On Bioelectric Potentials in an Inhomogeneous Volume Conductor

Green's theorem is used to derive two sets of expressions for the quasi-static potential distribution in an inhomogeneous volume conductor. The current density in passive regions is assumed to be linearly related instantaneously to the electric field. Two equations are derived relating potentials to an arbitrary distribution of impressed currents. In one, surfaces of discontinuity in electrical conductivity are replaced by double layers and in the other, by surface charges. A multipole equivalent generator is defined and related both to the potential distribution on the outer surface of the volume conductor and to the current sources. An alternative result involves the electric field at the outer surface rather than the potential. Finally, the impressed currents are related to electrical activity at the membranes of active cells. The normal component of membrane current density is assumed to be equal at both membrane surfaces. One expression is obtained involving the potentials at the inner and outer surfaces of the membrane. A second expression involves the transmembrane potential and the normal component of membrane current.     

Simple shifts in the voltage dependence of sodium channel gating caused by divalent cations

The effect of elevated divalent cation concentration on the kinetics of sodium ionic and gating currents was studied in voltage-clamped frog skeletal muscle fibers. Raising the Ca concentration from 2 to 40 mM resulted in nearly identical 30-mV shifts in the time courses of activation, inactivation, tail current decay, and ON and OFF gating currents, and in the steady state levels of inactivation, charge immobilization, and charge vs. voltage. Adding 38 mM Mg to the 2 mM Ca bathing a fiber produced a smaller shift of approximately 20 mV in gating current kinetics and the charge vs. voltage relationship. The results with both Ca and Mg are consistent with the hypothesis that elevated concentrations of these alkali earth cations alter Na channel gating by changing the membrane surface potential. The different shifts produced by Ca and Mg are consistent with the hypothesis that the two ions bind to fixed membrane surface charges with different affinities, in addition to possible screening.     

Comparison of membrane electroporation and protein denature in response to pulsed electric field with different durations

In this paper, we compared the minimum potential differences in the electroporation of membrane lipid bilayers and the denaturation of membrane proteins in response to an intensive pulsed electric field with various pulse durations. Single skeletal muscle fibers were exposed to a pulsed external electric field. The field‐induced changes in the membrane integrity (leakage current) and the Na channel currents were monitored to identify the minimum electric field needed to damage the membrane lipid bilayer and the membrane proteins, respectively. We found that in response to a relatively long pulsed electric shock (longer than the membrane intrinsic time constant), a lower membrane potential was needed to electroporate the cell membrane than for denaturing the membrane proteins, while for a short pulse a higher membrane potential was needed. In other words, phospholipid bilayers are more sensitive to the electric field than the membrane proteins for a long pulsed shock, while for a short pulse the proteins become more vulnerable. We can predict that for a short or ultrashort pulsed electric shock, the minimum membrane potential required to start to denature the protein functions in the cell plasma membrane is lower than that which starts to reduce the membrane integrity. Bioelectromagnetics 34:253–263, 2013. © 2012 Wiley Periodicals, Inc.     

MEMBRANE POTENTIAL OF THE SQUID GIANT AXON DURING CURRENT FLOW

The squid giant axon was placed in a shallow narrow trough and current was sent in at two electrodes in opposite sides of the trough and out at a third electrode several centimeters away. The potential difference across the membrane was measured between an inside fine capillary electrode with its tip in the axoplasm between the pair of polarizing electrodes, and an outside capillary electrode with its tip flush with the surface of one polarizing electrode. The initial transient was roughly exponential at the anode make and damped oscillatory at the sub-threshold cathode make with the action potential arising from the first maximum when threshold was reached. The constant change of membrane potential, after the initial transient, was measured as a function of the total polarizing current and from these data the membrane potential is obtained as a function of the membrane current density. The absolute value of the resting membrane resistance approached at low polarizing currents is about 23 ohm cm.². This low value is considered to be a result of the puncture of the axon. The membrane was found to be an excellent rectifier with a ratio of about one hundred between the high resistance at the anode and the low resistance at the cathode for the current range investigated. On the assumption that the membrane conductance is a measure of its ion permeability, these experiments show an increase of ion permeability under a cathode and a decrease under an anode.     

Voltage Clamp of Cardiac Muscle in a Double Sucrose Gap: A Feasibility Study

A method of stabilizing the membrane potential of a small area of cardiac muscle membrane and the limitations of this method are described. Tiny bundles or strands, approximately 80 μm in diameter, of electrically interconnected fibers from the ventricles of rabbit hearts were used in a double sucrose gap. Current records associated with step changes in voltage were complicated by two capacitive surges of current of nodal and nonnodal origin and large “leakage” currents of nonnodal origin resulting mainly from the multifibered nature of the preparation and emphasized by the method. The transient, inward membrane currents in response to moderate depolarizing steps in command potential had the same duration as the upstroke of the action potential. In good runs, currents were smooth and free from notches. These initial currents behaved qualitatively like the initial sodium currents in squid axon and in other excitable membranes. A fraction of the initial sodium current persisted at least as long as 300 ms. The relationship between peak initial current and voltage was graded and linear in the positive direction. In the negative region the relationship was often very steep, indicating insufficient voltage control of all the membranes despite the squareness of the voltage record. Other indications of inadequacy of control could occur and thus even with this optimum preparation of cardiac muscle it was not feasible to analyze quantitatively either the initial or the prolonged sodium currents.     

Mapping electric currents around skeletal muscle with a vibrating probe

A vibrating microelectrode, or vibrating probe (Jaffe and Nuccitelli, 1974), was used to map the pattern of artificially created electric currents flowing around single muscle fibers at the edge of frog cutaneous pectoris muscles. When a muscle fiber was impaled with a micropipette, a "point sink" of current was often created at the site of impalement because of injury to the cell membrane. Current, being drawn from the flanking membrane, flowed into the cell only at this point. This defined current allowed us to map the spatial resolving power of the vibrating probe by moving to different positions near the impalement site. The results suggest that under our experimental conditions the limit of resolution is a few tens of micrometers. The results were fit reasonably well by a computer model. Current was also passed through a micropipette and mapped at various positions with the vibrating probe. In this case, the current flowed to a remote reference electrode. With the current electrode in the extracellular fluid, the probe signal decayed as the inverse square of the distance, as expected. With the current electrode placed intracellularly, current was funneled along the muscle fiber axis, reflecting its cable-like properties. The signal recorded by the vibrating probe was altered accordingly, and the results could be well fit by a simple model.     

Electric field-induced functional reductions in the K+ channels mainly resulted from supramembrane potential-mediated electroconformational changes.

The goal of this study is to distinguish the supramembrane potential difference-induced electroconformational changes from the huge transmembrane current-induced thermal damages in the delayed rectifier K+ channels. A double Vaseline-gap voltage clamp was used to deliver shock pulses and to monitor the channel currents. Three pairs of 4-ms shock pulses were used to mimic the electric shock by a power-line frequency electric field. Each pair consists of two pulses with the same magnitude, starting from 350 to 500 mV, but with opposite polarities. The shock pulse-generated transmembrane ion flux and the responding electric energy, the Joule heating, consumed in the cell membrane, as well as the effects on the K+ channel currents, were obtained. Results showed that huge transmembrane currents are not necessary to cause damages in the K+ channel proteins. In contrast, reductions in the K+ channel currents are directly related to the field-induced supramembrane potential differences. By a comparison with the shock field-induced Joule heating effects on cell membranes, the field-induced supramembrane potential difference plays a dominant role in damaging the K+ channels, resulting in electroconformational changes in the membrane proteins. In contrast, the shock field-induced huge transmembrane currents, therefore the thermal effects, play a secondary, trivial role.     

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.     

Augmentation and suppression of action potentials by estradiol in the myometrium of pregnant rat.

The purpose of this study was to investigate the actions of estradiol on spontaneous and evoked action potentials in the isolated longitudinal smooth muscle cells of the pregnant rat. Single cells were obtained by enzymatic digestion from pregnant rat longitudinal myometrium. Action potentials and currents were recorded by whole-cell current-clamp and voltage-clamp methods, respectively. The acute effects of 17beta-estradiol on action potentials and inward and outward currents were investigated. The following results were obtained. The average resting membrane potential of single myometrial cells was -54 mV (n = 40). In many cells, an electrical stimulation evoked a membrane depolarization, and action potentials were superimposed on the depolarization. In some cells, spontaneous action potentials were observed. Estradiol (30 microM) slightly depolarized the membrane (ca. 5 mV) and attenuated the generation of action potentials by reducing the frequency and amplitude of the spikes. Afterhyperpolarization was also attenuated by estradiol (30 microM). On the other hand, in 5 of 35 cells, estradiol increased the first spike amplitude and action potential duration, while frequency of the spike generation and afterhyperpolarization were inhibited. In voltage-clamped muscle cells, estradiol inhibited both inward and outward currents. Acute inhibition or augmentation of spike generation by estradiol is due to the balance of inhibition of inward and outward currents. Inhibition of both currents also prevented afterhyperpolarization, causing potential-dependent block of Ca spikes.     

The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

Effect of sodium-free solutions on ionic currents of snail giant neurons

The ionic currents of the snail giant neurons were investigated by the voltage clamp method. The effect of sodium-free solutions on the inward and outward currents was studied. It is shown that the current entering the cells is created mainly by sodium ions. When a preparation is immersed into a solution not containing sodium ions, most neurons (tentatively neurons of type "a") "lose" the inward currents. In other neurons (tentatively of type "b") this process lasts 40 min and more. A number of peculiarities of type "b" neurons were noted. The response of the excitable membrane to conditioning polarization was also investigated. The data obtained permit the conclusion that 85–90% of the sodium-transfer system is activated in the case of a voltage clamp from the level of the resting potential.A. A. Bogomolets Institute of Physiology, Kiev. Translated from Neirofiziologiya, Vol. 2, No. 3, pp. 314–320, May–June, 1970.     

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.     

Membrane Potential Hyperpolarization in Mammalian Cardiac Cells by Synchronization Modulation of Na/K Pumps

In previously reported work, we developed a new technique, synchronization modulation, to electrically activate Na/K pump molecules. The fundamental mechanism involved in this technique is a dynamic entrainment procedure of the pump molecules, carried out in a stepwise pattern. The entrainment procedure consists of two steps: synchronization and modulation. We theoretically predicted that the pump functions can be activated exponentially as a function of the membrane potential. We have experimentally demonstrated synchronization of the Na/K pump molecules and acceleration of their pumping rates by many fold through use of voltage-clamp techniques, directly monitoring the pump currents. We further applied this technique to intact skeletal muscle fibers from amphibians and found significant effects on the membrane resting potential. Here, we extend our study to intact mammalian cardiomyocytes. We employed a noninvasive confocal microscopic fluorescent imaging technique to monitor electric field–induced changes in ionic concentration gradient and membrane resting potential. Our results further confirm that the well-designed synchronization modulation electric field can effectively accelerate the Na/K pumping rate, increasing the ionic concentration gradient across the cell membrane and hyperpolarizing the membrane resting potential.     

Extracellular potential field of excited isolated frog muscle fibres immersed in a volume conductor

The extracellular potential field of isolated frog muscle fibres immersed in a volume conductor was studied at radial distances up to 3 mm during excitation. The shape of the field distant from both the point of the origin of the excitation and the end of the fibre as well as changes in the field when depolarization wave approached the fibre end were described. Different amplitude decrease rates in individual phases of the extracellular potential and the peak-to-peak amplitude at different temperatures were found. Extracellular potentials at long radial distances were recorded using an averaging technique. The shape of the extracellular potentials at long radial distances over the fibre and beyond its end were very similar to the shape of extraterritorial potentials of a single motor unit.     

对吸附式电极记录装置的技术改进

本文介绍一种用吸附式电极记录合体细胞组织生物电位的改进装置。它的特点是在建造负压的注射器和吸附式电极之间设置一分离的小室。这一小室既保障了放大器与实验标本之间的电路连系,又可直接放置在实验标本附近,负压由改进的注射器经过充有空气的塑料管抽吸,注射器可以放在任何方便的位置上。该方法在记录小动物,如蜗牛、青蛙、等的心脏、消化道等组织器官的生物电位时都能获得比较理想的效果,对研究小动物合体细胞组织的正常机能及药物作用等都具有较好的适用价值,并具有定位准确、操作方便的优点。     

THE ESCAPE OF HEMOGLOBIN FROM THE RED CELL DURING HEMOLYSIS

By means of measurements from cinematograph films of the time taken for human red cells to lose hemoglobin while hemolyzing, it is shown that small concentrations of saponin bring about a relatively small permeability of the cell membrane to the pigment, whereas large concentrations so destroy the membrane that the theoretical time for loss of pigment through a completely permeable membrane (0.16 second) is very nearly attained. These results are in agreement with those obtained from electrical measurements, and the dependence of permeability on lysin concentration can be explained on the basis of what is known about the rate of transformation of lysin as it reacts with the cell envelope. When cells are hemolyzed by hypotonic solutions, on the other hand, the permeability of the membrane to pigment is nearly constant, irrespective of the tonicity used to bring about lysis.     

Maintained depolarization of synaptic terminals facilitates nerve-evoked transmitter release at a crayfish neuromuscular junction

Presynaptic and postsynaptic potentials were examined by intracellular recording at a crayfish neuromuscular junction. During normal synaptic transmission, the action potentials were recorded in the terminal region of the excitatory axon and postsynaptic responses were obtained in the muscle fibers. We found that it was possible to modify the synaptic transmission by applying depolarizing or hyperpolarizing currents through the presynaptic intracellular electrode. Typically, a 7-15 mV depolarization lasting longer than 50 msec leads to a large (500%) enhancement of transmitter release, even though the preterminal action potential is reduced in amplitude. Hyperpolarization increases the amplitude of the action potential, but slightly reduces the transmitter release. These results are different from those reported for other neuromuscular synapses and the squid giant synapse, but are similar in many respects to the results reported for several invertebrate central synapses. We conclude, first, that different synapses may have markedly different responses to conditioning by membrane polarization and, secondly, that maintained low-level depolarization may induce a potentiated state in the nerve terminal, perhaps brought about by slow entry of calcium.     

Electrochemical classification of gram-negative and gram-positive bacteria

Intestinal bacteria were classified as gram-positive or gram-negative by an electrode system with a basal plane pyrolytic graphite electrode and a porous nitrocellulose membrane filter to trap bacteria. When the potential of the graphite electrode was run in the range of 0 to 1.0 V versus the saturated calomel electrode (SCE), gram-positive bacteria gave peak currents at 0.65 to 0.69 V versus the SCE. The peak potentials of gram-negative bacteria were 0.70 to 0.74 V versus the SCE. Gram-negative bacteria and gram-positive bacteria were also classified based on the ratio of the second peak current to the first peak current when the potential cycle was repeated twice. The numbers of cells on the membrane filter were determined from the peak currents. It was found that the peak currents result from the electrochemical oxidation of coenzyme A in the cells of Escherichia coli and Lactobacillus acidophilus.     

Permeability of Alkali Metal Cations in Lobster Muscle : A comparison of electrophysiological and osmometric analyses

Single muscle fibers from lobster walking legs are effectively impermeable to Na, but are permeable to K. They shrink in hyperosmotic NaCl; they swell in low NaCl media which are hyposmotic or which are made isosmotic with the addition of KCl. In conformity, the membrane potential is relatively insensitive to changes in external Na, while it responds according to the Nernst relation for changes in external K. When the medium is made isosmotic or hyperosmotic with RbCl the volume and membrane potential changes are of essentially the same magnitudes as those in media enriched with KCl. The time courses for attaining equilibrium are slower, indicating that Rb is less permeant than K. Substitution of CsCl for NaCl (isosmotic condition) produces no change in volume of the muscle fiber. Addition of CsCl (hyperosmotic condition) causes a shrinkage which attains a steady state, as is the case in hyperosmotic NaCl. Osmotically, therefore, Cs appears to be no more permeant than is Na. However, the membrane depolarizes slowly in Cs-enriched media and eventually comes to behave as an ideal Cs electrode. Thus, the electrode properties of the lobster muscle fiber membrane may not depend upon the diffusional relations of the membrane and ions, and the osmotic permeability of the membrane for a given cation may not correspond with the electrophysiologically deduced permeability. Comparative data on the effects of NH₄ and Li are also included and indicate several other degrees of complexity in the cell membrane.     

Experimentally verified model of mechanomyograms recorded during single motor unit contractions

The aim of the paper is to create a model which enables to observe the mechanomyographic (MMG) wave generated during single motor unit contractions in a muscle, while the muscle is immersed in paraffin oil. The muscle model is described as a rheological membrane. Both the muscle and the medium models have been built by using Stiff-Finite-Element-Method (SFEM), which allows one to simulate the muscle surface displacement and the acoustic propagation of this effect in the oil. Such a modelling enables one to determine the impact of the rheological properties of the liquid environment on the shape of the MMG wave. In order to verify the model, the MMG signals and the contraction forces have been recorded in vivo from the medial gastrocnemius muscle of a rat. In these experiments single motor units were stimulated with various stimulation frequencies. A piezotransducer, immersed in paraffin oil, has been used to record the MMG signal recording. The signals recorded during individual twitches of the motor units have been used to estimate the parameters of the model. Subsequently, the model has been experimentally verified. The signals recorded in experiments during unfused and fused tetani have been compared with the simulated model responses in the analogous stimulation program. It has been observed that the MMG signals obtained with the proposed linear model have been consistent with the results of in vivo experiments.