Correspondence to: David C. Dawson, Department of Physiology & Pharmacology, Oregon Health Sciences University, 3181 SW Sam Jackson Park Rd., L-334, Portland, OR 97201. Fax:503-494-4352 E-mail:dawsonda{at}ohsu.edu.
Released online: 29 November 1999
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Abstract |
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The cystic fibrosis transmembrane conductance regulator (CFTR) Cl channel exhibits lyotropic anion selectivity. Anions that are more readily dehydrated than Cl exhibit permeability ratios (PS/PCl) greater than unity and also bind more tightly in the channel. We compared the selectivity of CFTR to that of a synthetic anion-selective membrane [poly(vinyl chloride)tridodecylmethylammonium chloride; PVC-TDMAC] for which the nature of the physical process that governs the anion-selective response is more readily apparent. The permeability and binding selectivity patterns of CFTR differed only by a multiplicative constant from that of the PVC-TDMAC membrane; and a continuum electrostatic model suggested that both patterns could be understood in terms of the differences in the relative stabilization of anions by water and the polarizable interior of the channel or synthetic membrane. The calculated energies of anionchannel interaction, derived from measurements of either permeability or binding, varied as a linear function of inverse ionic radius (1/r), as expected from a Born-type model of ion charging in a medium characterized by an effective dielectric constant of 19. The model predicts that large anions, like SCN, although they experience weaker interactions (relative to Cl) with water and also with the channel, are more permeant than Cl because anionwater energy is a steeper function of 1/r than is the anionchannel energy. These large anions also bind more tightly for the same reason: the reduced energy of hydration allows the net transfer energy (the well depth) to be more negative. This simple selectivity mechanism that governs permeability and binding acts to optimize the function of CFTR as a Cl filter. Anions that are smaller (more difficult to dehydrate) than Cl are energetically retarded from entering the channel, while the larger (more readily dehydrated) anions are retarded in their passage by "sticking" within the channel.
Key Words: hydration energy, anion binding, pseudohalides, ion-selective electrodes, anion channels
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INTRODUCTION |
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The cystic fibrosis transmembrane conductance regulator (CFTR)1 channel functions as a PKA-activated ion channel that is predominantly expressed in epithelial cells. The channel selects for anions over cations (PNa/PCl 0.03) (
To gain insight into the nature of the physical interactions that are reflected in the peak and well energies that characterize anion permeation, we compared the selectivity of CFTR to that of a well-characterized, synthetic anion-selective membrane composed of plasticized poly(vinyl chloride) (PVC) doped with tridodecylmethylammonium chloride (TDMAC) for which the physical basis for the response to anion substitution is more readily apparent (
The continuum electrostatic approach provides a unified, quantitative interpretation of the observed energetics of permeation and block and offers a plausible explanation for the differential effects of mutations on these two processes that may be useful in understanding the physical nature of the conduction path, and in evaluating proposed structural models for the pore domain.
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MATERIALS AND METHODS |
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Molecular Models
To estimate anion dimensions and surface area, each of the ions used was modeled using the PC Spartan molecular modeling program from Wavefunction, Inc. The equilibrium geometry of each of the polyatomic species was optimized using ab initio molecular orbital calculations. For those ions with a regular geometry, all additive and trigonometric calculations were done using nucleus-to-nucleus measurements from the model, and then the overall dimensions were approximated by adding the appropriate van der Waal radii to the terminal atoms. For those ions with an irregular geometry, the solid dimensions were estimated from the smallest "box" into which the ion would fit. The equivalent radius was determined by taking the surface area of the model and determining the radius of a regular sphere with the same surface area (where surface area = 4r2). PC Spartan lacks basis values for gold so we could not perform the full set of calculations for Au(CN)2; however, we were able to model Ag(CN)2, which should have approximately the same dimensions. One of the advantages of the molecular orbital calculation method is that it permits an assessment of the charge distribution within the molecule. A hallmark of the halides and pseudohalides is that the negative charge is uniformly distributed (
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Born Calculation of the Free Energy of Hydration (See Appendix)
In the Born model, the free energy of ion-solvent interaction is equated with the work required to move a charged sphere of radius, r, from a vacuum into a structureless continuum characterized by a dielectric constant, (
= 80).2 There is reasonable agreement between the hydration energy calculated this way and the measured values for the halides and pseudohalides (
Ghyd| plotted versus reciprocal ionic radius. It is apparent that the polyatomic anions (often used for sizing anion-selective pores;
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PVC-TDMAC Membrane Measurements
The plasticized PVC-TDMAC membrane studied here is employed in an ion-selective electrode designed to detect small anions via a dissociated ion-exchange mechanism (
The electrode polymer membrane was composed of 1 wt% TDMAC, 33 wt% PVC, and 66 wt% ortho-nitrophenyloctyether (o-NPOE), a plasticizer. The ions were tested at a 10-mM concentration (as a Na or K salt) in distilled/deionized water, as well as in a 10-mM HEPES solution buffered at pH 7.4. The values were calculated from the average of six electrodes. The selectivity coefficient was calculated using the separate solution method (
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(1) |
where logKA,Bpotis the potentiometric selectivity coefficient, EA and EB are the experimentally determined potentials of the cells, R is the gas constant, T is temperature in degrees Kelvin, F is the Faraday constant, and z is the valence of the ion. The physical significance of Kpot and its relation to the free energy change associated with the transfer of an anion from water to the PVC membrane is presented in the Appendix and DISCUSSION sections. Dielectric constants of a number of electrode membranes were determined using an electrochemical impedance analyzer (6310; EG&G) as described by
The measured potentiometric selectivity coefficients (logK pot) for the ions used in this study are presented in Table 1. For ions like dicyanamide and tricyanomethanide, for which values for the free energy of hydration (Ghyd) were not available, we used the measured logK pot to estimate
Ghyd values by fitting a line through the data for ClO4, SCN, I, NO3, Br, and Cl using reported values of
Ghyd (
RNA Synthesis and Xenopus Oocyte Expression
Human wild-type CFTR (wtCFTR) in a pBluescript vector (Stratagene Inc.) (
Electrophysiology
Individual oocytes were perfused with an amphibian Ringer's solution containing (mM): 100.5 NaCl, 2 KCl, 1.8 CaCl, 1 MgCl, and 5 HEPES, pH 7.5. The oocyte was impaled with two microelectrodes with tips pulled (P-97; Sutter Instruments Co.) to give 0.51.5 M of resistance when filled with 3 M KCl. The open circuit membrane potential was continuously monitored on a strip chart recorder (Kipp & Zonen), and periodically the membrane was clamped (TEV-200; Dagan Corp.) and using a computer-driven protocol (Clampex; Axon Instruments), ramped from -120 to +60 mV at a rate of 100 mV/s for most analyses, although a step protocol (from -120 to +40 mV in 10-mV steps, 200 ms/step) was also used to check for time-dependent currents. The membrane conductance was calculated using the slope conductance over a 20-mV range centered on the reversal potential, and using chord conductances at various voltages. For ramp data, a correction for the capacitive transient was estimated by comparing the current measured at the holding potential to that determined at the same potential within the ramp, and the difference was subtracted from the entire event. The data was analyzed using an Excel (Microsoft Co.) spreadsheet, and secondary analyses were performed using Sigmaplot (SPSS Inc.).
After the oocyte recovered from impalement, CFTR was stimulated by adding a cocktail containing 10 mM forskolin and 1 mM 3-isobutyl-methylxanthine (IBMX) (Research Biochemicals, Inc.) to the perfusate. For ion substitution protocols, the basic amphibian Ringer's was modified to reduce interference from the endogenous Ca2+-activated Cl channel (
Calculation of Permeability Ratios, Relative Barrier Height, Relative Binding, and Relative Well Depth
Permeability ratios were calculated using the Goldman-Hodgkin-Katz equation (Equation 2) as follows:
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(2) |
where Erev is the measured shift in zero current potential after Clo is replaced with the substitute ion, subo, [Cl]'o is the bath concentration of Cl, [Cl]o is the residual Cl in the substituted solution, [sub]o is the concentration of the substitute ion, and R, T, z, and F have their usual meaning. The central goal of the analysis presented here was to use measurements of relative anion permeability and relative anion blockade to estimate the energies associated with transferring an anion from water into the channel. This required that we adopt a model (or models) for the anion translocation process that would permit us to estimate the energetic significance of differences in anion permeability or binding. It is important to note that the primary aim was not to arrive at absolute values for these energies, but rather to determine the trend in the change in the energies from one anion to another so that this trend could be compared with the change in anion size.
The relation used to interpret permeability ratios in terms of energy differences can be obtained using either of two complimentary approaches. Rate theory models for permeation predict that permeability ratios are determined by the difference in peak height for the two ions. For example, for Cl and a substitute anion the permeability ratio is given by Equation 3:
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(3) |
where (
G)peak is the difference in free energy between Cl and the substitute ion. This calculation applies to any number of barriers as long as the difference in barrier height,
(
G)peak, is the same for all barriers (peak energy offset condition;
A second route to the relation described by Equation 3 is to use a lumped Nernst-Planck model in which the permeability is expressed (Equation 4):
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(4) |
where ßi is the water-channel equilibrium partition coefficient, Di is the diffusion coefficient within the channel, A is the cross-sectional area, and x is the length of the channel. If it is assumed that the long-range, anionchannel interaction is reflected in the apparent value of ß; and that D is approximately equal for different anions, then (Equation 5):
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(5) |
where -(
G)eq is the difference in the equilibrium transfer free energy between Cl and the substitute ion. In the discussion, a simple model is used to show how these two approaches, one focusing on peak energy and the other on an equilibrium transfer energy, can yield the same result; i.e.,
(
G)peak =
(
G)eq.
Blocking efficacy was determined by exposing the oocyte to a 5-mM concentration of the substitute anion (some of the salts are only available as K salts and, for those experiments, a 5-mM KCl control was added to the protocol). Percent block was determined by measuring the decrease in the slope conductance (+/- 10 mV) at the reversal potential. Each anion was characterized by a half-maximal inhibition constant, K i1/2, calculated by assuming blockade to be a unimolecular binding event that can described by Michaelis-Menten kinetics (
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(6) |
where [x] is the concentration of added blocker, gb is the conductance measured in the presence of the blocker, and go is the conductance measured in the absence of the blocker. To convert the relative values of K i1/2 to differences in well depths, we assumed that all blocking anions bound at the same site and that blockade was the result of competition between the blocking anion and Cl for that site (
and [Cl] is the concentration of Cl at the site, KCl is the binding constant for Cl at the site and KA is the binding constant for the blocking anion at the site. If it is further assumed that the value of [Cl] and KCl are independent of the nature of the blocking anion, then the ratio of any two values of K i1/2 is given by Equation 7:
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(7) |
where (
G)well is the difference in well depth between the two ions,
GAwell -
GBwell.
We note two qualifications as regards this approach to determining relative well depth. First, the blocking anions used were all permeant to varying extents and were expected, therefore, to contribute to the measured current. Errors due to permeation of the blocking anion were minimized by using a blocker concentration (5 mM) that was ~5% that of Cl (105 mM). Second, multiple anion occupancy of CFTR (
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RESULTS |
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Selectivity Patterns for CFTR and the PVC-TDMAC Membrane
The experimentally derived parameters that comprise the selectivity patterns for CFTR and the PVC-TDMAC membrane are presented in Table 2. Permeability ratios are tabulated in two ways; using either the least permeant anion, Cl, or the most permeant anion, C(CN)3, as a reference. The latter were used to calculate (
G)peak so that each number this column reflects the increase in peak height seen by each anion over that seen by C(CN)3. The table also contains the K1/2 for blockade of Cl currents for each anion and the ratio of each K1/2 to that measured for C(CN)3. The latter values were used to calculate
(
G)well, which represents the change in well depth for each anion relative to C(CN)3, so that positive values indicate a shallower well and negative values a deeper well. Also tabulated in Table 2 are values for logKpot, obtained as described in MATERIALS AND METHODS from anion substitution protocols using the PVC-TDMAC membrane and expressed relative to Cl and to C(CN)3. As with permeability ratios and inhibitory constants, the values for logKpot were used to calculate
(
G)trans (see Appendix), which represents the increase in transfer free energy from water to the synthetic membrane for each of the anions with respect to C(CN)3.
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The values for permeability ratios and relative values of K i1/2 span a range from 1 to 8 for the former and 1 to 14 mM for the latter, and the energies associated with these indices of anion permeation and binding range from ~0.45 kJ/mol. As expected (
In Figure 2, the energy differences associated with anion permeation (A) and block (B) are plotted versus the corresponding energies derived from the response of the PVC-TDMAC membrane. The high correlation of these values (with the exception of iodide, see below) indicates that the selectivity pattern exhibited by CFTR, as judged by either relative permeability or relative binding, is qualitatively identical to that of the synthetic membrane, differing in each case only by a multiplicative constant. Anions that see a barrier height that is increased relative to that of C(CN)3 also experience a more positive (less favorable) transfer free energy between water and the synthetic membrane. Similarly, anions that bind less tightly than C(CN)3 are those for which the water-synthetic membrane transfer free energy is less favorable. It is apparent from Figure 2 that the peak and well energies change in a parallel fashion. SCN, for example, sees an energy barrier to entering the CFTR channel that is lower than that of Cl, and also sees an equilibrium free energy associated with partitioning into the synthetic membrane that is more favorable than that of Cl. Similarly, the tighter binding of SCN (relative to Cl) is correlated with ease of partitioning into the synthetic membrane. These results are, perhaps, not surprising in that the selectivity patterns for both CFTR and the PVC-TDMAC membrane have both been previously identified as being consistent with the "lyotropic" or Hofmeister series, which is ordered according to relative free energy of hydration (
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Analysis of Selectivity Patterns
To understand the physical basis of the selectivity patterns common to CFTR and the PVC-TDMAC membrane, it was necessary to relate the energy differences associated with anion permeability ratios, relative anion binding affinities, and anion partitioning into the synthetic membrane to some physical property of the anions. As exemplified by the seminal work of (
G)trans (see Appendix) are plotted versus the reciprocal of ionic radius (Table 1). In Figure 3 B, the relative heights of the energy barriers associated with entering the CFTR channel obtained from permeability ratios (Table 2) are plotted versus the reciprocal of the anionic radius. Because C(CN)3, the largest and most permeant ion, was chosen as the reference anion for both plots, for each anion, either the increase in equilibrium transfer energy (synthetic membrane) or the increase in barrier height (CFTR) relative to that seen by C(CN)3 is plotted versus 1/r. In both cases, the energy difference increases linearly with 1/r.
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The physical significance of the plots of energy difference versus reciprocal radius can be appreciated by expressing the total free energy of transfer as the sum of two components; one due to the difference in hydration energy and the other the difference in the energy of solvation of the anion within the synthetic membrane or CFTR. The former measures the energy of interaction of the anion with water, while the latter is a measure of the energy of interaction of the anion with the channel and its contents. The relative free energy of transfer, (
Gtrans), associated with either differential anion partitioning into the synthetic membrane (see Appendix) or the barrier to entry into the channel,3 can be written as in Equation 8:
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(8) |
where (
Ghyd) is the relative hydration energy and
(
Gsolv) the relative solvation energy in the membrane, both calculated using C(CN)3 as a reference (i.e., Equation 9 and Equation 10):
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(9) |
and
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(10) |
where GhydA,
GhydC(CN)3,
GsolvA, and
GsolvC(CN)3are the energies of hydration and solvation, respectively for anion, A, and C(CN)3 expressed with respect to a vacuum phase.
The solid lines in Figure 3A and Figure B, represent the values of |(
Ghyd)| relative to C(CN)3 calculated as the Born charging energy (see Appendix) using corrected radii as described in MATERIALS AND METHODS (Table 1). Note that, although the values of
(
Ghyd) are negative, they are plotted here as absolute values for convenience of comparison with
(
Gtrans). The hydration component of the energy difference will be identical for any channel or membrane, as the necessity to remove an ion from bulk water is a universal constant for any permeation process (
The linear, monotonic behavior of (
Gtrans) and
(
Ghyd) suggested a straightforward calculation of
(
Gsolv) as the difference between these two functions, and the predicted behavior of the solvation energy is indicated by the dotted lines in Figure 2A and Figure B. The selectivity patterns exhibited by the PVC-TDMAC membrane and CFTR can be readily understood in terms of the differences in the relative interaction energy of the anions with water,
(
Ghyd), and with the membrane,
(
Gsolv). In the synthetic membrane, the work required to transfer an anion from water to the plasticized PVC decreases with increasing anion radius because
(
Ghyd) is a steeper function of 1/r than is
(
Gsolv). In other words, anions larger than Cl experience weaker interactions with water and with the synthetic membrane, but they partition into the membrane more readily because they see the smallest difference between these two energies.
The linear relation between the apparent solvation energy for the PVC-TDMAC membrane and reciprocal anionic radius (Figure 3 A) suggests that Gsolv, the anion-membrane interaction energy for the PVC-TDMAC membrane, behaves precisely as predicted by the Born energy (see Equation A13) for a spherical anion contained within a polarizable medium having a dielectric constant somewhat less than that of water. The slope of the plot predicts an effective dielectric constant,
eff, for the synthetic membrane of 4.1. The measured dielectric constant of the PVC-TDMAC membrane was
= 11.5 ± 0.6, as compared with a published value of
= 14 for o-NPOE plasticized PVC membranes constructed without TDMAC (
Gsolv of changes in the dielectric constant.
Gsolv for a 1-Å sphere increases rapidly as
increases from 1 to ~20, but changes are minimal for
> 20. From the perspective of the continuum analysis of solvation energy, a medium having a dielectric constant >20 is effectively as polarizable as water (
= 80).
Figure 3 B shows the behavior of (
Gpeak),
(
Ghyd), and
(
Gsolv) for CFTR. It is immediately apparent from Figure 3 B that the modest permeability selectivity of CFTR can be attributed to the fact that the energies of hydration and solvation differ very little over the range of anion sizes examined. In other words, a visiting anion is solvated within the CFTR pore nearly as well as it is in bulk water. Accordingly, the solvation energy predicts an effective dielectric constant within the pore of ~19. The near identity of the value of
Ghyd and
Gsolv justifies treating the energies associated with anion entry as a near equilibrium process. The point is made more explicitly in Figure 4, in which are shown the predicted values expressed with respect to a vacuum reference phase for
Gpeak,
Ghyd, and
Gsolv, calculated using a value of 19 for the effective dielectric constant within the channel. This plot predicts a peak energy for Cl of 14.5 kJ/mol (5.86 RT), which agrees well with the values derived by
G of ~4.6 RT (
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Figure 5 A contains data taken from the analysis of
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Anion Binding to CFTR
Figure 6A and Figure B, shows values for the binding energies derived from the comparative analysis of blockade of CFTR by halides and pseudohalides, which we presume to reflect the presence in the permeation path of at least one energy well. Figure 6 A shows that the relative energies of binding, like the barriers to permeation, decrease with increasing values of 1/r. The implications of the variation in well depth depicted in Figure 6 A are more readily apparent from a plot of estimated values for the anionchannel interaction energies calculated at the binding site with respect to a vacuum reference (Figure 6 B). The values plotted in Figure 6 B were calculated by fixing the well depth for SCN at 12.5 kJ/mol (5.1 RT) on the basis of the dissociation constant of 6.4 mM reported by
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The anionchannel interaction energy derived from an analysis of anion binding behaves as if it consists of two components: a constant, negative energy that is similar for all anions and a radius-dependent portion that increases with decreasing anion size. Well depth, the difference between the anionchannel interaction energy (dashed line) and the hydration energy (solid line), increases with increasing anion size because, as with the barrier height, the change in hydration energy is a steeper function of 1/r than is the apparent anionchannel interaction energy at the binding site. As anionic size increases, the hydration energy decreases more rapidly than does the anionpore energy so that the net effect is to deepen the well. This result appears to be counter intuitive, because the anion that is most tightly bound experiences the smallest anionchannel interaction energy. However, relative well depth always reflects changes in both anionchannel and anionwater interactions.
The dotted line in Figure 6 B represents the anionchannel interaction energy derived from relative permeability measurements taken from Figure 4, plotted for comparison and to emphasize an important point, namely that the radius-dependent portion of the anion-channel interaction energy is similar, regardless of whether it is defined by relative permeability (peak height) or relative blocking affinity (well depth). This plot shows why larger anions experience not only a reduced barrier to entering the channel, but also a deeper energy well within the channel.
Iodide Permeation and Block
In terms of permeability selectivity, iodide stands out as an anomaly. In Figure 2 A, it can be seen that the value of PI/PCl determined for human wtCFTR expressed in Xenopus oocytes is well below that predicted for an ion that is easier to dehydrate than Cl.
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DISCUSSION |
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The Physical Significance of Lyotropic Selectivity Patterns
The measurements and analysis presented here provide a plausible explanation for the anion selectivity pattern often referred to as the lyotropic or "Hofmeister" sequence that is seen in a variety of Cl channels and in synthetic, anion-selective membranes. In both cases, the selectivity pattern can be predicted by assuming that the energy of interaction of the anion with the channel or synthetic membrane is dominated by the electrostatic energy associated with the stabilization of a charged sphere in a dielectric medium. The analysis of selectivity by Eisenman and co-workers (reviewed in
The analysis presented here provides a physical basis for "weak field strength" selectivity. In the continuum electrostatic model, the field strength is that due to the polarization of dipolar entities that are subject to the field of the visiting anion. The magnitude of the ionchannel interaction energy depends on the size of the anion and the effective dielectric constant experienced by the anion when it resides within the channel. It is important to point out that the value of the effective dielectric constant would not be expected to be governed solely by the properties of amino acid side chains that might line the pore. Although the polarizability of such entities would contribute to eff, other contributions would be expected from the remainder of the protein, including side chains and the peptide backbone, water molecules that may reside within the channel, the surrounding lipid, and even water bathing the membrane. The term "effective dielectric constant" embraces this notion (
The Effective Dielectric Constant and the Solvation of Permeant Ions
The Born-type model employed here is, from both a conceptual and computational perspective, the simplest approach to accounting for the apparent solvation energies of anions that traverse the pore. The model represents the heterogeneous ensemble of components that comprise the environment of an anion as an equivalent continuum of infinite extent characterized by an effective dielectric constant, eff. The most important result of the analysis is not the value of
eff, however. Rather, it is the fact that the lyotropic selectivity pattern can be predicted by presuming that anions interact with the channel much as they do with water, such that the stabilization energy is linearly related to reciprocal anion radius.
Attempts to measure or predict the value of the apparent dielectric constant seen by an anion inside a channel have produced widely varying results. In a large bore (minimum diameter ~10 Å), anion-selective porin (phoE, for example), eff for the pore of 24, whereas
eff may be elusive because the value is likely to depend on the type of electrostatic interaction used to define it. As indicated in MATERIALS AND METHODS,2 the value of
eff could also depend on the approach taken to define the radius of the ion (
eff, determined here, as an empirical parameter that provides a measure of the relative ability of the channel to solvate a permeating ion that offers a useful first approach to conceptualizing the electrostatic origins of the selectivity pattern.
The behavior of ions in physical or biological systems has been analyzed previously using an approach similar to the one adopted here. An analysis of the swelling and shrinking of gels by eff = 55. More recently,
eff of 21.527 for gramicidin A, and an absolute barrier for Na entry of 1014 kJ/mol.
Structural Implications for Cl-selective Channels
As regards the structure of the CFTR pore domain, the most important implication of the analysis presented here is the prediction that the permeability selectivity pattern characteristic of CFTR, as well as several other nonhomologous anion channels, does not depend on the interaction of the permeating anion with some specific component of the channel. The basic selectivity pattern, common to anion permeability and anion binding, can be viewed as the result of the interaction of the anion with a volume that exhibits the generalized property of dielectric polarizability. This type of environment could presumably be provided by a configuration of the membrane spanning segments of CFTR which, along with the resident water molecules, forms a polarizable "tunnel" through which the anions can pass (
The selectivity of anion binding by CFTR differs from relative permeability in at least two ways. First, in contrast to permeability, binding is highly sensitive to point mutations, particularly in transmembrane segments 5 and 6 (
A Working Model for Anion Permeation and Binding
The analysis of permeation and binding energetics undertaken here provides the basis for a working model of the anion conduction process in CFTR and perhaps the GABAR, GlyR, and T84-ORCC as well. In the case of CFTR, it is possible to envision two sorts of CFTR pores: those that bind anions, exemplified by the wild-type channel, and those that do not, exemplified by mutant CFTRs like G314E or Q (
Consider first a channel that does not bind anions (Figure 8 A). It is useful to envision permeant anions in the bulk solution as coordinated by an inner sphere of water molecules and surrounded by an outer sphere or shell that is the remainder of the bulk solution (
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To arrive at a model for anion binding, we begin by envisioning the lining of the wild-type pore as a "thin-walled" tube immersed in bulk water (Figure 8 B). When the anion encounters the channel in this (albeit hypothetical) condition, it enters with little or no energy cost as it retains its inner sphere water, and the outer sphere energy within the thin-walled tube is virtually identical to that experienced by the anion in bulk water. As the anion moves along the lining of the wild-type channel, however, it encounters a narrowing where some portion of the inner sphere water molecules are replaced by interactions with the polar or charged groups that line this region of the pore. These inner-sphere anionchannel interactions with the wall of the pore are somewhat more favorable than those with water so that an energy well is created. The profile for this hypothetical thin-walled anion-binding channel residing in water is depicted as the dashed line in Figure 8 D. This binding might be imagined as being analogous to that seen with anion inclusion compounds, like the katapinates, that form inner sphere interactions with Cl and Br in aqueous solution (
If these two profiles are summed (Figure 8 C), they give rise to the familiar two-barrier, one-well profile that is depicted as the dotted line in D. Although the shape of the profile as depicted in Figure 8 D is largely arbitrary, the diagram makes the point that it is possible, in principle, to account for the energetics of anion permeation through CFTR in a relatively straightforward way and illustrates how the summing of an equilibrium transfer energy with a single, localized energy well could give rise to the familiar two-barrier, one-site channel model.
Figure 8 E illustrates how radius-dependent variation in the outer sphere anion energy could vary the peak heights and well depths in a parallel fashion if the inner-sphere contribution in the binding region of the channel was roughly size independent. Large anions that experience a reduced barrier height, and enter the channel more readily, also see a deeper energy well and bind more tightly because of the reduced, radius-dependent equilibrium transfer energy.
The Significance of Ion Selectivity Patterns: from Bias to Recognition
The permeability selectivity exhibited by CFTR, and shared by GABAR, GlyR, and T84-ORCC, represents the most primitive type of ion discrimination, characteristic of a permeation path that functions as a polarizable tunnel that can stabilize a partially dehydrated ion as it passes through. This situation is a striking contrast to that envisioned for the bacterial K channel that selects for K by means of a clearly identifiable structure, the selectivity filter, consisting of a tetrahedral array of oxygen ligands (
Permeability and Anion Size
The analysis employed here emphasizes one aspect of the relation of anion size to permeation, namely that halides and pseudohalides having an equivalent sphere radius larger than that of Cl enter the pore more readily due to lower anion-water interaction energies. There is clearly a limit, however, to any "larger is better" theory of permeation. As anion size increases, the physical dimension of the pore, its effective diameter, must become limiting. Several of the "larger" molecules that were the focus of this study are roughly cylindrical in shape and the actual physical diameter of the cylinder is less than that of the diameter of the equivalent sphere (dicyanoaurate, for example, has a cylindrical diameter of ~3.4 Å at its widest point, while the equivalent sphere diameter of the molecule is ~6 Å; Table 1). On the other hand, the trimmest right cylinder into which tricyanomethanide, which has flattened pyramidal geometry, could fit would be ~7.4 Å in diameter, its widest dimension, due to the fact that there is no way to "twist" the pyramid to fit it into a smaller cylinder. This may seem to be inconsistent with the effective pore diameter of ~5.5 Å determined by
It may be necessary, however, to exercise some caution in imputing effective pore size from the behavior of poorly permeant ions. As indicated in Figure 1, polyatomic molecules like gluconate are characterized by a hydration energy that is much larger than their physical size would predict, an effect that is presumably due in part to a nonuniform charge distribution (eff = 19 for the CFTR pore predicts a peak barrier height of 15.9 kJ/mol (6.4 RT), and the difference in this value and that for Cl [14.5 kJ/mol (5.86 RT), see RESULTS] predicts a permeability ratio (Pgluconate/PCl) of ~0.58. This may be compared with the experimentally determined values of 0.071 and 0.013 reported by
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Footnotes |
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2 It has been pointed out that the magnitude of the correction to the Born radius is expected to be solvent dependent (
Dr. Smith's and Dr. Dawson's present address is Department of Physiology & Pharmacology, Oregon Health Sciences University, Portland, OR 97201
1 Abbreviations used in this paper: CFTR, cystic fibrosis transmembrane conductance regulator; GABAR, gamma amino butyric acid receptor; GlyR, glycine receptor; o-NPOE, ortho-nitrophenyloctyether; ORCC, outwardly rectifying chloride channel; PVC, poly(vinyl chloride); TDMAC, tridodecylmethylammonium chloride; wtCFTR, wild-type CFTR.
3 Here we assume that we may treat anion entry into CFTR as a quasi equilibrium process, as implied in the Nernst-Planck interpretation of the permeability ratio (see MATERIALS AND METHODS and DISCUSSION).
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Acknowledgements |
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We thank Fong Sun for her essential assistance with the molecular biology and all aspects of oocyte maintenance and care, James Schaefer and Colin Cooke for their assistance with the initial experiments, Marc Post for the Excel Macros that were used in routine data analysis, Vincent Pecoraro for his assistance in our initial modeling of ions and helpful discussion regarding the chemistry of pseudohalides, and Wayne Huang of Wavefunction Inc. for his assistance with PC-Spartan.
This work was supported by grants from the National Institutes of Health (DK45880 to D.C. Dawson and GM-28882 to M.E. Meyerhoff), the University of Michigan G.I. Peptide Center, and The Center for Membrane Toxicity Studies at the Mount Desert Island Biological Laboratory.
Submitted: 1 April 1999
Revised: 29 October 1999
Accepted: 1 November 1999
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Appendix |
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An Electrostatic Analysis of the Selectivity of the Plasticized PVC-TDMAC Membrane
Anion-selective membranes were constructed of a mixture of 66% (by weight) o-NPOE, 33% PVC, and 1% TDMAC. Within the ~100-µm-thick membrane, TDMAC functions as a completely dissociated anion exchanger that favors the extraction of mobile anions and excludes cations by a Donnan mechanism (
We treat the potential across this "thick" membrane as comprised of three components, two phase boundary potentials, 1 and
2, that represent the electrical potentials associated with the solutionmembrane interfaces, and an intramembrane diffusion potential,
d, due to the mixing of Cl and the test anion within the membrane (
1, the phase boundary potential at the membrane surface in contact with the test solution. We further assume that the kinetics of transfer across this boundary are rapid with respect to those of the intramembrane mixing process so that the solutionmembrane interface may be approximated as an equilibrium anionic distribution.
Anion equilibrium between the aqueous and membrane phases is defined by the equality of the anion chemical potential in the two phases (Equation A1):
![]() |
(A1) |
where µ*w and µ*m are the standard chemical potentials for the anion in the aqueous and membrane phases, respectively; [A-]w and [A-]m are the concentrations of the anion in the two phases and Vw and Vm the respective electrical potentials. The values of concentration and electrical potentials are taken to be defined at distances sufficiently far from the membranesolution interface to exclude the space-charge region (1, is given by Equation A2:
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(A2) |
The first term on the right hand side represents the contribution to 1 due to the unequal distribution of the anion, caused by the presence of the completely dissociated ionophore, TDMAC, this is the familiar Donnan potential (
The second term in Equation A2 represents the contribution to 1 due to the differential solubility of the anion in water and in the plasticized PVC, as reflected in the membranewater partition coefficient, ß, defined at
1 = 0, given by Equation A3:
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(A3) |
Outside of the space charge region, electroneutrality dictates that the concentration of the mobile anions be equal to that of the dissociated ionophore, as shown in Equation A4:
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(A4) |
where [X+]m is the concentration of the ionophore in the bulk membrane phase. Inserting Equation A3 and Equation A4 into Equation A2 yields Equation A5:
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(A5) |
in which the total phase boundary potential, 1, is expressed as the sum of two components: one the Donnan potential and the other due to the differential partitioning of the anion between the aqueous and membrane phases. Now, we consider the change in
1,
1, that occurs when a test anion, A, is substituted for the reference anion, Cl. For a complete equimolar replacement of Cl by S, the first term in Equation A5 will be identical for both anions because (Equation A6):
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(A6) |
so that, 1 is given by (Equation A7):
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(A7) |
In the analytical chemistry literature (1/RT is defined as lnK pot, where (Equation A8)
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(A8) |
Recalling Equation A3, we can write Kpot as a function of the standard chemical potentials for the two anions (Equation A9):
![]() |
(A9) |
where µ*A and
µ*Cl represent the difference in standard chemical potential between the aqueous and membrane phases for the test anion, A and Cl, respectively.
Each of these differences in standard chemical potential can be expressed as the difference in the free energy associated with bringing the anion from a reference phase (defined as a vacuum) to the aqueous phase or to the membrane phase, respectively, so that for the substitute ion and Cl, Equation A10 and Equation A11 apply:
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(A10) |
and
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(A11) |
For any anion, the difference in standard chemical potential, and hence the partition coefficient, may be regarded as a reflection of the difference between the energy of interaction of the anion with water, Ghyd, and with the membrane,
Gsolv, respectively. We denote this difference for each anion,
Gtrans, the work required to move one mole of the anion from water to the membrane phase. The value of Kpot is a reflection of the value of
Gtrans relative to that of the test ion and Cl, and we denote this as
(
Gtrans).
An Electrostatic Model for (
Gtrans)
Following the approach of Ghyd and
Gsolv by assuming that the dominant contribution to these energies will be the electrostatic energy associated with the net charge on the anion. This energy is calculated by letting each anion be represented by a sphere of radius, r, and calculating the work required to move the ion from a vacuum reference phase to water or to the membrane. This is given by the difference in the work required to discharge the anion in vacuo (
= 1) and that required to recharge it in water or the plasticized PVC membrane.
Each of these phases is represented as being an infinite, structureless continuum, characterized by a dielectric constant, , a reflection of its polarizability. The values of
Ghyd and
Gsolv will both be negative because the dielectric constants of the two phases are both greater than unity (
water = 80,
m ~ 14). The values for
Ghyd and
Gsolv are thus given by Equation A12 and Equation A13:
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(A12) |
and
![]() |
(A13) |
where r is the anionic radius, is the dielectric constant, and K is a constant given by Equation A14:
![]() |
(A14) |
where N is Avogadro's number, e is the electronic charge, and 0 is the permittivity of free space.
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