated in cytoplasmic membranes by an external oscillating electric field, is presented. Theoretical considerations show that sigma e is directly proportional to the local relative increase in membrane area and/or to the local relative decrease in its thickness. The magnitude of this stress depends on the position of the analyzed point of the membrane in relation to field direction. The maximal value, sigma eo, is reached at the cell "poles." The magnitude of sigma eo depends on electric and geometric parameters (in particular on field frequency) of the system studied. The foregoing analysis can be applied to quantitatively describe the destabilizing effects of the electric field on the cellular membrane, leading to its poration, fusion, and destruction.

Bioelectrorheological model of the cell. 5. Electrodestruction of cellular membrane in alternating electric field

Recently proposed analysis of the extensil stress developed in a cellular membrane subjected to an alternating electric field (Pawłowski, P., and M. Fikus, 1993. Bioelectrorheological model of the cell. 4. Analysis of the extensil deformation of the membrane in an alternating field. Biophys. J. 65:535-540) was applied in calculations of extensil stress threshold values, sigma eo[d], producing experimentally observed electrodestruction of cells within the frequency range of 7 x 10(1) - 3 x 10(5) Hz. It was shown that the susceptibility (s[d] = 1/sigma eo[d]), of the membrane to this process varies with field frequency and depends on the type of cells. Electrodestruction is facilitated in the 10(5)-Hz field. A rheological hypothesis explaining the experimentally observed dependence of membrane stability on electric field frequency was proposed and successfully tested for two other phenomena: electroporation and electrofusion.

Bioelectrorheological model of the cell. 3. Viscoelastic shear deformation of the membrane

An analytical electromechanical model of a spherical cell exposed to an alternating electric field was used to calculate shear stress generated in the cellular membrane. Shape deformation of Neurospora crassa (slime) spheroplasts was measured. Statistical analysis permitted empirical evaluation of creep of the cellular membrane within the range of infinitesimal stress. Final results were discussed in terms of various rheological models.