Electrokinetic membrane processes in relation to properties excitable tissues. II. Some theoretical considerations

A quantitative theory is presented for the behavior of a membrane-electrolyte system subject to an electric current flow (the "membrane oscillator"). If the membrane is porous, carries "fixed charges," and separates electrolyte solutions of different conductances, it can be the site of repetitive oscillatory changes in the membrane potential, the membrane resistance, and the hydrostatic pressure difference across the membrane. These events are accompanied by a pulsating transport of bulk solutions. The theory assumes the superposition of electrochemical and hydrostatic gradients and centers round the kinetics of resistance changes within the membrane, as caused by effects from diffusion and electro-osmotic fluid streaming. The results are laid down in a set of five simple, basic expressions, which can be transformed into a pair of non-linear differential equations yielding oscillatory solutions. A graphical integration method is also outlined (Appendix II). The agreement between the theory and previous experimental observations is satisfactory. The applied electrokinetic concepts may have importance in relation to analyses of the behavior of living excitable cells or tissues.     

Oscillation of the electric potential of frog skin under the effect of Li+: Experimental approach

Summary When a frog skin is used to separate two compartments, and lithium is added to the external medium, transmembrane electric potential oscillations frequently occur. When no external current is imposed, sustained oscillations, with a period of about 10 min, are maintained for several hours. An oscillation of the Na⁺ influx accompanies the electric oscillation, though the two oscillations are out of phase to a greater or less extent.Theophyllin promotes a significant decrease in the mean electric potential of the skin, but it does not affect very much the characteristics of the oscillation. Important factors influencing the oscillation are temperature, permeability of the external membrane to lithium, and potassium concentration in the internal medium. No correlation can be detected between oscilation characteristics and skin area. This suggests that the oscillation is of a local nature, possibly originating at the cellular level. Occurrence of macroscopic oscillations implies coupling between local oscillators. Coupling between two epithelia has been studied under diverse conditions. The coupling is of an electrical nature: by varying the value of the coupling resistance, it is possible to control synchronization of the oscillations.     

The Use of an Enzyme Electrode in the Analysis of Indole-3-acetic Acid Oxidase Activity in Avena

The rapid reduction in cell electropotentials induced by metabolic inhibitors is strong evidence for an electrogenic ion pump. According to Ohm's law, such a depolarization might be explained by a reduction in electric current, I, with unidirectional transport of a given ion, or an increase in permeability (decrease in resistance). With cells of etiolated seedlings of Pisum sativum L. cv. Alaska and Zea mays cv. Golden Bantam, carbon monoxide inhibition, which occurs only in the dark and is readily reversed by light, allows repeated cycling of depolarization and repolarization; there is no effect on cell membrane resistance. In contrast, cyanide inhibition results in a marked increase in membrane electrical resistance; with cyanide following repeated pulses of current used in measuring cell membrane resistance, the resistance eventually (about 10 minutes) shows an abrupt drop as in the “punch-through” effect reported by H. G. L. Coster (1965. Biophys. J. 5: 669-686).     

The cylindrical cell with a time-variant membrane resistance. Measuring passive parameters.

The passive electrical properties of a cable can be measured by injecting a step of current at a point and fitting the resulting potentials at several positions along the cable with analytic solutions of the cable equation. An error analysis is presented for this method (which is based on constant membrane resistance) when the membrane resistance is not constant, but increases linearly with time. The increase of rm produces a "creep" in the membrane potential at long times, as observed in cardiac, skeletal, and smooth muscle. The partial differential equation describing the time-varying cable was solved numberically for a step of current and these "data" were fit by standard constant-resistance methods. Comparing the resulting parameter values with the known true values, we suggest that a correction of the standard methods is not satisfactory for resistance changes of the kind observed; instead, the cable equation must be solved again for the particular form of rm(t). The practical implementation of a method by Adrian and Peachey for measuring the membrane capacitance and an approximate method for estimating the rate-of-change of membrane resistance are discussed in appendices.     

Current Oscillations Under Voltage-Clamp Conditions: An Interplay of Series Resistance and Negative Slope Conductance

Using the patch-clamp technique, we observed profound oscillations of the whole-vacuole outward current across the tonoplast of Mesembryanthemum crystallinum L. (common ice plant). These current oscillations showed a clear voltage dependence and appeared at membrane potentials more positive than 90–100 mV. This paper describes the oscillations in terms of two separate mechanisms. First, the Mesembryanthemum vacuolar membrane shows a negative slope conductance at membrane potentials more positive than 100–120 mV. The fact that the oscillations and the negative slope conductance show a similar threshold potential suggests that (part of) the same mechanism is involved in both phenomena. The second mechanism involved is the voltage drop across the series resistance. As a result, the potential actually experienced by the vacuolar membrane deviates from the command potential defined by the patch-clamp amplifier. This deviation depends in an Ohmic manner on the current magnitude. We suggest that the interplay of the negative slope conductance and the voltage drop across the series resistance can cause a positive feedback which is responsible for the current oscillations. Received: 30 April 1999/Revised: 9 September     

Reconstitution of Biological Molecular generators of electric current. Bacteriorhodopsin.

1. Photoinduced generation of electric current by bacteriorhodopsin, incorporated into the planar phospholipid membrane, has been directly measured with conventional electrometer techniques. 2. Two methods for bacteriorhodopsin incorporation have been developed: (a) formation of planar membrane from a mixture of decane solution of phospholipids and of the fraction of violet fragments of the Halobacterium halobium membrane (bacteriorhodopsin sheets), and (b) adhesion of bacteriorhodopsin-containing reconstituted spherical membranes (proteoliposomes) to the planar membrane in the presence of Ca2+ or some other cations. In both cases, illumination was found to induce electric current generation directed across the planar membrane, an effect which was measured by macroelectrodes immersed into electrolyte solutions on both sides of the membrane. 3. The maximal values of the transmembrane electric potential were of about 150 mV at a current of about 10(-11) A. The electromotive force measured by means of counterbalancing the photoeffect by an external battery, was found to reach the value of 300 mV. 4. The action spectrum of the photoeffect coincides with the bacteriorhodopsin absorption spectrum (maximum about 570 nm). 5. Both components of the electrochemical potential of H+ ions (electric potential and delta pH) across the planar membrane affect the bacteriorhodopsin photoelectric response in a fashion which could be expected if bacteriorhodopsin were a light-dependent electrogenic proton pump. 6. La3+ ions were shown to inhibit operation of those bacteriorhodopsin which pump out H+ ions from the La3+-containing compartment. 7. The photoeffect, mediated by proteoliposomes associated with thick planar membrane, is decreased by gramicidin A at concentrations which do not influence the planar membrane resistance in the light. On the contrary, a protonophorous uncoupler, trichlorocarbonylcyanidephenylhydrazone, decreases the photoeffect only if it is added at a concentration lowering the light resistance. The dark resistance is shown to be higher than the light one, and decreases to the light level by gramicidin. 8. A simple equivalent electric scheme consistent with the above results has been proposed.     

The Ventral Photoreceptor Cells of Limulus : III. A voltage-clamp study

In the dark, the ventral photoreceptor of Limulus exhibits time-variant currents under voltage-clamp conditions; that is, if the membrane potential of the cell is clamped to a depolarized value there is an initial large outward current which slowly declines to a steady level. The current-voltage relation of the cell in the dark is nonlinear. The only ion tested which has any effect on the current-voltage relation is potassium; high potassium shifts the reversal potential towards zero and introduces a negative slope-conductance region. When the cell is illuminated under voltage-clamp conditions, an additional current, the light-induced current, flows across the cell membrane. The time course of this current mimics the time course of the light response (receptor potential) in the unclamped cell; namely, an initial transient phase is followed by a steady-state phase. The amplitude of the peak transient current can be as large as 60 times the amplitude of the steady-state current, while in the unclamped cell the amplitude of the peak transient voltage never exceeds 4 times the amplitude of the steady-state voltage. The current-voltage relations of the additional light-induced current obtained for different instants of time are also nonlinear, but differ from the current-voltage relations of the dark current. The ions tested which have the greatest effect on the light-induced current are sodium and calcium; low sodium decreases the current, while low calcium increases the current. The data strongly support the hypothesis that two systems of electric current exist in the membrane. Thus the total ionic current which flows in the membrane is accounted for as the sum of a dark current and a light-induced current.     

Dielectric breakdowm in the membranes of itValonia utricularis. The role of energy dissipation

The electrical properties of the membranes of Valoniautricularis were investigated using intracellular electrodes. Using short (0.5–1.0 ms) current pulses it was found that at a critical membrane potential difference of 0.85 V there was a large and discontinuous decrease in the membrane impedance and the slope resistance beyond this potential was virtually zero.The electrical breakdown of the membranes did not lead to global damage of the cells and after a resealing time of approx. 5 s could be repeated with identical results.Experiments with long current pulses and long bursts of pulses repeated at 1 kHz are described which show that the electrical breakdown is not due to thermal damage arising from localized heating in the membrane. Thus a dissipation of some 10³–10⁵ times the energy normally dissipated during the onset of breakdown did not lead to breakdown itself unless the critical membrane potential was exceeded.The results also show that punch-through and avalanche ionization are not likely to be important in the breakdown mechanism. The results are consitent, however, with there being a critical instability in the electro-mechanical stresses set up in the membrane at large electric field strengths.     

Dynamic properties of polyelectrolyte calcium membranes

Summary Shashoua observed spontaneous oscillations in a polyelectrolyte membrane formed by interfacial precipitates of polyacid and polybase. We have here undertaken experimental and theoretical studies of polyglutamic acid-Ca⁺⁺ membrane in order to clarify the processes involved in this dynamic behavior. We find a region of distinct hysteresis in the voltage current curve for this system. A sharp transition from a state of low membrane resistance to one of high resistance occurs at a current density different from that of inverse transition.This membrane system is modeled as a two layer structure: a negatively charged layer made of ionized polyelectrolyte in series with a neutral region in which the polymeric ionic sites are masked by calcium ion. This structure results in a difference in the transference number for the mobile ions, causing salt accumulation at the interfacial region during a current flow in the to direction. This altered salt concentration induces a change of polymeric conformation, which in turn affects the membrane permeability and the rate of accumulation. Based upon nonequilibrium thermodynamic flow equations, and a two-state representation of membrane macromolecular conformation, this model displays a region of hysteresis in the current range of experimental observations.     

Flicker noise of ion-selective membranes and turbulent convection in the depleted layer

Flicker noise of electric currents through ion-selective membranes is explained. It is attributed to the depletion of salt on one side of the membrane, which creates a thin layer of high resistance. Joule heating in this depletion layer and the ensuing temperature gradient, as well as the concentration gradient, give rise to buoyant forces which may create a turbulent convection current. The turbulence mixes the depletion layer so that the electric resistance fluctuates, and consequently the current flickers.Experiments with ion-selective membranes support this conjecture. They show that 1) Noise is coincident with the increase of the electric resistance by the depletion process. 2) When the current density is reduced, it reaches a critical value, below which the convection current changes from turbulent to laminar, and the noise disappears. 3) Noise reduces with temperature, because the expansion coefficient of water decreases with temperature, and its viscosity increases. 4) A non-ionic water-soluble polymer added to the compartment on the side of the depletion layer reduces the noise, by increasing the bulk viscosity of the solution. 5) Noise depends on the membrane's orientation in the gravitational field. 6) The convection-current in the depletion layer can be observed directly, using a laser-beam, by adding latex particles which create optical noise as they drift with the convection current across the beam. The optical noise is observed only coincidently with the current noise.A. Katzir-Katchalsky Fellow     

Kinetic Theory Model for Ion Movement through Biological Membranes: II. Interionic Selectivity

The equation presented in the previous paper for steady-state membrane ionic current as a function of externally applied electric field strength is numerically analyzed to determine the influence of ionic and membrane molecule parameters on current densities. The model displays selectivity between different ions. A selectivity coefficient S_i, defined as the ratio of current carried by an ionic species i at a given field strength to the current carried by a reference species at the same field strength, has the following properties: (a) S_i is a function of electric field strength except for ion-membrane molecule interactions yielding velocity independent collision frequencies; (b) for ion-membrane molecule interactions characterized by a collision frequency that is a decreasing (increasing) function of increasing ionic velocity, ions whose S_i > 1 (<1) at zero field strength will show maxima (minima) (minima[maxima]) in their S_i vs. electric field strength curves.     

Theory of single-file noise.

A general theoretical approach to the analysis of electric fluctuations generated by the so-called single-file diffusion through narrow channels is presented. The formalism is a slight extension of an approach to electric fluctuations in discrete transport systems with negligible interactions between the particles recently developed by one of the authors. In the single-file transport mechanism interactions between the particles must be taken into account. Three main results of principal interest are: (a) the electric fluctuations around stationary states (at equilibrium and non-equilibrium) are determined by the time-dependent solutions of the macroscopic single-file transport equations, (b) as a direct consquence of the interactions between the ions in the single-file transport the macroscopic time-dependent current and the autocorrelation function of the microscopic current fluctuations can exhibit damped oscillatory behavior, and the current noise spectrum can show peaking, (c) the number of binding sites for the ions within the pores seems to have a strong influence on the oscillatory behavior: with increasing number of binding sites the damping of the oscillations decreases and the peaking of the spectrum becomes stronger.     

Interplay of Intrinsic and Synaptic Conductances in the Generation of High-Frequency Oscillations in Interneuronal Networks with Irregular Spiking

High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.     

Characterization of two ectocellularly oriented 67 K presynaptic proteins. Lack of effect of their removal on acetylcholine release

A presynaptic plasma membrane fraction was purified after subfractionation of pure cholinergic synaptosomes prepared from Torpedo electric organ. Two 67 kdalton proteins were highly enriched in the synaptosomal plasma membrane (SPM): the hydrophobic form of AChE and a protein against which we raised a monoclonal antibody (C1–8). These two proteins exhibit similar biochemical properties: both exist as disulphide linked dimers with the same molecular weight; they are glycoproteins binding Concanavalin A; they are exposed on the external surface of the SPM and detached as almost entire molecules by Pronase. Nevertheless, using the C1–8 monoclonal antibody, it was possible to show that they are different proteins. The C1–8 binding protein appears to be specific for the SPM in Torpedo electric organ since it was not detected in plasma membranes from the electroplaque, the electric nerve trunks or the electric lobe. The hydrophobic AChE and the C1–8 binding protein appear therefore to be useful markers of the SPM. Pronase treatment of intact synaptosomes removes most of the ectocellularly exposed proteins of the SPM, which amount to 35% of the SPM protein. Presynaptic AChE and the C1–8 binding protein are detached. But ACh release can still be induced by depolarization of the Pronase treated synaptosomes. This demonstrates that the two 67 kdalton presynaptic proteins are not directly involved in the release of the neurotransmitter.     

The Electrophysiology of Electric Organs of Marine Electric Fishes : I. Properties of electroplaques of Torpedo nobiliana

Single electroplaques of Torpedo nobiliana have been studied with microelectrode recording. Direct evidence is presented that the only electrogenically reactive membrane of the cells is on the innervated surface and that this membrane is electrically inexcitable. Responses are not evoked by depolarizing currents applied to this membrane, but only by stimulating the innervating nerve fibers. The responses arise after a latency of 1 to 3 msec. This latency is not affected by large depolarizing or hyperpolarizing changes in membrane potential. Various properties that have been theoretically associated with electrically inexcitable responses have been also demonstrated to occur in the electroplaques. The neurally evoked response is not propagated actively in the membrane and may have different amplitudes and forms in closely adjacent regions. The maximal responses frequently are slightly larger than the recorded resting potential but the apparent small overshoot may be due to difficulty in recording the full resting potential. The responses are subject to electrochemical gradation and appear inverted in sign on applying strong outward currents across the innervated membrane. This membrane is cholinoceptive and shows marked desensitization. The membrane of the uninnervated surface has a very low resistance, a factor that aids maximum output of current during the discharge of the electric organ.     

Mechanisms of membrane potential oscillation in bursting neurons on the snail,Helix pomatia

• 1.1. The mechanism of generation of membrane potential (MP) oscillations was studied in identified bursting neurons from the snail Helix pomatia.
• 2.2. Long-lasting stimulation of an identified peptidergic interneuron produced a persistent bursting activity in a non-active burster.
• 3.3. External application of calcium channel blockers (1 mM Cd²⁺ or 5 mM La²⁺) resulted in a transient increase in the slow-wave amplitude and subsequent prevention of pacemaker activity generation in bursting neurons. Application of these blockers together with endogenous neuropeptide initiating bursting activity generation, increased MP wave amplitude without prevention of bursting activity generation.
• 4.4. Replacement of all NaCl in normal Ringer's solution with isoosmotic CaCl₂, glucose or Tris-HCl produced a reversible block of bursting activity generation. Stationary current-voltage relation (CVR) of bursting neuron membrane has a region of negative resistance (NRR) and does not intersect the potential axis in threshold region for action potential (AP) generation in normal Ringer's solution. In Na-free solution stationary CVR is linear and intersects the potential axis near — 52 mV.
• 5.5. Novel potential- and time-dependent outward (E_rev = − 58 mV) current, I_B, activated by hyperpolarization was found in the bursting neuron membrane. Having achieved a maximal value, this current decayed with a time constant of about 1 sec. Hyperpolarization inactivated maximal conductance, g_B, responsible for I_B, and depolarization abolished inactivation of g_B.
• 6.6. Short-lasting (0.01 sec) hyperpolarization of the bursting neuron membrane by inward current pulse induced the development of prolonged hyperpolarization wave lasting up to 10 sec.
• 7.7. These results suggest that: (a) persistent bursting activity of RPal neuron in the snail Helix pomatia is not endogenous but is due to a constant activation of peptidergic synaptic inputs of these neurons; (b) Ca²⁺ ions do not play a pivotal role in the ionic mechanism of MP oscillations but play a determining role in the process of secretion of a peptide initiating bursting activity by the interneuron presynaptic terminal; (c) depolarizing phase of the MP wave is due to specific properties of stationary CVR and hyperpolarization phase is due to regenerative properties of hyperpolarization-activated outward current I_B. The minimal mathematical version of MP oscillations based on the experimental data is presented.

     

Current-voltage characteristics and self-sustained oscillations in dioleyl phosphate-millipore membranes

For an artificial membrane prepared by infiltrating dioleyl phosphate (DOPH) into pores of a Millipore filter, we propose a theoretical model for explaining observed data on electric behavior, such as d.c. current-voltage characteristics and self-sustained oscillations of the electric potential. The model consists of a simple electric circuit composed of electric resistances and capacitances as given functions of internal variables which represent conformational states of DOPH molecules and salt concentration inside the pore concerned. The kinetic equations for these variables are the same as those presented previously for describing a phase transition of DOPH. except for a slight modification taking account of effects of salt accumulation inside the pore. The present theory can describe well the I-V hysteresis and various features of spike-like oscillations with long periods of up to a few hours in the absence of external force and also short-period oscillations with periods of the order of 1 s under pressure difference.