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Department of Obstetrics and Gynecology, Oregon Health Sciences University, Portland, Oregon 97201
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ABSTRACT |
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0.6 in 1 µM free Ca2+. A lower open probability of 0.05 in 1 µM Ca2+ was also observed, and channels switched spontaneously between behaviors. The occurrence of these switches and the amount of time channels spent displaying high open probability behavior was Ca2+ dependent. The two behaviors shared many features including the open times and the short and intermediate closed times, but the low open probability behavior was characterized by a different, long Ca2+-dependent closed time in the range of hundreds of milliseconds to seconds. Small-conductance Ca- activated K+ channel gating was modeled by a gating scheme consisting of four closed and two open states. This model yielded a close representation of the single channel data and predicted a macroscopic activation time course similar to that observed upon fast application of Ca2+ to excised inside-out patches.
Key Words: potassium channel • calcium-activated • single channel • afterhyperpolarization • gating
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; Latorre et al., 1989; Ishii et al., 1997). While BK channels have been studied extensively, the biophysical properties of SK and IK channels are less well characterized.
SK channels were first identified in cultured rat skeletal muscle, where they appeared to open independent of membrane potential (Blatz and Magleby, 1986). These channels were more sensitive to Ca2+ and had a smaller single channel conductance than BK channels. In addition, they were blocked by the bee venom toxin apamin, but not by 5 mM tetraethylammonium (Blatz and Magleby, 1986). Since their initial discovery, SK channels have been described from a number of cell types including a rat pituitary cell line (Lang and Ritchie, 1987), T lymphocytes (Grissmer et al., 1992), and adrenal chromaffin cells (Park, 1994). In these cell types, SK channels were activated by submicromolar concentrations of intracellular Ca2+ (EC50 = 0.5–0.7 µM) in a voltage-independent manner. The single channel conductance was 4–14 pS in symmetrical 150–170 mM K+ and channels were blocked by apamin. Channels with similar characteristics have been observed in cultured rat hippocampal neurons (Lancaster et al., 1991). These channels were activated by 1 µM intracellular Ca2+ in a voltage-independent manner. In contrast to the above examples, these channels were not blocked by apamin (25 nM) and exhibited a single channel conductance of 18 pS in symmetrical 140 mM K+ (Lancaster et al., 1991).
The observation of apamin-sensitive and -insensitive Ca-activated channels with otherwise similar characteristics suggested the possibility of SK channel subtypes. The cloning of SK channels has revealed the existence of at least three members of a family (SK1–3). The amino acid sequence of the three subtypes was highly conserved, and hydrophobicity analysis predicted a secondary structure with six membrane-spanning regions. Further, two subtypes examined, rSK2 and hSK1, displayed a calcium dependence and single channel conductance similar to that observed for native channels (Köhler et al., 1996). As seen with native SK channels, differences in apamin sensitivity were observed for the cloned channels. For example, rSK2 was blocked by picomolar concentrations of apamin, whereas hSK1 was apamin insensitive (Köhler et al., 1996). Northern blot analysis showed the mRNA for rSK2 to be present in adrenal gland (Köhler et al., 1996), in agreement with the observation of apamin-sensitive SK channels in adrenal chromaffin cells (Park, 1994). In situ hybridization revealed that the mRNA encoding SK1 was expressed in rat hippocampus (Köhler et al., 1996).
SK channels underlie the prolonged afterhyperpolarization (slow AHP) following trains of action potentials in many neurons (Sah, 1996). The slow AHP differs between tissues in its time course and pharmacology. For example, in bullfrog sympathetic neurons (Pennefather et al., 1985; Goh and Pennefather, 1987), the slow AHP decays within several hundred milliseconds and is blocked by apamin. In contrast, the slow AHP recorded from hippocampal pyramidal neurons follows a slower time course, decaying over several seconds, and is insensitive to apamin (Lancaster and Adams, 1986; Storm, 1987). Both apamin-sensitive and -insensitive AHPs are present in rat and guinea pig vagal neurons (Sah and McLachlan, 1991; Sah, 1993) and cat cortical neurons (Schwindt et al., 1992). Apamin-sensitive and -insensitive AHPs from different tissues have properties suitable for a role in modulating the frequency of action potential firing (Lang and Ritchie, 1990; Neely and Lingle, 1992; Park, 1994; Yarom et al., 1985). This phenomenon has been studied in detail in hippocampal pyramidal neurons, where it is referred to as spike frequency adaptation (Madison and Nicoll, 1984).
In this study, the single channel properties of rSK2 and their dependence on voltage and calcium was examined. Two types of SK channel activity with very different open probabilities were observed, with the two behaviors sharing many characteristics. They were described by two open and three closed times. The open times and the short and intermediate closed times were the same for both types of channel activity, whereas the long closed time differed 10-fold. Only the long closed time was Ca dependent. Although relative contributions of open and closed times differed between the two types of channel activity, elevated intracellular Ca2+ favored longer openings and short closures in both behaviors.
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). Oocytes were studied 15–48 h after injection with 2 ng of mRNA.
Solutions
During recording, oocytes were bathed in 116 mM K-gluconate, 4 mM KCl, 10 mM HEPES, 5 mM EGTA, adjusted to pH 7.2 with KOH. To yield the reported concentration of free Ca2+, CaCl2 was added as calculated using published stability constants (Martell and Smith, 1974). For Ca2+ concentrations >1 µM, EGTA was omitted from the bathing solution and gluconate was used to buffer free Ca2+, assuming a stability constant for calcium gluconate of 15.9 M–1 (Dawson et al., 1969). Electrodes were filled with a solution containing 116 mM K-gluconate, 4 mM KCl, 10 mM HEPES, pH 7.2.
Electrophysiology
All recordings were performed on excised inside-out patches (Hamill et al., 1981) using thick-walled quartz electrodes (13–15 M
). Membrane patches were voltage clamped with an Axopatch 200 amplifier using a CV 201A headstage (Axon Instruments, Foster City, CA). Continuous recordings were low pass filtered at 1 kHz with an eight pole Bessel filter (Frequency Devices Inc., Haverhill, MA), acquired at 10 kHz using Pulse software (Heka Electronik, Lambrecht, Germany) and stored directly on a Macintosh Quadra 650 computer. All experiments were performed at room temperature. Except for Figs. 2 and 3, a holding potential of –80 mV was used; however, a variable offset up to 20 mV occurred upon patch excision and was not corrected.
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) and all bins were used for fitting. The number of statistically significant components was determined using the method of maximum likelihood ratios (Horn and Lange, 1983), which assumes a chi-squared distribution for 2·ln (likelihood 1/likelihood 2). Missed events were not corrected. Open probability was calculated using a computer program (ReadEvents1.37; Dr. Scott Eliasof, Vollum Institute) to divide the sum of all open times by the total time of recording. All patches included in the analysis, except one, had periods of high channel open probability lasting long enough to establish that only a single channel was present in the patch. No double-level openings were seen in the patch that had only low channel open probability, and closed times were similar to the ones observed in other single-channel patches.
Single channel kinetics were simulated using CSIM 2.0 (Axon Instruments). Simulations were run at the same output rate as the experimental sampling rate, 0.15 pA RMS of pseudo-random Gaussian noise was added to the data, and a Gaussian low pass filter was applied at 1 kHz. Resulting simulated data files were analyzed in the same fashion as channel recordings. Initial estimates of rate constants were obtained from the life times and relative amplitudes of each exponential component in the duration histograms, and from the channel open probability. The simulated traces and duration histograms were compared with the experimental data, and rate constants were adjusted to obtain good agreement. For the model containing three open and four closed states presented in Figs. 10 and 11, 46 estimates of rate constants were examined. Macroscopic currents were simulated using SCoP (Simulation Resources, Inc., Berrien Springs, MI). Values were expressed as mean ± SD and P values were derived from unpaired, two-tailed Student's t tests. Results were considered significantly different at P < 0.01.
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). At the single channel level, this dependence manifested itself as an increase in open probability as a function of increased intracellular Ca2+ concentration. Fig. 1 A shows traces recorded from an excised inside-out patch containing a single rSK2 channel. In these traces, openings became more frequent as the Ca2+ concentration was increased from 0.6 to 5 µM. In four patches, the average open probability was 0.42 ± 0.12 in 0.6 µM Ca2+ and 0.74 ± 0.16 in 1 µM Ca2+. Fig. 1 B shows a plot of the open probability as a function of Ca2+ concentration for the patch in A. Fitting of the data to the Hill equation yielded an EC50 of 0.74 µM and a Hill coefficient of 2.2, mean values from three patches were 0.62 ± 0.14 µM and 3.2 ± 1.0, respectively. The EC50 was the same as that observed using macropatches (0.63 ± 0.23, P > 0.1). The Hill coefficient was somewhat reduced from the value of 4.8 ± 1.5 seen in macropatches (Köhler et al., 1996), although the difference was not statistically significant (P > 0.01, see DISCUSSION).
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). Traces recorded from the patch in Fig. 1 at –60 and –100 mV were shown together with the corresponding open-time distributions (left) and closed-time distributions (right) in Fig. 2. Traces recorded at the two membrane potentials showed no obvious differences in channel activity. Both traces contained short and long openings, and open-time distributions were best fit by the sum of two exponentials with time constants of 1 and 11 ms. Independent of membrane potential, three exponentials were needed to adequately fit closed-time distributions. Time constants were similar at both membrane potentials and were 0.7, 4.5, and 30 ms. The voltage dependence of the single channel behavior is summarized in Fig. 3. As discussed in detail below, only some of the parameters describing SK channel kinetics were Ca2+ dependent. Since the three patches examined were exposed to different Ca2+ concentrations, the Ca2+-dependent parameters were plotted individually for each patch, whereas Ca2+-independent parameters were shown as mean values. Patch membrane voltage did not significantly affect channel open probability (Fig. 3 A). As seen in Fig. 2, open-time histograms were best fit by the sum of two exponentials. The mean time constants were plotted as a function of voltage in Fig. 3 B. Voltage did not significantly affect either open-time constant. In addition, the relative contribution of each time constant to the open-time histogram was similar at all voltages examined (Fig. 3 C).
Three exponentials were needed to fit the closed-time histograms in two patches, whereas two exponentials were adequate for a third patch (see Fig. 3, legend). The short and intermediate closed times, present in all three patches, were shown as mean values in Fig. 3 D, and the long closed time was plotted for the two patches individually in Fig. 3 E. As was the case for the open times, voltage did not significantly affect the three closed-time constants, as illustrated by the exponential fits (Fig. 3, D and E, solid lines). Finally, the relative amplitudes of the short (Fig. 3 F, closed symbols) and intermediate (Fig. 3 F, open symbols) closed-time components were also insensitive to voltage. Because membrane potential did not affect any of the open and closed times, a single holding potential of –80 mV (plus off-set, see METHODS) was used during the remainder of this study.
Ca2+ Affected the Longest Closed Time as well as Open- and Closed-Time Distributions
Fig. 4 shows 2-s segments of recordings from a single channel patch exposed to different concentrations of intracellular Ca2+. As seen in Fig. 1, the open probability increased with higher Ca2+ concentration. The change in open probability was reflected in both the open- and closed-time distributions. In all three concentrations of Ca2+, open-time histograms (Fig. 4, left) showed two components with lifetimes independent of Ca2+. However, an increased concentration of intracellular Ca2+ resulted in a larger fraction of long openings. For the recordings in Fig. 4, 49% of all openings in 0.4 µM intracellular Ca2+ contributed to the long open-time constant compared with 66% in 1 µM Ca2+. Independent of Ca2+ concentration, closed-time histograms showed three components (Fig. 4, right). The short and intermediate closed times were unaffected by a change in Ca2+ concentration (see Fig. 5). In contrast, the long closed time increased from 20 ms in 1 µM to 60 ms in 0.4 µM free Ca2+. Ca2+ also affected the relative amplitude of the closed-time components, shifting the distribution towards the shorter closed times. For the patch in Fig. 4, 71% of all closures in 1.0 µM Ca2+ were of the short time-constant compared with 63% in 0.4 µM.
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SK Channel Behavior Changed Spontaneously
The traces in Fig. 6 A represent part of a continuous recording obtained from an inside-out patch bathed in 1 µM Ca2+. Approximately 13 s after patch excision (Fig. 6 A, arrow), the open probability of the channel decreased spontaneously. In this example, the decline of activity appeared to be somewhat gradual. However, in other examples, channel behavior changed more abruptly. Open probability remained low for 47 s before it reverted back to the starting level (Fig. 6 A, arrow). Fig. 6 B shows the open probability during 1-s intervals plotted as a function of time after patch excision. During the segment of lower activity, the open probability was 0.03 compared with 0.81 during the combined segments of high activity.
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) was calculated by multiplying the single channel open probability from a recording of high open probability behavior (Fig. 7 B, •; EC50 = 0.43 µM, Hill coefficient = 3.3) by the relative amount of time channels spent exhibiting high open probability behavior (Fig. 7 A, inset). Fitting the effective open probability to the Hill equation predicted a macroscopic EC50 of 0.63 µM and Hill coefficient of 3.6 (see DISCUSSION).
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Fig. 8 shows steady state recordings from a patch containing a channel that displayed predominantly low open probability activity (0.05 in 1.0 µM calcium). The same patch showed high open probability for almost 3 min, revealing that only a single channel was present. Channel activity during low open probability periods was Ca sensitive and open probability increased as a function of Ca2+ concentration by a factor similar to that in high open probability behavior (Fig. 8). During low open probability periods, SK channel activity exhibited similar open state kinetics as observed during high open probability. Independent of the Ca2+ concentration, open-duration histograms were best fit by the sum of two exponentials (Fig. 8). Average time constants in seven patches were 0.93 ± 0.23 and 9.9 ± 4.4 ms. These open times were not statistically different from those observed during high open probability activity (1.1 ± 0.3 and 10.6 ± 2.9 ms, eight patches, P > 0.05). However, an obvious difference between the two types of SK channel activity was that short-duration openings predominated during low open probability behavior. For example, 71% of the openings observed in 1.0 µM free Ca2+ contributed to the short open-time constant during low open probability behavior (Fig. 8), while only 34% of openings were of short duration during high open probability activity (Fig. 4). Despite this difference, the relative amplitude of the short open-time component decreased with increasing Ca2+ concentration in both types of channel behavior. For example, in the patch shown in Fig. 8, 29% of openings contributed to the long open-time constant in 1.0 µM free Ca2+, compared with 17% in 0.4 µM.
SK channel closed state kinetics during low open probability activity exhibited three exponential components (Fig. 8). The average short and intermediate closed-time constants of 0.9 ± 0.4 and 5.9 ± 1.5 ms (seven patches) were not statistically different from those observed during high open probability activity (0.7 ± 0.2 and 4.6 ± 1.3 ms, eight patches, P > 0.01), but accounted for a smaller fraction of closures (60 ± 12% vs. 92 ± 6% in 1.0 µM Ca2+, three and four patches, P < 0.01). In contrast, the third closed-time constant was significantly longer, measuring 295 ± 26 ms in 1.0 µM Ca2+ during low open probability, compared with 25.9 ± 5.8 ms during high open probability (five and three patches, respectively, P < 0.01). As observed for high open probability behavior, the longest closed time was Ca2+ dependent and decreased from 1,290 ± 320 ms to 295 ± 26 ms (P < 0.01, three patches) when the free Ca2+ concentration was increased from 0.4 to 1.0 µM (see Fig. 9 C). During both types of channel behavior, higher Ca2+ concentrations shifted the distributions toward the shorter closed-time constants. For example, in the patch in Fig. 8, the longest closed-time constant accounted for 32% of closures in 1.0 µM and 43% in 0.4 µM Ca2+.
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; Valiante et al., 1997; Sah and Isaacson, 1995; Sah, 1995). As might be expected from the high degree of homology between apamin-sensitive and -insensitive recombinant subtypes (66% amino acid identity between rSK2 and hSK1; Köhler et al., 1996), results from these studies were similar to the results reported here for cloned apamin-sensitive SK channels. Apamin-insensitive SK channels recorded from cultured rat hippocampal neurons possessed open times that were fit with a single exponential time constant of 7.8 ms and closed times that were fit with two exponentials with time constants of 0.49 and 1.49 ms. These channels exhibited an open probability of 0.5 in 1 µM Ca2+ (Lancaster et al., 1991). Analyses of current fluctuations during the slow AHP in dentate granule neurons yielded similar results. For example, the mean channel open time was 6.9 ms throughout the time course of the slow AHP, whereas the decay of the slow AHP was accompanied by an increase in the mean closed time (Valiante et al., 1997). Assuming that the decay of the slow AHP resulted from the clearance of Ca2+ from the vicinity of the channels, this finding agrees with our observation that only the longest closed time was Ca dependent. Somewhat shorter open times of 1.7 and 3.8 ms were measured using fluctuation analysis of IAHP in hippocampal pyramidal neurons (Sah and Isaacson, 1995) and vagal motoneurons (Sah, 1995), respectively.
SK Channel Activation Could Be Modeled as a Markov Process
The activation of SK channels may be described as a time-homogeneous Markov chain. Single rSK2 channels recorded from oocytes showed open-time distributions that were best fit by the sum of two exponentials, whereas three exponentials were necessary to fit closed-time distributions. The high open probability behavior could be modeled using a gating scheme with two open and four closed states as illustrated in Fig. 10, where the forward transition rates between closed states were dependent on intracellular Ca2+. Strictly sequential gating schemes with two open states that were either connected or separated by closed states did not fit the data. Several gating schemes containing closed loops were also examined and did not yield satisfying results. A scheme similar to the one presented in Fig. 10 but consisting of two open and three closed states yielded a reasonable representation of the data, but only if rate constants were allowed to have a nonlinear dependence on Ca2+ concentration. Since Ca2+-dependent transitions were assumed to reflect simple bimolecular reactions, their rates should vary linearly with Ca2+ concentration. This was achieved by adding a fourth closed state. Due to the similarity of two of the predicted time constants, the gating scheme in Fig. 10 yielded closed-time histograms with three resolvable components rather than the theoretical four components. The rate constants were adjusted such that the predicted lifetimes and relative amplitudes were similar to what was observed experimentally for a representative patch exposed to two Ca2+ concentrations (compare Figs. 4 and 10). As seen in single channel recordings, channel open times and the short and intermediate closed times were unchanged when channel activity was simulated with rate constants for 0.4 and 1.0 µM free Ca2+, respectively. In contrast, the long closed time increased as a function of decreased Ca2+ concentration. In addition, the model correctly predicted the changes in the relative amplitudes of open- and closed-time components.
The low open probability behavior was modeled separately using the same gating scheme (Fig. 11). The best agreement with the experimental data was obtained if all Ca2+-dependent rates were reduced by a factor of 6.7. The model for low open probability behavior predicted dwell times similar to experimentally derived values for the two Ca2+ concentrations used in the simulation (see Figs. 7 and 11). It also reflected the changes seen with changing Ca2+ concentration. A possible shortcoming of the modified model was that it predicted a somewhat larger fraction of intermediate compared with short closures than was observed experimentally. However, this discrepancy was most prominent in low Ca2+, where openings were rare with the obtained histograms containing a relatively small number of events.
The presented gating schemes predict that both long- and short-duration openings should be grouped; i.e., after a long opening, the channel is more likely to reenter the same long open state rather than transition into the short open state. The same should be true for short openings. Consistent with this prediction, long openings were predominantly followed by other long openings in all three patches examined. Fig. 12 A shows histograms containing all openings (left), openings after openings shorter than 1 ms (middle), and openings after openings longer than 10 ms (right) for the patch illustrated in Fig. 4 exposed to 0.4 µM Ca2+. All three histograms were best fit with two exponentials, and the lifetimes of each exponential component were similar under the three conditions. In contrast, the relative amplitudes of the two components varied considerably with the percentage of long openings decreasing from 49% (of all openings) to 20%, when only openings after short openings were included, and increasing to 74% after long openings. Similar correlations between successive openings were seen in simulations of the model. For the example shown in the insets, 49% of all openings, 23% of openings after short openings, and 81% of openings after long openings were of the long time constant. As illustrated in Fig. 12 B, similar results were obtained for the channel displaying low open probability behavior shown in Fig. 7 (1 µM Ca2+) and the gating scheme in Fig. 11.
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The mechanism underlying switches between high and low open probability behavior is unknown, except that the process has some dependence on Ca2+. Since channels reversibly switched behaviors in the absence of added ATP or Mg2+, it seemed unlikely that channel phosphorylation plays a role, and the two behaviors may reflect intrinsic conformational states of the channel. The Ca dependence of the time channels spent exhibiting each behavior (Fig. 7 A) suggested that switches between the two behaviors could contribute to the Ca2+ dependence of the macropatch current. This was illustrated by the calculation of an effective open probability in Fig. 7 B, which was right-shifted and somewhat steeper than the single channel open probability.
Comparison with Gating Schemes and Mode Shifts Seen with Other Channels
The gating scheme presented here is the first attempt at modeling the Ca2+-dependent activation of SK channels. The model shares some similarities with gating schemes used to describe the voltage- and Ca2+-dependent properties of BK channels in the major gating mode. In particular, the model proposed by DiChiara and Reinhart (1995) for cloned drosophila and human BK channels can be thought of as an expanded version of this model containing an additional closed state connected to a third open state. In addition, DiChiara and Reinhart (1995) also found that only the (three) longest closed states were Ca2+ dependent. However, studies on BK channels from rat skeletal muscle found two of three open times to be Ca2+ dependent and proposed a model in which open states were connected by Ca2+-dependent transitions (McManus and Magleby, 1991). Earlier studies on rat muscle BK channels incorporated into lipid bilayers (Moczydlowski and Latorre, 1983) and cultured rat muscle cells (Magleby and Pallotta, 1983) also found a Ca2+ dependency of the mean open time. A simple sequential model containing two closed and two open states was proposed in the former and a branched model containing three closed and two parallel open states in the latter study. Differences between these models may at least partially be due to differences in the time resolution. The time resolution used in this study was the same as that used by Magleby and Pallotta (1983).
In addition to the normal mode of gating, four kinetic modes have been observed for BK channels in rat skeletal muscle (McManus and Magelby, 1988; Rothberg et al., 1996). All of them are characterized by a lower channel open probability compared with the normal mode, but together only account for <10% of channel openings at Ca2+ concentrations below 10 µM. Three of the lower open probability modes, termed the intermediate open, brief open, and buzz mode, may result from excluded entry into certain states of the scheme used to describe normal mode gating (McManus and Magelby, 1988). In contrast, the SK channels in this study entered a low open probability mode that appeared to have the same number of open and closed states as the high open probability mode. The frequency and duration of sojourns to the low activity mode of BK channels increased with increasing Ca2+ concentration (Rothberg et al., 1996), while the low open probability mode of recombinant SK channels was entered more frequently in low Ca2+ concentrations.
In contrast to the mode shifting in native BK channels, which occurred rapidly and was followed by periods of stable activity (McManus and Magelby, 1988), cloned Drosophila BK channels expressed in oocytes displayed large slow fluctuations between changing levels of open probability (Silberberg et al., 1996). This behavior was termed wanderlust kinetics. Except for the very slow time course of the fluctuations, wanderlust kinetics appears similar to the changes in open probability reported here for cloned SK channels. During low activity periods, recombinant BK and SK channels show bursts of activity with kinetics similar to those seen during high activity. These bursts are separated by long closures not seen during periods of high activity. For both channels, the main difference between time constants describing high and low activity behavior was in the longest closed-time component(s). Silberberg et al. (1996) suggested that wanderlust kinetics can be described by a single gating scheme if one assumes one or more multiplicative factors modifying the Ca2+-dependent rate constants.
Low activity modes have been observed for a number of other ion channels. These include glutamate-activated channels from locust muscle (Patlak et al., 1979), Aplysia voltage-gated cation channels (Wilson and Kaczmarek, 1993), cardiac calcium channels (Hess et al., 1984), frog skeletal muscle sodium channels (Patlak et al., 1986), acetylcholine receptors in frog muscle (Auerbach and Lingle, 1986), M-channels in bullfrog sympathetic neurons (Marrion, 1993), and N-methyl-D-aspartate receptors (Donelly and Pallotta, 1995). The gating modes observed for the Aplysia voltage-gated cation channel appeared most similar to those of cloned SK channels in that the two modes differ mainly by the presence or absence of long closures, whereas the open and the shorter closed times are similar for the two modes.
SK Channel Kinetics May Account for the Time Course of Apamin-sensitive AHPs
The gating scheme and rate constants presented in Fig. 10 could be used to predict the activation time constant of a macroscopic SK current elicited by a fast jump in Ca2+ concentration. A current trace evoked by a jump from 0 to 9.5 µM Ca2+ is shown in Fig. 13 A, superimposed with a simulation of the gating scheme in Fig. 10. The current activated with a time constant of 4.9 ms and, upon removal of free Ca2+, deactivated with a time constant of 58 ms. Averages from six Ca2+ jumps (two patches) were 4.1 ± 0.6 ms for the activation and 57.3 ± 11.1 ms for the deactivation time constant. Simulations of the model (Fig. 10) are shown in Fig. 13 B for jumps to 0.2, 0.5, 1, 5, and 10 µM Ca2+. Since macroscopic currents would be dominated by channels displaying high open probability behavior, only this type of channel behavior was considered here. Fitting of the simulated traces to single exponentials yielded activation time constants of 5 ms in 5 µM and 50 ms in 0.5 µM free Ca2+. Fig. 13 C shows a plot of the activation rate (
–1) versus Ca2+ concentration. Over the range of 0.2 to 10 µM Ca2+, the model predicted an approximately linear relationship between the activation rate of the macroscopic current and the Ca2+ concentration with a forward rate constant of 47 µM–1 s–1. This rate was somewhat slower than the slowest Ca2+-dependent rate (80 µM–1 s–1) of the gating scheme in Fig. 10, possibly reflecting the requirement for several Ca2+-dependent transitions before channel opening. An apparent Ca2+ binding rate of 26 µM–1 s–1 was estimated from the macroscopic current activation (Fig. 13 C, 
). A rate of 21 µM–1 s–1 was seen in rat sympathetic neurons using flash photolysis of photosensitive Ca2+ chelators (Gurney et al., 1987). Both rates are fast and, considering the uncertainty associated with access of Ca2+ to the patch (this study) or with determinations of the amount of released Ca2+ (Gurney et al., 1987), are in reasonable agreement with our model. In the study of Gurney et al. (1987), a lower limit of 25 s–1 for channel closure upon Ca2+ removal was estimated by extrapolation of the data to 0 Ca2+. This rate was somewhat faster than, but not markedly different from, the 17 s–1 measured during rapid Ca2+ removal ( = 58 ms, Fig. 13 A) and the 13 s–1 ( = 76 ms, Fig. 13 B) predicted by our model. In comparison, the apamin-sensitive component of the AHP in bullfrog sympathetic ganglion cells decayed with a time constant of 150 ms, corresponding to a rate of 7 s–1 (Lancaster and Pennefather, 1987).
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) activates rapidly and is maximal <5 ms after the voltage step used to evoke an action potential. This time course suggests that SK channels in these cells are located near voltage-dependent calcium channels. In contrast, the apamin-insensitive component of the AHP has a slower time course activating with a time constant of 550 ms in guinea pig vagal neurons (Sah, 1993). The apamin-insensitive member (SK1) of the cloned SK channel subtypes is highly homologous to apamin-sensitive members (SK2 and SK3) and shares the same Ca2+ sensitivity (Köhler et al., 1996). As expected, preliminary experiments show that hSK1 and rSK2 have similar open and closed times. Stationary and nonstationary fluctuation analysis of the current at the peak of the apamin-insensitive slow AHP yielded open probabilities of 0.4 in hippocampal pyramidal neurons (Sah and Isaacson, 1995), 0.6 in dentate granule neurons of the hippocampus (Valiante et al., 1997), and 0.7 in vagal motoneurons (Sah, 1995). Assuming that apamin-sensitive and -insensitive SK channels possess similar single channel kinetics, this suggests that the effective Ca2+ concentration at the channel was in the range of 0.7–1.2 µM. In this concentration of Ca2+, the model for the high open probability behavior predicts an activation time constant of 20–30 ms, >10-fold faster than the time constant of the apamin-insensitive slow AHP in vagal neurons (Sah, 1993). This suggests that SK channel kinetics alone are insufficient to explain the time course of the apamin-insensitive AHP, in agreement with data from hippocampal pyramidal neurons using flash photolysis of caged Ca2+ (Lancaster and Zucker, 1994).
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ACKNOWLEDGMENTS |
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This work was supported by a National Institutes of Health (NIH) Cardiology Training Grant and a National Research Service Award to B. Hirschberg and by NIH grants to J.P. Adelman, J. Maylie, and N.V. Marrion.
Submitted: 16 September 1997
Accepted: 5 February 1998
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 W. Li and R. W. Aldrich Activation of the SK potassium channel-calmodulin complex by nanomolar concentrations of terbium PNAS, January 27, 2009; 106(4): 1075 - 1080. [Abstract] [Full Text] [PDF]
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 M. D. Johnson and C. C. McIntyre Quantifying the Neural Elements Activated and Inhibited by Globus Pallidus Deep Brain Stimulation J Neurophysiol, November 1, 2008; 100(5): 2549 - 2563. [Abstract] [Full Text] [PDF]
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C. Gunay, J. R. Edgerton, and D. Jaeger Channel Density Distributions Explain Spiking Variability in the Globus Pallidus: A Combined Physiology and Computer Simulation Database Approach J. Neurosci., July 23, 2008; 28(30): 7476 - 7491. [Abstract] [Full Text] [PDF]
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 M. Teagarden, J. F. Atherton, M. D. Bevan, and C. J. Wilson Accumulation of cytoplasmic calcium, but not apamin-sensitive afterhyperpolarization current, during high frequency firing in rat subthalamic nucleus cells J. Physiol., February 1, 2008; 586(3): 817 - 833. [Abstract] [Full Text] [PDF]
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J. Ledoux, A. D. Bonev, and M. T. Nelson Ca2+-activated K+ Channels in Murine Endothelial Cells: Block by Intracellular Calcium and Magnesium J. Gen. Physiol., January 28, 2008; 131(2): 125 - 135. [Abstract] [Full Text] [PDF]
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A. Bruening-Wright, W.-S. Lee, J. P. Adelman, and J. Maylie Evidence for a Deep Pore Activation Gate in Small Conductance Ca2+-activated K+ Channels J. Gen. Physiol., November 26, 2007; 130(6): 601 - 610. [Abstract] [Full Text] [PDF]
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 N. Ozgen, W. Dun, E. A. Sosunov, E. P. Anyukhovsky, M. Hirose, H. S. Duffy, P. A. Boyden, and M. R. Rosen Early electrical remodeling in rabbit pulmonary vein results from trafficking of intracellular SK2 channels to membrane sites Cardiovasc Res, September 1, 2007; 75(4): 758 - 769. [Abstract] [Full Text] [PDF]
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 D. J. Loane, P. A. Lima, and N. V. Marrion Co-assembly of N-type Ca2+ and BK channels underlies functional coupling in rat brain J. Cell Sci., March 15, 2007; 120(6): 985 - 995. [Abstract] [Full Text] [PDF]
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A. Gillies and D. Willshaw Membrane Channel Interactions Underlying Rat Subthalamic Projection Neuron Rhythmic and Bursting Activity J Neurophysiol, April 1, 2006; 95(4): 2352 - 2365. [Abstract] [Full Text] [PDF]
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 J. Yao, X. Chen, H. Li, Y. Zhou, L. Yao, G. Wu, X. Chen, N. Zhang, Z. Zhou, T. Xu, et al. BmP09, a "Long Chain" Scorpion Peptide Blocker of BK Channels J. Biol. Chem., April 15, 2005; 280(15): 14819 - 14828. [Abstract] [Full Text] [PDF]
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M. Lioudyno, H. Hiel, J.-H. Kong, E. Katz, E. Waldman, S. Parameshwaran-Iyer, E. Glowatzki, and P. A. Fuchs A "Synaptoplasmic Cistern" Mediates Rapid Inhibition of Cochlear Hair Cells J. Neurosci., December 8, 2004; 24(49): 11160 - 11164. [Abstract] [Full Text] [PDF]
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S.-I. Yamada, H. Takechi, I. Kanchiku, T. Kita, and N. Kato Small-Conductance Ca2+-Dependent K+ Channels Are the Target of Spike-Induced Ca2+ Release in a Feedback Regulation of Pyramidal Cell Excitability J Neurophysiol, May 1, 2004; 91(5): 2322 - 2329. [Abstract] [Full Text] [PDF]
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D. Z. Wetmore and S. N. Baker Post-spike distance-to-threshold trajectories of neurones in monkey motor cortex J. Physiol., March 15, 2004; 555(3): 831 - 850. [Abstract] [Full Text] [PDF]
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J. Maylie, C. T. Bond, P. S. Herson, W.-S. Lee, and J. P. Adelman Small conductance Ca2+-activated K+ channels and calmodulin J. Physiol., January 15, 2004; 554(2): 255 - 261. [Abstract] [Full Text] [PDF]
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H. J. Abel, J.C.F. Lee, J. C. Callaway, and R. C. Foehring Relationships Between Intracellular Calcium and Afterhyperpolarizations in Neocortical Pyramidal Neurons J Neurophysiol, January 1, 2004; 91(1): 324 - 335. [Abstract] [Full Text]
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W.-S. Lee, T. J. Ngo-Anh, A. Bruening-Wright, J. Maylie, and J. P. Adelman Small Conductance Ca2+-activated K+ Channels and Calmodulin: CELL SURFACE EXPRESSION AND GATING J. Biol. Chem., July 3, 2003; 278(28): 25940 - 25946. [Abstract] [Full Text] [PDF]
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 E. S. L. Faber and P. Sah Calcium-Activated Potassium Channels: Multiple Contributions to Neuronal Function Neuroscientist, June 1, 2003; 9(3): 181 - 194. [Abstract] [PDF]
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M.C.W. van Rossum, B. J. O'Brien, and R. G. Smith Effects of Noise on the Spike Timing Precision of Retinal Ganglion Cells J Neurophysiol, May 1, 2003; 89(5): 2406 - 2419. [Abstract] [Full Text] [PDF]
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C. A. Sailer, H. Hu, W. A. Kaufmann, M. Trieb, C. Schwarzer, J. F. Storm, and H.-G. Knaus Regional Differences in Distribution and Functional Expression of Small-Conductance Ca2+-Activated K+ Channels in Rat Brain J. Neurosci., November 15, 2002; 22(22): 9698 - 9707. [Abstract] [Full Text] [PDF]
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P.B. Goforth, R. Bertram, F.A. Khan, M. Zhang, A. Sherman, and L.S. Satin Calcium-activated K+ Channels of Mouse {beta}-cells are Controlled by Both Store and Cytoplasmic Ca2+: Experimental and Theoretical Studies J. Gen. Physiol., August 26, 2002; 120(3): 307 - 322. [Abstract] [Full Text] [PDF]
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G. M Herrera and M. T Nelson Differential regulation of SK and BK channels by Ca2+ signals from Ca2+ channels and ryanodine receptors in guinea-pig urinary bladder myocytes J. Physiol., June 1, 2002; 541(2): 483 - 492. [Abstract] [Full Text] [PDF]
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F. Vogalis, J. R Harvey, and J. B Furness TEA- and apamin-resistant KCa channels in guinea-pig myenteric neurons: slow AHP channels J. Physiol., January 15, 2002; 538(2): 421 - 433. [Abstract] [Full Text] [PDF]
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T. Tabata and M. Kano Heterogeneous Intrinsic Firing Properties of Vertebrate Retinal Ganglion Cells J Neurophysiol, January 1, 2002; 87(1): 30 - 41. [Abstract] [Full Text] [PDF]
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V. G. Shakkottai, I. Regaya, H. Wulff, Z. Fajloun, H. Tomita, M. Fathallah, M. D. Cahalan, J. J. Gargus, J.-M. Sabatier, and K. G. Chandy Design and Characterization of a Highly Selective Peptide Inhibitor of the Small Conductance Calcium-activated K+ Channel, SkCa2 J. Biol. Chem., November 9, 2001; 276(46): 43145 - 43151. [Abstract] [Full Text] [PDF]
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T. R Neelands, P. S Herson, D. Jacobson, J. P Adelman, and J. Maylie Small-conductance calcium-activated potassium currents in mouse hyperexcitable denervated skeletal muscle J. Physiol., October 15, 2001; 536(2): 397 - 407. [Abstract] [Full Text] [PDF]
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J. Wolfart, H. Neuhoff, O. Franz, and J. Roeper Differential Expression of the Small-Conductance, Calcium-Activated Potassium Channel SK3 Is Critical for Pacemaker Control in Dopaminergic Midbrain Neurons J. Neurosci., May 15, 2001; 21(10): 3443 - 3456. [Abstract] [Full Text] [PDF]
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 G. M. Herrera, T. J. Heppner, and M. T. Nelson Voltage dependence of the coupling of Ca2+ sparks to BKCa channels in urinary bladder smooth muscle Am J Physiol Cell Physiol, March 1, 2001; 280(3): C481 - C490. [Abstract] [Full Text] [PDF]
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C. A. Syme, A. C. Gerlach, A. K. Singh, and D. C. Devor Pharmacological activation of cloned intermediate- and small-conductance Ca2+-activated K+ channels Am J Physiol Cell Physiol, March 1, 2000; 278(3): C570 - C581. [Abstract] [Full Text] [PDF]
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J. H. Jaggar, V. A. Porter, W. J. Lederer, and M. T. Nelson Calcium sparks in smooth muscle Am J Physiol Cell Physiol, February 1, 2000; 278(2): C235 - C256. [Abstract] [Full Text] [PDF]
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J. E. Keen, R. Khawaled, D. L. Farrens, T. Neelands, A. Rivard, C. T. Bond, A. Janowsky, B. Fakler, J. P. Adelman, and J. Maylie Domains Responsible for Constitutive and Ca2+-Dependent Interactions between Calmodulin and Small Conductance Ca2+-Activated Potassium Channels J. Neurosci., October 15, 1999; 19(20): 8830 - 8838. [Abstract] [Full Text] [PDF]
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R. Cordoba-Rodriguez, K. A. Moore, J. P. Y. Kao, and D. Weinreich Calcium regulation of a slow post-spike hyperpolarization in vagal afferent neurons PNAS, July 6, 1999; 96(14): 7650 - 7657. [Abstract] [Full Text] [PDF]
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P. Sah and J. D. Clements Photolytic Manipulation of [Ca2+]i Reveals Slow Kinetics of Potassium Channels Underlying the Afterhyperpolarization in Hipppocampal Pyramidal Neurons J. Neurosci., May 15, 1999; 19(10): 3657 - 3664. [Abstract] [Full Text] [PDF]
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C. M. Fanger, S. Ghanshani, N. J. Logsdon, H. Rauer, K. Kalman, J. Zhou, K. Beckingham, K. G. Chandy, M. D. Cahalan, and J. Aiyar Calmodulin Mediates Calcium-dependent Activation of the Intermediate Conductance Channel, IKCa1 J. Biol. Chem., February 26, 1999; 274(9): 5746 - 5754. [Abstract] [Full Text] [PDF]
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P. Pedarzani, J. Mosbacher, A. Rivard, L. A. Cingolani, D. Oliver, M. Stocker, J. P. Adelman, and B. Fakler Control of Electrical Activity in Central Neurons by Modulating the Gating of Small Conductance Ca2+-activated K+ Channels J. Biol. Chem., March 23, 2001; 276(13): 9762 - 9769. [Abstract] [Full Text] [PDF]
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W. J. Joiner, R. Khanna, L. C. Schlichter, and L. K. Kaczmarek Calmodulin Regulates Assembly and Trafficking of SK4/IK1 Ca2+-activated K+ Channels J. Biol. Chem., October 5, 2001; 276(41): 37980 - 37985. [Abstract] [Full Text] [PDF]
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Y. Li and D. R. Halm Secretory modulation of basolateral membrane inwardly rectified K+ channel in guinea pig distal colonic crypts Am J Physiol Cell Physiol, April 1, 2002; 282(4): C719 - C735. [Abstract] [Full Text] [PDF]
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, 
, 1 µM; 
, 0.8 µM) and different types of channel behavior (high and low open probability behavior, see later), but for all patches open probability was essentially voltage independent. The line was drawn for display purposes only and has no physical meaning. (B) Average short and long open times for the patches in A. Data are shown as mean ± SD, and the lines represent the best fit of the data to single exponential functions. (C) Relative amplitude of the short open-time component as a function of voltage shown individually for each patch in A. The line was drawn for display purposes only. Data from each patch are represented by the same symbol in A, C, E, and F. (D) Short and intermediate closed times for the patches in A. Data are shown as mean ± SD and the lines represent the best fit of the data to exponential functions. (E) Long closed times shown for two patches individually and fit to a single exponential (solid lines). In the patch with the highest open probability, too few events were associated with the longest time constant to reliably fit this component. (F) Relative amplitudes of the short (closed symbols) and intermediate (open symbols) closed-time components plotted individually for the patches in A.
tube of 0 and 9.5 µM Ca2+. At a holding potential of –80 mV, Ca2+ was pulsed on and off by rapidly moving the solution interface across the patch pipette tip using a bimorph translator (Morgan Matroc Inc., Bedford, OH) attached to the