Computation of axon gating currents from dipole moment changes in channel subunits.

The gating polarizational currents were computed on the basis of the dipole moment changes occurring in nerve membrane ionic channel subunits. Membrane thickness and surface density of channels were the only parameters used in addition to the Hodgkin-Huxley model. The gating currents computed for membrane potentials where the Hodgkin-Huxley empirical formulae are reliable were found to be in good agreement with the available experimental data. It is demonstrated that the gating currents of the n and h subunits are responsible for the late slowly decaying gating currents.     

Charge dissociation and the rising phase of gating currents

Gating currents from voltage-sensitive channels are generally attributed to the translocation or redistribution of ionic charge associated with the channel molecule. Such charge moves in the direction of the applied field to produce a decreasing current in the external circuit. An early rising phase for the gating current is observed for a number of channel systems and might be either some special kinetic redistribution of charge or an experimental artifact. A model that produces net charge in the channel through sequential molecular dissociation of a charged channel segment gives a rising phase for the gating current. Translocation of the charged segment produces the decay phase for a biphasic gating current. This kinetic molecular explanation constitutes a physical explanation for the biphasic gating currents that is consistent with present views of channel structure.     

Origin of the rising phase of gating currents

It is suggested that the delayed rise of gating currents may result from a dielectric relaxation process within the membrane, not of the gating systems themselves but of molecules in the neighborhood of the gating systems. Such dielectric relaxation may prevent the electric fields at the locations of the gates from rapidly attaining their final, "clamped," values. Calculations based on this concept, using the Hodgkin Huxley m-process as an example, are shown to lead to gating currents whose shapes are similar to those observed experimentally. One possible interpretation in terms of membrane structure is proposed.     

Sodium ionic and gating currents in mammalian cells

Ionic and gating currents from voltage-gated sodium channels were recorded in mouse neuroblastoma cells using the path-clamp technique. Displacement currents were measured from whole-cell recordings. The gating charge displaced during step depolarizations increased with the applied membrane potential and reached saturating levels above 20 mV Prolonged large depolarizations produced partial immobilization of the gating charge, and only about one third of the displaced charge was quickly reversed upon return to negative holding potentials. The activation and inactivation properties of macroscopic sodium currents were characterized by voltage-clamp analysis of large outside-out patches and the single-channel conductance was estimated from nonstationary noise analysis. The general properties of the sodium channels in mouse neuroblastoma cells are very similar to those previously reported for various preparations of invertebrate and vertebrate nerve cells.Offprint requests to: O. Moran     

Pharmacological and kinetic analysis of K channel gating currents

We have measured gating currents from the squid giant axon using solutions that preserve functional K channels and with experimental conditions that minimize Na channel contributions to these currents. Two pharmacological agents were used to identify a component of gating current that is associated with K channels. Low concentrations of internal Zn2+ that considerably slow K channel ionic currents with no effect on Na channel currents altered the component of gating current associated with K channels. At low concentrations (10-50 microM) the small, organic, dipolar molecule phloretin has several reported specific effects on K channels: it reduces K channel conductance, shifts the relationship between channel conductance and membrane voltage (Vm) to more positive potentials, and reduces the voltage dependence of the conductance-Vm relation. The K channel gating charge movements were altered in an analogous manner by 10 microM phloretin. We also measured the dominant time constants of the K channel ionic and gating currents. These time constants were similar over part of the accessible voltage range, but at potentials between -40 and 0 mV the gating current time constants were two to three times faster than the corresponding ionic current values. These features of K channel function can be reproduced by a simple kinetic model in which the channel is considered to consist of two, two-state, nonidentical subunits.     

Properties of deactivation gating currents in Shaker channels

The charge versus voltage relation of voltage-sensor domains shifts in the voltage axis depending on the initial voltage. Here we show that in nonconducting W434F Shaker K⁺ channels, a large portion of this charge-voltage shift is apparent due to a dramatic slowing of the deactivation gating currents, Ig_D (with τ up to 80 ms), which develops with a time course of ∼1.8 s. This slowing in Ig_D adds up to the slowing due to pore opening and is absent in the presence of 4-aminopyridine, a compound that prevents the last gating step that leads to pore opening. A remaining 10–15 mV negative shift in the voltage dependence of both the kinetics and the charge movement persists independently of the depolarizing prepulse duration and remains in the presence of 4-aminopyridine, suggesting the existence of an intrinsic offset in the local electric field seen by activated channels. We propose a new (to our knowledge) kinetic model that accounts for these observations.     

Sodium channel gating currents. Origin of the rising phase

There has been some uncertainty in the past as to the origin of the rising phase of the gating current. We present evidence here that proves that the gating current does not have a rising phase and that the observed rising phase is due to an uncompensated series resistance in the Frankenhaeuser-Hodgkin (F-H) space. When a squid giant axon is bathed in a solution that is 10-20% hyperosmotic with respect to the internal solution, the rising phase of the gating current is eliminated. In parallel with this, a component of the capacity transient (time constant, 20 microseconds) is reduced so that the capacity transient now appears to be closer to a single fast (5-10 microseconds) component. These changes in the capacity transient and gating current occur without altering the amount of charge moved in either. This indicates that the charge is simply redistributed in time. The gating current without a rising phase can still be immobilized by inactivation. Supporting evidence is provided by measuring the accumulation and washout of K+ from the F-H space. It was found that K+ washes out 35% faster when the axon is bathed in hyperosmotic solution. It was estimated that the F-H space thickness (theta) increased 2.5 +/- 0.4-fold (mean +/- SEM) in hyperosmotic solution. Similarly, K+ accumulation in the F-H space was decreased, leading to an estimate of a 5 +/- 1.4-fold increase in theta in hyperosmotic solution. These results are consistent with the simple structural model presented.     

Sodium channel gating currents in frog skeletal muscle

Charge movements similar to those attributed to the sodium channel gating mechanism in nerve have been measured in frog skeletal muscle using the vaseline-gap voltage-clamp technique. The time course of gating currents elicited by moderate to strong depolarizations could be well fitted by the sum of two exponentials. The gating charge exhibits immobilization: at a holding potential of -90 mV the proportion of charge that returns after a depolarizing prepulse (OFF charge) decreases with the duration of the prepulse with a time course similar to inactivation of sodium currents measured in the same fiber at the same potential. OFF charge movements elicited by a return to more negative holding potentials of -120 or -150 mV show distinct fast and slow phases. At these holding potentials the total charge moved during both phases of the gating current is equal to the ON charge moved during the preceding prepulse. It is suggested that the slow component of OFF charge movement represents the slower return of charge "immobilized" during the prepulse. A slow mechanism of charge immobilization is also evident: the maximum charge moved for a strong depolarization is approximately doubled by changing the holding potential from -90 to -150 mV. Although they are larger in magnitude for a -150-mV holding potential, the gating currents elicited by steps to a given potential have similar kinetics whether the holding potential is -90 or -150 mV.     

The gating currents of sodium channels: Pore-population-size effects

Sodium-channel behavior has been modeled in order to determine the answer to the following question: How large must a population of “on-off” Sodium pores be before the inherently random behavior of the individual channels becomes smoothed to yield the expected gating current-conductance relationships which would be predicted from an infinite pore array? Results of this analysis show that for the “opening” situation, an excellent fit was obtained whenever more than about 10 pores were considered. Significant discrepanciesd were observed in the “Closeing” situation, however, for pore arrays of 50 or less. Marked hysteresis is apparent in the behavior of small pore populations.     

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).     

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.     

Electrically induced phase transitions via the dipole model in excitable membranes

Calculations based upon the membrane dipole model have been carried out and indicate the possibility of cooperative behavior during the membrane excitation process. An explicit expression is obtained for the critical electric field,E, which must be present to initiate the cooperative structural transition assumed to occur during membrane excitation. An hypothesis concerning the occurrence of two distinct phase transitions in the membrane resulting in the rapid influx of sodium ions and sodium ion inactivation, respectively, is presented.     

Phosphorylation shifts the time-dependence of cardiac Ca++ channel gating currents.

A general mechanism for the physiological regulation of the activity of voltage-dependent Na+, Ca++, K+, and Cl channels by neurotransmitters in a variety of excitable cell types may involve a final common pathway of a cyclic AMP-dependent phosphorylation of the channel protein. The functional correlates of channel phosphorylation are known to involve a change in the probability of opening, and a negative or positive shift in the voltage dependence for activation of the conductance. The voltage dependence for activation appears to be governed by the properties of the charge movement of the voltage-sensing moiety of the channel. This study of the gating charge movement of cardiac Ca++ channels has revealed that isoproterenol or cAMP (via a presumed phosphorylation of the channel) speeds the kinetics of the Ca++ channel gating charge movement. These results suggest that the changes in the kinetics and voltage dependence of the cardiac calcium currents produced by beta-adrenergic stimulation are initiated, in part, by parallel changes in the gating charge movement.     

A quantitative description of KcsA gating II: single-channel currents

The kinetic transitions of proton-activated WT KcsA and the noninactivating E71A mutant were studied at the single-channel level in purified, liposome-reconstituted preparations. Single-channel currents were recorded using patch-clamp techniques under nonstationary and steady-state conditions. Maximum-likelihood analyses reveal that the key influence of acidic pH is to increase the frequency of bursting without an effect on the intraburst open and closed dwell times, consistent with the finding from macroscopic currents that protons promote activation without a significant effect on inactivation. However, in steady-conditions of pH, voltage not only alters the burst frequency but also affects their properties, such as the frequency of the flickers and the dwell times of the closed and open states. This is to be expected if voltage modulates pathways connecting open and inactivated states. Upon opening, KcsA can enter at least two closed states that are not part of the activation pathway. The frequency and duration of these closed states was found to be voltage dependent and therefore these are likely to represent short-lived inactivated states. Single-channel recordings of WT KcsA also show varying propensity for the presence of subconductance states. The probability of occurrence of these states did not show clear modulation by voltage or pH and their origin remains unclear and a focus for further investigation. A kinetic model is proposed to describe the gating events in KcsA that recapitulates its macroscopic and single-channel behavior. The model has been constrained by the single-channel analyses presented in this work along with data from macroscopic currents in the preceding paper.     

Patch recordings from the electrocytes of electrophorus. Na channel gating currents

Gating currents were recorded at 11 degrees C in cell-attached and inside-out patches from the innervated membrane of Electrophorus main organ electrocytes. With pipette tip diameters of 3-8 microns, maximal charge measured in patches ranged from 0.74 to 7.19 fC. The general features of the gating currents are similar to those from the squid giant axon. The steady-state voltage dependence of the ON gating charge was characterized by an effective valence of 1.3 +/- 0.4 and a midpoint voltage of -56 +/- 7 mV. The charge vs. voltage relation lies approximately 30 mV negative to the channel open probability curve. The ratio of the time constants of the OFF gating current and the Na current was 2.3 at -120 mV and equal at -80 mV. Charge immobilization and Na current inactivation develop with comparable time courses and have very similar voltage dependences. Between 60 and 80% of the charge is temporarily immobilized by inactivation.