The ubiquinol-cytochrome c reductase (or the bc complex) is a key component of the energy-conserving electron transfer chains of mitochondria and many respiratory and photosynthetic bacteria. It catalyzes the oxidation of ubiquinol by cytochrome c and the coupled vectorial translocation of protons to generate a transmembrane pH gradient. Although many aspects of the structure and function of this enzyme complex have been elucidated(1, 2, 3, 4, 5, 6, 7) , the nature of the protein structures involved in the binding and reactions of ubiquinone and ubiquinol remain an active area of inquiry, and the identification of the residues involved in subunit interaction is in the initial stages.

The cytochrome bc complex from the purple photosynthetic bacterium Rhodobacter sphaeroides has been purified and characterized in several laboratories(8, 9, 10, 11, 12, 13) . The purified complex contains four protein subunits with five redox cofactors: two b-type cytochromes (b and b), one c-type cytochrome (cytochrome c), one high potential iron-sulfur cluster (the Rieske [2Fe-2S]), and at least one ubiquinone (Q). ()This bc complex is functionally analogous to mitochondrial ubiquinol-cytochrome c reductase, and the three largest subunits are homologous to their mammalian counterparts (14) . The degree of sequence similarity is particularly striking among the cytochrome b polypeptides from a wide range of species (2) .

The cytochrome b polypeptide contains the two b hemes and participates in the ubiquinol oxidation and ubiquinone reduction reactions of the Q cycle(6) . He et al.(15) have identified two regions of the bovine cytochrome b subunit that may participate in quinone binding using specific labeling with photoreactive quinone analogs. We have created a number of relatively conservative amino acid replacements in the region of the R. sphaeroides protein that corresponds to the first of these putative quinone-binding regions in the bovine cytochrome b. While screening the chromatophore membranes isolated from photosynthetically grown R. sphaeroides cells expressing the various mutated forms of cytochrome b, we noted that the substitution of a serine for threonine at position 160 resulted in the loss of about two-thirds of the ubiquinol-cytochrome c reductase activity in the membranes relative to membranes from control cells. Combined with the fact that this threonine residue is one of the most conserved amino acids in the primary structure of cytochrome b, this result may indicate that Thr is an important residue involved in the structure and function of the bc complex. Here we report the purification and further characterization of the complexes containing conservative substitutions at position 160 of cytochrome b, which affect the activity of the enzyme and the properties of redox centers residing in separate subunits. In general, the results are consistent with current models, placing this region of cytochrome b at or near the quinol-oxidizing center and the intersubunit interface with the iron-sulfur subunit. However, the substitution of serine for threonine 160 also has an effect on cytochrome b, which is not generally thought to interact directly with the quinol-oxidizing center. Thr may also play a role in the proper interaction of subunit IV and cytochrome b.

EXPERIMENTAL PROCEDURES

Materials

Growth of Bacteria

Construction of Mutation(s)

()

Figure 1: Plasmids constructed for mutagenesis, transfer, and expression of the R. sphaeroides fbc operons containing mutated fbcB genes encoding altered cytochromes b. A, pSELNB3503 was derived from pALTER-1 (pSELECT-1) by insertion of a 3.5-kilobase pair R. sphaeroides DNA fragment containing the fbc operon (see ``Experimental Procedures''). fbcF, fbcB, and fbcC denote the genes encoding the iron-sulfur subunit, the cytochrome b subunit, and the cytochrome c subunits, respectively. The restriction sites marked by asterisks were engineered in vitro to facilitate verification and transfer of the segment of the fbcB gene containing the mutations (see text). Only selected restriction sites are shown. B and C, broad-host-range plasmids pRKDNB3503, containing the engineered wild-type fbcFBC operon, and pRKDNB35KmBP were constructed to facilitate subcloning, conjugal transfer to R. sphaeroides, and expression of cytochrome bc complexes containing altered cytochromes b.

Construction of Vectors for the Expression of Mutated Complexes in R. sphaeroides

Other Recombinant DNA Techniques

Isolation of Chromatophores and Purification of bc1 Complexes

The cytochrome bc complexes were purified from chromatophores by a modification of the procedure of McCurley et al.(11) . Dodecyl maltoside was used to solubilize the bc complexes and 20% glycerol was included during the solubilization and loading of the first column (after Andrews et al.(12) ) to help stabilize mutated bc complexes in case they prove to be less stable to the extraction conditions. Chromatophore suspensions were adjusted to about 18 µM cytochrome b by addition of 50 mM Tris-HCl (pH 8.0 at 0 °C) containing 20% glycerol, 1 mM MgSO, and 1 mM phenylmethylsulfonyl fluoride. Dodecyl maltoside (10% solution in 50 mM Tris-HCl (pH 8.0 at 0 °C) containing 20% glycerol and 1 mM MgSO) was added to the chromatophore suspension to 0.525 mg/nmol cytochrome b, and the mixture was stirred for 30 min at 0 °C and then centrifuged at 27,000 g for 30 min. The hard precipitates at the bottom of the centrifuge tubes were discarded, and the loose pellets and supernatants were collected. 4 M NaCl was added to a final concentration of 0.1 M, and the suspension was stirred for 1 h at 0 °C. The mixture was centrifuged at 200,000 g for 90 min. The supernatants were collected and applied to a DEAE-Biogel A column equilibrated with 50 mM Tris-HCl (pH 8.0 at 0 °C) containing 20% glycerol, 100 mM NaCl, 1 mM MgSO, 5 mM NaN, and 0.01% dodecyl maltoside (TMGD buffer containing 100 mM NaCl). The column was washed with, in sequence, 3.33 volumes of TMGD buffer containing 100 mM NaCl, 2 volumes of TMD buffer (TMGD buffer without glycerol) containing 150 mM NaCl, and 2 volumes of TMD buffer containing 200 mM NaCl. The crude cytochrome bc complex was eluted from the column with TMD buffer containing 300 mM NaCl. The collected bc complex was diluted with one-half volume of TMD containing 40% glycerol and applied to a DEAE-Sepharose CL-6B column equilibrated with TMD buffer containing 100 mM NaCl. The column was washed with 2 column volumes each of TMD buffer containing 150 mM NaCl, 200 mM NaCl, and 250 mM NaCl. The nearly pure cytochrome bc complex was eluted with TMD buffer containing 375 mM NaCl and concentrated using a Centriprep-10 concentrator to a final concentration of 100 µM cytochrome b or greater. Glycerol was added to about 20%, and the purified complex was stored at -80 °C. The purity of the bc preparations estimated by SDS-PAGE was 90-95%.

Biochemical and Spectroscopic Methods

SDS-PAGE was performed according to Laemmli (42) and to Schägger and von Jagow (43) using a Bio-Rad Mini-Protean dual slab vertical cell. Disaggregation of the sample and resolution was best obtained using a freshly prepared solubilization buffer containing 5% SDS, 10 mM EDTA (pH 8.0), 5% 2-mercaptoethanol, 1 mM phenylmethylsulfonyl fluoride, and 10% glycerol, followed by separation on a 16.5% polyacrylamide gel as described(43) . Samples were incubated for 1-2 h at 30-37 °C immediately prior to loading onto the gel. Chromatophores were extracted with acetone/methanol (36) before solubilization. Western blotting was carried out as described (44) using rabbit antibody raised against purified subunit IV (33) or against purified subunit II (cytochrome c)(45) . The polypeptides separated in the SDS-PAGE gel were transferred to a 0.2-µm polyvinylidene difluoride membrane for immunoblotting. Goat anti-rabbit IgG conjugated to alkaline phosphatase or protein A conjugated to horseradish peroxidase was used as the second antibody.

Low temperature EPR spectra were obtained with a Bruker ER 200D spectrometer equipped with an Air Products flow cryostat. Some spectra were recorded at 77 °K using a liquid N Dewar. Instrument setting details are provided in the legends of the relevant figures.

RESULTS

Expression and Purification of Cytochrome bcComplexes Containing Altered Cytochrome b

The mutation Thr Tyr (T160Y) was also subsequently prepared. R. sphaeroides cells expressing this variant of cytochrome b are also able to grow photosynthetically at a reduced rate. The cytochrome b content of membranes from these cells is also elevated relative to membranes from complement cells (Table 1) but to a slightly lesser extent than membranes containing the T160S complex. The specific ubiquinol-cytochrome reductase activity of these membranes was even lower than that of membranes containing the T160S complex, only 10-20% of that found in complement membranes.

The bc complexes were extracted with dodecyl maltoside and purified by a modification of described methods (see ``Experimental Procedures'') from chromatophore membranes of Rs BC17 cells expressing the Thr Ser or Tyr mutations and from membranes of BC17 expressing the cloned wild-type complex (complement cells). The T160S complex is spectrally identical to the complement complex (Fig. 2) but retains the lower activity seen in the chromatophores. The absorbance spectrum of T160Y bc is also similar to that of the complement bc, but the ratio of b to c is lower for T160Y. The biochemical properties of the purified enzymes are summarized in Table 2. SDS-PAGE (Fig. 3) shows that the T160S and T160Y complexes contain the same four subunits as the wild-type and complement enzymes, but the T160S complex has a reduced level of subunit IV (estimated by densitometry to be about one half the level present in the complement bc complex). Indeed, addition of purified, recombinant subunit IV to the enzyme caused a 70% increase in the activity of the T160S bc complex (Fig. 4). Addition of subunit IV to the complement bc complex also produced some stimulation of the activity. By comparison, addition of exogenous subunit IV to purified three-subunit complex (completely lacking subunit IV(46) ) resulted in a 5-fold stimulation of the basal specific activity under the conditions used (Fig. 4). Apparently not all of the recombinant subunit IV preparation used was in an active conformation for interaction with depleted bc complexes, because full stimulation of the three-subunit bc required more than three molecules of subunit IV per bc complex. Examination of additional preparations of wild-type, complement, and mutant bc complexes by SDS-PAGE (not shown) indicated that the relative amount of subunit IV present varies somewhat for each preparation, but purified T160S bc had a consistently lower ratio of IV relative to subunits I-III than complement or wild-type complexes.

Figure 2: Reduced minus oxidized optical absorption spectra of purified bc complexes. Ferricyanide-oxidized and dithionite-reduced spectra of bc complexes diluted to 2.5 µM cytochrome b were recorded at room temperature in 50 mM Tris-HCl (pH 7.5), 100 mM NaCl, 1 mM MgCl, 0.01% dodecyl maltoside, and 20% glycerol, and the difference spectra were calculated.

Figure 3: SDS-PAGE of purified bc complexes and Western analysis for subunit IV. Aliquots of mutated, complement, and wild-type bc complexes containing approximately 75 pmol cytochrome b were analyzed on duplicate gels by SDS-PAGE using the tricine buffer system (A). One gel was transferred to a polyvinylidene difluoride membrane and probed with antibody raised against R. sphaeroides subunit IV (B). Lanes 1, bc from wild-type R. sphaeroides; lanes 2, bc from R. sphaeroides BC17 complement strain; lanes 3, prestained molecular mass standards; lanes 4, bc from R. sphaeroides BC17 expressing the T160Y mutation; lanes 5, bc from R. sphaeroides BC17 expressing T160S mutation. The concentration of the sample in lane 1 was overestimated prior to loading on the gel.

Figure 4: Activation of T160S and three-subunit bc complexes by addition of exogenous, recombinant subunit IV. Cytochrome bc complexes of T160S () and the three-subunit core complex () diluted to 2.5 µM cytochrome b were mixed with varying amounts subunit IV in a total volume of 30-50 µl of 50 mM Tris-HCl (pH 8.0 at 0 °C), 250 mM NaCl, 1 mM MgCl, 0.01% dodecyl maltoside, and 10% glycerol and incubated on ice for 1-2 h. 3-µl aliquots were withdrawn for assay of ubiquinol-cytochrome c reductase activity. The amount of subunit IV added was based on determination of the protein content by the method of Lowry(35) . The concentration of bc complex present was redetermined after dilution by optical difference spectroscopy and was based on the cytochrome c content.

In order to examine the relative amount of subunit IV initially present in the membranes of the mutant and complement cells, mutant and complement cells were grown side by side, and chromatophore membranes were prepared at the same time. Examination of these chromatophores by SDS-PAGE and subsequent Western blots developed with antibodies raised against subunit IV indicates that the membranes from the cells expressing T160S cytochrome b contain a significantly lower ratio of subunit IV to cytochrome b when compared with the complement membranes. It was estimated to be about 40% of the ratio found in the complement cells by densitometry corrected for the apparent relative transfer efficiency (see Fig. 5). T160Y membranes contain a modestly lower ratio of subunit IV to cytochrome b (estimated to be 80% of the complement level). Complement membranes, in turn, appear to contain a lower ratio of subunit IV than membranes from wild-type R. sphaeroides (not shown). It thus appears that R. sphaeroides cells overproducing the fbc genes due to the presence of multiple copies of the operon on a plasmid and/or other factors either do not induce a concomitant increase in the levels of subunit IV or have a more rapid turnover of that subunit. This effect is most pronounced in the case of the T160S substitution.

Figure 5: Western analysis of chromatophore membranes from mutated and complement bc complexes. Membrane samples containing 75 pmol (lanes 1-4) or 150 pmol (lanes 6-9) cytochrome b were extracted with acetone/methanol to remove pigments, redissolved in loading buffer containing SDS and 2-mercaptoethanol, and subjected to tricine SDS-PAGE on duplicate gels. One gel was transferred electrophoretically to a polyvinylidene difluoride membrane. The membrane was cut into two pieces so that the upper part contained proteins with a molecular mass greater than about 23 kDa, and the bottom section contained the low molecular mass proteins. The top section of the membrane was probed with antibodies to R. sphaeroides subunit II (cytochrome c) and developed with a horseradish peroxidase system, whereas the bottom section was probed with antibodies to subunit IV and developed with an alkaline phosphatase system. Only the Western analysis of the membrane is shown. Lane 1, chromatophores (75 pmol b) from R. sphaeroides BC17 expressing the T160S mutation; lane 2, chromatophores (75 pmol b) from BC17 expressing the T160Y mutation; lane 3, chromatophores (75 pmol b) from BC17 complement; lane 4, chromatophores (75 pmol b) from Q strain (46) lacking subunit IV; lane 5, prestained molecular mass standards; lane 6, chromatophores (150 pmol b) from BC17 expressing the T160S mutation; lane 7, chromatophores (150 pmol b) from BC17 expressing the T160Y mutation; lane 8, chromatophores (150 pmol b) from BC17 complement; lane 9, chromatophores (150 pmol b) from Q strain (46) lacking subunit IV.

Effect of Mutation on the Antimycin-sensitive Radical Associated with the Quinone-reducing Site

Figure 6: EPR spectra of the antimycin-sensitive ubisemiquinone radical in the T160S cytochrome bc complex. Oxidized complement and T160S cytochrome bc complexes containing about 300 µM cytochrome b in 50 mM Tris-HCl (pH 8.0), 300 mM NaCl, 1 mM MgCl, 0.01% dodecyl maltoside, and 20% glycerol were mixed with a fumarate/succinate mixture (40:1) such that the final concentration of succinate was 3 mM and a catalytic amount of bovine succinate-ubiquinone reductase. After recording the spectra over a range of microwave powers, the samples were thawed and a 2-fold excess of antimycin A was added. The EPR spectra of the T160S complex at 0.2 milliwatts in the absence (1) and presence (2) of antimycin are shown together with their difference (1-2; the antimycin-sensitive radical) spectrum. The inset shows the uncorrected power saturation curves of the samples. EPR instrument parameters were a microwave frequency of 9.32 GHz, a modulation amplitude of 4 G, a time constant of 0.05 s, a scan rate of 2.5 G/s, and a temperature of 140 K.

Effect of Mutation on the Rieske Iron-Sulfur Cluster

()

Figure 7: EPR spectra of the iron-sulfur cluster in T160S and complement bc complexes. A, cytochrome bc complexes (300 µM cytochrome b) were partially reduced by the addition of sodium ascorbate to 1 mM. The samples were incubated on ice for about 20 min and frozen in liquid nitrogen. EPR spectra were recorded at 8 K. The instrument settings were: microwave frequency, 9.27 G; microwave power, 2 milliwatts; modulation amplitude, 6.3 G; time constant, 0.1 s; scan rate, 20 G/s. B, the samples used in A were thawed on ice and reduced by the addition of a small excess of sodium dithionite from a buffered solution. The samples were refrozen, and the EPR spectra were recorded at 10 K. Instrument settings were the same as in A.

Effect of Mutation on the b Cytochromes

Figure 8: EPR spectra of b cytochromes in T160S and complement bc complexes. The ascorbate-reduced bc complexes were prepared as described in the legend to Fig. 7. The EPR spectra were recorded at 15 K with the following instrument settings: microwave frequency, 9.20 GHz; microwave power, 20 milliwatts; modulation amplitude, 20 G; time constant, 0.1 s; scan rate, 5 G/s.

DISCUSSION

Threonine 160 is a highly conserved residue in the primary sequence of cytochrome b, present in all known mitochondrial and eubacterial cytochromes b, except those from nematodes (2) . Its position in the primary sequence is near residues that are altered in mutations conferring resistance to Q center inhibitors (Gly, Ile, and Thr), and it is contained within a segment of the cytochrome b polypeptide that corresponds to a peptide specifically labeled by azido-quinone in the bc complex from beef heart(15) . Current interpretations of experimental data and modeling efforts place this region in an amphipathic helix, designated as helix-cd, located on the positive side of the membrane and forming part of the Q center of the complex. This region should also be close to cytochrome b, which is reduced by semiquinone in the Q center. Indeed, a mutation at the position corresponding to Ile in Rhodobacter exhibits an altered circular dichroism spectrum for cytochrome b of yeast(56) . Furthermore, the Rieske [2Fe-2S] cluster should also be located nearby, although it is bound to a different subunit of the complex, because it is reduced by quinol in the Q center and binds certain Q center inhibitors. As a conserved residue in a perhaps pivotal region of the complex, Thr proves to be a good candidate for investigation using the method of site-directed mutagenesis combined with biochemical and biophysical characterization.

Expression of the T160S mutation in cytochrome b results in a bc complex having a significant loss of activity partially compensated by a small decrease in the apparent K. Interestingly, cells expressing this mutated cytochrome b during photosynthetic growth appear to induce an increased level of the three largest subunits of the bc complex. This induction could be a regulatory response of cells expressing the mutated complexes to lowered electron transfer activity or an elevated ``redox poise.'' Alternatively, the effect could be caused by a spontaneous second-site mutation that leads to enhanced expression and is positively selected by photosynthetic growth. The latter possibility is unlikely, however, because three T160S clones independently isolated following mutagenesis all displayed elevated levels of the bc complex during the first round of photosynthetic growth following initial amplification by aerobic growth in the dark. The purified T160S complex contains a significantly reduced amount of subunit IV, relative to the bc complex purified from complemented cells. Addition of recombinant subunit IV to the partially depleted preparations results in an increase in activity; however, the final activity of reconstituted T160S bc complex still remains lower than that of the complement bc complex. Given the apparent low content of subunit IV in the T160S bc preparations, the less than 2-fold activity increase seen upon incubation with added exogenous subunit IV is surprising. One possible explanation is that a large fraction of the purified T160S bc complex is in a conformation that no longer interacts with subunit IV, perhaps due to aggregation or partial denaturation. Another possibility is that the low level of subunit IV found in the T160S membranes in the first place, as well as any conformational changes, in some measure results from a decreased affinity of subunit IV for the modified cytochrome b. The possibility that Thr in cytochrome b is directly or indirectly involved in the binding of subunit IV to the bc complex is currently under investigation. In contrast to the expression levels observed with T160S, membranes isolated from T160Y contain levels of subunit IV more comparable with the complement chromatophores. Possibly this more hydrophobic substitution has an effect on the interaction of subunit IV with cytochrome b different from that of the T160S change.

The EPR spectra of the T160S complex display altered signatures for both the Rieske iron-sulfur center and cytochrome b. Interestingly, the broad g = 3.50 signal attributed to b is shifted to lower field, whereas the g = 3.75 signal due to b appears to be essentially unchanged in the spectra of the mutated complex. This is somewhat surprising, because it is b that is thought to be located near the quinol-oxidizing center and the positive side of the membrane, whereas b resides in the central portion of the membrane or closer to the negative side and the quinone-reducing center of the complex(3, 5, 6) . Thus, the effect of the T160S substitution on the b spectrum would appear to be indicative of a long range interaction between the oxidizing center and b or of a geometry placing the two in closer proximity than current models. It is noted that long-range effects of mutations at other positions in cytochrome b have been previously reported, e.g. the redox midpoint potentials of cytochrome c were affected by substitutions in cytochrome b(27) .

The substitutions at T160 in cytochrome b also affected the EPR signature of the Rieske [2Fe-2S] center, which is located in a separate subunit of the complex. The iron-sulfur subunit is thought to bind in the general vicinity of b on the positive side of the membrane to form part of the quinol-oxidizing center, because the cluster is a primary electron acceptor from the quinol. The particular line shape observed for the [2Fe-2S] cluster is thought to be mediated by the oxidation state of the ubiquinone present in the Q center(11, 12, 50, 51, 52, 53, 57) . When oxidized quinone is present, the EPR signal is sharper than when quinol is present. The change is most apparent in the case of the g resonance, which in the bc from R. sphaeroides is found at g = 1.81 when oxidized ubiquinone is present but shifts to 1.76 and becomes much broader when ubiquinol is present. The substitutions at Thr resulted in a broadened [2Fe-2S] EPR signature with g=1.76, which is unaltered by accessible changes in the redox state of the samples. There was no detectable difference between the EPR spectra of the mutated complexes and the ``reduced state'' spectrum of the complement or wild-type bc complex. The effect of the mutations on the iron-sulfur cluster spectrum suggests that the Thr residue of cytochrome b interacts with the quinol-oxidizing center and/or the [2Fe-2S] cluster. This idea is consistent with current models of the structure and function of this part of the complex.

The effect of the T160 substitutions on the iron-sulfur cluster is also reminiscent of the change observed for the substitution of Leu for Phe (F144L) in the cytochrome b from R. capsulatus(58) . The F144L bc complex in R. capsulatus chromatophores was reported to have a very low turnover rate and a dysfunctional Q center (having less than 10% of the wild-type activity for the ubiquinol to cytochrome b reduction step). The EPR spectrum of F144L was broadened and insensitive to redox state with g assigned a value of 1.765. It was suggested that these properties of the F144L complex resulted from a reduced affinity for quinone and quinol exhibited by the Q center of the mutated complex. In a subsequent study of the effect of the extraction of ubiquinone from chromatophore membranes on the iron-sulfur cluster, Ding et al.(52) found that the g signal became very broad and was located at approximately 1.765 upon depletion of ubiquinone from R. capsulatus chromatophore membranes. These workers were able to distinguish the ``depleted state'' spectrum having g 1.765 from the ``reduced state'' spectrum with g = 1.777 and found that the line shape of the quinone-depleted state was broadened considerably beyond that seen in the presence of either ubiquinone or ubiquinol. With our EPR instrumentation we cannot assign g values with such a high degree of precision given the broadness of the g feature in the reduced and the putative quinone-depleted states. However, there was no significant difference in the width or depth of the g = 1.76 signals of the R. sphaeroides T160S and T160Y bc complexes relative to the spectrum of the complement bc in the reduced state. Thus, the changes in the iron-sulfur cluster EPR spectra resulting from the T160 substitutions in the R. sphaeroides system do not exhibit the extremely broad line shape reported for the quinone-depleted state and are probably not due to a complete absence of quinone and quinol binding to the Q center. The nature of these interactions will be the subject of future investigations. One possibility, which would account for the reduced turnover of the mutant complexes and their ``reduced state'' EPR spectra, is that ubiquinol binds more tightly to the quinol-oxidizing center of the mutated complexes than ubiquinone, raising its effective redox potential beyond the optimal range for transfer to the [2Fe-2S] cluster. Destabilization of the transient ubisemiquinone state required at the Q center would also inhibit turnover.

FOOTNOTES

*

This work was supported in part by the Oklahoma Center for the Advancement of Science and Technology Grant HN3-008 (to M. W. M.) and National Institutes of Health Grant GM 30721 (to C.-A. Y.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

§

To whom correspondence should be addressed: Dept. of Biochemistry and Molecular Biology, 246B Noble Research Center, OAES, Oklahoma State University, Stillwater, OK 74078. Tel.: 405-744-9336; Fax: 405-744-7799; mmather@bmb-fs1.biochem.okstate.edu.

()

The abbreviations used are: Q, ubiquinone; EPR, electron paramagnetic resonance; Q, ubiquinol-oxidizing center; PAGE, polyacrylamide gel electrophoresis.

()

S. Usui and L. Yu, unpublished results.

()

Y. R. Chen, D. Tolkatchev, and C.-A. Yu, unpublished results.

ACKNOWLEDGEMENTS

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