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Department of Molecular and Cell Biology, University of California, Berkeley, California 94720-3202
Received 17 July 2007/ Accepted 14 September 2007
| ABSTRACT |
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| INTRODUCTION |
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AcrB utilizes the proton motive force as energy for its transport function (14, 34, 35). Charged residues within the TM helices of this transporter, including Asp407, Asp408, and Lys940, have been identified as amino acid residues essential for activity (19), presumably functioning as components of the proton relay system. We previously used site-directed mutants with mutations in these residues, as well as Thr978, which was also shown to be a likely partner in the proton relay network, in an attempt to obtain an AcrB conformation mimicking the transient conformation in the middle of drug extrusion (29, 27). Although the structures of the TM domains of the mutants showed that the mutations disrupt the close interaction among the four residues mentioned above, the conformation of the periplasmic domain, through which the drug molecules must be transported, was rather similar to that of the wild-type protein, in contrast to our expectations (27).
The recent elucidation of the crystallographic structures of the asymmetric trimers of AcrB (18, 26) resulted in important progress in our understanding of the transport process. In the asymmetric trimer, each protomer of AcrB has a conformation different from that of its neighbors. Murakami et al. (18) further succeeded in solving the structure of a trimer containing a bound drug molecule in one of the protomers and thus proposed that each protomer corresponds to one of the three functional states of the transport cycle, namely, "access," "binding," and "extrusion." The conformation of the proton-binding structure in the TM domain, involving the four amino acids mentioned above, was very similar in the extrusion protomer described by Murakami et al. (18) and our site-directed mutant proteins (27). However, the latter did not show the remarkable conformational alteration seen in the periplasmic domain of the extrusion protomer, presumably because this alteration requires cooperative conformational alterations of the neighboring protomers, which were not possible in our homotrimers, which contained the same mutant protomers at all three positions.
The model for the drug extrusion mechanism proposed by Murakami et al. (18) is thus very attractive. At present, however, it remains a model and proposal. We set out to test this model by taking advantage of the observation that the external cleft in the periplasmic domain becomes much narrower in the extrusion protomer and also the observation that there are significant changes in the interface between the periplasmic domains of protomers. We introduced cysteine residues by site-directed mutagenesis and examined if disulfide bonds were generated between certain residues and if the formation of such disulfide bonds inhibited the function of AcrB, presumably by fixing the conformation of one of the protomers within the trimeric structure.
| MATERIALS AND METHODS |
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was used for construction and propagation of various plasmid constructs. Cells were grown in Luria-Bertani (LB) broth supplemented with ampicillin (100 µg/ml), kanamycin (35 µg/ml), and/or spectinomycin (50 µg/ml) when necessary.
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To construct pU
acrB::Spcr, which was used to construct the
acrB::Spcr strain, pUCK151A (14) was digested with BsrGI and NsiI and blunt ended by the Klenow fragment of DNA polymerase I (New England Biolabs). A 1.4-kb NciI fragment containing the spectinomycin resistance gene (Spcr), aadA, from pGB2 (5) was end filled and inserted into the BsrGI-NsiI-restricted pUCK151A described above. Since the 3-kb BsrGI-NsiI fragment contained the acrB gene sequence from 231 bp downstream of the start codon to 46 bp downstream of the stop codon, in the resulting plasmid, pU
acrB::Spcr, 90% of the acrB gene was deleted and replaced by the aadA gene.
Site-specific mutagenesis. Point mutations were introduced into plasmid pSCLBH by PCR as described previously (29). Sequences of all primers used are available upon request.
Construction of strains.
An E. coli mutant with an acrB deletion, AG100YB (Table 1), was generated by a method involving the introduction of a linear homologous DNA fragment, often called "recombineering" (25), but the
red genes expressed from the pKD46 plasmid of Datsenko and Wanner was used (6). In this manner, no extraneous FLP recognition target sequences were introduced into the genome of the resulting strain. AG100 cultures containing the heat-labile plasmid pKD46 (6) were grown at 30°C, induced with 1 mM L-arabinose to express the red genes on the plasmid, and made competent for electroporation. A 5.0-kb portion of linear DNA containing
acrB::Spcr and the flanking regions was amplified by PCR from pU
acrB::Spcr, using primers K151AFw (5'-AGATCTCACTGAACAAATCC-3') and K151ARv (5'-CTGGATTACCGCCCACG-3'). Transformants were selected on LB agar containing spectinomycin (50 µg/ml) at 37°C and screened for the expected recombination by PCR.
For construction of AG100YBD (Table 1), the dsbA1::kan mutation of strain RI90 was transduced into AG100YB, using P1cml,clr100 phage according to the protocol described by Miller (16).
Drug susceptibility assays. E. coli HNCE1a (7), AG100YB, or AG100YBD cells harboring pSPORT1-derived plasmids were tested, without isopropyl-ß-D-thiogalactopyranoside (IPTG) induction, for drug susceptibility by the gradient plate method as described previously (4, 29). A linear concentration gradient of cholic acid (Sigma) was prepared in square LB agar plates containing 8,000, 10,000, and 16,000 or 18,000 µg/ml of cholic acid in the lower layer for HNCE1a, AG100YB, and AG100YBD, respectively. Mid-exponential-phase cultures were diluted to an optical density at 660 nm (OD660) of 0.1 with LB broth supplemented with ampicillin (100 µg/ml) and streaked as a line across the plate, parallel to the drug gradient. Bacterial growth across the plates, from low to high drug concentrations, was measured after 24 h at 37°C. All mutants were assayed at least four times, using strains harboring wild-type cysteineless pSCLBH and the vector pSPORT1 as controls. The relative activity of each mutated AcrB protein was calculated as described previously (29), and the activities of controls with full efflux activity (pSCLBH) and no efflux activity (pSPORT1) were defined as 100 and 0%, respectively.
Ethidium accumulation assay and effect of methanethiosulfonate (MTS) cross-linking reagents. AG100YBD cells harboring pSPORT1-derived plasmids were grown in LB medium with ampicillin without IPTG induction to an OD660 of 0.7 to 0.9 at 37°C. Cells were then harvested at room temperature, washed once, and resuspended in buffer A (50 mM sodium phosphate buffer [pH 7.0] containing 100 mM NaCl and 0.1% [vol/vol] glycerol). The accumulation of ethidium by cells was monitored by determining the fluorescence of the cells with a Shimadzu RF-5301PC spectrofluorometer (Shimadzu Scientific Instruments, Inc., Columbia, MD) at room temperature as described previously (13). The final concentration of ethidium bromide used was 5 µM, and the concentration of bacterial cells corresponded to an OD660 of 0.2. The excitation and emission wavelengths were 520 and 590 nm, respectively, with slit widths of 5 nm for excitation and 10 nm for emission.
To investigate the effect of MTS reagents on the ethidium accumulation, after 2 min of preincubation with ethidium bromide, 5 mM 1,2-ethanediyl bismethanethiosulfonate (MTS-2-MTS) and 10 mM pentyl MTS (5-MTS) (Toronto Research Chemicals, Toronto, Ontario, Canada), freshly dissolved in dimethyl sulfoxide-ethyl acetate (3:1, vol/vol), were added to the cells to final concentrations of 20 and 40 µM, respectively, and the accumulation of ethidium was followed. A similar cross-linking experiment was also carried out by using 1,5-pentanediyl bismethanesulfonate (MTS-5-MTS) (Toronto Research Chemicals) or dibromobimane (Molecular Probes).
To examine the effect of substrates on MTS-2-MTS cross-linking, cells were harvested at an OD660 of 0.7 to 0.9, washed once, and resuspended in buffer B (50 mM sodium phosphate [pH 7.0] containing 100 mM NaCl). Cells (1 ml; OD660, 0.4) were incubated for 5 min with 2 to 20 µM MTS-2-MTS with or without substrate (chloramphenicol) at final concentrations of 4.5 to 100 µM in buffer B at room temperature. The cells were then rapidly pelleted, washed once with buffer B, and resuspended in 2 ml of buffer A for measurement of the ethidium accumulation rate.
Analysis of AcrB expression levels and disulfide bond formation in whole cells and in the inner membrane fraction. Exponential-phase cells grown in LB broth supplemented with ampicillin were harvested, resuspended in 10 mM HEPES-KOH (pH 7.5) buffer at an OD660 of 10, and broken by sonication. In order to prevent the formation of new disulfide bonds during the manipulation, the buffer contained 20 mM iodoacetamide. In the analysis of whole cells, the sonicated suspensions were treated with the sample buffer (with 2-mercaptoethanol omitted) with or without 20 mM dithiothreitol (DTT), and proteins were resolved by sodium dodecyl sulfate-7.5% polyacrylamide gel electrophoresis. The method used for preparation of the inner membrane fraction was the method described previously (29), using 10 mM HEPES-KOH (pH 7.5) buffer containing 1.5% (wt/vol) N-lauroylsarcosine for solubilization. The levels of AcrB expression were monitored by Western blot analysis, using polyclonal rabbit antibody anti-AcrB (35) and an alkaline phosphatase-conjugated anti-rabbit secondary antibody (Sigma), and protein-antibody conjugates were visualized with nitroblue tetrazolium and 5-bromo-4-chloro-3-indolylphosphate.
Labeling and detection of free cysteine residues in Cys mutant AcrB with biotin-maleimide. HNCE1a or AG100YBD cells harboring pSPORT1-derived plasmids were grown at 37°C in LB medium with ampicillin without IPTG induction to an OD660 of 0.8 to 1.0. Cells from a 15-ml culture were collected, washed twice, and resuspended in 0.5 ml of 10 mM HEPES-KOH (pH 7.5). A freshly prepared 10 mM biotin-maleimide [N-biotinoyl-N'-(6-maleimidohexanoyl)hydrazide] (Sigma) solution in dimethylformamide was added to a final concentration of 0.2 mM, and then cells were left at room temperature for 30 min with gentle mixing. The reaction was stopped by addition of 2-mercaptoethanol to a final concentration of 20 mM, and then the cells were washed once and stored at –80°C. To purify AcrB proteins, the cells were resuspended in 300 µl of solubilization buffer (20 mM HEPES-KOH, 0.3 M NaCl, 20 mM imidazole, 10% [vol/vol] glycerol, 2% [wt/vol] dodecyl maltoside (DDM); pH 7.5), and membrane proteins were extracted with sonication, followed by a 30-min incubation on ice. After removal of cellular debris by ultracentrifugation at 150,000 x g for 30 min at 4°C, supernatants were incubated with 30 µl of BD TALON cobalt chelating resin (BD Bioscience) in Micro Bio-Spin chromatography columns (Bio-Rad) at 4°C for 1 h. The resin was washed with buffer C (20 mM HEPES-KOH, 0.3 M NaCl, 10% glycerol, 0.05% DDM; pH 7.5) containing 20 mM imidazole and then eluted with 50 µl of buffer C containing 200 mM imidazole. The purified AcrB fractions were obtained after buffer exchange with 20 mM HEPES-KOH (pH 7.5) containing 50 mM NaCl, 0.02% DDM, and 10% glycerol, using Bio-Gel P-6DG gel (Bio-Rad) with Micro Bio-Spin columns. Identical amounts of the purified AcrB mutant proteins, as determined by normalization after Western blotting with a polyclonal anti-AcrB antibody (35), were subjected to 7.5% sodium dodecyl sulfate-polyacrylamide gel electrophoresis, and the proteins were transferred to a nitrocellulose membrane, which was exposed to horseradish peroxidase-conjugated streptavidin (1:5,000; Pierce), and then visualized using Western Lightning chemiluminescence reagent plus (PerkinElmer LAS, Inc). The intensity of the bands was measured by use of the NIH ImageJ program. No band was detected for the cysteineless AcrB (CL-AcrB) protein, which was used as a control.
| RESULTS |
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In the extrusion protomer, the distances between residues on the two sides of the large external cleft of the periplasmic domain are 3.8 Å between D566 and T678, 4.2 Å between F666 and T678, and 4.4 Å between F666 and Q830, as measured between the ends of the side chains. (D566 and T678 are shown with the clefts in the binding and extrusion protomers, as examples, in Fig. 1.) In contrast, the same distances are over 9 Å in the access and binding protomers and also in the crystal structure of the symmetric trimer (19). In the subunit interface, the distances between F316 in the extrusion protomer and Q687, A688, and G854 in the neighboring access protomer are 3.7, 5.2, and 4.3 Å, respectively, although the distances are >6 and >5 Å between the binding and extrusion protomers and between the access and binding protomers, respectively. On the basis of these observations, we substituted Cys residue for the amino acids just mentioned. For some of the residues, Ser was also used as a control.
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acrD host strain HNCE1a expressing wild-type CL-AcrBHis and the strain containing only the vector, respectively, indicating that the CL-AcrBHis protein was fully functional in cholate efflux, as noted previously (27). As shown in Fig. 2, single-Cys substitutions, such as CL-D566C, CL-F666C, CL-T678C, and CL-Q830C in the cleft or CL-F316C, CL-Q687C, CL-A688C, and CL-G854C at the interface of subunits, did not severely diminish the transport function, although CL-F666C (73% ± 3%) and CL-T678C (77% ± 5%) showed slightly decreased activity (Fig. 2) as assayed by resistance to cholate. The same was true for single-Ser substitutions when such substitutions were examined (Fig. 2). Similar results were obtained for the resistance to ethidium bromide, chloramphenicol, tetracycline, sodium dodecyl sulfate, and tetraphenylphosphonium (results not shown).
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Expression levels and detection of disulfide linkages in AcrB. We noted that all of our mutant proteins were present in the inner membrane at levels similar to that of CL-AcrBHis (not shown).
We tried to detect disulfide-cross-linked AcrB by Western blot analysis of whole-cell extracts solubilized without the use of reducing agents. With the mutant AcrB proteins in which disulfide cross-links were expected in the cleft region, we could not detect a strong difference in migration, although some portions of the CL-D566C/T678C protein migrated slightly faster than others (not shown). With the proteins in which cross-linking was expected in the subunit interface, portions of double-Cys mutant proteins (CL-F316C/Q687C, CL-F316C/A688C, and CL-F316C/G854C) often occurred as very-high-molecular-weight bands, which failed to enter the gel (not shown). These results showed that there was formation of disulfide bonds, but they prevented us from carrying out more detailed analysis of the cross-links generated.
We tried to estimate the number of free Cys residues left in the Cys mutant AcrB by carrying out sulfhydryl-specific labeling with biotin-maleimide. The extent of labeling of the CL-D566C/T678C double-Cys mutant AcrB was 52% of the sum of the labeling of two single-Cys mutants, D566C and T678C, and the extent of labeling of CL-F666C/Q830C was 57% of the sum of the labeling of the two single mutants. The CL-F666C/T678C double-mutant protein was labeled even more poorly (7% of the sum of the component single-mutant proteins). As controls, the mutant AcrB proteins mentioned above were labeled after expression in a dsbA1::kan host strain that prevented the formation of disulfide bonds in the periplasm (see below); the double-mutant proteins were labeled at a level that was 101% ± 16% of the sum of the levels of the single mutants. These results suggest that in the dsbA+ wild-type host strain, some of the Cys residues in the double-mutant AcrB indeed become unavailable for maleimide modification, confirming the presence of disulfide bonds. It is also of interest that not all of the Cys residues become linked in disulfide bonds; in principle, this is consistent with the "functionally rotating model" of Murakami et al. (18) that predicted that only one of three protomers would have a conformation favoring the disulfide bond formation.
Effect of dsbA mutation on activity of double-Cys mutants.
The absence of activity in the double-Cys mutants (Fig. 2) does not unequivocally prove that the disulfide bond formation inactivates the transporter, because it is still possible that the combination of two mutations, which singly do not inactivate AcrB (Fig. 2), may inactivate AcrB by mechanisms that do not involve disulfide bonds. In order to obtain stronger evidence for the contribution of disulfide bonds to AcrB inactivation, we used dsbA mutants. In E. coli, the main enzyme catalyzing disulfide bond formation in the periplasm is DsbA, a 23-kDa protein with a thioredoxin-like fold (3, 10). Mutations in dsbA cause a pleiotropic defect in disulfide bond formation in the periplasm (3, 17). We constructed for our assay a pair of isogenic strains, AG100YB (
acrB::Spcr) and AG100YBD (
acrB::Spcr dsbA1::kan). Since the levels of resistance of the AG100YB and AG100YBD strains to cholate were different from that of HNCE1a, to evaluate the transport activity of each mutant on gradient plates, the concentration of cholic acid in the lower layer for the strains was adjusted to 10,000 µg/ml for AG100YB and to 16,000 or 18,000 µg/ml for AG100YBD. Under these conditions, the lengths of growth across the gradient were reproducibly
75 mm for both strain AG100YB and strain AG100YBD expressing CL-AcrBHis and
30 mm for the strain containing only the vector.
In the dsbA+ host strain AG100YB (Fig. 3A), double mutants with mutations in the cleft showed resistance patterns similar to those of HNCE1a, as expected. However, in dsbA strain AG100YBD, the activity of the AcrB efflux pump was restored in the CL-F666C/T678C double mutant; this activity was 1% ± 1% in AG100YB and 57% ± 6% in the dsbA strain. Similarly, the activity of CL-F666C/Q830C double-mutant AcrB increased from 19% ± 3% in AG100YB to 70% ± 4% in the isogenic dsbA host. These results strongly support the hypothesis that the inactivation of the double-Cys mutant AcrB in the dsbA+ host strains is indeed due to the formation of disulfide bonds. The activity of CL-D566C/T678C mutant AcrB, however, was not restored in the dsbA background (Fig. 3A). This may have been because the distance between the two Cys residues was too small (about 3.8 Å) in the extrusion protomer, and the remaining mechanisms for disulfide bond formation were sufficient for this pair.
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In contrast to these results with the cleft mutants, the dsbA mutation in the host did not restore AcrB efflux activity in any of the three double-Cys mutants at the subunit interface (Fig. 3B). Western blot analysis showed that portions of these proteins sometimes formed very-high-molecular-weight aggregates, which failed to enter the gel, as mentioned above. It is possible that the sulfhydryl forms of these proteins eventually formed improper disulfide bonds, leading to the formation of inactive large aggregates.
Cross-linking by use of fast-acting, SH-specific reagents.
In order to confirm further that the disulfide cross-linking between the two Cys residues is responsible for the inactivation of mutant AcrB proteins, we used MTS cross-linkers, which are known to act much more rapidly than the usual cross-linkers and which therefore can be used in "real-time" inactivation experiments with transporters (2, 11). MTS-2-MTS (
5.2-Å spacer) was added to AG100YBD cells expressing CL-F666C/Q830C in the presence of ethidium bromide. The double-Cys mutant AcrB was active in the efflux of ethidium, so that only very slow entry of ethidium, which causes fluorescence following dye binding to nucleic acids, was seen initially (Fig. 4, bottom right panel). However, upon addition of MTS-2-MTS, cross-linking apparently occurred, so that AcrB became inactivated, inducing rapid ethidium accumulation and increased fluorescence (Fig. 4, bottom right panel). In contrast, MTS-2-MTS had little effect on the ethidium entry rate in cells expressing no-Cys (CL-AcrBHis) or a single-Cys (CL-F666C and CL-Q830C) AcrB (Fig. 4). (Although there was a very slow, gradual increase in ethidium accumulation with the two single-Cys mutants, this could have been the result of cross-linking of Cys to amino groups, as all the electrophilic reagents do react with amino groups, albeit slowly.) As a control reagent, a non-cross-linker, 5-MTS (whose length is similar to that of MTS-2-MTS) was used; this produced no AcrB inactivation in any of the mutants (Fig. 4). As another positive control, 40 µM (final concentration) carbonyl cyanide m-chlorophenylhydrazone, a proton conductor, was added to the cells expressing CL-AcrBHis, resulting in a rapid influx of ethidium because of inactivation of AcrB due to the loss of the proton motive force (Fig. 4, top left panel).
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9.1-Å spacer) and dibromobimane (
5 Å long; not an MTS reagent) as cross-linkers and obtained similar results (not shown). However, inactivation of the double-Cys AcrB transporter occurred more slowly with dibromobimane, as expected. Attempts to detect the substrate-induced movement of the cleft. According to the asymmetric AcrB model of Murakami et al. (18), the two cysteine residues that we introduced on both sides of the cleft approach the cross-linking distance only in the extrusion protomer. Thus, we reasoned that the rapid cycling through of the three conformations of AcrB actively extruding the substrates may enhance the cross-linking. We incubated dsbA cells expressing double-cysteine mutants of AcrB in the presence of the MTS cross-linker MTS-2-MTS with and without substrates of AcrB, such as chloramphenicol and, after washing the cells, determined the degree of inactivation of AcrB with the ethidium influx assay. We have not been able to detect reproducible effects of the presence of substrate on the extent of inactivation in repeated trials under different conditions (not shown).
| DISCUSSION |
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In this work, we utilized the observation that the external large cleft in the periplasmic domain of AcrB appears to become closed in one of the protomers (extrusion protomer) in the asymmetric trimer model (18) (Fig. 1), and we demonstrated that the cleft indeed becomes closed in vivo, resulting in inactivation of AcrB. Double-Cys mutants with mutations at the cleft almost completely lost its function, even though a mutant protein was properly expressed and localized to the inner membrane of the cells. The fact that this was due to the formation of disulfide bonds and not the result of the presence of two cysteines per se was shown by the observation that CL-F666C/T678C and CL-F666C/Q830C showed restored activity in the dsbA background, which diminished the rate of disulfide bond formation in the periplasm. However, assays dependent on the formation of disulfide bonds had to rely on the slow and indirect assay of growth inhibition, during which assembly of newly made AcrB complex must take place (see below). We therefore also used MTS cross-linking reagents, which allowed us to observe inactivation of the pumps in situ in real time (that is, within a few seconds after the addition of the reagent). Our conclusion was supported by these experiments (Fig. 4). All these results provide proof that the external cleft in the periplasmic domain of AcrB, which is wide open in two of the protomers of the asymmetric trimer model, as well as in the symmetric trimer model, becomes sufficiently closed to allow the formation of a disulfide bridge or cross-linking, which results in a loss of flexibility in the conformation, inactivating the efflux pump. These results strongly support the model of Murakami et al. (18), requiring a cyclic conformational alteration in each of the protomers for drug export, a mechanism that becomes impossible when even one of the protomers becomes inflexible by cross-linking. In this context, it is interesting that we observed that a large fraction of the Cys sulfhydryl groups are still free for modification with biotin-maleimide after the nearly complete inactivation of the pump by disulfide cross-linking.
The attempt to inactivate AcrB by creating intersubunit disulfide bonds was not as successful as the intrasubunit disulfide bond experiments discussed above. We observed inactivation with double-Cys mutants and little inactivation with controls (Fig. 2). However, examination of cross-linked products by Western blotting showed that in some experiments a portion of the proteins formed very large aggregates, and the inactivation still occurred in the dsbA host strain (Fig. 3B). It is difficult to interpret these data in a conclusive way. One likely possibility is that the cross-linking occurs during the assembly of these multisubunit pumps. If this is true, it suggests possible pitfalls with in vivo disulfide cross-linking approaches that utilize a slow, growth-dependent assay and adds emphasis to the real-time assays performed with MTS cross-linkers with the cleft mutants, as discussed above.
Finally, we attempted to determine if the cross-linkers inactivate the functioning AcrB proteins more effectively, but we could not obtain convincing results (see Results). There are several explanations for this. First, even the "resting" AcrB transporters may exist as asymmetric trimers, and they may contain protomers whose conformation is either similar or identical to that of the extrusion protomer, which can be easily cross-linked. Second, even cells without the added substrate drugs may be pumping out endogenous substrates or, for that matter, the cross-linkers themselves. AcrB can use even (modified) phospholipids as substrates at least in vitro (35), and it may be difficult to keep a transporter with such wide specificity in a truly resting state. Lastly, the cross-linking reagent could have been too efficient, so that nearly complete inactivation could have resulted even under suboptimal conditions.
It is tempting to interpret the inactivation of cleft-cross-linked AcrB in terms of the model of Murakami et al. (18). However, it should be noted that alternative interpretations are also possible. The external cleft in question has been thought to be the site where AcrA molecules fit in (19). If this is the case, then AcrA access may become difficult for cross-linked AcrB. In this connection, we emphasize that AcrA is not simply a linker of two membranes; with the AcrB homolog AcrD, the presence of AcrA was necessary for the activity of the pump in vitro (1). Another possibility is that the cleft might be on the pathway of drugs for exclusion. We have indeed shown that the wall of the cleft can bind various substrates of AcrB (33), and substitution of Phe666 with other amino acid residues does decrease the efflux activity (33) (Fig. 2); thus, at present we cannot completely exclude the hypothesis that the cross-linking and closing of the cleft inactivate AcrB through prevention of substrate access. However, these alternative hypotheses appear to be rather unlikely in view of the fact that complete inactivation depends on the cross-linking and that the single-cysteine substitutions have either no or only minimal effect on activity (Fig. 2 and 4).
| ACKNOWLEDGMENTS |
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We thank Jason Hall for constructive criticism.
| FOOTNOTES |
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Published ahead of print on 28 September 2007. ![]()
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