Computing transient gating charge movement of voltage-dependent ion channels

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q–V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q–V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.     

Gating of the squid sodium channel at positive potentials. I. Macroscopic ionic and gating currents.

Macroscopic ionic sodium currents and gating currents were studied in voltage-clamped, dialyzed giant axons of the squid Loligo pealei under conditions of regular and inverse sodium gradients. Sodium currents showed regular kinetics but inactivation was incomplete, showing a maintained current for depolarizations lasting 18 ms. The ratio of the maintained current to the peak current increased with depolarization and it did not depend on the direction of the current flow or the sodium gradient. The time constant of inactivation was not affected by the sodium gradient. Double-pulse experiments allowed the separation of a normal inactivating component and a noninactivating component of the sodium currents. In gating current experiments, the results from double-pulse protocols showed that the charge was decreased by the prepulse and that the slow component of the 'on' gating current was preferentially depressed. As expected, charge immobilization was established faster at higher depolarizations than at low depolarizations, however, the amount of immobilized charge was unaffected by the pulse amplitude. This indicates that the incomplete sodium inactivation observed at high depolarizations is not the result of decreased charge immobilization; the maintained current must be due to a conductance that appears after normal charge immobilization and fast inactivation.     

Functional Expression of Rat Nav1.6 Voltage-Gated Sodium Channels in HEK293 Cells: Modulation by the Auxiliary β1 Subunit

The Na_v1.6 voltage-gated sodium channel α subunit isoform is abundantly expressed in the adult rat brain. To assess the functional modulation of Na_v1.6 channels by the auxiliary β1 subunit we expressed the rat Na_v1.6 sodium channel α subunit by stable transformation in HEK293 cells either alone or in combination with the rat β1 subunit and assessed the properties of the reconstituted channels by recording sodium currents using the whole-cell patch clamp technique. Coexpression with the β1 subunit accelerated the inactivation of sodium currents and shifted the voltage dependence of channel activation and steady-state fast inactivation by approximately 5–7 mV in the direction of depolarization. By contrast the β1 subunit had no effect on the stability of sodium currents following repeated depolarizations at high frequencies. Our results define modulatory effects of the β1 subunit on the properties of rat Na_v1.6-mediated sodium currents reconstituted in HEK293 cells that differ from effects measured previously in the Xenopus oocyte expression system. We also identify differences in the kinetic and gating properties of the rat Na_v1.6 channel expressed in the absence of the β1 subunit compared to the properties of the orthologous mouse and human channels expressed in this system.     

A gating charge interaction required for late slow inactivation of the bacterial sodium channel NavAb

Voltage-gated sodium channels undergo slow inactivation during repetitive depolarizations, which controls the frequency and duration of bursts of action potentials and prevents excitotoxic cell death. Although homotetrameric bacterial sodium channels lack the intracellular linker-connecting homologous domains III and IV that causes fast inactivation of eukaryotic sodium channels, they retain the molecular mechanism for slow inactivation. Here, we examine the functional properties and slow inactivation of the bacterial sodium channel NavAb expressed in insect cells under conditions used for structural studies. NavAb activates at very negative membrane potentials (V_1/2 of approximately −98 mV), and it has both an early phase of slow inactivation that arises during single depolarizations and reverses rapidly, and a late use-dependent phase of slow inactivation that reverses very slowly. Mutation of Asn49 to Lys in the S2 segment in the extracellular negative cluster of the voltage sensor shifts the activation curve ∼75 mV to more positive potentials and abolishes the late phase of slow inactivation. The gating charge R3 interacts with Asn49 in the crystal structure of NavAb, and mutation of this residue to Cys causes a similar positive shift in the voltage dependence of activation and block of the late phase of slow inactivation as mutation N49K. Prolonged depolarizations that induce slow inactivation also cause hysteresis of gating charge movement, which results in a requirement for very negative membrane potentials to return gating charges to their resting state. Unexpectedly, the mutation N49K does not alter hysteresis of gating charge movement, even though it prevents the late phase of slow inactivation. Our results reveal an important molecular interaction between R3 in S4 and Asn49 in S2 that is crucial for voltage-dependent activation and for late slow inactivation of NavAb, and they introduce a NavAb mutant that enables detailed functional studies in parallel with structural analysis.     

Gating of Na channels. Inactivation modifiers discriminate among models

Macroscopic Na currents were recorded from N18 neuroblastoma cells by the whole-cell voltage-clamp technique. Inactivation of the Na currents was removed by intracellular application of proteolytic enzymes, trypsin, alpha-chymotrypsin, papain, or ficin, or bath application of N-bromoacetamide. Unlike what has been reported in squid giant axons and frog skeletal muscle fibers, these treatments often increased Na currents at all test pulse potentials. In addition, removal of inactivation gating shifted the midpoint of the peak Na conductance-voltage curve in the negative direction by 26 mV on average and greatly prolonged the rising phase of Na currents for small depolarizations. Polypeptide toxins from Leiurus quinquestriatus scorpion and Goniopora coral, which slow inactivation in adult nerve and muscle cells, also increase the peak Na conductance and shift the peak conductance curve in the negative direction by 7-10 mV in neuroblastoma cells. Control experiments argue against ascribing the shifts to series resistance artifacts or to spontaneous changes of the voltage dependence of Na channel kinetics. The negative shift of the peak conductance curve, the increase of peak Na currents, and the prolongation of the rise at small depolarization after removal of inactivation are consistent with gating kinetic models for neuroblastoma cell Na channels, where inactivation follows nearly irreversible activation with a relatively high, voltage-independent rate constant and Na channels open only once in a depolarization. As the same kind of experiment does not give apparent shifting of activation and prolongation of the rising phase of Na currents in adult axon and muscle membranes, the Na channels of these other membranes probably open more than once in a depolarization.     

Gating of the bacterial sodium channel, NaChBac: voltage-dependent charge movement and gating currents

The bacterial sodium channel, NaChBac, from Bacillus halodurans provides an excellent model to study structure-function relationships of voltage-gated ion channels. It can be expressed in mammalian cells for functional studies as well as in bacterial cultures as starting material for protein purification for fine biochemical and biophysical studies. Macroscopic functional properties of NaChBac have been described previously (Ren, D., B. Navarro, H. Xu, L. Yue, Q. Shi, and D.E. Clapham. 2001. Science. 294:2372-2375). In this study, we report gating current properties of NaChBac expressed in COS-1 cells. Upon depolarization of the membrane, gating currents appeared as upward inflections preceding the ionic currents. Gating currents were detectable at -90 mV while holding at -150 mV. Charge-voltage (Q-V) curves showed sigmoidal dependence on voltage with gating charge saturating at -10 mV. Charge movement was shifted by -22 mV relative to the conductance-voltage curve, indicating the presence of more than one closed state. Consistent with this was the Cole-Moore shift of 533 micros observed for a change in preconditioning voltage from -160 to -80 mV. The total gating charge was estimated to be 16 elementary charges per channel. Charge immobilization caused by prolonged depolarization was also observed; Q-V curves were shifted by approximately -60 mV to hyperpolarized potentials when cells were held at 0 mV. The kinetic properties of NaChBac were simulated by simultaneous fit of sodium currents at various voltages to a sequential kinetic model. Gating current kinetics predicted from ionic current experiments resembled the experimental data, indicating that gating currents are coupled to activation of NaChBac and confirming the assertion that this channel undergoes several transitions between closed states before channel opening. The results indicate that NaChBac has several closed states with voltage-dependent transitions between them realized by translocation of gating charge that causes activation of the channel.     

Voltage-dependent membrane capacitance in rat pituitary nerve terminals due to gating currents

We investigated the voltage dependence of membrane capacitance of pituitary nerve terminals in the whole-terminal patch-clamp configuration using a lock-in amplifier. Under conditions where secretion was abolished and voltage-gated channels were blocked or completely inactivated, changes in membrane potential still produced capacitance changes. In terminals with significant sodium currents, the membrane capacitance showed a bell-shaped dependence on membrane potential with a peak at approximately -40 mV as expected for sodium channel gating currents. The voltage-dependent part of the capacitance showed a strong correlation with the amplitude of voltage-gated Na+ currents and was markedly reduced by dibucaine, which blocks sodium channel current and gating charge movement. The frequency dependence of the voltage-dependent capacitance was consistent with sodium channel kinetics. This is the first demonstration of sodium channel gating currents in single pituitary nerve terminals. The gating currents lead to a voltage- and frequency-dependent capacitance, which can be well resolved by measurements with a lock-in amplifier. The properties of the gating currents are in excellent agreement with the properties of ionic Na+ currents of pituitary nerve terminals.     

Allosteric voltage gating of potassium channels II. Mslo channel gating charge movement in the absence of Ca(2+).

Large-conductance Ca(2+)-activated K(+) channels can be activated by membrane voltage in the absence of Ca(2+) binding, indicating that these channels contain an intrinsic voltage sensor. The properties of this voltage sensor and its relationship to channel activation were examined by studying gating charge movement from mSlo Ca(2+)-activated K(+) channels in the virtual absence of Ca(2+) (<1 nM). Charge movement was measured in response to voltage steps or sinusoidal voltage commands. The charge-voltage relationship (Q-V) is shallower and shifted to more negative voltages than the voltage-dependent open probability (G-V). Both ON and OFF gating currents evoked by brief (0.5-ms) voltage pulses appear to decay rapidly (tau(ON) = 60 microseconds at +200 mV, tau(OFF) = 16 microseconds at -80 mV). However, Q(OFF) increases slowly with pulse duration, indicating that a large fraction of ON charge develops with a time course comparable to that of I(K) activation. The slow onset of this gating charge prevents its detection as a component of I(gON), although it represents approximately 40% of the total charge moved at +140 mV. The decay of I(gOFF) is slowed after depolarizations that open mSlo channels. Yet, the majority of open channel charge relaxation is too rapid to be limited by channel closing. These results can be understood in terms of the allosteric voltage-gating scheme developed in the preceding paper (Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277-304). The model contains five open (O) and five closed (C) states arranged in parallel, and the kinetic and steady-state properties of mSlo gating currents exhibit multiple components associated with C-C, O-O, and C-O transitions.     

The Inhibition of Sodium Currents in Myelinated Nerve by Quaternary Derivatives of Lidocaine

The inhibition of sodium currents by quaternary derivatives of lidocaine was studied in single myelinated nerve fibers. Membrane currents were diminished little by external quaternary lidocaine (QX). QX present in the axoplasm (<0.5 mM) inhibited sodium currents by more than 90%. Inhibition occurred as the sum of a constant, tonic phase and a variable, voltage-sensitive phase. The voltage-sensitive inhibition was favored by the application of membrane potential patterns which produce large depolarizations when sodium channels are open. Voltage-sensitive inhibition could be reversed by small depolarizations which opened sodium channels. One explanation of this observation is that QX molecules enter open sodium channels from the axoplasmic side and bind within the channels. The voltage dependence of the inhibition by QX suggests that the drug binds at a site which is about halfway down the electrical gradient from inside to outside of the sodium channel.     

Effects of Colchicine on the Surface Electrical Properties and Sodium Channel Current in Neuroblastoma Cells

We studied the effect of colchicine, an agent that suppresses microtubule assembly, on the passive membrane electrical properties (surface charge density, surface potential) and functioning of the sodium channel in neuroblastoma cells, N1E 115 clone. Colchicine (0.1 mM) caused an increase in net negative surface charge density, but the surface potential was not strongly affected. Colchicine strongly affected the sodium-channel currents: (a) colchicine blocked sodium currents through open sodium channels and the mean amplitude decreased about 50%; (b) the maximum sodium conductance was reduced to 6.0 pS; and (c) the voltage-dependent activation shifted by 10 mV in the direction of depolarization. Effects on the reversible potential and channel inactivation were not seen. Microtubules may play an important role in sodium channel current, and they could be involved in the regulation of the molecular structure of sodium channels.     

Gating currents from neuronal KV7.4 Channels: General features and correlation with the ionic conductance

The K_V7 (KCNQ) subfamily of voltage-gated K⁺ channels consists of five members (K_V7.1- K_V7.5) giving rise to non-inactivating, and slowly activating/deactivating currents mainly expressed in cardiac (K_V7.1) and neuronal (K_V7.2- K_V7.5) tissue. In the present study, using the cut-open oocyte voltage clamp, we studied the relation of the ionic currents from homomeric neuronal Kv7 channels (K_V7.2-K_V7.5) with the gating currents recorded after K⁺ conductance blockade from the same channels. Increasing the recording temperature from 18{degree sign}C to 28{degree sign}C accelerated activation/deactivation kinetics of the ionic currents in all homomeric K_V7 channels (activation Q10s at 0 mV were 3.8, 4.1, 8.3, and 2.8 for Kv7.2, Kv7.3, Kv7.4 and Kv7.5 channels, respectively), without large changes in currents voltage-dependence; moreover, at 28{degree sign}C, ionic currents carried by K_V7.4 channels also showed a significant increase in their maximal value. Gating currents were only resolved in K_V7.4 and K_V7.5 channels; the size of the ON gating charges at +40 mV was 1.34 ± 0.34 nC for K_V7.4, and 0.79 ± 0.20 nC for K_V7.5. At 28{degree sign}C, K_V7.4 gating currents had the following salient properties: 1) similar time integral of QON and QOFF, indicating no charge immobilization; 2) a left-shift in the V1/2 of the QON/V when compared to the G/V (≈ 50 mV in the presence of 2 mM extracellular Ba²⁺); 3) a QON decay faster than ionic current activation; and 4) a rising phase in the OFF gating charge after depolarizations larger than 0 mV. These observations suggest that, in K_V7.4 channels, VSD movement is followed by a slow and/or low bearing charge step linking to pore opening, a result which may help to clarify the molecular consequence of disease-causing mutations and drugs affecting channel gating.     

Rate-limiting Reactions Determining Different Activation Kinetics of Kv1.2and Kv2.1 Channels

To identify the mechanisms underlying the faster activation kinetics in Kv1.2 channels compared to Kv2.1 channels, ionic and gating currents were studied in rat Kv1.2 and human Kv2.1 channels heterologously expressed in mammalian cells. At all voltages the time course of the ionic currents could be described by an initial sigmoidal and a subsequent exponential component and both components were faster in Kv1.2 than in Kv2.1 channels. In Kv1.2 channels, the activation time course was more sigmoid at more depolarized potentials, whereas in Kv2.1 channels it was somewhat less sigmoid at more depolarized potentials. In contrast to the ionic currents, the ON gating currents were similarly fast for both channels. The main portion of the measured ON gating charge moved before the ionic currents were activated. The equivalent gating charge of Kv1.2 ionic currents was twice that of Kv2.1 ionic currents, whereas that of Kv1.2 ON gating currents was smaller than that of Kv2.1 ON gating currents. In conclusion, the different activation kinetics of Kv1.2 and Kv2.1 channels are caused by rate-limiting reactions that follow the charge movement recorded from the gating currents. In Kv1.2 channels, the reaction coupling the voltage-sensor movement to the pore opening contributes to rate limitation in a voltage-dependent fashion, whereas in Kv2.1 channels, activation is additionally rate-limited by a slow reaction in the subunit gating.     

Gating currents of sodium channels in neurons of the rat trigeminal ganglia

Using a voltage-clamp technique and intracellular dialysis, gating currents of sodium channels were first recorded and studied in neurons of the rat trigeminal ganglia. The rising phase of gating currents lasted 30 to 70 µsec; these currents decayed in a monoexponential manner with a time constant equal to that for activation of the sodium current. Voltage dependences for the gating charge and sodium conductance were also nearly identical. Analysis of the activation of sodium conductance demonstrated that the power n of the activation variable in the equation used changed from more than 6 to 3 at test potentials of –30 mV and 0 mV, respectively. It is hypothesized that, with a change in the test potential within this voltage range, the cooperativity of activation undergoes a twofold decrease. In the presence of 2 mM caffeine or theophylline in the external solution, curves of the voltage dependence of the gating charge and sodium conductance shifted toward more negative values of the test potential, by 5.4 ± 0.7 mV, the maximum gating charge increased by 8.4 ± 3.2%, and the slope factor for both curves decreased by 9.2 ± 3.4%. Since the above effects were identical for both xanthines and developed under conditions of constant intracellular dialysis, i.e., under conditions where the effect of a change in the intracellular calcium concentration was ruled out, the most probable reason for these effects is a direct action of the tested agents on sodium ion channels, which facilitates the movement of gating charges.Neirofiziologiya/Neurophysiology, Vol. 36, Nos. 5/6, pp. 370–376, September–December, 2004.This revised version was published online in April 2005 with a corrected cover date and copyright year.     

Allosteric Effects of Permeating Cations on Gating Currents during K+ Channel Deactivation

K⁺ channel gating currents are usually measured in the absence of permeating ions, when a common feature of channel closing is a rising phase of off-gating current and slow subsequent decay. Current models of gating invoke a concerted rearrangement of subunits just before the open state to explain this very slow charge return from opening potentials. We have measured gating currents from the voltage-gated K⁺ channel, Kv1.5, highly overexpressed in human embryonic kidney cells. In the presence of permeating K⁺ or Cs⁺, we show, by comparison with data obtained in the absence of permeant ions, that there is a rapid return of charge after depolarizations. Measurement of off-gating currents on repolarization before and after K⁺ dialysis from cells allowed a comparison of off-gating current amplitudes and time course in the same cells. Parallel experiments utilizing the low permeability of Cs⁺ through Kv1.5 revealed similar rapid charge return during measurements of off-gating currents at E_Cs. Such effects could not be reproduced in a nonconducting mutant (W472F) of Kv1.5, in which, by definition, ion permeation was macroscopically absent. This preservation of a fast kinetic structure of off-gating currents on return from potentials at which channels open suggests an allosteric modulation by permeant cations. This may arise from a direct action on a slow step late in the activation pathway, or via a retardation in the rate of C-type inactivation. The activation energy barrier for K⁺ channel closing is reduced, which may be important during repetitive action potential spiking where ion channels characteristically undergo continuous cyclical activation and deactivation.     

Inactivation and recovery of sodium currents in cerebellar Purkinje neurons: evidence for two mechanisms

We examined the kinetics of voltage-dependent sodium currents in cerebellar Purkinje neurons using whole-cell recording from dissociated neurons. Unlike sodium currents in other cells, recovery from inactivation in Purkinje neurons is accompanied by a sizeable ionic current. Additionally, the extent and speed of recovery depend markedly on the voltage and duration of the prepulse that produces inactivation. Recovery is faster after brief, large depolarizations (e.g., 5 ms at +30 mV) than after long, smaller depolarizations (e.g., 100 ms at -30 mV). On repolarization to -40 mV following brief, large depolarizations, a resurgent sodium current rises and decays in parallel with partial, nonmonotonic recovery from inactivation. These phenomena can be explained by a model that incorporates two mechanisms of inactivation: a conventional mechanism, from which channels recover without conducting current, and a second mechanism, favored by brief, large depolarizations, from which channels recover by passing transiently through the open state. The second mechanism is consistent with voltage-dependent block of channels by a particle that can enter and exit only when channels are open. The sodium current flowing during recovery from this blocked state may depolarize cells immediately after an action potential, promoting the high-frequency firing typical of Purkinje neurons.     

Variable ratio of permeability to gating charge of rBIIA sodium channels and sodium influx in Xenopus oocytes

Whole-cell gating current recording from rat brain IIA sodium channels in Xenopus oocytes was achieved using a high-expression system and a newly developed high-speed two-electrode voltage-clamp. The resulting ionic currents were increased by an order of magnitude. Surprisingly, the measured corresponding gating currents were approximately 5-10 times larger than expected from ionic permeability. This prompted us to minimize uncertainties about clamp asymmetries and to quantify the ratio of sodium permeability to gating charge, which initially would be expected to be constant for a homogeneous channel population. The systematic study, however, showed a 10- to 20-fold variation of this ratio in different experiments, and even in the same cell during an experiment. The ratio of P(Na)/Q was found to correlate with substantial changes observed for the sodium reversal potential. The data suggest that a cytoplasmic sodium load in Xenopus oocytes or the energy consumption required to regulate the increase in cytoplasmic sodium represents a condition where most of the expressed sodium channels keep their pore closed due to yet unknown mechanisms. In contrast, the movements of the voltage sensors remain undisturbed, producing gating current with normal properties.     

Batrachotoxin uncouples gating charge immobilization from fast Na inactivation in squid giant axons.

The fast inactivation of sodium currents and the immobolization of sodium gating charge are thought to be closely coupled to each other. This notion was tested in the squid axon in which kinetics and steady-state properties of the gating charge movement were compared before and after removal of the Na inactivation by batrachotoxin (BTX), pronase, or chloramine-T. The immobilization of gating charge was determined by measuring the total charge movement (QON) obtained by integrating the ON gating current (Ig,ON) using a double pulse protocol. After removal of the fast inactivation with pronase or chloramine-T, the gating charge movement was no longer immobilized. In contrast, after BTX modification, the channels still exhibited an immobilization of the gating charge (QON) with an onset time course and voltage dependence similar to that for the activation process. These results show that BTX can uncouple the charge immobilization from the fast Na inactivation mechanism, suggesting that the Na gating charge movement can be immobilized independently of the inactivation of the channel.     

Gating current in the membrane of nodes of Ranvier under conditions of linear alteration of the membrane potential

Asymmetrical displacement currents (Id) in the frog Ranvier node (R. ridibunda) treated with tetrodotoxin and tetraethylammonium were studied by the use of ramp-voltage pulses. In some experiments both ramp- and step-voltage pulses were used. The net Id consists of two components, one of which Id (I) can be blocked by local anesthetic trimecaine, or inactivated with the 10 ms depolarizing prepulse sufficiently large to inactivate the sodium current in the same node (before Na+ removal and TTX application). Parameters of the steady state charge distribution are very close (though not identical) to that of the peak sodium permeability vs. potential relation. The charge carrying Id (I) is estimated as 0.3--0.5 of the net displaced charge. The results suggest that trimecaine- and inactivation-sensitive component of Id may be the true gating current of Na+ channels.     

Voltage-dependent open-state inactivation of cardiac sodium channels: gating current studies with Anthopleurin-A toxin

The gating charge and voltage dependence of the open state to the inactivated state (O-->I) transition was measured for the voltage- dependent mammalian cardiac Na channel. Using the site 3 toxin, Anthopleurin-A (Ap-A), which selectively modifies the O-->I transition (see Hanck, D. A., and M. F. Sheets. 1995. Journal of General Physiology. 106:601-616), we studied Na channel gating currents (Ig) in voltage-clamped single canine cardiac Purkinje cells at approximately 12 degrees C. Comparison of Ig recorded in response to step depolarizations before and after modification by Ap-A toxin showed that toxin-modified gating currents decayed faster and had decreased initial amplitudes. The predominate change in the charge-voltage (Q-V) relationship was a reduction in gating charge at positive potentials such that Qmax was reduced by 33%, and the difference between charge measured in Ap-A toxin and in control represented the gating charge associated with Na channels undergoing inactivation by O-->I. By comparing the time course of channel activation (represented by the gating charge measured in Ap-A toxin) and gating charge associated with the O-->I transition (difference between control and Ap-A charge), the influence of activation on the time course of inactivation could be accounted for and the inherent voltage dependence of the O-->I transition determined. The O-->I transition for cardiac Na channels had a valence of 0.75 e-. The total charge of the cardiac voltage-gated Na channel was estimated to be 5 e-. Because charge is concentrated near the opening transition for this isoform of the channel, the time constant of the O-->I transition at 0 mV could also be estimated (0.53 ms, approximately 12 degrees C). Prediction of the mean channel open time-voltage relationship based upon the magnitude and valence of the O- ->C and O-->I rate constants from INa and Ig data matched data previously reported from single Na channel studies in heart at the same temperature.