Activation of Shaker Potassium Channels : II. Kinetics of the V2 Mutant Channel

This second of three papers, in which we functionally characterize activation gating in Shaker potassium channels, focuses on the properties of a mutant channel (called V2), in which the leucine at position 382 (in the Shaker B sequence) is mutated to valine. The general properties of V2''s ionic and gating currents are consistent with changes in late gating transitions, in particular, with V2 disrupting the positively cooperative gating process of the normally activating wild type (WT) channel. An analysis of forward and backward rate constants, analogous to that used for WT in the previous paper, indicates that V2 causes little change in the rates for most of the transitions in the activation path, but causes large changes in the backward rates of the final two transitions. Single channel data indicate that the V2 mutation causes moderate changes in the rates of transitions to states that are not in the activation path, but little change in the rates from these states. V2''s data also yield insights into the general properties of the activation gating process that could not be readily obtained from the WT channel, including evidence that intermediate transitions have rapid backward rates, and an estimate of a total charge 2 e₀ for the final two transitions. Taken together, these data will help constrain an activation gating model in the third paper of this series, while also providing an explanation for V2''s effects.     

Activation of Shaker Potassium Channels : I. Characterization of Voltage-dependent Transitions

The conformational changes associated with activation gating in Shaker potassium channels are functionally characterized in patch-clamp recordings made from Xenopus laevis oocytes expressing Shaker channels with fast inactivation removed. Estimates of the forward and backward rates for transitions are obtained by fitting exponentials to macroscopic ionic and gating current relaxations at voltage extremes, where we assume that transitions are unidirectional. The assignment of different rates is facilitated by using voltage protocols that incorporate prepulses to preload channels into different distributions of states, yielding test currents that reflect different subsets of transitions. These data yield direct estimates of the rate constants and partial charges associated with three forward and three backward transitions, as well as estimates of the partial charges associated with other transitions. The partial charges correspond to an average charge movement of 0.5 e₀ during each transition in the activation process. This value implies that activation gating involves a large number of transitions to account for the total gating charge displacement of 13 e₀. The characterization of the gating transitions here forms the basis for constraining a detailed gating model to be described in a subsequent paper of this series.     

Selectivity Changes during Activation of Mutant Shaker Potassium Channels

Mutations of the pore-region residue T442 in Shaker channels result in large effects on channel kinetics. We studied mutations at this position in the backgrounds of NH₂-terminal–truncated Shaker H4 and a Shaker -NGK2 chimeric channel having high conductance (Lopez, G.A., Y.N. Jan, and L.Y. Jan. 1994. Nature (Lond.). 367: 179–182). While mutations of T442 to C, D, H, V, or Y resulted in undetectable expression in Xenopus oocytes, S and G mutants yielded functional channels having deactivation time constants and channel open times two to three orders of magnitude longer than those of the parental channel. Activation time courses at depolarized potentials were unaffected by the mutations, as were first-latency distributions in the T442S chimeric channel. The mutant channels show two subconductance levels, 37 and 70% of full conductance. From single-channel analysis, we concluded that channels always pass through the larger subconductance state on the way to and from the open state. The smaller subconductance state is traversed in ∼40% of activation time courses. These states apparently represent kinetic intermediates in channel gating having voltage-dependent transitions with apparent charge movements of ∼1.6 e₀. The fully open T442S chimeric channel has the conductance sequence Rb⁺ > NH₄ ⁺ > K⁺. The opposite conductance sequence, K⁺ > NH₄ ⁺ > Rb⁺, is observed in each of the subconductance states, with the smaller subconductance state discriminating most strongly against Rb⁺.     

Fast Inactivation in Shaker K+ Channels : Properties of Ionic and Gating Currents

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as “charge immobilization” (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567–590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at −90 mV return potential changed from a single fast component to at least two components, the slower requiring ∼200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at −120 and −90 mV. In contrast, at higher potentials (−70 and −50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of “parallel” inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH₂-terminus region.     

KCNQ1 Channels Do Not Undergo Concerted but Sequential Gating Transitions in Both the Absence and the Presence of KCNE1 Protein

The co-assembly of KCNQ1 with KCNE1 produces I_KS, a K⁺ current, crucial for the repolarization of the cardiac action potential. Mutations in these channel subunits lead to life-threatening cardiac arrhythmias. However, very little is known about the gating mechanisms underlying KCNQ1 channel activation. Shaker channels have provided a powerful tool to establish the basic gating mechanisms of voltage-dependent K⁺ channels, implying prior independent movement of all four voltage sensor domains (VSDs) followed by channel opening via a last concerted cooperative transition. To determine the nature of KCNQ1 channel gating, we performed a thermodynamic mutant cycle analysis by constructing a concatenated tetrameric KCNQ1 channel and by introducing separately a gain and a loss of function mutation, R231W and R243W, respectively, into the S4 helix of the VSD of one, two, three, and four subunits. The R231W mutation destabilizes channel closure and produces constitutively open channels, whereas the R243W mutation disrupts channel opening solely in the presence of KCNE1 by right-shifting the voltage dependence of activation. The linearity of the relationship between the shift in the voltage dependence of activation and the number of mutated subunits points to an independence of VSD movements, with each subunit incrementally contributing to channel gating. Contrary to Shaker channels, our work indicates that KCNQ1 channels do not experience a late cooperative concerted opening transition. Our data suggest that KCNQ1 channels in both the absence and the presence of KCNE1 undergo sequential gating transitions leading to channel opening even before all VSDs have moved.     

Voltage Gating of Shaker K+ Channels : The Effect of Temperature on Ionic and Gating Currents

Ionic (I_i) and gating currents (I_g) from noninactivating Shaker H4 K⁺ channels were recorded with the cut-open oocyte voltage clamp and macropatch techniques. Steady state and kinetic properties were studied in the temperature range 2–22°C. The time course of I_i elicited by large depolarizations consists of an initial delay followed by an exponential rise with two kinetic components. The main I_i component is highly temperature dependent (Q₁₀ > 4) and mildly voltage dependent, having a valence times the fraction of electric field (z) of 0.2–0.3 e_o. The I_g On response obtained between −60 and 20 mV consists of a rising phase followed by a decay with fast and slow kinetic components. The main I_g component of decay is highly temperature dependent (Q₁₀ > 4) and has a z between 1.6 and 2.8 e_o in the voltage range from −60 to −10 mV, and ∼0.45 e_o at more depolarized potentials. After a pulse to 0 mV, a variable recovery period at −50 mV reactivates the gating charge with a high temperature dependence (Q₁₀ > 4). In contrast, the reactivation occurring between −90 and −50 mV has a Q₁₀ = 1.2. Fluctuation analysis of ionic currents reveals that the open probability decreases 20% between 18 and 8°C and the unitary conductance has a low temperature dependence with a Q₁₀ of 1.44. Plots of conductance and gating charge displacement are displaced to the left along the voltage axis when the temperature is decreased. The temperature data suggests that activation consists of a series of early steps with low enthalpic and negative entropic changes, followed by at least one step with high enthalpic and positive entropic changes, leading to final transition to the open state, which has a negative entropic change.     

Correlation between Charge Movement and Ionic Current during Slow Inactivation in Shaker K+ Channels

Prolonged depolarization induces a slow inactivation process in some K⁺ channels. We have studied ionic and gating currents during long depolarizations in the mutant Shaker H4-Δ(6–46) K⁺ channel and in the nonconducting mutant (Shaker H4-Δ(6–46)-W434F). These channels lack the amino terminus that confers the fast (N-type) inactivation (Hoshi, T., W.N. Zagotta, and R.W. Aldrich. 1991. Neuron. 7:547–556). Channels were expressed in oocytes and currents were measured with the cut-open-oocyte and patch-clamp techniques. In both clones, the curves describing the voltage dependence of the charge movement were shifted toward more negative potentials when the holding potential was maintained at depolarized potentials. The evidences that this new voltage dependence of the charge movement in the depolarized condition is associated with the process of slow inactivation are the following: (a) the installation of both the slow inactivation of the ionic current and the inactivation of the charge in response to a sustained 1-min depolarization to 0 mV followed the same time course; and (b) the recovery from inactivation of both ionic and gating currents (induced by repolarizations to −90 mV after a 1-min inactivating pulse at 0 mV) also followed a similar time course. Although prolonged depolarizations induce inactivation of the majority of the channels, a small fraction remains non–slow inactivated. The voltage dependence of this fraction of channels remained unaltered, suggesting that their activation pathway was unmodified by prolonged depolarization. The data could be fitted to a sequential model for Shaker K⁺ channels (Bezanilla, F., E. Perozo, and E. Stefani. 1994. Biophys. J. 66:1011–1021), with the addition of a series of parallel nonconducting (inactivated) states that become populated during prolonged depolarization. The data suggest that prolonged depolarization modifies the conformation of the voltage sensor and that this change can be associated with the process of slow inactivation.     

Voltage-insensitive Gating after Charge-neutralizing Mutations in the S4 Segment of Shaker Channels

Shaker channel mutants, in which the first (R362), second (R365), and fourth (R371) basic residues in the S4 segment have been neutralized, are found to pass potassium currents with voltage-insensitive kinetics when expressed in Xenopus oocytes. Single channel recordings clarify that these channels continue to open and close from −160 to +80 mV with a constant opening probability (P _o). Although P _o is low (∼0.15) in these mutants, mean open time is voltage independent and similar to that of control Shaker channels. Additionally, these mutant channels retain characteristic Shaker channel selectivity, sensitivity to block by 4-aminopyridine, and are partially blocked by external Ca²⁺ ions at very negative potentials. Furthermore, mean open time is approximately doubled, in both mutant channels and control Shaker channels, when Rb⁺ is substituted for K⁺ as the permeant ion species. Such strong similarities between mutant channels and control Shaker channels suggests that the pore region has not been substantially altered by the S4 charge neutralizations. We conclude that single channel kinetics in these mutants may indicate how Shaker channels would behave in the absence of voltage sensor input. Thus, mean open times appear primarily determined by voltage-insensitive transitions close to the open state rather than by voltage sensor movement, even in control, voltage-sensitive Shaker channels. By contrast, the low and voltage-insensitive P _o seen in these mutant channels suggests that important determinants of normal channel opening derive from electrostatic coupling between S4 charges and the pore domain.     

Gating kinetics of Shaker K+ channels are differentially modified by general anesthetics

TheShakerBK⁺ channel was used as a modelvoltage-gated channel to probe the interaction of volatile generalanesthetics with gating mechanisms. The effects of three anesthetics,chloroform (CHCl₃), isoflurane,and halothane, were studied using recombinant native and mutantShaker channels expressed inXenopus oocytes. Gating currents andmacroscopic ionic currents were recorded with the cut-open oocytevoltage-clamp technique. The effects ofCHCl₃ and isoflurane on gatingkinetics of noninactivating mutants were opposite, whereas halothanehad no effect. The effects on ionic currents were also agent dependent:CHCl₃ and halothane produced areduction of the macroscopic conductance, whereas isoflurane increasedit. The results indicate that the gating machinery of the channel ismostly insensitive to the anesthetics during activation until near theopen state. The effects on the conductance are mainly due to changes inthe transitions in and out of the open state. The data give support todirect protein-anesthetic interactions. The magnitude and nature of theeffects invite reconsideration ofShaker-likeK⁺ channels as important sites ofaction of general anesthetics.

     

Resolving the gating charge movement associated with late transitions in K channel activation.

We examined the late transitions in the activation sequence of potassium channels by analyzing gating currents of mutant Shaker IR channels and using the potassium channel blocker 4-aminopyridine (4AP). Gating currents were recorded from a double mutant of Shaker that was nonconducting (W434F mutation) and had the late gating transitions shifted to the right on the voltage axis (L382C mutation), thus separating the late transitions from the early ones. 4AP applied to the double mutant blocked the final transition and made possible novel observations of the isolated intermediate transitions, the ones that immediately precede the final opening of the channel. These transitions, which have not been well characterized previously, produce a distinct fast component in the gating current tails. Two intermediate transitions contribute to the fast component and carry 23% of the total gating charge. The effect of 4AP is well modeled as a selective block of the final gating transition, which opens the channel. The final transition contributes approximately 5% of the total gating charge.     

Intrinsic Voltage Dependence and Ca2+ Regulation of mslo Large Conductance Ca-activated K+ Channels

The kinetic and steady-state properties of macroscopic mslo Ca-activated K⁺ currents were studied in excised patches from Xenopus oocytes. In response to voltage steps, the timecourse of both activation and deactivation, but for a brief delay in activation, could be approximated by a single exponential function over a wide range of voltages and internal Ca²⁺ concentrations ([Ca]_i). Activation rates increased with voltage and with [Ca]_i, and approached saturation at high [Ca]_i. Deactivation rates generally decreased with [Ca]_i and voltage, and approached saturation at high [Ca]_i. Plots of the macroscopic conductance as a function of voltage (G-V) and the time constant of activation and deactivation shifted leftward along the voltage axis with increasing [Ca]_i. G-V relations could be approximated by a Boltzmann function with an equivalent gating charge which ranged between 1.1 and 1.8 e as [Ca]_i varied between 0.84 and 1,000 μM. Hill analysis indicates that at least three Ca²⁺ binding sites can contribute to channel activation. Three lines of evidence indicate that there is at least one voltage-dependent unimolecular conformational change associated with mslo gating that is separate from Ca²⁺ binding. (a) The position of the mslo G-V relation does not vary logarithmically with [Ca]_i. (b) The macroscopic rate constant of activation approaches saturation at high [Ca]_i but remains voltage dependent. (c) With strong depolarizations mslo currents can be nearly maximally activated without binding Ca²⁺. These results can be understood in terms of a channel which must undergo a central voltage-dependent rate limiting conformational change in order to move from closed to open, with rapid Ca²⁺ binding to both open and closed states modulating this central step.     

Macroscopic Na+ Currents in the “Nonconducting” Shaker Potassium Channel Mutant W434F

C-type inactivation in Shaker potassium channels inhibits K⁺ permeation. The associated structural changes appear to involve the outer region of the pore. Recently, we have shown that C-type inactivation involves a change in the selectivity of the Shaker channel, such that C-type inactivated channels show maintained voltage-sensitive activation and deactivation of Na⁺ and Li⁺ currents in K⁺-free solutions, although they show no measurable ionic currents in physiological solutions. In addition, it appears that the effective block of ion conduction produced by the mutation W434F in the pore region may be associated with permanent C-type inactivation of W434F channels. These conclusions predict that permanently C-type inactivated W434F channels would also show Na⁺ and Li⁺ currents (in K⁺-free solutions) with kinetics similar to those seen in C-type-inactivated Shaker channels. This paper confirms that prediction and demonstrates that activation and deactivation parameters for this mutant can be obtained from macroscopic ionic current measurements. We also show that the prolonged Na⁺ tail currents typical of C-type inactivated channels involve an equivalent prolongation of the return of gating charge, thus demonstrating that the kinetics of gating charge return in W434F channels can be markedly altered by changes in ionic conditions.     

Macroscopic Kinetics of Pentameric Ligand Gated Ion Channels: Comparisons between Two Prokaryotic Channels and One Eukaryotic Channel

Electrochemical signaling in the brain depends on pentameric ligand-gated ion channels (pLGICs). Recently, crystal structures of prokaryotic pLGIC homologues from Erwinia chrysanthemi (ELIC) and Gloeobacter violaceus (GLIC) in presumed closed and open channel states have been solved, which provide insight into the structural mechanisms underlying channel activation. Although structural studies involving both ELIC and GLIC have become numerous, thorough functional characterizations of these channels are still needed to establish a reliable foundation for comparing kinetic properties. Here, we examined the kinetics of ELIC and GLIC current activation, desensitization, and deactivation and compared them to the GABA_A receptor, a prototypic eukaryotic pLGIC. Outside-out patch-clamp recordings were performed with HEK-293T cells expressing ELIC, GLIC, or α₁β₂γ_2L GABA_A receptors, and ultra-fast ligand application was used. In response to saturating agonist concentrations, we found both ELIC and GLIC current activation were two to three orders of magnitude slower than GABA_A receptor current activation. The prokaryotic channels also had slower current desensitization on a timescale of seconds. ELIC and GLIC current deactivation following 25 s pulses of agonist (cysteamine and pH 4.0 buffer, respectively) were relatively fast with time constants of 24.9±5.1 ms and 1.2±0.2 ms, respectively. Surprisingly, ELIC currents evoked by GABA activated very slowly with a time constant of 1.3±0.3 s and deactivated even slower with a time constant of 4.6±1.2 s. We conclude that the prokaryotic pLGICs undergo similar agonist-mediated gating transitions to open and desensitized states as eukaryotic pLGICs, supporting their use as experimental models. Their uncharacteristic slow activation, slow desensitization and rapid deactivation time courses are likely due to differences in specific structural elements, whose future identification may help uncover mechanisms underlying pLGIC gating transitions.     

Activation of Slo2.1 channels by niflumic acid

Slo2.1 channels conduct an outwardly rectifying K⁺ current when activated by high [Na⁺]_i. Here, we show that gating of these channels can also be activated by fenamates such as niflumic acid (NFA), even in the absence of intracellular Na⁺. In Xenopus oocytes injected with <10 ng cRNA, heterologously expressed human Slo2.1 current was negligible, but rapidly activated by extracellular application of NFA (EC₅₀ = 2.1 mM) or flufenamic acid (EC₅₀ = 1.4 mM). Slo2.1 channels activated by 1 mM NFA exhibited weak voltage dependence. In high [K⁺]_e, the conductance–voltage (G-V) relationship had a V_1/2 of +95 mV and an effective valence, z, of 0.48 e. Higher concentrations of NFA shifted V_1/2 to more negative potentials (EC₅₀ = 2.1 mM) and increased the minimum value of G/G_max (EC₅₀ = 2.4 mM); at 6 mM NFA, Slo2.1 channel activation was voltage independent. In contrast, V_1/2 of the G-V relationship was shifted to more positive potentials when [K⁺]_e was elevated from 1 to 300 mM (EC₅₀ = 21.2 mM). The slope conductance measured at the reversal potential exhibited the same [K⁺]_e dependency (EC₅₀ = 23.5 mM). Conductance was also [Na⁺]_e dependent. Outward currents were reduced when Na⁺ was replaced with choline or mannitol, but unaffected by substitution with Rb⁺ or Li⁺. Neutralization of charged residues in the S1–S4 domains did not appreciably alter the voltage dependence of Slo2.1 activation. Thus, the weak voltage dependence of Slo2.1 channel activation is independent of charged residues in the S1–S4 segments. In contrast, mutation of R190 located in the adjacent S4–S5 linker to a neutral (Ala or Gln) or acidic (Glu) residue induced constitutive channel activity that was reduced by high [K⁺]_e. Collectively, these findings indicate that Slo2.1 channel gating is modulated by [K⁺]_e and [Na⁺]_e, and that NFA uncouples channel activation from its modulation by transmembrane voltage and intracellular Na⁺.     

The Role of Allosteric Coupling on Thermal Activation of Thermo-TRP Channels

Thermo-transient receptor potential channels display outstanding temperature sensitivity and can be directly gated by low or high temperature, giving rise to cold- and heat-activated currents. These constitute the molecular basis for the detection of changes in ambient temperature by sensory neurons in animals. The mechanism that underlies the temperature sensitivity in thermo-transient receptor potential channels remains unknown, but has been associated with large changes in standard-state enthalpy (ΔH^o) and entropy (ΔS^o) upon channel gating. The magnitude, sign, and temperature dependence of ΔH^o and ΔS^o, the last given by an associated change in heat capacity (ΔC_p), can determine a channel’s temperature sensitivity and whether it is activated by cooling, heating, or both, if ΔC_p makes an important contribution. We show that in the presence of allosteric gating, other parameters, besides ΔH^o and ΔS^o, including the gating equilibrium constant, the strength- and temperature dependence of the coupling between gating and the temperature-sensitive transitions, as well as the ΔH^o/ΔS^o ratio associated with them, can also determine a channel’s temperature-dependent activity, and even give rise to channels that respond to both cooling and heating in a ΔC_p-independent manner.     

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.     

Calculation of the Gating Charge for the Kv1.2 Voltage-Activated Potassium Channel

The atomic models of the Kv1.2 potassium channel in the active and resting state, originally presented elsewhere, are here refined using molecular dynamics simulations in an explicit membrane-solvent environment. With a minor adjustment of the orientation of the first arginine along the S4 segment, the total gating charge of the channel determined from >0.5 μs of molecular dynamics simulation is ∼12-12.7 e, in good accord with experimental estimates for the Shaker potassium channel, indicating that the final models offer a realistic depiction of voltage-gating. In the resting state of Kv1.2, the S4 segment in the voltage-sensing domain (VSD) spontaneously converts into a 3₁₀ helix over a stretch of 10 residues. The 3₁₀ helical conformation orients the gating arginines on S4 toward a water-filled crevice within the VSD and allows salt-bridge interactions with negatively charged residues along S2 and S3. Free energy calculations of the fractional transmembrane potential, acting upon key charged residues of the VSD, reveals that the applied field varies rapidly over a narrow region of 10-15 Å corresponding to the outer leaflet of the bilayer. The focused field allows the transfer of a large gating charge without translocation of S4 across the membrane.     

Kinetic Model for NS1643 Drug Activation of WT and L529I Variants of Kv11.1 (hERG1) Potassium Channel

Congenital and acquired (drug-induced) forms of the human long-QT syndrome are associated with alterations in Kv11.1 (hERG) channel-controlled repolarizing I_Kr currents of cardiac action potentials. A mandatory drug screen implemented by many countries led to a discovery of a large group of small molecules that can activate hERG currents and thus may act as potent antiarrhythmic agents. Despite significant progress in identification of channel activators, little is known about their mechanism of action. A combination of electrophysiological studies with molecular and kinetic modeling was used to examine the mechanism of a model activator (NS1643) action on the hERG channel and its L529I mutant. The L529I mutant has gating dynamics similar to that of wild-type while its response to application of NS1643 is markedly different. We propose a mechanism compatible with experiments in which the model activator binds to the closed (C3) and open states (O). We suggest that NS1643 is affecting early gating transitions, probably during movements of the voltage sensor that precede the opening of the activation gate.     

A Modeling Study of T-Type Ca Channel Gating and Modulation by L-Cysteine in Rat Nociceptors

L-cysteine (L-cys) increases the amplitude of T-type Ca²⁺ currents in rat T-rich nociceptor-like dorsal root ganglia neurons. The modulation of T-type Ca²⁺ channel gating by L-cys was studied by fitting Markov state models to whole-cell currents recorded from T-rich neurons. The best fitting model tested included three resting states and inactivation from the second resting state and the open state. Inactivation and the final opening step were voltage-independent, whereas transitions between the resting states and deactivation were voltage-dependent. The transition rates between the first two resting states were an order of magnitude faster than those between the second and third resting states, and the voltage-dependency of forward transitions through resting states was two to three times greater than for analogous backward transitions. Analysis with the best fitting model suggested that L-cys increases current amplitude mainly by increasing the transition rate from resting to open and decreasing the transition rate from open to inactivated. An additional model was developed that could account for the bi-exponential time course of recovery from inactivation of the currents and the high frequency of blank sweeps in single channel recordings. This model detected basically the same effects of L-cys on channel gating as the best fitting model.