Distinct Elements in the Proteasomal β5 Subunit Propeptide Required for Autocatalytic Processing and Proteasome Assembly*

Eukaryotic 20S proteasome assembly remains poorly understood. The subunits stack into four heteroheptameric rings; three inner-ring subunits (β1, β2, and β5) bear the protease catalytic residues and are synthesized with N-terminal propeptides. These propeptides are removed autocatalytically late in assembly. In Saccharomyces cerevisiae, β5 (Doa3/Pre2) has a 75-residue propeptide, β5pro, that is essential for proteasome assembly and can work in trans. We show that deletion of the poorly conserved N-terminal half of the β5 propeptide nonetheless causes substantial defects in proteasome maturation. Sequences closer to the cleavage site have critical but redundant roles in both assembly and self-cleavage. A conserved histidine two residues upstream of the autocleavage site strongly promotes processing. Surprisingly, although β5pro is functionally linked to the Ump1 assembly factor, trans-expressed β5pro associates only weakly with Ump1-containing precursors. Several genes were identified as dosage suppressors of trans-expressed β5pro mutants; the strongest encoded the β7 proteasome subunit. Previous data suggested that β7 and β5pro have overlapping roles in bringing together two half-proteasomes, but the timing of β7 addition relative to half-mer joining was unclear. Here we report conditions where dimerization lags behind β7 incorporation into the half-mer. Our results suggest that β7 insertion precedes half-mer dimerization, and the β7 tail and β5 propeptide have unequal roles in half-mer joining.

The degradation rates of intracellular proteins can vary over many orders of magnitude, with half-lives ranging from seconds to years (1)(2)(3)(4). In eukaryotes, most non-lysosomal protein degradation occurs through the ubiquitin-proteasome system. The 26S proteasome is a highly conserved and abundant protease complex comprising at least 33 different polypeptides arranged into a 2.5 MDa structure (5)(6)(7). For most substrates, their prior modification by ubiquitin polymers targets them to the proteasome, leading to their unfolding, deubiquitylation, and degradation. The proteasome is proving to be an attractive pharmacological target for the treatment of cancer and other disorders (8 -10).
Within the 26S proteasome, two major subcomplexes can be resolved: the 19S regulatory particle, which recognizes ubiquitylated substrates and unfolds them, and the 20S proteasome core particle, which is responsible for substrate proteolysis (5,11). The 20S proteasome is a dyad-symmetric 28-subunit complex made of 14 related but distinct subunits (12,13). Four heptameric rings of subunits stack coaxially, with an outer pair of ␣-subunit rings bracketing an inner pair of ␤-subunit rings. The ␣ rings provide the interface with the 19S particle and other regulators, and they bear narrow central pores that gate substrate entry into a central proteolytic chamber. The central chamber is formed by the two ␤ rings. Of the seven ␤ subunits in each ring, only three bear active sites: ␤1, ␤2, and ␤5. These active subunits are synthesized as N-terminally extended precursors that are processed autocatalytically to yield the mature enzyme. The Thr1 side chain of the mature active subunits serves as the active-site nucleophile, and the N-terminal amino group participates in catalysis as well (13)(14)(15). Structural variants of the 20S proteasome have been widely documented, including several with distinct complements of active ␤ subunits; these latter particles are important for MHC class I antigen presentation (16 -18).
There are many high resolution crystal structures available for eukaryotic 20S proteasomes (19,20), but the mechanism of assembly is still far from understood (21). At least three conserved 20S proteasome-specific assembly factors promote its biogenesis (22)(23)(24). The first discovered was yeast Ump1 (called hUMP1, POMP, or proteassemblin in humans) (25). In yeast, it is believed that Ump1 associates along with or shortly after the first ␤ subunits (␤2, ␤3, and ␤4) have been added to a full ␣-subunit ring (26). This species has been called the 13S or 15S intermediate (26 -29); we will use the "13S" name here because the "15S" designation has also been used (30) to refer to a later, nearly complete half-proteasome species that lacks only ␤7, the "half-mer(-␤7) intermediate" (26). Yeast cells lacking Ump1 are viable but accumulate proteasomal particles with partially processed subunits (25). In human cells, depletion of hUmp1 appears to be lethal, and no 20S proteasomal particles with unprocessed ␤ subunits accumulate, suggesting an earlier assembly function for hUMP1 not shared with yeast (31).
The other two known 20S proteasome assembly chaperones are the heterodimers Pba1/Pba2 (human PAC1/PAC2) and Pba3/Pba4 (human PAC3/PAC4) (6,23,26,32,33). These proteins function early in the assembly of the ␣-subunit ring, and Pba3/Pba4 dissociates before completion of the 13S intermediate. Pba1/Pba2 remains bound to the assembling proteasome all the way to formation of the "pre-holoproteasome," in which half-mers have associated but the ␤-subunit precursors are not yet fully processed. After ␤-subunit maturation, a conformational change in the ␣ rings is triggered, which leads to both release of Pba1/Pba2 and enhanced 20S affinity for the 19S regulatory particle (30,32,34). Degradation of the entrapped Ump1 factor accompanies 20S maturation (25).
In addition to the extrinsic assembly factors that promote 20S proteasome biogenesis, intrinsic elements of the 20S subunits are critical. Subunit-specific appendages that are part of the mature subunits as well as ␤-subunit propeptides contribute to assembly by supplementing specific subunit-subunit interfaces within the assembling proteasome and possibly by recruiting or positioning extrinsic assembly chaperones (25,26,35). The most prominent "intramolecular chaperone" is the ␤5 propeptide (26,36). In yeast, this 75-residue propeptide, ␤5pro, 5 is normally essential, and it can function in trans with the truncated mature domain of the ␤5 subunit (36,37). Precisely how it promotes assembly is not understood.
Several conditions have been found that allow bypass of the requirement for ␤5pro. In ump1⌬ cells, the ␤5 propeptide is no longer essential, and the same is true if the propeptide of the ␤6 subunit is genetically removed (25,26). The most robust suppression of the ␤5 propeptide deletion defect occurs through overexpression of the ␤7 subunit (26). Suppression by excess ␤7 requires a C-terminal extension of ␤7 that helps to clamp together the two proteasomal half-mers. This result and additional genetic data strongly suggested that ␤5pro promotes 20S assembly at least in part by promoting the proper association of two precursor half-mers (26).
In the current work we perform a structure-function analysis of the ␤5 propeptide to clarify its contributions to 20S proteasome biogenesis in Saccharomyces cerevisiae. We find that ␤5pro associates only transiently with Ump1-containing precursors even though it is thought to act with Ump1 during assembly (25). Interestingly, large segments of ␤5pro, particularly in the N-terminal half, are dispensable for viability, although deletions cause substantial maturation defects. Propeptide sequences closer to the autoprocessing site are better conserved and contribute to assembly steps after formation of the 13S intermediate. Sequences immediately adjacent to the processing site are not critical for assembly per se but contribute strongly to autocleavage. In addition, we describe a high copy suppression screen of cells lacking a functional ␤5pro that yielded ␤7. Importantly, we found conditions under which ␤7 incorporates before dimerization of two 15S half-mer (-␤7) complexes, and this addition is likely to drive the proper asso-ciation of half-mers. The results support a model in which the ␤7 subunit and the ␤5 propeptide have distinct but overlapping roles in half-proteasome dimerization.

Experimental Procedures
Yeast and Bacterial Media and Methods-Yeast rich (YPD) and minimal (SD) media were prepared as described, and standard methods were used for genetic manipulation of yeast (38). For all phenotypic tests cells were initially grown for several days on rich medium at 30°C. Cells were tested for growth at 30°C on SD plates containing 1 g/ml canavanine and lacking arginine, on SD complete plates containing 30 M CdCl 2 , and on either YPD or SD medium at 37°C. Escherichia coli strains used were MC1061, MC1066, and JM101, and standard methods were employed for recombinant DNA work (26).
Plasmid Constructions-A plasmid expressing N-terminally hemagglutinin (HA)-tagged ␤5(Doa3)-His 6 from the CUP1 promoter (pCIS ϭ YATAG200-CUP1p-HA-DOA3-HIS6) was constructed by amplifying DOA3-His 6 from YCplac22-DOA3-His 6 (12) with flanking SacI sites and inserting this fragment into the SacI site of the YATAG200 plasmid (GenBank TM U37457). A StyI site was added by silent mutation of ␤5 codon 73 (GCA to GCC) using QuikChange mutagenesis (Stratagene). The plasmid expressing wild-type (WT) HA-␤5 propeptide (␤5pro) from the CUP1 promoter (pTRANS ϭ YEplac112CUP1p-HA-DOA3LS) was prepared as follows. The 5Ј primer directed amplification beginning at the 5Ј end of the CUP1 promoter of pCIS, whereas the 3Ј primer retained the added StyI site and added a stop codon immediately after the Gly75 codon. Flanking XbaI sites were also added by the two primers. After amplification and cloning into pGEM-T EZ, the XbaI fragment was excised and ligated into the corresponding site in YEplac112 (39), which had its EcoRI site removed by cutting, blunting with Klenow polymerase, and religating (YEplac112⌬EcoRI).
Seven charged-to-alanine mutations along the ␤5pro sequence were introduced into pTRANS and pCIS by two-step PCR. Briefly, in two separate reactions, the 5Ј outer primer from the CUP1 promoter region was used together with a long antisense primer containing the desired mutation(s), whereas the other half of the gene was amplified with the 3Ј outer primer and a sense primer exactly complementary to the mutant antisense primer, each using pTRANS as template. These two products were annealed to each other and extended in a third PCR reaction, and the mutant fragment was amplified using the same two outer primers. The mutant sequences were subcloned into pCIS and pTRANS using an EcoRI site at the 3Ј end of the CUP1 promoter (from YATAG200) and the StyI site introduced into the end of the ␤5pro sequence and verified by DNA sequencing. The H74A mutation was introduced into pCIS and pTRANS individually as it is 3Ј of the StyI site used to subclone the other mutants. The plasmid pCIS-H74A was constructed by two-step PCR and cloning into YATAG200. The pTRANS-H74A plasmid was generated from the HA-␤5pro coding sequence by amplification from pTRANS using a 5Ј outer primer from the CUP1 promoter that had a flanking XbaI site and a 3Ј primer containing the H74A mutation, a stop codon at the 3Ј end of ␤5pro, and a flanking XbaI site. The resulting PCR product was ligated into the XbaI site of YEplac112⌬EcoRI. All other site-directed point mutations in ␤5 were introduced by QuikChange mutagenesis with YCplac22-DOA3-His 6 as template. Leaky expression from the CUP1 promoter obviated the need for adding copper to growth media.
N-terminally truncated ␤5-His 6 constructs were produced essentially as described above for pCIS, except that 5Ј primers began amplifying from either codon 42 or 56. The resulting plasmids, YATAG200-DOA3⌬2-41 and YATAG200-DOA3⌬2-55, had the N-terminal HA-tag sequences deleted using QuikChange mutagenesis. Internal deletions of codons 42-55 or 56 -73 within the N-terminal propeptide coding region of ␤5 were constructed by a two-stage PCR protocol followed by QuikChange mutagenesis (40) using YCplac22-DOA3-His 6 as the template. The resulting alleles were under the control of the natural ␤5 promoter. The ␤7 (PRE4) gene was isolated by PCR amplification from genomic DNA and subcloned into yeast-Escherichia coli shuttle vectors YEplac181, YEplac112, and YCplac111. Their functional integrity was verified by complementation of the yeast pre4⌬ mutant.
Construction of Yeast Strains-Yeast strains used in this study are listed in supplemental Table S1. MHY1030 was isolated by sporulation and tetrad dissection of a heterozygous diploid transformant. MHY1179 was a segregant from a cross between MHY784 and MHY1030, and MHY2920 was derived from a cross between MHY1180 and MHY1326. All CIS strains were made by transforming MHY784 (12) with plasmids bearing the ␤5 alleles, and TRANS strains were made by cotransforming both pRS317-Ub-doa3⌬pro-His 6 and pTRANS plasmids into MHY784. Plasmid shuffling was then performed by plating transformants on media containing 5-fluoroorotic acid to identify cells that had lost the URA3-marked YCp50-DOA3 (WT) plasmid (43). All other strains were constructed by plasmid shuffling using the appropriate deletion strains and plasmids. Growth rates of strains with tagged subunits were identical to congenic strains lacking epitope tags.
High-copy Suppressor Screening-TRANS-27/29 and TRANS-69/71 strains were transformed with a yeast high-copy genomic library in the 2/LEU2 YEp13 vector (44). Transformants were plated on SD LeuϪ plates and incubated at 35°C. Temperature-resistant clones were retested. Transformants bearing library plasmids with a full-length ␤5 gene were weeded out by colony PCR with primers that amplified the ␤5 gene. The remaining positive library plasmids were recovered in E. coli (MC1066) by selection on M9 (LeuϪ) minimal plates. Plasmids were transformed back into the original TRANS mutant strain, and those found to continue to show suppression were sequenced. When more than one gene was present within a suppressing genomic fragment, the gene responsible for the suppression was identified by subcloning.
Protein Gel Electrophoresis, Immunoblotting, and Quantitative Analysis of Protein Levels-SDS-polyacrylamide gel electrophoresis (PAGE) of proteins was carried out according to standard procedures (45). For separation of low molecular mass proteins, such as HA-␤5pro, 16% Tricine gels were used (46). Otherwise, protein electrophoresis was generally performed using 12% SDS-PAGE gels followed by electrotransfer to Immobilon (Millipore) membranes and immunoblotting. Antibodies used included anti-HA monoclonal 16B12 (Babco), mononclonal MCP231 against 20S proteasome ␣ subunits (Enzo Life Sciences), anti-20S proteasome antiserum (a gift from K. Tanaka), and an anti-LMP7 (␤5-His 6 ) polyclonal antiserum (gift of Y. Yang). Anti-␤7 polyclonal antisera were raised in rabbits using ␤7-His6 protein purified from E. coli as immunogen or were a gift of W. Heinemeyer. Proteins were detected using ECL reagents (Amersham Biosciences). For protein quantitation, [ 125 I]protein A (PerkinElmer Life Sciences) was used. Pulse-chase analysis was carried out as described (47).

Results
Conserved Elements in the ␤5 Propeptide-Across all eukaryotic species, ␤5pro is the longest of the active subunit propeptides (ϳ50 -85 residues), and studies in different eukaryotes have shown that it has a major role in 20S proteasome assembly (36,50,51). Although the sequence of ␤5pro varies far more among species than does the sequence of the mature domain of the subunit, some common features can be discerned (Fig. 1A). First, the C-terminal-most region of the propeptide is well conserved. This region includes the invariant terminal glycine (at Ϫ1 relative to the cleavage site) that is required for autocleavage (36,52,53), but also conserved are hydrophobic residues at Ϫ4 and Ϫ6 and, most strikingly, a histidine residue at the Ϫ2 position. A histidine residue at the Ϫ2 position is present in precur-sors of all three human ␤5 paralogs (␤5, ␤5i, and ␤5t). Less commonly, a lysine is found at Ϫ2; this is observed in nematodes, plants, diatoms, and excavates ( Fig. 1A and not shown). Histidine or lysine occurs at Ϫ2 in the ␤5 precursor of all surveyed eukaryotic sequences. A second, more loosely conserved region is a segment rich in prolines slightly farther upstream of the processing site (residues 42-52 in S. cerevisiae ␤5).
Fusion of the ␤5 Propeptide to the ␤1 Subunit-We first asked if all relevant cis-acting autoprocessing elements are encoded within the ␤5 propeptide (other than the conserved catalytic residues found in the mature portions of all active ␤ subunits, such as the catalytic Thr-1 residue). To test this we replaced the propeptide of the ␤1 subunit with ␤5pro; the ␤5pro-␤1 chimera was the only ␤1 subunit expressed in these cells (Fig. 1B, lane 3). The ␤1 propeptide is not required for cell viability (42) ( Table 1, row 3). Previously we observed that in the reciprocal exchange, where the propeptide of ␤5 was replaced with that of ␤1, a nonfunctional protein resulted; the fusion also failed to incorporate into proteasomes in cells co-expressing WT ␤5 to maintain viability (36). In strong contrast, the ␤5pro-␤1 chimera supported relatively robust growth at 30°C (Table 1, row 2). Because ␤1 is essential for viability, this implies that the chimera inserted properly into the proteasome.
Nevertheless, the great majority of the chimera remained unprocessed, with a trace of intermediately processed subunit detected (Fig. 1B, Interm; compare lane 3 to lanes 1 and 2). Thus, the persistence of two full-length ␤5 propeptides (one per ␤ ring) within most proteasomes is relatively well tolerated. That the chimera was incorporated into the proteasome and could be partially processed there was supported by the observation that replacement of the ␤2 subunit with a catalytically inactive version, ␤2-T30A (52), caused a lengthening of the partially processed ␤5pro-␤1 chimera (Fig. 1B, lanes 4 and 5), as expected as the propeptide is normally trimmed inside the catalytic chamber by neighboring active sites but now could no longer be trimmed by ␤2 (53). We conclude that efficient autocleavage of the ␤5 propeptide requires that it be attached to its own mature domain. This presumably reflects a requirement for it being in the normal ␤5 position in proteasomal precursors or for its proper juxtaposition to elements unique to the ␤5 mature domain.
Of note, if the only cellular source of ␤5 propeptide was the ␤5pro-␤1 chimera, cells could grow, albeit poorly (Table 1, row 6). A similar observation had been made for the homologous human chimera ␤5pro i -␤1 i (LMP7 propeptide fused to the LMP2 mature domain) (28). This trans effect was not nearly as effective as isolated ␤5pro expressed in trans (Table 1, row 5), and the ␤5pro-␤1 chimera appeared to interfere with the latter ( Table 1, compare rows 5 and 7).
Trans-expressed ␤5pro Is Not Stably Associated with Later Assembly Intermediates-The apparent interfering effect of the ␤5pro-␤1 chimera on trans-expressed ␤5pro led us to ask if ␤5pro associated noncovalently with precursor forms of the 20S proteasome. To examine this we resolved mature proteasomes from proteasomal subparticles by FPLC Superose-12

Rows
Relevant genotype 30°C 37°C size-exclusion chromatography (Fig. 2). For detection of the free propeptide by immunoblotting, it was N-terminally tagged with a HA epitope ( Fig. 2A). Cells expressing both the mature domain of ␤5 (␤5⌬pro-His 6 ) and HA-␤5pro along with HAtagged Ump1 were flash-frozen in liquid nitrogen and lysed under nondenaturing conditions. Extracts were fractionated and assayed by immunoblotting (Fig. 2B). The 13S assembly intermediate can be resolved from mature 20S proteasomes as well as smaller species.
In otherwise WT cells, HA-␤5pro was not detected in either the 13S fractions (Fig. 2B, peak fractions 18 and 19; marked by Ump1 and the ␤2 precursor, the latter followed in a parallel fractionation) or the mature proteasome (fractions 15 and 16; marked by mature ␤2, ␤5, and ␤7 subunits). Interestingly, the HA-␤5pro peak eluted slightly earlier (fraction 25) than the free ␤5⌬pro subunit (fraction 26), suggesting that it also was not tightly associated with the mature domain of ␤5. Because the 9-kDa HA-␤5pro is smaller than ␤5⌬pro-His 6 , its earlier elution implies either that it is associated with itself or another unidentified protein or that it has a highly extended conformation. Roughly half of the propeptide is predicted to be random coil based on secondary structure predictions.
The Ump1 assembly factor becomes entrapped within the 20S proteasome during 20S assembly and is then degraded upon active-site maturation at the end of assembly (25). A similar fate is anticipated for the ␤5 propeptide. We, therefore, tested if trans-expressed ␤5pro could be detected in association with mature 20S proteasomes if proteasomal proteolytic activity was impaired. Superose-12 fractionation of extracts from a pre1Ϫ1 mutant, which expresses a mutated ␤4 subunit that causes a significant defect in proteolysis (54), did indeed allow detection of HA-␤5pro in association with fully formed proteasome particles (Fig. 2C). Therefore, ␤5pro likely associates with the proteasomal precursor after 13S formation and is then degraded upon completion of assembly and active-site maturation.
Deletion Analysis of the ␤5 Propeptide-As noted, the ␤5-propeptide sequence is only weakly conserved outside of a few small regions (Fig. 1A). We used deletion analysis to examine the significance of the different propeptide regions for ␤5-precursor processing and proteasome assembly (Fig. 3). A deletion leaving only the initiator methionine and the last two residues of the propeptide (⌬2-73) was lethal (Fig. 3A). This result indicates that the remaining highly conserved residues, His-74 and Gly-75, are not sufficient for propeptide function. Deletion of the poorly conserved region upstream of the proline-rich element (⌬2-41) was relatively well tolerated with only a minor impediment to growth under optimal conditions; however, ␤5⌬2-41-expressing cells were inviable when grown on the amino acid analog canavanine, a condition poorly tolerated by proteasome-deficient cells (Fig. 3B). Similarly, removal of the Pro-rich region (⌬42-55) allowed near-normal growth under most conditions, with the exception of canavanine. In contrast, a deletion encompassing both of the preceding deletions (⌬2-55) caused a much more severe growth defect under all tested conditions, although the cells were still viable. This suggested a partially redundant function shared by regions 2-41 and 42-55. Cells also grew poorly when the region just upstream of the precursor-processing site was deleted (⌬56 -73); if this deletion was extended to include the Pro-rich segment (⌬42-73), cells were no longer viable (Fig. 3, A and B), again suggesting functional redundancy.
The growth defects exhibited by the ␤5 propeptide deletion mutants could be due to impaired chaperone function or reduced autocleavage at the ␤5 processing site, which is known to cause a severe growth defect, or both. Propeptide processing in the viable deletion mutants was examined by immunoblotting with an antibody that recognized the C-terminally His 6tagged ␤5 proteins (Fig. 3C). All of the deletions impaired autocleavage compared with WT ␤5. Interestingly, the ⌬2-41 and ⌬2-55 strains yielded comparable levels of apparently mature ␤5 (␤5 m ), yet the latter mutant had a much more severe growth defect. This suggested that the redundant growth-promoting function shared by regions 2-41 and 42-55 is related at least partly to the assembly function of the propeptide. Gel filtration analysis suggested fewer fully assembled and matured proteasomes in the ⌬2-55 mutant compared with ⌬2-41 based on the ratio of unprocessed to mature species, although in all cases processed ␤5m was seen in assembled particles (Fig. 3D). Finally, propeptide cleavage was more severely affected by deletion of the region upstream of the cleavage site (⌬56 -73) (Fig. 3,  C and D), suggesting that impaired cleavage made a major contribution to the growth defect of this mutant.
In summary, the deletion analysis indicated first, that even the poorly conserved N-terminal region of the ␤5 propeptide contributes to its intramolecular chaperone function, and second, that there is redundancy for this function between the N-terminal half of the propeptide and its Pro-rich region. In addition, sequences closer to the C terminus of the propeptide are especially important for efficient self-cleavage.
Autoprocessing Defects in ␤5 Propeptide Point Mutants-Deletions provide a relatively crude picture of functional elements within a protein. We next generated a set of ␤5 derivatives with selected point mutations. Clusters of charged-to-alanine mutations were made (Fig. 4A) with the aim of targeting surface residues whose mutation might disrupt protein-protein interactions but are less likely to affect the folding of the propeptide. Most were double mutants, giving a total of 15 mutated residues in 8 separate alleles. The propeptide mutations were made in two different forms of the ␤5 protein: in the context of the full-length protein ("CIS") and in the propeptide expressed from a plasmid separate from the WT mature domain ("TRANS"). None of the mutations was lethal in either form. Both the full-length ␤5 and ␤5pro constructs carried an N-terminal HA tag, which allowed trans-expressed ␤5pro and unprocessed ␤5 to be detected by immunoblotting. The resulting strains are hereafter referred to as CIS and TRANS followed by the positions of the residues that were mutated to alanine.
None of the eight CIS mutants showed detectable differences in growth rate as compared with the WT control except when grown on cadmium. The four mutants with substitutions nearest the processing site (CIS-57,59; CIS-61,62,64; CIS-69,71; CIS-74) were mildly hyper-resistant to cadmium (data not shown), which we have noted in the past is usually indicative of a minor defect in proteasome function (52). Immunoblotting of HA-␤5-His 6 revealed that these same four mutants, especially CIS-74, displayed inefficient intramolecular propeptide processing and accumulation of intermediately processed forms, which is due to cleavage by other 20S active sites (Fig. 4B). The processing defect of CIS-74 was also evident by pulse-chase analysis (Fig. 4C). These point mutagenesis results support and extend the conclusion from the preceding deletion analysis that the ϳ20-residue segment just upstream of the autocleavage site plays a significant role in propeptide processing.
The H74A mutant (CIS-74) showed the most severe processing defect, and histidine at position Ϫ2 is broadly conserved in ␤5 homologs (Fig. 1A). To get a better idea of how in vivo processing of ␤5 that has nonlethal deletions in its propeptide. Extracts from strains expressing the indicated plasmid-borne constructs (same as panel B) were subjected to SDS-PAGE followed by immunoblotting with serum raised against human LMP7-His 6 . Asterisks to the left of the lanes mark intermediately processed precursors. Pgk1 (phosphoglycerate kinase) was used as loading control. D, gel filtration analysis of ␤5 proteins lacking various propeptide segments. Superose-6 chromatography of whole-cell extracts was followed by anti-LMP7 (␤5i) immunoblot analysis. All the ␤5 proteins have a C-terminal His 6 tag, which is necessary for anti-LMP7 detection. Yeast strains, from the top: MHY3543, MHY3544, MHY2970, MHY3545, and MHY2890. The WT ␤5 precursor, which is present at low levels, was not detected at this film exposure. Positions of calibration standards are indicated at the bottom.
His-74 might function in the ␤5 precursor, we also changed the residue to lysine or phenylalanine within full-length ␤5. For these constructs we omitted the N-terminal HA tag because it appeared to interfere slightly with propeptide processing (compare lanes 1 in Fig. 4, B and D). Replacement of His-74 with Lys, a residue found at the Ϫ2 position in the ␤5 propeptides of certain eukaryotic lineages (see above), caused only minimal reduction in propeptide processing efficiency (Fig. 4D). In contrast, mutation of His-74 to Ala or even to Phe, whose aromatic side chain is similar in size to that of histidine, resulted in the accumulation of unprocessed and intermediately processed subunits (Fig. 4D). As we had found previously (36), impaired processing of ␤5 leads to its overexpression, and levels of mature ␤5 in the processing-defective strains approached those in WT cells.
Together, these data suggest that autocatalytic cleavage of the ␤5 precursor utilizes sequences in the propeptide in a way not used in the other active-subunit precursors, which lack a conserved His/Lys residue at the Ϫ2 position of their propeptides. This residue is unlikely to function as a general base in the ␤5 autocatalytic cleavage reaction as processing, although inhibited, is still observed in the Ala and Phe substitution mutants. Recent crystallographic data on the Phe mutant are consistent with this conclusion. 6 Impaired Proteasome Function in Trans-expressed ␤5 Propeptide Mutants-Analysis of growth phenotypes for the eight TRANS alanine mutants revealed that all but TRANS-16,17 and TRANS-61,62,64 were defective for growth under at least one of the tested conditions (Fig. 5A). Expression levels of most of the mutated TRANS propeptides were similar to the WT control, although TRANS-61,62,64 and TRANS-74 propeptide levels were slightly reduced (Fig. 5B). This suggests that except for possibly TRANS-74, differences in propeptide expression cannot account for the growth defects. The short-lived model proteasomal substrates MAT␣2 and Deg1-␤-galactosidase were stabilized ϳ2-fold in both the TRANS (WT) and TRANS-27,29 strains (data not shown) relative to their published halflives in WT cells (45), indicating a modest proteasomal defect when the ␤5 propeptide is expressed in trans. This might be due to partial acetylation of the ␤5 Thr-1 ␣-amino group (42). Pulse-chase analysis of MAT␣2 at 37°C, a nonpermissive growth temperature for TRANS-27,29, revealed a further 1.5fold stabilization in this strain relative to TRANS (WT) (data not shown). This additional defect at high temperature could derive from impairment of particular 20S proteasome active sites or from defective proteasome assembly.
To distinguish between these two possibilities, the two most severe mutants, TRANS-27,29 and TRANS-69,71, were assayed for their relative specific activities based on active sitespecific peptidase activity measurements of gradient-purified proteasomes. All of the three diagnostic peptidase activities in proteasomes from these two mutants were similar to or slightly higher than those from the TRANS (WT) strain (Fig. 5C). This result suggests that there are no defects in the active sites in these mutants that could account for the observed proteolytic and growth defects.
To assay potential defects in proteasome assembly, we measured the rate of processing of the ␤2 subunit in TRANS (WT) and in TRANS-27,29 strains by pulse-chase analysis (Fig. 5D). Normally, pre␤2 accumulates in the Ump1-containing 13S assembly intermediate, where it remains unprocessed; once assembly has proceeded to pre-holoproteasomes, pre␤2 rapidly self-cleaves (25). The pre␤2 processing rate is, therefore, directly related to the rate of conversion of the 13S intermediate into mature proteasomes. The TRANS (WT) strain was already processed fairly slowly, consistent with the in vivo proteolytic defects noted above. Nonetheless, we observed substantially slower processing with the TRANS-27,29 mutant (Fig. 5D), suggesting that TRANS-27,29 is defective for proteasome assembly and/or maturation. Additional evidence for an assembly defect is provided below.
High-copy Suppressors of Trans-expressed ␤5 Propeptide Mutants-The apparent assembly defects of the above TRANS mutants might result from reduced interaction between ␤5pro and proteasome assembly intermediates or in a general loss of ␤5pro function. ␤5pro-interacting proteins or proteins FIGURE 4. Point mutagenesis of the ␤5 propeptide in the context of pre␤5 (CIS). A, the yeast ␤5 propeptide sequence with residues mutated to alanine are underlined. B, propeptide processing in pre␤5 charged-to-alanine scanning mutants assayed by anti-LMP7-His 6 immunoblotting. Interm, intermediates generated by processing within the proteasome. C, pulse-chase analysis of pre␤5 processing in the H74A mutant. 35 S-Labeled proteins were immunoprecipitated with anti-LMP7-His 6 serum. Asterisks, cleavage products produced when autoprocessing at the normal G-T cleavage site is inhibited. D, propeptide processing of pre␤5 mutants with His-74 mutations. Anti-LMP7-His 6 was used for immunoblot analysis. Strains used, from the left: MHY3410 to MHY3413. Pgk1, loading control.
involved in proteasome assembly that can overcome ␤5pro defects when overexpressed might therefore be identified by screening for high-copy suppressors. We performed such a screen by selecting for high-copy suppressors of the strong temperature sensitivity of the TRANS-27,29 and TRANS-69,71 strains. Approximately 45,000 2-m genomic-library transformants were screened in total, corresponding to ϳ18 genome equivalents (44). The high-copy suppressors isolated are listed in Table 2.
Not unexpectedly, the WT ␤5 (DOA3) gene was isolated multiple times and was the strongest suppressor. Also obtained in the screen was a plasmid with an insert bearing the ␤5 promoter and propeptide coding sequence up to a Sau3AI site, which is predicted to produce a WT version of ␤5pro through residue 72 followed by a 10-residue missense peptide. This plasmid suppressed the temperature sensitivity of both TRANS-27,29 and TRANS-69,71 strains nearly as well as overexpression of the WT ␤5pro and also suppressed very strongly the lethality of the ␤5⌬pro mutation (Table 2). These results indicate that the C-terminal three residues of ␤5pro are not critical for function in trans, although the last two residues are critical in cis for efficient propeptide processing (see Fig. 4 and Ref 36).
The second strongest suppressor, ␤7 (PRE4), was identified 15 times and strongly suppressed both TRANS-27,29 and TRANS-69,71 defects (Fig. 6A). Moreover, high-copy expression of ␤7 suppressed a complete deletion of ␤5pro ( Fig. 6B and Ref. 26). Because the lethality of the ␤5⌬pro mutation can also be suppressed by deletion of the UMP1 gene (25), we asked if there were some link between ␤7 HC and Ump1 levels. However, co-overexpression of UMP1-HA 2 with ␤7 in ␤5⌬pro cells had no effect on growth, suggesting that suppression by overexpression of ␤7 is independent of Ump1 levels (Fig. 6B). Interestingly, when 20S proteasomes were purified from ␤5⌬pro cells that overproduced ␤7, the particles were essentially indistinguishable from proteasomes from WT ␤5 cells (Fig. 6C) as noted earlier (26). However, the efficiency of proteasome maturation appeared slightly impaired, as we could detect the precursor form of the ␤2 (Pup1) subunit in these affinity-purified particles (arrowhead in Fig. 6C).
The ability of high ␤7 levels to suppress the growth defects associated with ␤5 propeptide mutations correlated with enhanced formation of proteasomes. Proteasomes were isolated by glycerol-gradient fractionation of equal amounts of cellular protein from the indicated strains in Fig. 6D. Using the specific-activity values from Fig. 5C and peptidase measure-  MHY1976. B, expression levels of trans-expressed ␤5 propeptide point mutants. SDS lysates from equal OD at A600 cell equivalents were separated on a 16% Tricine SDS-PAGE gel followed by anti-HA immunoblot analysis. Strains used were, from the left, MHY1968 -MHY1976. C, specific activity of 20S proteasomes in selected mutants. Spheroplasts of cells grown at 30°C were lysed, and equal amounts of total protein based on Bradford assays were fractionated on 10 -40% glycerol gradients. Gradient conditions are described in Ref. 42. Proteasome-containing fractions were pooled and analyzed for three peptidase activities. Relative specific activities were determined by quantitative [ 125 I]protein-A immunoblotting using anti-20S antibodies. Each bar represents the mean value calculated from triplicate measurements from three independent extracts. Error bars denote S.D. D, pulse-chase analysis of pre␤2-HA 2 (Pup1) processing in a strain with a trans-expressed ␤5pro point mutant. Analysis was done at 30°C in MHY2006 (TRANS) and MHY2007 (TRANS- 27,29). Cells were radiolabeled for 20 min with and chased for the indicated times. ␤2-HA 2 was immunoprecipitated with an anti-HA antibody.

TABLE 2
High-copy suppressors of ␤5 propeptide mutants [N], very small visible colonies formed that then stopped growing.

Times cloned
Protein function
a Allele expresses a ␤5 fragment ending in HRTGVVAMIA after the WT propeptide sequence residues 1-72 (residues 73 AHG 75 of the propeptide missing). ments, we calculated the relative levels of proteasomes in cells either with or without overexpressed ␤7. By this measure, ϳ20 -30% decreases in proteasomes were seen in the TRANS-27,29 and TRANS-69,71 mutants relative to the control TRANS (WT) strain. The deficit of proteasomes in these mutants was overcome by increased dosage of ␤7 (Fig. 6D).
Higher levels of proteasomes were also seen when TRANS (WT) cells expressed excess ␤7. We observed a similar, but smaller increase in proteasomes in fully WT cells overproducing ␤7 (not shown), suggesting that ␤7 levels may normally be at least partially rate-limiting for 20S proteasome assembly in yeast cells. . Suppression of trans-expressed ␤5 propeptide mutants by overexpressed ␤7 proteasome subunit and ␤7 incorporation into half-proteasomes. A, suppression of high temperature growth defects of ␤5pro mutants by overexpressed ␤7. 10-Fold serial dilutions of MHY1968, MHY1972, and MHY1975 strains transformed with empty vector or 2 vector-borne ␤7 were spotted on SD LeuϪ plates and grown as indicated. B, high levels of ␤7 bypass the need for the ␤5 propeptide by a mechanism not requiring reduced Ump1 levels. The strain MHY2008 was transformed with a high-copy vector that was either empty or expressed UMP1-HA2 from the UMP1 or GPD promoter. 10-Fold serial dilutions were spotted onto selective plates and incubated at 30°C for 3 days. Lysates from these same strains were used for immunoblotting with anti-HA and anti-Pgk1 antibodies (lower panels). C, proteasomes purified from ␤5 WT (MHY2831) and ␤5⌬pro (MHY2832) cells overexpressing ␤7 have similar composition, but the latter appear to mature less efficiently. Proteasomes were purified from yeast by anti-FLAG (␤4 tag) affinity chromatography as described (26). The SDS gel was stained with Coomassie Blue. The arrowhead marks the position of the ␤2 precursor, identified by mass spectrometry of the excised band. The band immediately below it is likely to be mature ␤2, and its levels are slightly lower than in WT particles, as predicted if ␤2 maturation is less efficient. D, the reduced levels of proteasomes in TRANS-27,29 and TRANS-69,71 ␤5 propeptide mutants are restored by high-copy ␤7. Equal amounts of cell protein from each strain were fractionated in parallel on glycerol gradients, and peptidase activities of the gradient-purified proteasomes were measured as in Fig. 5C; specific activities were determined from the data in Fig. 5C were used to calculate relative proteasome levels. E, Superose-6 chromatographic fractionation of extracts from cells (left, MHY3541; right, MHY3542) bearing a low-copy (LC) plasmid expressing ␤7. Immunoblot analysis was performed with anti-␤5 and anti-␤7 antibodies.
Four additional genes also isolated in the screen weakly suppressed both TRANS-27,29 and TRANS-69,71 mutants but did not support growth in the complete absence of propeptide (Table 2). Fpr3 is a peptidylprolyl isomerase that concentrates in the nucleolus and has multiple functions (55). SUI2 encodes a subunit of translation initiation factor eIF-2 (56). Hyp2, also called eIF5A, promotes translation elongation, especially through consecutive proline residues (57). All three of these high-copy suppressors might suppress propeptide defects by promoting increased translation of one or more limiting proteasome subunits or assembly factors. The fourth gene, OLE1, encodes the ⌬9 fatty acid desaturase that produces mono-unsaturated fatty acids (58). Although suppression of mutant ␤5pro by overexpression of OLE1 was not particularly strong, it was the only gene in this group of four that suppressed the full deletion of the ␤5pro, after loss of a WT ␤5 plasmid, for enough generations to allow very small colonies to form before growth halted. The proteasome is required for transcription of OLE1 (59). That overexpression of OLE1 can suppress the deletion defect of ␤5⌬pro and, therefore, the cessation of proteasome assembly for more than a few generations supports the suggestion that control of Ole1 levels is an essential function of the proteasome (59).
The ␤7 Subunit Is Incorporated before Half-mer Joining-Previous results from our laboratory and others indicated that ␤7 is the final subunit to be added during 20S proteasome assembly (26,31,60). Importantly, ␤7 incorporation is tightly coupled to the joining of two half-proteasomes (half-mers) that form the pre-holoproteasome. This close temporal linkage has prevented the determination of the actual sequence of assembly events at this critical juncture. One possibility is that ␤7 adds to the half-mer, and this subsequently promotes the joining of completed half-mers. Alternatively, half-mers lacking ␤7 might transiently associate, creating binding sites for ␤7 addition and allowing completion of core particle assembly. Further analysis of ␤7 suppression of the ␤5⌬pro proteasome assembly defect has unexpectedly allowed us to address this question.
As noted above, proteasome formation in ␤5⌬pro cells overexpressing ␤7 appears to be less efficient than in WT ␤5 cells (Fig. 6C). We, therefore, separated mature 20S and 26S proteasomes from precursor complexes using Superose-6 FPLC gel filtration followed by immunoblot analysis of column fractions (Fig. 6E). When ␤7 was expressed from a low-copy plasmid in cells expressing WT ␤5, virtually all of the detected ␤7 was in full-size proteasomes, consistent with the tight link between ␤7 addition and half-mer joining (Fig. 6E, left). The ␤7 subunit is synthesized as a precursor that is N-terminally processed by a neighboring active site (␤2) in the newly matured proteasome (53). No ␤7 precursor was detected in any proteasomal particles, and no ␤7 could be detected outside of the proteasome, suggesting that ␤7 was present in limiting amounts for proteasome assembly. In striking contrast, when the same low-copy ␤7 plasmid was present in ␤5⌬pro cells, extensive accumulation of free ␤7 was detected (Fig. 6E, right, fractions 30 -32; partially proteolyzed in the extract). Most importantly, a new peak (fraction 21; arrowhead) containing the ␤7 precursor eluted just ahead of the 13S intermediate peak, consistent with the addition of ␤7 to the half-mer (-␤7) complex before half-mer joining and subunit processing. These data strongly suggest that ␤7 adds to the half-mer, and this helps drive half-mer joining rather than the reverse sequence.

Discussion
In yeast, ␤5pro is the only propeptide that is normally essential for proteasome assembly, but before the present study it had not been subject to any systematic mutagenesis analysis. Using both deletion and scanning charged-to-alanine mutagenesis, we find that S. cerevisiae ␤5pro, despite relatively poor primary sequence conservation, bears elements through much of its length that contribute to both proteasome assembly and processing; sequences in the latter half of the 75-residue propeptide are the most critical. Although propeptide sequences near the ␤5 precursor cleavage site are crucial for autoprocessing, the trans functions of ␤5pro remain less well understood. Surprisingly, our data suggest only weak interaction of ␤5pro with other proteins within proteasome precursors, which include the Ump1 assembly factor. Other results provide support for a role for the propeptide in the joining of half-mer particles, a function partially shared with the ␤7 subunit, which we now show can incorporate into half-mers before dimerization.
Previously we found that interactions between the tail of the ␤7 subunit in one ␤ ring and a binding pocket in the opposing ␤ ring allowed overexpressed ␤7 to suppress the inviability caused by deletion of the ␤5 propeptide (26). Such overexpression also suppressed a specific ␤5 mutant allele known to have a destabilized ␤-␤ ring interface (12). This led to the inference that ␤5pro helps guide half-mer joining. A simple way to imagine how ␤5pro functions in half-mer dimerization would be for it to directly bind specific subunits in the opposing ␤ ring, even potentially the other ␤5 propeptide, in the juxtaposed half-mer complex. Although computational structure prediction with PHYRE2 (61) failed to yield high confidence predictions of S. cerevisiae ␤5pro folding, it is intriguing that the strongest similarity found was between the central segment of ␤5pro (residues  and the dimerization domain of E. coli EF-Ts (domain d1efub4; 36% sequence identity) (not shown). Potentially, these segments of the ␤5 propeptides from apposed halfmers could make direct contacts and facilitate dimerization of the two subcomplexes. Although we have not detected ␤5pro-␤5pro interactions by yeast two-hybrid or split-ubiquitin binding assays, 7 weak interactions might suffice, especially because ␤5pro is normally covalently tethered to the nascent ␤ ring.
One view of the poor sequence conservation of the ␤5 propeptide is that most of it is of little relevance. Alternatively, there might be functional redundancy within the propeptide or new functions that have evolved rapidly in the less structurally constrained propeptide compared with the mature domain (or both). Our deletion and point mutagenesis argue that even the poorly conserved segments contribute to ␤5pro activity. For example, removal of the first 41 residues of the propeptide, which show minimal sequence conservation (Fig. 1A), nevertheless leads to a pronounced autoprocessing defect (which might be due to reduced incorporation into assembling protea-7 C. S. Arendt, and M. Hochstrasser, unpublished data. somes) and an inability of the mutant cells to grow under proteotoxic stress conditions (Fig. 3). The deletion data also indicate functional redundancy within the propeptide. For example, separate deletions of residues 42-55 and 56 -73 yield viable cells capable of proteasome formation, but combining the two (⌬42-73) is lethal (Fig. 3). Moreover, it is likely that ␤5pro has evolved distinct specializations in different organisms, which would lead to sequence divergence as well. For instance, the propeptides of two ␤5 paralogs in humans, ␤5/PSMB5 and ␤5i/LMP7, have markedly different assemblypromoting activities (62,63). The propeptide of the third human ␤5 paralog, ␤5t, has been shown to allow incorporation of ␤5t at an earlier assembly stage than the constitutive ␤5 subunit, again implying functional specialization (64).
A recent chemical cross-linking study of the 15S half-mer (-␤7) intermediate revealed two cross-links involving the ␤5 propeptide segment: one cross-linked Lys-69 of the propeptide to ␤4 and the other was between Lys-16 of ␤5pro and ␣6 (30). As noted by the authors, the latter cross-link suggested that the ␤5 propeptide at this assembly stage pointed toward the ␣ ring rather than toward the future interface with a second half-mer. The former cross-link, however, involved a ␤4 side chain (Lys-28) that is on the outside surface of the mature 20S proteasome; therefore, in the 15S intermediate or the full half-mer, the ␤5pro domain might well extend beyond the ␤-ring surface and facilitate contacts with the other half-mer. Such flexibility and the large distances between these two ␤5pro cross-links are consistent with an extended conformation of ␤5pro (Fig. 2) and the prediction of a significant fraction of intrinsic disorder in the propeptide.
A systematic protein interaction study of the proteasome reported a yeast two-hybrid signal between Ump1 and ␤5, although the segment(s) of ␤5 responsible for the apparent binding to Ump1, which might be indirect, was not determined (65). Our data indicate that the yeast ␤5 propeptide is not sufficient for tight association with Ump1 or any other component of the 13S precursor (Fig. 2). By contrast, experiments with human ␤5 and ␤5i precursors suggest that the propeptide contributes to association with hUMP1 (17).
The alanine-scanning mutagenesis of the trans-expressed ␤5pro, which should be minimally disruptive to folding, suggests that two widely separated propeptide surfaces ( 27 ESD 29 and 69 KIK 71 ) are especially sensitive to mutation (Fig. 5). These data would be consistent with defects in protein-protein interaction, and our high-copy suppression screen of these mutants yielded hits that all could be consistent with an ability to overcome such a defect. Specifically, the screen yielded multiple factors that are involved in protein translation, which by overexpression might enhance levels of limiting factors (such as ␤7 or mutant ␤5pro) capable of promoting proteasome biogenesis. The Hyp2/eIF5A translation-elongation factor is known to be important for translation through consecutive prolines (57). It could potentially augment expression of ␤5pro by translation through the proline-rich segment of the propeptide. Another of the translation-related factors, Fpr3, is a peptidyprolyl isomerase known to enhance ribosome biogenesis, among other functions (55,66). Fpr3 might have a more direct impact on folding of proteasome subunits, including potentially the proline-rich element of ␤5pro. A conformation switch in the ␤5 propeptide that repositions Ump1 would be consistent with a previously proposed mechanism for its essential assembly activity (25).
Autocatalytic ␤5 propeptide cleavage depends strongly on sequences immediately surrounding the cleavage site and the propeptide segment upstream of the cleavage site ( Fig. 4 and Ref. 36). The histidine two residues upstream of the cleavage site, although highly conserved, is not absolutely essential, arguing against a direct catalytic role for this residue. It is potentially important for stabilizing a structure of the propeptide necessary for efficient cleavage. In the crystal structure of a 20S mutant with an incompletely processed ␤1 subunit, the ␤1 propeptide assumes a ␥-turn conformation around the glycine (at Ϫ1) residue (67). A His (or Lys) residue preceding this conserved glycine might promote such a conformation in the ␤5 propeptide. 6 However, additional information beyond the propeptide and flanking residues is required for ␤5 autocleavage inasmuch as fusion of ␤5pro to the mature domain of ␤1 completely blocks proper cleavage even though a substantial fraction, at least, of the chimeric subunit is correctly incorporated into the proteasome ( Fig. 1B; Table 1). Misplacement of ␤5pro in the pre-holoproteasome may prevent its interactions with neighboring subunits or Ump1 that normally place the precursor into an autocleavage-competent conformation.
Results with both yeast and mammalian 20S proteasome assembly indicate that ␤7 is the last subunit to incorporate into precursor complexes, and this is tightly coupled to half-mer dimerization (24). It had been unclear whether ␤7 adds to the 15S half-mer (-␤7) complex, which is then rapidly followed by dimerization, or if two 15S half-mers form a metastable complex that is subsequently stabilized by ␤7 additions. Fortuitously, we have found that low-copy plasmid expression of the ␤7/PRE4 gene in ␤5⌬pro cells leads to a build-up of the ␤7 subunit precursor in a complex with an apparent size just slightly greater than the 13S intermediate (Fig. 6E). The peak is substantially below the size of the 20S proteasome (ϳ670 kDa), and the pre-holoproteasome is expected to be even larger than mature 20S (26). Therefore, these data are most consistent with ␤7 adding to the half-mer before dimerization. It is possible that the full half-mers are nonproductive intermediates, but it is unclear why this would be the case. We also cannot fully exclude the possibility that half-mers associate, bind ␤7 subunits, and then dissociate again; however, ␤7 addition should stabilize the dimer, so this idea seems unlikely. We propose that the addition of ␤7 to the 15S intermediate induces structural changes in the ␤ ring (30) and provides a key additional trans-␤-ring interaction through its conserved C-terminal tail to drive rapid dimerization. In cells lacking ␤5pro but expressing excess ␤7, a step downstream of ␤7 addition but before dimerization appears to become limiting, consistent with a distinct role for ␤5pro in half-mer joining.
The current study provides new insight into the function of the ␤5 propeptide in 20S proteasome assembly and ␤5 precursor processing. It also clarifies the entry point of the ␤7 subunit into the proteasome assembly pathway, reinforcing the hypothesis that ␤7 and ␤5pro have overlapping but unequal functions in promoting dimerization of proteasome half-mers. Future structural and biochemical studies of the ␤5 propeptide in the The Yeast Proteasomal ␤5 Propeptide Chaperone context of various proteasomal precursors will be needed to get a finer-grained understanding of its precise and potentially evolving roles in proteasome biogenesis.
Author Contributions-X. L., Y. L., C. A. S., and M. H. performed all the experiments and analyzed the data. M. H. wrote the paper, which was reviewed and approved by all the authors.