From the Department of Pharmacology and Physiology, University of Rochester Medical Center, Rochester, New York 14642
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ABSTRACT |
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We measured unidirectional K+ in- and efflux through an inward rectifier K channel (IRK1) expressed in Xenopus oocytes. The ratio of these unidirectional fluxes differed significantly from expectations based
on independent ion movement. In an extracellular solution with a K+ concentration of 25 mM, the data were described by a Ussing flux-ratio exponent, n', of ~2.2 and was constant over a voltage range from 50 to
25 mV.
This result indicates that the pore of IRK1 channels may be simultaneously occupied by at least three ions. The
IRK1 n' value of 2.2 is significantly smaller than the value of 3.5 obtained for Shaker K channels under identical
conditions. To determine if other permeation properties that reflect multi-ion behavior differed between these
two channel types, we measured the conductance (at 0 mV) of single IRK1 channels as a function of symmetrical
K+ concentration. The conductance could be fit by a saturating hyperbola with a half-saturation K+ activity of 40 mM, substantially less than the reported value of 300 mM for Shaker K channels. We investigated the ability of simple permeation models based on absolute reaction rate theory to simulate IRK1 current-voltage, conductance,
and flux-ratio data. Certain classes of four-barrier, three-site permeation models are inconsistent with the data, but
models with high lateral barriers and a deep central well were able to account for the flux-ratio and single channel
data. We conclude that while the pore in IRK1 and Shaker channels share important similarities, including K+ selectivity and multi-ion occupancy, they differ in other properties, including the sensitivity of pore conductance to
K+ concentration, and may differ in the number of K+ ions that can simultaneously occupy the pore: IRK1 channels may contain three ions, but the pore in Shaker channels can accommodate four or more ions.
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INTRODUCTION |
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The permeation properties of K channels are quite
complex and are not consistent with the independent
movement of ions through simple aqueous pores.
Rather, these complex properties suggest that the
channel pore may simultaneously be occupied by several ions. Some of the properties of ion channels that
are consistent with multi-ion pore occupancy include:
(a) an apparent concentration-dependent ion selectivity, (b) a voltage sensitivity of pore block by ions that depends on the concentration of the permeant ion or the
blocking ion (or both), (c) pore current (or conductance or permeability ratio) that is a nonmonotonic
function of the mole fraction of two types of ions (the
so-called "anomalous mole-fraction effect"), and (d)
deviations from the Ussing (1949) flux ratio test for independent ion movement.
This latter test, as applied by Hodgkin and Keynes
(1955), relies on a modified form of the Ussing flux ratio test for independent ion movement:
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(1) |
where me and mi are unidirectional K+ efflux and influx, respectively, [K]i and [K]o are the intracellular and extracellular K+ concentrations, Vm is the membrane voltage, and R, T, and F have their usual thermodynamic meanings. The flux-ratio exponent, n', is 1 for a pore in which ion movements are independent; that is, a pore that never contains more than a single ion.
The flux-ratio test has been applied to several types of
K channels in native cells, including delayed rectifier
channels in cephalopod axons (Hodgkin and Keynes,
1955; Begenisich and De Weer, 1980
), the Ca2+-activated K channel in erythrocytes (Vestergaard-Bogind
et al., 1985
), and the inward rectifier K channel in skeletal muscle (Horowicz et al., 1968
; Spalding et al.,
1981
). In all these cases, the flux-ratio exponent was
found to be significantly >1.0, demonstrating the
multi-ion nature of these types of channels.
We recently determined the flux-ratio exponent for
cloned Shaker K channels expressed in Xenopus oocytes
(Stampe and Begenisich, 1996). We found a value of
~3.5 at
30 mV, which is essentially the same as that
from native squid axon K channels (Begenisich and De
Weer, 1980
). The largest n' value for native inward-rectifier K channels is ~2 (Horowicz et al., 1968
; Spalding
et al., 1981
), considerably less than the values for native
and expressed voltage-gated K channels.
To determine if these different n' values for voltage-gated and inward-rectifier K (IRK1)1 channels represent fundamental differences in the permeation properties of these two types of channels or result from
methodological differences, we determined flux-ratio
exponents for IRK1 channels with conditions identical
to those used for Shaker K channels (Stampe and Begenisich, 1996). We found a constant n' value near 2.2 over the potential range from
25 to
50 mV, which is
significantly smaller than the Shaker value of ~3.5.
To determine if other permeation properties that reflect multi-ion behavior differed between these two
channel types, we measured the conductance (at 0 mV)
of single IRK1 channels as a function of symmetrical K+
concentration. The conductance could be fit by a saturating hyperbola with a half-saturation K+ activity of 40 mM, generally similar to that observed for the weak inward rectifier channel ROMK1 (Lu and MacKinnon,
1994), but substantially less than the reported value of
300 mM for Shaker K channels (Heginbotham and
MacKinnon, 1993
). We found that a simple four-barrier, three-site permeation model can account for the
IRK1 flux ratio, as well as the single channel current-
voltage and conductance data.
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METHODS |
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Oocyte Preparation
Stage V and VI Xenopus oocytes were isolated by methods similar
to those described by Goldin (1992). Oocytes were manually defolliculated after a 90-min incubation in 2 mg/ml collagenase Type 1A (Sigma Chemical Co., St. Louis, MO) in Ca-free OR-2 solution (82.5 mM NaCl, 2.5 mM KCl, 1 mM MgCl, and 5 mM
HEPES, pH 7.6 with NaOH) and maintained at 18°C in ND-96
(96 mM NaCl, 2 mM KCl, 1.8 mM CaCl, 1 mM MgCl, 5 mM
HEPES, and 2.5 mM Na-pyruvate, pH 7.6 with NaOH). Oocytes
were injected with mRNA transcribed (T3 mMessage mMachine;
Ambion Inc., Austin, TX) from IRK1 (Kir2.1) channel cDNA
(Kubo et al., 1993
), subcloned into a modified pBluescript vector
containing the 5' and 3' untranslated regions of the Xenopus globin gene. Oocytes used for unidirectional flux measurements were injected with 0.5 to 1.5 ng of mRNA. Oocytes used for single channel current measurements were injected with 0.16 to 0.5 ng of mRNA. The vitelline membrane was removed before patch
clamp recordings.
Two-Microelectrode Voltage Clamp
The experiments in which we measured unidirectional fluxes
were done with a custom two-microelectrode voltage clamp system (see Stampe and Begenisich, 1996, 1998
for additional details). The clamp design included a high output voltage (±150 V)
amplifier and provision for series resistance compensation. As a
result of the inward rectification properties of IRK1 channels, uncompensated series resistance errors were negligible at the more
depolarized potentials used in this study (
25 and
30 mV) and
<1 mV at the most negative potential (
50 mV). To minimize
electrical coupling between the two microelectrodes, the current-passing electrode was coated with a (grounded) conducting
paint layer and a second insulating coating. Both electrodes were
filled with 3 M KCl and had resistances typically between 0.3 and
0.5 M
. The ionic currents are shown (see Fig. 1) without correction for leak or capacity currents. All measurements were made
at room temperature (22-24°C).
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Single Channel Measurements
We measured single IRK1 channel currents from inside-out
patches excised from oocytes 3-5 d after mRNA injection. These
currents were obtained with an Axopatch 1D amplifier (Axon Instruments, Foster City, CA). Patch electrodes (typically 5-12 M)
were pulled from Corning 7052 glass and coated with Sylgard
(Dow Corning Corp., Indianapolis, IN). Patches selected for
analysis exhibited inward but not outward currents before excision, consistent with IRK1 channel properties (Kubo et al., 1993
).
To minimize inhibition of outward current by any residual
polyamines (Ficker et al., 1994
; Lopatin et al., 1994
), voltage
steps to positive potentials were made from a negative voltage
(usually
80 mV). At K concentrations >200 mM, we observed a
fast "flickery" channel (which was also present in uninjected oocytes), but these were readily distinguished from IRK1 channels
by their very different kinetic properties. The recordings were
made at room temperature (22-24°C).
Solutions
The external (bath) solution used for the unidirectional flux measurements consisted of (mM): 25 KCl, 75 NaCl, 5 MgCl2, 10 HEPES, pH 7.4. The 42K (2 mCi/mM) was obtained from the Research Reactor Facility at the University of Missouri (Columbia, MO).
The external (pipette) solution for single channel measurements consisted of (mM): 1 MgCl2, 0.3 CaCl2, 10 HEPES, pH 7.1, and 50, 100, 200, 300, or 400 KCl. The internal solution consisted of (mM): 5 EGTA, 5 EDTA, 10 HEPES, pH 7.4, and 50, 100, 200, 300, or 400 KCl. We also recorded single channel currents in similar 25 mM K solutions but with 75 mM N-methyl-D-glucamine.
Some single channel currents measurements were done in Cl-free solutions with methanesulfonic acid as the replacement anion. We were unable to obtain single IRK1 channel activity at K
concentrations >400 mM due to a decreased probability of seal
formation and the lack of active channels in those patches with
good seals (Heginbotham and MacKinnon, 1993).
Unidirectional Fluxes and the Flux-Ratio Exponent
The flux-ratio exponent, n', was computed from a rearranged form of Eq. 1:
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(2) |
The determination of n' from Eq. 2 requires values for both unidirectional influx and efflux. As in previous work, we did not measure both fluxes from the same oocyte. Rather, we measured one unidirectional flux and the time integral of ion current (net flux), and computed the remaining unidirectional flux through the following equation:
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(3) |
These are called the efflux and influx methods (Begenisich and
De Weer, 1980; Stampe and Begenisich, 1996
) according to the unidirectional flux that is directly measured. The unidirectional fluxes were obtained from gamma counting (Gamma 4000; Beckman Instruments, Inc., Brea, CA) of trace amounts of 42K.
For measurements of unidirectional influx, the oocyte was
placed in a low (75 µl) volume chamber and voltage clamped in
the external solution without radiotracer. We used a holding potential (+20 mV) at which most of the IRK1 channels are
blocked by internal polyamines and Mg2+ ions (Ficker et al.,
1994; Lopatin et al., 1994
; Yang et al., 1995
). The oocyte was allowed a period of time to recover from the electrode impalements. A radiolabeled solution was then introduced into the
chamber and for 4 min the membrane potential was stepped (for
300 ms at 1 Hz) to
25,
30, or
50 mV. The oocyte was then rapidly and extensively washed with the external solution without radiotracer with the membrane voltage maintained at +20 mV.
The oocyte was then unclamped, the electrodes removed, and
the amount of 42K in the oocyte was determined.
To determine the amount of 42K radioactivity not associated
with influx through IRK1 channels, we measured 42K influx in (a)
oocytes injected with IRK1 RNA and maintained only at the +20
mV holding potential for 4-6 min, (b) oocytes not injected with
RNA but subjected to the same voltage protocol as injected cells,
and (c) uninjected oocytes maintained at the +20-mV holding
potential but without pulsing. As with similar experiments with
Shaker K channels (Stampe and Begenisich, 1996), there were no
significant differences among these three groups of oocytes and
the computed influx was linearly related to the K-specific activity. This relationship was then used to correct each influx experiment for the amount of radioactivity not associated with influx
through IRK1 channels.
For the efflux method, the oocytes were loaded with 42K by
soaking them for 8-12 h in a high specific activity solution. After a thorough wash, the oocyte was transferred to the experimental chamber. The external solution was perfused at 1 ml/min by
peristaltic pumps and the outflow routed to a fraction collector.
1-min samples were collected for counting of 42K. Unidirectional
42K efflux was obtained at a constant holding potential of 25
mV; the unidirectional influx was computed by subtraction of the
measured efflux and the time integral of channel current.
The short half-life of the isotope makes it unrealistic to wait for equilibrium to occur between 42K in the soaking solution and the oocytes. We obtained the specific activity of the internal 42K solution by counting each oocyte at the end of the experiment and determining the internal K+ content by flame photometry (IL343; Instrumentation Laboratories, Lexington, MA). Oocytes were rapidly washed in a K+-free solution (100 mM N-methyl-D-glucamine/HCl, 5 mM MgCl2, 10 mM HEPES, pH 7.4), and subsequently disintegrated by vortexing in LiCl. The average K+ content for the oocytes for which 42K efflux was determined was 79 ± 4.7 nmol (±SEM, n = 4). The diameter of Stage V and VI oocytes is generally between 1.0 and 1.3 mm; for a 1.1-mm-diameter oocyte, this K content would represent an internal K concentration of 118 mM.
Determination of K+ equilibrium potential
The determination of
the flux-ratio exponent from Eq. 2 requires the value of the K+
equilibrium potential, VK, which we obtained from the IRK1
channel zero current potential (described in detail below, see
Fig. 1). We found an average VK value of 38 ± 0.7 mV (n = 17)
with a range of
47 to
32.5 mV. The mean value corresponds
to an internal K concentration (ignoring any difference between
internal and external K activity coefficients) of 115 mM, quite
similar to the estimate above from the analysis of internal K content. These VK values from our IRK1 experiments were similar to
but somewhat more depolarized than the mean value of
40 mV
we obtained under identical conditions with Shaker K channels
(Stampe and Begenisich, 1996
).
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RESULTS |
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IRK1 Currents and Fluxes
Fig. 1 A shows examples of currents from an oocyte expressing IRK1 channels. The membrane voltage was
maintained at +20 mV and pulsed (for 300 ms) to the
potentials indicated. The currents in Fig. 1 B were measured at the end of the 300-ms pulses at the potentials
of the abscissa. This strongly rectifying current-voltage relation is expected for the IRK1 channel (Kubo et al.,
1993). Fig. 1, inset, illustrates the method of determining VK necessary for computation of the flux-ratio exponent (see Eq. 2). Currents were recorded at 5-mV intervals near the reversal potential and a second-order
polynomial was fit to the data from which the VK value
was obtained (
38 mV in this case).
The unidirectional K influx was obtained by repetitively applying 300-ms pulses from a holding potential
of +20 mV (see METHODS for details). The net flux
was obtained by collecting all the associated current
records and integrating these over the duration of the
applied pulse. The unidirectional efflux was obtained
from these two measurements (see Eq. 3) and, with the
measured VK value, the flux-ratio exponent, n', was
computed (Eq. 2). Fig. 2 summarizes n' values obtained at 50,
30, and
25 mV plotted as a function of the measured influx. Most values are near or between 2 and 3 and appear independent of membrane
potential and influx value. This latter observation controls for any systematic error that might have been associated with measurements of small flux values.
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Fig. 3, inset, illustrates an experiment designed to
measure unidirectional K efflux. As described in METHODS, the amount of 42K leaving the oocyte was collected
at 1-min intervals in the tubes of a fraction collector.
The inset represents the amount of 42K in each sample
converted to flux units. It is apparent that after a brief
period during which the membrane was maintained at
+20 mV, the efflux appears to reach a relatively constant value. The efflux increased substantially after a
change of the holding potential to 25 mV and decreased to near baseline value when the potential was
returned to +20 mV. The net current associated with
the period at
25 mV was integrated to obtain the net
flux and the influx computed by subtraction. As with
the influx method, the K+ equilibrium potential was
measured, and the flux-ratio exponent computed.
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Fig. 3 summarizes the flux-ratio exponent values obtained at 50,
30, and
25 mV (
and
). We determined n' at
25 mV using both the influx and efflux
methods and found quite similar values: 2.4 ± 0.26 (n = 5,
) and 2.1 ± 0.21 (n = 4,
) for the influx and efflux methods, respectively. Considering the very different sources of experimental errors associated with
these two methods (Begenisich and De Weer, 1980
;
Stampe and Begenisich, 1996
), the similarity of the results adds confidence to the values obtained. The n' values at
30 and at
50 mV were found to be 2.1 ± 0.29 (3) and 2.5 ± 0.23 (5), respectively.
Our intention was to compare the flux-ratio exponent values of IRK1 and Shaker K channels. The very
different voltage range for activation of these two channel types constrains this comparison to voltages near
30 mV. The average value for Shaker channels at
30
mV is 3.4 ± 0.27 (7) (Stampe and Begenisich, 1996
)
and this value is included in Fig. 3 (
). As noted above,
the value for IRK1 channels at
30 mV was 2.1, considerably smaller than that for Shaker channels. The number of successful IRK1 experiments at
30 mV was limited because many oocytes had VK values rather close to
this potential (see METHODS), which makes the computation of n very sensitive even to small errors in Vm or
VK. However, as can be seen in Fig. 3, the IRK1 flux-
ratio exponent was quite insensitive to membrane potential over the range
50 to
25 mV with a value between 2.1 and 2.5.
The results presented in Fig. 3 show that the flux-
ratio exponent values of IRK1 channels were considerably smaller than comparable values from Shaker K
channels. As discussed below, such differences could
reflect differences in the number of K+ ion binding
sites in the pores of these two channel types. Alternatively, the number of sites in each type of pore could be
the same, but other properties of the pore may result in
the manifestation of different n' values (Hille and
Schwarz, 1978; see also Fig. 6). A useful method to
probe other possible differences in the permeation pathway is to measure the single channel conductance
as a function of the symmetrical concentration of K+
flanking the pore (Hille and Schwarz, 1978
).
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IRK1 Single Channel Currents
Fig. 4 A contains single channel currents obtained from
an excised inside-out patch of Xenopus oocyte membrane expressing an IRK1 channel in symmetrical 100 mM K+. From many such records at each potential, current histograms were constructed, and Fig. 4 B illustrates an example for currents recorded at 80 mV
from the same patch. Superimposed on the histogram is the fit of two Gaussian functions with the nonzero
component reflecting a single channel current of
1.7
pA. The complete current-voltage relation for the
channel in this patch is illustrated in Fig. 4 C. Most single channel current-voltage relations were relatively linear, but some, like the example in Fig. 4 C, were
slightly inward rectifying (see Lopatin and Nichols,
1996
, for similar examples). To obtain the zero-voltage
slope conductance from even nonlinear current-voltage relations, a second-order polynomial was fit to the
data. For the example in Fig. 4 C (line), a value of 19 pS
was obtained.
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Fig. 5 summarizes our single channel conductance
data. For this figure, the K concentrations have been
converted to ion activities with activity coefficients from
Kielland (1937). The data can be fit by a saturating hyperbola (Fig. 5, line) with a maximum conductance of
32 pS and a half-maximal K activity of 40 mM.
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Permeation Models
The process of ion permeation is quite complex, especially if, as appears to be the case for many types of ion
channels, it involves simultaneous occupancy of the pore
by two or more ions. Some insight into this process has
been obtained by considering experimental data in
some theoretical context, and reaction rate theory
(Glasstone et al., 1941) has been quite useful for this purpose (but see Eisenberg, 1996
, and the discussion
in Chen et al., 1997
, for an alternative formalism). Hille
and Schwarz (1978)
described how the multi-ion properties of many types of K channel can be understood in
terms of barrier models of permeation. We used this
form of analysis to determine the general types of barrier models that could be consistent with the available
data on K+ permeation through IRK1 channels.
Since we found flux-ratio values for IRK1 channels
between 2 and 3, a barrier model for such a pore must
have at least three K ion binding sites. Consequently,
we considered a model consisting of four barriers and
three sites. Ions move in single file from site to empty
site across the intervening energy barrier. The rate of
movement decreases exponentially with the free-energy difference between the site and the intervening barrier,
biased for membrane potential. We did not assume any
repulsion between ions in the model as doing so would
add another free parameter and would, for any given
energy profile and ion concentration, have the effect of
lowering the computed flux-ratio exponent (Hille and
Schwarz, 1978). The mathematics and computations
for this model were extended from the three-barrier,
two-site model of Begenisich and Cahalan (1980a)
and
has been used to simulate some permeation properties
of native (Begenisich and Smith, 1984
) and expressed
voltage-gated K channels (Pérez-Cornejo and Begenisich, 1994
).
Fig. 6 contains simulations of some permeation properties for several classes of a model with the energy barrier profiles illustrated at the top (1 RT = 0.58 kcal/ mol). Shown are the computed single channel current-voltage relation, conductance activity, and voltage dependence of the flux-ratio exponent (Fig. 6, top to bottom, respectively).
The ion energy barrier profile for the model in Fig. 6
(left) is dominated by a single large barrier. This model
predicts (dashed line) an outwardly rectifying current-
voltage relation with a symmetrical ion activity of 50 mM.
The solid line represents the current-voltage relation
for a 200-mM symmetrical solution. The predicted conductance-activity relation for this barrier profile reaches
a maximum near 150 mM, and then decreases. Lastly,
even though this is a three-ion pore, the predicted flux-ratio exponent is 1.0 over the voltage range from 100
to 100 mV. The shape of the current-voltage relation is
sensitive to the location of the largest barrier (Begenisich and Cahalan, 1980b
). The activity at which the
peak conductance occurs is less sensitive to barrier position (Hille and Schwarz, 1978
). The flux-ratio exponent value is quite insensitive to the position of the
rate-limiting barrier and is negligibly larger than 1.0. Thus, this class of permeation barrier models is inconsistent with the IRK1 permeation data, especially the
flux-ratio exponent data of Fig. 3.
Hille and Schwarz (1978) noted that, for a barrier
model to exhibit a flux-ratio exponent that approaches
the number of ion binding sites, the lateral barriers
need to be significantly larger than the interior barriers. This arrangement enhances several multi-ion permeation properties by maximizing the likelihood that occupancy vacancies are filled by ions within the pore
rather than by a new ion entering it. The energy barrier
profile in Fig. 6 (middle) is the three-site extension of
one of those analyzed by Hille and Schwarz (1978)
.
This model reproduces the near linear IRK1 single
channel current-voltage relations as well as the experimental conductance-activity relation. The flux-ratio exponent of this model has a maximum value near 1.4, significantly less than our measured values. For this
general type of barrier profile, the flux-ratio exponent
can be increased to near 1.8 by increasing the depth of
the three energy wells by only 1 RT. However, doing so
significantly reduces the single channel current (and
conductance) and causes the conductance-activity relation to saturate at very low K concentrations (not
shown).
Fig. 6 (right) contains the predictions of a simple alteration in the middle barrier profile, making only the central well deeper. This modification increases the flux-ratio exponent to values near 2.2, in close agreement with our experimental results, but preserves single-channel current voltage and conductance saturation relations, consistent with the experimental data. Thus, a three-site pore with an energy profile consisting of high lateral, low internal barriers, and a deep central well is quite consistent with the fundamental permeation properties of IRK1 channels.
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DISCUSSION |
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We measured unidirectional K+ fluxes through IRK1
channels expressed in Xenopus oocytes. In each experiment, we measured net flux (ion current) and either
unidirectional influx or efflux. The remaining unidirectional flux was computed from the measured flux
and net current (see METHODS). With these unidirectional fluxes, we determined the flux-ratio exponent, n'
(Eq. 2), which had values between 2 and 2.5 over the
voltage range from 50 to
25 mV. The flux-ratio was
determined at
25 mV in experiments in which unidirectional influx was measured and in experiments in
which efflux was directly measured. These two types of
experiments yielded results that did not significantly
differ from one another (P = 0.5), with an overall
mean n' value of 2.3 ± 0.16 (9).
Northern blot analysis indicates that mRNA coding
for IRK1 channels is present at high concentrations in
skeletal muscle (Kubo et al., 1993) and the inward rectifier K channels expressed in this tissue are likely comprised, in large part, of IRK1 protein. Unidirectional
K+ fluxes across the surface membrane of skeletal muscle have been measured and the flux-ratio exponent
determined (Horowicz et al., 1968
; Spalding et al.,
1981
). At low external K concentrations, the flux-ratio
exponent was found to be near 1.0, and near 2 for high
concentrations. In spite of very different experimental
conditions, our results are in general agreement with
the latter value.
The experimental conditions used here were identical to those used to determine n' values for Shaker K
channels (Stampe and Begenisich, 1996), and so a direct comparison between results from these two channel types is possible. At
30 mV, Shaker channels exhibit an n' value of 3.4 ± 0.27 (7), significantly larger
than the IRK1 values at
30 and
25 mV of 2.1 ± 0.29 (3) and 2.3 ± 0.16 (9), respectively.
We determined IRK1 single channel slope conductance (at 0 mV) as a function of symmetrical K+ concentration in the absence of Mg2+, and polyamines that
produce the inward rectification of this channel (Lopatin et al., 1994; Ficker et al., 1994
). Our results are
quite similar to data obtained in symmetrical 100- and
140-mM K+ solutions by Aleksandrov et al. (1996)
and
Ficker et al. (1994)
, respectively. We found that the
conductance-activity relation could be described by a
saturating hyperbola with a half-saturation K+ activity
of 40 mM and a predicted maximum of 32 pS.
The conductance-concentration relation of IRK1
channels determined in this study was generally similar
to the behavior of the weak inward rectifier channel,
ROMK1, for K+ concentrations as large as 400 mM (Lu
and MacKinnon, 1994). At larger K concentrations, the
conductance of single ROMK1 channels decreases, another manifestation of multi-ion pores (Lu and MacKinnon, 1994
; Hille and Schwarz, 1978
).
The dependence of the conductance of voltage-gated
K channels on K+ concentration is quite different than
the inward rectifier channels ROMK1 and IRK1. The
conductance of single Shaker K channels reaches a maximum near a K+ activity of 1 M with a half-maximal concentration near 300 mM (Heginbotham and MacKinnon, 1993), which is quite similar to the behavior of the
macroscopic conductance of voltage-gated K channels in the squid giant axon (Wagoner and Oxford, 1987
).
A variety of theoretical approaches have been used to
provide an interpretation of flux-ratio exponent values
>1.0 (e.g., Hodgkin and Keynes, 1955; Heckmann,
1972
; Hille and Schwarz, 1978
; see references in Levitt,
1986
; Schumaker, 1992
; Bek and Jakobsson, 1994). In
spite of the mathematical formalism used, the same
conclusion is reached: only permeation models that allow multiple ion occupancy of the pore predict flux-
ratio exponent values >1.0. In all these calculations
(except for one limiting case, Hodgkin and Keynes, 1955
), the flux-ratio exponent may approach, but cannot exceed, the number of ions that can simultaneously
occupy the pore. For any particular model parameters,
the flux-ratio exponent may be much less than the
maximum (e.g., see Fig. 6). Thus, the flux-ratio exponent provides an estimate of the minimum number of
ions that may occupy the pore. Our results show that
the pore in IRK1 channels is capable of containing at
least three K+ ions.
We showed that a relatively simple four-barrier,
three-site permeation model can quantitatively account
for the flux-ratio and conductance-activity data and
qualitatively for the current-voltage relations. Since
our goal was to examine some general classes of such
models, we made no effort to adjust the model parameters to quantitatively reproduce the current-voltage
data. Nevertheless, this exercise revealed that the presence of a deep central well is a key feature for enhancing the magnitude of the predicted flux-ratio exponent. This same feature was found useful in describing ion selectivity in Ca2+ channels (Dang and McClesky,
1998) and in describing the interactions of Na+ and K+
ions in some types of voltage-gated K channels (Kiss
et al., 1998). While far from confirming the existence
of a dominant high affinity binding site for permeant
ions, the convergence of several investigations toward a
similar conclusion suggests that it may be worthwhile to
design experimental tests of this idea.
Conclusion
As discussed above, the flux-ratio exponent does not directly determine the number of ions that may occupy
the pore. Rather, it establishes only the minimum number of ions that may do so. Thus, the different n' values
for Shaker and IRK1 channels could each be consistent
with a pore that could simultaneously be occupied by
four (or more) ions. Furthermore, Lu and MacKinnon
(1994) showed that the difference between the ROMK1
and Shaker conductance-concentration relations could
result simply from a change in ion entry rates in one
type of permeation model. Thus, establishing the maximum occupancy of a pore requires other data.
A Rb+ Fourier difference map of a prokaryotic K
channel (KcsA) shows that in 150 mM RbCl this channel is occupied by three Rb+ ions (Doyle et al., 1998).
Two of these are within ~7.5 Å of each other, at the
ends of the highly conserved selectivity filter sequence
(TVGYG; Heginbotham et al., 1994
) in the channel
pore region. K+ ions may occupy similar sites since Rb+
and K+ share much physical similarity and have generally similar permeation properties. The KcsA channel is
structurally similar to IRK1 in having two membrane
spanning domains and the K channel selectivity filter
sequence. So even though the other amino acids in the
KcsA pore region are much more similar to Shaker than
to IRK1 channels, the simplest picture of inward rectifier K channels consistent with all the permeation data
is that these channels have three sites that may all be simultaneously occupied. We showed that the flux-ratio
and permeation data for IRK1 channels can be simulated by at least one class of three-site permeation models.
As noted above, the flux-ratio exponent for Shaker K
channels is near 3.5, much larger than that determined
for inward rectifier channels. This result and the results
of a study of Ba2+ block of Ca2+-activated K channels
(Neyton and Miler, 1988) indicates that some classes of
K channels can accommodate at least four K+ ions.
Thus, the structural picture of Rb+ ion occupancy of
the KcsA may not apply to K+ ion occupancy of all
classes of K channels. Either KcsA channels can be occupied by more K+ than Rb+ ions or (more likely)
there may be ion coordinating structures in voltage-gated K channels not represented in KscA (or inward rectifier) channels. Candidates for additional K+ binding sites may include regions in S6 and the S4-S5 linker since mutations in these areas alter K channel permeation properties (Isacoff et al., 1991; Choi et al., 1993
;
Slesinger et al., 1993
; Lopez et al., 1994
).
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FOOTNOTES |
---|
Address correspondence to Ted Begenisich, Department of Pharmacology & Physiology, Box 711, University of Rochester Medical Center, Rochester, NY 14642. Fax: 716-244-9283; E-mail: tbb{at}crocus.medicine.rochester.edu
Original version received 16 April 1998 and accepted version received 3 August 1998.
We are grateful to L.Y. Jan for providing the IRK1 cDNA and to Jay Yang for the high expression Xenopus vector. We thank Jill Thompson for technical assistance with the experiments and for critically reading the manuscript.
This work was supported in part by National Science Foundation grant IBN-9514389 (T. Begenisich).
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Abbreviation used in this paper |
---|
IRK1, inward rectifier K channel.
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