Leak Current Rectification in Myxicola Giant Axons : Constant field and constant conductance components

Early leak current, i.e. for times similar to the time to peak of the transient current was measured in Myxicola giant axons in the presence of tetrodotoxin. The leak current-voltage relation rectifies, showing more current for strong depolarizing pulses than expected from symmetry around the holding potential. A satisfactory practical approximation for most leak corrections is constant resting conductance. The leak current-voltage curve rectifies less than expected from the constant field equation. These curves cannot be reconstructed by summing the constant field currents for sodium and potassium using a P_Na/P_K ratio obtained in the usual way, from zero current constant field fits to resting membrane potential data. Nor can they be reconstructed by summing the constant field current for potassium with that for any other single ion. They can be reconstructed, however, by summing the constant field current for potassium with a constant conductance component. It is concluded that the leak current and the resting membrane potential, therefore, are determined by multiple ionic components, at least three and possibly many. Arguments are presented suggesting that ion permeability ratios obtained in the usual way, by fitting the constant field equation to resting membrane potential data should be viewed with skepticism.     

Quantitative description of sodium and potassium currents and computed action potentials in Myxicola giant axons

All analysis of the sodium and potassium conductances of Myxicola giant axons was made in terms of the Hodgkin-Huxley m, n, and h variables. The potassium conductance is proportional to n². In the presence of conditioning hyperpolarization, the delayed current translates to the right along the time axis. When this effect was about saturated, the potassium conductance was proportional to n³. The sodium conductance was described by assuming it proportional to m³h. There is a range of potentials for which τ_h and h_∞ values fitted to the decay of the sodium conductance may be compared to those determined from the effects of conditioning pulses. τ_h values determined by the two methods do not agree. A comparison of h_∞ values determined by the two methods indicated that the inactivation of the sodium current is not governed by the Hodgkin-Huxley h variable. Computer simulations show that action potentials, threshold, and subthreshold behavior could be accounted for without reference to data on the effects of initial conditions. However, recovery phenomena (refractoriness, repetitive discharges) could be accounted for only by reference to such data. It was concluded that the sodium conductance is not governed by the product of two independent first order variables.     

Barbiturates Block Sodium and Potassium Conductance Increases in Voltage-Clamped Lobster Axons

Sodium pentobarbital and sodium thiopental decrease both the peak initial (Na) and late steady-state (K) currents and reduce the maximum sodium and potassium conductance increases in voltage-clamped lobster giant axons. These barbiturates also slow the rate at which the sodium conductance turns on, and shift the normalized sodium conductance vs. voltage curves in the direction of depolarization along the voltage axis. Since pentobarbital (pK_a = 8.0) blocks the action potential more effectively at pH 8.5 than at pH 6.7, the anionic form of the drug appears to be active. The data suggest that these drugs affect the axon membrane directly, rather than secondarily through effects on intermediary metabolism. It is suggested that penetration of the lipid layer of the membrane by the nonpolar portion of the barbiturate molecules may cause the decrease in membrane conductances, while electrostatic interactions involving the anionic group on the barbiturate, divalent cations, and "fixed charges" in the membrane could account for the slowing of the rate of sodium conductance turn-on and the shift of the normalized conductance curves along the voltage axis.     

Fast and slow inactivation of sodium channels: effects of photodynamic modification by methylene blue.

Illumination of crayfish giant axons, during internal perfusion with 0.5 mM methylene blue (MB), produces photodynamic effects that include (i) reduction in total sodium conductance, (ii) shifting of the steady-state inactivation curve to the right along the voltage axis, (iii) reduction in the effective valence of steady-state inactivation and, (iv) potentially complete removal of fast inactivation. Additionally, the two kinetic components of fast inactivation in crayfish axons are differentially affected by MB+light. The intercept of the faster component (tau h1) is selectively reduced at shorter MB+light exposure times. Neither tau h1 nor the slower (tau h2) process was protected from MB+light by prior steady-state inactivation of sodium channels. However, carotenoids provide differing degrees of protection against each of the photodynamic actions listed above, suggesting that the four major effects of MB+light are mediated by changes occurring within different regions of the sodium channel molecule.     

Analysis of K Inactivation and TEA Action in the Supramedullary Cells of Puffer

Under the voltage clamp condition, the K inactivation was analyzed in cells bathed in the isosmotic KCl Lophius-Ringer solution. After conditioning hyperpolarization, the cells respond to depolarizations with increased K permeability, which in turn is decreased during maintained depolarizations. The steady-state levels of the K inactivation as a function of the membrane potential are related by an S-shaped curve similar to that which describes the steady-state Na inactivation in the squid giant axon. TEA reduced the K conductance by a factor which is independent of the potential, and without a shift of the inactivation curve along the voltage axis. The rapid phase of the K activation is less susceptible to TEA than the slow phase of the K activation. Hyperpolarizing steps remove the K inactivation, the rate of the removal being faster the larger the hyperpolarization from the standard potential of about -60 mv.     

Anticonvulsants modify inactivation but not activation processes of sodium channels in Myxicola axons

The effects of pronase and the anticonvulsant drugs diphenylhydantoin, bepridil, and sodium valproate on fast and slow Na+ inactivation were examined in cut-open Myxicola giant axons with loose patch-clamp electrodes applied to the internal surface. Pronase completely eliminated fast Na+ inactivation without affecting the kinetics of Na+ activation or the maximum Na+ conductance. The time and voltage dependences of slow inactivation following pronase treatment were identical to those measured before enzyme application in the same axons. All three anticonvulsants slowed the time course of recovery from fast Na+ inactivation in untreated axons, and shifted the steady-state fast inactivation curve in the hyperpolarizing direction along the voltage axis. Anticonvulsants enhanced steady-state slow inactivation and retarded recovery from slow inactivation in both untreated and pronase-treated axons. Although some quantitative differences were seen, the order of potency of the anticonvulsants on slow Na+ inactivation was the same as that for recovery from fast inactivation.     

Magnitude and location of surface charges on Myxicola giant axons

The effects of changes in the concentration of calcium in solutions bathing Myxicola giant axons on the voltage dependence of sodium and potassium conductance and on the instantaneous sodium and potassium current-voltage relations have been measured. The sodium conductance-voltage relation is shifted along the voltage axis by 13 mV in the hyperpolarizing direction for a fourfold decrease in calcium concentration. The potassium conductance-voltage relation is shifted only half as much as that for sodium. There is no effect on the shape of the sodium and potassium instantaneous current-voltage curves: the normal constant-field rectification of potassium currents is maintained and the normal linear relationship of sodium currents is maintained. Considering that shifts in conductances would reflect the presence of surface charges near the gating machinery and that shape changes of instantaneous current-voltage curves would reflect the presence of surface charges near the ionic pores, these results indicate a negative surface charge density of about 1 electronic charge per 120 A2 near the sodium gating machinery, about 1 e/300 A2 for the potassium gating machinery, and much less surface charge near the sodium or potassium pores. There may be some specific binding of calcium to these surface charges with an upper limit on the binding constant of about 0.2 M-1. The differences in surface charge density suggest a spatial separation for these four membrane components.     

Sodium channel inactivation in the crayfish giant axon. Must channels open before inactivating?

Experiments on sodium channel inactivation kinetics were performed on voltage-clamped crayfish giant axons. The primary goal was to investigate whether channels must open before inactivating. Voltage-clamp artifacts were minimized by the use of low-sodium solutions and full series resistance compensation, and the spatial uniformity of the currents was checked with a closely spaced pair of electrodes used to measure local current densities. For membrane potentials between -40 and +40 mV, sodium currents decay to zero with a single exponential time-course. The time constant for decay is a steep function of membrane potential. The time-course of inactivation measured with the double-pulse method is very similar to the decay of current at the same potential. Steady-state inactivation curves measured with different test pulses are identical. The time-course of double pulse inactivation shows a lag that roughly correlates with the opening of sodium channels, but detailed comparisons with the time course of the prepulse current suggest that it is not strictly necessary for channels to open before inactivating. Measurements of the potential dependence of the integral of sodium conductance area also inconsistent with the simplest cases of models in which channels must open before inactivating.     

Structural stability,alternate descriptions and information

The inactivation properties of a model of the nerve membrane are examined. The inactivation kinetics are closely first order and may be characterized by Hodgkin-Huxley (H-H) parameters h_∞ and τ_h which depend on potential in agreement with experiments. Some differences from the H-H equations are identified. The forms predicted for τ_h variation with hyper-polarization and change of external [K⁺] agree with available data. While the inactivation time delay predicted by the model is too small to be detected experimentally, there are grounds for expecting that it may be larger in other tissues, as observed in Myxicola giant axons. The variation of the delay with test potential is predicted to be exponential. Although the model is coupled in the sense defined by Hoyt, it gives rise to an inactivation shift of negligible magnitude. However, introducing a simple variability in one physical parameter leads to the observed form of both the peak transient current voltage relation and the inactivation shift. Inactivation shift thus does not unambiguously indicate coupling; that it results from parametric heterogeneity may be a better hypothesis, and is readily testable. The inactivation shift dependence on current ratio, from experimental data, can be used to correct for the effects of parametric heterogeneity and obtain the value of a previously predicted fundamental parameter of excitable membranes. It is suggested that the effects of parametric heterogeneity must be considered in interpreting experiments and designing models for excitable systems.     

A Test of the Theory of the Steady-State Properties of an Ion Exchange Membrane with Mobile Sites and Dissociated Counterions

An experimental model system, formally equivalent to a liquid ion exchange membrane having completely dissociated sites and counterions, has been devised in order to test the steady-state properties recently deduced theoretically for such a membrane by Conti and Eisenman, (1966). In this system we have obtained quantitative experimental confirmation of the following theoretical expectations. (a) The current-voltage relationship is nonlinear and exhibits finite limiting currents with strong applied fields. (b) The mobile sites rearrange within the “membrane” under applied electric field to give a linear concentration profile and a logarithmic electric potential profile in the steady state. We have also extended the theory to consider the instantaneous conductance in the steady state. Theory and experiment indicate that in a mobile site membrane the instantaneous conductance in the steady state is not given by the chord conductance of the steady-state current-voltage relationship, in contrast to the situation in a fixed site membrane. This finding suggests a way of testing whether ions permeate across an unknown membrane by a fixed site or a dissociated mobile site mechanism.     

Potassium currents in the giant axon of the crab Carcinus maenas

Measurements were made of the kinetic and steady-state characteristics of the potassium conductance in the giant axon of the crab Carcinus maenas. These measurements were made in the presence of tetrodotoxin, using the feedback amplifier concept introduced by Dodge and Frankenhaeuser (J. Physiol, (London) 143:76-90). The conductance increase during depolarizing voltage-clamp pulses was analyzed assuming that two separate potassium channels exist in these axons. The first potassium channel exhibited activation and fast inactivation gating which could be fitted using the m3h, Hodgkin-Huxley formalism. The second potassium channel exhibited the standard n4 Hodgkin-Huxley kinetics. These two postulated channels are blocked by internal application of caesium, tetraethylammonium and sodium ions. External application of 4 amino-pyridine also blocks these channels.     

Inactivation of the sodium channel. I. Sodium current experiments

Inactivation of sodium conductance has been studied in squid axons with voltage clamp techniques and with the enzyme pronase which selectively destroys inactivation. Comparison of the sodium current before and after pronase treatment shows a lag of several hundred microseconds in the onset of inactivation after depolarization. This lag can of several hundred microseconds in the onset of inactivation after polarization. This lag can also be demonstrated with double-pulse experiments. When the membrane potential is hyperpolarized to -140 mV before depolarization, both activation and inactivation are delayed. These findings suggest that inactivation occurs only after activation are delayed. These findings suggest that inactivation occurs only after activation; i.e. that the channels must open before they can inactivate. The time constant of inactivation measured with two pulses (τ(c)) is the same as the one measured from the decay of the sodium current during a single pulse (τ(h)). For large depolarizations, steady-state inactivation becomes more incomplete as voltage increases; but it is relatively complete and appears independent of voltage when determined with a two- pulse method. This result confirms the existence of a second open state for Na channels, as proposed by Chandler and Meves (1970. J. Physiol. [Lond.]. 211:653-678). The time constant of recovery from inactivation is voltage dependent and decreases as the membrane potential is made more negative. A model for Na channels is presented which has voltage-dependent transitions between the closed and open states, and a voltage-independent transition between the open and the inactivated state. In this model the voltage dependence of inactivation is a consequence of coupling to the activation process.     

Ionic Conductance Changes in Voltage Clamped Crayfish Axons at Low pH

Giant axons from the crayfish have been voltage clamped with an axial wire system. General characterististics of observed ionic currents under normal conditions are similar to those measured in other giant axons and in nodes of Ranvier. As the pH of the external bath is lowered below 7, a marked, reversible slowing of potassium currents is seen with little effect on sodium currents. The steady-state potassium conductance-voltage curve is shifted along the voltage axis in a manner consistent with the development of a hyperpolarizing surface charge. Results suggest that this potential shift accounts for part, though not all, of the observed increase in τ_n. From the behavior of the kinetics of the delayed current with external pH these alterations in potassium conductance are attributed to the titration of a histidine imidazole residue of a membrane protein. Chemical modification of histidine by carbethoxylation at pH 6 slows and strongly depresses potassium currents. The results suggest that in addition to the introduction of electrostatic forces, possibly resulting from a hyperpolarizing surface charge, protonation of a histidine group at low pH also alters the nonelectrostatic chemical interactions determining the ease with which potassium gates open and close. The evidence indicates that the modified histidine residue is closely associated with the membrane components involved in the control of potassium conductance.     

Sodium inactivation in nerve fibers

A number of models proposed to account for the sodium conductance changes are shown to fall into two classes. The Hodgkin-Huxley (HH) model falls into a class (I) in which the conductance depends on two or more independent variables controlled by independent processes. The Mullins, Hoyt, and Goldman models fall into class II in which conductance depends directly on one variable only, a variable which is controlled by two or more coupled processes. The HH and Hoyt models are used as specific examples of the two classes. It is shown that, contrary to a recently published report, the results from double experiments can be equally well accounted for by both models. It is also shown that steady-state conditioning, or “inactivation,” curves, obtained at more than one test potential, can be used to distinguish the two models. The HH equations predict that such curves should be shifted, by very small amounts, in the hyperpolarizing direction when more depolarizing test potentials are used, while the Hoyt model predicts that they should be shifted in the depolarizing direction, by quite appreciable amounts. Several pieces of published experimental information are used as tests of these predictions, and give tentative support to the class II model. Further experiments are necessary before a definite conclusion can be reached.     

Potassium ion currents in the crayfish giant axon. Dynamic characteristics.

The kinetics of the voltage-sensitive potassium channel in crayfish axon have been examined. The conductance increase after a step depolarization from rest can be described by a first-order kinetic process raised to the third power. When conditioning voltage levels preceded the test pulse, the steady-state conductance was found to be independent of initial conditions. Depolarizing conditioning voltages in general allowed superposition of test voltage potassium currents by a shift along the time axis. Hyperpolarizing conditioning voltages produced a delay in onset of conductance during the test pulse and changed the kinetics so that superposition was not possible. The delay increased during the hyperpolarization with a first-order lag having a time constant in the range of 1.5-3 ms. Return to the resting level caused recovery from the delayed state to follow a single exponential decay with a time constant of 1.9-2.2 ms. The steady state delay vs. voltage curves were not saturated at potentials as negative as -180 mV.     

Intracellular pH and ionic channels in the Loligo vulgaris giant axon.

Squid giant axons were used to investigate the reversible effects of intracellular pH(pHi) on the kinetic properties of ionic channels. The pharmacologically separated K+ and Na+ currents were measured under: (a) internal perfusion, (b) enzymatic Pronase treatment, and (c) continuous estimate of periaxonal ion accumulation. Variation of internal pH from 4.8 to 11 resulted in: (a) a decrease of steady-state sodium inactivation at positive potentials similar to the effect of the proteolytic enzyme Pronase, (b) a shift of the h infinity (E) curve toward depolarizing voltages, and (c) a decrease of the time constant of inactivation for potentials below -20 mV (an increase above). A plot of the steady-state sodium conductance at E = +40 mV as a function of pHi suggests that two groups with pKa 10.4 and 5.6 affect respectively the inactivation gate and the rate constants for the transition from the inactivated to the second open state (h2) (Chandler and Meves, 1970b). The voltage shifts of the kinetic parameters predicted by the Gouy-Chapman-Stern theory are well satisfied at high pHi and less at low. Once corrected for voltage shifts, the forward rate constants for channel opening were found to be slowed with the acidity of the internal or external solution.     

Selective modification of sodium channel gating in lobster axons by 2, 4, 6-trinitrophenol: Evidence for two inactivation mechanisms

Trinitrophernol (TNP) selectively alters the sodium conductance system of lobster giant axons as measured in current clamp and voltage clamp experiments using the double sucrose gap technique. TNP has no measurable effect on potassium currents but reversibly prolongs the time-course of sodium currents during maintained depolarizations over the full voltage range of observable currents. Action potential durations are increased also. Tm of the Hodgkin-Huxley model is not markedly altered during activation of the sodium conductance but is prolonged during removal of activation by repolarization, as observed in sodium tail experiments. The sodium inactivation versus voltage curve is shifted in the hyperpolarizing direction as is the inactivation time constant curve, measured with conditioning voltage steps. This shift speeds the kinetics of inactivation over part of the same voltage range in which sodium currents are prolonged, a contradiction incompatible with the Hodgkin-Huxley model. These results are interpreted as support for a hypothesis of two inactivation processes, one proceeding directly from the resting state and the other coupled to the active state of sodium conductance.     

n-Alkanols potentiate sodium channel inactivation in squid giant axons.

The effects of n-octanol and n-decanol on nerve membrane sodium channels were examined in internally perfused, voltage-clamped squid giant axons. Both n-octanol and n-decanol almost completely eliminated the residual sodium conductance at the end of 8-ms voltage steps. In contrast, peak sodium conductance was only partially reduced. This block of peak and residual sodium conductance was very reversible and seen with both internal and external alkanol application. The differential sensitivity of peak and residual conductance to alkanol treatment was eliminated after internal pronase treatment, suggesting that n-octanol and n-decanol enhance the normal inactivation mechanism rather than directly blocking channels in a time-dependent manner.     

Interaction of n-alkylguanidines with the sodium channels of squid axon membrane

The effects of n-alkylguanidine derivatives on sodium channel conductance were measured in voltage clamped, internally perfused squid giant axons. After destruction of the sodium inactivation mechanism by internal pronase treatment, internal application of n-amylguanidine (0.5 mM) or n-octylguanidine (0.03 mM) caused a time-dependent block of sodium channels. No time-dependent block was observed with shorter chain derivatives. No change in the rising phase of sodium current was seen and the block of steady-state sodium current was independent of the membrane potential. In axons with intact sodium inactivation, an apparent facilitation of inactivation was observed after application of either n-amylguanidine or n-octylguanidine. These results can be explained by a model in which alkylguanidines enter and occlude open sodium channels from inside the membrane with voltage-independent rate constants. Alkylguanidine block bears a close resemblance to natural sodium inactivation. This might be explained by the fact that alkylguanidines are related to arginine, which has a guanidino group and is thought to be an essential amino acid in the molecular mechanism of sodium inactivation. A strong correlation between alkyl chain length and blocking potency was found, suggesting that a hydrophobic binding site exists near the inner mouth of the sodium channel.     

Sodium currents in the giant axon of the crab Carcinus maenas

Measurements were made of the kinetics and steady-state properties of the sodium conductance changes in the giant axon of the crab Carcinus maenas. The conductance measurements were made in the presence of small concentrations of tetrodotoxin and as much electrical compensation as possible in order to minimize errors caused by the series resistance. After an initial delay of 10-150 microsec, the conductance increase during depolarizing voltage clamp pulses followed the Hodgkin-Huxley kinetics. Values of the time constant for the activation of the sodium conductance lay on a bell-shaped curve with a maximum under 180 microsec at -40 mV (at 18 degrees C). Values of the time constant for the inactivation of the sodium conductance were also fitted using a bell-shaped curve with a maximum under 7 msec at -70 mV. The effects of membrane potential on the fraction of Na channels available for activation studied using double pulse protocols suggest that hyperpolarizing potentials more negative than -100 mV lock a fraction of the Na channels in a closed conformation.