Glycocalyx bending by an electric field increases cell motility

The application of physiological strength electric fields may produce a wide range of effects on cells. The mechanisms by which cells detect the presence of these fields, however, are not fully understood. Previous experiments have shown that directionality of cells in the field is governed by an electromechanical mechanism in which the field exerts a torque on the negatively charged, inner glycocalyx that is then transmitted as a force on the cytoskeleton. This mechanism is similar to that by which cells detect fluid shear forces. Several authors, however, have reported that cell directionality and motility behave differently in an electric field. We propose here a second electromechanical mechanism in which the field bends the negatively charged, outer glycocalyx in proximity to the substrate, increasing cell adhesion and, thus, cell motility. The increase in motility depends not only on the field strength, but also on the adhesion of the cell to the substrate prior to application of the field. We show that these mechanisms are common to both human cells and amoebae and, hence, are evolutionarily conserved. Furthermore, the mechanism for detection of electric fields is simply an extension of the mechanism for detecting fluid shears. Bioelectromagnetics. 38:482-493, 2017. © 2017 Wiley Periodicals, Inc.

Cytoskeletal forces produced by extremely low-frequency electric fields acting on extracellular glycoproteins

The physical mechanism by which cells transduce an applied electric field is not well understood. This article establishes for the first time a direct, quantitative model that links the field to cytoskeletal forces. In a previous article, applied electric fields of physiological strength were shown to produce significant mechanical torques at the cellular level. In this article, the corresponding forces exerted on the cytoskeleton are computed and found to be comparable in magnitude to mechanical forces known to produce physiological effects. In addition to the electrical force, the viscous drag force exerted by the surrounding medium and the restoring force exerted by the neighboring structures are considered in the analysis. For an applied electric field of 10 V/m, the force transmitted to the CD44 receptor of a hyaluronan chain in cartilage is about 1 pN at 10 Hz and 7 pN at 1 Hz. For an applied electric field of 100 V/m, the force transmitted to the cytoskeleton at one focus of the glycocalyx is about 0.5 pN at 10 Hz and 1.3 pN at 1 Hz. Mechanical forces of similar magnitude have been observed to produce physiological effects. Hence, this electromechanical transduction process is a plausible mechanism for the production of physiological effects by such electric fields.

The mechanical transduction of physiological strength electric fields

In this article it is proposed that electric fields of physiological strength (approximately 100 V/m) are transduced by the mechanical torque they exert on glycoproteins. The resulting mechanical signal is then transmitted to the cytoskeleton and propagated throughout the cell interior. This mechanical coupling is analyzed for transmembrane glycoproteins, such as integrins and the glycocalyx, and for glycoproteins in the extracellular matrix of cartilage. The applied torque is opposed by viscous fluid drag and restoring forces exerted by adjacent molecules in the membrane or cartilage. The resulting system represents a damped, driven harmonic oscillator. The amplitude of oscillation is constant at low frequencies, but falls off rapidly in the range 1-1000 Hz. The transition frequency depends on parameters such as the viscosity of the surrounding fluid and the restoring force exerted by the surrounding structure. The amplitude increases as the fourth power of the length of the transmembrane glycoproteins and as the square of the applied field. This process may operate in concert with other transduction mechanisms, such as the opening of voltage-gated channels and electrodiffusion/osmosis for DC fields.

Glycoproteins bound to ion channels mediate detection of electric fields: A proposed mechanism and supporting evidence

The mechanism by which animals detect weak electric and magnetic fields has not yet been elucidated. We propose that transduction of an electric field (E) occurs at the apical membrane of a specialized cell as a consequence of an interaction between the field and glycoproteins bound to the gates of ion channels. According to the model, a glycoprotein mass (M) could control the gates of ion channels, where M > 1.4 x 10(-18)/E, resulting in a signal of sufficient strength to overcome thermal noise. Using the electroreceptor organ of Kryptopterus as a mathematical and experimental model, we showed that at the frequency of maximum sensitivity (10 Hz), fields as low as 2 microV/m could be detected, and that the observation could be explained if a glycoprotein mass of 0.7 x 10(-12) kg (a sphere 11 microm in diameter) were bound to channel gates. Antibodies against apical membrane structures in Kryptopterus blocked field transduction, which was consistent with the proposal that it occurred at the membrane surface. Although the target of the field was hypothesized to be an ion channel, the proposed mechanism can easily be extended to include other kinds of membrane proteins.

Integrins may serve as mechanical transducers for low-frequency electric fields

A hypothesis is presented that a transduction mechanism for low frequency electric fields of physiological strength ( approximately 1 V/cm) is the same as that for sinusoidal fluid shear stresses, the force exerted on an integrin. Simple calculations show that the forces exerted on a model integrin by transverse electric fields and fluid shears that produce cellular effects are comparable in magnitude, about 1 fN. The electric force is provided by the interaction of the surface charges on the integrin with the tangential component of the applied field. The mechanical shear force is the transverse fluid drag force exerted on the cylindrical surface of the integrin. Either force is coupled mechanically to the actin cortex within the cell. The mechanical network which exists within a cell and connects a cell to its surroundings would then be directly coupled to an applied electric field. The fundamental transduction mechanism for some electric field effects may then be ultimately mechanical in nature.

Effect of cell electroporation on the conductivity of a cell suspension

An increased permeability of a cell membrane during the application of high-voltage pulses results in increased transmembrane transport of molecules that otherwise cannot enter the cell. Increased permeability of a cell membrane is accompanied by increased membrane conductivity; thus, by measuring electric conductivity the extent of permeabilized tissue could be monitored in real time. In this article the effect of cell electroporation caused by high-voltage pulses on the conductivity of a cell suspension was studied by current-voltage measurements during and impedance measurement before and after the pulse application. At the same time the percentage of permeabilized and survived cells was determined and the extent of osmotic swelling measured. For a train of eight pulses a transient increase in conductivity of a cell suspension was obtained above permeabilization threshold in low- and high-conductive medium with complete relaxation in <1 s. Total conductivity changes and impedance measurements showed substantial changes in conductivity due to the ion efflux in low-conductive medium and colloid-osmotic swelling in both media. Our results show that by measuring electric conductivity during the pulses we can detect limit permeabilization threshold but not directly permeabilization level, whereas impedance measurements in seconds after the pulse application are not suitable.

An analytical model for the calculation of the change in transmembrane potential produced by an ultrawideband electromagnetic pulse

The electric field pulse shape and change in transmembrane potential produced at various points within a sphere by an intense, ultrawideband pulse are calculated in a four stage, analytical procedure. Spheres of two sizes are used to represent the head of a human and the head of a rat. In the first stage, the pulse is decomposed into its Fourier components. In the second stage, Mie scattering analysis (MSA) is performed for a particular point in the sphere on each of the Fourier components, and the resulting electric field pulse shape is obtained for that point. In the third stage, the long wavelength approximation (LWA) is used to obtain the change in transmembrane potential in a cell at that point. In the final stage, an energy analysis is performed. These calculations are performed at 45 points within each sphere. Large electric fields and transmembrane potential changes on the order of a millivolt are produced within the brain, but on a time scale on the order of nanoseconds. The pulse shape within the brain differs considerably from that of the incident pulse. Comparison of the results for spheres of different sizes indicates that scaling of such pulses across species is complicated.

Modelling the anisotropic electrical properties of skeletal muscle

We present a numerical model used to analyse the anisotropic electrical properties of frog muscle, measured in vivo. The model represents the anisotropic, irregularly shaped muscle as a set of cubic elements. We develop a finite difference method to calculate the electrical resistance between two electrodes inserted longitudinally or transversely into the muscle in terms of longitudinal and transverse muscle conductivities. Comparison of the measured impedance values with the calculated resistances yields the separate variation with frequency of the two conductivity components. We also compare the results of the numerical, finite difference method with those of two simple, analytical models.

The low-frequency dielectric properties of octopus arm muscle measured in vivo

The conductance and capacitance of octopus arm are measured in vivo over the frequency range 5 Hz to 1 MHz. Measurement of these parameters for a number of electrode separations permits the determination of the variations in tissue conductivity and dielectric constant with frequency. In the range 1-100 kHz the conductivity is independent of the frequency f and the dielectric constant varies as f-1. These results, in conjunction with those reported previously for frog skeletal muscle, are consistent with the fractal model for the dielectric properties of animal tissue proposed by Dissado. Transformation of the results to complex impedance spectra indicates the presence of a dispersion above 100 kHz.

Cell culture dosimetry for low-frequency magnetic fields

Calculations of the current density and electric field distributions induced in cell cultures by an applied low-frequency magnetic field have assumed that the medium is uniform. This paper calculates these distributions for a more realistic, inhomogeneous, anisotropic model in which the cells are regarded as conducting squares surrounded by insulating membranes. Separate parameters are used to specify the resistivities of the cell interior, the cell membrane parallel to its surface, the cell membrane perpendicular to its surface, and the intercellular junction parallel to the membrane. The presence of gap junctions connecting the interiors of adjacent cells is also considered. For vertical applied magnetic fields, the induced currents and field distributions may deviate considerably from the homogeneous medium model if there is sufficiently tight binding of the cells to each other. The presence of gap junctions can produce relatively large transmembrane electric fields or intracellular current densities. These considerations are generally less important for horizontal applied fields. A simple microscopic model of the cell surface is also discussed.

Spreadsheet method for calculating the induced currents in bone-fracture healing by a low-frequency magnetic field

A commercially available spreadsheet program is used on a microcomputer to calculate the induced current density and electric field patterns produced in a nonhomogeneous, anisotropic model of tissue by a localized, low-frequency magnetic field source. Specific application is made to coils used to promote the healing of bone fractures in limbs. The variation of the conductivity of the fracture gap during healing causes the induced current density pattern to change correspondingly, whereas the induced electric field remains relatively unchanged. Use of more simplified, isotropic models for the bone and for the soft tissue leads to results that differ significantly from those obtained from the full model. The magnetic field beyond the region of the coils contributes little to the induced currents in the fracture gap if the gap is located near the center of the coils.

In vivo measurement of the low-frequency dielectric spectra of frog skeletal muscle

Capacitance, conductance and dielectric loss spectra are obtained, in vivo, for a number of electrode separations in the gastrocnemius muscle of a frog. At each frequency the reciprocals of these parameters are plotted versus electrode separation. From the slopes of the resulting lines the complex permittivity and the conductivity of the muscle can be determined, with electrode effects eliminated. The sequence of power-law responses which is found is consistent with the fractal model proposed by Dissado. The electrical properties measured in vivo with needle electrodes are similar to those measured with surface electrodes for frequencies between 1 kHz and 1 MHz.

Use of a spreadsheet program to calculate the electric field/current density distributions induced in irregularly shaped, inhomogeneous biological structures by low-frequency magnetic fields

A commercially available spreadsheet program is used on a microcomputer to calculate the electric field/current density distributions induced in irregularly shaped, inhomogeneous objects by low-frequency magnetic fields. A finite-difference method is applied to an impedance grid that represents the object being modeled. This approach is validated by comparison with 1) the analytical results of an eccentric cylinder model and 2) measurements made on a square dish containing a saline solution and square, insulating inclusions. Application of the method is also made to a culture dish with a layer of sediment exposed to a horizontal magnetic field.

Numerical and analytical methods to determine the current density distributions produced in human and rat models by electric and magnetic fields

Some numerical and analytical methods used to estimate the internal electric fields and current densities produced within human and animal models by low-frequency electric and magnetic fields are surveyed. A major goal of such modeling is the design of laboratory experiments on cellular systems or animal models to produce a dosage comparable to that experienced by humans in a particular situation. Specific comparisons are made between the results of ellipsoidal approximations and finite-difference methods applied to irregularly-shaped, homogeneous, human and rat models for applied 60 Hz electric (10 kV/m) and magnetic (10(-4) T) fields. For scaling purposes, the induced current densities in various parts of the body are compared for rat and human models for both types of field. In addition, the current density distribution induced in rectangular culture dishes by applied magnetic fields is also described. The extension of these methods to inhomogeneous models and localized sources may not be simple.

Electric fields induced in rat and human models by 60-Hz magnetic fields: comparison of calculated and measured values

The calculated distribution of electric fields induced in homogeneous human and rat models by a 60-Hz magnetic field is compared with values measured in instrumented mannequins. The calculated values agree well with measured values.

Use of a spread sheet to calculate the current-density distribution produced in human and rat models by low-frequency electric fields

The current-density distribution produced inside irregularly shaped, homogeneous human and rat models by low-frequency electric fields is obtained by a two-stage finite-difference procedure. In the first stage the model is assumed to be equipotential. Laplace's equation is solved by iteration in the external region to obtain the capacitive-current densities at the model's surface elements. These values then provide the boundary conditions for the second-stage relaxation solution, which yields the internal current-density distribution. Calculations were performed with the Excel spread-sheet program on a Macintosh-II microcomputer. A spread sheet is a two-dimensional array of cells. Each cell of the sheet can represent a square element of space. Equations relating the values of the cells can represent the relationships between the potentials in the corresponding spatial elements. Extension to three dimensions is readily made. Good agreement was obtained with current densities measured on human models with both, one, or no legs grounded and on rat models in four different grounding configurations. The results also compared well with predictions of more sophisticated numerical analyses. Spread sheets can provide an inexpensive and relatively simple means to perform good, approximate dosimetric calculations on irregularly shaped objects.

The extremely low frequency electrical properties of plant stems

The electrical properties (variation of capacitance and conductance with frequency) of a plant stem can be conveniently measured in vivo by time domain dielectric spectroscopy. In this technique a voltage step is applied to a stem. The resulting polarization current is sampled by a microprocessor and Fourier-transformed to yield these properties. Spectra were obtained for seven electrode separations along a Poinsettia stem. The inverse capacitance and conductance were plotted vs separation for 50 frequencies from .35 to 350 Hz. Least-square fits yielded the effective dielectric constant and conductivity of the stem over this frequency range. In this way electrode effects were eliminated. A similar procedure was carried out for Coleus. A log-log plot of dielectric constant vs frequency shows a two-stage linear decrease for both plants. The conductivity is primarily DC. The dielectric loss decreases smoothly with frequency for Coleus. These results are compared to those for bone and the inorganic material hollandite. The dielectric properties seem best described by a cooperative, many-body approach.

Sensitivity to change in electrical environment: a new bioelectric effect

The action of a 60-Hz, 5 kV/m electric field on erythrocyte parameters in mice was determined. No effects attributable to the magnitude of the field were found, but a transition either from or to an environment containing the field caused decreased red blood cell concentrations and decreased hematocrits. The failure of others to observe effects on erythrocyte parameters following exposure to low-frequency electric fields may have been due to an inappropriate choice of duration of exposure.

Space osteoporosis: an electromagnetic hypothesis

Loss of body calcium during spaceflight is a potential problem in long voyages. This loss does not appear to be caused by a deficiency in diet or exercise. The idea is advanced that the altered electromagnetic environment experienced in space may be at least partially responsible. We show that the electric field induced inside astronauts because of their motion in the geomagnetic field is greater than that which has produced a wide variety of biological effects in earth-bound experiments.