Breakdown of lipid bilayer membranes in an electric field

The behaviour of lipid bilayer membranes, made of oxidized cholesterol, and UO₂²⁺-modified azolectin membranes in a high electric field has been investigated using the voltage clamp method. When a voltage pulse is applied to the membrane of these compositions, the mechanical rupture of the membranes is preceded by a gradual conductance increase which remains quite reversible till a certain moment. The voltage drop at this reversible stage of breakdown leads to a very rapid (characteristic time of less than 5 μs) decrease in the membrane conductance. At repeated voltage pulses of the same amplitude with sufficient intervals between them (approx. 10 s), the current oscillograms reflecting the reversible resistance decrease are well reproduced on the same membrane. The time of attainment of the predetermined level of the membrane conductance is strongly dependent on voltage. At different stages of breakdown we have investigated changes in the conductance of UO₂²⁺-modified membrane after the application of two-step voltage pulses, the kinetics of development of the reversible decrease in the membrane resistance in solutions of univalent and divalent ions, and also the influence of sucrose and hemoglobin on the current evolution. The relationship between the reversible conductance increase, the reversible electrical breakdown [15] and the rupture of membrane in an electric field is discussed. We propose the general interpretation of these phenomena, based on the representation of the potential-dependent appearance in the membrane of pores, the development of which is promoted by an electric field.     

Heterogeneity of membrane transport quantified by the analysis of a unidirectional flux transient of charged tracer

A planar mosaic membrane consists of patches, each with a given area, diffusion coefficient, and mobility of charged tracer; a common electric field, constant in space and time, lies across all the patches. Given the properties of the patches, the transient of the total unidirectional flux (summed over the patches) is predictable. Here we deal with the inverse problem: Given only the observed transient of the total unidirectional flux (as defined experimentally by Ussing), the unknown transport heterogeneity of the mosaic membrane is to be analyzed. Results obtained previously for uncharged tracers are generalized to include effects of the field. In particular, the ratio of the arithmetic and harmonic means (both area-weighted) of the diffusion coefficients, evaluated over the membrane, is expressed in terms of only the observed transient and the field strength and is used to characterize the heterogeneity; and the unique exact solution of the inverse problem for two kinds of patches is recovered at any field strength. If the mosaic consists of n distinct kinds of patches, a sweep of the field strength from low to high values reveals (at most) n steplike shapes in the time course of the total unidirectional flux (normalized to its final steady value), which permit an approximate analysis of the heterogeneity by elementary means.     

Properties of internally perfused, voltage-clamped, isolated nerve cell bodies

The membrane properties of isolated neurons from Helix aspersa were examined by using a new suction pipette method. The method combines internal perfusion with voltage clamp of nerve cell bodies separated from their axons. Pretreatment with enzymes such as trypsin that alter membrane function is not required. A platinized platinum wire which ruptures the soma membrane allows low resistance access directly to the cell's interior improving the time resolution under voltage clamp by two orders of magnitude. The shunt resistance of the suction pipette was 10-50 times the neuronal membrane resistance, and the series resistance of the system, which was largely due to the tip diameter, was about 10(5) omega. However, the peak clamp currents were only about 20 nA for a 60-mV voltage step so that measurements of membrane voltage were accurate to within at least 3%. Spatial control of voltage was achieved only after somal separation, and nerve cell bodies isolated in this way do not generate all-or-none action potentials. Measurements of membrane potential, membrane resistance, and membrane time constant are equivalent to those obtained using intracellular micropipettes, the customary method. With the axon attached, comparable all-or-none action potentials were also measured by either method. Complete exchange of Cs+ for K+ was accomplished by internal perfusion and allowed K+ currents to be blocked. Na+ currents could then be blocked by TTX or suppressed by Tris-substituted snail Ringer solution. Ca2+ currents could be blocked using Ni2+ and other divalent cations as well as organic Ca2+ blockers. The most favorable intracellular anion was aspartate-, and the sequence of favorability was inverted from that found in squid axon.     

Axon voltage-clamp simulations. I. Methods and tests.

This is the first in a series of four papers in which we present the numerical simulation of the application of the voltage clamp technique to excitable cells. In this paper we describe the application of the Crank-Nicolson (1947) method for the solution of the parabolic partial differential equations that describe a cylindrical cell in which the ionic conductances are functions of voltage and time (Hodgkin and Huxley, 1952). This method is compared with other methods in terms of accuracy and speed of solution for a propagated action potential. In addition, differential equations representing a simple voltage-clamp electronic circuit are presented. Using the voltage clamp circuit equations, we simulate the voltage clamp of a single isopotential membrane patch and show how the parameters of the circuit affect the transient response of the patch to a step change in the control potential.The stimulation methods presented in this series of papers allow the evaluation of voltage clamp control of an excitable cell or a syncytium of excitable cells. To the extent that membrane parameters and geometrical factors can be determined, the methods presented here provide solutions for the voltage profile as a function of time.     

A new algorithm for voltage clamp by iteration: A learning control of a nonlinear neuronal system

Voltage-clamp of excitable membrane allows the measurement of membrane currents associated with electrical potential changes across the membrane. However, it has been impossible in practice to apply the conventional analog feedback voltageclamp circuits to single electrode voltage clamping in central neurons. The reason for this is that the feedback system becomes unstable because of the positive feedback required for compensation of capacitative loss through the wall of the microelectrode. Park et al. (1981) proposed a new iterative technique to solve this problem. It requires that the potential to be clamped repeats itself with little or no change. The amount of current needed to clamp the membrane potential is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Since the feedback loop is open in real time, the system has great stability, and this advantage can be exploited in single electrode preparations. The computation algorithm which calculates the current waveform based on the voltage deviation during the last trial is the central part of the iterative voltage-clamp system. In this paper, we propose a new algorithm, which has several theoretical and practical advantages over the original one proposed by Park et al. First, two parameters used in the new algorithm are predetermined by a current-clamp experiment. Second, the speed of convergence of the new algorithm is faster than that of the Park's original algorithm. This was shown by computer simulation of iterative voltage clamp of artificial membrane following Hodgkin-Huxley equations for squid axon membrane and Rall's compartment model for a neuron with dendrites. Finally, we offer proof that the new algorithm is certain to converge for the general cases of voltage-clamp experiments with active membrane properties, synaptic membranes, etc. Consequently, the new algorithm for iterative voltage clamp is very suitable for single electrode voltage clamp in the central neurons. The new algorithm has been successfully applied to voltage-clamp experiments on rubrospinal neurons of cats (Tsukahara, Murakami, Kawato, Oda, and Etoh, in preparation).     

Membrane electric properties by combined patch clamp and fluorescence ratio imaging in single neurons.

An experimental method has been established to measure the electric properties of a cell membrane by combination of patch clamp and dual-wavelength ratio imaging of a fluorescent potentiometric dye, 1-(3-sulfonatopropyl)-4-[beta[2-(di-n-octylamino)-6-naphthyl]vinyl ]pyridinium betaine (di-8-ANEPPS). Pairs of fluorescence images from the dye-stained membrane of neuroblastoma N1E-115 cells excited at two wavelengths were initially obtained to calculate ratio images corresponding to the resting transmembrane potential. Subsequently, a whole-cell patch was established and the membrane potential clamped to levels varying from -100 to +60 mV; at each voltage, a pair of dual-wavelength images were acquired to develop a calibration of the fluorescence ratio. Using this method, the resting potentials could accurately be measured showing that the differentiated cells were 17 mV more polarized than undifferentiated cells. The combination of electrical and optical methods can also follow changes in other membrane electric properties, such as dipole potential, and thus permit a detailed analysis of the membrane electrical properties underlying the voltage regulation of ion channels.     

Dielectric Breakdown of Cell Membranes

With human and bovine red blood cells and Escherichia coli B, dielectric breakdown of cell membranes could be demonstrated using a Coulter Counter (AEG-Telefunken, Ulm, West Germany) with a hydrodynamic focusing orifice. In making measurements of the size distributions of red blood cells and bacteria versus increasing electric field strength and plotting the pulse heights versus the electric field strength, a sharp bend in the otherwise linear curve is observed due to the dielectric breakdown of the membranes. Solution of Laplace's equation for the electric field generated yields a value of about 1.6 V for the membrane potential at which dielectric breakdown occurs with modal volumes of red blood cells and bacteria. The same value is also calculated for red blood cells by applying the capacitor spring model of Crowley (1973. Biophys. J. 13:711). The corresponding electric field strength generated in the membrane at breakdown is of the order of 4 · 10⁶ V/cm and, therefore, comparable with the breakdown voltages for bilayers of most oils. The critical detector voltage for breakdown depends on the volume of the cells. The volume-dependence predicted by Laplace theory with the assumption that the potential generated across the membrane is independent of volume, could be verified experimentally. Due to dielectric breakdown the red blood cells lose hemoglobin completely. This phenomenon was used to study dielectric breakdown of red blood cells in a homogeneous electric field between two flat platinum electrodes. The electric field was applied by discharging a high voltage storage capacitor via a spark gap. The calculated value of the membrane potential generated to produce dielectric breakdown in the homogeneous field is of the same order as found by means of the Coulter Counter. This indicates that mechanical rupture of the red blood cells by the hydrodynamic forces in the orifice of the Coulter Counter could also be excluded as a hemolysing mechanism. The detector voltage (or the electric field strength in the orifice) depends on the membrane composition (or the intrinsic membrane potential) as revealed by measuring the critical voltage in E. coli B harvested from the logarithmic and stationary growth phases. The critical detector voltage increased by about 30% for a given volume on reaching the stationary growth phase.     

Kinetics of Excitable Membranes : Voltage amplification in a diffusion regime

An understanding of the properties of excitable membranes requires the calculation of ion flow through the membrane, including the effects of nonuniformity in the transverse membrane properties (mobilities, fixed charge, electric field). Permeability is apparently controlled at the external interface. Two factors may be involved here: the statistical blocking of pores by divalent cations, and activation energy. Only the former is included in the present treatment. When the total transmembrane voltage is varied, a redistribution in ionic concentration occurs. This can cause a change in boundary (zeta) potential, large in comparison with the applied voltage change—"voltage amplification." The result is a steep change in membrane conductance. The calculated flow curves are compared with experimental results. The Appendix gives an outline of the numerical method used for solving the boundary value problem with several diffusible ions, across a nonuniform regime.     

Slow inactivation of a tetrodotoxin-sensitive current in canine cardiac Purkinje fibers.

We used the two-microelectrode voltage clamp technique and tetrodotoxin (TTX) to investigate the possible occurrence of slow inactivation of sodium channels in canine cardiac Purkinje fibers under physiologic conditions. The increase in net outward current during prolonged (5-20 s) step depolarizations (range -70 to +5 mV) following the application of TTX is time dependent, being maximal immediately following depolarization, and declining thereafter towards a steady value. To eliminate the possibility that this time-dependent current was due to inadequate voltage control of these multicellular preparations early during square clamp pulses, we also used slowly depolarizing voltage clamp ramps (range 5-100 mV/s) to ensure control of membrane potential. TTX-sensitive current also was observed with these voltage ramps; the time dependence of this current was demonstrated by the reduction of the peak current magnitude as the ramp speed was reduced. Reducing the holding potential within the voltage range of sodium channel inactivation also decreased the TTX-sensitive current observed with identical speed ramps. These results suggest that the TTX-sensitive time-dependent current is a direct measure of slow inactivation of canine cardiac sodium channels. This current may play an important role in modulating the action potential duration.     

Synchronization modulation of Na/K pump molecules can hyperpolarize the membrane resting potential in intact fibers

Previously, we have theoretically studied the possibility of electrical rhythmic entrainment of carrier-mediated ion transporters, and experimentally realized synchronization and acceleration of the Na/K pumping rate in the cell membrane of skeletal muscle fibers by a specially designed synchronization modulation electric field. In these studies we either used cut fibers under a voltage clamp or intact fibers, but in the presence of ion channels blockers. A question remained as to whether the field-induced activation observed in the pump molecules could effectively increase the intracellular ionic concentration and the membrane potential at physiological conditions. In this paper, we studied the effects of the field on intact fibers without any channel blockers. We monitored the field-induced changes in the ionic concentration gradient across the cell membrane and the membrane potential non-invasively by using a fluorescent probe and confocal microscopic imaging techniques. The results clearly show that the entrainment of the pump molecules by the synchronization modulation electric field can effectively increase the ionic concentration gradient, and hence, hyperpolarize the membrane potential.     

The N-Shaped Current-Potential Characteristic in Frog Skin: II. Kinetic Behavior during Ramp Voltage Clamp

Previous step voltage-clamp measurements on frog skin showed the presence of an N-shaped current-potential (I-V) relation in excitable skin. However, the collection and reconstruction of I-V data using discrete step changes of skin potential was tedious because of the long refractory period (up to 1 min) in frog skin. A direct and rapid (5 msec) method for recording the N-shaped I-V characteristic in real time is presented. Ramp functions are used as the command to the clamp system instead of a step function. Consequently the skin potential is forced to change in a linear manner (as commanded) and the skin current can be recorded as a continuous function of the controlled change of skin potential. With the ramp clamp, a low-resistance membrane state ( 10 Omega . cm(2)) resembling a breakdown phenomenon was observed at high skin potential ( 300 mv). Entry into the low resistance state resulted in a collapse of the N-shaped I-V relation to a nearly linear function. The utility of the ramp measurement is demonstrated by predicting (1) that the maximum rate of rise of the spike occurs at a voltage corresponding to the valley (local minimum) in the N-shaped I-V curve, (2) that the rate of rise of the spike increases with increasing clamp currents, (3) the voltage peak of the spike, and (4) the time course of the rising phase of the spike.     

Axon voltage-clamp simulations. III. Postsynaptic region.

This is the third in a series of four papers in which we present the numerical simulations of the application of the voltage clamp technique to excitable cells. In this paper we discuss the problem of voltage clamping a region of a cylindrical cell using microelectrodes for current injection and voltage recording. A recently developed technique (Llinás et al., 1974) of internal application of oil drops to electrically insulate a short length of the postsynaptic region of the squid giant synapse is evaluated by simulation of the voltage clamp of an excitable cylindrical cell of finite length with variable placement of the current and voltage electrodes. Our results show that ENa can be determined quite accurately with feasible oil gap lengths but that the determination of the reversal potential for the synaptic conductance, ES, can be considerably in error. The error in the determination of ES dependp, and especially the membrane resistance at the time the synaptic conductance occurs. It is shown that the application of tetraethylammonium chloride to block the active potassium conductance very significantly reduces the error in the determination of ES. In addition we discuss the effects of cable length and electrode position on the apparent amplitude and time course of the syn aptic conductance change. These results are particularly relevant to the application of the voltage clamp technique to cells with nonsomatic synapses. The method of simulation presented here provides a tool for evaluation of voltage clamp analysis of synaptic transmission for any cell with known membrane parameters and geometry.     

Transient potassium currents in slow muscle fibers.

Transient changes in potassium conductance in chronically depolarized slow muscle fibers have been studied using a voltage clamp method. The transient behavior included current decays from initial to steady state for hyperpolarizing and depolarizing voltage clamp steps. A two-pulse voltage clamp sequence (conditioning step followed by test step) showed the initial potassium test current to depend sigmoidally on conditioning potential implicating the involvement of a membrane-bound charged group in regulating potassium current.     

Kinetic properties and inactivation of the gating currents of sodium channels in squid axon.

Associated with the opening and closing of the sodium channels of nerve membrane is a small component of capacitative current, the gating current. After termination of a depolarizing step the gating current and sodium current decay with similar time courses. Both currents decay more rapidly at relatively negative membrane voltages than at positive ones. The gating current that flows during a depolarizing step is diminished by a pre-pulse that inactivates the sodium permeability. A pre-pulse has no effect after inactivation has been destroyed by internal perfusion with the proteolytic enzyme pronase. Gating charge (considered as positive charge) moves outward during a positive voltage step, with voltage dependent kinetics. The time constant of the outward gating current is a maximum at about minus 10 mV, and has a smaller value at voltages either more positive or negative than this value.     

ACTION POTENTIAL OF NITELLA INTERNODES

The ionic current during a non-propagating action potentialis analysed from the voltage clamp experiments. The shape ofthe action potential of the Nitella internode can be reconstructedfrom the data of the voltage clamp experiments. The N-shapedcurrent-voltage characteristics (I-V curve) of the Nitella membraneis not constant with time as it is in the tunnel diode, butdecays with time, converging finally into a delayed rectificationcurve. The temporal locus of the potential at which each I-Vcurve crosses the voltage axis coincides almost exactly withthe action potential. The membrane resistance which is calculatedfrom the slope of the I-V curve at each intersection with thevoltage axis also changes in parallel to the action potential.Such correlations are found in the Nitella not only in the pondwater, but also in high Na, high Ca or high Mg medium, wherethe shape of the action potential is modified in various ways.It is highly probable that the action potential is a locus ofthe change of the membrane potential so that the net membranecurrent may be maintained at zero after the transient modificationof the membrane structure by stimulation. (Received June 30, 1966; )     

Erythrocyte and ghost cytoplasmic resistivity and voltage-dependent apparent size.

Particle resistivity is explicitly included in the equations relating volume to voltage pulse, in electronic cell sizing or resistive pulse spectroscopy (RPS). It has long been known that in high electric fields cell resistivity decreases as the membrane undergoes dielectric breakdown. At sufficiently high electric field strengths, well past dielectric breakdown, the red cell membrane becomes electrically transparent, or nearly so, and apparent cell size becomes essentially a function of the cytoplasmic resistivity. Electronic cell sizing is traditionally carried out at low electric field strengths, and corrections made for the influence of cell shape by use of the Laplace equation. We find the Laplace solution to be still applicable at very high electric field strengths for purposes of calculating specific cytoplasmic resistivity from RPS measurements. Our value for discocytes, 220 omega X cm, is in good agreement with published results obtained by other researchers using other techniques. We have also applied these same procedures to determine the time course of voltage-dependent resistivity changes in ghosts and intact spherocytes, during the first 5 min after suspension in hypotonic medium. We believe these to be the first explicit calculations of particle specific resistivity from post-dielectric-breakdown apparent size, using traditional electronic sizing techniques.     

Effects of physostigmine on the voltage dependent ionic conductances of skeletal muscle fibres

The voltage dependent ionic conductances were studied by analysing the phase plane trajectories of action potentials evoked by electrical stimulation of the sartorius muscles of the frog (Rana esculenta). The delayed outward potassium current was measured also under voltage clamp conditions on muscle fibres of either the frog (Rana esculenta) or Xenopus laevis. On analysing the effect of physostigmine decreasing the peak amplitude, the rate of both the rising and falling phases of the action potentials, it was revealed that the alkaloid at a concentration of 1 mmol/l reduced significantly both the delayed potassium conductance and the outward ionic current values during the action potentials. The inhibition of sodium conductance and inward ionic current was less expressed. The maximum value of delayed potassium conductance measured under voltage clamp conditions was decreased by 1 mmol/l physostigmine. The time constant determined from the development of delayed potassium conductance was increased at a given membrane potential. The voltage vs. n relationship describing the membrane potential dependence of the delayed rectifier was not influenced by physostigmine. It has been concluded that physostigmine changes the time course of the action potentials by decreasing the value of both voltage dependent ionic conductances and by slowing down their kinetics. It is discussed that results obtained from the phase plane analysis of complex pharmacological effects can only be accepted with some restrictions.     

A laser-temperature-jump method for the study of the rate of transfer of hydrophobic ions and carriers across the interface of thin lipid membranes

The first application of a laser-temperature-jump apparatus for the study of ion transport through planar (artificial) lipid membranes is described. The relaxation of the electric current is detected, either continuously at a constant applied voltage or discontinuously by a series of short voltage pulses. The second technique, a combined voltage- and temperature-jump method, is especially appropriate to investigate the kinetics of the adsorption/desorption process of hydrophobic ions and neutral carriers of cations at the membrane interface and to separate this phenomenon from the diffusion process through the unstirred aqueous layers adjacent to the membrane. The aim is to determine the rate-limiting step of transport. The permeation rate of the hydrophobic anion 2,4,6-trinitrophenolate is limited by the inner membrane barrier. For tetraphenylberate the rate constant of translocation across the inner barrier and that of desorption from the membrane into water are found to be of comparable magnitude. The membrane permeability of the neutral macrocyclic ion carrier enniatin B is strongly interface limited by its comparatively small rate of desorption into water. These results show that the frequently used a priori assumption of partition equilibrium at the membrane interfaces during transport is not justified.     

Influence of intercellular clefts on potential and current distribution in a multifiber preparation.

A theoretical model is presented for current and voltage clamp of multifiber bundles in a double sucrose gap. Attention is focused on methodological errors introduced by the intercellular cleft resistance. The bundle is approximated by a continuous geometry. Voltage distribution, as a function of radial distance and time, is defined by a parabolic partial differential equation which is specified for different membrane characteristics. Assuming a linear membrane, analytical solutions are given for current step and voltage step conditions. The theoretical relations (based on Bessel functions) may be used to calculate membrane conductance and capacity from experimental clamp data. The case of a nonlinear membrane with standard Hodgkin-Huxley kinetics for excitatory Na current is treated assuming maximum Na conductances (gNa) of 120, 10, and 1 mmho/cm2. Numerical simulations are presented for potential and current distribution in a bundle of 60 microns diameter during depolarizing voltage steps. Adequate voltage control is restricted to the peripheral fibers of the bundle whereas the membrane potential of the inner fibers deviates from the command level during early inward current, tending to the Na equilibrium potential. In the peak current-voltage diagram the loss of voltage control is reflected by an increased steepness of the negative region and a decreased slope conductance of the positive region. With gNa = 120 mmho/cm2, the positive slope conductance is approximately 25% of the slope expected from ideal space clamping. With the lower values of gNa, the slope conductance ratio is in the order of 50%. Implications of the results for an experimental voltage clamp analysis of early inward current on multifiber preparations are discussed.     

The sodium currents of nerve under voltage clamp as heterogeneous kinetics: A model that is consistent with possible kinetic behavior

Voltage clamp; Na⁺ current; Dielectric relaxation: Charge mobility: Intramemhrune diffusion A model is presented which explains the Na⁺ currents of voltage-clamped nerve as resulting from a heterogeneous initiation of a sequential kinetic process. This is in analogy with the heterogeneity of the kinetics of other dielectric relaxations. The results suggest that: (1) The kinetic processes responsible for the voltage response occur within the membrane rather than at the surface; (2) The heterogeneity is due to simultaneous thermal diffusion and electric field-induced charge migration; (3) The slow turnoff upon prolonged depolarization is a voltage-independent, thermally controlled process: (4) The fast turnoff upon instantaneous repolarizalion is the reverse of the turning-on process. All the kinetic parameters depend on the transmembrane potential in accord with the possible behavior expected from activated-stale theory. The diffusion coefficient of the charged species in the membrane as found from the data agrees with that found by photobleaching experiments on general proteins in membranes. The charge on the molecule responsible for the heterogeneous ‘gating’ can be calculated unambiguously from the data.