Admittance change of squid axon during action potentials. Change in capacitive component due to sodium currents.

Since the discovery of Cole and Curtis (1938. Nature (Lond.). 142:209 and 1939. J. Gen. Physiol. 22:649) that the imaginary components, i.e., capacitive and inductive components, of the admittance of squid axon membrane remained unchanged during the action potential, there have been numerous studies on impedance and admittance characteristics of nerves. First of all, it is now known that the dielectric capacitance of the membrane is frequency dependent. Second, the recent observation of gating currents indicates that dipolar molecules may be involved in the onset of ionic currents. Under these circumstances, the author felt it necessary to reinvestigate the membrane admittance characteristics of nerve axons. The measurements by Cole and Curtis were performed mainly at 20 kHz, indicating that their observation was limited only to the passive membrane capacitance. To detect the change in the capacitive component during the action potential, we performed transient admittance measurements at lower frequencies. However, the frequency range of the measurements was restricted because of the short duration of the normal action potential. In addition, a change in the inductive component obscured the low frequency behavior of the capacitance. To use wider frequency range and simplify the system by eliminating the inductive component, the potassium current was blocked by tetraethyl ammonium, and the increase in the capacitive component was reinvestigated during the long action potential. The admittance change under this condition was found to be mostly capacitive, and conductance change was very small. The increase in the capacitive component was from 1.0 to 1.23 muF/cm2.     

Electrogenic transport of sodium ions in cytoplasmic and extracellular ion access channels of Na+,K+-ATPase probed by admittance measurement technique

Electrogenic movements of sodium ions in cytoplasmic and extracellular access channel of the Na⁺,K⁺-ATPase have been studied by the admittance measurement technique which allows the detection of small changes of the membrane capacitance and conductance induced by phosphorylation of the ion pump. The measurements were carried out on a model system consisting of a bilayer lipid membrane, to which membrane fragments with ion pumps were adsorbed that contain the ion pumps in high density. Small changes of the membrane capacitance and conductance were induced by a fast release of ATP from caged ATP. The effect was measured at various frequencies and in solutions with different Na⁺ concentrations. The experimentally observed frequency dependences were explained using a theoretical model assuming that Na⁺ movement through the cytoplasmic access channel occurs in one step and through the extracellular access channel, in two steps. The phosphorylation of the protein by ATP leads to a block of the cytoplasmic access channel and an opening the extracellular access channel. The disappearance of electrogenic Na⁺ movements on the cytoplasmic side produces a negative change of capacitance and conductance, while the emergence of extracellular Na⁺ movements generates a positive change. Fitting the experimental dependences of capacitance and conductance by theoretical curves allowed the determination equilibrium and kinetic parameters of sodium transport in the access channels. The text was submitted by the authors in English.     

Effects of membrane potential on the capacitance of skeletal muscle fibers

A method for measuring muscle fiber capacitance using small test pulses applied with the three-microelectrode voltage clamp is presented. Using this method, three membrane potential-dependent changes in capacitance were observed: (a) Capacitance of polarized fibers increased by 5--15% with depolarization from V less then -100 mV to voltages slightly below the contraction threshold. (b) Capacitance of fibers depolarized to -30 mV by 100 mM Rb solution decreased by roughly 8% with further depolarization to about +50 mV and increased with repolarization, exhibiting a maximum increase of about 10% at -80 to -90 mV. (c) Capacitance of fibers depolarized to -15 mV by 100 mM K solution increased by about 19% with further depolarization to +43 mV and decreased by about 23% with repolarization to -62 mV. Effects a and b are attributed to changes in specific membrane capacitance due to voltage-dependent redistribution of mobile charged groups within surface of T-tubule membranes. Effect c is caused by changes in the T-system space constant lambdaT due to the voltage dependence of K conductance (inward rectification). Analysis of c showed that in 100 mM K solution lambdaT congruent to 30 mum when inward rectification was fully activated by hyperpolarization and that the density of inward rectifier channels is about the same in surface and tubular membranes. Fiber internal resistance was found to be independent of voltage, a necessary condition for the interpretation of the capacitance measurements.     

Involvement of protons in the ion transport cycle of Na<Superscript>+</Superscript>,K<Superscript>+</Superscript>-ATPase

The effect of pH on electrogenic sodium transport by the Na⁺,K⁺-ATPase has been studied. Experiments were carried out by admittance recording in a model system consisting of a bilayer lipid membrane with adsorbed membrane fragments containing purified Na⁺,K⁺-ATPase. Changes in the membrane admittance (capacitance and conductance increments in response to photo-induced release of ATP from caged ATP) were measured as function of AC voltage frequency, sodium ion concentration, and pH. In solutions containing 150 mM Na⁺, the frequency dependence of capacitance increments was not significantly dependent on pH in the range between 6 and 8. At a low NaCl concentration (3 mM), the capacitance increments at low frequencies decreased with the increasing pH. In the absence of NaCl, the frequency-dependent capacitance increment at low frequencies was similar to that measured in the presence of 3 mM NaCl. These results may be explained by involvement of protons in the Na⁺,K⁺-ATPase pump cycle, i.e., electroneutral exchange of sodium ions for protons under physiological conditions, electrogenic transport of sodium ions at high pH, and electrogenic transport of protons at low concentrations (and in the absence) of sodium ions.     

Delayed kinetics of squid axon potassium channels do not always superpose after time translation.

The activation of potassium ion conductance in squid axons by voltage-clamp depolarization is delayed when the depolarizing step is preceded by a conditioning hyperpolarization of the axonal membrane. Moreover, the control conductance kinetics superpose with the delayed kinetics when they are translated along the time axis by an amount equal to the delay. We have found that the degree of superposition with internally perfused axons depends upon voltage-clamp protocol. The kinetics superpose almost exactly for modest test depolarizations, whereas they clearly fail to superpose completely for more positive levels of membrane depolarization. We have modeled these results by incorporating a time dependence into the rate constant of activation of potassium channel gates in the Hodgkin and Huxley model of potassium ionic conductance.     

Conditioning hyperpolarization delays in squid axon potassium channels.

Activation of potassium conductance in squid axons with membrane depolarization is delayed by conditioning hyperpolarization of the membrane potential. The delayed kinetics superpose with the control kinetics almost, but not quite, exactly following time translation, as demonstrated previously in perfused axons by Clay and Shlesinger (1982). Similar results were obtained in this study from nonperfused axons. The lack of complete superposition argues against the Hodgkin and Huxley (1952) model of potassium conductance. The addition of a single kinetic state to their model, accessible only by membrane hyperpolarization, is sufficient to describe this effect (Young and Moore, 1981).     

Effects of batrachotoxin on membrane potential and conductance of squid giant axons

The effects of batrachotoxin (BTX) on the membrane potential and conductances of squid giant axons have been studied by means of intracellular microelectrode recording, internal perfusion, and voltage clamp techniques. BTX (550–1100 nM) caused a marked and irreversible depolarization of the nerve membrane, the membrane potential being eventually reversed in polarity by as much as 15 mv. The depolarization progressed more rapidly with internal application than with external application of BTX to the axon. External application of tetrodotoxin (1000 nM) completely restored the BTX depolarization. Removal or drastic reduction of external sodium caused a hyperpolarization of the BTX-poisoned membrane. However, no change in the resting membrane potential occurred when BTX was applied in the absence of sodium ions in both external and internal phases. These observations demonstrate that BTX specifically increases the resting sodium permeability of the squid axon membrane. Despite such an increase in resting sodium permeability, the BTX-poisoned membrane was still capable of undergoing a large sodium permeability increase of normal magnitude upon depolarizing stimulation provided that the membrane potential was brought back to the original or higher level. The possibility that a single sodium channel is operative for both the resting sodium, permeability and the sodium permeability increase upon stimulation is discussed.     

去甲肾上腺素引起蟾蜍背根神经节神经细胞膜电位变化的离子机制

本文应用细胞内记录方法,对去甲肾上腺素(NA)引起蟾蜍背根神经节(DRG)神经细胞膜电位去极化或超极化反应时的膜电导及翻转电位值进行了测量,并观察了钾和钙离子通道阻断剂灌流DRG对NA引起膜电位反应的影响。当NA引起去极化反应时,15个细胞的膜电导减小32.6％。少数细胞膜电导开始增加,继而减小(n=4)。NA超极化反应时膜电导增加13.2％(n=8)。NA去极化反应的翻转电位值为-88.5±0.9mV((?)±SE,n=4),NA超极化反应在膜电位处于-89至-92mV时消失。 钾通道阻断剂四乙铵可使NA去极化幅值增加73.7±11.9％((?)±SE,n=7),并使NA超极化幅值减小40.5％(n=4)。细胞内注入氯化铯使苯肾上腺素去极化幅值增加34.5％(n=4)。钙通道阻断剂氯化锰使NA去极化及超极化反应分别减小50.5±9.9％((?)±SE,n=10)和89.5±4.9％((?)±SE,n=7)。结果提示,NA引起DRG神经细胞膜电位的去极化或超极化反应,可能与膜的钾及钙通道活动的改变有关。     

Potential dependence of the admittance ofChara plasmalemma

Summary A computer-controlled apparatus is described, which combines the two powerful methods of voltage-clamping and admittance measurement. The 5-Hz admittance ofChara plasmalemma is obtained for transmembrane PD from −400 mV to 0. DC conductance is also measured by the bipolar staircase method. Both the DC and 5-Hz conductances at steady state display a central maximum at ≈−250 mV. This feature is attributed to the conductance/voltage characteristics of the H⁺ pump. The steady-state capacitance does not show any trend throughout the potential interval. At the time of the delay, before excitation commences, the 5-Hz conductance is smaller than after excitation. At the time of excitation the 5-Hz conductance echoes the time-course of the ionic current, while the capacitance undergoes a sharp decrease followed by an increase. A possible explanation of the capacitance behavior is attempted involving transport number effects and reactances associated with the Hodgkin-Huxley gating mechanism. At punchthrough the membrane becomes inductive.     

Dipole moment changes and voltage dependent membrane capacity of squid axon

Changes in the membrane capacity of squid axons during hyper- and depolarizations are measured between ?160 and +40 mV. After corrections for the series resistance and fringe effect, we found that the membrane capacity increased from 0.68 to 1.2 μF/cm² with depolarization. It was further observed that tetrodotoxin in the external medium eliminated the change in membrane capacity without affecting the conductivity. The voltage-dependent membrane conductivity is, in turn, greatly reduced by the internal cesium ion. These observations clearly indicate that the voltage-dependent membrane capacity and conductivity are closely related to ionic channels. Particularly, the increase in membrane capacity with depolarizations may be due to sodium channels. The change in the dipole moment associated with sodium sites was determined using values of α_{m and}β_m at various depolarizations. We found, based on voltage clamp measurements, that the increase in the dipole moment of the sodium site between ?40 and ?5 mV is 1230 Debye units (D.U.) and 930 D.U. between ?5 and +60 mV, indicating that the depolarization of sodium channels may consist of two different steps.     

The Effects of Mechanical Stimulation on Some Electrical Properties of Axons

Rapid, short duration mechanical compression of lobster giant axons by a crystal-driven stylus produces a depolarization and an increase in membrane conductance which develop immediately with compression but take several seconds to recover. The conductance increase occurs even when the depolarization is prevented electrically. If sodium is removed from the external medium or if procaine is added to it, compression produces almost no depolarization. Small bundles of myelinated frog fibers are depolarized by rapid compression but recover very rapidly (milliseconds); "off" responses are occasionally seen. The results are discussed in terms of the mechanoelectric transducer behavior of an axon membrane.     

Fusion of membranes during fertilization. Increases of the sea urchin egg''s membrane capacitance and membrane conductance at the site of contact with the sperm

The early events of fertilization that precede and cause activation of an egg have not been fully elucidated. The earliest electrophysiological change in the sea urchin egg is a sperm-evoked increase of the egg's membrane conductance. The resulting depolarization facilitates entry of the fertilizing sperm and precludes the entry of supernumerary sperm. The sequence of the increase in the egg's membrane conductance, gamete membrane fusion, egg activation, and sperm entry, including causal relationships between these events, are not known. This study reports the use of whole egg voltage clamp and loose patch clamp to monitor simultaneously changes of membrane conductance and capacitance at the site of sperm-egg contact. Measurements were made during sperm-egg interactions where sperm entry readily proceeded or was precluded by maintaining the egg's membrane potential either at large, negative values or at positive values. Whenever the sperm evoked an increase of the egg's membrane conductance, that increase initiated abruptly, was localized to the site of sperm attachment, and was accompanied by a simultaneous abrupt increase of the membrane capacitance. This increase of capacitance indicated the establishment of electrical continuity between gametes (possibly fusion of the gametes' plasma membranes). If sperm entry was blocked by large negative membrane potentials, the capacitance cut off rapidly and simultaneously with a decrease of the membrane conductance, indicating that electrical continuity between gametes was disrupted. When sperm entry was precluded by positive membrane potentials, neither conductance nor capacitance increased, indicating that sperm entry was halted before the fusion of membranes. A second, smooth increase of capacitance was associated with the exocytosis of cortical granules near the sperm in eggs that were activated. Electrical continuity between the gametes always preceded activation of the egg, but transient electrical continuity between the gametes alone was not always sufficient to induce activation.     

Analysis of nerve conduction block induced by direct current

The mechanisms of nerve conduction block induced by direct current (DC) were investigated using a lumped circuit model of the myelinated axon based on Frankenhaeuser–Huxley (FH) model. Four types of nerve conduction block were observed including anodal DC block, cathodal DC block, virtual anodal DC block, and virtual cathodal DC block. The concept of activating function was used to explain the blocking locations and relation between these different types of nerve block. Anodal/cathodal DC blocks occurred at the axonal nodes under the block electrode, while virtual anodal/cathodal DC blocks occurred at the nodes several millimeters away from the block electrode. Anodal or virtual anodal DC block was caused by hyperpolarization of the axon membrane resulting in the failure of activating sodium channels by the arriving action potential. Cathodal or virtual cathodal DC block was caused by depolarization of the axon membrane resulting in inactivation of the sodium channel. The threshold of cathodal DC block was lower than anodal DC block in most conditions. The threshold of virtual anodal/cathodal blocks was about three to five times higher than the threshold of anodal/cathodal blocks. The blocking threshold was decreased with an increase of axonal diameter, a decrease of electrode distance to axon, or an increase of temperature. This simulation study, which revealed four possible mechanisms of nerve conduction block in myelinated axons induced by DC current, can guide future animal experiments as well as optimize the design of electrodes to block nerve conduction in neuroprosthetic applications.     

Fluctuation and linear analysis of Na-current kinetics in squid axon

The power spectrum of current fluctuations and the complex admittance of squid axon were determined in the frequency range 12.5 to 5,000 Hx during membrane voltage clamps to the same potentials in the same axon during internal perfusion with cesium. The complex admittance was determined rapidly and with high resolution by a fast Fourier transform computation of the current response, acquired after a steady state was attained, to a synthesized signal with predetermined spectral characteristics superposed as a continuous, repetitive, small perturbation on step voltage clamps. Linear conduction parameters were estimated directly from admittance data by fitting an admittance model, derived from the linearized Hodgkin-Huxley equations modified by replacing the membrane capacitance with a "constant-phase-angle" capacitance, to the data. The constant phase angle obtained was approximately 80 degrees. At depolarizations the phase of the admittance was 180 degrees, and the real part of the impedance locus was in the left-half complex plane for frequencies below 1 kHz, which indicates a steady-state negative Na conductance. The fits also yielded estimates of the natural frequencies of Na "activation" and "inactivation" processes. By fitting Na-current noise spectra with a double Lorentzian function, a lower and an upper corner frequency were obtained; these were compared with the two natural frequencies determined from admittance analysis at the corresponding potentials. The frequencies from fluctuation analyses ranged from 1.0 to 10.3 times higher than those from linear (admittance) analysis. This discrepancy is consistent with the concept that the fluctuations reflect a nonlinear rate process that cannot be fully characterized by linear perturbation analysis. Comparison of the real part of the admittance and the current noise spectrum shows that the Nyquist relation, which generally applies to equilibrium conductors, does not hold for the Na process in squid axon. The Na-channel conductance, gamma Na, was found to increase monotonically from 0.1 to 4.8 pS for depolarizations up to 50 mV from a holding potential of -60 mV, with no indication of a maximum value.     

Fusion pore conductance: experimental approaches and theoretical algorithms.

Time-resolved admittance measurements provide the basis for studies showing that membrane fusion occurs through the formation and widening of an initially small pore, linking two previously separated aqueous compartments. Here we introduce modifications to this method that correct the cell-pipette (source) admittance for attenuation and phase shifts produced by electrophysiological equipment. Two new approaches for setting the right phase angle are discussed. The first uses the displacement of a patch-clamp amplifier C-slow potentiometer for the calculation of phase. This calculation is based on amplitudes of observed and expected (theoretical) changes in the source admittance. The second approach automates the original phase adjustment, the validity of which we prove analytically for certain conditions. The multiple sine wave approach is modified to allow the calculation of target cell membrane parameters and the conductance of the fusion pore. We also show how this technique can be extended for measurements of the resting potential of the first (voltage-clamped) membrane. We introduce an algorithm for calculation of fusion pore conductance despite a concurrent change in the resistance of the clamped membrane. The sensitivity of the capacitance restoration algorithm to phase shift errors is analyzed, and experimental data are used to demonstrate the results of this analysis. Finally, we show how the phase offset can be corrected "off-line" by restoring the shape of the capacitance increment.     

Distribution and kinetics of membrane dielectric polarization. II. Frequency domain studies of gating currents

We have studied the admittance of the membrane of squid giant axon under voltage clamp in the absence of ionic conductances in the range of 0-12 kHz for membrane potentials (V) between --130 and 70 mV. The admittance was measured at various holding potentials (HP) or 155 ms after pulsing from a given holding potential. Standard P/4 procedure was used to study gating currents in the same axons. We found that the membrane capacity Cm (omega) is voltage as well as frequency dependent. For any given V, the voltage-dependent part of the membrane capacitance has a maximum as the frequency approaches zero and requires at least a two-time constant equivalent circuit to be described. When the holding potential is varied, the voltage-dependent capacitance follows a bell- shaped curve with a maximum change of 0.15 muF/cm2 at about --60 mV. With the pulse method, the maximum is at --40 mV for HP = --70 and it shifts to --70 mV for HP = 0. The shift in the maximum of the voltage- dependent capacitance is consistent with the shift in the charge (Q) vs. V curve observed in our experiments with regular P/4 procedure when the HP is varied. Our data can be explained qualitatively by a four- state model for the sodium channel gating, where a charged particle can move within the field and interact with another particle not affected by the field.     

Capacitance of bilayers in the presence of lipophilic ions

The capacitance of glycerolmonooleate and egg phosphatidylcholine bilayer membranes in the presence of NaCl solutions containing tetraphenylborate, tetraphenylarsonium or dipicrylamine ions has been measured using alternating current techniques over a wide range of frequencies (1–200 kHz). The concentrations of ions corresponded to the lower limits of conductance saturation. Similar determinations were also made with solutions containing no lipophilic ions. The experimental method used in this work requires correction of admittance measurements for the solution resistance in series with the membrane, as well as careful area determinations. In all cases membrane capacitance levels off at sufficiently high frequencies to values which are independent of frequency. The high-frequency capacitance, which is regarded as the ‘geometrical capacitance’ due to dielectric polarization, is practically unaffected by the presence of lipophilic ions. The results support the assumption made in other studies, such as in charge pulse investigations, that the adsorption of lipophilic ions at concentrations up to the saturation range does not have an important effect on the dielectric properties of bilayers.     

Depletion and accumulation of potassium in the extracellular clefts of cardiac Purkinje fibers during voltage clamp hyperpolarization and depolarization: experiments in sodium-free bathing media

Voltage clamp hyperpolarization and depolarization result in currents consistent with depletion and accumulation of potassium in the extracellular clefts o cardiac Purkinje fibers exposed to sodium-free solutions. Upon hyperpolarization, an inward current that decreased with time (id) was observed. The time course of tail currents could not be explained by a conductance exhibiting voltage-dependent kinetics. The effect of exposure to cesium, changes in bathing media potassium concentration and osmolarity, and the behavior of membrane potential after hyperpolarizing pulses are all consistent with depletion of potassium upon hyperpolarization. A declining outward current was observed upon depolarization. Increasing the bathing media potassium concentration reduced the magnitude of this current. After voltage clamp depolarizations, membrane potential transiently became more positive. These findings suggest that accumulation of potassium occurs upon depolarization. The results indicate that changes in ionic driving force may be easily and rapidly induced. Consequently, conclusions based on the assumption that driving force remains constant during the course of a voltage step may be in error.     

The effects of L-glutamate and its analogues upon the membrane conductance of central murine neurones in culture

Neurones from brain and spinal cord of foetal mice were grown dissociated in monolayer cultures for 4--6 weeks prior to electropharmacological analysis. Neurones were immersed in a Hanks balanced salt solution while drugs and ions were applied by pressure microperfusion during intracellular recordings obtained by conventional techniques. L-Glutamate and its analogues, L-aspartate, DL-homocysteate, N-methyl-D-aspartate, and DL-ibotenate activated two distinct mechanisms of excitation. The primary effect was depolarization accomplished by an apparent decrease of neurone input conductance (Gm). However, in most instances an expected increase in Gm was also observed, especially if membrane potential was reduced by tonic depolarization. Another glutamate analogue, DL-kainate, never decreased Gm and invariably increased Gm at all membrane potentials tested. The decrease of Gm evoked by glutamate and related compounds was strongly dependent upon membrane potential. It was most pronounced at potentials near resting values (-40 to -60 mV) and diminished both with depolarization or hyperpolarization from this range. This apparent decrease favoured the electrogenesis of regenerative potentials that were insensitive to tetrodotoxin. A voltage-dependent increase in sodium and (or) calcium conductance (GNa, GCa) or a decrease in potassium conductance (GK) is suggested to account for this decrease in Gm. Divalent cations (Mg and Co) reduced the depolarizing actions of all amino acids except for those to kainate. The decrease in Gm was more sensitive to Mg than was the increase of Gm. However, the receptor antagonist DL-alpha-aminoadipate blocked both changes in conductance and responses to all amino acids with the exception of those to kainate. The possible existence of multiple receptors for glutamate is also discussed.     

Primary afferent depolarization in frog spinal cord is associated with an increase in membrane conductance

The mechanism of primary afferent depolarization (PAD) was studied in the isolated frog spinal cord using intrafibre recording (microelectrodes filled with 0.6 M potassium sulfate) from large myelinated axons of dorsal roots. Standard current-clamp technique was used to obtain voltage-current (V-I) relationship. It was found that: (i) PAD is voltage dependent: its amplitude and rate of rise are increased with hyperpolarization; (ii) the slope of the linear part of the V-I curve obtained during PAD is decreased compared with the V-I curve at rest; (iii) the PAD equilibrium potential, estimated by extrapolation, ranged from -66 to -40 mV. These results suggest that PAD is associated with an increase in conductance of primary afferent terminals and thus seem to provide the first experimental evidence for the hypothesis that shunting of primary afferent membrane is the mechanism of presynaptic inhibition in the vertebrate nervous system.