On the stochastic properties of single ion channels

It is desirable to be able to predict, from a specified mechanism, the appearance of currents that flow through single ion channels (a) to enable interpretation of experiments in which single channel currents are observed, and (b) to allow physical meaning to be attached to the results observed in kinetic (noise and relaxation) experiments in which the aggregate of many single channel currents is observed. With this object, distributions (and the means) are derived for the length of the sojourn in any specified subset of states (e.g. all shut states). In general these are found to depend not only on the state in which the sojourn starts, but also on the state that immediately follows the sojourn. The methods described allow derivation of the distribution of, for example, (a) the number of openings, and total length of the burst of openings, that may occur during a single occupancy, and (b) the apparent gap between such bursts. The methods are illustrated by their application to two simple theories of agonist action. The Castillo-Katz (non-cooperative) mechanism predicts, for example, that the number of openings per occupancy, and the apparent burst length, are independent of agonist concentration whereas a simple cooperative mechanism predicts that both will increase with agonist concentration.     

Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events.

The openings and shuttings of individual ion channel molecules can be described by a Markov process with discrete states in continuous time. The predicted distributions of the durations of open times, shut times, bursts of openings, etc. are all described, in principle, by mixtures of exponential densities. In practice it is usually found that some of the open times, and the shut times, are too short to be detected reliably. If a fixed dead-time tau is assumed then it is possible to define, as an approximation to what is actually observed, an 'extended opening' or e-opening which starts with an opening of duration at least tau followed by any number of openings and shuttings, all the shut times being shorter than tau; the e-opening ends when a shut time longer than tau occurs. A similar definition is used for e-shut times. The probability densities, f(t), of these extended times have previously been obtained as expressions which become progressively more complicated, and numerically unstable to compute, as t-->infinity. In this paper we present, for the two-state model, an alternative representation as an infinite series of which a small number of terms gives a very accurate approximation of f (t) for large t. For the general model we present an asymptotic representation as a mixture of exponentials which is accurate for all except quite small values of t. Some simple model-independent corrections for missed events are discussed in relationship to the exact solutions.     

Gating of single non-Shaker A-type potassium channels in larval Drosophila neurons

The voltage-dependent gating of transient A2-type potassium channels from primary cultures of larval Drosophila central nervous system neurons was studied using whole-cell and single-channel voltage clamp. A2 channels are genetically distinct from the Shaker A1 channels observed in Drosophila muscle, and differ in single-channel conductance, voltage dependence, and gating kinetics. Single A2 channels were recorded and analyzed at -30, -10, +10, and +30 mV. The channels opened in bursts in response to depolarizing steps, with three to four openings per burst and two to three bursts per 480-ms pulse (2.8-ms burst criterion). Mean open durations were in a range of 2-4 ms and mean burst durations in a range of 9-17 ms. With the exception of the first latency distributions, none of the means of the distributions measured showed a consistent trend with voltage. Macroscopic inactivation of both whole-cell A currents and ensemble average currents of single A2 channels was well fitted by a sum of two exponentials. The fast time constants in different cells were in a range of 9-25 ms, and the slow time constants in a range of 60-140 ms. A six-state kinetic model (three closed, one open, two inactivated states) was tested at four command voltages by fitting frequency histograms of open durations, burst durations, burst closed durations, number of openings per burst, and number of bursts per trace. The model provided good fits to these data, as well as to the ensemble averages. With the exception of the rates leading to initial opening, the transitions in the model were largely independent of voltage.     

Regulation of cytoplasmic pH of cultured bovine corneal endothelial cells in the absence and presence of bicarbonate

Summary Single sodium-channel currents were measured in neuroblastoma cells after inhibition of inactivation by chloramine-T (CHL-T), sea anemone toxin II (ATX-II) and scorpion toxin (SCT). The decaying phase of the averaged single-channel currents recorded with 90-msec pulses in cell-attached patches was clearly slower than that of the unmodified channels, suggesting inhibition of macroscopic inactivation. Each substance caused repetitive openings and a moderate increase in the channel open time. AtV _m =RP+20 mV andT=12°C, the mean channel open times were 1.4, 1.6 and 1.8 msec for CHL-T, ATX-II and SCT, respectively, as opposed to 1.07 msec for native channels. Open-time histograms could be best fitted by the sum of two exponentials. The time constants of the fits were similar for histograms constructed from single openings and from openings during bursts. This suggests that the population of channels is homogeneous and that in bursts the same open conformations of channels occur as in single openings. Mean burst durations for bursts consisting of more than one opening atV _m =RP+20 mV were 4.9, 5.8 and 6.1 msec for CHL-T, ATX-II and SCT, respectively. Burst open-time histograms constructed from two or three openings were fitted by the gamma function. The different time constants of the fits obtained for ATX-II and SCT suggested multiple open conformations of channels for openings of bursts. However, significantly different open-time histograms constructed from the first, second and third openings of bursts could not be obtained systematically. A positive correlation was found for the dwell time of the first and the second, as well as for the second and the third opening of bursts with each substance, but a negative one for the dwell time of an opening and the neighboring closing of bursts with ATX-II. The results suggest a model with multiple open and inactivated states. In this model the inactivated states are weakly absorbing.     

Divalent cation activation and inhibition of single calcium release channels from sheep cardiac sarcoplasmic reticulum

Single Ca2+ release channels from vesicles of sheep cardiac junctional sarcoplasmic reticulum have been incorporated into uncharged planar lipid bilayers. Single-channel currents were recorded from Ca2(+)-activated channels that had a Ca2+ conductance of approximately 90 pS. Channel open probability increased sublinearly as the concentration of free Ca2+ was raised at the myoplasmic face, and without additional agonists the channels could not be fully activated even by 100 microM free Ca2+. Lifetime analysis revealed a minimum of two open and three closed states, and indicates that Ca2+ activated the channels by interacting with at least one of the closed states to increase the rate of channel opening. Correlations between adjacent lifetimes suggested there were at least two pathways between the open- and closed-state aggregates. An analysis of bursting behavior also revealed correlations between successive burst lengths and the number of openings per burst. The latter had two geometric components, providing additional evidence for at least two open states. One component appeared to comprise unit bursts, and the lifetime of most of these fell within the dominant shorter open-time distribution associated with over 90% of all openings. A cyclic gating scheme is proposed, with channel activation regulated by the binding of Ca2+ to a closed conformation of the channel protein. Mg2+ may inhibit activation by competing for this binding site, but lifetime and fluctuation analysis suggested that once activated the channels continue to gate normally.     

Kinetic diversity of Na+ channel bursts in frog skeletal muscle

Individual Na+ channels of dissociated frog skeletal muscle cells at 10 degrees C fail to inactivate in 0.02% of depolarizing pulses, thus producing bursts of openings lasting hundreds of milliseconds. We present here a kinetic analysis of 87 such bursts that were recorded in multi-channel patches at four pulse potentials. We used standard dwell-time histograms as well as fluctuation analysis to analyze the gating kinetics of the bursting channels. Since each burst contained only 75-150 openings, detailed characterization of the kinetics from single bursts was not possible. Nevertheless, at this low kinetic resolution, the open and closed times could be well fitted by single exponentials (or Lorentzians for the power spectra). The best estimates of both the open and closed time constants produced by either technique were much more broadly dispersed then expected from experimental or analytical variability, with values varying by as much as an order of magnitude. Furthermore, the values of the open and closed time constants were not significantly correlated with one another from burst to burst. The bursts thus expressed diverse kinetic behaviors, all of which appear to be manifestations of a single type of Na+ channel. Although the opening and closing rates were dispersed, their average values were close to those of alpha m and 2 beta m derived from fits to the early transient Na+ currents over the same voltage range. We propose a model in which the channel has both primary states (e.g., open, closed, and inactivated), as well as "modes" that are associated with independent alterations in the rate constants for transition between each of these primary states.     

Openings of the rat recombinant alpha 1 homomeric glycine receptor as a function of the number of agonist molecules bound

The functional properties of rat homomeric alpha 1 glycine receptors were investigated using whole-cell and outside-out recording from human embryonic kidney cells transfected with rat alpha1 subunit cDNA. Whole-cell dose-response curves gave EC(50) estimates between 30 and 120 microM and a Hill slope of approximately 3.3. Single channel recordings were obtained by steady-state application of glycine (0.3, 1, or 10 microM) to outside-out patches. Single channel conductances were mostly 60-90 pS, but smaller conductances of approximately 40 pS were also seen (10% of the events) with a relative frequency that did not depend on agonist concentration. The time constants of the apparent open time distributions did not vary with agonist concentration, but short events were more frequent at low glycine concentrations. There was also evidence of a previously missed short-lived open state that was more common at lower glycine concentrations. The time constants for the different components of the burst length distributions were found to have similar values at different concentrations. Nevertheless, the mean burst length increased with increasing glycine. This was because the relative area of each burst-length component was concentration dependent and short bursts were favored at lower glycine concentrations. Durations of adjacent open and shut times were found to be strongly (negatively) correlated. Additionally, long bursts were made up of longer than average openings separated by short gaps, whereas short bursts usually consisted of single isolated short openings. The most plausible explanation for these findings is that long bursts are generated when a higher proportion of the five potential agonist binding sites on the receptor is occupied by glycine. On the basis of the concentration dependence and the intraburst structure we provide a preliminary kinetic scheme for the activation of the homomeric glycine receptor, in which any number of glycine molecules from one to five can open the channel, although not with equal efficiency.     

On the kinetics of large-conductance glutamate-receptor ion channels in rat cerebellar granule neurons

Ion channels activated by glutamate, aspartate, and N-methyl-D-aspartate (NMDA) have been investigated in outside-out patches from cultured cerebellar granule neurons of the rat. Openings of these channels occur in bursts, within which the individual openings are separated by brief shuttings or gaps. The shut-time distributions obtained with each agonist were fitted with four exponential components. The briefest two components were considered as 'gaps within bursts'. Their mean time-constants were: glutamate, 58.0 microseconds and 592 microseconds; aspartate, 31.3 microseconds and 644 microseconds; NMDA, 40.5 microseconds and 903 microseconds. Distributions of burst durations were fitted with three exponential components. The mean time-constants obtained for the longest two components were: glutamate, 1.33 ms and 10.5 ms; aspartate, 2.15 ms and 10.3 ms; NMDA, 2.42 ms and 10.5 ms. Evidence is given that these two components of burst duration reflect the gating kinetics of 50 pS openings and not the fact that each agonist produces openings to more than one conductance level. Not only do openings occur in bursts, but these bursts were observed to occur in clusters, which can be hundreds of milliseconds long. We discuss the relation between the kinetics of single-channel openings observed in patches and the spectral components detected in whole-cell current noise.     

Stochastic modelling of a single ion channel: interdependence of burst length and number of openings per burst

Previous modelling of single channel behaviour based on Markov processes has been concerned mainly with means and marginal distributions of particular quantities. The present study derives the joint distribution, conditional distributions, and associated mean values for the burst length (T) and the number (N) of openings per burst in two simple three-state models in which bursting is possible, one for an agonist-only and one for a channel blocking mechanism. In both models the conditional mean burst length (E(T/N = r)) increases linearly as a function of the number of openings per burst, while the conditional mean number of openings per burst (E(N/T = x)) is a nonlinear strictly increasing function of burst length, which is asymptotically linear for large burst length. The asymptotic intercept for each model is shown to be less than, equal to, or greater than unity according as mean channel closed-time is less than, equal to, or greater than mean open-time. For parameter values typical of the nicotinic receptor, this intercept is less than unity for the agonist-only model and greater than unity for the blocking model. As a result of the dependence between the number of openings per burst and burst length, it is shown that experimental estimates of the unconditional mean number of openings per burst may be biased if bursts of only short duration are collected.     

Monotonic and non-monotonic single channel open time distributions with two sequential open states

Some conditions under which kinetic schemes including two sequential open states of identical conductance will display a non-monotonic (i.e. with a deficit of short open times and a maximum at t>0) distribution of single channel open times are described theoretically. Neither a closed cyclic scheme nor exclusively irreversible transitions between states are required for non-monotonic distributions. A required condition for the schemes considered here is that all openings are to a state from which closing is not possible. It is the presence of a precursor process to channel closing that produces the non-monotonic distribution. Following each channel opening some time is required for a transition into the second open state from which all closings proceed. Simple schemes of this sort cannot provide the basis of any experimental reports of non-monotonic distributions.     

Cell responses to single pheromone molecules may reflect the activation kinetics of olfactory receptor molecules

Olfactory receptor cells of the silkmoth Bombyx mori respond to single pheromone molecules with "elementary" electrical events that appear as discrete "bumps" a few milliseconds in duration, or bursts of bumps. As revealed by simulation, one bump may result from a series of random openings of one or several ion channels, producing an average inward membrane current of 1.5 pA. The distributions of durations of bumps and of gaps between bumps in a burst can be fitted by single exponentials with time constants of 10.2 ms and 40.5 ms, respectively. The distribution of burst durations is a sum of two exponentials; the number of bumps per burst obeyed a geometric distribution (mean 3.2 bumps per burst). Accordingly the elementary events could reflect transitions among three states of the pheromone receptor molecule: the vacant receptor (state 1), the pheromone-receptor complex (state 2), and the activated complex (state 3). The calculated rate constants of the transitions between states are k(21)=7.7 s(-1), k(23)=16.8 s(-1), and k(32)=98 s(-1).     

Two-dimensional components and hidden dependencies provide insight into ion channel gating mechanisms

Correlations between the durations of adjacent open and shut intervals recorded from ion channels contain information about the underlying gating mechanism. This study presents an additional approach to extracting the correlation information. Detailed correlation information is obtained directly from single-channel data and quantified in a manner that can provide insight into the connections among the states underlying the gating. The information is obtained independently of any specific kinetic scheme, except for the general assumption of Markov gating. The durations of adjacent open and shut intervals are binned into two-dimensional (2-D) dwell-time distributions. The 2-D (joint) distributions are fitted with sums of 2-D exponential components to determine the number of 2-D components, their volumes, and their open and closed time constants. The dependency of each 2-D component is calculated by comparing its observed volume to the volume that would be expected if open and shut intervals paired independently. The estimated component dependencies are then used to suggest gating mechanisms and to provide a powerful means of examining whether proposed gating mechanisms have the correct connections among states. The sensitivity of the 2-D method can identify hidden components and dependencies that can go undetected by previous correlation methods.     

Single channel recordings from calcium-activated potassium channels in cultured rat muscle

Single channel recordings from cultured rat skeletal muscle have revealed a large conductance (230 pS) channel with a high selectivity for K⁺ over Na⁺. In excised patches of membrane, the probability of channel opening is sensitive to micromolar concentrations of calcium ions at the intracellular surface of the patch. Channel openings appear grouped together into bursts whose duration increases with Ca²⁺ and membrane depolarization. Statistical analysis of the individual open times during each burst showed that there are two distinct open states of similar conductance but dissimilar average lifetimes. These channels might contribute to a macroscopic calcium-activated potassium conductance in rat skeletal muscle and other preparations.     

Coupled and uncoupled Markov systems: a possible way to distinguish between them

The conditional distributions of openings and closings are computed for Markov schemes with two open and two closed states and with different pathways connecting the open and closed aggregates. The computation is performed for uncoupled schemes by directly applying the probability laws and by using a convolution algorithm for coupled schemes. The results show that, for coupled schemes, conditional distributions can be nonmonotonic functions of the dwell time duration. Simulations, illustrating how the difference between coupled and uncoupled models can be detected, are also reported.     

Single-channel currents from diethylpyrocarbonate-modified NMDA receptors in cultured rat brain cortical neurons

The role of histidine residues in the function of N-methyl-D-aspartate (NMDA)-activated channels was tested with the histidine-modifying reagent diethylpyrocarbonate (DEP) applied to cells and membrane patches from rat brain cortical neurons in culture. Channels in excised outside-out patches that were treated with 3 mM DEP for 15-30 s (pH 6.5) showed an average 3.4-fold potentiation in steady state open probability when exposed to NMDA and glycine. Analysis of the underlying alterations in channel gating revealed no changes in the numbers of kinetic states: distributions of open intervals were fitted with three exponential components, and four components described the shut intervals, in both control and DEP-modified channels. However, the distribution of shut intervals was obviously different after DEP treatment, consistent with the single-channel current record. After modification, the proportion of long shut states was decreased while the time constants were largely unaffected. Burst kinetics reflected these effects with an increase in the average number of openings/burst from 1.5 (control) to 2.2 (DEP), and a decrease in the average interburst interval from 54.1 to 38.2 ms. These effects were most likely due to histidine modification because other reagents (n- acetylimidazole and 2,4,6-trinitrobenzene 1-sulfonic acid) that are specific for residues other than histidine failed to reproduce the effects of DEP, whereas hydroxylamine could restore channel open probability to control levels. In contrast to these effects on channel gating, DEP had no effect on average single-channel conductance or reversal potential under bi-ionic (Na+:Cs+) conditions. Inhibition by zinc was also unaffected by DEP. We propose a channel gating model in which transitions between single- and multi-opening burst modes give rise to the channel activity observed under steady state conditions. When adjusted to account for the effects of DEP, this model suggests that one or more extracellular histidine residues involved in channel gating are associated with a single kinetic state.     

Multiple Conductance Substates in Pharmacologically Untreated Na+ Channels Generating Persistent Openings in Rat Entorhinal Cortex Neurons

Na⁺-channel activity recorded in cell-attached patches from entorhinal cortex neurons in the absence of gating-modifying drugs was examined to determine the possible occurrence of substate openings. Brief sojourns to subconductance levels were occasionally observed within prolonged (“persistent”) burst openings. Subconductance occurrence and amplitude were determined following two distinct, complementary approaches: (1) direct visual inspection and (2) automated detection by application of a method that exploits the current variance of fixed-width tracing segments to sort amplitude estimations. The two approaches led to comparable results. At least six subconductance levels in addition to the full open state were revealed, with amplitudes that were approximately 20%, 30%, 40%, 50%, 60% and 75% that of full openings. The global probability of subconductance opening occurrence within a burst as well as the probability of observing one particular subconductance level within a burst showed no clear dependence upon membrane potential in the −40 to +10 mV range. Open- and closed-time distributions of substate openings could either be similar to those observed in burst full openings or show distinct patterns. Low-amplitude late openings were also observed in isolation, separately from full-size openings. These openings corresponded to conductance levels very similar to those of the substates observed within full-size burst openings; therefore, they were interpreted as isolated subconductance openings. Early, transient openings responsible for the fast-inactivating whole-cell Na⁺-current component also manifested distinct conductance levels, the two most prominent of which were in an approximate 75:100 amplitude ratio. Interestingly, the 75% conductance level observed among early openings occurred much more frequently than in “persistent” burst openings. We conclude that pharmacologically untreated Na⁺ channels from native neurons generate substate openings that may influence differently the multiple gating modes displayed by these channels. Angel Alonso is deceased.     

Cholinergic excitation of smooth muscles: Multiple signaling pathways linking M2 and M3 muscarinic receptors to cationic channels

Acetylcholine, the main neurotransmitter of the parasympathetic nervous system, depolarizes various smooth muscles and initiates their contraction via activating muscarinic cholinergic receptors. In most visceral smooth muscle tissues, such as the gastrointestinal tract, airways, and the urinary system, muscarinic receptors are comprised of predominant M₂ (about 80%)and minor M₃ (about 20%) subtypes. Cholinergic excitation is generally mediated by the opening of ion channels selective for monovalent cations (under physiological conditions, Na⁺ and K⁺); among them the cationic channel of an about 60 pS unitary conductance has been recently identified as the main target for acetylcholine action. The signal transduction leading to channel opening is very complex and involves activation of G_o protein (an M₂ effect), activation of phospholipase C (an M₃ effect), and [Ca²⁺]_i and voltage dependence of channel opening. These multiple signaling pathways were difficult to reconcile with the channel gating mechanisms since only a simplified two-state channel mechanism (e.g., one open and one shut state) was until recently available. However, our recent studies of channel gating in isolated outside-out membrane patches revealed a greater complexity. Thus, this cationic channel shows transitions between at least eight states, four open and four shut, with strong connections between adjacent shut and open states. Therefore, four pairs of connected states have been identified, which showed voltage-dependent transitions in each pair of shut/open states. Since the membrane potential did not affect the relative proportions between the pairs, we have assumed that these effects are controlled by ligands that bind to the channel and, thus, stabilize its various open conformations. In this work, direct tests of the above hypothesis have been performed, and their results showed that spontaneous brief channel gating exists in the absence of receptor or G-protein activation, which is strongly voltage-dependent (increasing at depolarized potentials). Furthermore, this activity was potentiated at a low agonist concentration, while channel openings generally remained brief. An increasing receptor occupancy by the agonist produced long channel openings, indicating a shift of gating towards a long open/brief shut pair of the channel states. These findings are interpreted in the context of the established signal transduction pathways;certain predictions for the whole-cell current are also examined.Neirofiziologiya/Neurophysiology, Vol. 36, Nos. 5/6, pp. 446–454, September–December, 2004.This revised version was published online in April 2005 with a corrected cover date and copyright year.     

Stochastic properties of ion channel openings and bursts in a membrane patch that contains two channels: evidence concerning the number of channels present when a record containing only single openings is observed.

If a single ion channel record is observed in which two ion channels are never simultaneously open, then it is often of interest to know whether the observations indeed arose from the activity of only one ion channel. This question can be answered if it is possible to calculate the distribution of the duration of runs of single openings in a membrane patch that contains two active channels. If the observed run of single openings is much longer than that expected for a patch with two channels it is likely that only one channel was active. An approximate method is presented for calculating the distribution of the duration of runs of single openings in a patch with two active channels; this method has the advantage that it can be calculated from observable quantities, and requires no knowledge of the details of the ion-channel mechanism or its rate constants. The accuracy of this approximation is tested by exact calculations of the properties of runs of single openings, and of single bursts, for two specific mechanisms and a large range of rate constants. The approximation is good in all cases in which openings occur singly, or in closely spaced bursts. If, as is common in practice, openings occur in clusters that are separated by long shut periods, then overlap of clusters from two different channels may be detected, if no double opening is produced, as a period in the middle of a cluster in which the probability of being open doubles. The results derived here can be applied to such a period to test whether it results from the simultaneous activity of two channels, rather than from a change in the properties of a single channel.     

Capsaicin activation of the pain receptor,VR1: multiple open states from both partial and full binding

Capsaicin, the pungent ingredient of hot peppers, has long been used to identify nociceptors. Its molecular target, the vanilloid receptor VR1, was recently cloned and confirmed functionally as a polymodal detector of multiple pain stimuli: heat, acid, and vanilloids. Previous electrophysiology studies have focused on whole-cell characteristics of the receptor. Here, we provide the first in-depth single-channel kinetic study of VR1 to understand its activation mechanism. At low to medium concentrations, channel activity appeared as bursts. Not only did the durations of the interburst gaps vary with capsaicin, the bursts also appeared ligand-dependent, with high capsaicin prolonging bursts and stabilizing openings. Gating involved at least five closed and three open states, with strong correlations between short closures and long openings, and long closures and short openings. Increasing capsaicin reduced the long closures with little effect on short ones. The open time constants changed little with capsaicin concentration, though their relative proportions varied. These results suggest that 1), the channel contains multiple capsaicin binding sites; 2), both partial and full binding are capable of opening the channel; 3), when activated, multiple open states are accessible irrespective of the level of binding; and 4), capsaicin association occurs preferentially to the closed channel.     

Mechanism of ivermectin facilitation of human P2X4 receptor channels

Ivermectin (IVM), a widely used antiparasitic agent in human and veterinary medicine, was recently shown to augment macroscopic currents through rat P2X(4) receptor channels. In the present study, the effects of IVM on the human P2X(4) (hP2X(4)) receptor channel stably transfected in HEK293 cells were investigated by recording membrane currents using the patch clamp technique. In whole-cell recordings, IVM (< or =10 microM) applied from outside the cell (but not from inside) increased the maximum current activated by ATP, and slowed the rate of current deactivation. These two phenomena likely result from the binding of IVM to separate sites. A higher affinity site (EC(50) 0.25 microM) increased the maximal current activated by saturating concentrations of ATP without significantly changing the rate of current deactivation or the EC(50) and Hill slope of the ATP concentration-response relationship. A lower affinity site (EC(50) 2 microM) slowed the rate of current deactivation, and increased the apparent affinity for ATP. In cell-attached patch recordings, P2X(4) receptor channels exhibited complex kinetics, with multiple components in both the open and shut distributions. IVM (0.3 microM) increased the number of openings per burst, without significantly changing the mean open or mean shut time within a burst. At higher concentrations (1.5 microM) of IVM, two additional open time components of long duration were observed that gave rise to long-lasting bursts of channel activity. Together, the results suggest that the binding of IVM to the higher affinity site increases current amplitude by reducing channel desensitization, whereas the binding of IVM to the lower affinity site slows the deactivation of the current predominantly by stabilizing the open conformation of the channel.