Correspondence to: Philip A. Knauf, Dept. of Biochemistry and Biophysics, Box 712, University of Rochester Medical Center, 601 Elmwood Avenue, Rochester, NY 14642. Fax:716-275-6007 E-mail:philip_knauf{at}urmc.rochester.edu.
Released online: 31 January 2000
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Abstract |
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WW781 binds reversibly to red blood cell AE1 and inhibits anion exchange by a two-step mechanism, in which an initial complex (complex 1) is rapidly formed, and then there is a slower equilibration to form a second complex (complex 2) with a lower free energy. According to the ping-pong kinetic model, AE1 can exist in forms with the anion transport site facing either inward or outward, and the transition between these forms is greatly facilitated by binding of a transportable substrate such as Cl-. Both the rapid initial binding of WW781 and the formation of complex 2 are strongly affected by the conformation of AE1, such that the forms with the transport site facing outward have higher affinity than those with the transport site facing inward. In addition, binding of Cl- seems to raise the free energy of complex 2 relative to complex 1, thereby reducing the equilibrium binding affinity, but Cl- does not compete directly with WW781. The WW781 binding site, therefore, reveals a part of the AE1 structure that is sensitive to Cl- binding and to transport site orientation, in addition to the disulfonic stilbene binding site. The relationship of the inhibitory potency of WW781 under different conditions to the affinities for the different forms of AE1 provides information on the possible asymmetric distributions of unloaded and Cl--loaded transport sites that are consistent with the ping-pong model, and supports the conclusion from flux and nuclear magnetic resonance data that both the unloaded and Cl--loaded sites are very asymmetrically distributed, with far more sites facing the cytoplasm than the outside medium. This asymmetry, together with the ability of WW781 to recruit toward the forms with outward-facing sites, implies that WW781 may be useful for changing the conformation of AE1 in studies of structurefunction relationships.
Key Words: red blood cell, oxonol, band 3, ping-pong mechanism, obligatory exchange
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INTRODUCTION |
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The AE1 (band 3) protein in human red blood cells catalyzes a very tightly coupled one-for-one exchange of Cl- for HCO3- that functions together with the enzyme carbonic anhydrase to increase the carrying capacity of the blood for CO2 (
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In attempting to relate this kinetic mechanism to structural changes in the AE1 protein, two questions are central. First, what changes in protein conformation take place during the transporting conformational change from ECli to EClo, or vice-versa, and second, what is there about binding of certain substrates that lowers the transition state free energy so as to make the transporting conformational change take place at an appreciable rate? This latter effect is apparent even for slowly transported substrates, such as iodide, because the rate of reorientation of the EIi or EIo complex is still many orders of magnitude faster than the rate of the Ei to Eo transition, which is at least 10,000x slower than the rate of Cl- exchange (
Oxonol dyes, such as WW781 {[3-methyl-1-p-sulfophenyl-5-pyrazolone-(4)]-[1,3-dibutylbarbituric acid]-pentamethine oxonol}, have proven to be very useful chemical probes for investigating the Cl- exchange system (
WW781, because of its sulfonic acid moiety, should not penetrate into the interior of red blood cells at an appreciable rate (
In the present work, we have used external WW781 binding, measured by the inhibitory effect on Cl- exchange at 0°C, to probe possible changes in AE1 conformation caused by substrate binding and by the reorientation of the transport site from the inward- to the outward-facing form. Brief reports of some of these experiments have been presented in abstract or summary form (
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MATERIALS AND METHODS |
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Nomenclature
Because of the complicated nature of the ping-pong model and the need to specify the various forms of AE1 with WW781 bound (see Figure 4 and Figure 5), we will use the following standardized nomenclature.
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Forms of AE1 and other molecules, such as WW781 and Cl-, are indicated in roman type, while dissociation constants and rate constants are in italic.
Dissociation constants for binding equilibria are indicated by Ka,b, where a is the molecule bound (e.g., Cl-) and b is the form of AE1 to which it is bound; e.g., Eo. For simplicity, in the subscripts, anions are shown without a - superscript, and WW781 is designated as W. For example, the dissociation constant for binding of Cl- to Eo is designated KCl,Eo.
Rate constants for conversion of one form of AE1 to another are designated ka,b, where a is the initial form of AE1 and b is the form resulting from the conversion.
The total of both inward- and outward-facing forms (e.g., Eo and Ei) is designated without a subscript; e.g., E. Dissociation constants for binding to both forms are indicated in a similar manner (e.g., KCl,E). The total of all forms of the AE1 protein is simply designated AE1.
The complex (complex 1) formed by the initial rapid binding of WW781 to an AE1 conformation is designated by between W and the form of AE1; e.g., WEo. The second complex, which is formed more slowly, complex 2, is designated by a -; e.g., W-Eo. The total of the two complexes (e.g., WEo + W-Eo) is indicated with no intervening symbol; e.g., WEo. Dissociation constants for WW781 binding after equilibration with both complex 1 and complex 2 are indicated by an eqW subscript; e.g., KeqW,Eo. The dissociation constant for WW781 binding to form complex 1 is designated with a 1W subscript; e.g., K1W,Eo. For general cases, where a dissociation constant can be taken to mean either that for the formation of complex 1 or that at equilibrium, a plain W subscript is used; e.g., KW,Eo. The constant describing the equilibrium ratio between complex 2 and complex 1 for a particular form of AE1 (e.g., Eo) is defined as K2/1W,Eo. Apparent dissociation constants for binding to all forms of AE1 are designated without a second subscript; e.g., K1W or KeqW.
Materials
All chemicals were reagent grade, except for WW781, which was either supplied by Dr. J.C. Freedman (SUNY Health Science Center at Syracuse, Syracuse, NY), or else purchased from Molecular Probes. WW781 stocks were dissolved in ethanol. The total ethanol concentration in all flux and pretreatment media was maintained at 1% vol/vol.
Cell Preparation
Blood was obtained, with heparin as anticoagulant, from apparently healthy volunteers, with informed consent. The blood was washed three times in 150 KH (150 mM KCl, 20 mM HEPES, 24 mM sucrose, pH 6.9 at room temperature with KOH), and the white cell layer was removed during the washes. Cells were made up to 50% hematocrit.
Treatment with WW781 and Flux Measurement
For some experiments, cells were pretreated at a hematocrit of 0.25% with WW781 in 10-ml syringes with 400-µl Eppendorf microfuge tubes attached, as described previously ( - Pt] versus time, where Pt is the cpm in an aliquot of cell-free medium at a particular time, and P
represents the cpm in a similar aliquot after complete isotope equilibration. Intracellular Cl- content was determined as previously described (
When extracellular [Cl-] was lower than intracellular [Cl-], Cl- was replaced by sucrose or a mixture of sucrose and K3citrate (with 200 mM sucrose and 25 mM citrate taken as equivalent to 150 mM KCl), as indicated. For experiments in which the external [Cl-] was much lower than the [Cl-] in the cells, appropriate corrections for the ratio of the amount of Cl- in the internal and external compartments were made, as described in detail elsewhere (
Determination of Parameters
The strategies for determining dissociation constants for various conformations of AE1 were as previously described and used in our laboratory (
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(1) |
where Ju is the flux with no inhibitor present. Nonlinear least-squares fits were done either with Enzfitter (Elsevier Biosoft) or with Origin (Microcal) software.
A problem, particularly when WW781 is allowed to equilibrate with cells, is that the inhibitory potency is so large that the concentration required for half inhibition is comparable to the concentration of AE1 molecules in the cell suspension, even at the very low hematocrits used. As noted previously (
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RESULTS |
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Determination of Dissociation Constant for Complex 1 (K1W)
We have previously shown that WW781 (W) binds to AE1 by a two-step mechanism (
Figure 3 shows K1W values calculated from several similar experiments in cells that had been equilibrated with media with different Cl- concentrations by the nystatin technique (except for those in 150 mM Cl-). If WW781 inhibits anion exchange by competing with Cl- for the transport (substrate) site, then K1W should increase with increasing [Cl-]. In contrast to this prediction, if anything there is a decrease in K1W with increasing [Cl-], although the slope of a best-fit straight line (solid line) relating K1W to [Cl-] is not significantly different from zero (P = 0.14). The mean values of K1W at various [Cl-] are shown in Table 1, together with SEM and number of experiments. In no case are the K1W values for different [Cl-] significantly different (P 0.26).
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Effect of AE1 Conformation on K1W
Because WW781 is not a competitive inhibitor, it may in principle bind to any of the different forms of the anion exchange protein, with the transport site facing inward or outward and unloaded or loaded with Cl- (Figure 4), and each of these forms may bind WW781 by a two-step process, as shown in Scheme 1 and Figure 4. If these transport-related changes in AE1 conformation affect the binding of WW781, the affinities of WW781 for the various conformations may be different.
To see whether this is the case for the initial binding step (Figure 5 A), we measured the effect of short exposure to WW781 on the Cl- exchange flux and used Dixon plot intersection techniques (
Figure 6 shows data for a typical experiment. The line for fluxes measured in 150 mM Cl- medium () intersects that for fluxes in 4 mM Cl- medium (
) at a point whose x value is equal to -K1W,Eo, the dissociation constant for binding of WW781 to Eo. It can be seen that this value is much smaller than the concentration required for half-inhibition of the Cl- flux in 150 mM Cl- medium under similar conditions (K1W), given by the negative of the x intercept for the 150 mM Cl- line, which lies far to the left of the y axis in Figure 6. As previously shown (
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Because of the rapid equilibration of ECli and EClo, and because the ratio of EClo to ECli is fixed by the ratio of kECli,EClo to kEClo,ECli (see Figure 4 and Figure 5 A), it is not possible to determine the value of K1W,EClo for WW781 binding to the EClo form by any flux technique. This can be done, however, for the Eo form that is associated with a slowly transported anion, such as iodide. As shown in Figure 6, the dissociation constant for EIo, designated K1W,EIo, is given by the negative of the x value of the intersection point for the data with 4 mM Cl- media either without () or with () iodide (6 mM) present (
Similar techniques can be used to measure K1W,Ei and K1W,EIi, as shown in Figure 7, except that in this case the external Cl- concentration is maintained constant at 20 mM. Note that the dissociation constant for initial WW781 binding to Ei, K1W,Ei, given by the negative of the x coordinate of the intersection point of the line for 20 mM [Cli] () and that for 50 mM [Cli] (
), is much larger than K1W,Eo (compare with Figure 6; note difference in abscissa scale). The corresponding value for K1W,EIi, given by the intersection point of the lines for cells with 20 mM [Cli] and either no (
) or 30 mM () [Ii], is similar to K1W,Ei, suggesting little effect of binding of even a large anion on the WW781 affinity for Ei.
Table 2 shows the average K1W values for various forms of AE1 obtained from a number of experiments similar to those shown in Figure 6 and Figure 7. The only statistically significant difference in the K1W values is that K1W,Ei is significantly larger (P = 0.03) than K1W,Eo. This is true despite the fact that the K1W,Ei values show considerably greater scatter than the values of K1W,Eo. This is mainly due to the fact that K1W,Ei is larger, so the intersection point occurs at more negative values of WW781, which necessarily are farther from the positive values at which actual measurements of fluxes can be done, but the greater difficulty of loading cells with different [Cl-] and the fact that at low [Cli] the ratio of [Cli]/[Clo] often deviates somewhat from unity also may contribute to the scatter in K1W,Ei. The mean K1W,EIo value is somewhat larger than K1W,Eo, but the difference is not significant (P = 0.18), and the single value of K1W,EIi is very similar to the K1W,Ei value, suggesting that binding of anions to either Eo or Ei has only a relatively small effect on the affinity of AE1 for the initial binding of WW781.
As shown by
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(2) |
where A is the asymmetry factor for the unloaded transporter (without anions bound), defined as the ratio Eo/Ei with [Cli] = [Clo] ( 0, because under these conditions the only forms of the transporter present are Ei and Eo. If we take the y intercept of the best-fit straight line in Figure 3 as a reasonable estimate for K1W,E, we can calculate the K1W,Ei value that would be required to give the observed intercept K1W,E value, assuming the mean value of K1W,Eo shown in Table 2 and various values of the asymmetry factor, A. A plot of K1W,Ei versus A is shown in Figure 8. Note that for A values of 0.050.1, corresponding to the values obtained by other measurement techniques (
Determination of Equilibrium Dissociation Constant, KeqW
To measure the apparent dissociation constant after WW781 comes into equilibrium with both complex 1 and complex 2, designated KeqW (Figure 5 B), cells were exposed to WW781 for at least 4 min before Cl- exchange fluxes were measured, as described in MATERIALS AND METHODS. On the basis of the rate constants measured for the WW781 complex formation in 150 mM [Cl-] medium, this should be sufficient time for WW781 inhibition to approach its maximum value. Indeed, it was found that 1 or 2 h of pretreatment produced no significant increase in inhibition (decrease in the apparent KeqW value) as compared with the standard pretreatment protocol, and that the plots of appearance of isotope versus time in media with the same [WW781] as in the pretreatment medium were nearly linear (data not shown), as expected if little further inhibition of Cl- exchange occurs during the flux measurement.
To see whether or not inhibition under these conditions still fits to a one-site binding model, fluxes were plotted against the WW781 concentration and the data were fitted to the equation for single-site inhibition. Data for cells loaded with 600 mM [Cl-] are shown in Figure 9, plotted in the form of a Dixon plot (1/J versus [WW781]). Although there is some scatter at the highest WW781 concentrations, where the fluxes are smallest, in general the fit to a straight line is very good, indicating that equilibrium inhibition can be well described by a single-site model. The straight line through the data in Figure 9 was drawn using the parameters obtained from a nonlinear fit of the single-site inhibition equation (Equation 1) to the original flux versus WW781 plot. The negative of the x intercept of this line gives the apparent KeqW under these conditions.
Figure 10 shows the results of several such experiments at different Cl- concentrations. Note that in this case the concentrations required for half-inhibition of Cl- exchange (KeqW) are much lower than those shown in Figure 3 (K1W), where exposure to WW781 was for very short times. In this case, the slope of a best-fit straight line (solid line) is significantly different from zero (P = 0.008), indicating that Cl- binding does affect the equilibrium of WW781 with complex 2.
Table 1 shows the comparison of the mean values of KeqW with those of K1W. For every case except the 600-mM Cl- data, the difference is significant, and in the latter case it approaches significance (P = 0.06). Particularly for the low [Cl-] condition, the KeqW is substantially lower than K1W, demonstrating that the equilibrium between complex 1 and complex 2 is strongly in favor of complex 2 under these conditions.
Effect of AE1 Conformation on Equilibrium Affinity for WW781
As for the initial binding, the equilibrium binding dissociation constants of the various forms of AE1 for WW781 may differ (Figure 5 B). For the equilibrium binding, the dissociation constants are designated KeqW,Eo, KeqW,EClo, etc. To see whether or not the AE1 conformation affects the equilibrium affinity for WW781, we first varied external [Cl-], which should affect the fraction of Eo relative to the other forms of AE1. As shown in Table 1, the KeqW with 2 mM [Cl-] outside was significantly lower than that with 150 mM [Cl-] outside, indicating that the Eo form has a higher affinity for WW781 than the mixture of the other forms of AE1 that prevails in 150 mM [Cl-] medium.
To determine KeqW,Eo, the dissociation constant for equilibrium binding to Eo, the effects of WW781 were measured in cells with ~150 mM [Cl-] inside and different external [Cl-] concentrations. Combined data for four such experiments are shown in Figure 11. In this case, particularly at the low external Cl- concentration (), inhibition is very pronounced even at the lowest WW781 concentrations (Figure 11 A). Although it was not possible to obtain data between 0 and ~0.1 µM WW781, because the binding to AE1 causes depletion of the WW781 in the medium under these conditions (
As shown in Figure 4, for each form of AE1, an equation for the two-step binding can be written, analogous to the equation for the total AE1 present. For Eo (Scheme 2),
where kWEo,W-Eo and kW-Eo,WEo are the rate constants for formation and breakdown of complex 2 (Scheme 2). The constant describing the equilibrium ratio between complex 2 and complex 1 for Eo is defined as:
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(3) |
K2/1W,Eo can be determined from K1W,Eo and KeqW,Eo in a manner analogous to equation 6 of
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(4) |
From the data in Table 2, K2/1W,Eo is 28, corresponding to a free energy difference, G0 [= exp(-K2/1W,Eo/RT)], between complex 2 and complex 1 (for the Eo form of AE1) of -7.6 kJ/mol. As in the case of the K1W values, binding of iodide to Eo causes an apparent increase in KeqW that is not statistically significant, but which corresponds to a K2/1W,EIo value of 12.5, suggesting that binding of iodide to Eo destabilizes complex 2 and thus decreases the equilibrium ratio of complex 2 to complex 1.
From the y intercept of the straight line fit to the KeqW values in Figure 10, it is possible to obtain a value for KeqW,E, the equilibrium dissociation constant for binding to both forms of AE1 without Cl- bound (Eo and Ei), with [Clo] = [Cli], which is 0.046 µM. As for the K1W values, this can be used together with the value of KeqW,Eo to calculate values of KeqW,Ei that are consistent with the ping-pong model (see Equation A8). As shown in Figure 12, the minimum value of KeqW,Ei consistent with the model is equal to KeqW,E, 0.046 µM, and the maximum value of A is 0.0926. Thus, the equilibrium binding data provide further evidence for at least 10-fold asymmetry in favor of Ei versus Eo, in agreement with other determinations of this parameter (
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Although it is not possible to measure the dissociation constants for WW781 binding to the individual Cl--loaded forms of AE1, ECli, and EClo, it is possible to estimate a value for the dissociation constant, KeqW,ECl (see Equation A5), for the combination of EClo and ECli, whose ratio is a constant determined by the value of the asymmetry factor for Cl--loaded forms of AE1, ACl (= kECli,EClo/kEClo,ECli = EClo/ECli) (
An alternate method for determining KeqW,E and KeqW,ECl involves fitting all of the K1W or KeqW data to Equation A6, which gives the half-inhibitory concentration as a function of KW,E, KW,ECl, and [Cl-], under conditions where [Cli] = [Clo]. If this is done for the K1W data in Figure 3, assuming that KCl,E = 50 mM ( 0.129.
Similar calculations for the KeqW data in Figure 10 (without the lowest point at 150 mM [Cl-]) (dashed line) give KeqW,ECl = 0.19 µM and KeqW,E = 0.033 µM, which corresponds to the minimum possible value of KeqW,Ei. Consistent results are obtained with A 0.134.
From the estimates of KeqW,ECl, it is further possible to calculate the values of KeqW,ECli that are compatible with the other measured parameters. This requires some knowledge of KeqW,EClo, which cannot be directly measured. However, if KeqW,EClo lies somewhere between the value of KeqW,Eo and KeqW,EIo, the value with I- bound (which seems reasonable because the smaller Cl- ion would be expected to have less effect on WW781 binding than does the larger iodide), then calculations of KeqW,ECli as a function of ACl can be done using Equation A10, as shown in Figure 13. The minimum value of KeqW,ECli consistent with the data is 0.170.19 µM (depending on which KeqW,ECl value is used), considerably higher than the minimum value of KeqW,Ei (0.0330.046 µM). Regardless of which value of KeqW,EClo is chosen, there is some value of ACl at which KeqW,ECli becomes infinite; that is, no consistent solution can be found. Thus, (based on the assumption that KeqW,EClo is within 1 SEM KeqW,EIo value) the data provide evidence that ACl < 0.28, consistent with previous nuclear magnetic resonance (NMR) experiments indicating that ACl is similar to A (
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Measurements of the KeqW,Ei and KeqW,EIi parameters by techniques similar to those used for the K1W parameters in Figure 7 are difficult because the effects of WW781 on the fluxes are so much larger than those of either [Cli] or [Ii] that the Dixon plot lines tend to be nearly parallel and the intersection points are difficult to determine with any precision. The two experiments that were performed to measure KeqW,EIi, however, gave values of 0.21 and 0.35 µM (data not shown), which, while not statistically different from the corresponding KeqW,Eo and KeqW,EIo values (Table 2), are reasonable in light of the constraints imposed on KeqW,ECli (0.17 µM) according to the analyses in Figure 13.
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DISCUSSION |
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Accuracy of Initial and Equilibrium Estimates of WW781 Affinities
The methods used to distinguish the effects of initial binding of WW781 from the effects after equilibrium is reached have the disadvantage that, since some complex 2 is formed even at early times, apparent values of K1W obtained from early time samples are always at least slightly contaminated by additional inhibition caused by the second binding step. The measurements of equilibrium parameters have the opposite problem in that the extent of the second binding step will be underestimated if the time of exposure to WW781 is not sufficient to ensure that equilibrium has been attained. Fortunately, the effects of these errors are in opposite directions, resulting in underestimates of K1W and overestimates of KeqW. Since KeqW < K1W, such errors will tend to bring the measured K1W and KeqW values closer together than they actually are. The fact that K1W is over nine times larger than KeqW for [Cl-] 150 mM (Table 1) argues that the method, while not completely accurate, is at least able to detect a considerable difference in the initial and equilibrium affinities for WW781. The significant effect of increasing [Cl-] on KeqW (Figure 10), but not on K1W (Figure 3) provides further evidence that even this first-order method is sufficient to distinguish different effects on the two parameters.
Time Course of Binding
In general, the differential equations describing the time course of the binding and transport inhibition are exceedingly complex, since each form of AE1 has its own individual parameters, as shown in Figure 4. If, however, the forms of AE1 without WW781 equilibrate rapidly with each other, as well as with their corresponding complex 1 forms, then the time course of complex 2 formation should be described by a single rate constant. This seems to be the case, at least at 150 mM [Cl-], where our previous analysis was consistent with a simple exponential approach to equilibrium for both the "on" and "off" binding reactions (
Preference for Forms of AE1
Both for the initial binding and equilibrium association, WW781 exhibits a strong preference (by >10-fold) for the Eo form of AE1 as compared with the Ei form. Previous brief reports of this work (
Conclusions about the WW781 affinity of the Cl--loaded forms, based as they are on the [Cl-] dependence of the KeqW, must be tempered by the possibility that binding of Cl- to the inhibitory modifier site may also affect the affinity for WW781. Although the dissociation constant for binding of Cl- to the modifier site (over 300 mM;
Although the binding of an oxonol analogue of WW781, diBA(5)C4, is mutually exclusive with the disulfonic stilbene, DNDS (
Effects of WW781 Binding on AE1 Conformation
Because of the preference for AE1 forms with the transport site facing outward (Eo and EClo), the addition of even as little as 1 µM of WW781 should cause a pronounced reorientation of AE1 toward the outward-facing conformations. Calculations for various cases based on values for A and ACl consistent with the present and previous data are shown in Figure 14. With 5 mM [Cl-] inside and outside, AE1 is highly biased toward the Ei form, and >93% of AE1 is in some inward-facing form. Addition of WW781 causes this to shift so that ~60% is in the outward-facing form. A Cl- gradient across the membrane, with 150 mM inside and 2 mM outside, normally results in ~56% of the sites facing outward, but with WW781 this is increased to >98%. Even with a much smaller gradient, such as 150 mM [Cli] and 30 mM [Clo], the preference for outward-facing forms is >80% in the presence of WW781 (data not shown). With symmetric 150 mM Cl- concentrations, where >90% of the sites face inward, WW781 causes rearrangement toward a more uniform distribution among the various forms, with ~55% of the transport sites facing outward.
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Because of this property, WW781 may be a useful tool for changing the orientation of sites, for studies aimed at detecting differences between the inward and outward-facing conformations, one of the central questions that must be answered if AE1 anion exchange is to be understood at the molecular level. The reorientation by WW781 toward outward-facing sites may also help to explain the early observation by
Information About the Asymmetry of the AE1 Mechanism
The data presented here add to a growing body of evidence that the AE1 transport sites are very asymmetrically distributed. The conclusion that A 0.1 is in good agreement with most of the data from flux measurements and other techniques (
0.28 agrees with 35Cl NMR binding measurements, which give an average ACl value of ~0.1, based on a measured external Cl- dissociation constant (Ko) of ~40 mM in eosin-5-maleimidetreated cells (
The data presented here demonstrate the usefulness of an oxonol inhibitor to distinguish the various conformations of AE1 and to both measure and alter the distribution among the various forms. Further work is needed to define the structural requirements that confer conformational selectivity on WW781, and to determine whether or not other oxonols with different structures exhibit the same or different conformational preferences.
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Footnotes |
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1 Abbreviations used in this paper: diBA(5)C4, bis-(1,3-dibutylbarbituric acid)-pentamethine oxonol; DNDS, 4,4'-dinitro-stilbene-2,2'-disulfonate; Ei, inside form of the AE1 protein; Eo, outside form of the AE1 protein; NMR, nuclear magnetic resonance; WW781, [3-methyl-1-p-sulfophenyl-5-pyrazolone-(4)]-[1,3-dibutylbarbituric acid]-penta-methine oxonol.
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Acknowledgements |
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The authors gratefully acknowledge the invaluable assistance of Mr. Alvin Law in analyzing data and preparing the figures in this paper and the excellent technical assistance of Ms. Jacqueline Brescia. The assistance of Dr. J.C. Freedman in providing initial samples of WW781, as well as the suggestions of Dr. Alan Weinstein (Cornell University Medical College, New York, NY) concerning the nomenclature, are also appreciated.
This study was supported by a grant from the National Institute of Diabetes, Digestive and Kidney Diseases (R01-DK-27495).
Submitted: 30 September 1999
Revised: 29 December 1999
Accepted: 4 January 2000
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Appendix 1 |
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Dependence of KW on [Cl-] with [Cli] = [Clo]
KW is defined as the concentration of WW781 that causes 50% inhibition of transport. Depending on whether experiments are done under initial binding conditions or equilibrium conditions, KW can be thought of as either K1W or KeqW.
KCl,E, the concentration of Cl- that gives half-maximal Cl- exchange, with [Cli] = [Clo], is given in Equation A8 in
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(A1) |
where A is the asymmetry ratio (Eo/Ei) for the forms of AE1 with the transport site unloaded and with [Cli] = [Clo], and ACl is the asymmetry ratio (EClo/ECli) for the Cl--loaded forms of AE1. A = (kECli,EClo KCl,Eo)/(kEClo,ECli KCl,Ei) and ACl = kECli,EClo/kEClo,ECli, where the various constants are defined as described in MATERIALS AND METHODS and Figure 4 and Figure 5. If we define ECl as the sum of ECli plus EClo and E as the sum of Ei + Eo, then their ratio is given by:
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(A2) |
KW can be defined as an apparent dissociation constant:
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(A3) |
where W is WW781, WE represents the sum of the E forms associated with WW781; that is, the sum of WEi plus WEo, and WECl represents the sum of WECli + WEClo (Figure 4 and Figure 5).
We can also define the apparent dissociation constant for binding of WW781 to the unloaded forms of AE1 as:
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(A4) |
and that for the Cl--loaded forms as:
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(A5) |
Substituting Equation A4, and Equation A5 into A3, we obtain:
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(A6) |
This equation was used to determine the dashed lines in Figure 3 and Figure 10. It can be solved for KW,ECl if KW,E is known as well as the KW for any given [Cl-]:
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(A7) |
This equation was used to calculate KW,ECl values from the KW values with 600 mM [Cl-].
As shown by
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(A8) |
which corresponds to Equation 2 for K1W,E. Similarly, KW,ECl is given by (see equation 42b of
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(A9) |
If KW,ECl is known, KW,ECli can be calculated as a function of ACl and KW,EClo, as in Figure 13, as follows:
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(A10) |
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References |
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Dalmark, M. 1976. Effects of halides and bicarbonate on chloride transport in human red blood cells. J. Gen. Physiol. 67:223-234[Abstract].
Freedman, J.C., Novak, T.S. 1983. Membrane potentials associated with Ca-induced K conductance in human red blood cells: studies with a fluorescent oxonol dye, WW781. J. Membr. Biol. 72:59-74[Medline].
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