A proposed membrane model for generation of sodium currents in squid giant axons

An experimental review to show that axonal undercoat and cytoskeletal structures underneath the axolemma of squid giant axons play an important role in generating sodium currents is presented. Correspondingly, two alternative membrane models are proposed; one is that the undercoat and cytoskeletal structures support the functioning of sodium channels and the other is that they are directly incorporated with the molecular mechanism of generating sodium currents. This latter model is probable in squid giant axons. The model of direct participation of the underlying cytoskeleton in the sodium activation mechanism modifies the sodium activation gating kinetics in the Hodgkin-Huxley scheme; that is, the transition velocities between the open and closed states of the activation gate depend not only on membrane potentials but also on the time after the onset of application of a potential step.     

Removal of sodium channel inactivation in squid axon by the oxidant chloramine-T

We have investigated the effects of a mild oxidant, chloramine-T(CT), on the sodium and potassium currents of squid axons under voltage-clamp conditions. Sodium channel inactivation of squid giant axons can be completely removed by CT at neutral pH. Internal and external CT treatment are both effective. CT apparently removes inactivation in an irreversible, all-or-none manner. The activation process of sodium channels is little affected, as judged from the voltage dependence of peak sodium currents, the rising phase of sodium currents, and the time course of tail currents following the repolarization. The removal of inactivation by CT is pH-dependent; higher pH decreases the removal rate, whereas lower pH increases it. Internal metabisulfite, a strong reductant, does not protect inactivation from the action of external CT, nor does external metabisulfite protect from internal CT application. CT slightly depresses the peak potassium currents at comparable concentrations but has no apparent effects on their kinetics. Our results suggest that the neutral form of CT modifies an embedded methionine residue that is involved in sodium channel inactivation.     

Effects of Internal Divalent Cations on Voltage-Clamped Squid Axons

We have studied the effects of internally applied divalent cations on the ionic currents of voltage-clamped squid giant axons. Internal concentrations of calcium up to 10 mM have little, if any, effect on the time-course, voltage dependence, or magnitude of the ionic currents. This is inconsistent with the notion that an increase in the internal calcium concentration produced by an inward calcium movement with the action potential triggers sodium inactivation or potassium activation. Low internal zinc concentrations (~1 mM) selectively and reversibly slow the kinetics of the potassium current and reduce peak sodium current by about 40% with little effect on the voltage dependence of the ionic currents. Higher concentrations (~10 mM) produce a considerable (ca. 90%) nonspecific reversible reduction of the ionic currents. Large hyperpolarizing conditioning pulses reduce the zinc effect. Internal zinc also reversibly depolarizes the axon by 20–30 mV. The effects of internal cobalt, cadmium, and nickel are qualitatively similar to those of zinc: only calcium among the cations tested is without effect.     

Axonal excitability revisited

The original papers of Hodgkin and Huxley (J. Physiol. 116 (1952a) 449, J. Physiol. 116 (1952b) 473, J. Physiol. 116 (1952c) 497, J. Physiol. 117 (1952d) 500) have provided a benchmark in our understanding of cellular excitability. Not surprisingly, their model of the membrane action potential (AP) requires revisions even for the squid giant axon, the preparation for which it was originally formulated. The mechanisms they proposed for the voltage-gated potassium and sodium ion currents, IK, and INa, respectively, have been superceded by more recent formulations that more accurately describe voltage-clamp measurements of these components. Moreover, the current-voltage relation for IK has a non-linear dependence upon driving force that is well described by the Goldman-Hodgkin-Katz (GHK) relation, rather than the linear dependence on driving force found by Hodgkin and Huxley. Furthermore, accumulation of potassium ions in the extracellular space adjacent to the axolemma appears to be significant even during a single AP. This paper describes the influence of these various modifications in their model on the mathematically reconstructed AP. The GHK and K+ accumulation results alter the shape of the AP, whereas the modifications in IK and INa gating have surprisingly little effect. Perhaps the most significant change in their model concerns the amplitude of INa, which they appear to have overestimated by a factor of two. This modification together with the GHK and the K+ accumulation results largely remove the discrepancies between membrane excitability of the squid giant axon and the Hodgkin and Huxley (J. Physiol. 117 (1952d) 500) model previously described (Clay, J. Neurophysiol. 80 (1998) 903).     

Gating currents in the node of Ranvier: voltage and time dependence.

Like the axolemma of the giant nerve fibre of the squid, the nodal membrane of frog myelinated nerve fibres after blocking transmembrane ionic currents exhibits asymmetrical displacement currents during and after hyperpolarizing and depolarizing voltage clamp pulses of equal size. The steady-state distribution of charges as a function of membrane potential is consistent with Boltzmanns law (midpoint potential minus 33.7 mV; saturation value 17200 charges/mum-2). The time course of the asymmetry current and the voltage dependence of its time constant are consistent with the notion that due to a sudden change in membrane potential the charges undergo a first order transition between two configurations. Size and voltage dependence of the time constant are similar to those of the activation of the sodium conductance assuming m-2h kinetics. The results suggest that the presence of ten times more sodium channels (5000/mum-2) in the node of Ranvier than in the squid giant axon with similar sodium conductance per channel (2-3 pS).     

The relationship between the inactivating fraction of the asymmetry current and gating of the sodium channel in the squid giant axon

A quantitative comparison between the voltage dependence of the inactivating component of the asymmetrical charge transfer in the squid giant axon and that of the sodium conductance indicates that activation of the sodium system involves either three subunits operating in parallel or a three-step series mechanism. This is confirmed by an examination of the relative timing of the flow of asymmetry and ionic currents during the opening and closing of the sodium channels. In agreement with previous suggestions, inactivation is coupled sequentially to activation. The evidence appears to argue against a trimeric system with three wholly independent subunits and favours a monomeric system that undergoes a complex sequence of conformational changes.     

Single sodium channels from the squid giant axon

Since the work of A. L. Hodgkin and A. F. Huxley (1952. J. Physiol. [Lond.].117:500-544) the squid giant axon has been considered the classical preparation for the study of voltage-dependent sodium and potassium channels. In this preparation much data have been gathered on macroscopic and gating currents but no single sodium channel data have been available. This paper reports patch clamp recording of single sodium channel events from the cut-open squid axon. It is shown that the single channel conductance in the absence of external divalent ions is approximately 14 pS, similar to sodium channels recorded from other preparations, and that their kinetic properties are consistent with previous results on gating and macroscopic currents obtained from the perfused squid axon preparation.     

Potassium Ion Current in the Squid Giant Axon: Dynamic Characteristic

Measurements of the potassium current in the squid axon membrane have been made, after changes of the membrane potential to the sodium potential of Hodgkin and Huxley (HH), from near the resting potential, from depolarizations of various durations and amplitudes, and from hyperpolarizations of up to 150 mv. The potassium currents I given by I = I_∞ {1 - exp [- (t + t₀)/τ]}²⁵, where t₀ is determined by the initial conditions, represent the new data and approximate the HH functions in the regions for which they are adequate. A corresponding modification for the sodium current does not appear necessary. The results support the HH assumptions of the independence of the potassium and sodium currents, the dependence of the potassium current upon a single parameter determined by the membrane potential, and the expression of this parameter by a first order differential equation, and, although the results drastically modify the analytical expressions, they very considerably extend the range of apparent validity of these assumptions. The delay in the potassium current after severe hyperpolarization is used to estimate a potassium ion mobility in the membrane as 10^-5 of its value in aqueous solutions.     

Impulses and Physiological States in Theoretical Models of Nerve Membrane

Van der Pol''s equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting “BVP model” has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer''s theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a “physiological state diagram,” with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.     

Cultured Giant Fiber Lobe of Squid Expresses Three Distinct Potassium Channel Activities in Selective Combinations

Neurons from the giant fiber lobe (GFL) of squid Loligo bleekeri were dissociated and cultured. The ionic currents were recorded using whole-cell patch clamp methods. The sodium current and the noninactivating potassium current like those elicited by the giant axon were among the currents expressed in axonal bulbs and bulblike structures upon dissociation. Meanwhile axonless cell bodies did not elicit such currents. Axonless cell bodies and some bulblike structures elicited two kinds of inactivating potassium currents, the slow- and the fast-inactivating current, which differed in their inactivation kinetics and pharmacology. Within 24 hr of plating, the current composition remained the same. While the noninactivating current was not sensitive to 4-aminopyridine, the two inactivating currents were sensitive, the slow-inactivating current being more sensitive. Selective combinations of the sodium current and the three potassium currents expressed in different structures of the acutely dissociated GFL could have resulted from cellular control of synthesis and transportation of the channel proteins to the somatic and the axonal membrane. The sodium current and the noninactivating potassium current could be recorded from some axonless cell bodies maintained in culture for over three days, indicating that the separation of the giant axon from its somata could result in the transportation of the channels normally expressed on the giant axon membrane to the somatic membrane. Received: 24 October 1995/Revised: 5 March 1996     

Unidirectional sodium and potassium fluxes through the sodium channel of squid giant axons.

Unidirectional 22Na-traced sodium influx or 42K-traced potassium efflux across the membranes of voltage-clamped squid giant axons was measured at various membrane potentials under bi-ionic conditions. Tetrodotoxin almost entirely eliminated the extra K+ efflux induced by short repetitive depolarizations in the presence of tetraethylammonium or 3,4-diaminopyridine. A method of determining the voltage dependence of the unidirectional flux through voltage-gated channels is described. This technique was used to obtain the unidirectional flux-voltage relation for the sodium channel in bi-ionic and single-ion conditions. It allows the determination of the unidirectional flux at the zero-current potential which, for influx, was found to be approximately 20% of the value measured 80 mV negative to the zero-current potential. The unidirectional flux ratio under bi-ionic conditions was also measured and the flux ratio exponent found to average 1.15 with an external sodium and an internal potassium solution. A three-barrier, two-site, multi-occupancy model previously obtained for other conditions was found to predict a similar non-unity average for the flux ratio exponent. It is also shown that some single-occupancy models can predict non-unity values for the flux ratio exponent in bi-ionic conditions.     

Shaker potassium channel gating. III: Evaluation of kinetic models for activation

Predictions of different classes of gating models involving identical conformational changes in each of four subunits were compared to the gating behavior of Shaker potassium channels without N-type inactivation. Each model was tested to see if it could simulate the voltage dependence of the steady state open probability, and the kinetics of the single-channel currents, macroscopic ionic currents and macroscopic gating currents using a single set of parameters. Activation schemes based upon four identical single-step activation processes were found to be incompatible with the experimental results, as were those involving a concerted, opening transition. A model where the opening of the channel requires two conformational changes in each of the four subunits can adequately account for the steady state and kinetic behavior of the channel. In this model, the gating in each subunit is independent except for a stabilization of the open state when all four subunits are activated, and an unstable closed conformation that the channel enters after opening. A small amount of negative cooperativity between the subunits must be added to account quantitatively for the dependence of the activation time course on holding voltage.     

Orientation of the tryptophans responsible for the photoinactivation of nerve sodium channels

UV irradiation of squid giant azons at wavelengths of 280 or 290 nm produces nearly the same rate of irreversible decrease of sodium currents. The rate of photodeactivation is unaffected by extensive removal of axoplasm with pronase, and it is independent of temperature in the range 5° to 20°C. The photochemical effect appears to be all or nothing. It does not alter the time course and the voltage dependence for activation and inactivation of the residual currents. Similar deactivation rates were produced by irradiations of the same intensity, but linearly polarized either parallel or perpendicular to the axon. The efficiency of the deactivation process is close to that expected if it was caused by the photooxidation of a single tryptophan residue per sodium channel. Owing to the geometry of the preparation the lack of polarization asymmetry suggests that this residue assumes nearly random (or pseudo-random) orientation in the three-dimensional structure of the sodium channel corresponding to the closed state.     

A series-parallel model of the voltage-gated sodium channel

A series-parallel model of the kinetics of the voltage-gated sodium channel is described. It goes some way towards reconciling the time-courses of the gating and macroscopic sodium currents in the squid giant axon with the molecular structure of the channel.     

The causal theory of the resting potential of cells

In this pedagogical article the causal theory of the resting potential of cells is presented, which for given extracellular ion concentrations predicts the intracellular ones simultaneously with the resting potential. In addition to the Na, K-pump, fixed charges on the membrane surfaces are taken into account. The equation determining the resting potential in the causal theory suggests a new explanation of the genesis of the resting potential. The usual criterion for an ion pump to be electrogenic is not relevant for the whole of the resting potential, and may therefore be misleading. The physical meaning of the Goldman-Hodgkin-Katz formula for the membrane potential as a diffusion potential is also explained and tested with numbers for the giant axon of the squid. A significant discrepancy between theory and experiment is found which calls for an experimental re-examination of the constitutive equations for passive potassium and sodium currents.     

A calculation of the current voltage characteristic of a voltage-controlled model membrane ion channel

A simple calculation is made of the current-voltage characteristic of a model ion channel in which the ion transfer rate is controlled by an electrical potential gradient rather than by mechanical gating particles. Although the model deals with sodium and potassium channels similarly, very different characteristics are obtained that approximate to those measured in the squid giant axon. The difference is due essentially to the very different Nernst potentials for these two ions. The ability of the model to predict channel activation due to both depolarization and hyperpolarizing voltage transients is described.     

Phosphorylation modulates potassium conductance and gating current of perfused giant axons of squid

The presence of internal Mg-ATP produced a number of changes in the K conductance of perfused giant axons of squid. For holding potentials between -40 and -50 mV, steady-state K conductance increased for depolarizations to potentials more positive than approximately -15 mV and decreased for smaller depolarizations. The voltage dependencies of both steady-state activation and inactivation also appears shifted toward more positive potentials. Gating kinetics were affected by internal ATP, with the activation time constant slowed and the characteristic delay in K conductance markedly enhanced. The rate of deactivation also was hastened during perfusion with ATP. Internal ATP affected potassium channel gating currents in similar ways. The voltage dependence of gating charge movement was shifted toward more positive potentials and the time constants of ON and OFF gating current also were slowed and hastened, respectively, in the presence of ATP. These effects of ATP on the K conductance occurred when no exogenous protein kinases were added to the internal solution and persisted even after removing ATP from the internal perfusate. Perfusion with a solution containing exogenous alkaline phosphatase reversed the effects of ATP. These results provide further evidence that the effects of ATP on the K conductance are a consequence of a phosphorylation reaction mediated by a kinase present and active in perfused axons. Phosphorylation appears to alter the K conductance of squid giant axons via a minimum of two mechanisms. First, the voltage dependence of gating parameters are shifted toward positive potentials. Second, there is an increase in the number of functional closed states and/or a decrease in the rates of transition between these states of the K channels.     

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.     

Interactions of aminopyridines with potassium channels of squid axon membranes.

The effects of aminopyridines on ionic conductances of the squid giant axon membrane were examined using voltage clamp and internal perfusion techniques. 4-Aminopyridine (4-AP) reduced potassium currents, but had no effect upon transient sodium currents. The block of potassium channels by 4-AP was substantially less with (a) strong depolarization to positive membrane potentials, (b) increasing the duration of a given depolarizing step, and (c) increasing the frequency of step depolarizations. Experiments with high external potassium concentrations revealed that the effect of 4-AP was independent of the direction of potassium ion movement. Both 3- and 2-aminopyridine were indistinguishable from 4-AP except in potency. It is concluded that aminopyrimidines may be used as tools to block the potassium conductance in excitable membranes, but only within certain specific voltage and frequency limits.     

Modification of sodium and potassium channel gating kinetics by ether and halothane

The effect of ether and halothane on the kinetics of sodium and potassium currents were investigated in the crayfish giant axon. Both general anesthetics produced a reversible, dose-dependent speeding up of sodium current inactivation at all membrane potentials, with no change in the phase of the currents. Double-pulse inactivation experiments with ether also showed faster inactivation, but the rate of recovery from inactivation at negative potentials was not affected. Ether shifted the midpoint of the steady-state fast inactivation curve in the hyperpolarizing direction and made the curve steeper. The activation of potassium currents was faster with ether present, with no change in the voltage dependence of steady-state potassium currents. Ether and halothane are known to perturb the structure of lipid bilayer membranes; the alterations in sodium and potassium channel gating kinetics are consistent with the hypothesis that the rates of the gating processes of the channels can be affected by the state of the lipids surrounding the channels, but a direct effect of ether and halothane on the protein part of the channels cannot be ruled out. Ether did not affect the capacitance of the axon membrane.