Correspondence to: Ted Begenisich, Department of Pharmacology and Physiology Box 711, University of Rochester Medical Center, Rochester, NY 14642. Fax:716-244-9283 E-mail:ted_begenisich{at}urmc.rochester.edu.
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Abstract |
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We have examined the interaction between internal and external ions in the pore of potassium channels. We found that external tetraethylammonium was able to antagonize block of Shaker channels by internal TEA when the external and internal solutions contained K+ ions. This antagonism was absent in solutions with Rb+ as the only permeant ion. An externally applied trivalent TEA analogue, gallamine, was less effective than the monovalent TEA in inhibiting block by internal TEA. In addition, block by external TEA was little affected by changes in the concentration of internal K+ ions, but was increased by the presence of internal Na+ ions in the pore. These results demonstrate that external and internal TEA ions, likely located at opposite ends of the pore selectivity filter, do not experience a mutual electrostatic repulsion. We found that these results can be simulated by a simple 4-barrier-3-site permeation model in which ions compete for available binding sites without long-range electrostatic interactions.
Key Words: ion channels, voltage-clamp, tetraethyl ammonium, gallamine, ion permeation
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INTRODUCTION |
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Ion channels have a variety of physiological roles that depend critically on their ability to allow only certain types of ions to rapidly pass through the pore in these proteins. High selectivity implies an intimate interaction between the ion and the pore and may have an adverse effect on ion flux.
It is often considered that electrostatic ion repulsion in multi-ion channel pores is a key element for overcoming the tight binding implied by high selectivity. First proposed for Ca channels (
The current view of a through-space interaction in K channels comes, in part, from experiments in which K+ ions on one side of the membrane antagonize positively charged blocking molecules applied to the other. These blocking molecules include (among others) the cations tetraethylammonium (
While these results are consistent with a through-space electrostatic interaction between a K+ ion at one site and the blocking ion at another, they do not establish this mechanism. In these types of experiments, the permeant K+ ion could entirely cross the pore and bind at (or extremely close to) the blocking site. In fact, in many cases only permeant ions can antagonize blocking molecules (e.g.,
The interaction between impermeant ions may represent a better test for direct electrostatic repulsion.
There are several possible tests of the through-space electrostatic repulsion mechanism for the antagonism between internal and external TEA ions. (a) The antagonism would be quantitatively mutual. That is, internal TEA would antagonize external TEA block by the same amount that external TEA antagonizes block by internal TEA. (b) If the antagonism between TEA ions is electrostatic in nature, it cannot depend on the identity of the permeant ion. And (c) a multivalent TEA analogue should produce larger antagonism than monovalent TEA.
The study of
We have further examined the issue of antagonism between TEA ions in K channels. We made two experimental tests of the electrostatic mechanism. We found that the antagonism between external and internal TEA ions, present in K+-containing solutions, was absent when the K+ ions were replaced by Rb+. We found that an externally applied trivalent TEA analogue, gallamine, was less, not more, effective at inhibiting block by internal TEA. In addition, we found, in contrast to the report by
Our results support the notion that the apparent interaction between external and internal TEA ions is not electrostatic in nature, but depends on the ionic conditions. We tested the possibility that the apparent antagonism between TEA might result from competition for occupancy of a limited number of sites in the pore. A very simple form of a 4-barrier-3-site permeation model was able to reproduce our results. Thus, we conclude that the apparent antagonism between internal and external TEA ions observed in K+ but not Rb+ solutions is not electrostatic in nature and is consistent with a competition between ions for sites in the pore.
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METHODS |
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K Channel Constructs
Most of the experiments reported here were done on the inactivation-deletion version of Shaker B, ShB 6-46 (
Oocyte Isolation and Microinjection
Frogs, Xenopus laevis, were maintained as described by
Electrophysiological Recordings
Potassium channel currents were assayed electrophysiologically 15 d after RNA injection. Electrophysiological recordings were done at room temperature (2022°C) with excised inside/out or outside/out macropatches using an Axopatch 1-D amplifier (Axon Instruments, Inc.). Three types of glass were used in these experiments. Most of the data were obtained with Corning 7052 glass (Garner Glass Co.) with tip diameters of ~24 µm. Some data were obtained with GC-150F glass (Warner Instrument Corp.), also with 24-µm openings. We also used fused quartz (Garner Glass Co.) fabricated with a laser puller (P-2000; Sutter Instrument Co.) to tip diameters of 13 µm. The measured junction potentials for the solutions used were all within 4 mV of one another, and so no correction for these was applied. The holding potential was -70 mV. Data acquisition was performed using a 12-bit analogue/digital converter controlled by a personal computer. Current records were usually filtered at 5 kHz.
The standard external solution contained (mM): 5 KCl, 135 NMDG-Cl, 2 CaCl2, 2 MgCl2, 10 mM HEPES, pH 7.2 (with NMDG). Gallamine triethiode (Sigma-Aldrich) up to 5 mM was added to this solution. TEA was included in this solution by equimolar replacement of NMDG. The standard internal solution consisted of (mM): 110 KCl, 25 KOH, 10 EGTA, 10 HEPES, pH 7.2 with HCl. We also used similar solutions but with K+ replaced by Rb+. TEA, up to 5 mM, was added to the internal solution as required. Na+-free internal solutions of different K+ concentrations were made by an equimolar replacement of K+ by NMDG in the standard internal solution. Solutions with different Na+ concentrations were made from a solution of 20 mM K+ and 115 NMDG by equimolar replacement of NMDG. We also used a solution with nominally zero external K+ concentration: flame photometry analysis showed that this solution contained <5 µM potassium.
Data Analysis
As described in RESULTS, several different equations were fit to the data. These were done using the Simplex algorithm (
Permeation Model Simulations
We used a 4-barrier-3-site permeation model to simulate our results. In this model, the ions are considered to move from site to site by overcoming an intervening energy barrier. We used a three-site model since there are at least this number of ions in the pore (
where k, T, and h are Boltzmann's constant, the absolute temperature, and Planck's constant, respectively. Q and Q* are the partition functions for the ion at the energy minimum and near the peak of the energy barrier, respectively. The parameter <<>>has been described as "an ad hoc fudge factor (transmission coefficient)" (
Considerable effort has gone into computing the pre-exponential component of this equation appropriate for ion permeation through membrane ion channels. This computation is quite complex, especially in aqueous solutions. Moreover, the KscA structure shows that the prefactor may be different for different steps in the permeation processes. For example, the ion is at least partially hydrated in the external solution just outside the narrow selectivity filter and in the relatively large "cavity" at the inner side of the selectivity filter. Thus, these steps will likely require a prefactor appropriate for aqueous solutions that will include the ion translocation and dehydration processes. In contrast to bulk aqueous solutions, there are very few water molecules associated with the ions in the selectivity filter and the ions are likely interacting strongly with the pore lining, and so permeation steps in the selectivity may require a different prefactor.
There are several derivations of the form that the prefactor may take. The simplest of these is just kT/h (
where D is the diffusion coefficient for the ion which is 2 x 10-5 cm2/s for K+ ions. Ions in solution have a mean free path on the order of 0.1 Å. However, the "jump," for example, from the external aqueous solution to the first site in the selectivity filter will not be the same as for the translocation of the ion in aqueous solution as the former certainly requires considerable dehydration. If this occurs over a distance of, say, 1 Å, for a 10-RT barrier, then the Kramer prefactor would be ~7 x 1011 s-1.
where D is the diffusion coefficient and R represents a "capture distance." is the thermal de Broglie wavelength given by:
where m is the mass of the ion. For K+ ions and an arbitrary (but reasonable) capture distance of 2.5 Å, the Hill prefactor is ~5 x 1011 s-1.
where a and
define the shape of parabolic energy minimum and maximum: the distance over which the energy level changes by 1 RT. If these distances are each 0.5 Å, then the Andersen prefactor is near 2.5 x 1011 s-1.
The latter three calculations produced quite similar prefactor values of 2.57 x 1011 s-1, about an order of magnitude smaller than the 5.8 x 1012 s-1 value of kT/h. We used the permeation model to simulate block by external and internal TEA ions, a computation that requires only ratios of the simulated currents. Thus, our simulations (see Fig 11) are independent of the precise value of the prefactor. Nevertheless, we used a prefactor value of 3 x 1011 s-1, which, according to the calculations above, is a reasonable value for permeation steps from aqueous solutions into the pore selectivity filter. For simplicity, we used this same prefactor for all rate constants in our simulations of the three-site permeation model.
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where p is the total number of rate constants in the model, ki is the rate constant for the ith step (forward rate constants are odd numbers, reverse rate constants are even), and ff is the prefactor used. We used this formalism for presentation of the model parameters in Fig 11.
Mathematical details for a two-site version of this model can be found in
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RESULTS |
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TEA Antagonism in Shaker K Channels
The most extensive analysis of the antagonism between internal and external TEA was done with RBK1 (rKv1.1) channels (
Fig 1 (top) contains Shaker channel currents at several potentials before, during, and after application of 2 mM internal TEA. In the absence of external TEA, internal TEA substantially blocked the channel. Fig 1 (bottom) shows that this concentration of internal TEA was much less effective if applied in the presence of 100 mM external TEA.
Fig 2 summarizes the results of many similar experiments. Shown is the fraction of current at a membrane potential of 0 mV that was blocked by the indicated concentration of internal TEA in the absence () and presence (
) of 100 mM external TEA. The data are consistent with the binding of a single TEA ion to the channel that results in block of the channel:
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(1) |
The lines in Fig 2 are best fits of Equation 1 to the data. In the absence of external TEA, internal TEA blocked the channels with a Kd value of 0.56 mM, similar to the value of 0.7 mM of
With both external and internal TEA present, there are four possible states of the channel: unblocked channels, channels blocked by internal TEA, channels blocked by external TEA, and channels occupied by both external and internal TEA. To quantitatively evaluate the interaction between the TEA ions, consider the following:
The first two lines represent the interaction of external and internal TEA, respectively, in the absence of any TEA on the opposite side of the channel. In the third line, external TEA binds to a channel with internal TEA already occupying the internal binding site. With internal TEA present, the on rate for external TEA (k1) is reduced by a factor a and the off rate (k-1) increased by a factor b. For electrostatic repulsion between the TEA ions, these two factors would be the same but, in general, need not be. The interaction of internal TEA with a channel already occupied by external TEA is likewise modified, as shown in the last line.
With this scheme, the apparent binding constant for internal TEA will be a function of the concentration of external TEA:
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(2) |
where Kd is the binding constant in the absence of external TEA and Ko (= k-1/k1) is the affinity of external TEA for its binding site (in the absence of internal TEA). With Q = a · b, this is the form of the equations used by
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(3) |
Thus, the parameter Q in Equation 2 can be used to provide a quantitative measure of the ability of external TEA to reduce the effectiveness of internal TEA in blocking the channel. To extract this parameter, the binding affinity of external TEA (Ko) is required. This is obtained from the concentration dependence of block of the channels by external TEA, as illustrated in Fig 2, inset. The data are well described by Equation 1 with a binding affinity of 17 mM.
The apparent dissociation constants for internal TEA block at 0 and 100 mM external TEA obtained from the data in Fig 2 are shown in Fig 3 with additional values obtained at 25 and 50 mM external TEA. The data are well described by Equation 2 (with Ko = 17 mM) with an interaction parameter Q of 4.6. This is similar to the value of 5.3 that
We also tested the antagonism between external and internal TEA ions with the wild-type threonine at position 449 replaced with a tyrosine, the amino acid in native RBK1 channels, that produces a high affinity TEA receptor in Shaker channels. We found that 2 mM internal TEA (in the absence of external TEA) blocked 77 ± 0.4% (n = 4) of the current. This is equivalent to an apparent Kd value of 0.62 mM, quite similar to the value for wild-type channels (Fig 2). In the presence of 1 mM external TEA, this concentration of internal TEA only blocked 64 ± 7% (n = 3) of the current, equivalent to a Kd value of 1.4 mM. We determined that the Kd value of the T449Y channels for external TEA was ~0.43 mM (data not shown), very similar to the 0.59 mM value reported by
TEA Antagonism in Shaker K Channels in Rb+ Solutions
If the ability of external TEA to antagonize the effectiveness of internal TEA is due to a through-space electrostatic repulsion between these ions, then the antagonism should be independent of which permeant ion is used to carry current. However, as illustrated in Fig 4, the antagonism between external and internal TEA present with K+-containing solutions was absent in solutions in which Rb+ replaced K+.
Shown in Fig 4 (top) are channel currents in Rb+ solutions at several potentials before, during, and after recovery from application of 2 mM internal TEA. As with solutions containing K+ as the permeant ion, this concentration of internal TEA inhibited a substantial amount of channel current. Fig 4 (bottom) shows that, in contrast to the results with K+ as the permeant ion, external TEA did not protect from block by internal TEA with Rb+ as the permeant ion.
Fig 5 summarizes the results of many similar experiments. Shown is the fraction of current at a membrane potential of 0 mV that was blocked by the indicated concentration of internal TEA in the absence () and presence (
) of 100 mM external TEA. Both sets of data are well described by Equation 1 (lines) with apparent Kd values of 0.4 and 0.41 in the absence and presence of 100 mM TEA, respectively. That is, with Rb+ as the permeant ion, external TEA was entirely ineffective in protecting the channels from block by internal TEA.
The inability of external TEA to protect the channels from internal TEA block in the presence of Rb+ could occur if external TEA did not bind to the channel. The data in Fig 5 (inset), however, show that, if anything, external TEA had a greater affinity for the channel in Rb+ solutions. The data are best fit by Equation 1, with a Kd value of 11 mM that is somewhat smaller than the value of 17 mM obtained in the presence of K+ ions (Fig 2).
Apparent Kd values, obtained in Rb+ solutions, for block by internal TEA as a function of external TEA are illustrated in Fig 6 (), along with the comparable data in K+ solutions from Fig 3 (
). In contrast to the results in K+ solution, with Rb as the permeant ion, block of Shaker channels by internal TEA was independent of external TEA. The data in Rb+ solutions are consistent with a constant Kd value of 0.4 mM (and a value of Q = 1). Thus, the apparent interaction between external and internal TEA depends on the identity of the permeant ion and so is not likely to be mediated by a through-space electrostatic repulsion mechanism.
Antagonism between Multivalent TEA Ions
We made another test of the electrostatic mechanism for the interaction between TEA ions in K+ solutions. If the antagonism between these ions is electrostatic in nature, it will be much stronger between internal TEA and an external multivalent TEA analogue. It is possible to quantitatively predict the magnitude of this increased interaction by determining the expected value of the interaction parameter, Q. The value of Q for interaction of an external TEA analogue of valence z Qz compared with the value of monovalent TEA (Q1) is given by (see Appendix) Q z = Q z1.
Since, from Fig 3, Q1 is 4.6, the value of Q for the electrostatic interaction between internal TEA and external divalent and trivalent TEA analogues is expected to be 4.62 (21) and 4.63 (97), respectively.
The neuromuscular blocking agent, gallamine, (Fig 7 A, inset) contains three tetraethylammonium groups connected by ether oxygen linkages to a benzene ring. The data in Fig 7 A shows that this compound blocked Shaker K channels with an affinity (0.53 mM) substantially higher than that of TEA (17 mM, Fig 2). We determined the voltage dependence of block of wild-type channels by 0.25 mM external gallamine (Fig 7 B, ). Such data are often analyzed with the
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(4) |
where Kd(0) represents the affinity of the channel for gallamine at zero membrane voltage, z is the valence (+3), and is the location (fraction of the membrane field) where gallamine blocks the channel. There are difficulties in applying this equation to data from multi-ion pores (e.g.,
near 0.15 (
The analysis of the data in Fig 7 B shows that gallamine blocked wild-type Shaker channels with an apparent value of z of 0.28, equivalent to two of the three charges located at the same electrical distance as monovalent TEA. This same concentration of gallamine was considerably more effective in blocking T449Y channels (
) and with a reduced voltage sensitivity. Thus, it is likely that gallamine binds at, or very close to, the same external location as TEA, with an effective valence at least twice that of TEA.
Consequently, gallamine may be considered a suitable multivalent TEA analogue for the test of the electrostatic interaction mechanism. We determined internal TEA block of the channels in the presence of various concentrations of external gallamine. Fig 8 A shows that 5 mM external gallamine slightly decreased block by internal TEA. The apparent dissociation constant for internal TEA increased from 0.56 mM in the absence to 0.95 mM in the presence of 5 mM external gallamine.
We determined the Kd value for internal TEA block at several concentrations of external gallamine and these are illustrated in Fig 8 B. The data are best fit by Equation 2 with a value of the interaction parameter, Q, of 2. Gallamine blocked the channels as if two of its three charges were at the external TEA site. Thus, an electrostatic interaction would predict a value of Q of 21 (see above). Shown in Fig 8 B are the predictions (dashed lines) for internal TEA interactions with trivalent (Q = 97), divalent (Q = 21), and monovalent (Q = 4.6) charges. Thus, external gallamine interacted with internal TEA much less than predicted for a divalent interaction and even less than monovalent external TEA. This result and the lack of interaction of TEA ions in the presence of Rb+ argue against a through-space, electrostatic repulsion between quaternary ammonium ions in the pore of the Shaker K channel.
Interaction between Internal Ions and External TEA
As noted in the INTRODUCTION, the observed reduction in RBK1 channel block by external TEA with elevated internal K+ ions (
Fig 9 (inset) contains Shaker channel currents recorded in 135 (left) and 20 (right) mM internal K+. Currents in the absence (larger) and presence of 25 mM external TEA are illustrated. In contrast to the results of ) mM internal K+. The apparent Kd value for external TEA block in 135 and 20 mM internal K+ was 17 ± 1 and 22 ± 2.8 mM, respectively. From additional, similar data (not shown), we determined that channel block with 50 mM internal K+ was consistent with an apparent Kd value of 17.6 ± 2.7 mM. Removal of external K+ (see METHODS) with 20 mM internal K+ had little or no effect on block by 25 mM external TEA (Fig 9,
).
Thus, an almost sevenfold change in internal K+ and removal of external K had little effect on block of Shaker channels by external TEA. If anything, we found slightly more block in solutions with elevated internal K+. This result is in contrast to that of
Fig 10 A contains data obtained with 20 mM internal K+ in the absence of Na+, and B contains data obtained with 20 mM K+ and 50 mM Na+. The insets show currents measured in the absence (larger) and presence of 5 mM external TEA. With no internal Na+, this concentration of TEA produces only a small block of the current, consistent with the results shown in Fig 9. This same concentration of TEA, however, blocked a substantial amount of current with 50 mM internal Na+. The currentvoltage relations in these conditions are also illustrated before (), during (
), and after recovery from () application of 5 mM TEA. The decline of current at large positive potentials in the presence of Na+ is due to a voltage-dependent channel block by this ion, a behavior common to many types of K channels (e.g.,
From other experiments like those illustrated in Fig 10, we determined that external TEA blocked Shaker channels with an apparent Kd value of 7.5 ± 0.85 mM in 20 mM internal K+ and 50 mM Na+ (three measurements each at three external TEA concentrations). This is considerably smaller than the value of 22 mM (see above and Fig 9) obtained in the absence of internal Na+ ions. From additional experiments with 115 mM internal Na+, we obtained an apparent Kd value for block by external TEA of 7.6 ± 1.2 mM (three measurements each at five internal TEA concentrations), not significantly different from the value with 50 mM internal Na+. Thus, the presence of an internal blocking ion (Na+) increased the ability of external TEA to block the channels. This is in the opposite direction expected for an electrostatic repulsion between an internal blocking ion (Na+) and external TEA. It is also opposite to the action of internal TEA, which inhibits block by external TEA (
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DISCUSSION |
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The objective of the study described here was to critically examine the evidence supporting through-space electrostatic repulsion between TEA ions in the pore of K channels. Certainly, ions of like charge repel each other, but in the context of multi-ion pores the relevant questions are: (a) Over what distance and over which structures does this occur? (b) How strong is the repulsion? and (c) Does repulsion play an important role in ion selectivity and permeation?
Under some conditions, there appears to be mutual antagonism between internal and external TEA ions (
If the mutual antagonism between internal and external TEA (in K+ solutions) is due to electrostatic repulsion between these ions, then multivalent ions should demonstrate a considerably stronger antagonism. We made this test with an external multivalent TEA analogue. Not only was the antagonism with internal TEA not nearly as strong as predicted, it was actually weaker than that produced by monovalent TEA.
This latter result is the opposite expected of an electrostatic mechanism and also argues against another possibility. Perhaps there is electrostatic repulsion between external and internal TEA ions in K+ solutions, but this is balanced by some other stabilization energy when K+ ions are replaced by Rb+. If so, then the threefold stronger repulsion between external gallamine and internal TEA in K+ solutions would still be expected to result in an increased antagonism that was not observed.
The apparent antagonism between internal K+ ions and external TEA has also been cited as evidence in favor of electrostatic repulsion in the pore of K channels. We found that reducing the concentration of internal K+ ions did not allow increased channel block by external TEA unless Na+ ions were used as K+ replacements. The ability of an internal blocking ion like Na+ to increase block by external TEA cannot be explained by an electrostatic repulsion mechanism.
Taken together, our results suggest that internal and external TEA ions in the pore of Shaker K channels do not experience a mutual electrostatic repulsion. If the antagonism observed between external and internal TEA ions in K+ solutions is not mediated by electrostatic repulsion, then how does this occur?
The common theme in our results and those of
Permeation Model Simulations
We used the 4-barrier-3-site model described in METHODS. We used a profile for K ions with high lateral and low internal barriers, known to be able to simulate all known multi-ion permeation properties (
Our results (and those of
To determine whether this proposition was at all reasonable, we attempted to simulate our results with a permeation model based on Eyring rate theory (
Fig 11 illustrates the simulation of the interaction between external and internal TEA with K+ and Rb+ as permeant ions. Details of the modeling are described in METHODS. The left ordinate of Fig 11 A is the RCR (
We used the model rate constants for K+ and TEA ions and simulated dose-dependent block by internal TEA in the absence and at various concentrations of external TEA. These data allowed computation of the apparent Kd for internal TEA block as a function of external TEA as shown in Fig 11 B. We made no attempt to quantitatively simulate the interaction between external and internal TEA. The K+ ion profile used was symmetric, simple and the same as one used previously to simulate our flux-ratio results (), this simple model not only simulated our experimental findings, but the value of Q obtained by fitting Equation 2 to the simulations was quite similar to the experimental data with K+ as the permeant ion (
Even in this simple model with symmetrical barrier shapes, there are 10 adjustable parameters that describe the permeant ion properties: four energy maxima, three energy minima, and three positions for the minima. To simulate the antagonism between TEA ions in Rb+ solutions, any or all of these could be adjusted. Instead, we took as simple an approach as possible and chose to give Rb+ ions all the same properties of K ions except one: a larger second energy maximum (Fig 11 A, dotted line). With this profile for the permeant ions, there was very little antagonism between external and internal TEA (Fig 11 B, ).
Thus, this simple version of a three-site permeation model was able to simulate the antagonism between external and internal TEA ions in K+ solutions without invoking electrostatic repulsion or a conformational change. The model also predicted that this antagonism depends on the nature of the permeant ion. Only a small change in the properties of the permeant ion predicted an elimination of the TEA antagonism, as we observed with Rb+ as the permeant ion.
As described in METHODS, we computed the probabilities for occupancy of various states in the model. We tested whether the addition of TEA to the external side of the model pore would cause a redistribution of occupancy of the permeant ions. We found that, like the antagonism between TEA ions, redistribution depends on the properties of the permeant ion. For example, with the model parameters for K ions, the probability of occupancy of all three sites by the permeant ion was ~0.37. When 5 mM TEA was added to the model, this value was increased to 0.52 for those channels not blocked by TEA. With the Rb+ ion model profile, addition of TEA caused little or no redistribution of permeant ion occupancy. The largest change was in the state with the middle and inner sites occupied, where TEA increased the probability only slightly from 0.49 to 0.52. Thus, our observation that the antagonism between external and internal TEA ions depended on the permeant ion is consistent with a competition between blocking and permeant ions for the availability of limited sites in the pore. According to the model simulation, this can arise if TEA occupancy of its external binding site causes a redistribution of the occupancy of permeant ions in the pore.
Possible Implications
Our results suggest that the antagonism between external and internal TEA ions in the pore of the Shaker K channels is not due to mutual electrostatic repulsion. These blocking ions likely occupy sites at opposite ends of the narrow selectivity filter (
Thus, we suggest that long-range electrostatic repulsion between permeant ions may not be the mechanism that overcomes the high ion affinity and allows high flux rates. While an appealing and intuitive concept, there is no direct evidence supporting long-range electrostatic repulsion between permeant ions in any channel. Moreover, repulsion between ions in pores is not the only mechanism for assuring high selectivity and high flux rates.
Thus, while not directly addressing repulsion between permeant ions within the pore selectivity filter, our results are a reminder that the presence of electrostatic interactions between permeant ions located at opposite ends of this structure has not been established. Likewise, it has been shown only that permeation based on stepwise changes in binding affinity can simulate experimental data. Clearly, considerable additional data are required to determine the mechanism by which K channels provide both high affinity and high flux rates.
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Footnotes |
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1 Abbreviation used in this paper: RCR, rate constant representation.
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Acknowledgements |
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We thank Dr. Claire Quinn and Dr. Robert Dirksen for critically reading an early version of the manuscript. We thank Dr. Ed McCleskey for providing Thieu Dang's implementation of the 4-barrier-3-site permeation model. We acknowledge a useful discussion with Dr. Zhe Lu on this work, especially the possibility that some action of permeant ions could balance electrostatic repulsion between TEA ions.
This work was supported, in part, by National Institutes of Health grant NS-14138 and a grant from the National Science Foundation (IBN-9514389).
Submitted: 16 March 2000
Revised: 24 April 2000
Accepted: 24 April 2000
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Appendix |
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If the antagonism between these ions is electrostatic in nature, it will be much stronger between internal TEA and an external multivalent TEA analogue. It is possible to quantitatively predict the magnitude of this increased interaction by determining the expected value of the interaction parameter, Q.
The equilibrium binding constant for a reaction is exponentially related to the free energy change, G0 of the reaction: Keq = exp(-
G0/RT), which can be divided into entropic (
S) and enthalpic (
H) components:
G0 =
H - T
S.
One component of the change in enthalpy will arise from the electrostatic energy between the interacting ions: G0 =
He +
Hr - T
S, where
He represents the electrostatic component and
Hr the rest of the change in enthalpy. Thus, the equilibrium constant can be written as: Keq = exp(-
He/RT) · exp[(-
Hr + T
S)/RT] or Keq = exp(-
He/RT) · Keq0, where Keq0 is the equilibrium constant in the absence of electrostatic interaction. The relation to the interaction parameter, Q, of Equation 2 can be seen by considering the binding of internal TEA to a channel occupied by external TEA. The equilibrium constant for this reaction is: K*i = a · b · k-2/k2 = Q · Ki, where Ki is the binding constant without the electrostatic presence of external TEA. Comparing the last two equations allows an assignment for Q = exp(-
He/RT).
Even with a known channel structure and precise location of the interacting ions, an exact calculation of the electrostatic energy, He, is challenging. However, this quantity certainly is proportional to the product of the valences of the interacting ions. Therefore, the value for the interaction between internal TEA and an external ion of valence z will be: Q z = exp(-z
H1/RT) and Qz = Q z1.
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