Correspondence to: Ian C. Forster, Physiologisches Institut der Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Fax:Fax: 41 1 636 6814; E-mail:forster{at}physiol.unizh.ch.
Released online: 11 October 1999
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Abstract |
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The substituted cysteine accessibility approach, combined with chemical modification using membrane-impermeant alkylating reagents, was used to identify functionally important structural elements of the rat type IIa Na+/Pi cotransporter protein. Single point mutants with different amino acids replaced by cysteines were made and the constructs expressed in Xenopus oocytes were tested for function by electrophysiology. Of the 15 mutants with substituted cysteines located at or near predicted membrane-spanning domains and associated linker regions, 6 displayed measurable transport function comparable to wild-type (WT) protein. Transport function of oocytes expressing WT protein was unchanged after exposure to the alkylating reagent 2-aminoethyl methanethiosulfonate hydrobromide (MTSEA, 100 µM), which indicated that native cysteines were inaccessible. However, for one of the mutants (S460C) that showed kinetic properties comparable with the WT, alkylation led to a complete suppression of Pi transport. Alkylation in 100 mM Na+ by either cationic {[2-(trimethylammonium)ethyl] methanethiosulfonate bromide (MTSET), MTSEA} or anionic [sodium(2-sulfonatoethyl)methanethiosulfonate (MTSES)] reagents suppressed the Pi response equally well, whereas exposure to methanethiosulfonate (MTS) reagents in 0 mM Na+ resulted in protection from the MTS effect at depolarized potentials. This indicated that accessibility to site 460 was dependent on the conformational state of the empty carrier. The slippage current remained after alkylation. Moreover, after alkylation, phosphonoformic acid and saturating Pi suppressed the slippage current equally, which indicated that Pi binding could occur without cotransport. Presteady state relaxations were partially suppressed and their kinetics were significantly faster after alkylation; nevertheless, the remaining charge movement was Na+ dependent, consistent with an intact slippage pathway. Based on an alternating access model for type IIa Na+/Pi cotransport, these results suggest that site 460 is located in a region involved in conformational changes of the empty carrier.
Key Words: mutagenesis, phosphate transport, electrophysiology, Xenopus laevis oocyte
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INTRODUCTION |
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Type II sodium/phosphate (NaPi-II)1 cotransporters belong to a unique class of Na+-coupled cotransport proteins that show no amino acid homology to other known cotransport proteins (
One technique that offers considerable potential for identifying functionally important residues and/or domains is the substituted-cysteine-accessibility method (SCAM;
In the present study, we have adopted a cysteine replacement strategy and substituted 15 selected amino acids with cysteine residues with the aim of identifying sites where the reaction with MTS reagents would lead to a detectable change in transport function. Having no precedent for the selection of residues, we based our choice on the following criteria: (a) residues located between hydrophobic and hydrophilic regions were chosen because these intervening regions could be likely candidates for substrate binding or conformational changes during the transport process (
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We have used the Xenopus oocyte expression system and electrophysiological methods to characterize the results of the mutagenesis. We report that of the 15 mutants assayed, only one (S460C) was sensitive to MTS reagents. We show that this mutant, under normal conditions, behaved essentially the same as the wild-type (WT) protein insofar as its kinetic characteristics were concerned. However, after exposure to membrane-impermeant MTS reagents, the kinetic properties of the chemically modified protein suggested that the native Ser-460 lies in a region involved in voltage-dependent conformational changes during the cotransport process. Moreover, Ser-460 appeared to be neither involved directly in the binding of the first Na+ ion, nor the subsequent Pi binding, but alkylation of the substituted cysteine at this site led to an inhibition of the final cotransport transition.
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MATERIALS AND METHODS |
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Molecular Biology
Mutations were introduced following the Quickchange Site-Directed Mutagenesis Kit manual (Stratagene Inc.). In brief, 10 ng of the plasmid containing the rat NaPi-IIa cDNA were amplified with 2.5 U PfuTurbo® (Strategene Inc.) DNA polymerase in the presence of 250 nM of primers. PCR amplification was performed with 20 cycles of 95°C (30 s), 55°C (1min), and 68°C (12 min). Next, 10 U of Dpn I were added directly to the amplification reaction and the sample was incubated for 1 h at 37°C to digest the parental, methylated DNA. XL1-blue supercompetent cells were transformed with 1 µl reaction mixture and plated onto LB-ampicillin-methicillin plates. The sequence was verified by sequencing. All constructs were cloned in pSport1 (GIBCO BRL). In vitro synthesis and capping of cRNAs were done by incubating the rat NaPi IIa constructs, previously linearized by NotI digestion, in the presence of 40 U of T7 RNA polymerase (Promega) and Cap Analogue (New England Biolabs Inc.) (
Immunoblotting of Oocyte Homogenates
Yolk-free homogenates were prepared 3 d after injection (H2O or cRNA). Pools of five oocytes were lysed together with 100 µl of homogenization buffer [1% Elugent (Calbiochem) in 100 mM NaCl, 20 mM Tris/HCl, pH 7.6], by pipetting the oocytes up and down (
Streptavidin Precipitation of Biotinylated Protein
Groups of five oocytes expressing C460S or the WT protein were incubated for 5 min in 100 µM 2-aminoethyl MTS hydrobromide (MTSEA)Biotin. Biotin-streptavidin precipitation was performed as described previously (
Oocyte Preparation and Injection
Stage VVI oocytes were prepared as previously described (
Solutions and Reagents
All standard chemicals and reagents were obtained from either Sigma Chemical Co. or Fluka AG. The MTS reagents, MTSEA, [2-(triethylammonium)ethyl] MTS bromide (MTSET), and sodium(2-sulfonatoethyl) MTS (MTSES), were obtained form Toronto Research Biochemicals and freshly prepared in DMSO. The concentration of DMSO did not exceed 1% and control experiments indicated no effect on transport function by DMSO at this concentration.
The solution compositions (mM) were as follows. (a) Oocyte incubation (modified Barth's solution): 88 NaCl, 1 KCl, 0.41 CaCl2, 0.82 MgSO4, 2.5 NaHCO3, 2 Ca(NO3)2, 7.5 Tris, pH 7.6, and supplemented with antibiotics (10 mg/liter penicillin, streptomycin). (b) Control superfusate (ND100): 100 NaCl, 2 KCl, 1.8 CaCl2, 1 MgCl2, and 5 HEPES, titrated to pH 7.4 with KOH. For presteady state recording, where necessary, isomolar BaCl2 was substituted for CaCl2 to reduce contamination from endogenous Ca2+-activated Cl- currents that were observed for V > -10 mV, except for experiments involving phosphonoformic acid (PFA), which otherwise complexes with Ba2+. (c) Control superfusate (ND0): as for ND100, but with N-methyl-D-glucamine or choline chloride replacing Na+ to maintain iso-osmolar external solutions. Solutions were titrated with HCl and KOH to pH 7.4. (d) Substrate test solutions: inorganic phosphate (Pi) was added to ND100 from a K2HPO4/KH2PO4 stock preadjusted to pH 7.4. For PFA-containing solutions, to take account of this being a trisodium salt, the Na+ concentration of the control solution was increased by 9 mM to maintain the same transmembrane Na+ gradient.
Functional Assays
Tracer uptake.
The procedure used for the 32P-uptake assay has been described in detail elsewhere (
Electrophysiology.
The standard two-electrode voltage clamp technique was used as previously described (
Kinetic Characterization
The modified Hill equation was fit to the dose-response data:
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(1) |
where [S] is the substrate concentration, Ipmax is the extrapolated maximum current, Kms is the concentration of substrate S, which gives a half maximum response or apparent affinity constant, and n is the Hill coefficient.
Presteady state charge movements were quantified by first subtracting records obtained in 3 mM PFA to eliminate endogenous currents. An exponential fitting routine, based on the Chebychev transform (e.g.,
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(2) |
where Qmax is the maximum charge translocated, Qhyp is the steady state charge at the hyperpolarizing limit and depends on the holding potential, V0.5 is the voltage at which the charge is distributed equally between the two states, z is the apparent valency per cotransporter, e is the electronic charge, k is Boltzmann's constant, and T is the absolute temperature.
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RESULTS |
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Cysteine Mutagenesis and Identification of One Methanethiosulfonate-sensitive Construct
Figure 1 shows the location of the residues within the rat isoform of the Na/Pi-IIa protein that we mutated individually to cysteines according to the above criteria. All mutations were confirmed by DNA sequencing and were identical to the WT except for the appropriate base changes. Each of the 15 mutants was expressed in Xenopus oocytes and tested for electrogenic transport activity under whole cell voltage-clamp conditions. For this initial functional assay, oocytes were challenged with a nearly saturating concentration of Pi (1 mM) in the presence of 100 mM Na+, pH 7.4. The Pi-activated current, measured at a holding potential of -50 mV, was compared with that of oocytes expressing the WT protein, obtained from the same donor frog. As shown in Table 1, six mutants were found to be still active and gave comparable electrogenic responses to the wild type.
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To test if alkylation of the cysteine residues by the methanethiosulfonate derivative MTSEA would affect the basic transport function, as indicated by the above electrophysiological assay, we incubated oocytes expressing these six active mutants, as well as the WT protein, in 100 µM MTSEA, and then retested for activity under the same conditions as before. The Pi-induced change in holding current, exhibited by the WT (Figure 2 A) as well as five of the active mutants (S318C, S373C, A393C, S532C, and S538C; data not shown), was unaffected by MTSEA (Table 1). In contrast, after incubation in MTSEA, the electrogenic response of mutant S460C showed a significant inhibition (Figure 2 A) during application of 1 mM Pi. Moreover, prolonged incubation (up to 30 min) in the standard bath medium did not lead to a restoration of function (data not shown). We also found that after alkylation, 32P uptake of S460C was completely suppressed (data not shown), which confirmed that Pi transport was fully inhibited. To demonstrate that the suppression of electrogenic response was an effect of the alkylation and not simply due to the addition of charge in this region (MTSEA is positively charged), we repeated the experiment with the negatively charged MTS reagent, MTSES. Like MTSEA, incubation in 100 µM MTSES, also induced a positive shift in the baseline current during Pi application; i.e., the normal inward current induced by Pi was fully suppressed (data not shown). We also incubated oocytes in 100 µM MTSET, which has been reported to be less permeant than MTSEA (
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As a further confirmation that chemical modification (alkylation) of Cys-460 was involved, we incubated oocytes that had been previously exposed to either MTSEA (n = 3) or MTSES (n = 3) in the reducing reagent dithiothreitol (DTT, 10 mM, 15 min) and retested for functional activity. As shown in Figure 2 B for a representative oocyte expressing S460C, exposure to 1.5 µM MTSEA suppressed the Pi-induced response to ~30% of the initial magnitude, and subsequent DTT incubation restored the Pi-activated response almost to the original level. This finding was consistent with dealkylation occurring in Cys-460, which would thereby restore the original Cys residue and cotransporter function.
The effect of MTSEA on Pi-induced response for S460C was both time and dose dependent and short MTSEA exposures (30 s) resulted in large variations (up to 50%) in the amount of suppression of the Pi-activated response for oocytes from the same batch. Although the speed of recovery from Pi application prevented repeated testing of the Pi response after exposure to MTSEA for times shorter than 1 min, application of 100 µM MTSEA, together with continuous application of Pi, showed that the suppression of Pi-induced inward current was complete within 2 min (data not shown). The optimal concentration range was determined from dose-response data (Figure 2 C) whereby the Pi response (1 mM) was tested after successive 2-min applications of increasing concentrations of MTSEA. These data gave an apparent half-maximal concentration of MTSEA = 0.5 µM (n = 5). MTSEA concentrations up to 100 µM did not result in a further change in the Pi response. In all subsequent experiments, therefore, we routinely applied MTSEA at
10 µM for 23 min. The response to 1 mM Pi recorded from oocytes expressing the WT NaPi-IIa under the same conditions with repeated application of increasing MTSEA concentrations decreased by ~20%. This was within the normally observed rundown limits for NaPi-IIa when superfused for periods exceeding 30 min (
Finally, to establish that the loss of transport function by S460C was due to a specific reaction of MTSEA with the Cys-460, we incubated oocytes expressing mutant S460C, as well as the WT protein, in biotin-labeled MTSEA (biotin-MTSEA) and precipitated the protein with immobilized streptavidin (see MATERIALS AND METHODS). Expression of both proteins was confirmed by Western blot of the lysate before streptavidin precipitation. This showed that both were expressed at comparable levels (Figure 3 A). However, as indicated by the immunoprecipitation shown in Figure 3 B, only the mutant protein and not the WT could be precipitated after incubation with the biotin labeled MTSEA.
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Mutant S460C Displays Electrogenic Characteristics Typical for Type II Na+/Pi Cotransporters
The electrophysiological assay used above provided only a basic confirmation that mutant S460C behaved like the WT. Before making a detailed characterization of the effect of MTS reagents on S460C, we examined whether the replacement of Ser-460 with a cysteine altered any of the specific properties of the cotransporter that have been previously identified from steady state and presteady state measurements of the WT (
We first confirmed that S460C exhibited a dose dependency for the respective substrates (Pi, Na+) that was consistent with the WT. These findings are shown in Figure 4 A for the Pi-activated dose response and B for the Na+-activated dose response, pooled from representative oocytes expressing the mutant S460C. In each case, a set of original records at the substrate test concentrations is given for a representative oocyte. These were indistinguishable from the typical WT responses under the same conditions (data not shown). For both substrate activation data sets, the steady state currents at the test concentration were normalized to the maximum current predicted from a fit to the whole data set for each cell using the modified Hill equation (Equation 1). The Pi-activated response was determined at 100 mM Na+ and fits to the data gave a Hill coefficient, nPi = 1.04 ± 0.1 mM and an apparent affinity for Pi (KmPi) of 0.08 ± 0.01 mM. The Na+ dose response was determined at 1 mM Pi and fits to the data gave a Hill coefficient, nNa = 2.4 ± 0 2 mM and an apparent Na+ affinity (KmNa) of 56 ± 4 mM. These parameters were sufficiently close to the previously reported values for the WT under the same measurement conditions (e.g., nPi = 0.96, KmPi = 0.057, nNa = 2.9, KmNa = 52 mM;
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In the absence of Pi and presence of Na+ in the external medium, type IIa cotransporters exhibit a Na+-dependent slippage (or leak) current. For the WT expressed in oocytes, this is inhibited by the Pi analogue and competitive inhibitor for Na+/Pi cotransport, PFA (
Voltage dependence was the final property of type IIa Na+/Pi cotransport investigated for the S460C mutant, normally characterized in terms of steady state and presteady state behavior. Figure 5 A shows the steady state voltage dependence of the Pi-induced current (left currentvoltage plot), which was obtained by subtracting the holding current in the absence of Pi from that under saturating Pi (1 mM) and 100 mM Na+ (pH 7.4). These data indicate that the voltage dependence of the WT and S460C were indistinguishable for V < 0 mV. Moreover, the voltage dependence of the normalized slippage current (right currentvoltage plot) for the WT and S460C, using 3 mM PFA as the blocking agent, was essentially unchanged.
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Presteady state charge movements result from voltage-dependent steps in the type II Na+/Pi cotransporter kinetics ( at -50 mV of the cotransporter can be estimated from Equation 3:
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(3) |
where Ip-50 is the Pi-induced current at Vh = -50 mV. For S460C, substitution of the Boltzmann fit data gave = 13.5 ± 2.3 s-1 (n = 5), compared with
= 14 s-1 for the WT.
These data indicate that neither the voltage dependence of the steady state charge distribution nor the apparent valency of the cotransporter substantially changed after mutagenesis. Moreover, the transport turnover in the cotransport mode was unchanged.
Sensitivity of Mutant S460C to Methanethiosulfonate Reagents
A noteworthy result of incubation in MTSEA on the Pi response was the reduction of holding current during Pi application (Figure 2 A). We investigated this further by testing the response to 3 mM Pi or 3 mM PFA before and after 100 µM MTSEA incubation as shown for a representative oocyte in Figure 6. These substrate concentrations were chosen to ensure saturation of the responses. After alkylation, the response to PFA remained unchanged, whereas the Pi response was now identical to the PFA response. Moreover, this behavior was found to be consistent for all potentials in the range -80 to 0 mV (data not shown). This result suggested that: (a) alkylation of Cys-460 did not affect the slippage mode, (b) Na+, the cation responsible for slippage current, was still able to bind to the carrier after alkylation, and (c) Pi can still bind to the carrier after alkylation, but subsequent cotransport was suppressed. Noninjected oocytes from the same batch showed small changes in holding current with either Pi or PFA application, under the same conditions, but which were <10% of the responses recorded from S460C-expressing oocytes.
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It has been recently reported for SGLT-1 that membrane voltage and substrates can confer an apparent protection to cysteine residues from externally applied MTS reagents (
The currently proposed kinetic scheme for type II Na+/Pi cotransport (see Figure 9) predicts that a voltage step will induce presteady state relaxations, contributed by the empty carrier and Na+ binding/debinding, before reaching the final steady state in the slippage mode. Since this mode appeared to be unchanged by alkylation, we would still expect presteady state charge movements to be detectable after alkylation. Figure 7 shows presteady state relaxations recorded from a representative oocyte for voltage steps to five test potentials in the presence (A) and absence (B) of external Na+. As before, the endogenous capacitive charging transient was removed by subtracting the response to 3 mM PFA in ND100. Although MTSEA treatment resulted in a significant apparent suppression of relaxations, there was still a charge movement detectable after the endogenous membrane charging was complete (typically after 11.5 ms). Moreover, the relaxations were significantly faster in ND0 solution, which indicated that alkylation had altered the kinetics of the empty carrier. The available signal resolution and low expression levels (steady state currents induced by 1 mM Pi were typically 100150 nA) prevented a full analysis of these relaxations. Nevertheless, single exponential fitting of relaxations induced by large voltage steps indicated that, in 0 mM Na+, alkylation led to an approximately eightfold faster time constant, as shown in Table 2 for three test potentials. Since the relaxations recorded from S460C-expressing oocytes after MTSEA treatment were comparable with the speed of membrane charging, we also confirmed that, under the same perfusion conditions, significant charge movements could not be detected from noninjected oocytes from the same batch once the main capacitive charging was complete.
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In a final set of experiments, we investigated whether holding potential (Vh) during MTSEA application would also protect against alkylation as reported in the case of SGLT1 (
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DISCUSSION |
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In this study, we investigated the effect of membrane impermeant alkylating reagents on mutant constructs of the type IIa Na+/Pi cotransporter (rat NaPi-IIa). Amino acid residues, hypothesized to be in functionally sensitive regions according to specific criteria based on the topological scheme for NaPi-IIa (Figure 1), were replaced with cysteine residues. Six of the sites were located intracellularly according to this scheme and might be considered inaccessible to externally applied MTS reagents. Nevertheless, we included them in this study since we could neither fully exclude other candidate topologies (
Cys-460 Is Alkylated from the cis Side
Of the six functional mutants, only Pi-induced electrogenic response of construct S460C was suppressed by MTSEA. Since this was reversible by DTT, and the WT protein was insensitive to the externally applied MTS reagents MTSEA, MTSES, and MTSET, these findings suggested that only Cys-460 was strongly implicated as the site of alkylation. Moreover, tracer flux studies confirmed that alkylation had indeed suppressed 32P uptake. The immunodetection experiments confirmed that alkylation had left the protein intact and furthermore provided additional evidence that Cys-460 was located extracellularly (predicted to be in the third extracellular loop) (
It has been reported that MTSEA is slightly membrane permeant (
S460C Behaves According to the Ordered, Alternating Access Model for Type II Na+/Pi Transport
Based on steady state and presteady state kinetics of the WT rat NaPi-IIa and flounder NaPi-IIb isoforms, we have proposed a kinetic model for type II Na+/Pi cotransport (
In Figure 9, at least three modes of operation are possible. In the empty carrier mode, the orientation of the charged empty carrier is favored towards the cis side (state 1) when the membrane is depolarized, which increases the accessibility of Na+ ions to a binding site. After the binding of one Na+ ion (transition 1 2), the system operates in the slippage mode, whereby one Na+ ion forms a neutral complex with the empty carrier and slippage occurs through the protein (transition 2
9) in the absence of Pi. Occupancy of state 2 increases the affinity of the protein for Pi, which then binds (transition 2
3) in its divalent form (
4 and 4
5). In this cotransport mode (transition 4
5), reorientation of the fully loaded, neutral carrier to the trans side (transition 4
5) is now favored, and release of the substrates can occur as a result of the low internal Na+ concentration. The cycle is completed by a reorientation of the empty carrier (transition 10
1).
The Pi analogue PFA, which inhibits both slippage and cotransport modes, is assumed to place the system in state 2* when bound. This is consistent with the findings of 9 (see Equation A3, Appendix). Despite this departure from WT behavior, the general similarity of S460C and the WT indicated that the model scheme (Figure 9) was also valid for this construct.
Effect of Alkylation on the Kinetics of S460C: StructureFunction Implications
Two questions arise with respect to mutant S460C: (a) Can the behavior of S460C after alkylation be explained in terms of the above kinetic scheme? and (b) Which kinetic transitions are associated with the alkylated Cys-460?
The change in the steady state characteristics after alkylation, whereby saturating Pi induced a reduction in holding current that exactly matched that of PFA both before and after alkylation, suggested that site 460 was located in a functionally sensitive region of the molecule. In terms of Figure 9, an intact slippage pathway after alkylation indicates that the protein can still cycle around the loop 1 2
9
10
1, as well as occupy state 2* when PFA is bound. Moreover, the identical responses to Pi and PFA after alkylation suggest that state 3 (with Pi bound) is also intact, but alkylation of Cys-460 prevents one or more of the subsequent transitions leading to the cotransport mode. This behavior would also strongly suggest that Pi and PFA bind to the same site.
Further support for this interpretation comes from our finding that presteady state charge movements, albeit with significantly faster relaxation time constants, were still detectable after alkylation for both the empty carrier and slippage modes. From our recordings, it appeared that alkylation also caused a suppression of the charge movement, even though the magnitude of the slippage current and its steady state voltage dependence remained unchanged. However, we were unable to resolve charge movements at times earlier than 1.5 ms after the voltage step onset and, therefore, one explanation for this apparent discrepancy between the presteady state and the steady state data might be that part of the charge movement simply remained undetected.
To investigate this further, we modeled the behavior of a four-state scheme comprising states 1, 2, 9, and 10 (see Appendix).The model predicts presteady state relaxations similar to those observed before and after alkylation. Analysis of the model indicated that the steady state slippage current remains constant, as observed experimentally, if the ratio of the zero voltage rate constants for the empty carrier (transition 1 10) was held constant (see Equation A3, Appendix). We simulated effect of alkylation by arbitrarily increasing both zero voltage rate constants for this transition 10-fold, to accord with our finding of faster presteady state relaxations in 0 mM Na+. In terms of an EyringBoltzmann transition rate model, this would imply that alkylation reduces the height of the apparent energy barrier of this step. Since the apparent valencies for the voltage-dependent steps are assumed to remain the same, the increased rates for the empty carrier conformational change after alkylation would not change the overall steady state charge distribution.
Our finding of no difference between anionic and cationic MTS reagents in suppressing the Pi response would further suggest that the charge of the alkylated Cys-460 is not in the electric field, and therefore cannot alter the voltage dependence of the empty carrier. This is also consistent with an invariant steady state charge distribution after alkylation.
That Cys-460 is associated with the conformational state of the empty carrier is also suggested from our finding that in 0 mM Na+ the inhibition of the Pi response was dependent on the holding potential during MTS application; i.e., accessibility to Cys-460 was voltage dependent. In the empty carrier mode, membrane potential determines the probability of occupancy of state 1 or state 10. Since such a voltage-dependent change of state implies the movement of charged species within the membrane, the associated conformational changes are hypothesized to alter the accessibility of Cys-460. In 100 mM Na+, we found no protection with holding potential (between -50 and +20 mV) and, similarly, no protection was observed in the presence of either Pi or PFA (together with 100 mM Na+). These findings suggest that once the protein is in state 2 (Na+ bound), state 2* (PFA bound), or state 3 (Pi bound), Cys-460 is readily accessible by externally applied MTS reagents. Interestingly, in the study by
Conclusions
Our findings indicate that site 460 is located in a functionally sensitive region of the NaPi-IIa molecule, most likely associated with conformational changes of the empty carrier. As indicated in Figure 9, states 10, 1, 2, and 3 remain intact after alkylation. The subsequent transition or transitions, which are altered by alkylation and thereby inhibit the cotransport mode, remain to be identified. Our findings complement those of
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Footnotes |
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Georg Lambert and Ian C. Forster contributed equally to this work and should be considered co-first authors.
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Acknowledgements |
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The work was supported by grants to H. Murer from the Swiss National Science Foundation (31-46523), the Hartmann Müller-Stiftung (Zurich), the Olgar Mayenfisch-Stiftung (Zurich), and the Schweizerischer Bankgesellschaft (Zurich) (Bu 704/7-1).
Submitted: 2 July 1999
Revised: 30 August 1999
Accepted: 30 August 1999
1used in this paper: DTT, dithiothreitol; MTS, methanethiosulfonate; MTSEA, 2-aminoethyl MTS hydrobromide; MTSES, sodium(2-sulfonatoethyl)MTS; MTSET, [2-(trimethylammonium) ethyl] MTS bromide; NaPi-IIa, type IIa sodium-phosphate cotransporter; PFA, phosphonoformic acid; SDS, sodium-dodecyl sulfate; SGLT-1, sodium/glucose cotransporter; WT, wild-type
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Appendix |
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Simulation of a Four-State Scheme to Predict Behavior in Slippage Mode
The slippage mode was modeled as the four-state "iso uni uni" system depicted in Figure 10 ( through the membrane between the external and internal Na+ binding sites. A single Na+ ion moves an equivalent electrical distance
' on the cis side and
'' on the trans side to the respective binding sites (
' +
+
'' = 1. The translocation (step 2
3) with Na+ bound is electroneutral. The eight pseudo first order rate constants, assuming symmetrical energy barriers for each transition, are then given by:
and µ = eV/2kT, where, Nao and Nai are the external and internal Na+ concentrations (M), respectively, V is the transmembrane voltage, e is the electronic charge, k is Boltzmann's constant, T is the absolute temperature, and k012, k021, etc., are the rate constants at V = 0.
Steady State and PreSteady State Simulations
The time-dependent, net transmembrane current in response to a voltage step is given by the sum of all charge movements that occur within the transmembrane field. Simulations were performed by solving the differential equations describing the transitions using the matrix method to find the eigen values and eigen vectors (
Figure 10 B shows simulated presteady state ON relaxations in response to ideal voltage steps, corresponding to those obtained in Figure 7, before (left) and after (right) alkylation. The effect of alkylation was modeled by assuming that only the zero-voltage rate constants for the empty carrier (k014, k041) were increased 10-fold with no changes to other parameters to account for the faster relaxation time constants measured in 0 mM external Na+ (Table 2). Note that for a general four-state system, three nonzero eigen values exist, which would give three time constants in the relaxation. The limited signal resolution available for our data meant that we could resolve a single component that corresponds to the slower component seen in the simulations. The steady state levels preceding the voltage step and after the relaxation is complete are the steady state slippage current at holding potential and target potential, respectively. For the parameters chosen, the expanded traces in Figure 10 C indicate that the slippage current is unaffected by the change in relaxation kinetics, as our data show. Note that the effect of finite voltage-clamp speed and signal filtering on the relaxation time course have not been included in the simulations. Moreover, blanking the first 1.5 ms of the recordings (Figure 7) would significantly reduce the amount of detectable charge after alkylation.
A Steady State Approximation
Here we consider the dependence of the steady state current on the rate constants under rate-limiting conditions. The only transmembrane transition involving net charge transfer is 1 4, therefore the steady state current, Is, is given by Equation 10:
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(10) |
where C1 and C4 are the relative occupancies of states 1 and 4, respectively, and F is the Faraday constant. C1 and C4 can be found using the King-Altman method (
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(A2) |
If transition 2 3 is rate limiting, Equation A2 further simplifies to:
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(A3) |
Equation A3 shows that for fixed Na+ concentrations and apparent valencies, Is is a function of k023 and the ratios of zero voltage rate constants for the other transitions.
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