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.     

Modification of electrokinetic properties of nuclei in human buccal epithelial cells by electric fields

The influence of an alternating (50 Hz) electric field (5--110 V/cm) on the state of human buccal epithelium cells was studied by the methods of intracellular microelectrophoresis, heterochromatin staining with orcein, and indigo carmine staining for viability and membrane integrity evaluations. Electric field exposure induced an increase in electrophoretic mobility of cell nuclei, decreased numbers of heterochromatin granules near the inner membrane of cell nucleus, and induced cell membrane damage; but cell viability was conserved. Nuclear and cell membrane properties varied with electric field strength and age of the donors. The data obtained are interpreted as evidence of electric field induced activation of the functional state of nuclei.     

Enzyme reactions at the surface of living cells. II. Destabilization in the membranes and conduction of signals

The dynamics of a bound-enzyme reaction is studied when the diffusion of both the substrate and the product is coupled to their electric repulsion and to enzyme reaction. Contrary to what is occurring when substrate diffusion is uncoupled with electric repulsion and enzyme reaction, no hysteresis loop of the partition coefficient exists. The electric partition coefficient monotonically declines as substrate or product concentration is increased in the reservoir. The random perturbation of a steady state may generate a localized destabilization of substrate and product concentration. This destabilization must propagate in the membrane and may be viewed as the conduction of a signal. These conduction phenomena are entirely due to electric effects. In the absence of these effects, the system is homeostatic, that is it returns back to its initial steady state after a perturbation. Obviously under these conditions conduction of signals cannot occur. Increasing the ionic strength of the external milieu tends to stabilize the system and to suppress conduction effects in the membrane.     

Threshold for inhibition of Na, K-ATPase by ELF alternating currents.

Alternating currents can increase or decrease the ATP-splitting activity of the membrane enzyme Na,K-ATPase. Either change depends on the AC frequency, and the greatest effect appears to be in the ELF range at about 100 Hz. The threshold for enzyme inhibition by AC was determined, and it is estimated to be an internal electric field circa 5 microV/cm. The corresponding current-density threshold approximates 8 nA/cm2.     

Resonance electroconformational coupling: A proposed mechanism for energy and signal transductions by membrane proteins

Recent experiments show that membrane ATPases are capable of absorbing free energy from an applied oscillating electric field and converting it to chemical bond energy of ATP or chemical potential energy of concentration gradients. Presumably these enzymes would also respond to endogenous transmembrane electric fields of similar intensity and waveform. A mechanism is proposed in which energy coupling is achieved via Coulombic interaction of an electric field and the conformational equilibria of an ATPase. Analysis indicates that only an oscillating or fluctuating electric field can be used by an enzyme to drive a chemical reaction away from equilibrium.In vivo, the stationary transmembrane potential of a cell must be modulated to become locally oscillatory if it is to derive energy and signal transduction processes.     

Ion channel enzyme in an oscillating electric field

To explain the electrical activation of several membrane ATPases, an electroconformational coupling (ECC) model has previously been proposed. The model explained many features of experimental data but failed to reproduce a window of the field intensity for the stimulated activity. It is shown here that if the affinities of the ion for the two conformational states of the transporter (one with binding site on the left side and the other on the right side of the membrane) are dependent on the electric field, the field-dependent transport can exhibit the observed window. The transporter may be described as a channel enzyme which opens to one side of the membrane at a time. It retains the energy-transducing ability of the earlier ECC models. Analysis of the channel enzyme in terms of the Michaelis-Menten kinetics has been done. The model reproduced the amplitude window for the electric field-induced cation pumping by (Na,K)-ATPase.     

Kinetics of a multistate enzyme in a large oscillating field.

A simple, general, and efficient method for calculating the response of a set of coupled first-order (or pseudo-first-order) chemical reactions to an arbitrarily large periodic field is described. The method is applied to a four-state membrane transport enzyme that is electroconformationally coupled to an ac field, i.e., the enzyme has electric charges that move concomitantly with a conformational transition. The calculation is done both for enzymes in a planar membrane and for enzymes in the spherical membrane of a cell or vesicle in suspension.     

Electric birefringence study of the purple membrane of Halobacterium halobium

An electric birefringence study was carried out on aqueous suspensions of the purple membrane of Halobacterium halobium. In addition to the characterization of both native and modified membrane samples, the dependence of electric birefringence on pH and ionic strength was also investigated. The results indicate that purple membrane shows electric birefringence at a field strength as low as 200 V/cm. The permanent dipole moment and polarizability ranged from 20,500 debyes and 1.01 × 10^?14 cm³ for a purple membrane concentration of 0.40 mg/mL to 41,000 debyes and 2.05 × 10^?14 cm³ for a concentration of 0.80 mg/mL. It was also found that removal of the retinyl group of bacteriorhodopsin substantially decreases but does not eliminate the electric birefringence of the membrane. The solubilization of the membrane by Triton X-100, however, completely abolishes the electric birefringence. These experiments indicate that there is an interaction between adjacent bacteriorhodopsin molecules within the purple membrane via the retinyl chromophore moiety that builds up the permanent dipole moment. They also suggest that there are two types of response when purple membrane suspensions are placed in an electric field. One is an alignment of the disk-shaped particles with the field. The other is a stacking of the particles following their alignment by the electric field, which is promoted by the induced dipole moment.     

Fluorescence imaging in the millisecond time range of membrane electropermeabilisation of single cells using a rapid ultra-low-light intensifying detection system

A fast and sensitive fluorescence image acquisition system is described which uses an ultra-low-light intensifying camera able to acquire digitised fluorescence images with a time resolution of 3.33 ms/image. Two modes of recording were employed. The synchronisation mode allowed acquisition of six successive 3.33 ms-images synchronised with an external trigger, while the memorisation mode allowed acquisition of twelve successive 3.33 ms images starting after a 20 ms-time lag from the external trigger. Interaction of ethidium bromide (EB) with the membrane of electropermeabilised living cells was studied using this imaging system. We observed enhanced fluorescence of the dye when associated with electropermeabilised cells. Using single cells, 3.33 ms-images of the fluorescence interaction patterns of ethidium bromide showed well-defined membrane labelling. The enhanced fluorescence patterns were shown to represent the electropermeabilised area of the cell membrane. The average level of fluorescence associated with the labelled part of the cell membrane increased linearly during and immediately (less than 7 ms) after the electropermeabilisation pulse. Steady-state EB interaction with the membrane was achieved in a maximum 20 ms-time lag after electropermeabilisation. The membrane labelled parts were always observed in the cell regions facing the electrodes. They were present only when the electric field strength was higher than a threshold value which was different for the two cell sides. An increase in electric field intensity led to an increase in the dimensions of the labelled cell region. Received: 7 August 1997 / Revised version: 14 November 1997 / Accepted: 15 January 1998     

Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon.

Transient membrane permeabilization by application of high electric field intensity pulses on cells (electropermeabilization) depends on several physical parameters associated with the technique (pulse intensity, number, and duration). In the present study, electropermeabilization is studied in terms of flow of diffusing molecules between cells and external medium. Direct quantification of the phenomenon shows that electric field intensity is a critical parameter in the induction of permeabilization. Electric field intensity must be higher than a critical threshold to make the membrane permeable. This critical threshold depends on the cell size. Extent of permeabilization (i.e., the flow rate across the membrane) is then controlled by both pulse number and duration. Increasing electric field intensity above the critical threshold needed for permeabilization results in an increase membrane area able to be permeabilized but not due to an increase in the specific permeability of the field alterated area. The electroinduced permeabilization is transient and disappears progressively after the application of the electric field pulses. Its life time is under the control of the electric field parameters. The rate constant of the annealing phase is shown to be dependent on both pulse duration and number, but is independent of electric field intensity which creates the permeabilization. The phenomenon is described in terms of membrane organization transition between the natural impermeable state and the electro-induced permeable state, phenomenon only locally induced for electric field intensities above a critical threshold and expanding in relation to both pulse number and duration.     

Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

Electric field control of lipase membrane activity

Lipase (EC 3.1.1.3., from Pseudomonas sp.) was entrapped in collagen membrane containing liquid crystal (4-methoxybenzilidene-4′-n-butylaniline). The activity of the lipase–liquid crystal membrane at an applied voltage of 4 V was 3.4 compared to a membrane tested without imposition of an external electric field. A linear relationship was observed between the activity of the lipase–liquid crystal membrane and the current. The apparent Michaelis constant (K′_m) of the lipase–liquid crystal membrane under electric field was identical to that of the membrane under ordinary condition. Activation of the lipase–liquid crystal membrane was observed repeatedly, i.e., activation in the presence of an electric field and reversion to a basal level upon removal of the field occurred cyclically. Activity control of immobilized enzymes is desirable for switching devices of a bioreactor. Possible mechanisms of the lipase activation by electric field are discussed.     

Permeabilization of tumor cells induced by pulsed electric fields in vitro

The permeabilization of tumor cells in vitro under the action of pulsed electric fields with a duration of 6 mks in the range of amplitudes 1-7 kV/cm was studied. In the mode of excitation in the ambience of localized plasma discharge in a chamber of special design, an enhanced damage to cells in suspension was observed. It is assumed that the enhancement is due to the synchronous action of the electric field and acoustic shock wave pulses. In the mode without the plasma breakdown of ambience, when the pulse duration of electric field of intensity of 1-2 kV/cm was increased to 60 mks, the efficiency of permeabilization increases nearly by one order. The experimental results are compared with the known theoretical models of cell membrane electroporation.     

A theory of charge separation,ion, electron and proton transport in photosynthetic membranes based on asymmetry of surface charges

We present a model for the light-induced charge separation, proton and ion transport across photosynthetic membranes based on an assumption of the transmembrane surface charge asymmetry. In dark equilibrium, this asymmetry gives rise to an internal membrane electric field whose direction is perpendicular to the membrane surfaces. The role of the field in the light-induced charge separation is similar to the function of the built-in electric field across a solid-state p-n junction. Light-generated free charge carriers in the membrane flow according to its direction and upon recombination on the surface give rise to an electrochemical potential difference for electrons across the membrane. The associated coupled electron-proton transport, and ion diffusion can be viewed as a response of the system to the light-induced redox and electric potential changes.     

Interpretation of the effect of an oscillating electric field on membrane enzymes.

Theoretical expressions for the frequency and amplitude dependence of the rate of a catalyzed reaction are fitted to the data of Graziana et al. (1990) [Graziana, A., Ranjeva, R., & Teissié, J. (1990) Biochemistry 29, 8313-8318] for Ca2+ uptake by carrot protoplasts in an oscillating electric field. This uptake is a direct (linear) measure of the rate of increase of ATP caused by a plasma membrane enzyme in the oscillating field. The fit gives 20 ms and 33 microseconds for the relaxation times of the enzyme and roughly 3 for the effective number of elementary changes displaced across the membrane by a conformational change of the enzyme in its catalytic cycle. Additional experiments are suggested to define further the mechanism of the enzymatic reaction.     

Computer simulation of synchronization of Na/K pump molecules

The behavior of Na/K pump currents when exposed to an oscillating electric field is studied by computer simulation. The pump current from a single pump molecule was sketched based on previous experimental results. The oscillating electric field is designed as a symmetric, dichotomous waveform varying the membrane potential from −30 to −150 mV around the membrane resting potential of −90 mV. Based on experimental results from skeletal muscle fibers, the energy needed to overcome the electrochemical potentials for the Na and K-transports are calculated in response to the field’s two half-cycles. We found that a specially designed oscillating electric field can eventually synchronize the pump molecules so that all the individual pumps run at the same pumping rate and phase as the field oscillation. They extrude Na ions during the positive half-cycle and pump in K ions during the negative half-cycle. The field can force the two ion-transports into the corresponding half-cycles, respectively, but cannot determine their detailed positions. In other words, the oscillating electric field can synchronize pumps in terms of their pumping loops but not at a specific step in the loop. These results are consistent with our experimental results in measurement of the pump currents.     

Constant electric field simulations of the membrane potential illustrated with simple systems

Advances in modern computational methods and technology make it possible to carry out extensive molecular dynamics simulations of complex membrane proteins based on detailed atomic models. The ultimate goal of such detailed simulations is to produce trajectories in which the behavior of the system is as realistic as possible. A critical aspect that requires consideration in the case of biological membrane systems is the existence of a net electric potential difference across the membrane. For meaningful computations, it is important to have well validated methodologies for incorporating the latter in molecular dynamics simulations. A widely used treatment of the membrane potential in molecular dynamics consists of applying an external uniform electric field E perpendicular to the membrane. The field acts on all charged particles throughout the simulated system, and the resulting applied membrane potential V is equal to the applied electric field times the length of the periodic cell in the direction perpendicular to the membrane. A series of test simulations based on simple membrane-slab models are carried out to clarify the consequences of the applied field. These illustrative tests demonstrate that the constant-field method is a simple and valid approach for accounting for the membrane potential in molecular dynamics studies of biomolecular systems. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Elastic, electrostatic and electrokinetic forces influencing membrane curvature

Many cellular and intracellular processes critically depend on membrane shape, but the shape generating mechanisms are still to be fully understood. In this study we evaluate how electrostatic/electrokinetic forces contribute to membrane curvature. Membrane bilayer had finite thickness and was either elastically anisotropic or anisotropic overall, but isotropic per sections (heads and tails). The physics of the situation was evaluated using a coupled system of elastic and electrostatic/electrokinetic (Poisson-Nernst-Planck) equations. The fixed charges present only on the upper membrane surface lead to the accumulation of counter-ions and depletion of co-ions that decay spatially very rapidly (Debye length<1nm), as does the potential and electric field. Spatially uneven electric field and the permittivity mismatch also induce charges at the membrane-solution interface, which are not fixed but influence the electrostatics nevertheless. Membrane bends due to - Coulomb force (caused by fixed membrane charges in the electric field) and the dielectric force (due to the non-uniform electric field and the permittivity mismatch between the membrane and the solution). Both act as membrane surface forces, and both depend supra-linearly on the fixed charge density. Regardless of sign of the fixed charges, the membrane bends toward the charged (upper) surface owing to the action of the Coulomb force, but this is opposed by the smaller dielectric force. The spontaneous membrane curvature becomes very pronounced at high fixed charge densities, leading to very small spontaneous radii (<50nm). In conclusion the electrostatic/electrokinetic forces contribute significantly to the membrane curvature.     

Membrane electropermeabilization effects of frequency and membrane surface order on liposome leakage

Liposomes containing fluorescence marker were exposed to an alternating electric field of 80 V peak to peak square electric waves at different frequencies 0.01, 1, and 100 kHz to perturb the liposome permeation. The efflux of fluorescence dye after application of the electric field was measured by recording the fluorescence emission due to the complex formation reaction between the fluorescence dye and calcium ions in the bulk medium solution. Two independent sets of experiments were conducted: 1) calcium ions were present during electropulsation; and 2) they were added after electric field application. Two parameters, fluorescence emission intensity and increment of temperature of the solution in the chamber, were studied. The effect of membrane surface order on the fluorescence dye leakage from the liposomes was studied by addition of urea at threshold concentration before the liposomes sealed. The data demonstrate the existence of frequency dependency window at 1 kHz. Furthermore, the data were interpreted according to the theory of interactions of electromagnetic fields with highly polarized and deformed materials such as liposome particles. The urea caused an enhancement of the fluorescence dye leakage at frequency of 100 kHz. This effect could be explained as a decrease of the membrane binding rigidity due to the disordering effect of urea on the membrane lipid surface. Our conclusion is that the frequency and the membrane surface order are additional parameters that influence the processes of membrane electropermeabilization.