Rate of opening of a population of Na channels in frog skeletal muscle fibers

Linear Systems convolution analysis of muscle sodium currents was used to predict the opening rate of sodium channels as a function of time during voltage clamp pulses. If open sodium channel lifetimes are exponentially distributed, the channel opening rate corresponding to a sodium current obtained at any particular voltage, can be analytically obtained using a simple equation, given single channel information about the mean open-channel lifetime and current.Predictions of channel opening rate during voltage clamp pulses show that sodium channel inactivation arises coincident with a decline in channel opening rate.Sodium currents pharmacologically modified with Chloramine-T treatment so that they do not inactivate, show a predicted sustained channel opening rate.Large depolarizing voltage clamp pulses produce channel opening rate functions that resemble gating currents.The predicted channel opening rate functions are best described by kinetic models for Na channels which confer most of the charge movement to transitions between closed states.Comparisons of channel opening rate functions with gating currents suggests that there may be subtypes of Na channel with some contributing more charge movement per channel opening than others.Na channels open on average, only once during the transient period of Na activation and inactivation.After transiently opening during the activation period and then closing by entering the inactivated state, Na channels reopen if the voltage pulse is long enough and contribute to steady-state currents.The convolution model overestimates the opening rate of channels contributing to the steady-state currents that remain after the transient early Na current has subsided.     

State-dependent inactivation of K+ currents in rat type II alveolar epithelial cells

Inactivation of K+ channels responsible for delayed rectification in rat type II alveolar epithelial cells was studied in Ringer, 160 mM K-Ringer, and 20 mM Ca-Ringer. Inactivation is slower and less complete when the extracellular K+ concentration is increased from 4.5 to 160 mM. Inactivation is faster and more complete when the extracellular Ca2+ concentration is increased from 2 to 20 mM. Several observations suggest that inactivation is state-dependent. In each of these solutions depolarization to potentials near threshold results in slow and partial inactivation, whereas depolarization to potentials at which the K+ conductance, gK, is fully activated results in maximal inactivation, suggesting that open channels inactivate more readily than closed channels. The time constant of current inactivation during depolarizing pulses is clearly voltage-dependent only at potentials where activation is incomplete, a result consistent with coupling of inactivation to activation. Additional evidence for state-dependent inactivation includes cumulative inactivation and nonmonotonic from inactivation. A model like that proposed by C.M. Armstrong (1969. J. Gen. Physiol. 54: 553-575) for K+ channel block by internal quaternary ammonium ions accounts for most of these properties. The fundamental assumptions are: (a) inactivation is strictly coupled to activation (channels must open before inactivating, and recovery from inactivation requires passage through the open state); (b) the rate of inactivation is voltage-independent. Experimental data support this coupled model over models in which inactivation of closed channels is more rapid than that of open channels (e.g., Aldrich, R.W. 1981. Biophys. J. 36:519-532). No inactivation results from repeated depolarizing pulses that are too brief to open K+ channels. Inactivation is proportional to the total time that channels are open during both a depolarizing pulse and the tail current upon repolarization; repolarizing to more negative potentials at which the tail current decays faster results in less inactivation. Implications of the coupled model are discussed, as well as additional states needed to explain some details of inactivation kinetics.     

Modeling-independent elucidation of inactivation pathways in recombinant and native A-type Kv channels

A-type voltage-gated K⁺ (Kv) channels self-regulate their activity by inactivating directly from the open state (open-state inactivation [OSI]) or by inactivating before they open (closed-state inactivation [CSI]). To determine the inactivation pathways, it is often necessary to apply several pulse protocols, pore blockers, single-channel recording, and kinetic modeling. However, intrinsic hurdles may preclude the standardized application of these methods. Here, we implemented a simple method inspired by earlier studies of Na⁺ channels to analyze macroscopic inactivation and conclusively deduce the pathways of inactivation of recombinant and native A-type Kv channels. We investigated two distinct A-type Kv channels expressed heterologously (Kv3.4 and Kv4.2 with accessory subunits) and their native counterparts in dorsal root ganglion and cerebellar granule neurons. This approach applies two conventional pulse protocols to examine inactivation induced by (a) a simple step (single-pulse inactivation) and (b) a conditioning step (double-pulse inactivation). Consistent with OSI, the rate of Kv3.4 inactivation (i.e., the negative first derivative of double-pulse inactivation) precisely superimposes on the profile of the Kv3.4 current evoked by a single pulse because the channels must open to inactivate. In contrast, the rate of Kv4.2 inactivation is asynchronous, already changing at earlier times relative to the profile of the Kv4.2 current evoked by a single pulse. Thus, Kv4.2 inactivation occurs uncoupled from channel opening, indicating CSI. Furthermore, the inactivation time constant versus voltage relation of Kv3.4 decreases monotonically with depolarization and levels off, whereas that of Kv4.2 exhibits a J-shape profile. We also manipulated the inactivation phenotype by changing the subunit composition and show how CSI and CSI combined with OSI might affect spiking properties in a full computational model of the hippocampal CA1 neuron. This work unambiguously elucidates contrasting inactivation pathways in neuronal A-type Kv channels and demonstrates how distinct pathways might impact neurophysiological activity.     

Inactivation of Kv2.1 potassium channels.

We report here several unusual features of inactivation of the rat Kv2.1 delayed rectifier potassium channel, expressed in Xenopus oocytes. The voltage dependence of inactivation was U-shaped, with maximum inactivation near 0 mV. During a maintained depolarization, development of inactivation was slow and only weakly voltage dependent (tau = 4 s at 0 mV; tau = 7 s at +80 mV). However, recovery from inactivation was strongly voltage dependent (e-fold for 20 mV) and could be rapid (tau = 0.27 s at -140 mV). Kv2.1 showed cumulative inactivation, where inactivation built up during a train of brief depolarizations. A single maintained depolarization produced more steady-state inactivation than a train of pulses, but there could actually be more inactivation with the repeated pulses during the first few seconds. We term this phenomenon "excessive cumulative inactivation." These results can be explained by an allosteric model, in which inactivation is favored by activation of voltage sensors, but the open state of the channel is resistant to inactivation.     

The Link between Ion Permeation and Inactivation Gating of Kv4 Potassium Channels

Kv4 potassium channels undergo rapid inactivation but do not seem to exhibit the classical N-type and C-type mechanisms present in other Kv channels. We have previously hypothesized that Kv4 channels preferentially inactivate from the preopen closed state, which involves regions of the channel that contribute to the internal vestibule of the pore. To further test this hypothesis, we have examined the effects of permeant ions on gating of three Kv4 channels (Kv4.1, Kv4.2, and Kv4.3) expressed in Xenopus oocytes. Rb⁺ is an excellent tool for this purpose because its prolonged residency time in the pore delays K⁺ channel closing. The data showed that, only when Rb⁺ carried the current, both channel closing and the development of macroscopic inactivation are slowed (1.5- to 4-fold, relative to the K⁺ current). Furthermore, macroscopic Rb⁺ currents were larger than K⁺ currents (1.2- to 3-fold) as the result of a more stable open state, which increases the maximum open probability. These results demonstrate that pore occupancy can influence inactivation gating in a manner that depends on how channel closing impacts inactivation from the preopen closed state. By examining possible changes in ionic selectivity and the influence of elevating the external K⁺ concentration, additional experiments did not support the presence of C-type inactivation in Kv4 channels.     

A voltage-dependent role for K+ in recovery from C-type inactivation.

Recovery from C-type inactivation of Kv1.3 can be accelerated by the binding of extracellular potassium to the channel in a voltage-dependent fashion. Whole-cell patch-clamp recordings of human T lymphocytes show that Ko+ can bind to open or inactivated channels. Recovery is biphasic with time constants that depend on the holding potential. Recovery is also dependent on the voltage of the depolarizing pulse that induces the inactivation, consistent with a modulatory binding site for K+ located at an effective membrane electrical field distance of 30%. This K(+)-enhanced recovery can be further potentiated by the binding of extracellular tetraethylammonium to the inactivated channel, although the tetraethylammonium does not interact directly with the K(+)-binding site. Our findings are consistent with a model in which K+ can bind and unbind slowly from a channel in the inactivated state, and inactivated channels that are bound by K+ will recover with a rate that is fast relative to unbound channels. Our data suggest that the kinetics of K+ binding to the modulatory site are slower than these recovery rates, especially at hyperpolarized voltages.     

Mechanism of 4-aminopyridine action on voltage-gated potassium channels in lymphocytes

The mechanism by which 4-aminopyridine (4-AP) blocks the delayed rectifier type potassium (K+) channels present on lipopolysaccharide-activated murine B lymphocytes was investigated using whole-cell and single channel patch-clamp recordings. 4-AP (1 microM-5 mM) was superfused for 3-4 min before applying depolarizing pulses to activate the channel. During the first pulse after application of 4-AP above 50 microM, the current inactivated faster, as compared with the control, but its peak was only reduced at high concentrations of 4-AP (Kd = 3.1 mM). During subsequent pulses, the peak current was decreased (Kd = 120 microM), but the inactivation rate was slower than in the control, a feature that could be explained by a slow unblocking process. After washing out the drug, the current elicited by the first voltage step was still markedly reduced, as compared with the control one, and displayed very slow activation and inactivation kinetics; this suggests that the K+ channels move from a blocked to an unblocked state slowly during the depolarizing pulse. These results show that 4-AP blocks K+ channels in their open state and that the drug remains trapped in the channel once it is closed. On the basis of the analysis of the current kinetics during unblocking, we suggest that two pathways lead from the blocked to the unblocked states. Computer simulations were used to investigate the mechanism of action of 4-AP. The simulations suggest that 4-AP must bind to both an open and a nonconducting state of the channel. It is postulated that the latter is either the inactivated channel or a site on closed channels only accessible to the drug once the cell has been depolarized. Using inside- and outside-out patch recordings, we found that 4-AP only blocks channels from the intracellular side of the membrane and acts by reducing the mean burst time. 4-AP is a weak base (pK = 9), and thus exists in ionized or nonionized form. Since the Kd of channel block depends on both internal and external pH, we suggest that 4-AP crosses the membrane in its nonionized form and acts from inside the cell in its ionized form.     

Fast activation of dihydropyridine-sensitive calcium channels of skeletal muscle. Multiple pathways of channel gating

Dihydropyridine (DHP) receptors of the transverse tubule membrane play two roles in excitation-contraction coupling in skeletal muscle: (a) they function as the voltage sensor which undergoes fast transition to control release of calcium from sarcoplasmic reticulum, and (b) they provide the conducting unit of a slowly activating L-type calcium channel. To understand this dual function of the DHP receptor, we studied the effect of depolarizing conditioning pulse on the activation kinetics of the skeletal muscle DHP-sensitive calcium channels reconstituted into lipid bilayer membranes. Activation of the incorporated calcium channel was imposed by depolarizing test pulses from a holding potential of -80 mV. The gating kinetics of the channel was studied with ensemble averages of repeated episodes. Based on a first latency analysis, two distinct classes of channel openings occurred after depolarization: most had delayed latencies, distributed with a mode of 70 ms (slow gating); a small number of openings had short first latencies, < 12 ms (fast gating). A depolarizing conditioning pulse to +20 mV placed 200 ms before the test pulse (-10 mV), led to a significant increase in the activation rate of the ensemble averaged-current; the time constant of activation went from tau m = 110 ms (reference) to tau m = 45 ms after conditioning. This enhanced activation by the conditioning pulse was due to the increase in frequency of fast open events, which was a steep function of the intermediate voltage and the interval between the conditioning pulse and the test pulse. Additional analysis demonstrated that fast gating is the property of the same individual channels that normally gate slowly and that the channels adopt this property after a sojourn in the open state. The rapid secondary activation seen after depolarizing prepulses is not compatible with a linear activation model for the calcium channel, but is highly consistent with a cyclical model. A six- state cyclical model is proposed for the DHP-sensitive Ca channel, which pictures the normal pathway of activation of the calcium channel as two voltage-dependent steps in sequence, plus a voltage-independent step which is rate limiting. The model reproduced well the fast and slow gating models of the calcium channel, and the effects of conditioning pulses. It is possible that the voltage-sensitive gating transitions of the DHP receptor, which occur early in the calcium channel activation sequence, could underlie the role of the voltage sensor and yield the rapid excitation-contraction coupling in skeletal muscle, through either electrostatic or allosteric linkage to the ryanodine receptors/calcium release channels.     

N type rapid inactivation in human Kv1.4 channels: functional role of a putative C-terminal helix

Voltage gated potassium channels are tetrameric membrane proteins, which have a central role in cellular excitability. Human Kv1.4 channels open on membrane depolarization and inactivate rapidly by a 'ball and chain' mechanism whose molecular determinants have been mapped to the cytoplasmic N terminus of the channel. Here we show that the other terminal end of the channel also plays a role in channel inactivation. Swapping the C-terminal residues of hKv1.4 with those from two non-inactivating channels (hKv1.1 and hKv1.2) affects the rates of inactivation, as well as the recovery of the channel from the inactivated state. Secondary structure predictions of the hKv1.4 sequence reveal a helical structure at its distal C-terminal. Complete removal or partial disruption of this helical region results in channels with remarkably slowed inactivation kinetics. The ionic selectivity and voltage-dependence of channel opening were similar to hKv1.4, indicative of an unperturbed channel pore. These results demonstrate that fast inactivation is modulated by structural elements in the C-terminus, suggesting that the process involves the concerted action of the N- and C-termini.     

N type rapid inactivation in human Kv1.4 channels: functional role of a putative C-terminal helix

Voltage gated potassium channels are tetrameric membrane proteins, which have a central role in cellular excitability. Human Kv1.4 channels open on membrane depolarization and inactivate rapidly by a ‘ball and chain’ mechanism whose molecular determinants have been mapped to the cytoplasmic N terminus of the channel. Here we show that the other terminal end of the channel also plays a role in channel inactivation. Swapping the C-terminal residues of hKv1.4 with those from two non-inactivating channels (hKv1.1 and hKv1.2) affects the rates of inactivation, as well as the recovery of the channel from the inactivated state. Secondary structure predictions of the hKv1.4 sequence reveal a helical structure at its distal C-terminal. Complete removal or partial disruption of this helical region results in channels with remarkably slowed inactivation kinetics. The ionic selectivity and voltage-dependence of channel opening were similar to hKv1.4, indicative of an unperturbed channel pore. These results demonstrate that fast inactivation is modulated by structural elements in the C-terminus, suggesting that the process involves the concerted action of the N- and C-termini.     

Aminopyridine block of transient potassium current

The blocking action of 4-aminopyridine (4-AP) and 3, 4-diaminopyridine (Di-AP) on transient potassium current (IA) in molluscan central neurons was studied in internal perfusion voltage-clamp experiments. Identical blocking effects were seen when the drugs were applied either externally or internally. It was found that aminopyridines have two kinds of effects on IA channels. The first involves block of open channels during depolarizing pulses and results in a shortening of the time to peak current and an increase in the initial rate of decay of current. This effect of the drug is similar to the block of delayed potassium current by tetraethylammonium (TEA). The other effect is a steady block that increases in strength during hyperpolarization, is removed by depolarization, and is dependent on the frequency of stimulation. The voltage dependence of steady state block approximates the voltage dependence of inactivation gating a changes e-fold in approximately 10 mV. These data suggest that the strength of block may depend on the state of IA gating such that the resting state of the channel with open inactivation gate is more susceptible to block than are the open or inactivated states. A multistate sequential model for IA gating and voltage-dependent AP block is developed.     

A structural interpretation of voltage-gated potassium channel inactivation

After channel activation, and in some cases with sub-threshold depolarizing stimuli, Kv channels undergo a time-dependent loss of conductivity by a family of mechanisms termed inactivation. To date, all identified inactivation mechanisms underlying loss of conduction in Kv channels appear to be distinct from deactivation, i.e. closure of the voltage-operated activation gate by changes in transmembrane voltage. Instead, Kv channel inactivation entails entry of channels into a stable, non-conducting state, and thereby functionally reduces the availability of channels for opening. That is, if a channel has inactivated, some time must expire after repolarization of the membrane voltage to allow the channel to recover and become available to open again. Dramatic differences between Kv channel types in the time course of inactivation and recovery underlie various roles in regulating cellular excitability and repolarization of action potentials. Therefore, the range of inactivation mechanisms exhibited by different Kv channels provides important physiological means by which the duration of action potentials in many excitable tissues can be regulated at different frequencies and potentials. In this review, we provide a detailed discussion of recent work characterizing structural and functional aspects of Kv channel gating, and attempt to reconcile these recent results with classical experimental work carried out throughout the 1990s that identified and characterized the basic mechanisms and properties of Kv channel inactivation. We identify and discuss numerous gaps in our understanding of inactivation, and review them in the light of new structural insights into channel gating.     

External pore collapse as an inactivation mechanism for Kv4.3 K+ channels

Kv4 channels are thought to lack a C-type inactivation mechanism (collapse of the external pore) and to inactivate as a result of a concerted action of cytoplasmic regions of the channel. To investigate whether Kv4 channels have outer pore conformational changes during the inactivation process, the inactivation properties of Kv4.3 were characterized in 0 mM and in 2 mM external K+ in whole-cell voltage-clamp experiments. Removal of external K+ increased the inactivation rates and favored cumulative inactivation by repetitive stimulation. The reduction in current amplitude during repetitive stimulation and the faster inactivation rates in 0 mM external K+ were not due to changes in the voltage dependence of channel opening or to internal K+ depletion. The extent of the collapse of the K+ conductance upon removal of external K+ was more pronounced in NMG+-than in Na+-containing solutions. The reduction in the current amplitude during cumulative inactivation by repetitive stimulation is not associated with kinetic changes, suggesting that it is due to a diminished number of functional channels with unchanged gating properties. These observations meet the criteria for a typical C-type inactivation, as removal of external K+ destabilizes the conducting state, leading to the collapse of the pore. A tentative model is presented, in which K+ bound to high-affinity K+-binding sites in the selectivity filter destabilizes an outer neighboring K+ modulatory site that is saturated at approximately 2 mM external K+. We conclude that Kv4 channels have a C-type inactivation mechanism and that previously reported alterations in the inactivation rates after N- and C- termini mutagenesis may arise from secondary changes in the electrostatic interactions between K+-binding sites in the selectivity filter and the neighboring K+-modulatory site, that would result in changes in its K+ occupancy.     

Measurement of calcium channel inactivation is dependent upon the test pulse potential.

We have developed two methods to measure Ca2+ channel inactivation in Lymnaea neurons-one method, based upon the conventional double-pulse protocol, uses currents during a moderately large depolarizing pulse, and the other uses tail currents after a very strong activating pulse. Both methods avoid contamination by proton currents and are unaffected by rundown of Ca2+ current. The magnitude of inactivation measured differs for the two methods; this difference arises because the measurement of inactivation is inherently dependent upon the test pulse voltage used to monitor the Ca2+ channel conductance. We discuss two models that can generate such test pulse dependence of inactivation measurements-a two-channel model and a two-open-state model. The first model accounts for this by assuming the existence of two types of Ca2+ channels, different proportions of which are activated by the different test pulses. The second model assumes only one Ca2+ channel type, with two closed and open states; in this model, the test pulse dependence is due to the differential activation of channels in the two closed states by the test pulses. Test pulse dependence of inactivation measurements of Ca2+ channels may be a general phenomenon that has been overlooked in previous studies.     

MiRP2 forms potassium channels in skeletal muscle with Kv3.4 and is associated with periodic paralysis

The subthreshold, voltage-gated potassium channel of skeletal muscle is shown to contain MinK-related peptide 2 (MiRP2) and the pore-forming subunit Kv3.4. MiRP2-Kv3.4 channels differ from Kv3.4 channels in unitary conductance, voltage-dependent activation, recovery from inactivation, steady-state open probability, and block by a peptide toxin. Thus, MiRP2-Kv3.4 channels set resting membrane potential (RMP) and do not produce afterhyperpolarization or cumulative inactivation to limit action potential frequency. A missense mutation is identified in the gene for MiRP2 (KCNE3) in two families with periodic paralysis and found to segregate with the disease. Mutant MiRP2-Kv3.4 complexes exhibit reduced current density and diminished capacity to set RMP. Thus, MiRP2 operates with a classical potassium channel subunit to govern skeletal muscle function and pathophysiology.     

Inactivation of voltage-gated delayed potassium current in molluscan neurons. A kinetic model.

Voltage-gated delayed potassium current in molluscan neurons is characterized by a marked inactivation. Inactivation can accumulate between repetitive pulses, giving rise to current patterns in which the maximum current during a second voltage pulse is less than the current at the end of the preceding pulse (cumulative inactivation). Other features of inactivation of this current include an onset time-course that can be characterized by the sum of two exponential processes and an early minimum in the recovery-vs.-time curve. A simple four-state model is developed that can, when supplied with rate constants derived from voltage-clamp experiments, reproduce these features of inactivation. The model incorporates state-dependent inactivation rates. Upon depolarization, both open and closed channels can be inactivated, although inactivation of closed channels is much faster. Upon repolarization, recovery from inactivated states is sufficiently slow that little recovery occurs during a short interpulse interval. Cumulative inactivation comes about as a result of fast inactivation during the second pulse, further limiting the peak current from the level at the end of the previous pulse.     

Effects of KC 3791 on sodium and potassium channels in frog node of Ranvier

Effects of a new antiarrhytmic compound KC 3791 on sodium (INa) and potassium (IK) currents were studied in frog myelinated nerve fibres under voltage clamp conditions. When applied externally to the node of Ranvier, KC 3791 (KC) at concentrations of 10(-5)-10(-4) mol.l-1 produced both tonic and cumulative (use-dependent) inhibition of INa. An analysis of the frequency-, voltage- and time dependence of cumulative block by KC suggested that this block resulted from a voltage-dependent interaction of the drug with open Na channels. The progressive decrease in INa during repetitive pulsing was due to accumulation of Na channels in the resting-blocked state: closing of the activation gate after the end of each depolarizing pulse stabilized the KC-"receptor" complex. To unblock these channels a prolonged washing of the node had to be combined with a subsequent repetitive stimulation of the membrane; this suggested that channel could not become cleared of the blocker unless the activation gate has opened. KC also proved to be capable of blocking open K channels at outwardly directed potassium currents (IK). This block increased during membrane depolarization. Unblocking of K channels after the end of a depolarizing pulse proceeded much faster than unblocking of Na channels under identical conditions. Cumulative inhibition of outward IK during high-frequency membrane stimulation was therefore readily reversible upon a decrease in pulsing frequency.