Voltage clamp simulations for multifiber bundles in a double sucrose gap: cable complications

A theoretical model is presented for voltage clamp of a bundle of cylindrical excitable cells in a double sucrose gap. The preparation in the test node is represented by a single one-dimensional cable (length/diameter ratio approximately) with standard Hodgkin-Huxley kinetics for transmembrane Na current. Imperfections of voltage control due to internal (longitudinal) resistivity and external (radial) resistance in series to the membrane are analysed. The electrical behavior of a fiber is described by the cable equation with appropriate boundary conditions and subsidiary equations reflecting the membrane characteristics. Membrane voltage and current distribution in response to a step command was obtained by numerical integration. The results are described in two papers. The present paper deals with the effect of internal resistivity with the external resistance being neglected. The closed loop response of a fiber displays a strong tendency to oscillate. To stabilize the system a phase lead was inserted and the gain of the control amplifier was reduced. Conditions for stability were examined by Nyquist analysis. When the Na system was activated by a command pulse below ENa, a voltage gradient developed between a depolarization (relative to the command signal) at the end where voltage was monitored and a hyperpolarization at the site of current injection. In spite of a poor voltage control the total measured current appeared to have a smooth transient. With large voltage gradients a small, second inward current was seen. At a low (high) Na conductance maximum peak inward current was larger (smaller) that the current expected from ideal space clamping.     

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.     

Breakdown in helium in high-voltage open discharge with subnanosecond current front rise

Investigations of high-voltage open discharge in helium have shown a possibility of generation of current pulses with subnanosecond front rise, due to ultra-fast breakdown development. The open discharge is ignited between two planar cathodes with mesh anode in the middle between them. For gas pressure 6 Torr and 20 kV applied voltage, the rate of current rise reaches 500 A/(cm² ns) for current density 200 A/cm² and more. The time of breakdown development was measured for different helium pressures and a kinetic model of breakdown in open discharge is presented, based on elementary reactions for electrons, ions and fast atoms. The model also includes various cathode emission processes due to cathode bombardment by ions, fast atoms, electrons and photons of resonant radiation with Doppler shift of frequency. It is shown, that the dominating emission processes depend on the evolution of the discharge voltage during the breakdown. In the simulations, two cases of voltage behavior were considered: (i) the voltage is kept constant during the breakdown; (ii) the voltage is reduced with the growth of current. For the first case, the exponentially growing current is maintained due to photoemission by the resonant photons with Doppler-shifted frequency. For the second case, the dominating factor of current growth is the secondary electron emission. In both cases, the subnanosecond rise of discharge current was obtained. Also the effect of gas pressure on breakdown development was considered. It was found that for 20 Torr gas pressure the time of current rise decreases to 0.1 ns, which is in agreement with experimental data.     

A voltage clamp study of the sodium, calcium and chloride spikes of chick skeletal muscle cells grown in tissue culture.

Conventional voltage clamp techniques with microelectrodes were applied to chick muscle cells grown in tissue culture. The similarities and differences in electrophysiological data obtained from normal myotubular muscle fibers and from rounded myosacs, produced by incubation with colchicine, were examined. Under voltage clamp both cellular types generated three distinguishable voltage and time-dependent currents which corresponded, respectively, to the Na⁺, Ca²⁺, and Cl^? spikes evoked under constant current conditions. The presumed Ca²⁺ currents were too small to allow quantitative comparisons. In myosacs, but not in myotubes, there was good correspondence, for both the Na⁺ and Cl^? systems, between their spike thresholds and peak membrane potentials, measured under constant current conditions, and their current thresholds and reversal potentials, measured under voltage clamp conditions. This correspondence is attributed to the isopotentiality of the myosac intracellular space and suggests that myosacs provide more accurate quantitative data in voltage clamp studies than myotubes.     

Experimental study of the processes accompanying argon breakdown in a long discharge tube at a reduced pressure

Results are presented from experimental studies of the breakdown stage of a low-pressure discharge (1 and 5 Torr) in a glass tube the length of which (75 cm) is much larger than its diameter (2.8 cm). Breakdowns occurred under the action of positive voltage pulses with an amplitude of up to 9.4 kV and a characteristic rise time of 2–50 μs. The discharge current in the steady-state mode was 10–120 mA. The electrode voltage, discharge current, and radiation from the discharge gap were detected simultaneously. The dynamic breakdown voltage was measured, the prebreakdown ionization wave was recorded, and its velocity was determined. The dependence of the discharge parameters on the time interval between voltage pulses (the socalled “memory effect”) was analyzed. The memory effect manifests itself in a decrease or an increase in the breakdown voltage and a substantial decrease in its statistical scatter. The time interval between pulses in this case can reach 0.5 s. The effect of illumination of the discharge tube with a light source on the breakdown was studied. It is found that the irradiation of the anode region of the tube by radiation with wavelengths of ≤500 nm substantially reduces the dynamic breakdown voltage. Qualitative explanations of the obtained results are offered.     

Gating current harmonics. II. Model simulations of axonal gating currents

A kinetic model of sodium activation gating is presented. The kinetics are based on harmonic analysis of gating current data obtained during large-amplitude sinusoidal voltage clamp in dynamic steady state. The technique classifies gating kinetic schemes into groups based on patterns of the harmonic content in the periodic gating current records. The kinetics that simulate the experimental data contain two independently constrained processes. The model predicts (a) sizable gating currents in response to hyperpolarizing voltage steps from rest; (b) a substantial increase in the initial peak of the gating current following voltage steps from prehyperpolarized potentials; (c) a small delay in the onset of sodium ion current following voltage steps from prehyperpolarized potentials; and (d) flickering during the open state in single channel current records. Although fundamentally different in kinetic structure from the Hodgkin-Huxley model, the present model reproduces the phenomenological development of Na conductance during the initiation and development of action potentials. The implications for possible gating mechanisms are discussed. A model gate is presented.     

Whole-cell chloride conductances in cultured brushed human nasal epithelial cells.

Human airway epithelial cells were obtained by nasal brushing, thus avoiding the use of proteolytic enzymes for cell isolation. Whole-cell Cl- conductances were studied in these cells by means of the patch-clamp technique. During whole-cell recordings, cell swelling activated a Cl- conductance that was blocked by indanyloxyacetic acid (48 +/- 10% inhibition at 50 microM). The swelling-induced current outwardly rectified and showed inactivation at depolarizing voltages (> or = +60 mV) and activation at hyperpolarizing voltages (< or = -30 mV). The voltage sensitivity of current activation was approximately twice that of inactivation. Another Cl- current with different kinetics was observed when nonswollen airway cells were stimulated with ionomycin (2 microM) in the presence of 1 mM Ca2+. The Ca(2+)-induced current exhibited activation during depolarizing voltage steps (> or = +40 mV) and inactivation during hyperpolarizing voltage steps (< or = -40 mV). In contrast to the swelling-induced current, the activation of Ca(2+)-induced current was less sensitive to voltage compared with its inactivation. Tail current analysis suggested that Cl- channels having a linear current-voltage relation mediate the response to Ca2+. This study indicates that brushed human nasal epithelial cells possess Cl- conductances that are regulated by cell swelling and Ca2+ and that they represent a useful in vitro model for studying ion transport in epithelia.     

Interactions of amiloride and small monovalent cations with the epithelial sodium channel. Inferences about the nature of the channel pore.

The voltage dependence of amiloride-induced inhibition of current flow through apical membrane sodium channels in toad urinary bladder was studied at different ionic conditions. The "inert" salt N-methyl-D-glucamine HCl (NMDG HCl) affected neither the apparent inhibition constant (Kl) for the amiloride-induced current inhibition nor the apparent fraction of the transmembrane voltage that falls between the mucosal solution and the amiloride-binding site (delta). When NMDG+ was replaced with Na+, Kl increased, reflecting amiloride-Na+ competition, whereas delta was unchanged. Similar results were obtained with another permeant cation, Li+. When NMDG+ was replaced by K+, an impermeant but channel-blocking cation, Kl increased whereas delta decreased. Similar results were obtained using another impermeant, channel-blocking cation guanidinium. The results are interpreted on the premise that Na+ and K+ compete with amiloride by binding to cation binding sites within the channel lumen such that ion occupancy of these sites vary with voltage. Occupancy by K+, which cannot traverse the channel, will increase as the mucosal solution becomes positive, relative to the serosal solution. Occupancy by Na+, which can traverse the channel, is comparatively voltage independent. Ion movement through the channels was simulated using discrete-state kinetic models. Two types of models could describe the shape of the current-voltage relationship and the voltage dependence of the amiloride-induced channel block. One model had a single ion-binding site with a broad energy barrier at the inner (cytoplasmic) side of the site. The other model had two binding sites separated from each other and from the aqueous solutions by sharp energy barriers.     

The effect of displacement current on the measurement of reversal potential in squid giant axon

The measurement of the sodium reversal potential (Erev), as that potential where the early current reverses during voltage clamp, was found to exceed the true Erev by 4.1 +/- 2.4 mV (mean +/- SD) in squid giant axon. This error was found in both intact and internally perfused axons and is due to interference from the displacement current. This was shown by subtraction of the current records obtained before and after treatment with tetrodotoxin (TTX). The error in Erev is proportional to (Td/gNA)12 where Td is the time constant of the displacement current.     

Light-Induced Changes in Dye-Treated Lobster Giant Axons

Single giant axons from the lobster circumesophageal connective were studied using the sucrose gap voltage-clamp technique. The axon area in the gap was bathed in acridine orange for several minutes and then rinsed for several minutes. Subsequent illumination resulted in progressive prolongation of electrically stimulated action potentials to durations of 150 msec. The prolongation was accompanied by an increase in threshold. Currents in voltage clamp were altered such that transient current inactivation was greatly slowed. The turn on of transient current was somewhat slowed, the voltage at which peak transient current could be obtained was shifted to more positive internal potentials, and transient current at all potentials was decreased. Steady-state current was similarly affected. Low calcium following illumination partially counteracted some of the changes, but not the slowing of inactivation. Low calcium increased the duration of prolonged action potentials. Selective alteration of parameters in the Hodgkin-Huxley equations brought about a qualitative match between computations and data.     

Rate of opening of a population of Na channels in frog skeletal muscle fibers

Linear Systems convolution analysis of muscle sodium currents was used to predict the opening rate of sodium channels as a function of time during voltage clamp pulses. If open sodium channel lifetimes are exponentially distributed, the channel opening rate corresponding to a sodium current obtained at any particular voltage, can be analytically obtained using a simple equation, given single channel information about the mean open-channel lifetime and current.Predictions of channel opening rate during voltage clamp pulses show that sodium channel inactivation arises coincident with a decline in channel opening rate.Sodium currents pharmacologically modified with Chloramine-T treatment so that they do not inactivate, show a predicted sustained channel opening rate.Large depolarizing voltage clamp pulses produce channel opening rate functions that resemble gating currents.The predicted channel opening rate functions are best described by kinetic models for Na channels which confer most of the charge movement to transitions between closed states.Comparisons of channel opening rate functions with gating currents suggests that there may be subtypes of Na channel with some contributing more charge movement per channel opening than others.Na channels open on average, only once during the transient period of Na activation and inactivation.After transiently opening during the activation period and then closing by entering the inactivated state, Na channels reopen if the voltage pulse is long enough and contribute to steady-state currents.The convolution model overestimates the opening rate of channels contributing to the steady-state currents that remain after the transient early Na current has subsided.     

Gating of Shaker K+ channels: I. Ionic and gating currents.

Ionic and gating currents from noninactivating Shaker B K+ channels were studied with the cut-open oocyte voltage clamp technique and compared with the macropatch clamp technique. The performance of the cut-open oocyte voltage clamp technique was evaluated from the electrical properties of the clamped upper domus membrane, K+ tail current measurements, and the time course of K+ currents after partial blockade. It was concluded that membrane currents less than 20 microA were spatially clamped with a time resolution of at least 50 microseconds. Subtracted, unsubtracted gating currents with the cut-open oocyte voltage clamp technique and gating currents recorded in cell attached macropatches had similar properties and time course, and the charge movement properties directly obtained from capacity measurements agreed with measurements of charge movement from subtracted records. An accurate estimate of the normalized open probability Po(V) was obtained from tail current measurements as a function of the prepulse V in high external K+. The Po(V) was zero at potentials more negative than -40 mV and increased sharply at this potential, then increased continuously until -20 mV, and finally slowly increased with voltages more positive than 0 mV. Deactivation tail currents decayed with two time constants and external potassium slowed down the faster component without affecting the slower component that is probably associated with the return between two of the closed states near the open state. In correlating gating currents and channel opening, Cole-Moore type experiments showed that charge moving in the negative region of voltage (-100 to -40 mV) is involved in the delay of the conductance activation but not in channel opening. The charge moving in the more positive voltage range (-40 to -10 mV) has a similar voltage dependence to the open probability of the channel, but it does not show the gradual increase with voltage seen in the Po(V).     

Development changes in regulation of embryonic chick heart gap junctions

Summary Embryonic chick myocyte pairs were isolated from ventricular tissue of 4-day, 14-day, and 18-day heart for the purpose of examining the relationship between macroscopic junctional conductance and transjunctional voltage during cardiac development. The double whole-cell patch-clamp technique was employed to directly measure junctional conductance over a transjunctional voltage range of ±100 mV. At all ages, the instantaneous junctional current (or conductance=current/voltage) varied linearly with respect to transjunctional voltage. This initial response was followed by a time- and voltage-dependent decline in junctional current to new steady-state values. For every experiment, the steady-state junctional conductance was normalized to the instantaneous value obtained at each potential and the data was pooled according to developmental age. The mean steadystate junctional conductance-voltage relationship for each age group was fit using a two-state Boltzmann distribution described previously for other voltage-dependent gap junctions. From this model, it was revealed that half-inactivation voltage for the transjunctional voltage-sensitive conductance shifted towards larger potentials by 10 mV, the equivalent gating charge increased by approximately 1 electron, and the minimal voltage-insensitive conductance exactly doubled (increased from 18 to 36%) between 4 and 18 days of development. Decay time constants were similar at all ages examined as rate increased with increasing transjunctional potential. This data provides the first direct experimental evidence for developmental changes in the regulation of intercellular communication within a given tissue. This information is consistent with the hypothesis that developmental expression of multiple gap junction proteins (connexins) may confer different regulatory mechanisms on intercellular communication pathways within a given cell or tissue.     

A slowly inactivating potassium current in native oocytes of Xenopus laevis

Membrane currents were recorded in voltage-clamped oocytes of Xenopus laevis in response to voltage steps. We describe results obtained in oocytes obtained from one donor frog, which showed an unusually large outward current upon depolarization. Measurements of reversal potentials of tail currents in solutions of different K+ concentration indicated that this current is carried largely by K+ ions. It was strongly reduced by extracellular application of tetraethylammonium, though not by Ba2+ or 4-aminopyridine. Removal of surrounding follicular cells did not reduce the K+ current, indicating that it arises across the oocyte membrane proper. Activation of the K+ conductance was first detected with depolarization to about -12 mV, increased with a limiting voltage sensitivity of 3 mV for an e-fold change in current, and was half-maximally activated at about +10 mV. The current rose following a single exponential timecourse after depolarization, with a time constant that shortened from about 400 ms at -10 mV to about 15 ms at +80 mV. During prolonged depolarization the current inactivated with a time constant of about 4 s, which did not alter greatly with potential. The K+ current was independent of Ca2+, as it was not altered by addition of 10 mM Mn2+ to the bathing medium, or by intracellular injection of EGTA. Noise analysis of K+ current fluctuations indicated that the current is carried by channels with a unitary conductance of about 20 ps and a mean open lifetime of about 300 ms (at room temperature and potential of +10 to +20 mV).     

The voltage-dependent proton pumping in bacteriorhodopsin is characterized by optoelectric behavior

The light-driven proton pump bacteriorhodopsin (bR) was functionally expressed in Xenopus laevis oocytes and in HEK-293 cells. The latter expression system allowed high time resolution of light-induced current signals. A detailed voltage clamp and patch clamp study was performed to investigate the DeltapH versus Deltapsi dependence of the pump current. The following results were obtained. The current voltage behavior of bR is linear in the measurable range between -160 mV and +60 mV. The pH dependence is less than expected from thermodynamic principles, i.e., one DeltapH unit produces a shift of the apparent reversal potential of 34 mV (and not 58 mV). The M(2)-BR decay shows a significant voltage dependence with time constants changing from 20 ms at +60 mV to 80 ms at -160 mV. The linear I-V curve can be reconstructed by this behavior. However, the slope of the decay rate shows a weaker voltage dependence than the stationary photocurrent, indicating that an additional process must be involved in the voltage dependence of the pump. A slowly decaying M intermediate (decay time > 100 ms) could already be detected at zero voltage by electrical and spectroscopic means. In effect, bR shows optoelectric behavior. The long-lived M can be transferred into the active photocycle by depolarizing voltage pulses. This is experimentally demonstrated by a distinct charge displacement. From the results we conclude that the transport cycle of bR branches via a long-lived M(1)* in a voltage-dependent manner into a nontransporting cycle, where the proton release and uptake occur on the extracellular side.     

Voltage Clamp Experiments on Single Muscle Fibers of Rana pipiens

A voltage clamp for single muscle fibers has been developed. Stability of the system was achieved when an artificial node was created by enclosing a single muscle fiber in a petroleum jelly seal which served as an analogue of the myelin sheath. Typical voltage clamp records were obtained with large inward transient currents followed by a delayed rectification of the outward currents. These currents looked qualitatively similar when the transverse tubular system was destroyed. Errors in current measurement, especially those due to anomalous rectification, are discussed.     

Models of membrane resonance in pigeon semicircular canal type II hair cells

Pigeon vestibular semicircular canal type II hair cells often exhibit voltage oscillations following current steps that depolarize the cell membrane from its resting potential. Currents active around the resting membrane potential and most likely responsible for the observed resonant behavior are the Ca⁺⁺-insensitive, inactivating potassium conductance I _A (A-current) and delayed rectifier potassium conductance I _K. Several equivalent circuits are considered as representative of the hair cell membrane behavior, sufficient to explain and quantitatively fit the observed voltage oscillations. In addition to the membrane capacitance and frequency-independent parallel conductance, a third parallel element whose admittance function is of second order is necessary to describe and accurately predict all of the experimentally obtained current and voltage responses. Even though most voltage oscillations could be fitted by an equivalent circuit in which the second order admittance term is overdamped (i.e., represents a type of current with two time constants, one of activation and the other of inactivation), the sharpest quality resonance obtained with small current steps (around 20 pA) from the resting potential could be satisfactorily fit only by an underdamped term.     

Carbenoxolone-sensitive and cesium-permeable potassium channel in the rod cells of frog taste discs

The rod cells in frog taste discs display the outward current and maintain the negative resting potential in the condition where internal K⁺ is replaced with Cs⁺. We analyzed the properties of the Cs⁺-permeable conductance in the rod cells. The current–voltage (I/V) relationships obtained by a voltage ramp were bell-shaped under Cs⁺ internal solution. The steady state I/V relationships elicited by voltage steps also displayed the bell-shaped outward current. The activation of the current accelerated with the depolarization and the inactivation appeared at positive voltage. The gating for the current was maintained even at symmetric condition (Cs⁺ external and internal solutions). The wing cells did not show the properties. The permeability for K⁺ was a little larger than that for Cs⁺. Internal Na⁺ and NMDG⁺ could not induce the bell-shaped outward current. Carbenoxolone inhibited the bell-shaped outward Cs⁺ current dose dependently (IC₅₀: 27 μM). Internal arachidonic acid (20 μM) did not induce the linear current–voltage (I–V) relationship which is observed in two-pore domain K⁺ channel (K_2P). The results suggest that the resting membrane potentials in the rod cells are maintained by the voltage-gated K⁺ channels.     

Voltage clamp of the cardiac sodium current at 37 degrees C in physiologic solutions.

The cardiac sodium current was studied in guinea pig ventricular myocytes using the cell-attached patch voltage clamp at 37 degrees C in the presence of 145 mM external sodium concentration. When using large patch pipettes (access resistance, 1-2 M omega), the capacity current transient duration was typically 70 microseconds for voltage clamp steps up to 150 mV. At 37 degrees C the maximum inward sodium current peaked in approximately 200 microseconds after the onset of a clamp step and at this strong depolarization, less than 10% of the sodium current developed during the capacity transient. The sodium current developed smoothly and the descending limb of the current-voltage relationship usually spanned a range of 40 mV. Moreover, currents reduced by inactivation of sodium channels could be scaled to superimpose on the maximum current. Current tails elicited by deactivation followed a monoexponential time course that was very similar for currents of different sizes. Data obtained over a range of temperatures (15 degrees-35 degrees C) showed that the steady-state inactivation and conductance-voltage curves were shifted to more negative voltages at lower temperatures. These results demonstrate the feasibility of investigating the sodium current of mammalian cardiac cells at 37 degrees C in normal physiological solutions.     

Use of transmembrane current harmonics originating from electrostriction for clarifying mechanisms of ion transport in prepartions of sodium-potassium ATPase

The mechanisms of generation of transmembrane current harmonics arising due to electrostriction of the bilayer upon applying an alternating electric voltage to sodium/potassium ATPase sorbed on the support was studied. It is discussed what information can be obtained by measurements of transmembrane current harmonics to clarify the mechanism of ion transport in sodium/potassium ATPase preparations. It was shown that for studying the current harmonics upon electrostriction, the preparations should be sorbed on bilayer lipid membranes with a high modulus of elasticity. The kinetics of changes in the amplitude of the second current harmonics in response to an impulse addition of ATP to the preparation can have some specific features depending on the mechanism of ion transport.