©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Heterotetrameric Complex Formation of Inositol 1,4,5-Trisphosphate Receptor Subunits (*)

Toshiaki Monkawa (1) (2), Atsushi Miyawaki (1)(§), Tomoyasu Sugiyama (3), Hiroyuki Yoneshima (1), Miki Yamamoto-Hino (3), Teiichi Furuichi (1), Takao Saruta (2), Mamoru Hasegawa (3), Katsuhiko Mikoshiba (1) (4)

From the (1)Department of Molecular Neurobiology, Institute of Medical Science, University of Tokyo, Tokyo 108, the (2)Department of Internal Medicine, School of Medicine, Keio University, Tokyo 160, the (3)Tokyo Research Laboratories, Kyowa Hakko Kogyo Co., Ltd., Tokyo 194, and the (4)Molecular Neurobiology Laboratory, the Institute of Physical and Chemical Research (RIKEN), Tsukuba Life Science Center, Ibaraki 305, Japan

ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
FOOTNOTES
ACKNOWLEDGEMENTS
REFERENCES

ABSTRACT

The inositol 1,4,5-trisphosphate receptor (IPR) exists as a tetrameric complex to form a functional inositol 1,4,5-trisphosphate-gated Ca channel. Molecular cloning studies have shown that there are at least three types of IPR subunits, designated type 1, type 2, and type 3. The levels of expression of IPR subunits in various cell lines were investigated by Western blot analysis using type-specific antibodies against 15 C-terminal amino acids of each IPR subunit. We found that all the three types of IPR subunits were expressed in each cell line examined, but their levels of expression varied. To determine whether IPRs form heterotetramers, we employed immunoprecipitation experiments using Chinese hamster ovary cells (CHO-K1 cells), in which all three types are abundantly expressed. Each type-specific antibody immunoprecipitated not only the respective cognate type but also the other two types. This result suggests that distinct types of IPR subunits assemble to form heterotetramers in CHO-K1 cells. We also detected heterotetramers in rat liver, in which IPR type 1 and type 2 are expressed abundantly. Previous studies have shown some functional differences among IPR types, suggesting the possibility that various compositions of subunits show distinct channel properties. The diversity of IPR channels may be further increased by the co-assembly of different IPR subunits to form homo- or heterotetramers.


INTRODUCTION

Many cellular responses to hormones, neurotransmitters, and growth factors are mediated by the intracellular second messenger inositol 1,4,5-trisphosphate (IP)()(1) . IP releases Ca from intracellular stores by binding to an IP receptor (IPR)(2) , which composes an IP-gated Ca channel(3, 4, 5) . Molecular cloning studies showed that there are at least three types of IPR subunits derived from distinct genes, designated type 1 (IPR-1)(6, 7, 8, 9) , type 2 (IPR-2)(10, 11, 12) , and type 3 (IPR-3)(12, 13, 14) . Electron microscopic observations(15, 16) , cross-linking(5) , and sucrose gradient centrifugation experiments (17) have demonstrated that IPRs form tetramers. Structural and functional analyses revealed that the structure of IPR can be divided into three functionally different domains: an N-terminal IP-binding domain, a regulatory domain, and a channel domain near the C terminus(18, 19) . The channel domain is sufficient for assembly of the subunits to yield the tetrameric organization of the IPR (18, 19) and is well conserved (amino acid identity of 65-70%) among members of the IPR family (12).

The question remains as to whether distinct types of IPR subunits assemble to form heterotetramers. Previous studies described only homotetramers (5, 20) probably because in the studies cerebella were used as the material, where IPR-1 is predominant. In addition, because of the absence of an antibody that specifically recognizes IPR-2 or IPR-3, it was hard to determine IPR subunit composition. In situ hybridization studies showed distinct but overlapping expression patterns of IPRs(21, 22) . Some cell types coexpress two or three types of the IPR subunits. The coexistence of different types in individual cells suggests the possibility that the IPR complex is composed of heteromeric structures. On the basis of similarities in transmembrane topology, we have proposed that IPR is a member of the superfamily that includes the voltage- and second messenger-gated ion channels(23) . The voltage-gated K channels (24, 25) and the cyclic nucleotide-gated ion channels (26) have been demonstrated to form hetero-oligomers. By analogy, IPR-1, IPR-2 and IPR-3 subunits might also assemble to form heterotetramers.

In the present study, we sought a cell line in which all three types are abundantly expressed. Western blot analysis using type-specific monoclonal antibodies against IPR-1, IPR-2, and IPR-3 showed that all three types are abundantly expressed in Chinese hamster ovary cells (CHO-K1 cells). We also found that IPR-1 and IPR-2 are expressed in rat liver. By immunoprecipitation studies with the type-specific antibodies, we present here biochemical evidence that the three IPR subunits co-assemble in CHO-K1 cells and rat liver.


MATERIALS AND METHODS

Preparation of Membrane Proteins

CHO-K1 cells (kindly provided by Dr. Masahiro Nishijima, National Institute of Health, Japan) were cultured in Ham's F-12 medium supplemented with 10% fetal calf serum. The cells were mixed with 9 volumes of solution containing 0.25 M sucrose, 1 mM EDTA, 0.1 mM phenylmethylsulfonyl fluoride (PMSF), 10 µM leupeptin, 10 µM pepstatin A, 1 mM 2-mercaptoethanol, and 5 mM Tris-HCl, pH 7.4, and homogenized in a glass-Teflon Potter homogenizer with 10 strokes at 1,000 rpm. The homogenates were centrifuged at 1,000 g for 5 min at 4 °C. The supernatants were centrifuged at 105,000 g for 60 min at 2 °C to sediment the membrane proteins. The pellets were resuspended in 1 mM EDTA, 0.1 mM PMSF, 10 µM leupeptin, 10 µM pepstatin A, 1 mM 2-mercaptoethanol, and 50 mM Tris-HCl, pH 7.4 (buffer A). Protein concentrations were measured using the Bio-Rad protein assay kit. In the preparation of liver membrane proteins, adult Wistar rat (7-8 weeks old, male) were anesthetized by pentobarbital and perfused transcardially with phosphate-buffered saline. After the liver was removed and minced, the membrane proteins were prepared according to the same method as CHO-K1 cells.

Immunoprecipitation

The membrane proteins were solubilized by the addition of 10% Triton X-100 to give final protein and detergent concentrations of 3.0 mg/ml and 1.0%, respectively. The solution was stirred for 30 min at 4 °C and centrifuged at 20,000 g for 60 min at 2 °C, and the supernatant was used for the immunoprecipitation experiment. In non-denaturing conditions, the solubilized membrane proteins were added to immunoprecipitation buffer containing 0.15 M NaCl, 0.3% Triton X-100, 0.1% bovine serum albumin, 5 mM EDTA, 0.1 mM PMSF, 10 µM pepstatin A, and 10 mM sodium phosphate, pH 7.2, and precleared by Pansorbin (Calbiochem-Novabiochem Corp.). The precleared supernatants were incubated with 6 µg/ml mAb 18A10 (anti-IPR-1 antibody), mAb KM1083 (anti-IPR-2 antibody), or mAb KM1082 (anti-IPR-3 antibody) for 1 h at 4 °C. Then 6 µg/ml anti-rat IgG (Fc region-specific) and anti-mouse IgG (Fc region-specific) were added to the mAb 18A10 sample and the mAb KM1082 sample, respectively. Immune complexes were collected with Pansorbin. The Pansorbin particles were washed three times with 0.01% bovine serum albumin, 0.5% Triton X-100, 0.15 M NaCl, and 10 mM sodium phosphate, pH 7.2. The Pansorbin pellets were mixed with SDS-PAGE sampling buffer containing 4% SDS, 10% 2-mercaptoethanol, 20% glycerol, and 0.125 M Tris-HCl, pH 6.8, and then boiled for 3 min. After centrifugation, the supernatants were subjected to 5% SDS-PAGE in the buffer system of Laemmli(27) . After transferring the proteins electrophoretically to nitrocellulose filters, immunodetections probed with type-specific antibodies were performed. Bound antibodies were visualized by an ECL Western blotting system (Amersham Corp.).

In denaturing conditions, the solubilized membrane proteins were boiled for 5 min in buffer A containing 6 M urea, 20 mM dithiothreitol, 1% SDS, and 1% Triton X-100 and dialyzed against 0.15 M NaCl, 5 mM EDTA, 0.1 mM PMSF, 10 µM leupeptin, 10 µM pepstatin A, and 10 mM sodium phosphate, pH 7.2. The concentrations of SDS were decreased by 3.3-fold dilution of the sample with 0.15 M NaCl, 5 mM EDTA, 0.1 mM PMSF, 10 µM leupeptin, 10 µM pepstatin A, and 10 mM sodium phosphate, pH 7.2. These samples were subjected to the same immunoprecipitation experiments as the non-denaturing sample.

Expression of IPR Proteins from cDNA

cDNAs coding the entire protein of mouse IPR-1 (6) and human IPR-3 (12) were inserted into expression vector pBactS, which contains a -actin promoter and a simian virus 40 polyadenylation sequence(6) . These plasmid DNAs were introduced into NG108-15 cells by a calcium phosphate precipitation technique(28) . 20 µg of DNA were used for each 10-cm cell culture dish. When two cDNAs were co-transfected, 10 µg of each was used. Three days after transfection, the cells were collected. The membrane proteins of these transfected cells were prepared as mentioned above.


RESULTS

Expression of IPR Subunits in Cell Lines

Mouse mAbs KM1112, KM1083, and KM1082 were raised against synthetic peptides corresponding to 15 C-terminal amino acids of IPR-1 (human IPR-1 2681-2695)(8) , IPR-2 (human IPR-2 2687-2701)(12) , and IPR-3 (human IPR-3 2657-2671)(12) , respectively (). Detailed characterizations of these antibodies were described previously(29) .

In order to determine which types of IPR subunits are expressed in various cell lines, we performed Western blot analysis using mAb KM1112 (anti-IPR-1), mAb KM1083 (anti-IPR-2), and mAb KM1082 (anti-IPR-3) (Fig. 1). Almost all of the three types were expressed in each cell line examined, but the levels of expression were cell type-specific. IPR-1 was detected in LLC-PK1, OK, CHO-K1, RINm5F, PC12A, C6, NG108-15, Jurkat, Raji, and K562 cells and could be detected in Madin-Darby canine kidney cells with a longer exposure on immunodetection. The level of expression of IPR-2 was most variable. IPR-2 was detected in Madin-Darby canine kidney, LLC-PK1, CHO-K1, RINm5F, C6, NG108-15, Jurkat, Raji, and K562 cells and could be detected in OK and PC12A cells with a longer exposure on immunodetection. IPR-3 was detected in all cell lines examined. We found that all three types were abundantly expressed in CHO-K1 cells, and the tetrameric structure of IPR in this cell line was investigated.


Figure 1: Expression of IPR types in cell lines. 30 µg of membrane proteins of various cell lines were analyzed by Western blot using mAb KM1112 (anti-IPR-1, A), mAb KM1083 (anti-IPR-2, B), and mAb KM1082 (anti-IPR-3, C). Madin-Darby canine kidney (MDCK), LLC-PK1 pig kidney, OK American opossum kidney, CHO-K1 Chinese hamster ovary, RINm5F rat insulinoma, PC12A rat pheochromocytoma, C6 rat glial, NG108-15 mouse neuroblastoma rat glioma hybrid, Jurkat human T cell leukemia, Raji human Burkitt lymphoma, and K562 human chronic myelogenous leukemia cells are shown. The lower molecular weight bands seem to be degraded proteins of IPRs, because these bands were increased and the bands of IPRs were decreased by incubating the samples at 37 °C (data not shown). The bands of high molecular weight are seen in IPR-3, and are thought to represent dimer complexes.



Heterotetramers in CHO-K1 Cells

Membrane proteins of CHO-K1 cells were solubilized in 1% Triton X-100. To determine whether distinct IPR subunits assemble to form heterotetramers in CHO-K1 cells, we employed immunoprecipitation experiments using the type-specific antibodies. We used mAb 18A10 (30, 31) for immunoprecipitation of IPR-1, because this antibody immunoprecipitates IPR-1 more effectively than mAb KM1112. We examined to what extent the mAb immunoprecipitated their respective antigens from the solubilized membrane proteins in CHO-K1 cells. The immunoprecipitates with mAbs 18A10, KM1083, and KM1082 were immunoblotted with mAbs KM1112, KM1083, and KM1082, respectively. Judging from the intensity of the bands of the immunoblotting, we estimated that mAbs 18A10, KM1083, and KM1082 immunoprecipitated 62% of IPR-1, 98% of IPR-2, and 29% of IPR-3, respectively (). Then, we examined the presence of the three types of IPRs in each of the immunoprecipitates. The immunoprecipitate from mAb 18A10 was subjected to Western blot analysis using mAbs KM1112, KM1083, and KM1082. Monoclonal antibody 18A10 immunoprecipitated not only IPR-1 but also significant amounts of IPR-2 and IPR-3 (Fig. 2, lane 1). In the same way, mAb KM1083 and mAb KM1082 immunoprecipitated all three IPRs including their respective cognate antigens (Fig. 2, lanes 3 and 5). Although the band intensity does not necessarily reflect the total amount of IPR, it is possible to quantitate the immunoblot results. The immunoprecipitate of each mAb gave rise to immunosignals for the three IPR subunits with similar intensity (Fig. 2, lanes 1, 3, and 5). Similar results were obtained from repetitive experiments (n = 6). Besides, equal amounts of all three IPRs were detected in the supernatant of each mAb (data not shown). These results indicate that IPR-1, IPR-2, and IPR-3 associate with each other in CHO-K1 cells and that homomeric IPRs account for a relatively small fraction of the tetramer complexes. Nakade et al.(20) found that boiling the membranes in the presence of 6 M urea, 20 mM dithiothreitol, and 1% SDS dissociates tetramer complexes of IPR into monomers that are still capable of being immunoprecipitated. Co-immunoprecipitations of distinct types by each antibody were abolished under these denaturing conditions, whereas the respective cognate antigens were still immunoprecipitated ( Fig. 2lanes 2, 4, and 6); mAb 18A10 was somewhat ineffective in precipitating the denatured IPR-1. These findings exclude the possibility that co-immunoprecipitation of distinct types occurs through cross-reactivity of the antibodies or through nonspecific interaction with Pansorbin.


Figure 2: Immunoprecipitation of IPR subunits from CHO-K1 cells. CHO-K1 membrane proteins solubilized in 1% Triton X-100 (N, non-denaturing conditions; lanes 1, 3, and 5) or boiled in the presence of 6 M urea, 20 mM dithiothreitol, and 1% SDS (D, denaturing conditions; lanes 2, 4, and 6) were immunoprecipitated by the type-specific mAbs, as indicated at the top of each column. The immunoprecipitates were separated by 5% SDS-PAGE and transferred to nitrocellulose filters. Filters were incubated with mAb KM1112 (A), mAb KM1083 (B), and mAb KM1082 (C).



Next, we performed the same immunoprecipitation experiments using cDNA-transfected cells. When NG108-15 cells were transfected with both IPR-1 and IPR-3 cDNAs, mAb 18A10 immunoprecipitated not only IPR-1 (Fig. 3A, lane 1) but also IPR-3 (Fig. 3B, lane 1). In the same way, mAb KM1082 immunoprecipitated not only IPR-3 (Fig. 3B, lane 2) but also IPR-1 (Fig. 3A, lane 2). IPR-1 and IPR-3 subunits formed heterotetramers in the cells co-transfected with both cDNAs. On the other hand, when the cells were transfected separately with IPR-1 or IPR-3 cDNAs and mixed together prior to solubilization of membranes, the precipitation of IPR-3 by mAb 18A10 or of IPR-1 by mAb KM1082 was not detected (Fig. 3, A, lane 5, and B, lane 4). With longer exposure, very faint bands of IPR-1 precipitated by mAb KM1082 and of IPR-3 precipitated by mAb 18A10 appeared. These precipitates probably represent heteromeric complexes containing endogenous receptors of NG108-15 cells. These results demonstrated that IPR-1 and IPR-3 subunits assemble in cDNA-transfected cells and also rule out the possibility of artifactual rearrangement between subunits during the experimental procedures. It is therefore concluded that IPR-1, IPR-2, and IPR-3 subunits actually form heteromeric complexes in CHO-K1 cells.


Figure 3: Immunoprecipitation of IPR subunits from cDNA-transfected cells. The mixture of cDNAs of IPR-1 and IPR-3 was used to transfect NG108-15 cells. The solubilized membrane proteins of these cells were prepared and are labeled Co-transfected. The cells transfected separately with IPR-1 or IPR-3 cDNA were combined. The solubilized membrane proteins of these cells were prepared and are labeled MIX. The solubilized membrane proteins of the co-transfected or mixed cells were immunoprecipitated by mAb 18A10 (lanes 1 and 4) or mAb KM1082 (lanes 2 and 5). The immunoprecipitates together with the solubilized membrane proteins (lanes 3 and 6) were separated by 5% SDS-PAGE and transferred to nitrocellulose filters. Filters were incubated with mAb KM1112 (A) or mAb KM1082 (B). ppt, precipitate.



Heterotetramers in Liver

We investigated the presence of heterotetramers in tissues. Cerebellum and liver are often used to study IP-mediated Ca signaling. IPR-1 is predominant in the cerebellum, where it is difficult to detect heterotetramers. On the other hand, in liver, we found that IPR-1 and IPR-2 were abundantly expressed, whereas IPR-3 was scarcely detected (Fig. 4A). The cells composing the liver are relatively homogenous, and most of them are hepatocytes. We examined whether IPR-1 and IPR-2 subunits assemble to form heterotetramers in liver. Immunoprecipitation experiments using liver membrane proteins showed that mAb 18A10 immunoprecipitated IPR-2 as well as IPR-1 (Fig. 4B, lanes 1 and 4) and that mAb KM1083 immunoprecipitated IPR-1 as well as IPR-2 (Fig. 4B, lanes 2 and 5). These results indicate that IPR-1 and IPR-2 assemble in liver. With a longer exposure on immunodetection, we observed that mAb KM1082 immunoprecipitated IPR-1 and IPR-2 (data not shown), suggesting that IPR-3 subunits also associate with other IPR subunits in liver. It is therefore concluded that IPRs form heterotetrameric complexes in liver.


Figure 4: Immunoprecipitation of IPR subunits from rat liver. A, 20 µg of membrane proteins of liver were analyzed by Western blot using mAb KM1112 (lane 1), mAb KM1083 (lane 2), and mAb KM1082 (lane 3). B, liver membrane proteins solubilized in 1% Triton X-100 were immunoprecipitated by type-specific antibodies, as indicated at the top of each column. The immunoprecipitates were separated by 5% SDS-PAGE and transferred to nitrocellulose filters. Filters were incubated with mAb KM1112 (lanes 1-3), mAb KM1083 (lanes 4-6), and mAb KM1082 (lanes 7-9).




DISCUSSION

In the present study, we demonstrated by immunoprecipitation experiments using type-specific antibodies that IPRs form heterotetramers in CHO-K1 cells and the liver. Heterotetramers were not generated by mixing the cDNA-derived homotetramers. In addition, immunoprecipitation experiments in denaturing conditions showed no cross-reaction between the antibodies. The results of these experiments exclude the possibility that the receptor complexes are artifactually formed during the experimental procedures. We also detected heterotetramers in RINm5F and Jurkat cells (data not shown), suggesting that the heterotetrameric complex formation of IPR subunits is common to the cells expressing two or three types of the IPR subunits.

Northern blotting(22) , reverse transcriptase-polymerase chain reaction (32), and in situ hybridization studies (21, 22) showed that the mRNAs of IPR types were differentially expressed among mouse tissues. Recently, Sugiyama et al.(33) reported that the levels of expression of IPR subunits are quite different among hematopoietic cell lines and change dramatically with stimuli that induce differentiation. There seem to be functional differences among IPR subunits. IP binding measurements using the ligand binding domains of IPR-1 and IPR-2 indicated that IPR-2 has a higher affinity than IPR-1(10) . This suggests that different receptor types may respond to different IP levels within a cell. Mouse IPR-1 contains two phosphorylation sites of cAMP-dependent protein kinase at positions 1589 and 1755 (34), which were shown to be phosphorylated by cyclic AMP-dependent protein kinase both in vitro(35) and in intact cells(36) . Recently, we showed that phosphorylation by cyclic AMP-dependent protein kinase of IPR-1 that was immunoaffinity-purified from cerebella increased IP-induced Ca release (IICR) in reconstituted lipid vesicles(20) . These two sites are not conserved in IPR-2 and IPR-3(12) . We have also found that calmodulin binds IPR-1 in the presence of Ca and have determined its binding site in IPR-1(37) . The calmodulin binding site is conserved in IPR-2 but not in IPR-3. In fact, we were able to detect the Ca-dependent calmodulin binding to IPR-2 but not to IPR-3. Therefore, each member of the IPR family is possibly regulated in different manners by cross-talk with other intracellular signaling molecules. Thus far, the channel properties of IPR have been studied only with IP3R-1 homotetramers(5) . The channel properties of IPR-2 and IPR-3 homotetramers are currently unknown. In voltage-dependent K channels and cyclic nucleotide-gated cation channels, the hetero-oligomeric channels have distinct properties from the homomeric channels of the parent subunits(24, 25, 26) . By analogy, the heterotetramers of IPR might also exhibit distinct properties. The various subunit compositions of IPR tetramers could increase further the diversity of IPR channels.

Hepatocytes have been often used for studies of IP-mediated Ca signaling. We found that IPR-1 and IPR-2 proteins are abundantly expressed in the liver. This agrees with a recent study reported by De Smedt et al.(38) , who investigated the levels of expression of IPR mRNAs in rat liver by reverse transcriptase-polymerase chain reaction. Messenger RNAs encoding IPR-1, IPR-2, and IPR-3 accounted for 29.4%, 61.1%, and 3.0%, respectively. Interestingly, cerebellar Purkinje cells were shown to exhibit a lower IP sensitivity for IICR than hepatocytes(39, 40) . This difference may be explained by the presence of IPR-2 in the liver, which seems to have a higher affinity for IP than IPR-1(10) . Furthermore, our present study demonstrated that a large proportion of IPR-1 and IPR-2 subunits form heterotetramers in the liver. How the heterotetramers contribute to the liver-specific IP-mediated Ca signaling remains to be examined.

Recently, Mathias et al. showed that mAb 18A10 inhibited IICR mediated by phospholipase C- in CHO cells.()This inhibitory effect was also seen with microinjected heparin. Because heparin is a competitive antagonist of IPRs, it seems to inhibit IICR through all of the IPR channels. mAb 18A10 recognizes only IPR-1 and inhibits IICR only through IPR-1 (20). In this study, we have shown that all the three IPR subunits are expressed in CHO cells. Why did mAb 18A10 completely inhibit IICR in spite of the presence of a considerable amount of IPR-2 and IPR-3, which are insensitive to mAb 18A10? If all of the IPR tetramers are homotetrameric, mAb 18A10 cannot inhibit IICR through the homomeric channels composed of IPR-2 or IPR-3 subunits. Because our data suggest that IPRs form heterotetramers in CHO cells, one explanation for the findings of Mathias et al. that mAb 18A10 completely inhibits channel activity of these IPRs could be that virtually all heterotetramers contain at least one IPR-1 subunit. Therefore, the findings reported by Mathias et al. provide additional support to our biochemical findings that IPRs form heterotetrameric complexes.

  
Table: IPR type-specific monoclonal antibodies



FOOTNOTES

*
This work was supported by grants from the Ministry of Education, Science, and Culture of Japan, the Human Frontier Science Program, the Yamanouchi Foundation for Research on Metabolic Disorders, and the Brain Science Foundation. 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 Molecular Neurobiology, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo 108, Japan. Tel.: 81-3-5449-5319; Fax.: 81-3-5449-5420.

The abbreviations used are: IP, inositol 1,4,5-trisphosphate; IPR, IP receptor; IPR-1, IPR type 1; IPR-2, IPR type 2; IPR-3, IPR type 3; PMSF, phenylmethylsulfonyl fluoride; PAGE, polyacrylamide gel electrophoresis; mAb, monoclonal antibody; IICR, IP-induced Ca release; CHO, Chinese hamster ovary.

R. S. Mathias and H. E. Ives, submitted for publication.


ACKNOWLEDGEMENTS

We thank Drs. Takayuki Michikawa, Michio Niinobe, and J. M. Matheson for useful discussions.


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