Kinetics of activation of the potassium conductance in the squid giant axon

A quantitative re-investigation of the time course of the initial rise of the potassium current in voltage-clamped squid giant axons is described. The n4 law of the Hodgkin-Huxley equations was found to be well obeyed only for the smallest test pulses, and for larger ones a good fit of the inflected rise required use of the expression (1-exp[-t/tau n1])X-1(1-exp[-t/tau n2]), where both of the time constants and the power X varied with the size of the test pulse. Application of a negative prepulse produced a delay in the rise resulting mainly from an increase of X from a value of about 3 at -70 mV to 8 at -250 mV, while tau n1 remained constant and tau n2 was nearly doubled. The process responsible for generating this delay was switched on with a time constant of 8 ms at 4 degrees C, which fell to about 1 ms at 15 degrees C. Analysis of the inward tail currents at the end of a voltage-clamp pulse showed that there was a substantial external accumulation of potassium owing to the restriction of its diffusion out of the Schwann cell space, which, when duly allowed for, roughly doubled the calculated value of the potassium conductance. Computations suggested that the principal effect of such a build-up of [K]o would be to reduce the fitted values of tau n1 and tau n2 to two-thirds or even half their true sizes, while the power X would generally be little changed; but it would not affect the necessity to introduce a second time constant, nor would it invalidate our findings on the effect of negative prepulses.     

Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon.

Single-channel, macroscopic ionic, and macroscopic gating currents were recorded from the voltage-dependent sodium channel using patch-clamp techniques on the cut-open squid giant axon. To obtain a complete set of physiological measurements of sodium channel gating under identical conditions, and to facilitate comparison with previous work, comparison was made between currents recorded in the absence of extracellular divalent cations and in the presence of physiological concentrations of extracellular Ca2+ (10 mM) and Mg2+ (50 mM). The single-channel currents were well resolved when divalent cations were not included in the extracellular solution, but were decreased in amplitude in the presence of Ca2+ and Mg2+ ions. The instantaneous current-voltage relationship obtained from macroscopic tail current measurements similarly was depressed by divalents, and showed a negative slope-conductance region for inward current at negative potentials. Voltage dependent parameters of channel gating were shifted 9-13 mV towards depolarized potentials by external divalent cations, including the peak fraction of channels open versus voltage, the time constant of tail current decline, the prepulse inactivation versus voltage relationship, and the charge-voltage relationship for gating currents. The effects of divalent cations are consistent with open channel block by Ca2+ and Mg2+ together with divalent screening of membrane charges.     

A model for conductance changes in the squid giant axon. II. Channel kinetics

The kinetics of the sodium and potassium channels in voltage clamped squid giant axon following a relaxation of the membrane subunits are examined and compared with the Hodgkin-Huxley equations. Mechanisms are suggested for the turn-off of the sodium conductance and a set of kinetic states are proposed for the potassium channel which are consistent with the experimental observations. Determination of the rate constants for relaxation of the surface subunits which triggers the subsequent changes within the independent channels provide information on the equilibrium constant and free energy for this process. The free energy is observed to approach zero as the depolarizing voltage of the clamp approaches $\text{E}{}_{\mathrm{<mtext>Na</mtext>}}$, the voltage for zero sodium current in voltage clamped axons. Analysis of the final rate constants in the kinetic sequence for potassium indicates a symmetry of the channel when it is in its steady-state configuration during clamp in the absence of external gradients.     

The rate of action of tetrodotoxin on sodium conductance in the squid giant axon.

When tetrodotoxin is applied to or washed away from the squid giant axon, the rates at which the sodium conductatnce is blocked and unblocked are an order of magnitude smaller than those reported for the isolated node of Ranvier. This slowing is to be expected if in squid the tetrodotoxin binding sites act as a saturable sink in series with the barrier to free diffusion imposed by the presence of the Schwann cell. A comparison has been made between the rates observed experimentally and those calculated for a computer model of the system, in order to estimate the apparent density in the membrane of both specific and non-specific tetrodotoxin binding sites. The figure thus obtained for the number of sodium channels in the squid giant axon, several hundred per square micrometre, agrees well with those derived from other lines of argument.     

Calcium currents in squid giant axon.

Voltage-clamp experiments were carried out on intracellularly perfused squid giant axons in a Na-free solution of 100 mM CaCl2+sucrose. The internal solution was 25 mM CsF+sucrose or 100 mM RbF+50mM tetraethylammonium chloride+sucrose. Depolarizing voltage clamp steps produced small inward currents; at large depolarizations the inward current reversed into an outward current. Tetrodotoxin completely blocked the inward current and part of the outward current. No inward current was seen with 100 mM MgCl2+sucrose as internal solution. It is concluded that the inward current is carried by Ca ions moving through the sodium channel. The reversal potential of the tetrodotoxin-sensitive current was +54mV with 25 mM CsF+sucrose inside and +10 mV with 100 mM RbF+50 mM tetraethylammonium chloride+sucrose inside. From the reversal potentials measured with varying external and internal solutions the relative permeabilities of the sodium channel for Ca, Cs and Na were calculated by means of the constant field equations. The results of the voltage-clamp experiments are compared with measurements of the Ca entry in intact axons.     

Transient polarization currents in the squid giant axon.

It has been repeatedly noted that the change of conformation of the molecules that serve as the ion-selective channels for sodium and potassium conductance in the nerve membrane will be accompanied by a change in the dipole moment of the molecule. This time-dependent change of dipole moment will produce transient currents in the membrane. The canonical form for these currents is determined with conventional statistical mechanics formalism. It is pointed out that the voltage dependence of the conductance channel conductance determines the free energy of the system to within a factor that is an unknown function of the voltage. Since the dipole currents do not depend on this unknown function, they are completely determined 0y the observed properties of the conductance system. The predicted properties of these dipole currents, their time constants and strengths, are calculated. By using the observed properties of gating currents, the density of the sodium channels is computed. The predicted properties of the dipole currents are found to compare satisfactorily with the observed properties of gating currents.     

On the relation between displacement currents and activation of the sodium conductance in the squid giant axon.

The early time course of the current passing across the membrane in squid giant axons in which the ionic currents have been blocked reveals substantial asymmetries during and after the application of hyperpolarizing and depolarizing voltage-clamp pulses of identical size. Since the integral of the 'on' and 'off' current transients is zero, these currents must result from charge movements confined to the membrane and, therefore, they are nonlinear displacement currents. The steady state rearrangement of the charges as a consequence of sudden displacements of the membrane potential is consistent with a Boltzmann distribution of charges between two states characterized by different energy levels. Following changes in membrane potential the charges undergo a first order transition between these states. The relaxation time constant for the transition at a given temperature is a function of membrane potential. We propose that these displacement currents arise from a redistribution of the charges involved in the sodium gating system.     

Anion conductances of the giant axon of squid Sepioteuthis.

Anion conductances of giant axons of squid, Sepioteuthis, were measured. The axons were internally perfused with a 100-mM tetraethylammonium-phosphate solution and immersed in a 100-mM Ca-salt solution (or Mg-salt solution) containing 0.3 microns tetrodotoxin. The external anion composition was changed. The membrane currents had a large amount of outward rectification due to anion influx across Cl- channels of the membrane (Inoue, 1985). The amount of outward rectification depended on the species of anion used and was strongly influenced by temperature and internal pH. In contrast to the anion conductances themselves, the conductance relative to Cl- (gA/gCl) was found to be quite stable against changes in the membrane potential, temperature, and pH. It is therefore suggested that each gA/gCl is an intrinsic quantity of the Cl- channel of the squid axon membrane. The sequence and values of gA/gCl obtained in this study were NO3- (1.80) greater than I- (1.40) greater than Br- (1.07) greater than Cl- (1.00) greater than MeSO3- (0.46) greater than H2PO2- (0.33) greater than CH3COO- (0.29) greater than SO4(2-) (0.06).     

An analysis of conductance changes in squid axon

The membrane of the squid axon is considered on the basis of a pore model in which the distribution of the pore sizes strongly favors K⁺ transfer when there is no potential. Electrical asymmetry causes non-penetrating ions on the membrane capacitor to exert a mechanical force on both membrane surfaces and this force results in a deformation of the membrane pore system such that it assumes a distribution of sizes favoring the ions exerting mechanical force. The ions involved appear to be Ca⁺⁺ on the outside of the membrane and isethionate^-, (i^-) on the inside; as Ca⁺⁺ is equivalent in size to Na⁺, the charged membrane is potentially able to transfer Na⁺, when the ions deforming the membrane pore distribution are removed. A depolarization of the membrane leads to an opening of pores that will allow Na⁺ penetration and a release of the membrane from deformation. The pores revert to the zero-potential pore size distribution hence the Na permeability change is a transient. Calculation shows that the potassium conductance vs. displacement of membrane potential curve for the squid axon and the "inactivation" function, h, can be obtained directly from the assumed membrane distortion without the introduction of arbitrary parameters. The sodium conductance, because it is a transient, requires assumptions about the time constants with which ions unblock pores at the outside and the inside of the membrane.     

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.     

The effects of homologous series of anaesthetics on a resting potassium conductance of the squid giant axon

The effects of n-alkanes (n-pentane to n-octane), n-alkanols (n-pentanol to n-undecanol) and two carboxylic esters (methyl pentanoate and methyl octanoate) on the conductance of squid giant axons in a high potassium, zero sodium bathing solution have been examined. Sodium and delayed rectifier potassium channels were as far as possible pharmacologically blocked. A substantial fraction of the measured conductance is attributed to a recently-described, voltage-independent, potassium channel. Anaesthetics block this channel but its sensitivity is markedly different from those of other squid axon ion channels.     

Temperature effects on gating currents in the squid giant axon.

The effects of temperature (3 degrees-26 degrees C) on the nonlinear components of the displacement current were measured in internally perfused, voltage clamped squid axons. Steps of potential were applied from a holding potential of -70mV (outside ground) to values from -130 to +70mV and either the current or its integral (charge) was recorded as a function of time. For that component of the charge movement not linearly related to voltage, the total charge moved in a few milliseconds (about 1,500 electronic charges/micron2) between saturation limits (e.g. -100mV to +50mV) showed an apparent increase of 13 +/- 5% for a 10 degrees C rise in temperature. Attempts to fit the falling phase of the gating current (or charge) with the sum of two exponentials showed temperature effects on both components but there was considerable scattering. At short times, records for current or charge made at 16 degrees C, expanded by a factor alpha, superimposed on those made at 6 degrees C for alpha about 1.6. For long times alpha was about 2.3.     

Effects of barium on the potassium conductance of squid axon

Ba++ ion blocks K+ conductance at concentrations in the nanomolar range. This blockage is time and voltage dependent. From the time dependence it is possible to determine the forward and reverse rate constants for what appears to be an essentially first-order process of Ba++ interaction. The voltage dependence of the rate constants and the dissociation constants place the site of interaction near the middle of the membrane field. Comparison of the efficacy of Ba++ block at various internal K+ concentrations suggests that Ba++ is probably a simple competitive inhibitor of K+ interaction with the K+ conductance. The character of Ba++ block in high external K+ solutions suggests that Ba++ ion may be "knocked-off" the site by inward movement of external K+. Examination of the effects of other divalent cations suggests that the channel may have a closed state with a divalent cation inside the channel. The relative blockage at different temperatures implies a strong interaction between Ba++ and the K+ conductance.     

Kinetics of ion movement in the squid giant axon

The loss of Na²², K⁴², and Cl³⁶ from single giant axons of the squid, Loligo pealii, following exposure to an artificial sea water containing these radioisotopes, occurs in two stages, an initial rapid one followed by an exponential decline. The time constants of the latter stage for the 3 ion species are, respectively, 290, 200, and 175 minutes. The outflux of sodium is depressed while that of potassium is accelerated in the absence of oxygen; the emergence of potassium is slowed by cocaine, while that of sodium is unaffected. One cm. ends of the axons take up about twice as much radiosodium as the central segment; this difference in activity is largely preserved during exposure to inactive solution. Such marked differences are not observed with radiopotassium. From the experimental data estimates are given of the influxes and outfluxes of the individual ions. The kinetics of outflux suggests a cortical layer of measureable thickness which contains the ions in different proportions from those in the medium and which governs the rate of emergence of these ions from the axon as though it contained very few but large (relative to ion dimensions) pores.     

Nuclear magnetic resonance study of squid giant axon

Using a spin-echo technique, the spin-lattice and spin-spin relaxation times (T1 and T2) of water protons in a single nerve fiber (giant axon of squid) were determined. Similar measurements were also carried out on axoplasm extruded from these nerve fibers. It was found that the relaxation times of water protons of both the intact fiber and the extruded axoplasm are approximately equal (and much less than those of a free solution), suggesting that the relaxation times of cellular water are shortened mainly by water-protein interactions rather than by water-membrane interactions.