Johan Larsbrink

Atsushi Izumi

Farid Ibatullin

Azadeh Nakhai

Harry J Gilbert

Gideon J Davies

Harry Brumer

Structural and enzymatic characterisation of a Glycoside Hydrolase Family 31 α-xylosidase from Cellvibrio japonicus involved in xyloglucan saccharification

Keywords: xyloglucan, plant cell wall, enzymology, hemicellulose, saccharification

The desire for improved methods of biomass conversion to fuels and feedstocks has re-awakened interest in the enzymology of plant cell wall degradation. The complex polysaccharide xyloglucan is abundant in plant matter, where it may account for up to 20% of the total primary cell wall carbohydrates. Despite this, few studies have focussed on xyloglucan saccharification, which requires a consortium of enzymes including endo-xyloglucanases, α-xylosidases, β-galactosidases and α-L-fucosidases, among others. Here, we present the characterisation of Xyl31A, a key α-xylosidase in xyloglucan utilisation by the model Gram-negative soil saprophyte Cellvibrio japonicus. CjXyl31A exhibits high regiospecificity for the hydrolysis xylogluco-oligosaccharides, with a particular preference for longer substrates. Crystallographic structures of both the apo enzyme and the trapped covalent 5-fluoro-β-xylosyl-enzyme intermediate, together with docking studies with the XXXG heptasaccharide, revealed, for the first time in glycoside hydrolase family 31, the importance of a PA14 domain insert in the recognition of longer oligosaccharides by extension of the active site pocket. The observation that CjXyl31A was localised to the outer membrane provided support for a biological model of xyloglucan utilisation by C. japonicus, in which xylogluco-oligosaccharides generated by the action of a secreted endo-xyloglucanase are ultimately degraded in close proximity to the cell surface. Moreover, this study diversifies the toolbox of glycosidases for the specific modification and saccharification of cell wall polymers for biotechnological applications.

Introduction

The enzymatic degradation of cellulose and matrix glycans of the plant cell wall into simple sugars provides energy for organisms from all kingdoms of life, and as such, represents a key aspect of the global carbon cycle [START_REF] Zhao | Drought-Induced Reduction in Global Terrestrial Net Primary Production from 2000 Through[END_REF]. This process is complex, with an implicit requirement for an enormous diversity of monosaccharide-and linkage-specific glycoside hydrolases and carbohydrate lyases [START_REF] Cantarel | The Carbohydrate-Active EnZymes database (CAZy): an expert resource for Glycogenomics[END_REF]. With the rising desire to convert the vast amounts of plant polysaccharides available to liquid fuels and value-added products, significant attention continues to be focussed on improving understanding of the mechanisms of microbial plant cell wall degradation [START_REF] Himmel | Biomass recalcitrance: Engineering plants and enzymes for biofuels production[END_REF].

Cellvibrio japonicus (previously Pseudomonas fluorescens subsp. cellulosa) is a saprophytic gram-negative bacterium, which was first isolated from Japanese soil [START_REF] Humphry | Reclassification of 'Pseudomonas fluorescens subsp. cellulosa' NCIMB 10462 (Ueda et al. 1952) as Cellvibrio japonicus sp. nov. and revival of Cellvibrio vulgaris sp. nov., nom. rev. and Cellvibrio fulvus sp. nov., nom. rev[END_REF]. The bacterium has been shown to utilise the major plant polysaccharides cellulose, mannan and xylan and, as such, is a good model for the study of bacterial plant polysaccharide degradation [START_REF] Hazlewood | Structure and function analysis of Pseudomonas plant cell wall hydrolases[END_REF]. Recently the genome of C. japonicus was sequenced, and not surprisingly, a vast array of carbohydrate degrading enzymes was identified [START_REF] Deboy | Insights into plant cell wall degradation from the genome sequence of the soil bacterium Cellvibrio japonicus[END_REF]. In contrast with anaerobic species, such as the Clostridia, the enzymes of C. japonicus that target polysaccharides integral to the plant cell walls do not form large membrane-attached cellulosome complexes [START_REF] Fontes | Cellulosomes: Highly Efficient Nanomachines Designed to Designed to Deconstruct Plant Cell Wall Complex Carbohydrates[END_REF], but are instead either secreted into the medium or attached to the cell membrane as lipoproteins. Indeed, about one third of the encoded carbohydrate-degrading enzymes have been predicted to be lipoproteins [START_REF] Deboy | Insights into plant cell wall degradation from the genome sequence of the soil bacterium Cellvibrio japonicus[END_REF], which may suggest that C. japonicus has developed a strategy involving the ultimate degradation of plant cell wall-derived oligosaccharides in close proximity to the cell, as has been shown, for example, in the case of xylan utilisation [START_REF] Beylot | Pseudomonas cellulosa expresses a single membrane-bound glycoside hydrolase family 51 arabinofuranosidase[END_REF][START_REF] Nagy | The membrane-bound alpha-glucuronidase from Pseudomonas cellulosa hydrolyzes 4-O-methyl-D-glucuronoxylooligosaccharides but not 4-O-methyl-D-glucuronoxylan[END_REF]. As a soil saprophyte, an abundant potential nutrient source for C. japonicus, apart from cellulose, is the group of non-crystalline cross-linking glycans commonly known as hemicelluloses. Among the most prevalent of these are the xyloglucans (XG), which are present in the primary cell wall of essentially all land plants. For instance, XGs may account for up to 20 % of the total carbohydrate content (dry weight) of the primary cell wall in dicots and non-graminaceous monocots, whereas more limited amounts are found in grass species [START_REF] Vogel | Unique aspects of the grass cell wall[END_REF]. XGs are a family of heterogeneous polysaccharides, which are typified by a β-(1→4)-D-glucan backbone substituted with α(1→6)-D-xylopyranosyl moieties at regular intervals. The basic repeating motifs may be further decorated with galactopyranose, arabinofuranose, fucopyranose and O-acetyl moieties in a tissue-and species dependent manner (Fig. 1) [11,[START_REF] Hsieh | Xyloglucans of Monocotyledons Have Diverse Structures[END_REF]. Thus, several enzymatic activities are required to degrade xyloglucan into its constituent monosaccharides. And whereas the endogenous enzymes responsible for the mobilisation of xyloglucans in plants have been previously studied in some detail [START_REF] Edwards | Purification and Properties of a Novel Xyloglucan-Specific Endo-(1-4)-Beta-D-Glucanase from Germinated Nasturtium Seeds (Tropaeolum majus L)[END_REF][14][START_REF] Crombie | A xyloglucan oligosaccharide-active, transglycosylating beta-D-glucosidase from the cotyledons of nasturtium (Tropaeolum majus L) seedlings -purification, properties and characterization of a cDNA clone[END_REF][16][START_REF] Leonard | Identification of an Arabidopsis gene encoding a GH95 alpha1,2-fucosidase active on xyloglucan oligo-and polysaccharides[END_REF][START_REF] Iglesias | Apoplastic glycosidases active against xyloglucan oligosaccharides of Arabidopsis thaliana[END_REF][19][20], the elucidation of the enzymes responsible for XG degradation by microorganisms such as C. japonicus is currently in its infancy [START_REF] Gilbert | How the walls come crumbling down: recent structural biochemistry of plant polysaccharide degradation[END_REF]. α(1→6)-Linked xylopyranose represents the second most abundant sugar in XGs, the cleavage of which is essential for the ultimate liberation of glucose from the polysaccharide backbone. α-Xylosidases have thus far only been identified in Glycoside Hydrolase Family 31 (GH31) (www.cazy.org, [START_REF] Cantarel | The Carbohydrate-Active EnZymes database (CAZy): an expert resource for Glycogenomics[END_REF]), which also contains diverse enzymes active on α-glucosidic bonds, such as α-glucosidases, sucrose-isomaltases, α-glucan lyases and isomaltosyltransglucosidases. Wholegenome analysis of C. japonicus has suggested that this organism produces only a single GH31 α-xylosidase, CjXyl31A [START_REF] Deboy | Insights into plant cell wall degradation from the genome sequence of the soil bacterium Cellvibrio japonicus[END_REF], which is thus likely to be a key player in XG degradation by this organism. We present here the biochemical characterisation of CjXyl31A together with the three-dimensional structure of the enzyme. Detailed kinetic data indicated a strict exo-specificity for non-reducing-end xylose moieties and increased specificity for extended, non-galactosylated xylogluco-oligosaccharides (XGOs). In harness, structural analysis revealed that this specificity was affected, in part, by a unique PA14 domain insert in the N-terminal domain of CjXyl31A that endowed the active site pocket with an extended substrate binding platform. Together, these data provide exquisite molecular insight into the enzymic features that enable C. japonicus to utilise the naturally abundant plant cell wall polysaccharide xyloglucan.

Experimental

Curve-fitting was performed using Origin 8 (OriginLab). Ultrapure water was used in all experiments and refers to water purified on a Milli-Q system (Millipore) with a resistivity of ρ > 18.2 MΩ•cm.

General analytical methods.

Mass spectrometry. For MALDI-TOF, a Biflex IV controlled by FlexControl 2.4 (Bruker Daltonics) was used, with 2,5-dihydroxy benzoic acid used as the matrix. ESI-MS on oligosaccharides was performed as described previously [START_REF] Martinez-Fleites | Crystal structures of Clostridium thermocellum xyloglucanase, XGH74A, reveal the structural basis for xyloglucan recognition and degradation[END_REF]. LC-ESI-MS was used for protein molar mass determination as described previously [START_REF] Sundqvist | A general, robust method for the quality control of intact proteins using LC-ESI-MS[END_REF].

NMR spectroscopy. NMR spectroscopic data were recorded on a Bruker Avance 400 instrument operating at 400.1 MHz for 1 H, using the residual solvent signal as reference. Chemical shifts (δ) are reported in ppm and coupling constants (J) are given in Hertz (Hz).

Native gel electrophoresis. Oligomerisation of Xyl31A was investigated by gel electrophoresis under native conditions, using a NuPAGE Novex 7 % Tris-Acetate gel (Invitrogen) with 25 mM Tris, 192 mM glycine (pH 8.3) as running buffer. Samples were loaded onto the gel in 50 mM Tris-HCl, 10 % glycerol, 0.05 % bromophenol blue (pH 8.6) and the molecular weights estimated by comparison with a high molecular weight marker for Native-PAGE (HMW Native Marker Kit, GE Healthcare). Proteins were visualised using PageBlue™ Protein Staining Solution (Fermentas).

High Performance Anion-Exchange Chromatography with Pulsed Amperometric Detection (HPAEC-PAD). Oligo-and monosaccharides were analysed on a Dionex ICS-3000 HPLC system operated by Chromelion software version 6.80 (Dionex) using a Dionex Carbopac PA200 column. Solvent A was water, solvent B 1 M sodium hydroxide and solvent C 1 M sodium acetate. Depending on the analytes, the following gradients were employed: Enzyme substrates p-Nitrophenyl (pNP) α-D-xylopyranoside, α-D-glucopyranoside, α-D-galactopyranoside and β-L-arabinopyranoside were purchased from Sigma. Tamarind seed xyloglucan and the derived oligosaccharides XXXG (Glc 4 Xyl 3 ; see [START_REF] Fry | An Unambiguous Nomenclature for Xyloglucan-Derived Oligosaccharides[END_REF] for oligosaccharide nomenclature), isoprimeverose (X, Xylp-α(1→6)-Glcp), and borohydride-reduced xylosyl-cellobiose (XGol, Xylp-α(1→6)-Glcp-β(1→4)-Glcp) were purchased from Megazyme (catalog numbers: O-X3G4, O-IPRM and O-XCBIR, respectively). XLLG (Glc 4 Xyl 3 Gal 2 ) and XXXGXXXG (Glc 8 Xyl 6 ) were prepared from tamarind xyloglucan as described previously [START_REF] Martinez-Fleites | Crystal structures of Clostridium thermocellum xyloglucanase, XGH74A, reveal the structural basis for xyloglucan recognition and degradation[END_REF]25].

The oligosaccharide XX (Glc 2 Xyl 2 ) was prepared from tamarind XG. 200 g XG was vigorously stirred in 2 l water at 65 °C to obtain a homogeneous mixture. The mixture was cooled to room temperature and ammonium acetate buffer (1 M, pH 4.5) was added until the desired pH was reached. Digestion was performed by addition of 1 g of the xgl1 endoglucanase (Dyadic NL) and the reaction proceeded at room temperature for four days with stirring. The reaction was stopped by heating at 80 °C for 30 minutes. The resulting suspension was centrifuged and the supernatant was collected, concentrated and precipitated using ethanol (4 equivalents v/v). The precipitate was collected and dissolved in water, followed by lyophilisation. A selected amount (4 g) of the XGO mixture was acetylated and purified by column chromatography as described previously [25], to obtain acetylated XX (0.15 g). The structure was verified by NMR (Supplemental Fig.

Bioinformatic analysis

The phylogenetic tree of GH31 was derived from the protein sequences of biochemically characterised entries in CAZy together with the sequence of Xyl31A. The predicted catalytic domains of the genes were aligned using MUSCLE [START_REF] Edgar | MUSCLE: a multiple sequence alignment method with reduced time and space complexity[END_REF], and the alignment was used to construct the phylogenetic tree using the maximum likelihood method with the program PhyML [27]. The reliability of the tree was analysed by bootstrap analysis of 100 resamplings of the dataset. The tree was displayed using MEGA4 [28].

Cloning of Xyl31A

The open reading frame encoding Xyl31A (GenBank accession number ACE86259. A c c e p t e d M a n u s c r i p t fragments were cloned into the pENTR/SD/D-TOPO entry vector (Invitrogen) according to the manufacturer's instructions. Chemically competent TOP10 cells were transformed with the cloning reaction and grown overnight. Plasmid DNA was extracted using the MiniPrep kit (Qiagen), and sequenced (Eurofins MWG Operon) to identify positive clones. The constructs were recombined, using the LR Clonase mix II (Invitrogen), into the pET-DEST42 destination vector (Invitrogen) (providing a C-terminal His 6 -tag) according to the manufacturer's instructions.

Recombinant gene expression and protein purification

Plasmids harbouring the Xyl31A gene were transformed into E. coli BL21(DE3) by electroporation, and the resulting transformants were grown in Terrific Broth containing 50 μg/ml Ampicillin at 37 °C to an OD 600 of 0.5-0.8. Gene expression was induced by addition of 0.5 mM isopropyl-1-thio-β-D-galactopyranoside (IPTG), and protein production was carried out at 25 °C overnight. The cells were collected by centrifugation at 3,800 ✕ g for 10 minutes, and were resuspended in Buffer A (20 mM sodium phosphate (pH 7.4), 0.5 M NaCl, 20 mM imidazole). The cells were passed twice through a French Press and centrifuged at 27,000 ✕ g for 45 min. The supernatant was loaded onto a Ni-sepharose fast flow column (GE Healthcare) using an ÄKTA FPLC (GE Healthcare) and washed thoroughly with buffer A. Xyl31A was eluted with a linear gradient of 0-100% of buffer B (20 mM sodium phosphate (pH 7.4), 0.5 M NaCl, 1.0 M imidazole). The eluted protein was washed and concentrated with 50 mM sodium phosphate (pH 7.5) with 10 kDa cutoff Amicon Ultra centrifugal filters (Millipore). The protein was further purified by size exclusion chromatography (SEC) using a HiPrep 26/60 Sephacryl S-300 column (GE Healthcare) using 50 mM sodium phosphate (pH 7.5).

Antibody generation and purification

Antibodies were raised against recombinant Xyl31A in rabbits (AgriSera AB). The immunisation was as follows: immunisation 1: 200 μg antigen (10 mg/ml) + Freund's complete adjuvant (FCA); immunisation 2, 3 and 4 (1, 2 and 3 months later, respectively): 100 μg antigen + Freund's incomplete adjuvant (FCI). The final bleeding was carried out eleven days after immunisation 4.

Xyl31A was coupled to a 1 ml HiTrap NHS-activated HP Column (GE Healthcare) according to the manufacturer's instructions. The column was washed using an ÄKTA FPLC (GE Healthcare) with several column volumes of PBST (PBS (pH 6.9) containing 0.05 % Tween20). To 4.5 ml antiserum containing antibodies against Xyl31A was added 0.5 ml 10x PBS and the solution was applied to the Xyl31A-coupled HP column. The column was washed with several column volumes of PBST. Antibodies bound to the column were eluted with 200 mM glycine, 1 mM EDTA (pH 2.5) in 0.5 ml fractions, to wells containing 50 μl 1M Tris and 75 μl 10x PBS (pH 6.9) to neutralise the eluent. The purified antibodies were passed through a PD10 column packed with His-tagged Albumin Binding Protein coupled to a NHS matrix to remove His-tag specific antibodies.

X-ray crystallography

Initial crystallisation conditions were screened using several kits and needle-shaped crystals were obtained from 20 % (w/v) PEG 4000, 0.1 M MES (pH 6.5), 5 mM NiCl 2 . Ultimately, two crystallisation conditions, using the hanging-drop vapor diffusion method, were optimised. Crystals of form 1 were cryo-protected using the reservoir solution alone whereas form 2 required elevation of the PEGmME concentration to 40 % PEG mME. Data for form 1 were collected on beamline ID14-2 of the European Synchrotron Radiation Facility (ESRF, Grenoble France) and that for form 2 on ESRF beamline ID29. Data were integrated using the HKL suite and MOSFLM/CCP4 [START_REF] Bailey | The Ccp4 Suite -Programs for Protein Crystallography[END_REF]. Data processing and structure refinement statistics are shown in Table 1.

The structure was solved by the molecular replacement method using the MalA structure (Sulfolobus solfataricus α-glucosidase, PDB ID 2g3m), which was selected by BALBES [START_REF] Long | BALBES: a molecularreplacement pipeline[END_REF], and the initial model was constructed using RESOLVE [START_REF] Terwilliger | SOLVE and RESOLVE: Automated structure solution and density modification[END_REF] and ARP/wARP [33] by using the 2.1 Å data from crystal form 1. Manual corrections were made using COOT [34]. All other computing used the CCP4 suite [START_REF] Bailey | The Ccp4 Suite -Programs for Protein Crystallography[END_REF] unless explicitly stated. The coordinate file and monomer library description for 5/4 PO/OH was prepared using PRODRG [START_REF] Schuttelkopf | PRODRG: a tool for highthroughput crystallography of protein-ligand complexes[END_REF] and PHENIX [START_REF] Adams | PHENIX: a comprehensive Python-based system for macromolecular structure solution[END_REF] whilst those for the trapped 5-fluoro-β-D-xylopyranosyl-enzyme intermediate were generated using the CCP4 suite. B-factors for all structures were refined with PHENIX by using TLS refinement with 5 TLS groups prepared by TLS motion determination web site (http://skuld.bmsc.washington.edu/~tlsmd/). The final structures were validated by MolProbity [START_REF] Chen | MolProbity: all-atom structure validation for macromolecular crystallography[END_REF] (http://molprobity.biochem.duke.edu/). Structure similarity searches were performed with DALI [38].

For docking analysis of the XXXG oligosaccharide, a library file containing oligosaccharide bond and torsion angle information was prepared using the PRODRG server (http://davapc1.bioch.dundee.ac.uk/prodrg/) from PDB ID 2cn3 [START_REF] Martinez-Fleites | Crystal structures of Clostridium thermocellum xyloglucanase, XGH74A, reveal the structural basis for xyloglucan recognition and degradation[END_REF]. Subsequently, the nonreducing end xylosyl unit of XXXG was superposed onto the 5-fluoro-β-D-xylopyranosyl group in the glycosyl-enzyme structure using the Superpose Ligands extension in COOT, followed by manual optimisation of glycosidic torsional angles to relieve obvious steric clashes.

Stopped assay for hydrolysis of pNP glycosides

Hydrolysis of pNP glycosides (2 mM) by Xyl31A was performed in 100 μl reactions at 25 °C in 50 mM citrate buffer (pH 6) using typically 2-10 μM enzyme. The reactions were stopped by addition of 100 μl 0.2 M NaCO 3 . Released p-nitrophenolate was measured in a Cary50 UV-vis spectrophotometer (Varian) at 410 nm, using 1 cm path length cuvettes (pNP anion extinction coefficient used for calculations was 18,500 M -1 •cm -1 [START_REF] Brumer | Lignocellulose degradation by Phanerochaete chrysosporium: purification and characterization of the main alphagalactosidase[END_REF]).

pH-rate profile

Measurements of the pH-dependence of Xyl31A were carried out using pNP-α-Xyl (2 mM) and the stopped assay. The following buffers were used (50 mM): sodium citrate (pH 3 -6.5), sodium phosphate (pH 6 -8), glycylglycine (pH 7.5 -9) and glycine (pH 9 -9.5).

Temperature stability

To monitor the temperature stability of Xyl31A, the enzyme was incubated at different temperatures with aliquots taken out at different time points [START_REF] Hazlewood | Structure and function analysis of Pseudomonas plant cell wall hydrolases[END_REF][START_REF] Vogel | Unique aspects of the grass cell wall[END_REF]20,[START_REF] Bailey | The Ccp4 Suite -Programs for Protein Crystallography[END_REF][START_REF] Gloster | Characterization and three-dimensional structures of two distinct bacterial xyloglucanases from families GH5 and GH12[END_REF]120, 240 min). The aliquoted enzyme was used in the stopped assay to determine remaining activity.

Specificity for XGO substrates

XGOs (XXXG, XLLG, XX, X) were incubated with Xyl31A (2.5 nM for longer XGOs, 2 μM for isoprimeverose) in 50 μl reactions containing 50 mM citrate buffer (pH 6) at 25 °C and the reactions stopped by addition of 1 μl 5 M NaOH. Product formation was assayed using HPAEC-PAD, with Gradient A used for XXXG, XLLG and XX and Gradient B for X. For the XGol substrate, the BCA reducing sugar assay was used [40,[START_REF] Mcfeeters | A Manual Method for Reducing Sugar Determinations with 2,2'-Bicinchoninate Reagent[END_REF]. 250 μl reactions were made in 50 mM citrate buffer (pH 6) with 20 nM Xyl31A, and stopped by addition of an equal amount of BCA reagent solution. Colour was developed by incubation at 80 °C and measured at 560 nm. Standard curves were made using xylose (Sigma).

XGO regiospecificity determination:

To fully degrade XXXG to cellobiose, Xyl31A was used together with a β-glucosidase (Clostridium thermocellum Glucosidase 1A, NZYTech, Lisbon, Portugal). The reactions were carried out in 200 mM citrate buffer (pH 6), at 37 °C for Xyl31A and 55 °C for Glc1A until the reactions had gone to completion. First, Xyl31A was added to hydrolyse the xylose moiety from the non-reducing end, followed by denaturation by boiling. The same procedure was carried out with the β-glucosidase, hydrolysing the now exposed glucose moiety. The procedure was cycled until cellobiose was obtained. Product formation was analysed by ESI-MS.

To further analyse the regiochemistry of Xyl31A, XXXG 2 was used as substrate with subsequent analysis by MALDI-TOF MS.

Cellular localisation of Xyl31A

C. japonicus Ueda107 was grown in 250 ml M9 minimal medium [START_REF] Miller | Experiments in molecular genetics[END_REF] containing tamarind seed XGOs (0.4 % [w/v]) as the sole carbon source at 30 °C for 24 h until an OD 600 of 1, corresponding to a late exponential phase [43]. The cells were collected by centrifugation at 4,400 ✕ g for 10 minutes and the supernatant was decanted and concentrated ca. 25-fold using 10 kDa-cutoff Amicon Ultra centrifugal filters (Millipore).

Periplasmatic proteins were collected by osmotic shock. The cells were washed with 10 ml 50 mM Tris-HCl (pH 7.7) and collected by centrifugation at 4,400 ✕ g for 10 minutes. The pellet was resuspended in 50 ml 30 mM Tris-HCl, 20 % (w/v) sucrose, 1 mM EDTA (pH 8.0) and the cells were incubated in room temperature for 10 minutes. The cells were collected by centrifugation at 4,400 ✕ g for 15 minutes. 50 ml ice cold 5 mM MgSO 4 was added and the cells were incubated on ice for 10 minutes. The cells were centrifuged at 14,000 ✕ g for 10 minutes and the supernatant collected.

The cell pellet were resuspended in 50 mM sodium phosphate buffer (pH 7.4) and passed twice through a French Press. The lysate was centrifuged at 5,000 ✕ g for 10 minutes to remove debris. The supernatant was centrifuged at 100,000 ✕ g for 1 hour and the supernatant containing the soluble proteins was collected. The pellet, containing the membrane fraction was resuspended in 100 mM sodium carbonate buffer (pH 9) to remove trapped soluble proteins and/or weakly membrane-associated proteins and centrifuged again at 100,000 ✕ g for 1 hour. The pellet was resuspended in 1 ml 50 mM sodium phosphate buffer (pH 7.4). Western blot was used to visualise the content of Xyl31A in the secreted, periplasmatic, soluble intracellular and membrane fractions. The purified anti-Xyl31A antibodies were used as the primary antibody, and anti-rabbit IgG (Sigma) coupled to alkaline phosphatase was used as the secondary antibody, followed by visualisation using SIGMAFAST BCIP/NBT tablets (Sigma) dissolved in water.

Depolymerisation of XG by secreted enzymes of C. japonicus

The secreted protein fraction from the cellular localisation studies, above, was screened for xyloglucanase activity using XG as substrate. The fraction was washed with 50 mM sodium phosphate buffer (pH 7.4) using 10 kDa cutoff Amicon Ultra centrifugal filters (Millipore) to remove traces of XGOs from the growth medium.

Reactions consisted of 10 μl of the protein fraction (0.04 mg/ml, determined by the Bradford method with a BSA standard curve) added to 145 μl 1.72 g/l XG in 69 mM ammonium acetate buffer (pH 5.5) and incubation at 37 °C for 10, 20, 30, 120, 275 minutes and 48 hours. The reactions were stopped by boiling for 10 minutes, with subsequent lyophilisation. The samples were re-dissolved in 350 μl DMSO and heated at 80 °C for 10 minutes. Gel permeation chromatography (GPC) analysis was used to monitor the depolymerisation of XG, as described previously [44] though using two PLgel 10 µm mixed B columns and a guard column (Agilent) in tandem kept at 70 °C. An 11 point pullulan standard curve (Mw 180-1660000 Da) was used for molecular weight estimation. HPAEC-PAD was used for product analysis of the formed XGOs after the full depolymerisation of XG, using Gradient C.

Results and discussion

Primary structure analysis of Cj Xyl31A and GH31 phylogeny Previous analysis of the genome of Cellvibrio japonicus predicted a vast array of polysaccharide degrading enzymes, of which CjXyl31A was annotated as the sole putative α-xylosidase belonging to Glycoside Hydrolase Family 31 (GH31) in the Carbohydrate-Active Enzymes (CAZy) classification [START_REF] Deboy | Insights into plant cell wall degradation from the genome sequence of the soil bacterium Cellvibrio japonicus[END_REF]. Re-analysis of the primary structure indicated that CjXyl31A had the highest protein sequence identity to the Sulfolobus. solfataricus GH31 α-xylosidase XylS (Genbank accession number CAB99206.1), with values of 27%, 39 %, and 35 % for the Nterminal, catalytic, and C-terminal domains, respectively. Also, a ca. 150 amino acid-long insert in the CjXyl31A N-terminal domain, which is not present in biochemically characterised GH31 enzymes, was identified. A BLAST search reveals that this sequence (amino acids 238-384) belongs to the PA14 superfamily (named after the protective antigen of anthrax toxin [START_REF] Petosa | Crystal structure of the anthrax toxin protective antigen[END_REF]), which is known to form inserts in a wide variety of enzymes and has been proposed to be involved in substrate binding [46]. Sequence analysis has previously indicated that the PA14 domain is also found in members of glycoside hydrolase families GH2, GH3, GH10, and GH20, in addition to GH31 [46]. However, little is presently known about the tertiary structure and function of PA14 domains in these enzymes. As a lone example, a recent report on the structurefunction analysis of the Kluyveromyces marxianus β-glucosidase has highlighted that the PA14 domain in that GH3 enzyme occludes the active site pocket, thus conferring a preference for A c c e p t e d M a n u s c r i p t disaccharide substrates [START_REF] Yoshida | Role of a PA14 domain in determining substrate specificity of a glycoside hydrolase family 3 beta-glucosidase from Kluyveromyces marxianus[END_REF]. In CjXyl31A, the PA14 domain is likewise positioned close to the active site, but in contrast appears to be involved in the extended recognition of longer xylogluco-oligosaccharides, as discussed below.

To delineate the diverse α-glucoside-and α-xyloside-processing activities in GH31, a phylogenetic tree was constructed using only the (β/α) 8 catalytic domain of all members of GH31 whose enzyme specificity has previously been determined (data from the CAZy database [START_REF] Cantarel | The Carbohydrate-Active EnZymes database (CAZy): an expert resource for Glycogenomics[END_REF], www.cazy.org), together with CjXyl31A (Fig. 2). In this phylogeny, a number of activities toward α-glucosidic bonds stood out clearly as distinct clades, including the α-1,4-glucan lyases, the isomaltosyl-and 6-α-glucosyltransglycosylases, and the sucrase-isomaltases. However, notably, the eight α-xylosidases characterised to-date did not clearly segregate, thus suggesting that α-xylosidase activity has arisen on separate occasions from gluco-specific enzymes. In particular, the known plant α-xylosidases (entries BAA99366.1 (Oryza sativa), AAD37363.1 (Arabidopsis thaliana), CAA10382.2 (Tropaeolum majus)) cluster with plant α-glucosidases, while the only other characterised eukaryotic α-xylosidase from Aspergillus nidulans (EAA62085.1) is most similar to the bacterial α-xylosidases (Fig. 2). The promiscuity of the A. thaliana α-xylosidase/α-glucosidase [19] further highlights that small differences in protein sequence can modulate substrate discrimination based on the presence or absence of the C-6 hydroxymethyl group on the pyranose ring [48] (see Fig 1B). Indeed, the E. coli GH31 α-xylosidase YicI has been converted into an α-glucosidase by site directed mutagenesis [START_REF] Okuyama | Structural elements to convert Escherichia coli alpha-xylosidase (YicI) into alpha-glucosidase[END_REF]. Given the comparatively limited data available to-date, it is clear that phylogenetic groupings do not unambiguously predict catalytic function in GH31, thus motivating further structural and functional characterisation of CjXyl31A.

It is worth noting here that an earlier suggestion [29] that bacterial GH31 members invariantly contain the consensus sequence KTDFGE surrounding the conserved catalytic nucleophile (underlined) appears to not be borne out in the analysis of larger datasets. CjXyl31A, in particular, contains the sequence WLDAVE, which is also similar to that of the wellcharacterised archeal α-xylosidase, SsXylS (WLDASE, [START_REF] Moracci | Identification and molecular characterization of the first alpha-xylosidase from an Archaeon[END_REF], see Supplemental Figure S3). Of the fifteen biochemically characterised bacterial genes used to construct the phylogenetic tree showing in Fig. 2, only E. coli YicI (GenBank accession AAC76680.1) and Lactobacillus pentosus XylQ (AAC62251.1) contain the exact KTDFGE sequence, while four bacterial isomaltosyltransglucosidases (BAB88401.1, BAD34979.1, BAB88403.1, BAC54957.1) possess the similar KTDFGg consensus sequence; the remainder of the bacterial enzymes in the present analysis contain the consensus sequence WnDmnE.

Heterologous expression and protein purification

CjXyl31A bearing a C-terminal hexahistidine tag was produced in E. coli BL21(DE3) cells; the positioning of the purification tag was chosen based on previous report which indicated that the N-terminal portion of GH31 enzymes may influence substrate binding [29]. The recombinant protein was purified by IMAC followed by SEC to remove low molar mass contaminants. SEC data, confirmed by native-PAGE on individual fractions, showed the protein being in mainly monomeric form (ca. 75 %), with minor fractions in dimeric, tetrameric and hexameric forms. The electrophoretically pure (SDS-PAGE, data not shown) pooled fractions from the SEC was used for all subsequent analyses. LC-ESI-MS indicated that the CjXyl31A so produced had a molar mass of 113644 ± 3 (calculated 113643.2), corresponding to the His-tagged protein less a A c c e p t e d M a n u s c r i p t 23 residue signal peptide. The LipoP 1.0 Server [START_REF] Juncker | Prediction of lipoprotein signal peptides in Gram-negative bacteria[END_REF] indicated that this was likely a lipoprotein signal peptide, which would anchor the enzyme to the plasma membrane through the sulfhydryl group of Cys23 after cleavage by Signal Peptidase II [52]. CjXyl31A was however produced in good yields (200 mg/l) as a soluble protein in E. coli, with Ser24 as the N-terminus after signal peptide processing.

Substrate specificity of the -1 (glycone) subsite

A range of para-nitrophenyl (pNP) α-glycopyranosides were used to screen the substrate specificity of CjXyl31A (Fig. 1B). In keeping with the original prediction of activity [START_REF] Deboy | Insights into plant cell wall degradation from the genome sequence of the soil bacterium Cellvibrio japonicus[END_REF] and sequence similarity to SsXylS (Fig. 2), CjXyl31A exhibited the highest activity toward pNPαXyl (Table 1). With the corresponding glucoside, activity was several orders of magnitude lower, and no activity was observed on pNPαGal or pNPβ-L-Arap substrates. Compared to the E. coli α-xylosidase YicI [29], CjXyl31A had a six-fold lower k cat /K m value on pNPαGlc (YicI 6.0 • 10 -3 mM -1 s -1 , CjXyl31A 1.2 • 10 -3 mM -1 s -1 ) and a ten-fold higher k cat /K m value on pNPαXyl (YicI 0.18 mM -1 s -1 , CjXyl31A 1.5 mM -1 s -1 ), which indicates a significantly higher specificity for xylose (i.e. discrimination against the 6-hydroxymethyl substituent) in the -1 subsite [START_REF] Davies | Nomenclature for sugar-binding subsites in glycosyl hydrolases[END_REF] of CjXyl31A.

pH dependence and thermostability studies

The pH dependence of catalysis by CjXyl31A was assayed using pNPαXyl. A classic bellshaped pH profile was obtained (Fig. 3), with an optimum at 6.5 and apparent pK a values of 4.3 and 8.8, which likely correspond to the ionisation of the catalytic nucleophile and acid/base residues, respectively. The thermal stability of CjXyl31A was assayed by incubating the enzyme at different temperatures and assaying remaining activity after defined time intervals (Fig. 3). At 35 ˚C and 45 ˚C, CjXyl31A exhibits good stability under the solution conditions used, with approximately 15 % activity loss after four hours at both temperatures. At higher temperatures (≥55 ˚C), the protein loses activity rapidly, as might be expected for an enzyme from a mesophile.

Specificity toward xylogluco-oligosaccharides (XGOs)

In nature, α-linked xylose is most prevalent in the plant cell wall polysaccharide xyloglucan [START_REF] Vogel | Unique aspects of the grass cell wall[END_REF]. To investigate the potential of CjXyl31A to participate in xyloglucan degradation, assays were performed on a small library of xylogluco-oligosaccharides (XGOs) obtained by enzymatic hydrolysis (Fig. 1C). CjXyl31A showed a clear preference for longer substrates, with the heptasaccharide XXXG yielding the highest k cat /K m value, which was similar to the tetrasaccharide XX (Table 1). On the trisaccharide alditol XGol, the k cat /K m value was about a third of that for XXXG. The disaccharide X (Xylp-α(1→6)-Glcp, Fig. 1A) was hydrolysed at a significantly slower rate than the other XGOs and had a 100-fold higher K m value compared to XXXG. Galactosylation also reduced the specificity of CjXyl31A for oligosaccharide substrates; the k cat /K m value for the nonasaccharide XLLG was 3-fold lower than for XXXG, due to a significantly higher K m value of the former.

Product analysis by ESI-MS indicated that for all of the XGO substrates, only one xylose residue was released (full data not shown; see e.g. XXXG, Table 2). Similarly, MALDI-TOF MS analysis of the reaction products following incubation of CjXyl31A with XXXGXXXG (Fig. 1C) indicated that a single xylosyl unit was cleanly released from the tetradecasaccharide (Fig. 4), presumably from the extreme non-reducing end. The strict non-reducing-end, exo-activity of CjXyl31A was confirmed by sequential incubation of the heptsaccharide XXXG with CjXyl31A and Clostridium thermocellum exo-β-glucosidase Glc1A, incorporating a heat-inactivation step between each enzyme treatment. Thus, XXXG was degraded by CjXyl31A to yield only GXXG, which could then by hydrolysed to XXG by CtGlc1A, which could again be cleaved by CjXyl31A to GXG, and so on, to yield cellobiose after the last xylosidase treatment (Table 2). Together, these results demonstrate that CjXyl31A is unable to access internal xylose residues in xyloglucan polymers, even when they are followed by an unbranched glucose residue in the backbone, as in XXXGXXXG. This behaviour is similar to that of previously characterised αxylosidases from plants and archea, which require a β-glucosidase for the full degradation of, e.g., the XXXG motif [START_REF] Crombie | A xyloglucan oligosaccharide-active, transglycosylating beta-D-glucosidase from the cotyledons of nasturtium (Tropaeolum majus L) seedlings -purification, properties and characterization of a cDNA clone[END_REF]16,[START_REF] Moracci | Identification and molecular characterization of the first alpha-xylosidase from an Archaeon[END_REF]. Analysis of the three-dimensional structure of CjXyl31A, reported below in apo and substrate-complexed forms, provides a clear rationalisation for this exquisite regiospecificity.

In the context of biotechnological applications, including plant biomass saccharification, CjXyl31A displays catalytic constants for the hydrolysis of the artificial substrate pNPαXyl (Table 1) similar to that of other GH31 -xylosidases. Thus, the k cat and K m values of mesophilic enzymes for pNPαXyl typically fall in the ranges of 0.1 -0.6 s -1 and 0.1 -1 mM, respectively (see [29] and references therein), whereas k cat values for the thermophilic xylosidase from Sulfolobus sulfataricus may approach 3 -10 s -1 in the temperature range 65 -85 C [START_REF] Moracci | Identification and molecular characterization of the first alpha-xylosidase from an Archaeon[END_REF] (assuming enzyme saturation at [S] = 37 mM used in that study). However, while CjXyl31A is more selective for pNPαXyl over pNPαGlc than the well-characterized E. coli YicI [29] (vide supra), the C. japonicus enzyme is a much poorer degrader of the minimal disaccharide isoprimeverose (k cat 2.9 s -1 , K m 55 mM, Table 1) than either its E. coli (k cat 51 s -1 , K m 0.55 mM, [START_REF] Okuyama | Overexpression and characterization of two unknown proteins, YicI and YihQ, originated from Escherichia coli[END_REF]) or S. sulfataricus (specific activity ca. 20 s -1 at [S] = 100 mM and 65 C, [START_REF] Moracci | Identification and molecular characterization of the first alpha-xylosidase from an Archaeon[END_REF]) homologs. Direct comparison with plant -xylosidases is hampered by a paucity of detailed kinetic analyses [19,20]. Thus, the kinetic data (Table 1) suggest that CjXyl31A is best suited to technical uses that involve the breakdown of larger xylogluco-oligosaccharides.

Overall three-dimensional structure of CjXyl31A

To illuminate the structural bases for catalysis and the potential role of the "PA14" domain, the three-dimensional structure of the xylosidase was solved. Crystals of CjXyl31A were obtained in the hexagonal space group P6 3 22 with one molecule in the asymmetric unit. The structure was solved by molecular replacement using the structure of the S. solfataricus α-glucosidase MalA (PDB ID 2g3m). The refined structure of the apo enzyme, the 5-fluoro-β-xylosyl-enzyme intermediate and the pentaerythritol propoxylate complex were solved at 2.6, 2.5 and 2.3Å resolution respectively, Table 3. As described above, mass spectrometric analysis indicated that the predicted signal sequence of 24 amino acids was processed during protein expression. In addition, no electron density was visible for the first 20 N-terminal residues of the mature protein in any of the structures. Thirty-one C-terminal residues of the apo structure and 32 C-terminal residues of the complex structures were also unresolved and are presumably disordered.

The CjXyl31A monomer structure has a complex modular architecture which is difficult to define unambiguously, but which may be considered as five domains consisting of two Nterminal "lobes", a central catalytic domain and two C terminal modules (Fig. 5). The central catalytic domain forms an (β/α) 8 -barrel consisting of residues 412-791 and with two significant "inserts" beyond the standard barrel termed insert region-1 (Ins1) at residue 512-556 and insert region-2 (Ins2) at residue 586-613. The (β/α) 8 -barrel contains the catalytic apparatus, as will be described subsequently in light of a covalent intermediate complex and by virtue of similarities to related GH31 and Clan GH-D enzymes of known 3-D structure. The N-terminal region clearly forms two essentially discrete lobes. The first, primarily N-terminal, lobe is defined by residues 45-237, which form a β-sandwich domain. The topology of this domain is complicated by the fact that the 3-D structure of the whole domain also involves residues 392-411 when they return from the excursion that forms the second N-terminal domain. This latter domain, also itself a βsandwich lobe, is an excursion between two of the strands of the N-terminal domain. This inserted domain, defined approximately by residues 238-391, is classified as a "PA14" domain (described previously, and in more detail below). The C-terminal domains follow a more regular topology defined by two discrete sequential β-sandwich domains approximately delineated by residues 793-870 and 871-988, respectively. Interface analysis using PISA [START_REF] Krissinel | Detection of protein assemblies in crystals[END_REF] suggests that none of the potential interfaces are significant in terms of a stable higher oligomeric complex.

The most striking difference between CjXyl31A and other known GH31/Clan GH-D tertiary structures is the unusual N-terminal "PA14" domain, the function of which is not generally known. The PA14 domain derives its name from the N-terminal cleaved domain of anthrax protective antigen [START_REF] Petosa | Crystal structure of the anthrax toxin protective antigen[END_REF], with which the corresponding residues in CjXyl31A display an rmsd of 2.3 Å over 105 matched Cα positions (DALI [38] Z-score = 8.6). The domain is also similar to a number of other sugar-binding domains such as the mannose-binding flocculation protein Flo5 protein [START_REF] Veelders | Structural basis of flocculin-mediated social behavior in yeast[END_REF] (PDB 2xj2, Z score 9.1 with 119 C overlapping, rmsd 2.5 Å). Most intriguingly, this domain shares high structural similarity with a number of other domains such as observed in a family GH3 β-glucosidase [START_REF] Yoshida | Role of a PA14 domain in determining substrate specificity of a glycoside hydrolase family 3 beta-glucosidase from Kluyveromyces marxianus[END_REF] (PDB 3abz, DALI Z-score 13.1, with 132 Cα overlapping, rmsd 2.7 Å), the family GH2β-glucuronidase [START_REF] Wallace | Alleviating Cancer Drug Toxicity by Inhibiting a Bacterial Enzyme[END_REF] (PDB 3k46, Z 9.1, 118 Cα overlapping, rmsd 3.5 Å), family GH2 βmannosidases (PDB 2je8, Z-score 7.9, 113 Cα overlapping, rmsd 3.2 Å) ,as well as other similar domains from both β-glucosidase and β-glucuronidases. The PA14 domain observed in CjXyl31A is, thus far, unique to GH31 enzymes of known structure -it is not, for example, found in E. coli YicI (Fig. 5). Given the proximity of the PA14 domain to the active site pocket of CjXyl31A, we speculate this domain play a role in the binding of oligosaccharides, contributing to the preference for longer XGOs, as will be described below.

3-D structure of a trapped covalent glucosyl-enzyme intermediate.

Crystals of "form 2" (see Methods) were soaked in the mother liquor supplemented with approximately2 mM of "5-fluoro-α-D-xylopyranosyl fluoride" (5FαXylF). Electron density for a covalently linked 5-fluoro-β-xylosyl residue was clearly seen in the -1 subsite with the anomeric carbon atom making a covalent bond to OD2 atom of D582 with 1.4 Å distance (Fig. 5). The ring conformation refined to a 1 S 3 (skew boat) conformation, consistent with that observed in structures of -glycosidases from GH31 and Clan GH-D described previously [29,[START_REF] Guce | Catalytic Mechanism of Human alpha-Galactosidase[END_REF]). D582 and D659 are predicted to act as the catalytic nucleophile and acid/base residues, as previously defined for this sequence family [29]. D470, H740, D659 and R642 all make hydrogen bonds to hydroxyl groups of the 5-fluoro--xylosyl ester, whilst F692 and W471 make Van der Waals' contacts with the ligand. A water molecule binding to D659 lies 3.1 Å from the C1 atom of the intermediate and would appear to be perfectly poised to act as the hydrolytic water in the reaction mechanism. Crystal form 1 also yielded a structure with the precipitant pentaerythritol propoxylate bound in the catalytic pocket. The environment of the pocket is almost same as that in apo and intermediate structures except that W347 and W471 are flipped away from the inside of the pocket by ca. 20˚ and 80˚, respectively. Pentaerythritol propoxylate settles between W347 and W542 and has a Van der Waals' contact to W471. Together, these data suggest plasticity of the binding site.

Relation of 3-D structure to observed kinetics and digestion patterns

Previous studies on α-xylosidases from Tropaeolum majus, Arabidopsis thaliana and Sulfolobus solfataricus have shown the selective hydrolysis of one xylose moiety from the non-reducing end of xylogluco-oligosaccharides (XGOs), without observed activity on internal xylose moieties [16,[START_REF] Iglesias | Apoplastic glycosidases active against xyloglucan oligosaccharides of Arabidopsis thaliana[END_REF][START_REF] Moracci | Identification and molecular characterization of the first alpha-xylosidase from an Archaeon[END_REF]. To date, the three dimensional structure has been determined for five members of GH31, with YicI from Escherichia coli being the only α-xylosidase [29]. These five enzymes all display a highly similar fold, with a central catalytic (α/β) 8 -barrel flanked by N-and C-terminal β-sheet domains of unknown functions, though the N-terminal domain has been suggested to be involved in substrate binding [29].

In the case of CjXyl31A, substrate specificity has two facets: (1) this strictly exo-acting enzyme is specific for a terminal, unsubstituted xyloside and (2) this xyloside must lie at the extreme reducing end of a xylogluco-oligosaccharide; there is no activity on the internal xylosides of substrates such as XXXG and XXXGXXXG. The specificity for an unmodified terminal xylose moiety is provided, as with other GH31 enzymes, by the constellation of residues that interact directly with the -1 subsite xyloside. W580, W656 and F692 together provide a steric barrier at the end of the active centre pocket, in which D470, H740, D659 and R642 make hydrogen bonds to the -1 subsite xyloside (described above in light of the xylosyl-enzyme intermediate structure; see also Fig. 5). There is thus no scope, simply in terms of sterics, to accommodate a xyloside with appended Gal or Gal-Fuc moieties, as found in oligosaccharides such as XLLG and XLFG (Fig. 1). The pocket itself, however, is more than merely a blunt-ended -1 subsite. The POCKETFINDER server (http://www.modelling.leeds.ac.uk/qsitefinder/help.html) estimates that the catalytic crevice has minimum dimensions of ~11 Å (depth) x 8 Å (width), although the binding surface could certainly be more extended as the mouth of the canyon expands into a larger estuary.

Our attempts to soak/co-crystallize with various XGOs did not yield a complexed structure, which, in the case of soaking, may partially reflect a two-fold axis of crystallographic symmetry that resulted in the active sites of two monomers facing each other. To circumvent this paucity of direct experimental data, a simple manual model of the Michaelis complex between CjXyl31A and XXXG was constructed based upon the 3-D structures of a known XGO/endo-xyloglucanase complex [START_REF] Martinez-Fleites | Crystal structures of Clostridium thermocellum xyloglucanase, XGH74A, reveal the structural basis for xyloglucan recognition and degradation[END_REF] and the glycosyl-enzyme intermediate described above. As shown in Fig. 6, interactions with the XXXG substrate extend beyond the active site pocket to the extended face provided by the PA14 domain. Another key feature the model is that the O4 atom of the +1 glucoside moiety is also enrobed by a tight surface comprised of, notably, R642 and the loop of residues 582-587, whose distal end begins one of the unusual insertions in the classical (βα) 8 barrel). Likewise, W542, from the second of the unusual insertions, lies under the potential +1/+2 boundary and may also play a role in discriminating against "endo" attack. Together these residues provide the steric features that prevent binding of a xyloside from an "internal" glucose moiety and demand that only the xylose on the extreme non-reducing end glucoside is accommodated. The data further suggest that if an internal xylose-cleaving enzyme is desired, homologs should be sought with truncations in these regions.

The unique PA14 domain lies on the side of the substrate binding cleft and could, potentially both facilitate binding of longer oligosaccharides and perhaps also play a role in productive binding both of the backbone of the xyloglucan oligosaccharides (W347, for example lies on the floor of the binding canyon such that it may interact with a +2 subsite glucoside) whilst also providing numerous H-bonding residues that may interact productively with appended xyloside moieties. Such proposals are clearly speculative, but it is fascinating to see that other similar PA14 domains in unrelated glycosidases have also been recruited to modulate the oligosaccharide specificity, such as in Bacteroides thetaiotaomicron Man2A where the domain serves to block off an otherwise "endo" active centre groove to provide the chain-end specificity demanded by a -mannosidase [START_REF] Tailford | Mannose foraging by Bacteroides thetaiotaomicron -Structure and specificity of the beta-mannosidase, BtMan2A[END_REF]. Similarly, the PA14 domain of the family GH3 glucosidase has recently been show to modify the exo/endo behaviour of that enzyme [START_REF] Yoshida | Role of a PA14 domain in determining substrate specificity of a glycoside hydrolase family 3 beta-glucosidase from Kluyveromyces marxianus[END_REF]. Clearly, our understanding of the potential roles of PA14 domains in only in its infancy, due to the limited number of structure-function studies available presently. However, given the wide distribution of this domain across GH families [46], we anticipate further focussed studies on the importance of PA14 in carbohydrate recognition and catalysis.

The physiological role of CjXyl31A in the scavenging of xyloglucan by Cellvibrio japonicus in the natural environment

The detailed protein structural and enzyme kinetic data presented here lay the initial groundwork for understanding the mechanism by which the soil saprophyte Cellvibrio japonicus scavenges xyloglucan in its habitat. As highlighted in the Introduction, complete saccharification of the plant polysaccharide likely involves the concerted action of one or more endo-acting xyloglucanases capable of generating shorter oligosaccharide fragments (e.g. EC 3.2.1.151) [START_REF] Gilbert | How the walls come crumbling down: recent structural biochemistry of plant polysaccharide degradation[END_REF], together with a battery of exo-acting glycosidases, including CjXyl31A, to release individual monosaccharides for cellular uptake.

Thus far, no xyloglucan-specific endo-glucanases have been described from C. japonicus, nor is there any general information on the ability of the organism to degrade xyloglucan polymers. Consequently, C. japonicus was grown on a minimal medium containing a mixture of tamarind seed XGOs as the sole carbon source, in an attempt to induce the production of xyloglucanactive enzymes. Subsequent analysis of the extracellular medium obtained during the lateexponential growth phase indeed indicated the presence of endo-xyloglucanase activity. Specifically, HPSEC and HPAEC-PAD analysis (Supplemental Fig. S3) indicated that this crude preparation was able to hydrolyse tamarind seed xyloglucan to the four component oligosaccharides, XXXG, XLXG, XXLG, and XLLG (see Fig. 1 for structures) by specific cleavage at the unbranched glucosyl unit. While the isolation and further characterisation of the individual enzyme(s) responsible for this activity are beyond the scope of this paper, these results clearly demonstrate that C. japonicus has the capacity to generate its own XGOs for further utilisation. It is also noteworthy that the extracellular fraction appears to be essentially devoid of β(1→2)-galactosidase and α(1→6)-xylosidase activities, as evidenced by the peak areas of the component oligosaccharides, which are similar to those obtained via digestion with purified endo-xyloglucanases [START_REF] Martinez-Fleites | Crystal structures of Clostridium thermocellum xyloglucanase, XGH74A, reveal the structural basis for xyloglucan recognition and degradation[END_REF]25,[START_REF] Gloster | Characterization and three-dimensional structures of two distinct bacterial xyloglucanases from families GH5 and GH12[END_REF].

The observation that CjXyl31A is encoded with a predicted lipoprotein signal peptide (vide supra) provided a further tantalizing clue about the potential mechanism by which C. japonicus systematically disassembles xyloglucan. To verify the membrane localisation of CjXyl31A in the native organism, Western blot analysis was performed on total membrane, soluble intracellular, periplasmatic and secreted protein fractions (Fig. 7). The analysis indicates CjXyl31A was most abundant in the total membrane fraction, but was also found in significant quantity in the soluble intracellular fraction, and, to a lesser extent, in the periplasm. In keeping with the HPLC data (Supplemental Fig. S3), essentially no CjXyl31A was found in the extracellular medium; trace amounts, detectable as a very faint band on the Western blot after prolonged staining, may be attributable to cell lysis late in the exponential growth phase. Localisation of CjXyl31A on the outer membrane is consistent with previous studies on membrane-bound glycosidases of C. japonicus [START_REF] Beylot | Pseudomonas cellulosa expresses a single membrane-bound glycoside hydrolase family 51 arabinofuranosidase[END_REF][START_REF] Nagy | The membrane-bound alpha-glucuronidase from Pseudomonas cellulosa hydrolyzes 4-O-methyl-D-glucuronoxylooligosaccharides but not 4-O-methyl-D-glucuronoxylan[END_REF]. Further, the absence of an aspartic acid residue at position +2 -this residue is a serine in CjXyl31A -is also suggestive of outer membrane localisation [START_REF] Juncker | Prediction of lipoprotein signal peptides in Gram-negative bacteria[END_REF].

Conclusion

Taken together, the data present an emerging picture of xyloglucan utilisation by C. japonicus, in which soluble, secreted endo-xyloglucanase activity liberates oligosaccharides that are further degraded to monosaccharides close to the cell surface (Fig. 8). Notably, this model of step-wise hydrolysis of xylogluco-oligosaccharides by non-reducing-end-specific exo-glycosidases also rationalises the low activity that CjXyl31A exhibits toward the disaccharide isoprimeverose (Xylp-α(1→6)-Glc, "X" in Fig. 1C), which would not generally be encountered; the shortest oligosaccharide hydrolysed by CjXyl31A would be xylosyl-cellobiose (Table 2), the alditol of which (XGol) is cleaved with essentially the same selectivity as the parent oligosaccharides XXXG and XLLG (Table 1). Although the identities of the α(1→2)-L-fucosidase, β(1→2)galactosidase(s), and β(1→4)-glucosidase necessary for the complete saccharification of XGOs are presently unknown, as is their potential to synergise with each other and with one or more unidentified sugar transporters, this model suggests fertile ground for future study. The detailed enzyme structure-function analysis in the present study has given new insight into the mechanisms of xyloglucan degradation by C. japonicus, yet there is still much information missing to fully describe the pathways of polysaccharide utilisation by this soil saprophyte. A c c e p t e d M a n u s c r i p t

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.



  Gradient B: 0 to 5 min, 10 % B, 0 % C; 5 to 10 min, 10 % B and a linear gradient from 0-30 % C; 10 to 10.1 min, 50 % B, 50 % C; 10.1 to 12.5 min, an exponential gradient of NaOH and NaOAc back to initial conditions; 12.5 to 15 min, initial conditions.  Gradient C: 0 to 4 min, 10 % B, 6 % C; 4 to 17 min, 10 % B and a linear gradient from 0-25 % C; 17 to 17.1 min, 50 % B, 50 % C; 17.1 to 18 min, an exponential gradient of NaOH and NaOAc back to initial conditions; 18 to 22 min, initial conditions.

  1) was amplified by PCR from genomic DNA of C. japonicus Ueda107 using Phusion polymerase (5′-CACCATGTTATCGGCACATCAGTG-3′ and 5′-TTAACGCGGGCGTTTAATGC-3′ with the forward primer incorporating the CACC overhang needed for TOPO cloning. The PCR Biochemical Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299

Crystal form 1

 1 grew from protein in 10 mM MES pH 6.5, 0.15 M NaCl with 40 % pentaerythritol propoxylate (5/4 PO/OH), 0.1 M BIS-TRIS (pH 7.0), 5 mM NiSO 4 at 20 ˚C. Crystal form 2 grew from protein in 10 mM MES (pH 6.5), 0.15 M NaCl, 5 mM NiSO 4 with 25 % PEG monomethyl ether 550 (PEG mME 550), 0.1 M BIS-TRIS (pH 7.0) at 20 ˚C. The 5-fluoro-β-D-xylopyranosyl-enzyme intermediate was obtained by using crystal form 2 after soaking with approximately 2 mM "5-fluoro-α-D-xylopyranosyl fluoride" (5FαXylF) [29], a kind gift from Professor Stephen Withers, University of British Columbia) for approximately 1 hr.

Biochemical

  Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299 A c c e p t e d M a n u s c r i p t

  Biochemical Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299

Biochemical

  Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299

Biochemical

  Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Biochemical

  Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Figure 1 (

 1 Figure 1 (double column). Structures of xyloglucan and CjXyl31A substrates. A. General structure of primary cell wall xyloglucans showing variable branching.. B. Aryl glycosides for -1 subsite specificity determination. C. Xylogluco-oligosaccharide used for extended specificity determination. Xyloglucan fragments are named according to [28].

Figure 2 (

 2 Figure 2 (double column). Phylogenetic tree of all biochemically characterised enzymes of GH31, including CjXyl31A. The genes are named by their GenBank accession numbers. Activities are designated as follows: Grey circle -α-glucosidase, Star -α-xylosidase, Diamond -transglycosylase, Triangle -α-glucan lyase and Black circle -sucrase-isomaltase. Accession numbers from eukaryotes are in black, those from bacteria and archaea are in grey.

Figure 3 (

 3 Figure 3 (single column). pH profile and thermostability of CjXyl31A. The buffers (50 mM) used in the pH-rate profile were citrate (pH 3-6.5 squares), phosphate (pH 6.5-8.5 circles), glycylglycine (pH 7.5-9 triangles) and glycine (pH 9, 9.5 inverted triangles). For the thermostability study, the enzyme was incubated at different temperatures (35 ˚C circles, 45 ˚C squares, 55 ˚C triangles, 65 ˚C diamonds), with aliquots of enzyme taken at different time intervals. The remaining activity was used to determine the level of thermal denaturation. 2 mM pNP-α-Xyl was used as the substrate for both the pH-rate profile and thermostability measurements.

Figure 4 (

 4 Figure 4 (single column). MALDI-TOF MS analysis of the XXXGXXXG tetradecasaccharide and its hydrolysis product GXXGXXXG obtained by incubation with CjXyl31A.

Figure 5 (

 5 Figure 5 (single column). Structures of the Cellvibrio japonicus Xyl31A and E. coli YicI 5-fluoroxylosyl enzyme intermediates. Global structures of CjXyl31A (A) and YicI (B), in wall-eyed stereo, highlighting the distinct PA14 insert of CjXyl31A (purple) in the N-terminal domain (green). The homologous domains of both enzymes are colored as follows: N-terminal domains, green; catalytic domains, cyan; loop inserts in the catalytic domains, blue; C-terminal domains, yellow and red. The catalytic amino acid residues are shown in ball-and-stick (dark grey) with the nucleophile bound to the 5F--Xyl ligand (yellow). C. Electron density map of 2 Fo -Fc around 5F--Xyl, including the nucelophilic water, shown at the 1.7 σ level. D. Diagram of the interactions around the 5F--Xyl ligand. The arrow indicates the distance in Ångströms between the anomeric carbon of eq-5FαXF and water molecule bound to Asp659. The figure was prepared using Pymol and ChemDraw.

Figure 6 (

 6 Figure 6 (single column). Molecular surface of CjXyl31A with docked heptasaccharide XXXG. A. Global view, B. Detailed view of the active site in wall-eyed stereo. The color scheme is identical to that used in Figure 5: Nterminal domain, green; PA14 domain, pink; catalytic domain, cyan; loop insert in the catalytic domain, blue; Cterminal domains, yellow and red. The figure was prepared using PyMol.

Figure 7 (

 7 Figure 7 (single column).Western blot analysis of C. japonicus fractions using a polyclonal antibody preparation raised against recombinant CjXyl31A. The protein contents of the fractions were normalised prior to loading the lanes: 1, membrane; 2, soluble intracellular; 3, periplasmatic; 4, secreted; X, recombinant CjXyl31A produced in E. coli. The SeeBlue® Plus2 ladder (Invitrogen) was used; note that the phosphorylase marker at 97 kDa faded during the Western protocol.

Figure 8 (

 8 Figure 8 (single column). Working model of xyloglucan utilisation by C. japonicus. Secreted endo-xyloglucanase activity and outer membrane-anchored CjXyl31A demonstrated in the present study are indicated. Hypothetical exo-glycosidases, sugar transporters, and their potential order of interaction are indicated with "?".

Table 1 .

 1 Activity of CjXyl31A on various substrates at pH 6. Substrate structures are shown in Fig. 1. b. ΔΔG ‡ was calculated using the formula: ΔΔG ‡ =-RTln[(k cat /K m XGO)/(k cat /K m XXXG)]

	Substrate a	k cat	K m	k cat /K m	ΔΔG ‡ b
		s -1	mM	s -1 mM -1	kJ mol -1
	pNPαXyl	0.58 ± 0.026	0.39 ± 0.06	1.48
	pNPαGlc	0.0066 ± 6 • 10 -4	5.31 ± 1.0	1.2 • 10 -3
	pNPαGal	N/Dv	N/D	N/D
	pNPβ-L-Arap	N/Dv	N/D	N/D
	XXXG	26.7 ± 1.5	0.54 ± 0.073	49.5	0
	XLLG	33.6 ± 3.2	2.6 ± 0.42	13.1	3.30
	XX	31.2 ± 1.5	0.72 ± 0.076	44.7	0.25
	XGol	9.39 ± 0.61	0.70 ± 0.013	13.4	3.23
	X (Isoprimeverose)	2.94 ± 0.36	55.00 ± 7.4	0.05	17.1
	a.

Table 2 .

 2 Product analysis following sequential rounds of XXXG hydrolysis by CjXyl31A and CtGlc1A.

		Biochemical Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299
	THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299	Compound XXXG GXXG XXG GXG XG GG A c c e p t e d M a n u s c r i p t Expected m/z [M+Na] + Observed m/z [M+Na] + 1085.34 1085.2706 953.30 953.2280 791.24 791.1766 659.20 659.1823 497.15 497.1376 365.11 365.0771

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Table 3 .

 3 X-ray diffraction and structure refinement statistics for CjXyl31A

		Biochemical Journal Immediate Publication. Published on 22 Mar 2011 as manuscript BJ20110299
		Name	apo (PDB ID 2xvg)	5FXyl (PDB ID 2xvl)	5/4 PO/OH (PDB ID 2xvk)
		Data collection
	THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110299	Space group Cell dimensions a, b, c (Å) α, β, γ (˚) Resolution (Å) (outer shell) R merge I / σI Completeness (%) Redundancy Refinement Resolution (Å) No. reflections R work / R free No. atoms Protein Ligand Water B-factors (Å 2 ) Protein* (TLS refinement) Water Ligand Ni Cl Other R.m.s deviations Bond lengths (Å) Bond angles (˚) A c c e p t e d M a n u s c r i p t P6 3 22 P6 3 22 P6 3 22 156.2, 156.2, 227.8 156.5, 156.5, 227.8 157.65, 157.65, 226.69 90, 90, 120 90, 90, 120 90, 90, 120 87 2.60 (2.74-2.60) 50 -2.5 (2.54-2.50) 58.5-2.30 (2.42-2.30) 0.11 (0.81) 0.072 (0.75) 0.172 (0.474) 14.4 (2.7) 32.2 (2.0) 16.3 (4.5) 99.9 (100.0) 99.0 (99.9) 100.0 ( 100.0) 11.0 (11.3) 10.1 (8.0) 11.3 (7.5) 49.9-2.6 50.0-2.5 54.5-2.3 50969 57181 74143 0.20/ 0.26 0.20/ 0.24 0.145/ 0.185 7578 7575 7583 Ni; 2, Cl; 4, SO 4 ; 4, EDO; 12 Ni; 1, Cl; 4, XYF; 10 Ni; 3, Cl; 7, SO4; 3, 5/4 PO/OH; 25 103 83 724 76.1 74.8 29.3 47.3 49.1 33.1 55.6 45.8 39.7 62 61.7 42 SO 4 ; 134.1, EDO; 81.4 XYF; 69.6 SO 4 ; 92.0, 5/4 PO/OH; 60.5 0.009 0.008 0.007 1.16 1.1 1.04

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

© 2011 The Authors Journal compilation © 2011 Portland Press Limited

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.© 2011 The Authors Journal compilation © 2011 Portland Press Limited

© 2011 The Authors Journal compilation © 2011 Portland Press Limited

Acknowledgements

Work in Stockholm and Newcastle was funded through the European Union WoodWisdom-Net ERA-NET project (www.woodwisdom.net) "FibreSurf -New biotechnological tools for wood fibre surface modification and analysis" by The Swedish Research Council Formas and UK Forestry, respectively. Supplemental funding from Formas via CarboMat -The KTH Advanced Carbohydrate Materials Consortium and the Wallenberg Wood Science Center is also greatfully acknowledged. Work in York was funded by the Biotechnology and Biological Sciences Research Council (BBSRC). GJD is a Royal-Society/Wolfson Research Merit Award recipient. We especially thank Professor Pedro M. Coutinho (Marseille) for his kind help with access to information on biochemically characterised enzymes from the CAZy database. Drs. Gustav Sundqvist and Chunlin Xu are thanked for assistance with mass spectrometric analyses.


Richard Zare

E I Dashevskaya

I Litvin

E E Nikitin

J Troe

Locking of Intrinsic Angular Momenta in the Capture of Quadrupole Diatoms by Ions

Keywords: Locking of angular momenta, Capture processes, Adiabatic channel model

The capture dynamics of rotationally polarized homonuclear diatoms in lowenergy collisions with ions is studied theoretically. The interaction potential includes charge-quadrupole and charge-induced dipole terms. The former, taken in the perturbed rotor approximation, exhibits an 3 -R anisotropic dependence and causes an only gradual locking of the intrinsic angular momentum of the diatom to the collision axis. As a result, the capture occurs in a regime of incomplete locking, and the passage over centrifugal barriers is accompanied by considerable gyroscopic effects. The j-specific capture cross sections for rotationally-aligned diatoms show a marked dependence on the polarization state which is not described by the conventional adiabatic channel model. The latter, however, provides a fair approximation for the cross sections of unpolarized diatoms. These features are due to a considerable angle of rotation of the collision axis before the barrier is reached and to a small angle of rotation during the passage across the barrier.

The numerically determined, scaled, capture cross sections are represented by an approximate analytical expression that interpolates between two limiting cases, very small (adiabatic channel model) and very large (fly wheel model) gyroscopic effects of the rotating diatom.

Introduction

In 1982, Rettner and Zare [1] introduced the notion of "orbital following" in the context of reactive collisions and discussed, in qualitative terms, the sudden and adiabatic regimes of the "orbital following". A similar phenomenon was known earlier for the field of atomic collisions (see e.g. the review [2]). For instance, Dashevskaya and Mokhova [3], already in 1973, have used the angular momentum recoupling in the calculation of depolarization cross sections of atomic collisions. They assumed a sudden transformation of atomic functions into molecular ones at a certain interatomic separation called the "matching radius". The model of the "orbital following" and the "sudden matching" was generalized later in a number of articles (see the reviews [4,5] and the book [START_REF] Andersen | Polarization, Alignment, and Orientation in Atomic Collisions[END_REF]) where the concept of the locking radius L R was introduced and the non-adiabatic behavior of the angular momentum states within the recoupling region of extension L R δ was discussed. In particular, the case of an atom in a state 1 = j was treated in detail [START_REF] Pouilly | [END_REF] and a classical model was elaborated for 1 >> j [8]. It appeared expedient to consider the locking in a framework of successions, when atoms approach or recede, of the Hund coupling cases e d c b a , , , , in a diatom [START_REF] Nikitin | Theory of Slow Atomic Collisions[END_REF][START_REF] Nikitin | [END_REF] or the ε δ γ β α , , , , coupling cases for a more complicated system, atom + diatomic molecule [11]. Basically, the locking occurs at the

distance L R R ≈
where the precession frequency of the intrinsic angular momentum about the collision axis, ) ( prec R ω , is close to the characteristic frequency of the Coriolios interaction , ) ( Cor R ω , which, in turn, is proportional to the frequency of rotation of the collision axis , ) ( rot R ω , for a given value of the total angular momentum. The range of the locking region, L R δ , that encompasses the interplay between the coupling of the intrinsic momentum to the collision axis (precession) and its decoupling from this axis due to the gyroscopic effect (Coriolis interaction) is proportional to the inverse logarithmic derivative of ) ( prec R ω with respect to R . In short, L R and L R δ are roughly determined by the expression The nonadiabatic interaction in a region centered at L R determines a part of the total scattering matrix, which can be incorporated into the latter by adiabatic matching.

) ( ) ( Cor prec L L R R ω ≈ ω (1) L R R L dR R d R = ω ≈ δ ) ( ln( prec
However, the interest for the study of the locking phenomenon as a half-collision event diminished once the locking could be handled by the powerful numerical codes for calculating full-collision or half-collision multichannel scattering matrices for atom-atom and atom-diatom systems such as discussed, e.g., in recent work on the theory of photodissociation (see refs [12,13] and the work cited therein). In this way, the account for long-range Coriolis coupling between asymptotically-degenerate states of the collision partners represents a considerable step forward compared to the pure statistical description of angular momentum recoupling in the formation and decay of long-lived molecular complexes [14,15]. Due to the rotational coupling, new effects arise termed "dynamical polarization" [16].

On the other hand, the standard method of calculating rate coefficients and product distribution functions for processes that proceed via formation of long-lived complexes, still uses the approaches that assume the conservation of the projection of the intrinsic angular momentum of partners onto the collision axis. This is the statistical adiabatic channel (AC) model of [17], also known, in its later versions, as the perturbed rotational (PR) state method [18], the adiabatic invariance (AI) method [19], and the adiabatic capture centrifugal sudden (ACCS) approximation [20]. These models were shown to be equivalent to each other, apart from the effects of more or less adequate numerical simplifications [20][START_REF] Troe | State selected and State-to-State Ion-Molecule Reaction Dynamics, Part 2: Theory[END_REF][START_REF] Ramillon | [END_REF]. Within the AC approach, the formation of the complex is associated with the passage across the barrier of the effective potential formed by superposition of the centrifugal energy and the AC potential. The latter is labeled, beside others, also by the parameter m . Taken literally, m can be interpreted as the projection of the intrinsic angular momentum onto the collision axis at large values of R , i.e. the locking is assumed to occur in the asymptotic region of R. This is clearly not quite correct, and, therefore, the question arises about the relation between the m , that enter into the definition of AC potentials, and their asymptotic counterparts.

L L R R << δ
. These two conditions are fulfilled at worst when the interfragment interaction is of long range, and, therefore, this case deserves detailed study without separating the capture event into the barrier crossing at a fixed value of m, and recoupling of the angular momentum far before the barrier is reached. It appears therefore interesting to consider an anisotropic potential proportional to 3 -R which is the leading long-range interaction for which the locking is possible in principle. A physical object exhibiting this type of interaction is the charge-quadrupolar rotor system. (Note that for an anisotropic potential proportional to 2 -R which is characteristic for a charge-dipolar rotor system, the locking does not occur at all since the potential and the Coriolis coupling show the same R-dependence, and Eq (1) has no solution at finite R ).

In the following article we consider the capture of a quadrupolar rotationallypolarized diatom in collisions with an ion in the regime when the perfect locking of the angular momentum to the collision axis in the region of centrifugal barriers is questionable. We adopt the perturbed rotor approximation for the Hamiltonian of this system and the classical description of the locking and capture dynamics. The first constraint is consistent with our earlier observations that the anisotropic quadrupolar interaction shows up on the background of isotropic charge-induced dipole interactions at low collision energies (applicability of the PR approximation). The second one is in line with our previous work on the study of classical capture [23,24]. We thus calculate the capture probability as a function of total angular momentum, intrinsic angular momentum and its projection onto the relative velocity vector, collision energy and the parameters of charge-quadrupole and charge-induced dipole interactions. In addition we determine the respective capture cross sections for axially-symmetric polarized diatoms. In this way we generalize our earlier work on capture in translational-rotational canonical ensembles [23] and in j-specific translational canonical ensembles [24] of unpolarized collision partners. This also provides more detailed insight into the capture dynamics of polarized diatoms compared to earlier work [25]. The plan of the article is the following. In Section 2 we specify the classical Hamiltonian that describes capture beyond the AC approximation. In Section 3 we discuss the locking/capture dynamics in terms of the properties of some characteristic trajectories. Section 4 presents the results of calculating capture cross sections for axially-aligned diatoms. Section 5 concludes the article.

Perturbed rotor

Hamiltonian for an ion-diatomic rigid rotor system.

The interaction of a homonuclear diatom with a charged particle includes chargequadrupole and charge-induced dipole interaction terms

4 2 2 3 2 ) (cos ) , ( R q P R qQ R U α - γ = γ ( 2
)
where R is the charge-diatom separation, γ is the angle between molecular the axis n and the collision axis R, ) (cos

2 γ P
is the Legendre polynomial, and α , ,Q q are the charge of the particle, the quadrupole moment and polarizability of the diatom, respectively. The potential in the perturbed rotor approximation, PR U , is derived from Eq (2) by averaging U over the angle of proper rotation of the rotor with the fixed angle β between vectors j and R. This is accomplished by using the addition theorem for Legendre polynomials (see e.g. [START_REF] Zare | Angular Momentum[END_REF]) with subsequent averaging over appropriate azimuthal angle, as discussed in [14,15]. The application of this approach to ) (cos

2 γ P yields 2 / ) (cos 2 β -P such that Eq (2) transforms into 4 2 2 3 2 ) (cos 2 ) , ( R q P R qQ R U PR α - β - = β (3)
The PR Hamiltonian is constructed as a sum of the relative kinetic energy and the PR potential energy:

) , ( 2
2 2 2 2 β + μ + μ = R U R L P H PR R PR (4)
( ) ( ) ( ) ( ) ( ) ( )( ) 3 / 1 3 / 2 2 3 / 1 2 / 1 6 / 1 3 / 1 2 / 1 6 / 5 3 / 1 2 / 1 6 / 1 2 / 1 2 / 1 3 / 1 3 / 1 ; , , ; ; , E Q q j J qQ E t qQ E P qQ E P E R qQ E R α = λ × μ = ι Ι × μ = τ × μ = π × μ = π × = ρ - - - - - φ - - - φ - - ρ - (5)
The scaled PR Hamiltonian PR η is defined as

λ ι Ι π φ ρ υ + π = λ ι Ι π φ π ρ η φ ρ φ ρ s s (6) and 4 2 3 2 2 2 2 2 2 2 2 eff, 2 ) / ( 2 2 cos 2 2 ) , , ; , , ( ρ λ - ι π ρ - ρ φ π - ι π - Ι - π - ι + Ι = = λ ι Ι π φ ρ υ φ φ φ φ φ P s s (7) ( 2 ) , , ; , , , ( eff, 2
where the superscript ) ( sign qQ s = appears as a result of the scaling through the absolute value of the product qQ . The first term at the r.h.s. of Eq ( 6) is the radial kinetic energy and the second can be regarded as an effective potential energy for the radial motion. The latter, given by Eq [START_REF] Pouilly | [END_REF], includes the centrifugal energy with the Coriolis interaction, the ACPR counterpart of the charge-quadrupole interaction, and the charge-induced dipole interaction. The Hamiltonian s η generates the canonical equations of motion for the evolution of the four quantities

) ( ), ( ), ( ), ( τ π τ φ τ π τ ρ φ ρ subject to certain initial conditions.
In this work, we assumed a uniform distribution over the initial azimuthal angle i φ and have taken i ρ large enough to set 2 , = π ρ i that corresponds to the initial scaled energy that correspond to the conditions when the intrinsic angular momentum j is substantially smaller or larger than a typical angular momentum L corresponding to the capture For L j << , one also has

Ι << ι
. Neglecting in Eq [START_REF] Pouilly | [END_REF] the two last terms in the expression for the centrifugal energy, one gets the standard expression for the ACPR Hamiltonian: . Figure 1 shows the allowed regions of AC For L j >> , all the terms in the numerator of the expression for the centrifugal energy are of the same order, and it is easier to derive the respective approximate Hamiltonian in the SF frame. The approximation uses the fact that since j is close to J, the orientation of j is approximately conserved in the space (this approximation combines the sudden limit with respect to the orientation of j and the adiabatic limit with respect to the change of the absolute value of j; it was called in [25] the fly-wheel, FW, approximation) and, therefore, the angle β between R and j is approximately equal to the angle θ between R and J. [START_REF] Nikitin | Theory of Slow Atomic Collisions[END_REF] in which the constant projection of the relative angular momentum ϖ onto the total angular momentum appears as a consequence of the cylindrical symmetry of the interaction, i.e. ϖ = π ϕ

4 AC 2 3 2 2 AC AC eff, AC AC eff, 2 AC AC 2 ) ( 2 2 ) , , ; ( ) , , ; ( 2 ) , , ; , ( ρ λ
- ς ρ - ρ Ι = λ ς Ι ρ υ λ ς Ι ρ υ + π = λ ς Ι π ρ η ρ ρ P s s s s (8)
- θ ρ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ θ ϖ + π ρ = λ ϖ Ι θ π ρ υ λ ϖ Ι θ π ρ υ + π = ϖ Ι θ π ρ π η θ θ θ ρ θ ρ P s s s ( 2 ) , ; , , , ( ρ λ
. The approximate Hamiltonian in Eq (9) looks more complicated than the approximate Hamiltonian in Eq (8) because the former contains more information (motion in space) than the latter (only radial motion).

Dynamics of locking

The locking dynamics is visualized best by considering individual representative trajectories. When the colliding partners approach each other, the intrinsic angular momentum vector ι (all the dynamical variables below are in reduced units) experiences the locking to the collision axis ρ which causes its reorientation in a space-fixed (SF) frame. Within the AC approximation, the reorientation of ι in the course of the collision is described as a fast precession of ι about the slowly rotating collision axis in the region where the momentum is locked to the axis.

One can envisage the following qualitative picture of the evolution of the

alignment index ι τ π = τ ς φ ) ( ) (
along the trajectory during a collision. During the approach of the partners, ) (τ ς changes first because of the rotation of the collision axis (initial part of the collision, ι is fixed in space, i ι ι = ); then ς becomes approximately constant (middle part of the collision, ι precesses about ρ ). If capture occurs, ς remains the same; in case of reflection (i.e. no capture), ι becomes uncoupled from ρ again, and ς changes again because of the rotation of the collision axis (final part of the collision, ι is fixed in space, f ι ι = ). The net result of the "non-capture" collision then is a certain rotation of the vector ι from its initial state i ι to the final state f ι . show what happens with the potential energy: it first increases when the system approaches the barrier and then suddenly drops, following the spiraling to the centre; the maximum value of ) (τ υ eff is below unity.

F

iii) The accurate trajectory without capture (full line). The incoming part of this trajectory is quite similar to the incoming part of the capture trajectory (see ii). The outgoing part corresponds to a collision with reorientation of the vector ι . For this reflected trajectory, the turning point of which corresponds to the maximum of the timedependent potential (equal to unity), the locking gradually becomes weaker, and finally

) (τ ς
shows a behavior which is typical for the uncoupled angular momentum. The function ) (τ ς is nearly symmetrical for the incoming and outgoing parts of the trajectory.

Note that a small change of the initial angle i φ noticeably affects the time-dependent potential barrier: it has of a bell-shaped symmetrical form for the reflected trajectory and an asymmetrical form for the capture trajectory. The former feature is related to the almost symmetric shape of the trajectory, while the latter corresponds to a strong acceleration of the relative motion once the barrier is overcome.

For comparison, we show another, quite asymmetrical, function ) (τ ς (dashed line) for a trajectory which starts with i ς from the range allowed for capture by the AC approach. Due to the Coriolis interaction, ) (τ ς decreases to such an extent that capture becomes impossible. The locking is quite loose for this trajectory. remains approximately constant. The larger number of precessional revolutions in Figure 3 and the smaller amplitude of the oscillations compared to those in Figure 2 are explained by the fact that the impact parameter for the former case is smaller, and, therefore, the locking is tighter. . Here, the gradual change of ) ( τ ς across the whole time interval can be interpreted roughly as the reflection of the rotation of the collision axis with the direction of j almost fixed in space which is due to higher gyroscopic effects of the rapidly rotating diatom. Indeed, two full oscillations of ) (τ ς in the barrier region reflect a rather weak coupling of j to R. Note also that in this case the profile of the barrier along the trajectories is of a complicated shape.

Capture cross sections

Each trajectory for the Hamiltonian in Eqs ( 6) and [START_REF] Pouilly | [END_REF]

∫ ∞ ς Ι Ι λ ι Ι ς π = λ ι ς σ i d P i s i s ) , , , ( ) , , ( (10)
where

i i β = ς cos .The AC counterpart of ) , , ( λ ι ς σ i s , ) , ( AC λ ς σ i s
, that corresponds to the PRAC potential in Eq (8), is

∫ ∞ Ι Ι λ ι Ι ς π = λ ς σ 0 AC ) , , , ( ) ,
i i i i i s i s d d d P ϕ ϖ π λ ϖ π ϕ ς π = λ ς σ θ θ ∫ ) , , , , ( 4 1 )
, ( FW FW (12) where FW s P is the capture probability (zero or one),

i i i θ = ς ≡ ς cos FW
, and

i i i ϕ θ π θ , , are
the initial values of dynamical variables that enter into the Hamiltonian in Eq [START_REF] Nikitin | Theory of Slow Atomic Collisions[END_REF]. Note that neither AC nor FW cross sections depend on ι . We also mention that the high-λ limit of all three cross sections is the scaled Langevin cross section

λ π = σ L . It was argued in [25] that ) , , ( λ ι ς σ i s is expected to be bracketed between i s ς = ς λ ς σ AC ) , ( AC AC (for 1 << ι ) and i s ς = ς λ ς σ FW ) , ( FW FW (for 1 >> ι
), though the relation between the two latter quantities could not be predicted a priory. Indeed, as was found earlier [25], the plots 3 and4 in ref [25]

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ι λ + = λ ι s g s s h f ) ( 1 1 ) , ( AC ; ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ι λ + ι λ = λ ι s s g s g s s h h f ) ( 1 ) ( ) , ( FW (14) and 10 . 1 1 = + g , 35 . 1 1 = - g , λ + = λ + 12 2 ) ( h , ) 1 ( 5 . 14 ) ( λ + ⋅ = λ - h ( 15
)
The essence of the expression in Eq ( 13) is schematically represented in the set of are bracketed between them in a narrow interval, see Figure 12.

Conclusion

The collision of molecules in its incoming part is accompanied by a reorientation of the intrinsic angular momenta of the partners from a direction fixed in space to the collision axis (locking). If the interparticle interaction is steep enough compared to the centrifugal interaction, the locking occurs across a narrow interval of interfragment distances. This allows one to separate the reorientation from other inelastic events which can be considered to occur with a conserved projection R J of the total angular guaranties the adiabatic behaviour with respect to transitions between rotational states of the diatom [START_REF] Nikitin | [END_REF], and of the applicability of a classical description of the relative motion (lower boundary). The ion-molecule interaction is restricted to the long-range potential that includes anisotropic charge-quadrupole and isotropic charge-induced dipole terms.

The former, featuring 3 -R dependence, is the most slowly-varying interaction among the inverse-power dependences of the n R -type for which a locking distance and range can be defined, and, therefore, is a most interesting optimal candidate for studying the effect of non-conservation of R J .The classical Hamiltonian derived in the perturbed-rotor approximation describes the relative radial motion of the partners and the reorientation of the intrinsic angular momentum (its magnitude j being conserved) of the diatom with respect to the BF frame (Section 2). The capture dynamics is visualized by the analysis of trajectories that demonstrate the locking and the passage/reflection via/from centrifugal barriers for representative initial conditions of the initial rotational polarization of the diatom (Section 3). The dependence of the capture cross section on the initial rotational alignment of the diatom with respective to the relative velocity vector is found to be noticeably different from that adopted in the standard adiabatic channel (AC) treatment of the capture, with minimum deviations from AC predictions for small intrinsic momenta (Section 3). These numerical results are summarized by fitting interpolation equations (4.5) that analytically represent the scaled alignment specific cross sections for different scaled values of intrinsic angular momenta and different anisotropies of the interaction.

The results are relevant for the calculation of j-specific cross sections and rate coefficients for formation of the complexes in collisions of ions with rotationallypolarized homonuclear diatomic molecules. For the capture of unpolarized molecules, one still can use the AC approach for calculating the low-energy capture cross sections, provided that inaccuracies in the capture cross sections of about 5-10% can be tolerated, although the formal condition of the applicability of the AC approach (conservation of the projection of the intrinsic angular momentum onto the collision axis) is not fulfilled. ) with initial conditions from the allowed AC range (initial conditions are listed in Dashed line illustrates the evolution of ) (τ ς along a reflected trajectory from an initial value in the allowed AC region to the final value in the forbidden AC region.

Figure 3. The same as in Figure 2 but with the initial conditions from the forbidden AC range (see Table 1). Also shown are the similar attributes for the separatrix (dashed ) with initial conditions from the forbidden AC range (see Table 1). ) with initial conditions from the allowed AC range (initial conditions are listed in

) (τ υ eff 1 ε = m sep ρ ) (τ ρ ) (τ υ sep eff ) (τ sep ζ 1 . 0 ι 0.55 = = Ι ) (τ ζ ρ(τ) ρ m , ζ(τ) , υ eff (τ) 3 1
Figure 3. The same as in Figure 2 but with the initial conditions from the forbidden AC range (see Table 1). Also shown are the similar attributes for the separatrix (dashed ) with initial conditions from the forbidden AC range (see Table 1).

ε

  equal to unity. Then the only essential parameter is the initial alignment index barrier (reflected trajectory) or very small (capture trajectory), after passing through the barrier. In order to monitor this behavior, we have calculated also the time dependence of the effective potential ) can be derived from the general PR Hamiltonian,

Figure 2 2 .

 22 Figure 2 shows two trajectories (full and dotted lines) with identical values of i ς (marked by the triangle at the left ordinate axis) from the range where AC theory predicts the capture, 3 / 1 ) 0 ( min AC, = ς > ς + i

Figure 3

 3 Figure 3 refers to the same value of ι and a smaller value of Ι , but with the value of i ς from the forbidden region of the AC capture, ) 0 ( min AC, + ς < ς i . Here, the capture turns out to be possible only as a result of the increase in ) (τ ς during the initial part of the collision to such an extent that the barrier can be overcome. The dynamics of the barrier crossing is almost adiabatic with respect to the Coriolis interaction (meaning that the latter can be ignored, 1 >> n). Beside the captured and reflected trajectories, which are similar to those in Figure2, this figure shows also the separatrix (superscript sep), a

Figure 4

 4 Figure 4 refers to a higher value of ι , with the value of i ς from the forbidden region of the AC capture, ) 0 ( min AC, + ς < ς i . Here, the gradual change of ) ( τ ς across the

  or very close to) this point. This conclusion was exemplified by Figures

  momentum J onto the collision axis R . Such a simplification of the collision dynamics disappears for gradual interactions and the question arises about the effects of a lack of the conservation of R J on the inelastic dynamics.This article addresses the discussed question by way of examples for the low-energy capture of a charged particle (an ion) by a rotating quadrupolar homonuclear The energy range considered is limited by the conditions of applicability of the perturbed-rotor approximation (upper boundary), which also

Figure 1 .

 1 Figure 1. Minimum and maximal values of the AC alignment indices max , AC ς and min , AC + ς

Figure 2

 2 Figure 2. Collision dynamics for 1 + = s along two trajectories for low value of ι ( 1 . 0 = ι) with initial conditions from the allowed AC range (initial conditions are listed in

Figure 4 .

 4 Figure 4. The same as in Figure 2 but for a higher value of ι ( 1 = ι) with initial

Figure 5 .Figure 12 .Figure 1 .

 5121 Figure 5. Dependence of the reduced alignment-specific cross sections ) , , ( λ ι ς σ i s

  Figure 2

Figure 3 - 2

 32 Figure 3

Figure 4 .

 4 Figure 4

Figure 5 .Figure 12 .

 512 Figure 5

Page 5 of 33 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics

	where μ is the reduced mass of the collision partners, R P is the momentum conjugate to
	R and 2 L is the square of the relative angular momentum. Once it is expressed in
	canonical variables, the Hamiltonian in Eq (4) generates equations of motion. These
	equations assume a simple form if the conservation of the total angular momentum J is
	explicitly taken into account.
	If one chooses a body-fixed frame, one replaces 2 L by	(	J -	) j	2	and introduces the
	dynamical variables φ , the azimuthal angle of j in the plane normal to the collision axis, F o and φ P , the projection of the intrinsic angular momentum onto the collision axis. On the
	r other hand, if one chooses a spaced-fixed frame and the vector J as a polar axis, one
	expresses 2 L through polar and azimuthal angles of the collision axis, ϕ θ, , and P conjugate momenta ϕ θ P P , ; in addition, ) (cos 2 β P should be expressed as a certain e function of ϕ θ, and of two other angular variables that fix the orientation of the vector j e r in the SF frame. This can be done also via addition the theorem of the Legendre
	polynomials. In the following, we adopt the BF frame, and use the SF frame only for R discussion of certain approximations (see below). e The perturbed rotor Hamiltonian PR H in the BF frame contains two dynamical v degrees of freedom (the radial relative motion of the partners and the precessional motion i of j about R); beside α , ,Q q , it contains two other parameters, the conserved scalar e w quantities J and j . It is expedient to pass to scaled variables and parameters, and
	replace the PR Hamiltonian conservation of the total energy E. The scaling is achieved by the transformations PR H by a scaled Hamiltonian PR η recognizing the O n
			l y
	6

  Identifying β with θ in PR U , we get the FW Hamiltonian in

									2
	FW s										FW eff,	,	,	;	,	,	)
	FW eff,	(	,	,	;	,	,	)	2 1	2	2	sin	2 2		2	3	2	(cos	)	2	4
			F o
							r
								P
									e e r
												R e v i e w
																				O n
																					l y
	the form:
																9

Table 1 .

 1 We see also that ς noticeably

	differs from i ς , implying that the AC approach cannot be applied to collisions with
	specific values of i ς . Presumably, the AC approach will yield reasonable results on
	average, i.e. after averaging over i ς . The graphs for	υ eff	) (τ
	F o
	r
	P
	e e r
	R e v i e w
			O n
			l y
	11

Page 12 of 33 URL: http://mc.manuscriptcentral.com/tandf/tmph

																															Molecular Physics
	where	s P	AC	(	ς	i	,	Ι	,	, ι	λ	)	=	Θ	( 1	-	υ	AC,* , eff s	(	ς	AC	,	Ι	,	λ	)	)	and	ς	i	≡	ς	AC	. Finally, the FW version of
	( σ i ς s	,	, ι	λ	)	,	σ	FW s	(	ς	i	,	λ	)	, has the form
					F o
															r
																					P
																								e e r
																														R e v i e w
																																			O n
																																			l y
	s	(		i									P s	AC				i				d							(11)
																																			13

  . Among other things, these figures illustrate how the effect of the initial alignment decreases with increasing λ , (i.e. with a decrease in the relative anisotropy of interaction).

	Figures 5 -11, where the shaded regions cover graphs of	( σ i ς s	,	, ι	λ	)	with different values
	of The capture cross sections for unpolarized diatoms,	σ s	, ( λ ι	)	,	( AC λ σ s	)	,	( FW λ σ s	)	,
	are obtained from	( σ i ς s	,	, ι	λ	)	,	σ	AC s	(	ς	i	,	λ	)	and	σ	FW s	(	ς	i	,	λ	)	by averaging over i ς within the
	range	-	1	/	2	≤	ς	i	≤	1	/	2	. It turns out that	( AC λ σ s	)	and	( FW λ σ s	)	are close to each other, and
	σ s	, ( λ ι	)

ι

Table 1 .

 1 Initial conditions for the two trajectories shown in Figures2-4: total angular momentum Ι , intrinsic angular momentum ι , initial alignment index i ς , initial angle i

	Page 15 of 33	Molecular Physics

URL: http://mc.manuscriptcentral.com/tandf/tmph

Page 19 of 33 URL: http://mc.manuscriptcentral.com/tandf/tmph

	Molecular Physics
	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	20

Table 1 )

 1 . Shown are the scaled interfragment distance dots to the captured trajectory. The symbols at the ordinate axis mark asymptotic (initial for captured and reflected trajectories, final for reflected trajectory) values of ς and the dotted horizontal line divides open and closed capture states in the AC approximation.

	τ ρ / ) (	ρ	m	, alignment index	) ς , (τ

Table 1 )

 1 . Shown are the scaled interfragment distance

	τ ρ / ) (	ρ	m	, alignment index	) ς , (τ

Page 23 of 33 URL: http://mc.manuscriptcentral.com/tandf/tmph

URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics

Acknowledgement

We thank R. N. Zare for his seminal contribution to this field [26] and his continuous interest in our work.