Correspondence to: Martin D. Rayner, Director, Békésy Laboratory of Neurobiology, 1993 East-West Rd., University of Hawaii, Honolulu, HI 96822-2359. Fax:808-956-6984 E-mail:martin{at}pbrc.hawaii.edu.
Released online: 17 January 2000
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Abstract |
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Time constants of slow inactivation were investigated in NH2-terminal deleted Shaker potassium channels using macro-patch recordings from Xenopus oocytes. Slow inactivation is voltage insensitive in physiological solutions or in simple experimental solutions such as K+o//K+i or Na+o//K+i. However, when [Na+]i is increased while [K+]i is reduced, voltage sensitivity appears in the slow inactivation rates at positive potentials. In such solutions, the I-V curves show a region of negative slope conductance between ~0 and +60 mV, with strongly increased outward current at more positive voltages, yielding an N-shaped curvature. These changes in peak outward currents are associated with marked changes in the dominant slow inactivation time constant from ~1.5 s at potentials less than approximately +60 mV to ~30 ms at more than +150 mV. Since slow inactivation in Shaker channels is extremely sensitive to the concentrations and species of permeant ions, more rapid entry into slow inactivated state(s) might indicate decreased K+ permeation and increased Na+ permeation at positive potentials. However, the N-shaped I-V curve becomes fully developed before the onset of significant slow inactivation, indicating that this N-shaped I-V does not arise from permeability changes associated with entry into slow inactivated states. Thus, changes in the relative contributions of K+ and Na+ ions to outward currents could arise either: (a) from depletions of [K+]i sufficient to permit increased Na+ permeation, or (b) from voltage-dependent changes in K+ and Na+ permeabilities. Our results rule out the first of these mechanisms. Furthermore, effects of changing [K+]i and [K+]o on ramp I-V waveforms suggest that applied potential directly affects relative permeation by K+ and Na+ ions. Therefore, we conclude that the voltage sensitivity of slow inactivation rates arises indirectly as a result of voltage-dependent changes in the ion occupancy of these channels, and demonstrate that simple barrier models can predict such voltage-dependent changes in relative permeabilities.
Key Words: Xenopus oocyte, patch clamp, selectivity, voltage ramp, reversal potential
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INTRODUCTION |
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Inactivation mechanisms of Shaker potassium channels have been divided into fast (N-type) and slower (C-type) components (
Monovalent cations appear to achieve their modulation of inactivation rates by binding to a site within the selectivity filter (
Nevertheless, it is now clear that C-type inactivation becomes markedly faster in experiments where Na+ replaces K+ as the primary permeating cation (
We conclude that both N-shaped I-V curves and voltage-sensitive slow inactivation rates result from relative increases in Na+ permeation at positive potentials.
Terminology
Recently,
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MATERIALS AND METHODS |
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Channel Expression
Data for this study were obtained using the Shaker 29-4 construct ( in previous papers (
is identical to that of Shaker B from S1 through S6; thus, Shaker channels will be used as a generic descriptor where results are presumed applicable to both Sh
and Shaker B channels. Xenopus laevis oocytes were prepared, injected with mRNA, and incubated at 18°C as previously described (
Electrophysiology
Results reported here were obtained from macropatch recordings ( in standard solutions. The Pulse+PulseFit software package (HEKA Elektronik) was used to control data acquisition. All experiments were carried out at room temperature (2022°C) from holding potentials of -100 or -80 mV. Analysis was performed using PulseFit and PulseTools (HEKA Elektronik) for initial processing of the data, and IgorPro (Wavemetrics) for further analysis and generation of figures. Leak and capacitive transients were either subtracted on-line using a variable -P/n correction (
Voltage ramps were programmed, and both leak and capacitive currents were subtracted online from the resulting data traces, using Pulse+PulseFit software. Recorded data traces were displayed either against time (as in Figure 5 A and 6 A) or against ramp potential (as in Figure 4, Figure 5 B, 6 B, and 7). Since any time displacement of the ramp current trace translates to a voltage displacement in the corresponding I-V plot, accurate delineation of I-V data (including reversal potentials) requires minimization of such errors. For 1-ms ramps, we find that analogue Bessel filters should be set to at least 10 kHz, while the sampling interval should not be >10 µs. Additionally, where nonlinear leak occurs in the control pulses, the entire I-V trace may be offset up- or downwards relative to the zero current axis. Such offsets can also produce substantial errors in Erev measurements. To avoid this problem, leak pulses should be carefully monitored and data should be discarded where excessive leak is noted. (The points noted above can be verified through control experiments using patches exposed to symmetric mono-ionic solutions.)
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Additional errors in Erev can arise from changes in ion concentrations associated with the pulse sequences used to make these measurements. Large initial currents can deplete ion concentrations on one side of the membrane while adding ions to the other side. Such changes may equilibrate within milliseconds or be relatively long lasting, depending on the magnitude and duration of the currents, as well as on the volumes of the diffusion-restricted spaces.
When single patches were exposed to multiple internal or external solutions, solution changes were carried out either (a) by exchange of the entire bath volume, or (b) by positioning the pipette tip in the outlet path of a valve-operated quartz-capillary manifold. Thus, inside-out patches were used to explore effects of internal solutions changes (Figure 7 A), whereas outside-out patches were used when external solution changes were required (Figure 7 B).
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Solutions
In addition to monovalent chloride counter ions, all external solutions contained 1.8 mM Ca2+ and 10 mM HEPES, adjusted to pH 7.2. Internal solutions contained 1.8 mM EGTA and 10 mM HEPES, adjusted to pH 7.2. External solutions used here contained (mM): NFR: 2.5 KCl, 115 NaCl; Na-Ringer: 115 NaCl; K-Ringer: 115 KCl; Tris-Ringer: 115 TrisCl. Internal solutions contained (mM): K-EGTA: 115 KCl; Na-EGTA: 115 NaCl; Tris-EGTA: 115 TrisCl. Appropriate complex solutions were created, as needed, by appropriate mixing of these stock solutions. In the figures, solutions are specified by the concentrations (mM) of monovalent cations: external//internal. Thus, solutions denoted as 115 Na+o//115 K+i, involve Na-Ringer as the external solution and K-EGTA as the internal solution, etc.
Data Analysis and Modeling
Double-exponential analysis of tail current time courses (see Figure 2) was carried out by fitting ionic current traces with the following equation:
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(1) |
where a0 is the predicted steady state current, a1 and a2 are the zero time intercepts of the first and second exponential components, and f and
s are the corresponding time constants for these components. Similarly, time constants for slow inactivation were determined by fitting a single exponential version of this equation to the dominant time constant of the inactivation process.
Ion permeation through a channel described by a one-site two-barrier Eyring model was calculated using a common-domain software program downloaded as described in
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RESULTS |
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Slow inactivation in Shaker potassium channels is less complete at negative potentials than at positive potentials and thus the steady state level of inactivation is voltage dependent. Nevertheless, slow inactivation develops with time constants that appear to be voltage insensitive (
Slow Inactivation Appears Voltage Sensitive at Positive Potentials when both Na+ and K+ Ions Are Present in the Internal Solution
Three representative families of macroscopic currents, obtained from inside-out macro patches in different experimental solutions are shown in Figure 1. Figure 1 A, with 115 mM Na+o and 115 mM K+i (see MATERIALS AND METHODS) shows the voltage-insensitive kinetics characteristic of slow inactivation under relatively physiological conditions. Test pulses were 500 ms in duration and ranged from -60 to +160 mV in 10-mV steps. Interpulse intervals were 5 s in these sequences to minimize cumulative slow inactivation. Similarly, Figure 1 B presents results from an experiment in which the internal potassium has been replaced by 115 mM Na+i. Although the slow inactivation rate is slow in Figure 1 A and very fast in B, no voltage sensitivity is apparent in either case. By contrast, when 10 mM K+ is added to the 115 mM internal Na+ solution (see Figure 1 C) changes in inactivation rate become readily visible at the more positive test potentials.
This surprising finding could be readily explained if the outward currents in Figure 1 C were all carried primarily by K+ ions, as was indicated by the work of
However, ) or in Na+o //Na+i solutions (), despite the ~50-fold difference in the inactivation time constants between these two conditions. By contrast, when both Na+ and K+ ions were present in the internal solution (
), we see that inactivation time constants near 0 mV are similar to the values of Figure 1 A, although at more than +150 mV, inactivation time constants approach closely those seen in B. If PK/PNa changes as a function of potential (as suggested by
Apparent Voltage Sensitivity of Slow Inactivation Rates Appears Correlated with Specific Components of the N-Shaped I-V Waveform
The results presented in Figure 1 suggest that the apparent voltage sensitivity of slow inactivation appears when both Na+ and K+ ions are present in the internal solutions. These same conditions have previously been found to produce the N-shaped I-V waveform (
In Figure 2 A, a, outward currents are shown for step depolarizations from holding potential to test potentials between -60 and -20 mV. These currents show typical features of outward K+ currents through Shaker channels: activation is steeply voltage sensitive, and slow inactivation becomes apparent in the -20- and -30-mV traces. Currents in Figure 2 A, b, correspond to the region of negative slope conductance in the I-V curves (Figure 2 B, -10 to +30 mV). Thus, peak outward current is largest at -10-mV test potential, with the smallest peak current being at +30 mV. In this voltage range, tail current peaks decrease in linear relation to the end-of-trace currents, and slow inactivation rates appear similar to those in Figure 2 A, a. In Figure 2 A, c, currents are relatively small and correspond to the "saddle" region of the I-V curves (Figure 2 B, +40 to +80 mV). However, in this region of the I-V curve, changes in the kinetics of slow inactivation are directly visible in the data traces. Over this range of potentials, the dominant slow inactivation time constant changes from ~500 ms at +40 mV to ~160 ms at +80 mV. Furthermore, the fast tail current peak noticeable in Figure 2 A, a and b, is markedly reduced and a slow component becomes more readily visible (see Figure 2 C, ). Currents in Figure 2 A, d, cover the range from +90- to +130-mV test potential. The peak current increases steeply with test potential, while the inactivation time constant falls from 150 to 55 ms between +90 and +130 mV. The most obvious voltage sensitivity of slow inactivation rates appears at more than +50 mV, while an apparent maximum rate is approached as outward currents increase at positive potentials (see Figure 1 D).
Figure 2 C provides two measures of the extent to which slow inactivation occurs during the isochronal (500-ms) pulses shown here. Open symbols show the ratio of the peak currents to the end-of-trace currents from the Figure 2 B I-V curves and report the fraction of noninactivated channels at the end of the test pulse. Closed symbols were obtained from double-exponential analysis of the tail currents from Figure 2 A (see Equation 1), and show the ratio a2/(a1+a2) where a1 and a2 are the weighting factors for the fast and slow kinetic components (f and
s, respectively) in these tail currents. As shown by
It seems clear that the negative slope conductance section of the I-V curve, corresponding to increased voltage-dependent Na+ block of outward K+ currents (
Although test pulse [K+]i depletion should be correlated with current magnitude, Figure 2 A, c, shows that inactivation rates start to increase in the saddle region of the N-shaped I-V curve, well before peak currents again reach the ~1-nA levels seen at around -20 mV (see Figure 2 A, a and b). Thus, if inactivation is getting faster although currents are still smaller than at their -20-mV level, then internal K+ depletion arising during each individual test pulse cannot explain these changes in inactivation rate. However, cumulative K+ depletion might occur as a result of the preceding sequence of ~1-nA currents, despite the 5-s interpulse intervals used here. Depletion that lasts 5 s or more suggests a larger diffusion-restricted space than seems likely to be present on the continuously perfused internal surface of an inside-out patch. Nevertheless, assuming that this might be the case, the cumulative depletion hypothesis was tested by reversing the pulse order (i.e., starting with a first pulse to +140 mV and working back to less positive potentials). No detectable hysteresis occurred in the N-shaped I-V curve, and essentially identical inactivation rates were obtained at positive potentials using this reversed pulse sequence. We conclude that neither pulse-specific nor cumulative depletion of [K+]i can be the direct cause of the rapid inactivation seen at potentials greater than +50 mV.
Thus, while it was appropriate that
If the apparent voltage sensitivity of slow inactivation in Figure 1 C arises from voltage-dependent changes in PK/PNa, then voltage sensitivity should not appear when either K+ or Na+ is the only cation present in the internal solution. Inactivation time constants change from ~5 s in symmetric 115 mM K+ solutions to ~50 ms in symmetric Na+ solutions. However, the voltage sensitivities of the time constants remain closely similar when evaluated using linear regression of ln (milliseconds) against Vtest (between 0 and approximately +130 mV). Mean slope for solutions containing 115 Na+o//115 Na+i; 115 K+o//115 K+i; 115 Na+o//115 K+i; 115 Tris+o//115 Na+i; and 115 Tris+o + 2.5 Na+o//115 K+i was -0.0016 ± 0.0064 mV-1 (n = 15 experiments). This slope is not significantly different from zero, indicating that slow inactivation remains voltage insensitive, even at very positive potentials in these simple solutions. Nevertheless, the time constant seen in Na+o//Na+i solutions at +160 mV (31.1 ± 2.9 ms, n = 3) is significantly slower than in Tris+o//Na+i at the same potential (4.4 ± 1.3 ms, n = 3), suggesting that external Na+ ions make an additional contribution to loading of the regulatory site.
If the apparent voltage sensitivity of slow inactivation arises from voltage-sensitive changes in PK/PNa, then inactivation will appear voltage sensitive when internal solutions contain significant quantities of both Na+ and K+ ions. To evaluate this prediction, internal solutions containing 10 mM K+i plus either 115 Na+i or 58 mM Na+i (Tris substituted) were used, yielding the general result that all "mixed" internal solutions (containing both Na+ and K+ ions) produced voltage-sensitive inactivation rates. However, small but significant differences were noted as a result of the external solutions used. These were either "simple" (115 mM Na+o or Tris+o) or mixed (containing Na+o or Tris+o, plus 2.510 mM of added K+o). The mean slope for simple external solutions was -0.0200 ± 0.0034 mV-1 (n = 7), which is equivalent to -50 mV per e-fold change. However, for mixed external solutions, the mean slope increased to -0.0303 ± 0.0029 mV-1 (n = 9), which is equivalent to -33 mV per e-fold change. By unpaired, two-tailed t test, both slopes were significantly different from zero (P < 0.0001). Furthermore, the difference between the slopes obtained in the presence and absence of mixed external solutions was also extremely significant (P < 0.0001). These findings support the hypothesis that PK/PNa changes as a function of voltage, although the additional effect of mixed Na+ + K+ external solutions suggests a continuing regulatory effect of external ion concentrations even during outward currents.
If Shaker channels permit Na+ ions to permeate more readily than K+ ions at very positive potentials, then inactivation rates seen at +160 mV should be relatively insensitive to the addition of internal K+ ions. When the time constant in Na+o//Na+i (31.1 ± 2.9 ms, n = 3,) is compared with that seen in Na+o//Na+i + 10 mM K+i (31.7 ± 18.9 ms, n = 14), no significant effect of internal K+ is noted. Similarly, this lack of effect of internal K+ persists at very positive potentials, even when Na+i is reduced first to 58 mM (31.0 ± 6.8 ms, n = 3), and then to 29 mM (30.8 ± 3.1 ms, n = 2). Apparently, adding 10 mM K+i does not permit internal K+ ions to reach the regulatory site to any significant extent at +160 mV, when as little as 29 mM Na+ is present in the internal solution. Given previous conclusions that the regulatory site lies within the permeation path (
Although the evidence presented above is indirect, this substantial series of observations suggests that the apparent voltage sensitivity of slow inactivation arises from changes in relative permeabilities for Na+ versus K+ ions, such that Na+ ions become increasingly likely to permeate Shaker channels at positive potentials and displace K+ ions from the inactivation-regulating site. We provide below additional evidence to support the concept that Na+ ions can permeate Shaker channels at very positive potentials, while also addressing the mechanisms that might underlie such voltage sensitive changes in PK/PNa.
Although our first test of the [K+]i depletion hypothesis (see above) shows that [K+]i depletion is not the cause of the changes in slow inactivation rates seen here, it is clear that [K+]i depletion permits Na+ permeation even at negative potentials in some potassium channels (
Outward Na+ Currents Increase Nonlinearly at Positive Potentials
To conclude that Na+ permeation increases at positive potentials would require either that [K+]i becomes rapidly depleted, or that Shaker channels are capable of passing significant outward Na+ currents at these potentials in the presence of internal K+ ions, despite the previously described block of Na+ tail currents by internal K+ ions at negative potentials (
For the solutions used in Figure 3 A, all outward currents must be carried by Na+ ions. Small inward currents are seen at negative potentials. However, at test potentials larger than +80 mV, outward Na+ current increases in a markedly nonlinear manner, reaching >2 nA at +140 mV. Clearly, large outward Na+ currents can occur at test potentials larger than +100 mV. Even after slow inactivation, the steady state outward Na+ current remains ~1 nA at +140 mV (); that is, at 43% of peak current magnitude. Slow inactivation in this +140-mV trace was well fitted by a single time constant of 37.5 ms, which seems reasonably comparable to the mean time constant of 31.1 ± 2.9 ms seen at +160 mV (see above).
In Figure 3 B (from a different patch), we show the effect of adding 10 mM internal K+, while retaining 2.5 mM external K+. The reversal potential is here approximately -35 mV, indicating that PK/PNa is ~400 and, hence, that Na+ permeation must be negligible at negative potentials, as shown in previous studies. The peak outward current maximum for the N-shaped I-V curve is shifted from -10 mV in Figure 2 B to +10 mV in Figure 3 B, with a zone of negative slope conductance between +10 and +60 mV leading to steeply increasing outward currents at more positive potentials. These outward currents increase in the same potential range as the outward Na+ currents seen in Figure 3 A. Similarly, the slow inactivation time constant is 74 ms at +140 mV in this record, as would be expected if Na+ was the primary, although not the only, determiner of inactivation rate under these conditions. Note also that the steady state outward current in inactivated channels is markedly suppressed by internal K+ ions, falling to 11% of peak current after 500 ms at +140 mV.
Fast Voltage Ramps Can Be Used for Evaluation of "Instantaneous" I-V Curves
In contrast to the indirect evidence offered above, relatively direct evidence as to the nature of the ions permeating at different potentials should be obtainable from comparisons of instantaneous I-V curves from the same patch in solutions of different ionic content. Unfortunately, the standard tail current method for evaluation of instantaneous I-V curves requires a series of pulses separated by intervals sufficient to permit full recovery from any slow inactivation that may have occurred. A faster method for recording instantaneous I-V curves would permit more complete data sets to be obtained from single patches, before significant channel rundown. We have therefore explored the use of fast (1-ms) voltage ramps for evaluation of instantaneous I-V curves.
Data shown in Figure 4A and Figure B, were obtained using both the fast ramp and standard tail current protocols from the same outside-out patch, following 10-ms prepulses to +40 mV. These prepulses were then followed either by a 1-ms descending ramp to a return potential of -100 mV, or by steps to different return potentials (see Figure 4 A) for conventional instantaneous I-V analysis. Data traces are shown in Figure 4 A. Figure 4 B shows the current recorded during the 1-ms ramp (continuous curve) plotted against the ramp potential, thus tracing out an instantaneous I-V plot. Such curves start from the end-of-trace current value reached after 10 ms at test potential (+40 mV), and finish at -100 mV return potential. For comparison, data points from analysis of tail current records (Figure 4 B, ) are also shown in these plots. The close correspondence seen here between the two methods suggests that the results obtained using fast ramps can be viewed with reasonable confidence.
The results presented in Figure 4C and Figure D, address an equivalent issue: the degree of correspondence between N-shaped I-V curves as seen in fast ramps and the N-shaped I-V curves demonstrated from test-pulse currents (see Figure 1 Figure 2 Figure 3). Data were recorded from an inside-out patch exposed to 115 mM Na+o//115 mM Na+i + 10 mM K+i while using 5-ms test pulses ranging from -60 to +150 mV. As shown in the pulse diagram of Figure 4 C, each test pulse was followed by a voltage ramp from test potential to -100 mV. Original data traces are shown in Figure 4 C; in Figure 4 D, data points () obtained from peak currents at test potential are compared with the ramp I-V from the most depolarized voltage step (continuous curve). In both cases, an N-shaped I-V is apparent, and satisfactory correspondence is demonstrated between the results of these methods at positive test potentials. At negative test potentials, the curves necessarily diverge, since test-pulse currents are limited by incomplete channel activation. Thus, a current maximum occurs at 0 mV in the test pulse I-V, but at approximately -40 mV in the ramp I-V.
These results provide additional evidence against [K+]i depletion being the mechanism that permits outward Na+ currents to occur at very positive potentials. That hypothesis requires the persistence of substantial [K+]i depletion between positive pulses 5-s apart, so as to bring about cumulative depletion of [K+]i during a sequence of 5-ms test pulses. However, as shown in Figure 4 D, the last pulse in the depolarizing sequence is followed by a downward ramp in which the observed current accurately reproduces the N-shaped I-V curve. If [K+]i falls sufficiently during the test-pulse sequence to permit outward Na+ currents to occur at more than +60 mV, it seems highly improbable that [K+]i could recover sufficiently to support outward K+ currents of approximately normal magnitude at 0 mV during the course of a 1-ms downward ramp from +150 mV. Thus, although it is clear that outward K+ currents will produce both transitory increases in [K+]o and decreases in [K+]i, these effects are neither large enough nor long lasting enough to be the primary cause of either the N-shaped I-V or its associated changes in slow inactivation rates.
Ramp I-V Curves from Noninactivated and Slow Inactivated Channels
As noted above, the hypothesis that voltage-dependent changes in relative Na+ and K+ permeation underlie the N-shaped I-V relationship should be addressable from detailed studies of I-V waveforms after changes in internal and external ion concentrations. However, slow inactivation alters channel selectivity (see
Effects of prepulse duration on ramp I-V waveforms were studied at two different test potentials, +40 mV (Figure 5) and +160 mV (Figure 6). The +40 mV test potential was chosen to represent the low point of the saddle in the N-shaped curve that would correspond, potentially, to the region of maximum Na+ block. By contrast, at +160 mV, Na+ block might well have been substantially relieved. Since both data sets were obtained from the same patch, similar quantitative estimates for the peak current at approximately -40 mV would indicate the equivalence of instantaneous conductance curves reached from these potentially dissimilar initial conditions. Furthermore, since slow inactivation rates are also quite different at these two potentials, we reasoned that the extent of this mechanism's involvement in the N-shaped I-V curve would also be readily apparent from such data.
Figure 5 A (left) shows superimposed data traces for 5-, 15-, and 45-ms test pulses (end-current levels for 165- and 600-ms pulses are indicated by dotted lines on this plot). Figure 5 A (right) shows the ramp current sections of these traces, superimposed, and on an expanded time base that is aligned with a schematic presentation of the voltage ramp. Figure 5 B shows the same currents plotted against ramp voltage. It is now clear that the artifact-like "spikes" in Figure 5 A resulted from the maximum current occurring in the negative region of the ramp I-V curve. Just as in Figure 4 D, this maximum occurs at approximately -40 mV. Also, Figure 5 B (left) shows suppression of these maximum currents in approximate proportion to the suppression of the end currents by slow inactivation. Figure 5 B (right) shows an expanded region of the ramp I-V traces. In the 5- and 15-ms traces, Erev shifts to the right (from -99 to -90 mV), and further right shifting occurs after 45 ms (to -83 mV), 165 ms (to -80 mV), and 600 ms (to -76 mV). Since these shifts do not seem to be proportionate to the small amount of slow inactivation shown from end-current reduction, they may be caused, in part, by extracellular K+ accumulation. In support of this interpretation, we note that peak tail currents increase (Figure 5 A) with prepulse duration, rather than decreasing, as would be expected from inactivation alone. Only after the longest prepulses (at +40 mV) will Erev be substantially affected by the accumulation of slow inactivated channels. This issue is further addressed in reference to Figure 6.
At +160 mV (Figure 6 A), inactivation is fast and appears nearly complete in 45 ms, while steady state outward current is suppressed by 10 mM internal K+ (compare Figure 3A and Figure B). Superimposed ramp currents obtained from these traces are plotted against time in Figure 6 A, and against ramp potential in Figure 6 B. Note that the -40-mV maximum current for the 5-ms test pulse is here quantitatively identical to maximum current for the 5-ms trace in Figure 5 B. However, this current becomes progressively reduced, while Erev shifts markedly to the right, as slow inactivation develops at the longer test-pulse durations. After a 5-ms test pulse, Erev is -92 mV, shifting to -82 mV after 15 ms. Erev then shifts further to -50 mV after 45 ms, and to -17 mV after 600 ms. Thus, the patch appears to be strongly K+ selective at -92 mV after a 5-ms pulse, where PK/PNa is >400. By contrast, after a 600-ms pulse, Erev moves far in the direction of the 0-mV reversal potential predicted for symmetric Na+ solutions and PK/PNa falls to 11, demonstrating the relative increase in PNa that coincides with the development of slow inactivation. Note that Erev shifts to the right in Figure 6 A, coincident with a reduction in peak tail current magnitude, indicating that this shift results from inactivation rather than accumulation of extracellular K+ ions (as in Figure 5 A).
It may seem surprising that Erev does not reach zero after the 600-ms pulse in these solutions with symmetrical internal and external Na+ concentrations, since slow inactivation might be expected to be fully equilibrated by this time. However, we find that peak outward currents are reduced at least 50-fold by this Na+i plus K+i internal solution, while outward Na+ currents through inactivated channels are reduced at least 10-fold by the internal K+ ions. Additionally, even though internal Na+ ions also block outward K+ currents, this block is smaller at negative potentials. Thus, the PK of a noninactivated Shaker channel could be as much as two orders of magnitude greater than the PNa of a slow inactivated Shaker channel in these solutions. Thus, even where slow inactivated states are strongly absorbing, a small number of noninactivated channels at negative potentials make a disproportionate contribution to the overall PK/PNa ratio.
The ramp I-V data of Figure 5 and Figure 6 clarify that N-shaped I-V curves are fully developed after the 5-ms test pulse, before any substantial slow inactivation has occurred. As slow inactivation develops in longer test pulses, these curves show reduced K+ permeation associated with a marked reduction in the maximum current at -40 mV. These effects appear after test pulses to both +40 and +160 mV (although at very different rates), and appear irreversible within the time course of any given ramp. By contrast, the phenomena that underlie the N-shaped I-V curve are apparently instantaneous since the changes in outward current magnitude can be accurately regenerated, without noticeable hysteresis, during the course of a 1-ms ramp.
We conclude that changes in slow inactivation rate cannot be the cause of the N-shaped I-V curve. Rather, it appears that changes in both slow inactivation rate and I-V waveform may result from voltage-dependent changes in the permeation properties of noninactivated channels. Furthermore, the quantitative equivalence of the 5-ms ramps in Figure 5 and Figure 6 indicate that the initial conditions at +40 and +160 mV are not sufficiently different to affect ramp waveforms. There is, therefore, no evidence to support differences in [K+]i as making significant contributions to the initial conditions faced by Shaker channels at these two potentials. By contrast, at +40 mV, we see increasing tail current peaks suggestive of accumulation of [K+]o, whereas no such change in tail current peaks appears after pulses to +160 mV. This evidence additionally supports the primary hypothesis presented here, that PK falls relative to PNa at positive potentials.
Ramp I-V Curves in Noninactivated Channels: Effects of Changing Ion Concentrations
In this section, we address whether different components of the ramp I-V curve are differentially affected by varying internal and external K+ concentrations. Our results support the general conclusion that Na+ permeation increases at positive potentials. When 115 mM Na+i competes against 10 mM K+i, the currents behave as if they are carried primarily by K+ ions at negative potentials, but by Na+ ions at potentials greater than +100 mV. However, we would presume that K+ ions become increasingly effective competitors even at positive potentials as [K+]i is increased beyond 10 mM and [Na+]i is reduced, although this point is not addressed in the experiments presented here.
We recognize that changes [K+]i and [K+]o will affect ramp I-V curves, in part through changes in K+ driving force. Thus, it might be expected that these data should be replotted as G-V curves to eliminate such driving force effects. Even where the relative contributions of Na+ and K+ ions to the observed currents are not clear, each I-V curve indicates a reversal potential, and Gtotal (i.e., the sum of GNa + GK) could be calculated as Itotal /(V - Erev). Unfortunately, such calculations could be highly misleading if the PK/PNa ratio and, therefore, the relevant Erev are suspected of changing as functions of test potential.
Changing intracellular K+ concentrations.
The effects of changing internal K+ concentrations are examined in Figure 7 A, using 5-ms test pulses where ramp I-V curves report the behavior of noninactivated channels. Note that [K+]i is indicated for each of the traces in Figure 7 A and that all traces were obtained from the same inside-out patch. When [K+]i is varied in the presence of constant 115 mM [Na+]i and [Na+]o, outward current at negative potentials is eliminated by reducing [K+]i to zero. When [K+]i is increased to 5 mM, the reversal potential shifts to -60 mV, yielding a PK/PNa ratio of ~220 using the Goldman-Hodgkin-Katz (GHK)1 formalism. Outward K+ currents are small at negative potentials, as would be expected from previous data describing Na+ block of these currents (
Changing extracellular K+ concentrations. Figure 7 B shows a series of ramp traces obtained from the same outside-out patch. Here the K+ concentrations indicated in the figure refer to [K+]o values. Thus, the N-shaped I-V curve associated with the 0 K+ trace was obtained in the same solutions as were used for Figure 5 and Figure 6. When [K+]o is varied against a background of constant internal and external Na+ concentrations, the findings at negative potentials confirm that currents in this range respond as if they are carried primarily by K+ ions. At positive potentials, increasing [K+]o reduces outward currents at +150 mV and right shifts the K+ current peak by about +60 mV (from -40 mV in 0 mM [K+]o to +20 mV in 10 mM [K+]o). Again, however, the marked effects of changing [K+]o on inward currents contrast with the relatively small effects of [K+]o on outward currents.
Effects of ion concentrations on reversal potentials. Although reversal potentials measured in ramp I-V curves may be distorted when large outward currents cause K+ ion accumulation in the pipette, reversal potentials in 115 Na+o//115 Na+i + 10 K+i solutions range from -85 to -105 mV, indicating a strongly K+-selective channel at these very negative potentials. However, reduction of internal K+ (Figure 7 A) from 10 to 5 mM shifts Erev to -50 mV, rather than to approximately -75 mV, as would have been expected if PK/PNa had remained unchanged.
Permeability ratios were calculated (data not shown) from a range of positive reversal potentials using outside-out patches and symmetrical Na+ solutions with 2.5, 5, or 10 mM K+ added only to the external solution. These solutions yielded reversal potentials of +18.3 ± 2.9, +34.7 ± 4.0, and +47.7 ± 6.8 mV, respectively, for three patches exposed to each solution. These reversal potentials imply a marked change away from the K+-selective behavior expected for a Shaker channel.
Ramp I-V Curves in Slow Inactivated Channels
In contrast to the complex results described above, slow inactivated Shaker channels appear effectively impermeant to K+ ions at all potentials, although they retain partial Na+ permeability. Thus, the ramp I-V curve for slow inactivated channels shown in Figure 6 B is remarkably linear with no significant deviation at either positive or negative potentials. Apparently, there is little increase in PNa even at very positive potentials in these slow inactivated channels, although it remains possible that such an effect does occur but is balanced by an increasingly effective K+ block of outward Na+ currents at more than +80 mV.
Is the N-Shaped I-V Caused by a Conformational Change?
The results presented above indicate that the N-shaped I-V curve results from changes in the relative K+ and Na+ permeabilities of noninactivated Shaker channels. Recent work by
Alternatively, voltage-dependent changes in relative permeabilities may result from the inherently constant properties of a single conformational state. This possibility will be evaluated further in the DISCUSSION.
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DISCUSSION |
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The present study was undertaken to address the mechanism by which internal and external solutions induce voltage-sensitive slow inactivation rates. Since
The principal results of this study demonstrate several things. (a) Slow inactivation rates in Shaker channels remain voltage insensitive under conditions in which there is no significant competition for permeation between K+ and Na+ ions (see Figure 1A and Figure B). Thus, in Na+o//K+i solutions, or in Na+o//Na+i and K+o//K+i solutions, or with Tris+ externally and either ion internally, slow inactivation remains voltage insensitive. (b) Even where internal solutions are used that contain both Na+ and K+ ions, slow inactivation rates do not show significant voltage sensitivity at "physiological" potentials (i.e., at test potentials less than +50 mV; see Figure 2 A, a and b). In this voltage range, the principal effect of increased [Na+]i is to reduce outward K+ currents, as has been shown for delayed rectifiers (
That permeant ion species can be profoundly important in determining slow inactivation rates has been noted by
The conclusions reached here fit well into such a general model, except that previous work has provided little reason to suppose that noninactivated Shaker K+ channels might become relatively Na+ selective at very positive potentials (but see
The present study provides a substantial amount of direct evidence linking changes in inactivation rate with the changes in slope of the N-shaped I-V curve. And this is complemented by indirect evidence suggesting that the changes in inactivation rate are related to changes in relative permeation by Na+ and K+ ions. We show that slow inactivation is voltage insensitive in simple solutions containing only one permeant ion on each side of the membrane. However, slow inactivation becomes voltage sensitive when predicted differences in the contributions of Na+ and K+ ions to outward currents might be approximately compensated by their relative concentrations. In other words, where competition for permeation might be expected to be maximal. Under these conditions, K+ ions gain the advantage at negative potentials, whereas Na+ ions seem to become the primary permeators at very positive potentials.
The ionic determinants of the N-shaped I-V curve should be addressable experimentally through evaluating the effects of different ionic solutions on ramp I-V waveforms. Figure 7 A shows a simple, though nonlinear, I-V curve in Na+o//Na+i solution and evaluates the effects of addition of internal K+ ions. Outward currents at negative potentials appear in 5 mM K+ and become well developed when [K+]i is increased to 10 mM. By contrast, outward currents at more than +50 mV are reduced rather than increased by these low internal K+ concentrations. Similarly, Figure 7 B shows that increasing external K+ concentration generates large inward currents at negative potentials while decreasing outward currents at positive potentials. These results seem to confirm the hypothesis that Shaker channels become relatively Na+ permeable at very positive potentials, although the resulting outward Na+ currents can be reduced by competition from K+ ions. This conclusion is consistent with the finding that slow inactivation time constants at +160 mV were statistically indistinguishable when measured in Na+o//Na+i solution, or after the addition of 10 mM K+ to the internal medium (see also Figure 1 D). Thus, the sum of our experimental evidence supports the interpretation that PK/PNa continues to change in favor of increased Na+ permeation at potentials greater than +50 mV.
Put simply, voltage-dependent Na+ block of outward K+ currents seems likely to involve entry of Na+ ions as far as some blocking site within the transmembrane field. Once this site is reached, a blocking ion could exit by travelling back against the applied field; alternatively, a Na+ ion can pass through the channel down the applied field, to exit on the outer side of the membrane. The more positive the applied potential, the more Na+ ions cross the membrane and the greater the outward Na+ current. If the probability of entry into the high field-strength region of the channel is controlled by ion-selective "filters" with voltage-dependent properties, then such a system should show the overall behavior seen here. What is not yet clear is whether the apparent voltage sensitivity of the filters results from a rapid voltage-dependent conformational change, or whether this might result from the direct effects of voltage on a continuously variable filter. This second possibility is discussed below.
The Voltage Dependence of the PK/PNa Ratio
Selectivity is usually determined from reversal potentials measured under biionic conditions, following an approach derived from GHK equations (see
The challenging nature of our principal conclusion, that relative permeabilities for Na+ and K+ ions in Shaker potassium channels may change substantially as a function of applied voltage, stimulated a search for simple models that could address the potential reasonability of this concept. One possibility would be a voltage-dependent conformational transition by which the selectivity filter would change from a primary, K+-selective, conformation favored at negative potentials to an alternative conformation, permitting increased Na+ permeation, at positive potentials. Our present data cannot rule out that model, although they suggest that such transitions, if present, must be very rapid.
On the other hand, interactions occurring between a permeating ion and the channel wall may be sufficient, by themselves, to produce voltage-dependent changes in apparent selectivity. Despite the appeal of the Poisson-Nernst-Planck model used by
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Models for ion permeation based on Eyring kinetic formulations must be carefully constrained if they are to generate constant permeability ratios across the experimental voltage range and conform to GHK equations (see
When this model is modified by lowering the height of the external barrier for Na+ ions, Na+ block of K+ efflux at positive potentials is decreased (not shown), thus increasing the total outward current at these potentials. As pointed out by
In overview, this paper has described a complex interaction between voltage- and state-dependent (i.e., slow inactivation related) changes in relative Na+ and K+ permeabilities. We demonstrate that the apparent voltage sensitivity of slow inactivation in outward currents occurs only when two different ion species might be expected to compete for passage via the permeation path to reach a relatively externally located regulatory site controlling slow inactivation rates. Our findings support the interpretation that the PK/PNa ratio would reach fractional levels at very positive potentials (as suggested by the simulations of Figure 8 D). At these high potentials, the residency time of K+ ions at the regulatory site should be much reduced compared with Na+ ion residencies, and entry into slow inactivated states would be consequently facilitated.
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Footnotes |
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1 Abbreviation used in this paper: GHK, Goldman-Hodgkin-Katz.
Portions of this work were previously published in abstract form (Rayner, M.D., J.G. Starkus, and S.H. Heinemann. 1999. Biophys. J. 76:A412).
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Acknowledgements |
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We thank R.S. Eisenberg for many stimulating discussions during the course of this work. Additionally, Karyn Karp and Mark Henteleff provided technical assistance on this project.
J.G. Starkus and M.D. Rayner have been supported in part by National Institutes of Health grant RO1-NS21151 (to J.G. Starkus), as well as by grants from the American Heart Association (Hawaii Affiliate). J.G. Starkus received additional support from Pacific Biomedical Research Center Bridging Funds, and from the Max Planck Society. S.H. Heinemann was supported by the Max Planck Society. M.D. Rayner received additional support from the Queen Emma Foundation.
Submitted: 29 March 1999
Revised: 9 December 1999
Accepted: 10 December 1999
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References |
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