A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon.

Sodium channel gating behavior was modeled with Markovian models fitted to currents from the cut-open squid giant axon in the absence of divalent cations. Optimum models were selected with maximum likelihood criteria using single-channel data, then models were refined and extended by simultaneous fitting of macroscopic ionic currents, ON and OFF gating currents, and single-channel first latency densities over a wide voltage range. Best models have five closed states before channel opening, with inactivation from at least one closed state as well as the open state. Forward activation rate constants increase with depolarization, and deactivation rate constants increase with hyperpolarization. Rates of inactivation from the open or closed states are generally slower than activation or deactivation rates and show little or no voltage dependence. Channels tend to reopen several times before inactivating. Macroscopic rates of activation and inactivation result from a combination of closed, open and inactivated state transitions. At negative potentials the time to first opening dominates the macroscopic current due to slow activation rates compared with deactivation rates: channels tend to reopen rarely, and often inactivate from closed states before they reopen. At more positive potentials, the time to first opening and burst duration together produce the macroscopic current.     

Pressure dependence of sodium gating currents in the squid giant axon

Asymmetric displacement currents, I_g, were measured in squid axons at different hydrostatic pressures, P, up to 60 MPa. Potassium and sodium currents were abolished by intracellular Cs⁺ and TEA⁺, by extracellular Tetrodotoxin (TTX), and by Na⁺ substitution with Tris⁺. The time course of Ig became progressively slower with increasing pressure, and the amplitude decreased. With appropriate scaling in time and amplitude, I_g records at any given P could be made to superimpose very well with those obtained at atmospheric pressure. The same scaling factors yielded a good superposition of all records obtained for voltage steps to membrane potentials in the range-30 to +42 mV. The ratio between the amplitude and time factors was larger than unity and increased with P, indicating a progressive decrease (up to 35% at 60 MPa) of the total charge displaced, Q, with no significant change in its voltage dependence. The time-scaling factor increased exponentially with P, as expected if all the steps involved in the opening of a sodium channel, and producing a major charge redistribution, have the same activation volume, V _g 17 cm³/mol. This value is roughly one-half of that characterizing the pressure dependence of sodium current activation, suggesting that some late, rate-limiting step in the opening of sodium channels has a large activation volume without being accompanied by an easily detected charge movement.Part of the decrease of Q with pressure could be attributed to an increase in sodium inactivation. However, we cannot exclude the possibility that there is a reversible reduction in the number of fast activating sodium channels, similar to the phenomenon that has been reported to occur at low temperatures (Matteson and Armstrong 1982).     

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.     

Kinetic properties and inactivation of the gating currents of sodium channels in squid axon.

Associated with the opening and closing of the sodium channels of nerve membrane is a small component of capacitative current, the gating current. After termination of a depolarizing step the gating current and sodium current decay with similar time courses. Both currents decay more rapidly at relatively negative membrane voltages than at positive ones. The gating current that flows during a depolarizing step is diminished by a pre-pulse that inactivates the sodium permeability. A pre-pulse has no effect after inactivation has been destroyed by internal perfusion with the proteolytic enzyme pronase. Gating charge (considered as positive charge) moves outward during a positive voltage step, with voltage dependent kinetics. The time constant of the outward gating current is a maximum at about minus 10 mV, and has a smaller value at voltages either more positive or negative than this value.     

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.     

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.     

Kinetic analysis of the sodium gating current in the squid giant axon

A critical study has been made of the characteristics of the kinetic components of the sodium gating current in the squid giant axon, of which not less than five can be resolved. In addition to the principal fast component Ig2, there are two components of appreciable size that relax at an intermediate rate, Ig3 alpha and Ig 3 beta. Ig3 alpha has a fast rise, and is present over the whole range of negative test potentials. Ig3 beta is absent below -40 mV, exhibits a delayed onset and disappears on inactivation of the sodium system. There are also two smaller components, Ig1 and Ig4, with very fast and much slower relaxation time constants, respectively.     

Potassium conductance of the squid giant axon. Single-channel studies

The patch-clamp technique was implemented in the cut-open squid giant axon and used to record single K channels. We present evidence for the existence of three distinct types of channel activities. In patches that contained three to eight channels, ensemble fluctuation analysis was performed to obtain an estimate of 17.4 pS for the single-channel conductance. Averaged currents obtained from these multichannel patches had a time course of activation similar to that of macroscopic K currents recorded from perfused squid giant axons. In patches where single events could be recorded, it was possible to find channels with conductances of 10, 20, and 40 pS. The channel most frequently encountered was the 20-pS channel; for a pulse to 50 mV, this channel had a probability of being open of 0.9. In other single-channel patches, a channel with a conductance of 40 pS was present. The activity of this channel varied from patch to patch. In some patches, it showed a very low probability of being open (0.16 for a pulse to 50 mV) and had a pronounced lag in its activation time course. In other patches, the 40-pS channel had a much higher probability of being open (0.75 at a holding potential of 50 mV). The 40-pS channel was found to be quite selective for K over Na. In some experiments, the cut-open axon was exposed to a solution containing no K for several minutes. A channel with a conductance of 10 pS was more frequently observed after this treatment. Our study shows that the macroscopic K conductance is a composite of several K channel types, but the relative contribution of each type is not yet clear. The time course of activation of the 20-pS channel and the ability to render it refractory to activation only by holding the membrane potential at a positive potential for several seconds makes it likely that it is the predominant channel contributing to the delayed rectifier conductance.     

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.     

Single ion occupancy and steady-state gating of Na channels in squid giant axon

The properties of the small fraction of tetrodotoxin (TTX)-sensitive Na channels that remain open in the steady state were studied in internally dialyzed voltage clamped squid giant axons. The observed Ussing flux ratio exponent (n') of 0.97 plus minus 0.03 (calculated from simultaneous measurements of TTX-sensitive current and (22)Na efflux) and nonindependent behavior of Na current at high internal [Na] are explained by a one-site ("1s") permeation model characterized by a single effective binding site within the channel pore in equilibrium with internal Na ions (apparent equilibrium dissociation constant K(Nai)(0) = 0.61 +/- 0.08 M). Steady-state open probability of the TTX-sensitive channels can be modeled by the product p(a)p(infinity), where p(a) represents voltage-dependent activation described by a Boltzmann distribution with midpoint V(a) = -7 mV and effective valence z(a) = 3.2 (Vandenberg, C.A., and F. Bezanilla. 1991. BIOPHYS: J. 60:1499--1510) coupled to voltage-independent inactivation by an equilibrium constant (Bezanilla, F., and C.M. Armstrong. 1977. J. Gen. Physiol. 70:549--566) K(eq) = 770. The factor p(infinity) represents voltage-dependent inactivation with empirical midpoint V(infinity)= -83 plus minus 5 mV and effective valence z(infinity) = 0.55 plus minus 0.03. The composite p(a)p(infinity)1s model describes the steady-state voltage dependence of the persistent TTX-sensitive current well.     

The effect of tetrodotoxin on the sodium gating current in the squid giant axon.

The effect of tetrodotoxin (TTX) on the sodium gating current in the squid giant axon was examined by recording the current that flowed at the pulse potential at which the ionic current fell to zero, first in the absence and then in the presence of TTX. The addition of 1 microM TTX to the bathing solution had no consistent effect on the size of the initial peak of the gating current, but resulted in small changes in the timecourse of its subsequent relaxation which were mainly caused by a reduction of about one quarter in the component that has a delayed onset and may possibly arise from changes in the state of ionization of groups in the channel wall when the lumen fills with water. Our findings suggest that the binding of TTX at the outer face of the sodium channel does not interfere with the mechanisms of activation and inactivation by the voltage sensors, but has an allosteric effect on the access of internal cations to the inside of the channel.     

Voltage-independent gating transitions in squid axon potassium channels.

We have investigated the actions of internal and external Zn2+ on squid axon K channel ionic and gating currents. As has been noted previously, application of Zn2+ to either membrane surface substantially slowed the activation of these channels with little or no change in deactivation. Internal Zn2+ (near 200-300 nM) slowed channel activation by up to sixfold over the range of membrane voltages from -30 to +50 mV. External Zn2+ (10 mM) produced an approximate twofold slowing of activation from -40 to +40 mV. We found that the changes in ionic current activation kinetics were accompanied by less than a twofold slowing of channel-gating currents in a narrow range of potentials near -30 mV. There was, at most, only a few percent reduction of charge movement associated with Zn2+ application. We conclude that these ions interact with channel components involved in weakly voltage-dependent conformational changes. Although there are some differences in detail, the general similarity of the actions of both internal and external Zn2+ on channel function suggests that the modified channel-gating step involves amino acids accessible to both the internal and external membrane surface.     

The early phase of sodium channel gating current in the squid giant axon

A fast component of displacement current which accompanies the sodium channel gating current has been recorded from the membrane of the giant axon of the squid Loligo forbesii. This component is characterized by relaxation time constants typically shorter than 25 µs. The charge displaced accounts for about 10% (or 2 nC/cm²) of the total displacement charge attributed to voltage-dependent sodium channels. Using a low noise, wide-band voltage clamp system and specially designed voltage step protocols we could demonstrate that this component: (i) is not a recording artifact; (ii) is kinetically independent from the sodium channel activation and inactivation processes; (iii) can account for a significant fraction of the initial amplitude of recorded displacement current and (iv) has a steady state charge transfer which saturates for membrane potentials above + 20 mV and below – 100 mV This component can be modelled as a single step transition using the Eyring-Boltzmann formalism with a quantal charge of 1 e^– and an asymmetrical energy barrier. Furthermore, if it were associated with the squid sodium channel, our data would suggest one fast transition per channel. A possible role as a sodium channel activation trigger, which would still be consistent with kinetic independence, is discussed. Despite uncertainties about its origin, the property of kinetic independence allows subtraction of this component from the total displacement current to reveal a rising phase in the early time course of the remaining current. This will have to be taken into account when modelling the voltage-dependent sodium channel.     

On the slowly rising phase of the sodium gating current in the squid giant axon.

High-resolution records of the sodium gating current in the squid giant axon demonstrate the existence of a slowly rising phase that is first apparent at pulse potentials slightly below zero, and becomes increasingly pronounced at more positive potentials. At +80 mV the current reaches its peak with a delay of 30 microseconds at 10 degrees C. It is suggested that this current is generated by the first two steps labelled R-->P and P-->A in the S4 units of all four domains of the series-parallel gating system, activating the channel before its opening by the third steps A-->B in domains I, II and III in conjunction with hydration. The kinetics of the slowly rising phase can only be explained by the incorporation of an appropriate degree of voltage-dependent cooperativity between the S4 voltage-sensors for their two initial transitions.     

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.     

Activation, inactivation and recovery in the sodium channels of the squid giant axon dialysed with different solutions.

Comparisons were made between families of ion currents recorded in voltage-clamped squid axons dialysed with 20 mM NaF and 330 mM CsF or TMAF, and bathed in a solution in which four fifths of the Na was replaced by Tris. The permeability coefficient PNa,fast for the fast-inactivating current in the initial open state was calculated as a function of test potential from the size of the initial peak of INa. The permeability coefficient PNa,non for the non-inactivating open state was calculated from the steady-state INa that persisted until the end of the test pulse. Dialysis with TMA had no direct effect on the QV curve for gating charge. The reversal potential for INa,non was always lower than that for INa,fast, the mean difference being about -9 mV when dialysing with Cs, but only about -1 mV with TMA. Except close to threshold, PNa,fast was roughly halved by dialysis with TMA as compared with Cs, but PNa,non was substantially increased. The time constant tau h inactivation of the sodium system was slightly increased during dialysis with TMA in place of Cs, and there were small shifts in the steady-state inactivation curve, but the rate of recovery from inactivation was not measurably altered. The flattening off of the tau h curve at increasingly positive test potentials corresponded to a steady reduction of the apparent inactivation charge until a value of about 0.2e was reached for pulses to 100 mV. The instantaneous I-V relationship in the steady state was also investigated. The results have a useful bearing on the effects of dialysis with TMA, on the differences between the initial and steady open states of the sodium channel, and on the relative voltage-dependences of the transitions in each direction between the resting and inactivated states.     

Induced capacitance in the squid giant axon. Lipophilic ion displacement currents

Voltage-clamped squid giant axons, perfused internally and externally with solutions containing 10(-5) M dipicrylamine (DpA-), show very large polarization currents (greater than or equal to 1 mA/cm2) in response to voltage steps. The induced polarization currents are shown in the frequency domain as a very large voltage-and frequency-dependent capacitance that can be fit by single Debye-type relaxations. In the time domain, the decay phase of the induced currents can be fit by single exponentials. The induced polarization currents can also be observed in the presence of large sodium and potassium currents. The presence of the DpA- molecules does not affect the resting potential of the axons, but the action potentials appear graded, with a much-reduced rate of rise. The data in the time domain as well as the frequency domain can be explained by a single-barrier model where the DpA- molecules translocate for an equivalent fraction of the electric field of 0.63, and the forward and backward rate constants are equal at -15 mV. When the induced polarization currents described here are added to the total ionic current expression given by Hodgkin and Huxley (1952), numerical solutions of the membrane action potential reproduce qualitatively our experimental data. Numerical solutions of the propagated action potential predict that large changes in the speed of conduction are possible when polarization currents are induced in the axonal membrane. We speculate that either naturally occurring substances or drugs could alter the cable properties of cells in a similar manner.