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

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.

Viscoelasticity of biofilms and their recalcitrance to mechanical and chemical challenges

We summarize different studies describing mechanisms through which bacteria in a biofilm mode of growth resist mechanical and chemical challenges. Acknowledging previous microscopic work describing voids and channels in biofilms that govern a biofilms response to such challenges, we advocate a more quantitative approach that builds on the relation between structure and composition of materials with their viscoelastic properties. Biofilms possess features of both viscoelastic solids and liquids, like skin or blood, and stress relaxation of biofilms has been found to be a corollary of their structure and composition, including the EPS matrix and bacterial interactions. Review of the literature on viscoelastic properties of biofilms in ancient and modern environments as well as of infectious biofilms reveals that the viscoelastic properties of a biofilm relate with antimicrobial penetration in a biofilm. In addition, also the removal of biofilm from surfaces appears governed by the viscoelasticity of a biofilm. Herewith, it is established that the viscoelasticity of biofilms, as a corollary of structure and composition, performs a role in their protection against mechanical and chemical challenges. Pathways are discussed to make biofilms more susceptible to antimicrobials by intervening with their viscoelasticity, as a quantifiable expression of their structure and composition.

Recalcitrance of biofilms against mechanical and chemical challenges has been looked at for ages from a microbiological perspective, but an approach based on viscoelastic properties of biofilms yields new insights in this recalcitrance.

Electrohydrodynamic model of vesicle deformation in alternating electric fields

We develop an analytical theory to explain the experimentally observed morphological transitions of quasispherical giant vesicles induced by alternating electric fields. The model treats the inner and suspending media as lossy dielectrics, and the membrane as an impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. Our approach, which is based on force balance, also allows us to describe the time evolution of the vesicle deformation, in contrast to earlier works based on energy minimization, which are able to predict only stationary shapes. Our theoretical predictions for vesicle deformation are consistent with experiment. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasispherical rest shape. The model can be used to rationalize the transient and steady deformation of biological cells in electric fields.

Mechanokinetic model of cell membrane: theoretical analysis of plasmalemma homeostasis, growth and division

A theoretical model dealing with endocytosis, exocytosis and caveolae invagination, describing plasmalemma homeostasis during cell growth and division, is proposed. It considers transmembrane pressure, membrane tension and mechanosensitivity of membrane processes. Membrane hydraulic conductivity and the flux of transmembrane nonvesicular transport are taken into account. The developed mathematical analysis operates with a formulated set of constitutive equations describing the mechanical state and kinetics of changes in an open dynamic membrane system. The standard version of a model with adjusted parameters was implemented, and predictions including a discussion on the effect of possible parameter modifications were presented. Computer simulations indicate big changes in the magnitude of membrane tension and elasticity, and in the number of membrane buddings in young cells and during mitosis. They also show the extent of cell growth inhibition resulting from a decrease in transmembrane transport or an increase in the exerted difference in osmotic pressure. Moreover, the simulations reveal that exocytosis regulated during mitosis may not be as important for cell growth, as sometimes presumed. Finally, practical application and possible extension of the model are discussed.

Theoretical model of reticulocyte to erythrocyte shape transformation

A theoretical model describing the kinetics of reticulocyte shape transformation was developed. The model considers the evolution of a simple cellular shape under transmembrane pressure difference, and proposes a four-parameter axisymmetric approximation of the cell surface. The mathematical analysis considers plasma membrane tension in the plane of bilayer leaflets, membrane spontaneous curvature and transmembrane transport of water. Cytoskeleton dilatational and shear rigidity, and the energetic barrier preventing the decrease of cell volume below a certain minimum are also incorporated. The set of adequate physical assumptions allowed for formulation of the equation for free energy of the investigated system. Computer simulations of cell shape changes, down to the state of free energy minimum, together with estimation of the time needed for the resulting transport of water, revealed a complex, three-phase picture of temporal alterations in cellular geometry with a wide spectrum of final results, and led to propose a standard model of reticulocyte-erythrocyte transformation. According to the model, both cell volume and surface undergo changes, and the work of the pressure, initially accumulated in the cytoskeleton, is consumed for local bending of the cell membrane. Further simulations with modified initial shape or parameters of the standard model show the trajectories of system evolution and help in better understanding the conditions for the erythro-, sphero-, ovalo-, stomato-, and leptoidal metamorphosis of maturing red blood cells. The stability of the final biconcave shape was also verified. Spherogenic modifications were discussed in the context of spherocytosis. Future development of the model was proposed.

Cell relaxation after electrodeformation: effect of latrunculin A on cytoskeletal actin

Precise measurement of the mechanical properties of a cell provides useful information about its structural organization and physiological state. It is interesting to understand the effect of individual components on the mechanical properties of the entire cell. In this study, we investigate the influence of the cytoskeletal actin on the viscoelastic properties of a cell. Actin-specific agents, including latrunculin A and jasplakinolide, are used to alter the organization of the cytoskeletal actin. Brassica oleracea protoplasts are treated with the drugs and deformed under an external electric potential. The relaxation processes of single protoplasts after electrodeformation are measured. The data are analyzed by a model-independent spectrum recovery algorithm. Two distinct characteristic time constants are obtained from the relaxation spectra. Treatment with latrunculin A increases both of the relaxation time constants. The longest relaxation times for control, latrunculin A treated, and jasplakinolide treated cells are determined to be 0.28, 1.0, and 0.21 s, respectively.

Viscoelastic relaxation in the membrane of the auditory outer hair cell

The outer hair cell (OHC) in the mammalian ear has a unique membrane potential-dependent motility, which is considered to be important for frequency discrimination (tuning). The OHC motile mechanism is located at the cell membrane and is strongly influenced by its passive mechanical properties. To study the viscoelastic properties of OHCs, we exposed cells to a hypoosmotic solution for varying durations and then punctured them, to immediately release the osmotic stress. Using video records of the cells, we determined both the imposed strain and the strain after puncturing, when stress was reset to zero. The strain data were described by a simple rheological model consisting of two springs and a dashpot, and the fit to this model gave a time constant of 40 +/- 19 s for the relaxation (reduction) of tension during prolonged strain. For time scales much shorter or longer than this, we would expect essentially elastic behavior. This relaxation process affects the membrane tension of the cell, and because it has been shown that membrane tension has a modulatory role in the OHC's motility, this relaxation process could be part of an adaptation mechanism, with which the motility system of the OHC can adjust to changing conditions and maintain optimum membrane tension.

Bioelectrorheological model of the cell. VI. Experimental verification of the rheological model of cytoplasmic membrane

The susceptibility of the Neurospora crassa (slime) cellular membrane to electroporation and electrodestruction in an alternating electric field was further investigated. The results were analyzed according to the dynamic rheological model of the cytoplasmic membrane. Based on an analytical description of membrane susceptibility to electroporation, the rheological parameters of the foregoing process in N. crassa cellular membrane were found: they closely resemble those previously determined for the membranes' destruction. This suggests that both processes are temporally related and are induced within the same structures of the membrane. The dependence of the destruction of the membrane on the time of application and the frequency of the electric field was theoretically predicted and experimentally confirmed.

Dielectrophoretic forces and potentials induced on pairs of cells in an electric field

A combined numerical/experimental study is reported of the membrane potentials and dielectrophoretically induced forces between cells, membrane pressures, and velocity of attraction of cells under the influence of an electric field. This study was designed to explore electrical and mechanical effects produced by a field on cells in close proximity or undergoing electrically induced fusion. Laplace's equation for pairs of membrane-covered spheres in close proximity was solved numerically by the boundary element method, and the electrically induced forces on the cells and between cells were obtained by evaluating the Maxwell stress tensor. The velocity of approach of erythrocyte ghosts or fused ghosts in a 60-Hz field of 6 V/mm was measured experimentally, and the data were interpreted by using Batchelor's theory for hydrodynamic interaction of hard spheres. The numerical results show clearly the origin of the dielectrophoretic pressures and forces in fused and unfused cells and the effects of a nearby cell on the induced membrane potentials. The experimental results agree well with predictions based on the simple electrical model of the cell. The analysis shows the strong effect of hydrodynamic interactions between the cells in determining their velocity of approach.

Cell fission and formation of mini cell bodies by high frequency alternating electric field

We report the use of high frequency alternating electric fields (AC) to induce deformation of sea urchin eggs, leading to budding of membrane vesicles or fission of cells. Several mini cell bodies can be prepared from a single egg by carefully manipulating the frequency and amplitude of the AC field and the ratio between the interelectrode spacing and the cell diameter, alpha. alpha values between 2.2 and 3.5 have been found to be optimal for inducing fission of sea urchin eggs. In a typical experiment, a sea urchin egg (diameter = 75 microns), suspended in a low ionic medium (conductance < 2 mS/m), was located under the microscope between two platinum wire electrodes, separated by a distance of approximately 200 microns. A medium strength AC field (< 100 V/cm at 2 MHz) was applied to attract the egg to one of the two electrodes via dielectrophoresis. This process took place in a few seconds. The voltage was then slowly increased to approximately 1000 V/cm over approximately 30 s. The cell elongated and separated into two fragments, the larger one containing the nucleus. When the field was turned off, the mother cell and the daughter vesicle retracted to form spherical mini cell bodies that appear to be stable as assessed by the absence of swelling for the duration of the experiment (approximately 15 min). This indicates that membranes of these mini cell bodies were not leaky to ions and small molecules. This procedure could be repeated a few times to make several mini cell bodies from a single egg. With practice, several minicell bodies could also be prepared in a single fission experiment by adjusting the field parameters and the a value. Cell fission is a result of the mechanical stress produced by the AC field. These procedures may be used to prepare mini membrane vesicles for voltage clamp experiments or to perform microsurgical manipulation of cells, embryos, or chromosomes.

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.