Anh Khanh Cong

Le

Luc Choisnard

Denis Wouessidjewe

Jean-Luc Putaux
email: jean-luc.putaux@cermav.cnrs.fr

Polymorphism of V-amylose cocrystallized with aliphatic diols

Keywords: V-amylose, diol, cocrystal, polymorphism

Chain-folded lamellar crystalline complexes of amylose with aliphatic diols were prepared and characterized by transmission electron microscopy as well as electron and X-ray diffraction. Four allomorphs were identified, depending on the complexing diol and crystallization conditions, that consisted of orthorhombic lattices of antiparallel 6-or 7-fold amylose single helices. Straightchain n-diols (ethane-1,2-diol, butane-1,4-diol, hexane-1,6-diol) yielded 6-fold helical complexes regardless the length of the linear chain, whereas a bulkier branched diol (2-methylpentane-2,4diol) induced the formation of 7-fold helices. Butane-1,3-diol, that contains a straight carbon chain with one end and one side hydroxyl group, induced both 6-and 7-fold helical conformations depending on the crystallization conditions. When a diol induced more than one allomorph, an adequate control of its concentration and crystallization temperature allowed targeting a specific crystalline form. Upon drying, all allomorphs were converted into more compact pseudohexagonal structures. The dried form of a given complex generally retained the same helical conformation as the hydrated one.

Introduction

Amylose, the mostly linear homopolymer of α(1-4)-linked D-glucosyl units extracted from native starch, cocrystallizes with a wide variety of small organic compounds [START_REF] Putseys | Amylose-inclusion complexes: Formation, identity and physico-chemical properties[END_REF][START_REF] Obiro | V-amylose structural characteristics, methods of preparation, significance, and potential applications[END_REF]. These compounds are referred to as V-amylose and contain amylose single helices with guest molecules located inside the helices, in-between or both [START_REF] Lourdin | Crystalline structure in starch[END_REF]. The V-amylose inclusion complexes present a number of interesting properties and potential applications, for instance in the food and pharmaceutical industries [START_REF] Conde-Petit | Structural features of starch-flavor complexation in food model systems[END_REF][START_REF] Carbinatto | Preparation and characterization of amylose inclusion complexes for drug delivery applications[END_REF]. Complexing agents such as n-butanol, thymol or menthone have been used for the fractionation of native starch into its amylopectin and amylose constituents [START_REF] Schoch | Fractionation of starch by selective precipitation with butanol[END_REF][START_REF] Bourne | Thymol and cyclohexanol as fractionating agents for starch[END_REF][START_REF] Kuge | Complexes of starchy materials with organic compounds: Part II. Complex formation in aqueous solution and fractionation of starch by l-menthone[END_REF].

Amylose complexes have been shown to efficiently encapsulate flavoring compounds [START_REF] Nuessli | Crystal structure of amylose complexes with small ligands[END_REF][START_REF] Ades | Complexation with starch for encapsulation and controlled release of menthone and menthol[END_REF] or fatty acids in order to modulate the rheological, taste and hydrolysis properties of starch-based matrices [START_REF] Singh | Effect of fatty acids on the rheological properties of corn and potato starch[END_REF][START_REF] Gelders | Amylose-lipid complexes as controlled lipid release agents during starch gelatinization and pasting[END_REF][START_REF] Marinopoulou | Morphological characteristics, oxidative stability and enzymic hydrolysis of amylose-fatty acid complexes[END_REF]. Their potential as delivery systems of bioactive agents has also been evaluated [START_REF] Oguchi | Structural change and complexation of strictly linear amylose induced by sealed-heating with salicylic acid[END_REF][START_REF] Lalush | Utilization of amylose-lipid complexes as molecular nanocapsules for conjugated linoleic acid[END_REF][START_REF] Lay Ma | Formation of inclusion complexes of starch with fatty acid esters of bioactive compounds[END_REF][START_REF] Zhang | Structural and release properties of amylose inclusion complexes with ibuprofen[END_REF].

Depending on the complexing agent and crystallization conditions, several V-amylose allomorphs have been reported in the literature that can be readily identified by their X-ray powder diffraction pattern. So far, it has not been possible to grow large crystals amenable to a threedimensional molecular structure determination by single crystal X-ray diffraction methods.

Nevertheless, V-amylose can be easily crystallized from dilute aqueous solution (0.05-0.1 wt%) in the form of ca. 10 nm-thick lamellar single crystals with a lateral size up to a few micrometers.

In these, the amylose chains are organized in helices, with their axis perpendicular to the base plane of the lamellae. When the chain length of amylose exceeds the lamellar thickness, a regular chain folding mechanism occurs, similar to the one described for flexible synthetic polymers [START_REF] St | Chain folding in amylose crystals[END_REF][START_REF] Yamashita | Single crystals of amylose V complexes. II. Crystals with 71 helical configuration[END_REF][START_REF] Jane | Structure studies of amylose-V complexes and retrograded amylose by action of alpha amylases, and a new method for preparing amylodextrins[END_REF]. For the not-so-flexible amylose molecule, chain folding is readily favored by a band-flip mechanism that is specific of α(1-4) glucans [START_REF] Jacob | Band-flip and kink as novel structural motifs in α-(1→4)-D-glucose oligosaccharides. Crystal structures of cyclodeca-and cyclotetradecaamylose[END_REF]. The V-amylose crystals yield high-quality electron diffraction, providing rich diffraction datasets useful for structural analysis [START_REF] Putaux | Helical conformation in crystalline inclusion complexes of V-amylose: A historical perspective[END_REF].

A generic classification of V-amylose allomorphs can be done according to the number of glucosyl units per helical turn (6, 7 or 8) but these main classes contain subfamilies with specific morphological and structural signatures [START_REF] Putaux | Helical conformation in crystalline inclusion complexes of V-amylose: A historical perspective[END_REF]. The V6 family comprises three crystal types: the pseudo-hexagonal V6I (or Vh), typically formed with linear alcohols [START_REF] Brisson | The crystal and molecular structure of VH amylose by electron diffraction analysis[END_REF][START_REF] Rappenecker | Detailed refinement of the crystal structure of Vhamylose[END_REF] and fatty acids [START_REF] Godet | Inclusion/exclusion of fatty acids in amylose complexes as a function of the fatty acid chain length[END_REF][START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF], the orthorhombic V6II prepared with Vn-butanol [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF] and a pseudo-tetragonal V6 reported for complexes with dimethyl sulfoxide (DMSO) [START_REF] Winter | Crystal and molecular structure of the amylose-DMSO complex[END_REF], ethylenediamine [START_REF] Simpson | X-ray diffraction of ethylenediamine-amylose complex[END_REF], and glycerol [START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF].

Although a V6III allomorph is mentioned in some works [START_REF] Biais | Structural and stoichiometric studies of complexes between aroma compounds and amylose. Polymorphic transitions and quantification in amorphous and crystalline areas[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF], the corresponding structure has been shown to be based on 7-fold helices [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF]. Therefore, in the following, the V6 complexes isomorphous to VDMSO and Vglycerol will be referred to as V6III. Seven-fold amylose helices have been found in two allomorphs: one, with an orthorhombic unit cell, has been prepared with propan-2-ol [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF][START_REF] Buléon | Single crystals of V amylose complexed with isopropanol and acetone[END_REF], some fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF], many alcohols and aroma compounds [START_REF] Nuessli | Crystal structure of amylose complexes with small ligands[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Putaux | Single crystals of V-amylose inclusion complexes[END_REF], and the other, recently identified for complexes with bicyclic compounds, with a pseudo-hexagonal unit cell [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF]. The latter will be referred to as V7I and the former as V7II [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF]. Quinoline and naphthalen-1-ol (1-naphthol) induce the formation of V8 helices organized in a tetragonal unit cell [START_REF] Putaux | Single crystals of V-amylose inclusion complexes[END_REF][START_REF] Yamashita | Single crystals of amylose V complexes. III. Crystals with 81 helical configuration[END_REF][START_REF] Cardoso | Single crystals of V-amylose complexed with α-naphthol[END_REF] while another V8 form, which structure has not been clearly described yet, has been reported for complexes with 2-hydroxybenzoic (salicylic) acid [START_REF] Oguchi | Structural change and complexation of strictly linear amylose induced by sealed-heating with salicylic acid[END_REF][START_REF] Shi | Starch-menthol inclusion complex: Structure and release kinetics[END_REF].

V-amylose crystallosolvates also contain a number of water molecules and dehydration / desolvation can induce structural transitions. The drying of the V6I and the V6II crystals prepared with fatty acids or aliphatic alcohols results in the pseudo-hexagonal anhydrous V6a [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Mikus | The complexes of fatty acids with amylose[END_REF][START_REF] Zobel | X-ray diffraction of oriented amylose fibers. II. Structure of V amyloses[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. However, it was shown that even after a strong dehydration treatment (heating under vacuum and over phosphorus pentoxide), a number of water molecules were still present in the crystal [START_REF] Valetta | Amylose "V" complexes: Low molecular weight primary alcohols[END_REF]. Similarly, upon drying, V7I and V7II were converted to a compact pseudohexagonal V7a [START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF][START_REF] Shi | Starch-menthol inclusion complex: Structure and release kinetics[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF][START_REF] Zaslow | Characterization of a second helical amylose modification[END_REF]. A V8a structure has been reported after drying of a V8 complex with salicylic acid [START_REF] Shi | Starch-menthol inclusion complex: Structure and release kinetics[END_REF]. The data suggested that it might also be pseudo-hexagonal. In all aforementioned cases, drying induced a compaction of the helices but the helicity was maintained.

A number of authors have proposed that the helix diameter depended on the cross-sectional diameter of the guest [START_REF] Yamashita | Single crystals of amylose V complexes. II. Crystals with 71 helical configuration[END_REF][START_REF] Biais | Structural and stoichiometric studies of complexes between aroma compounds and amylose. Polymorphic transitions and quantification in amorphous and crystalline areas[END_REF][START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF][START_REF] Zaslow | Characterization of a second helical amylose modification[END_REF][START_REF] Rutschmann | Formation of inclusion complexes of starch with different organic compounds. IV, ligand binding and variability in helical conformations of V amylose complexes[END_REF][START_REF] Yamashita | An electron microscopic study on crystals of amylose V complexes[END_REF]. More specifically, V6 complexes have been obtained with molecules containing a main linear carbon chain, regardless of the functional groups, while V7 and V8 complexes have been prepared with bulkier compounds containing branched chains or ring structures. Besides, Takeo and Kuge [START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF] and Takeo et al. [START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF] mentioned that the length of the linear chain of fatty acids and ketones were also key factors controlling the helix diameter. However, our recent structural investigation of V-amylose complexes with a series of straightchain saturated fatty acids (from C3 to C20) revealed that all the tested guests yielded V6 or V7 structures, depending on the crystallization conditions [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF]. In addition, some complexing agents such as acetone, DMSO, fatty acids, propan-2-ol, quinoline or salicylic acid induce more than one amylose helical conformation by varying the crystallization conditions [START_REF] Oguchi | Structural change and complexation of strictly linear amylose induced by sealed-heating with salicylic acid[END_REF][START_REF] Simpson | X-ray diffraction of ethylenediamine-amylose complex[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. The actual role of the guest molecule dimension can thus be questioned and other factors that control the conformation and packing arrangement in V-amylose allomorphs should be investigated. To our knowledge, such question has not been addressed so far for complexes prepared with aliphatic diols. Kowblansky [START_REF] Kowblansky | Calorimetric investigation of inclusion complexes of amylose with longchain aliphatic compounds containing different functional groups[END_REF] studied the thermal properties of complexes prepared with decane-1,10diol and decane-1,12-diol but did not characterize the corresponding structure, while Helbert [START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF] reported on the formation of V6I with linear ethane-1,2-diol, propane-1,3-diol and butane-1,4-diol.

This paper focuses on the formation of complexes of V-amylose with aliphatic diols differing by the carbon skeleton (linear or branched), chain length and position of the hydroxyl groups. The morphology and structure of model lamellar single crystals prepared from dilute amylose solutions were characterized by transmission electron microscopy (TEM) as well as electron and X-ray diffraction (ED and XRD, respectively). The influence of the guest molecule topology, its concentration and the crystallization temperature on the complex formation and resulting crystal structures were investigated, as well as the structural transitions induced upon drying.

Experimental section

Amylose and diols

Potato amylose was purchased from Sigma-Aldrich and further purified in laboratory as previously reported [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF]. According to the method described in Supplementary Data Fig. S1, the chain length distribution was determined by size exclusion chromatography (SEC) with multiangle laser light scattering (MALLS) from a solution of amylose dissolved in LiCl/1,3-dimethyl-2-imidazolidinone (LiCl/DMAc). The number-and weight-average degrees of polymerization were found to be 𝐷𝑃 # $$$$$ = 928 and 𝐷𝑃 % $$$$$$ = 2514, respectively, with a polydispersity index

P = 𝐷𝑃 % $$$$$$ /𝐷𝑃 # $$$$$ = 2.7. Ethane-1,2-diol (EDIOL), butane-1,3-diol (BBIOL), butane-1,4-diol (

Crystallization protocols and drying procedure

Aqueous amylose dispersions (10 mg in 10 mL) were submitted to nitrogen bubbling during 20 min, autoclaved in an oil bath at 160 °C for 30 min to erase all memory of crystallization, and cooled down to 90 °C. The amount of added diol and the way it was mixed with amylose depended on some of its physical properties. All diols were liquid at room temperature, except HDIOL (melting temperature: 43 °C). All diols were miscible with water except HDIOL and MPDIOL that were partly soluble. A predetermined amount of preheated diol (10-80 vol% EDIOL, BBIOL and BDIOL; 0.5-20 wt% HDIOL and 1-20 vol% MPDIOL) was then added to the amylose solution at 90 °C. After a brief manual homogenization, the mixtures were kept at a given temperature (25-75 °C) during one week and cooled down to room temperature or, after mixing, were allowed to slowly cool down in a Dewar vessel. When the incubation at 40-75 °C did not induce crystallization after one week, especially with a low diol concentration, the mixture was cooled down to 25 °C and monitored until a solid residue was formed. In all cases, the crystallized fractions were characterized shortly after collection. For drying experiments, the complexes were kept under primary pump vacuum at room temperature. Samples were taken after pumping periods of one day up to several weeks and analyzed by XRD. The sample was considered as "dry" when a stable XRD pattern was achieved. The term "partially dried " will refer to the intermediate state between the fully hydrated/solvated and dry states, during which changes in XRD profiles were still observed.

X-ray diffraction (XRD)

The crystal suspensions were centrifuged for 10 min at 13400 rpm (12000 g) and the pellets deposited on a 7-µm nylon bolting cloth (SaatiTech), laying on top of blotting paper. After absorption of the excess solvent, the crystals were either equilibrated for several days in a closed chamber equilibrated with a 95% relative humidity (RH) or dried in primary pump vacuum. Thin strips of the resulting films were inserted into 1 mm (outer diameter) glass capillaries which were immediately flame-sealed. The specimens were X-rayed in transmission in a Warhus vacuum camera with a Ni-filtered CuKα radiation (λ = 0.1542 nm), using a Philips PW3830 generator operating at 30 kV and 20 mA. Two-dimensional diagrams were recorded on Fujifilm image plates during 2 h and read with a Fujifilm BAS 1800-II bioimaging analyzer. XRD profiles were calculated by rotational averaging of the 2D patterns. The XRD data were calibrated using calcite and the unit cell parameters were refined using the Celref program [START_REF] Laugier | LMGP-Suite: Suite of programs for the interpretation of X-ray experiments[END_REF].

Transmission electron microscopy (TEM) and electron diffraction (ED)

Droplets of dilute crystal suspensions were deposited on glow-discharged carbon-coated grids.

After 2 min, the liquid in excess was wicked off with a filter paper and the preparation allowed to dry. The specimens were observed with a Thermo Scientific Philips CM200 'Cryo' microscope operating at 200 kV. For electron diffraction, after the last traces of liquid had visually disappeared from the carbon film surface, the TEM grids were mounted on a Gatan 626 specimen cryoholder and immediately fast-frozen into liquid nitrogen. Once in the microscope, the holder was cooled down with liquid nitrogen and the crystals were observed under low dose illumination at -177 °C.

Images and selected area ED patterns were recorded with a TVIPS TemCam F216 camera. The ED diagrams were calibrated using a gold-coated carbon film as standard. In the following, "baseplane ED patterns" will refer to patterns recorded along the [001] c-axis of the crystal structure, i.e. perpendicular to the (a,b) plane of the lamellae and parallel to the axis of the amylose helices.

Results and discussion

Morphology and crystal structure

The lamellar crystals formed in the presence of linear or branched diols (Scheme 1) under different crystallization conditions were divided into four types. The first type of crystal, with a more or less hexagonal shape and favoring a dislocation-centered spiral growth, was obtained with EDIOL, BDIOL, HDIOL and BBIOL (Fig. 1a-d, Supplementary Data Fig. S3). The baseplane ED patterns recorded on frozen-hydrated crystals (Fig. 1e) and the XRD patterns recorded on hydrated crystal mats (Fig. 1f) were almost identical to those reported for V6I prepared in the presence of linear alcohols [START_REF] Brisson | The crystal and molecular structure of VH amylose by electron diffraction analysis[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF] and fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF]. They were indexed on the basis of a hexagonal unit cell with space group P6522 [START_REF] Brisson | The crystal and molecular structure of VH amylose by electron diffraction analysis[END_REF] or a pseudo-hexagonal orthorhombic unit cell with space group P212121 [START_REF] Rappenecker | Detailed refinement of the crystal structure of Vhamylose[END_REF]. The two unit cells have in common the close packing of 6-fold left-handed amylose helices onto a hexagonal lattice, but they differ in the arrangement of the up and down chains, which would be statistically random in the hexagonal unit cell [START_REF] Brisson | The crystal and molecular structure of VH amylose by electron diffraction analysis[END_REF] and regularly alternating in the orthorhombic unit cell (Fig. 6b) [START_REF] Rappenecker | Detailed refinement of the crystal structure of Vhamylose[END_REF]. Our present data does not allow to distinguish between the two space groups. Consequently, for simplicity, we will only refer to the pseudo-hexagonal orthorhombic unit cell in the following. The average unit cell parameters determined by XRD (a = 1.37 nm, b = a√3 = 2.37 nm, and c = 0.81 nm) are in good agreement with those determined from ED patterns (a = 1.34 nm, b = 2.32 nm) (Table 1) and those reported by other authors for the V6I allomorph [START_REF] Brisson | The crystal and molecular structure of VH amylose by electron diffraction analysis[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF]. The complexing agent would only be located inside the helix cavity, since the interhelical space is too small [START_REF] Godet | Inclusion/exclusion of fatty acids in amylose complexes as a function of the fatty acid chain length[END_REF]. f obtained by vacuum drying of V7II complexes. c obtained by vacuum drying of V6I complexes.

g the unit cell contains 2 helices. d obtained by vacuum drying of V6II complexes.

h the unit cell contains 4 helices.

The second type of crystal, obtained with BDIOL, HDIOL and BBIOL, occurred in the form of stacks of rectangular lamellae. Stacks were individual (Fig. 2a and2d) or existed as twins forming an angle of approximately 60 or 90° (Fig. 2b and2c, Supplementary Data Fig. S4). This morphology is similar to that previously described for the V6II allomorph obtained with fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF], n-butanol and n-pentanol [START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF][START_REF] Yamashita | An electron microscopic study on crystals of amylose V complexes[END_REF]. The ED patterns recorded on hydrated stacks of lamellae perpendicularly to the (a,b) so-called base plane of the crystal, i.e. along the [001] c-axis, were unique, which means that all lamellae in a stack share a strict orientation relationship, characteristic of a homoepitaxial growth (Fig. 2e). Furthermore, ED and XRD patterns (Fig. 2f)

recorded on hydrated specimens are typical of V6II complexes [START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF][START_REF] Booy | Electron diffraction study of single crystals of amylose complexed with n-butanol[END_REF] and correspond to an orthorhombic unit cell with space group P212121 (Table 1). The parameters measured from baseplane ED diagrams of complexes with different diols (a = 2.68 nm, b = 2.72 nm) were in good agreement with those calculated from XRD data (a = 2.65 nm, b = 2.72 nm and c = 0.79 nm).

Helbert and Chanzy [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF] proposed a model where the amylose chains are organized in antiparallel pairs of 6-fold amylose helices inside the orthorhombic unit cell (Fig. 6c). The guest and water molecules would be included in the helical cavity and between helices. Our a and b parameters are reversed with respect to those proposed by Helbert and Chanzy since, as proposed by Donnay [START_REF] Donnay | Rules for the conventional orientation of crystals[END_REF], and to be consistent with all the other V-amylose allomorphs, we have used the convention that a would be smaller than b. The morphology of the third type of crystal was almost identical to that of V6I complexes regarding the hexagonal shape and dislocation-centered spiral growth (Fig. 3a). It was only observed with BBIOL. The ED (Fig. 3b) and XRD (Figs. 3c) patterns recorded on hydrated crystals were also qualitatively similar to those recorded from V6I crystals as they also exhibit a hexagonal symmetry. However, a careful calibration of the ED and XRD data showed that the reflections are globally located at smaller diffraction angles and were thus indexed on the basis of a larger pseudo-hexagonal orthorhombic unit cell (a = 1.50 nm, b = a√3 = 2.60 nm and c = 0.79 nm) (Table 1). Assuming a lattice of close-packed amylose helices, a larger helix diameter of 1.50 nm can be deduced. This value is identical to that reported for the 7-fold helix in V-amylose complexes prepared with branched alcohols or fatty acids [START_REF] Yamashita | Single crystals of amylose V complexes. II. Crystals with 71 helical configuration[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. We have recently reported V-amylose crystals with a similar morphology and structure based on close-packed 7-fold helices in complexes prepared with bicyclic compounds such as borneol, camphor, cis-decahydro-1-naphthol or decahydro-2-naphthol [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF]. We have proposed that this allomorph would be referred to as V7I, by analogy with the close-packed V6I, but also to differentiate it from another V7 allomorph, previously described by Nishiyama et al. [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF], obtained with propan-2-ol, and referred to as V7II in the following. It is worth noting that, as previously suggested by Zaslow [START_REF] Zaslow | Characterization of a second helical amylose modification[END_REF], a 7-fold helix cannot be crystallographically close-packed into a hexagonal unit cell. As a result, a pseudo-hexagonal unit cell with space group P1 has been used to describe the V7I structure (Fig. 6f). Due to the close packing, amylose helices are expected to be only separated by water molecules and the ligands would only be located inside the helix.

The fourth type of crystal, obtained with BBIOL and MPDIOL, occurred as rectangular lamellae frequently organized into flower-like aggregates (Fig. 4a-b and Supplementary Data Fig. S5). The ED patterns recorded on frozen-hydrated crystals (Fig. 4c) were indexed according to an orthorhombic unit cell with a = 2.79 nm and b = 2.96 nm, in agreement with the parameters calculated from XRD patterns (a = 2.83 nm and b = 2.98 nm. c could not be determined from the patterns) (Fig. 4d). Regarding their morphology and diffraction patterns, these crystals are isomorphous to the V7II crystals prepared with propan-2-ol [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF][START_REF] Buléon | Single crystals of V amylose complexed with isopropanol and acetone[END_REF], linear fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF], and many alcohols and aroma compounds [START_REF] Nuessli | Crystal structure of amylose complexes with small ligands[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Putaux | Single crystals of V-amylose inclusion complexes[END_REF]. The c-parameter of the unit cell was reported to be around 0.80 nm. The molecular model proposed by Nishiyama et al. [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF] is presented in 2 and Supplementary Data Table S2). The helix packings are those proposed for V a [START_REF] Zobel | X-ray diffraction of oriented amylose fibers. II. Structure of V amyloses[END_REF], Vh [START_REF] Rappenecker | Detailed refinement of the crystal structure of Vhamylose[END_REF], V butan-1-ol [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF], Vglycerol [START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF], V7a [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF], Vborneol [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF], and V propan-2-ol [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF], respectively. In these base-plane projections along the helical c-axis, only the amylose helices have been drawn. Hydrogen atoms have been omitted for clarity. The conformation of the hydroxymethyl groups has been fixed as gg in all cases for simplicity and the helices were kept undistorted. The blue ovals mark the interhelical cavities. The unit cells have been superimposed on the models. Pseudo-hexagonal orthorhombic unit cells have been drawn in models a, b, e and f.

It must be noted that we did not observe the presence of the double-helical B-type allomorph in the XRD profiles. As seen in Supplementary Data Fig. S6, a typical signature of B-type is the strong peak located at 2q = 5.5°, whose intensity depends on the specimen hydration [START_REF] Lourdin | Crystalline structure in starch[END_REF].

Although the specimens were characterized just after cooling down to room temperature, the slow formation of B-type amylose from the uncomplexed amylose fraction after a long-term storage cannot be ruled out.

Crystal structure as a function of complexing diol

The series of diols was selected based on the carbon chain (straight or branched), chain length, and the position of hydroxyl groups on the chain (Scheme 1). The allomorphs characterized as a function of the selected diol, its concentration and the crystallization temperature are listed in A general observation is that diols with a linear carbon chain and end hydroxyl groups induced the formation of V6 complexes, regardless of their chain length. More specifically, EDIOL induced the formation of V6I while BDIOL and HDIOL induced both V6I and V6II. In contrast, the bulkier MPDIOL that contains a branched carbon backbone and side hydroxyl groups, only yielded V7II complexes. Furthermore, with BBIOL, both 6-and 7-fold helical complexes were formed (V6I, V6II, V7I and V7II). Indeed, BBIOL contains structural characteristics that are compatible with both 6-fold (a linear carbon chain, one end hydroxyl group) and 7-fold helical conformations (one side hydroxyl group).

The above results support the conclusions of previous studies that the conformation of V-amylose depends on the cross-sectional diameter of the guest molecule compared to the average diameter of the helical cavity of the amylose helix, i.e. around 0.45 and 0.55 nm for 6-and 7-fold helices, respectively [START_REF] Biais | Structural and stoichiometric studies of complexes between aroma compounds and amylose. Polymorphic transitions and quantification in amorphous and crystalline areas[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Yamashita | Single crystals of amylose V complexes. III. Crystals with 81 helical configuration[END_REF][START_REF] Rutschmann | Formation of inclusion complexes of starch with different organic compounds. IV, ligand binding and variability in helical conformations of V amylose complexes[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part III. X-ray studies on amylose and cyclodextrin complexes[END_REF]. These studies showed that complexing agents such as straight-chain n-alcohols and n-fatty acids, with a cross-sectional diameter similar to that of straight-chain n-diols (ca. 0.30 nm), favored 6-fold helices. V7 complexes were usually obtained with bulkier precipitants such as branched alcohols, aromatic hydrocarbons and monoterpenes with larger cross-sectional diameters (ca. 0.45-0.60 nm). Like BBIOL, some complexing agents such as propan-2-ol, acetone, methylethylketone or fatty acids induce both 6-and 7-fold helical conformations [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. The linear carbon chain of these ligands contains a small side functional group (e.g. hydroxyl) or a larger end functional group (e.g. carboxyl). They exhibit intermediate cross-sectional diameters (0.36-0.45 nm) between those that are favorable for 6-and 7-fold helices. Since one turn of helix only consists of an integral number of glucosyl residues [START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part III. X-ray studies on amylose and cyclodextrin complexes[END_REF], a V6 or V7 allomorph, or both, can be formed depending on the crystallization conditions.

In addition to the different helical conformation, the different allomorphs contain a different helical packing. BDIOL, HDIOL and BBIOL induced 6-fold helices with two different packing arrangements: pseudo-hexagonal (V6I) and orthorhombic (V6II). A similar observation has also been reported for complexes with n-alcohols [START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF] as well as mono-and dicarboxylic acids [START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF].

Packing polymorphism seems to be much less prevalent for V7 complexes. So far, only BBIOL, cis-decahydro-1-naphthol and decahydro-2-naphthol have been shown to induce both V7I and V7II [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF], while a large variety of ligands yield only V7II [START_REF] Nuessli | Crystal structure of amylose complexes with small ligands[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part VI. Xray diffraction of amylose-n-aliphatic ketone complexes[END_REF][START_REF] Putaux | Single crystals of V-amylose inclusion complexes[END_REF]. However, it is difficult to draw a conclusion regarding the formation of V7I as it is possible that the right set of crystallization conditions has not been yet found for each complexing agent.

Effect of crystallization conditions

As shown in Table 2, each diol exhibits a minimum concentration at which crystalline inclusion complexes with amylose are formed. The critical concentration is lower for diols with a longer chain or a lower water solubility. For example, only 1 wt% of HDIOL or 2.5 vol% MPDIOL is necessary to form complexes with amylose at 25 °C, compared to 40 vol% for EDIOL. Besides, a higher concentration of diol allows the crystallization to be carried out at higher temperatures. Similar observations have been reported for fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF].

When a given diol such as BDIOL, HDIOL or BBIOL induced more than one crystal structure, the occurrence domain of each allomorph, defined by a set of conditions at which a specific allomorph crystallizes, can be independent or overlap onto one another (Table 2) [START_REF] Bernstein | Concomitant polymorphs[END_REF]. Similar phenomena have been reported for V-amylose prepared with some fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF]. When the occurrence domain is unique, only one crystal type is obtained, that is the most thermodynamically stable. In contrast, when two domains overlap, two or more allomorphs are energetically close and thus crystallize under the same conditions. In that case, the occurrence of both allomorphs is controlled by a competition between thermodynamic stability and kinetic factors [START_REF] Bernstein | Concomitant polymorphs[END_REF].

As shown in Table 2 and illustrated by XRD profiles of VBDIOL, VHDIOL and VBBIOL complexes in Supplementary Data Fig. S8a-c, the minimum diol concentration at which a given allomorph is formed can be arranged in the order: V7I > V6I > V7II > V6II. Similar observations have been reported for complexes with propan-2-ol, acetone and some fatty acids: V6I is preferred to V7II or V6II at a higher ligand concentration [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF][START_REF] Helbert | Données sur la structure du grain d'amidon et des produits de recristallisation de l'amylose[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. Indeed, V6II and V7II are less compact structures than V6I and V7I. There is more interstitial space in V6II and V7II where water and ligands can be located to stabilize the structure. Indeed, as detailed in the following section, the drying of V6II and V7II complexes induced a transition to compact hexagonal structures. A high concentration of complexing agent possibly results in a dehydration of amylose and thus favors the formation of the more compact structures (V6I and V7I). Moreover, the crystallization of VBBIOL showed that 6-fold helices were preferred over 7-fold ones at lower ligand concentration in both orthorhombic (V6II < V7II) and compact pseudo-hexagonal structures (V6I < V7I).

Hydration would thus play a significant role in governing the helical conformation of amylose.

Along with the control of diol concentration, variations in the crystallization temperature were explored. V6II and V7II complexes were obtained at relatively lower temperatures (25-40 °C) while V6I and V7I were formed within a wider range (25-75 °C) (Table 2). This observation agrees with our earlier findings on complexes with bicyclic organic compounds [START_REF] Shi | Starch-menthol inclusion complex: Structure and release kinetics[END_REF] or fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF]. We do not have any straightforward explanation to account for such a temperature influence toward the compactness of the crystals. It may be that a temperature increase favors a higher mobility of the amylose chains, which are therefore free to crystallize in compact packing of helices in close-contact arrangement. Supplementary Data Fig. S9 shows XRD profiles of VBDIOL, VHDIOL and VBBIOL complexes prepared with the same concentration of diol but at different temperatures. Some conclusions can be drawn: i) V6I was favored over V6II at higher temperatures (Fig. S9a,b); ii) V7II was favored over V6I and V6II at higher temperatures (Fig. S9c,d); iii) V7I was favored over V6I at higher temperatures (Fig. S9e,f). Our previous work on complexes with fatty acids showed that V6I was preferred to both V6II and V7II at higher crystallization temperatures. The difference between the conclusions in the two studies may be due to the different chemical nature of the complexing agents or the difference in the range of tested temperatures. The crystallization of Vfatty acid complexes was studied at T ≥ 40 °C compared to T ≥ 25 °C for Vdiol complexes. Our results with diols also show that V-amylose complexes could be formed at 25 °C, especially with a relatively low concentration of ligand (Table 2). In this case, the prior incubation of the amylose / ligand mixture for one week at a higher temperature (40-75 °C), during which the crystallization did not occur, resulted in a higher yield of crystals, while a significant amorphous fraction was observed with shorter incubation times (not shown).

A crystallization was thus successfully achieved when the amylose and ligands interacted for a sufficient time at higher temperature before cooling down. A similar phenomenon has been reported for complexes with fatty acids [START_REF] Le | Polymorphism of crystalline complexes of V-amylose with fatty acids[END_REF] and 1-naphthol [START_REF] Yamashita | Single crystals of amylose V complexes. III. Crystals with 81 helical configuration[END_REF].

Effect of drying

Fig. 7 shows XRD profiles of the four V-amylose allomorphs obtained with BBIOL and MPDIOL and collected in the never-dried hydrated state and after drying. The profile of the extensively dried V6I complex is typical of the anhydrous V6a (Fig. 7a), in agreement with the results reported for V6I complexes obtained with linear alcohols and fatty acids [START_REF] Takeo | Complexes of starchy materials with organic compounds: Part III. X-ray studies on amylose and cyclodextrin complexes[END_REF][START_REF] Shogren | X-ray diffraction study of crystal transformations in spherulitic amylose/lipid complexes from jet-cooked starch[END_REF]. This diagram can be indexed according to a pseudo-hexagonal orthorhombic unit cell with a = 1.32 nm, b = a√3 = 2.28 nm and c = 0.81 nm (Table 1). The slight difference in the unit cell parameters between V6I and V6a likely results from the release of water molecules from V6I, which would reduce the interhelical space without altering the helical conformation and compact packing [START_REF] Booy | Electron diffraction study of single crystals of amylose complexed with n-butanol[END_REF].

Like the V6I allomorph, V6II was also converted into the compact V6a after extended vacuum drying (Figs. 7b,c). Similar results have been reported for V6II prepared with butan-1-ol [START_REF] Booy | Electron diffraction study of single crystals of amylose complexed with n-butanol[END_REF][START_REF] Hinkle | X-ray diffraction of oriented amylose fibers. III. The structure of amylose-n-butanol complexes[END_REF] and some dicarboxylic acids [START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. However, the structural transition occurred more slowly for the complexes with diols, allowing us to study intermediate structures. Different ED patterns were recorded from quench-frozen specimens of VBBIOL crystals prepared from the same batch, which suggested that some preparations had partially dried before freezing and transfer into the microscope. Fig. 8e corresponds to the regular base-plane ED pattern of V6II crystals (Fig. 8a). Some of the diffraction spots are still present in the pattern of Fig. 8f but the diagram in Fig. 8g is very similar to the one reported by Hulleman et al. [START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF] for V6III complexes with glycerol. The same observation was made for VBDIOL complexes (Supplementary Data Fig. S10). The comparison of the XRD profiles recorded from a hydrated mat of VBBIOL crystals and after a 1-h vacuum drying confirmed that the partial drying induced the formation of a structure that diffracted like V6III (Fig. 7b). This structure was rather stable and slowly converted into V6a over several weeks of drying (Figs. 7b and8h).

Fig. 7c shows the XRD profile of the VHDIOL complex after a brief vacuum drying. The profile is not that of V6III as observed for VBBIOL and VBDIOL and contains peaks of the original V6II in addition to those of a different form. The base-plane ED patterns of quench-frozen VHDIOL crystals are shown in Fig. 9. Two types of diagrams were recorded from crystals located on different regions on the TEM grid. For some crystals (Fig. 9b), the constituting lamellae were not clearly visible, suggesting that a thin film of mother liquor was frozen with the crystals that would thus be considered as fully hydrated / solvated. The corresponding ED pattern was that of V6II as observed for VBBIOL and VBDIOL complexes (Fig. 9c). For other crystals where the lamellae were clearly visible (Fig. 9d), the diagram was more complex. A careful observation of the base-plane reflections showed that most rows contained misaligned spots (Fig. 9e). By isolating each set of spots, two different patterns were identified: pattern 1 was that of the original crystals, i.e. V6II, while pattern 2 was similar to that of the V7II allomorph (Figs. 9f and4c). The a * and b * reciprocal axes in patterns 1 and 2 were perfectly aligned. However, using the unit cell parameters of V6II as a reference, those of pattern 2 were found to be a = 2.55 nm and b = 2.65 nm, values that are significantly lower than those of V7II (a = 2.79 nm and b = 2.96 nm). The occurrence of 7-fold helices in this structure is thus unlikely and since the starting allomorph was V6II, we assumed that 6-fold helices were involved instead. The ED patterns recorded from the crystals after warming the specimen to room temperature were all similar to those with the superimposed patterns, although less resolved (not shown). A tentative model of the intermediate structure based on the arrangement of helices in the V7II allomorph but with 6-fold helices packed in a smaller unit cell is shown in Fig. 10b. Since no significant morphological change was observed in the crystals, we cannot determine whether some of the V6II constituting lamellae have been converted to the intermediate structure upon partial drying, or each lamella is a mosaic structure of locally converted domains. It must be noted that this structure has never been observed by direct crystallization of amylose and may be a new transitory organization of helices that occurs only under these drying conditions. The XRD profile of V6a was obtained after extended drying of the crystals (Fig. 7c).

The schemes in Fig. 10 summarize the changes in the packing of amylose helices in the (a,b) plane resulting from the drying of V6II (Fig. 10a and10b) and V7II (Fig. 10c) complexes, taking into account the up and down orientation of the antiparallel helices. The helix arrangements proposed for V6a and V6III in the literature are given in Fig. 10d. Two constraints were considered to describe the partially dried and dry structures of chain-folded crystals: the local movements of helices were minimal and the up and down orientations were preserved during the transitions.

In the initial V6II, amylose helices are organized in rows parallel to the b-axis of the unit cell and to the longer-dimension of the rectangular crystal, whereas the helices are staggered along the a-axis [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF]. Fig. 10a illustrates a first drying pathway. Upon partial drying, amylose helices became aligned along both a and b axes resulting in a small increase of the a-parameter from 2.66 nm to 2.71 nm, while b remained unchanged. This transition is puzzling, although it is supported by the diffraction data from VBBIOL (Figs. 7b and8) and VBDIOL (Supplementary Data Fig. S8).

The unit cell appears to be slightly larger than that of V6II while a compaction of the helices would be expected. This may suggest that during a first stage of drying the ligands reorganize in the interhelical space. Further experiments are necessary to fully understand this behavior by analyzing the crystal structures of V6II complexes after equilibration at different relative humidities, or by monitoring the transition in situ on a shorter timescale. After extended drying, the amylose helices reorganized into a close-packed pseudo-hexagonal arrangement, with a slight decrease of the b-parameter (2.64 nm) but a significant decrease of a (2.29 nm), consistent with the formation of longitudinal cracks in the dried crystals (Fig. 8d) and in agreement with the observation of Helbert and Chanzy for Vbutan-1-ol complexes [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF]. It must be noted that, although the helix arrangements in the (a,b) plane closely resemble those in V6III and V6a, the distribution of up and down helices differ from those proposed for these allomorphs in the literature (Fig. 10d) [START_REF] Winter | Crystal and molecular structure of the amylose-DMSO complex[END_REF][START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF]. Consequently, larger orthorhombic unit cells containing four amylose helices instead of two had to be considered. , V6III [START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF] and V7a (deduced from V7I [START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF]). The starting models are based on those displayed in Figure 6. Up and down antiparallel amylose helices are schematized as disks and circles, respectively, whereas 6-and 7-fold helices are draw in blue and red, respectively.

A second drying pathway of V6II crystals is proposed in Fig. 10b, supported by the diffraction data of VHDIOL crystals (Figs. 7c and9). The 6-fold helices would first reorganize into a pattern that resembles that of V7II but into a smaller unit cell, before settling into a close-packed pseudohexagonal arrangement. Again, although the positions of the helices of the intermediate structure are identical to those proposed for V7II in the (a,b) plane [START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF], the distribution of up and down orientations is different. After extended drying, the helices would adopt a pseudo-hexagonal close packing resembling that of V6a.

Our analysis of the diffraction data from all intermediate and dry structures mainly relied on hk0 reflections, allowing to propose plausible distributions of helices in the (a,b) base plane. As seen in Supplementary Data Tables S3 andS4 in the case of VBBIOL complexes, the number of XRD reflections indexed as hkl with l ¹ 0 is very small. Therefore, due to this lack of information along the c-axis, the proposed models cannot be fully validated and the proposed orientation of helices relied on chain-folding constraints rather than symmetry considerations.

According to Helbert and Chanzy [START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF] the transition from V6II to V6a observed for complexes with butan-1-ol and pentan-1-ol would be due to the release of volatile ligands located in the interhelical space. However, such release is less likely for non-volatile complexing agents such as solid dicarboxylic acids [START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF]. This suggests that the departure of water rather than the complexing agent would also be a significant cause for the structural transition induced by drying.

However, in our study, we did not have any quantitative evidence of the release of diol or water molecules from the crystals upon drying, although we can assume that the hygroscopic properties of diols, which should limit the departure of water, could be the reason for the slow transition observed for these complexes. The quantification of released molecules is thus an important aspect that must be addressed in a further study.

In the case of V7 crystals, different transition behaviors were noted for VBBIOL and VMPDIOL.

On the one hand, extensively dried VMPDIOL crystals (V7II) yielded an XRD profile identical to that of V7a obtained by dehydration of complexes with propan-2-ol, branched alcohols, ketones, fatty acids and ring compounds (Figs. 6e and7f) [START_REF] Nuessli | Crystal structure of amylose complexes with small ligands[END_REF][START_REF] Yamashita | Single crystals of amylose V complexes. II. Crystals with 71 helical configuration[END_REF][START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF][START_REF] Zaslow | Characterization of a second helical amylose modification[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part III. X-ray studies on amylose and cyclodextrin complexes[END_REF]. The parameters of the pseudo-hexagonal orthorhombic unit cell are a = 1.47 nm, b = a√3 = 2.55 nm and c = 0.78 nm (Table 1). Like in the dry close-packed structure based on 6-fold helices, the orientation of 7-fold helices is different from that expected from the drying of V7I crystals into V7a (Fig. 10c andd).

On the other hand, characteristic reflections of both V6a and V7a were found in the XRD profile of the dried V7I and V7II complexes with BBIOL (Fig. 7d and 7e, respectively), suggesting a partial helical transition from 7-to 6-fold. In previous studies, the transition from V7II to V6a only happened when the complexes were washed with aliphatic alcohols, followed by drying [START_REF] Biais | Structural and stoichiometric studies of complexes between aroma compounds and amylose. Polymorphic transitions and quantification in amorphous and crystalline areas[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part III. X-ray studies on amylose and cyclodextrin complexes[END_REF][START_REF] Shogren | X-ray diffraction study of crystal transformations in spherulitic amylose/lipid complexes from jet-cooked starch[END_REF]. Such treatments were shown to remove both water and guest molecules from the crystal. However, the transition from a 7-to a 6-fold helix in the VBBIOL crystal agrees with the fact that BBIOL is compatible with both 6-and 7-fold helices. Indeed, such partial conversion was not observed for VMPDIOL or many V7 complexes prepared with complexing agents that could not induce 6-fold helices [START_REF] Nuessli | Crystal structure of amylose complexes with small ligands[END_REF][START_REF] Yamashita | Single crystals of amylose V complexes. II. Crystals with 71 helical configuration[END_REF][START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF][START_REF] Takeo | Complexes of starch and its related materials with organic compounds. Part. X. X-ray diffraction of amylose-fatty acid complexes[END_REF][START_REF] Rutschmann | Formation of inclusion complexes of starch with different organic compounds. IV, ligand binding and variability in helical conformations of V amylose complexes[END_REF][START_REF] Takeo | Complexes of starchy materials with organic compounds: Part III. X-ray studies on amylose and cyclodextrin complexes[END_REF]. Therefore, the effect of extensive drying on V7 complexes prepared with complexing agents such as acetone, propan-2-ol or butanone, that are also compatible with both 6-and 7-fold helices should be studied.

Conclusions

Amylose was successfully cocrystallized with aliphatic diols in the form of chain-folded lamellar crystals. Four allomorphs (V6I, V6II, V7I and V7II) were identified from TEM images and diffraction data. On the one hand, the helical conformation of amylose was shown to depend on the cross-sectional diameter of the complexing agent. Linear n-diols yielded V6 complexes while bulkier diols with branched chain and/or side hydroxyl groups produced V7 crystals.

BBIOL, with both a linear carbon chain and a side hydroxyl group induced both V6 and V7. On the other hand, BDIOL, HDIOL and BBIOL could form more than one allomorph, depending on the diol concentration and crystallization temperature. The minimum diol concentration at which a given allomorph was formed could be arranged in the order: V7I > V6I > V7II > V6II. For all complexes with the exception of VMPDIOL, allomorphs with compact pseudo-hexagonal unit cells were favored at higher temperature and higher diol concentration.

Structural transitions occurred upon drying with a pathway that depended on the complexed diol. Transitions to more compact pseudo-hexagonal structures were also observed for all allomorphs after extensive drying. For most complexing agents, the helical conformation of amylose remained unchanged: V6I and V6II became V6a, and V7II became V7a. As an exception, both V7I and V7II formed with BBIOL were converted into a mixture of V6a and V7a. The change in helical conformation may be related to the fact that, depending on the crystallization conditions, BBIOL induced 6-or 7-fold helices. The departure of water would play a significant role in the structural transitions, although the concomitant loss of ligand upon drying was not quantified.

Therefore, rehydration / resolvation experiments should be conducted to see whether the transitions are reversible.

To complement this mainly descriptive study, further work will focus on several aspects.

First, the ED and XRD data will be quantitatively analyzed to describe the molecular structures more precisely using crystallographic refinement methods. Second, the stoichiometry of the complexes in relation with the distribution of ligands and water molecules inside the helical amylose scaffold will be determined. More detailed molecular models will help to understand how the crystal structure is stabilized and how different amylose conformations and helix arrangements are induced by a given ligand. Molecular dynamics calculations should also shed some light on the mechanisms at work during structural transitions, in particular upon drying the V-amylose complexes.

Scheme 1 :

 1 Scheme 1: Molecular structure of the diols tested in this study: a) ethane-1,2-diol (EDIOL); b) butane-1,4-diol (BDIOL); c) hexane-1,6-diol (HDIOL); d) butane-1,3-diol (BBIOL); e) 2-methylpentane-2,4-diol (MPDIOL) (drawn with MarvinSketch [50]). Three-dimensional molecular models are shown in Supplementary Data Fig. S2.

Fig. 1 .

 1 Fig. 1. The V6I allomorph: a-d) TEM images of V-amylose crystallized with BBIOL (a,b), EDIOL (c) and HDIOL (d); e) base-plane ED pattern recorded at low temperature from a frozen-hydrated VBBIOL crystal; f) XRD powder diagram recorded from VHDIOL crystals equilibrated at 95% RH.

Fig. 6g .

 6g Fig. 6g. The orthorhombic unit cell contains four antiparallel left-handed 7-fold helices. The helices are not all close-packed which allows the guest molecules to be located both inside and between the helices.

Fig. 2 .

 2 Fig. 2. The V6II allomorph: a-d) TEM images of V-amylose crystallized with BBIOL (a-c) and HDIOL (d); e) base-plane ED pattern recorded at low temperature from a frozen-hydrated VBBIOL crystal; f) XRD powder diagram recorded from VBDIOL crystals equilibrated at 95% RH.

Fig. 3 .

 3 Fig. 3. The V7I allomorph: a) TEM image of V-amylose crystallized with BBIOL; b) base-plane pseudo-hexagonal ED pattern recorded at low temperature from a frozen-hydrated crystal; c) XRD powder diagram recorded from crystals equilibrated at 95% RH.

Fig. 4 .

 4 Fig. 4. The V7II allomorph: a,b) TEM image of V-amylose crystals prepared with MPDIOL (a) and BBIOL (b); c) base-plane ED pattern recorded at low temperature from a frozen-hydrated VBBIOL crystal; d) XRD powder diagram recorded from VBBIOL crystals equilibrated at 95% RH.

Fig. 5 .

 5 Fig. 5. Typical XRD profiles of V-type allomorphs that result from the direct crystallization of amylose in the presence of aliphatic diols. A given diol can induce the formation of different allomorphs (Table2and Supplementary Data TableS2).

Fig. 6 .

 6 Fig.6. Geometrical molecular models of the seven allomorphs of V-amylose considered in this study: a) V6a, b) V6 I , c) V6 II , d) V6III, e) V7 a , f) V7 I , g) V7 II . The helix packings are those proposed for V a[START_REF] Zobel | X-ray diffraction of oriented amylose fibers. II. Structure of V amyloses[END_REF], Vh[START_REF] Rappenecker | Detailed refinement of the crystal structure of Vhamylose[END_REF], V butan-1-ol[START_REF] Helbert | Single crystals of V-amylose complexed with n-butanol or npentanol: structural features and properties[END_REF], Vglycerol[START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF], V7a[START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF], Vborneol[START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF], and V propan-2-ol[START_REF] Nishiyama | Molecular and crystal structure of 7-fold V-amylose complexed with 2-propanol[END_REF], respectively. In these base-plane projections along the helical c-axis, only the amylose helices have been drawn. Hydrogen atoms have been omitted for clarity. The conformation of the hydroxymethyl groups has been fixed as gg in all cases for simplicity and the helices were kept undistorted. The blue ovals mark the interhelical cavities. The unit cells have been superimposed on the models. Pseudo-hexagonal orthorhombic unit cells have been drawn in models a, b, e and f.

Fig. 7 .

 7 Fig. 7. Effect of drying on the XRD profiles of different V-amylose allomorphs prepared with BBIOL (a,b,d,e), HDIOL (c) and MPDIOL (f) in never-dried hydrated, partially dried and dry states. Upon drying, V6I was converted into V6a (a); V6II was first converted to V6III, then V6a (b), or into a mixture of V6II and a second V6 form, then V6a (c); V7I was converted into a mixture of V7a and V6a (d); V7II was converted into a mixture of V7a and V6a (e), or only into V7a (f).

Fig. 8 .

 8 Fig. 8. Effect of partial and extensive drying on VBBIOL crystals: TEM images (a-d) and corresponding properly oriented base-plane ED patterns (e-h) recorded at low temperature from frozen-hydrated crystals (e,f) and at room temperature (g,h), from the selected areas indicated by white circles. In f, the arrows indicate diffraction spots that still belong to the diagram in e. The V6II structure (e) is first converted to V6III after partial drying (g), then to V6a after extensive drying (h). The crystal in image d shows typical longitudinal drying cracks, as previously described by Helbert and Chanzy [27].

Fig. 9 .

 9 Fig. 9. a,b,d) TEM images of partially dried VHDIOL crystals (a). In image b, a thin layer of mother liquor was frozen with the crystal, yielding extra spots (arrows) in the corresponding V6II ED pattern (c). The lamellae are more clearly visible in the crystal in image d. In the corresponding ED pattern (e), some reflections are not in perfect alignment and others appear to be split (enlarged insets). The diagram is the superimposition of two patterns: pattern 1 (in red) is that of V6II while pattern 2 (in blue) is similar to that of V7II (f). However, the cell parameters calculated for pattern 2 are significantly smaller than those of V7II. ED patterns c and e have been recorded from the selected areas indicated by white circles in images b and d.

Fig. 10 .

 10 Fig. 10. Schemes describing tentative helix displacement upon drying of V6II and V7II complexes with diols, drawn in projection in the (a,b) plane: a) Drying of V6II from VBBIOL and VBDIOL; b) drying of V6II from VHDIOL; c) drying of V7II from VMPDIOL; d) structural models from the literature data: V6a[START_REF] Zobel | X-ray diffraction of oriented amylose fibers. II. Structure of V amyloses[END_REF], V6III[START_REF] Hulleman | Single crystals of V amylose complexed with glycerol[END_REF] and V7a (deduced from V7I[START_REF] Le | Single crystals of V-amylose complexed with bicyclic organic compounds[END_REF]). The starting models are based on those displayed in Figure6. Up and down antiparallel amylose helices are schematized as disks and circles, respectively, whereas 6-and 7-fold helices are draw in blue and red, respectively.

Table 1 .

 1 Average

	Allomorph	a	ED	b	a	XRD b	c
	V6I a,g	1.34 ± 0.02		2.32 ± 0.02	1.37 ± 0.00	2.37 ± 0.00	0.81 ± 0.01
	V6II a,h	2.68 ± 0.03		2.72 ± 0.02	2.66 ± 0.00	2.72 ± 0.01	0.79 ± 0.01
	V6III b,h	2.68 ± 0.02		2.68 ± 0.02	2.71 ± 0.00	2.71 ± 0.00	-
	V6a c,g	1.30 ± 0.00		2.25 ± 0.00	1.31 ± 0.02	2.27 ± 0.03	0.81 ± 0.01
	V6a d,h	2.25 ± 0.00		2.60 ± 0.00	2.29 ± 0.00	2.64 ± 0.00	0.81 ± 0.01
	V7I a,g	1.50 ± 0.00		2.60 ± 0.00	1.50 ± 0.00	2.60 ± 0.00	0.79 ± 0.00
	V7II a,h	2.79 ± 0.00		2.96 ± 0.00	2.83 ± 0.00	2.98 ± 0.01	-
	V7a e,g	1.47 ± 0.00		2.55 ± 0.00	1.47 ± 0.00	2.55 ± 0.00	0.78 ± 0.00
	V7a f,h	2.55 ± 0.00		2.94 ± 0.00	2.55 ± 0.00	2.94 ± 0.00	0.78 ± 0.00

unit cell parameters (nm) of different allomorphs of amylose cocrystallized with diols, determined from base-plane electron diffraction (ED) and powder X-ray diffraction (XRD) patterns. "-": not determined. a hydrated crystals.

e obtained by vacuum drying of V7I complexes. b obtained by partial drying of V6II complexes.

Table 2 .

 2 The corresponding XRD profiles are presented in Supplementary Data Figs. S7-S9.

Table 2 .

 2 V-amylose allomorphs as a function of complexing diol, diol concentration (C) and incubation temperature. C is expressed in vol% for EDIOL, BDIOL, BBIOL and MPDIOL, and wt% for HDIOL. The amylose and diol solutions were mixed at 90 °C, then kept at a given temperature during one week and cooled down to room temperature, or allowed to slowly cool down in a Dewar vessel after mixing. For mixtures, the major and minor allomorphs are indicated. "-": no precipitation was observed and the solution remained clear; "n. t.": not tested.

	Incubation temperature (°C)

Acknowledgements

We thank LabEx Arcane (Investissements d'Avenir, grant agreement #ANR-11-LABX-0003-01) for funding the PhD thesis of C.A.K.L., the NanoBio-ICMG platform (FR 2607, Grenoble) for granting access to the Electron Microscopy facility, the Glyco@Alps program (Investissements d'Avenir, grant agreement #ANR-15-IDEX-02), Noriyuki Isobe (University of Tokyo, Japan) for the chromatography analysis of native amylose, as well as Jacques Pécaut (CEA Grenoble), Karim Mazeau and Henri Chanzy (CERMAV) for stimulating discussions. CERMAV is part of Institut Carnot PolyNat (Investissements d'Avenir, grant agreement #ANR-11-CARN-030-01).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.polymer.2020.123302.

Abbreviations

BBIOL, butane-1,3-diol; BDIOL, butane-1,4-diol; EDIOL, ethane-1,2-diol; HDIOL, hexane-1,6diol; MPDIOL, 2-methylpentane-2,4-diol; ED, electron diffraction; TEM, transmission electron microscopy; XRD, X-ray diffraction.


Félix Bigand
email: felix.bigand@limsi.fr

Elise Prigent
email: elise.prigent@limsi.fr

Annelies Braffort
email: annelies.braffort@limsi.fr

Animating Virtual Signers : The Issue of Gestural Anonymization

Keywords: Sign Language, Virtual Signer, Motion Capture, Perception, Identity Recognition

This paper presents an ongoing PhD research project on visual perception and motion analysis applied to virtual signers (virtual agents used for Sign Language interaction).

Virtual signers (or signing avatars) play an important role in the accesibility of information in sign languages. They have been developed notably for their capability to anonymize shape and appearance of the content producer. While motion capture provides human-like, realistic and comprehensible signing animations, it also arises the question of anonymity. Human body movements contain important information about a person's identity, gender or emotional state. In the present work, we want to address the problem of gestural identity in the context of animated agents in French Sign Language. On the one hand, the ability to identify a person from signing motion is assessed through psychophysical experiments, using point-light displays. On the other hand, a computational framework is developed in order to investigate which features are critical for person identification and to control them over the virtual agent.

Since 2005 1 , French public institutions must provide accessible content to users regardless of their disability, including deaf people using Sign Language (SL). For now, accessibility in SL is mainly achieved by pre-recorded videos. This cannot enable real-time interaction nor anonymity for the content provider.

More generally, the need for producing messages anonymously is an important demand of deaf people as many of them have problems communicating through written content. Indeed, most deaf people communicate in a sign language. The spoken language of their country (e.g. French) is only a second language and is almost impossible to be learnt without any auditory cues. As a consequence, video remains the main communication tool used by native signers. It arises the question of anonymity and concerns many domains, from the work of professional journalists to the social networks where deaf users leave comments. The development of virtual signers is thus expanding, in order to make written material on internet more accessible to deaf users.

Several studies at LIMSI in Automatic Sign Language Processing are part of the elaboration of virtual signers [START_REF] Filhol | Extending the AZee-Paula shortcuts to enable natural proform synthesis[END_REF] [26] [START_REF] Benchiheub | Collecting and Analysing a Motion-Capture Corpus of French Sign Language[END_REF]. While this is not the only existing method [START_REF] Filhol | Extending the AZee-Paula shortcuts to enable natural proform synthesis[END_REF], these virtual agents tend to be animated using motion capture (mocap) on real actors [START_REF] Gibet | Building French Sign Language Motion Capture Corpora for Signing Avatars[END_REF], as it provides highly realistic and comprehensible content. Movements of the 'mocapped' person are then mapped to the virtual agent. With such accurate systems, the avatar motion convey rich information that can make the actor identifiable, such as the voice can allow a given person to be identified.

Realism, agreeableness and comprehensibility of virtual signers have been assessed in several studies [START_REF] Kipp | Sign language avatars: Animation and comprehensibility[END_REF] [14] [START_REF] Adamo-Villani | Effects of character geometric model on perception of sign language animation[END_REF]. Other studies evaluated SL mocap data from a linguistic approach [START_REF] Catteau | Variation prosodique et traduction poétique (LSF/français): Que devient la prosodie lorsquâĂŹelle change de canal?[END_REF] [17] [START_REF] Malaia | Kinematic parameters of signed verbs[END_REF]. However, the problem of anonymization and gestural identity have not been addressed in the context of SL animation. The aim of this work is to better understand how this critical information is hidden in the complex motion stimulus, in order to provide a better control of the virtual signers. For that, we extend the gestural identity problem to the specific motion patterns of French Sign Language. First, we aim at finding critical features which differentiate gestural styles of human signers. Second, we apply it to motion generation systems in order to provide an animated agent model with controllable gestural style.

In the next section (section 2), we present the current developments of the project and the last section (section 3) presents what has already been done and what action is planned.

PROPOSED METHODOLOGY : COMBINING PERCEPTION STUDIES AND COMPUTING APPROACHES

Humans can extract important information from biological motion (i.e. movements produced by humans or animals), such as one's intentions, emotions, or identity. How such information can be retrieved from complex movements remains a challenging question for both computer vision and visual perception areas. It seems crucial to consider this complex matter for the generation of virtual agents movements. Providing realistic, human-like and anonymized animations would ensure higher acceptability and comprehensibility than actual signing avatars.

We have adopted a pluridisciplinary approach, combining perception studies and computing methods. In a first step (section 2.1), we have to verify if the identity of a signer can be perceived only with motion cues. Then (section 2.2), we have to design methods that will allow us to extract the useful features using machine learning approaches.

Gestural identity perception

The studies of Johansson [START_REF] Johansson | Visual perception of biological motion and a model for its analysis[END_REF] [START_REF] Johansson | Spatio-temporal differentiation and integration in visual motion perception[END_REF] were the first to introduce the notion of point-light (PL) stimuli. This display separates information given by dynamic cues from characteristics such as shape or aspect of the person. This is why we have decided to use this method for our purpose. The key idea is to attach small point lights to the major joints of a person's body and film it in front of a dark background. Using this device, Johansson showed that humans could recognize a set of moving dots as a human walker. Point-light displays are widely used since then. Different studies demonstrated that they contain enough information to recognize familiar people from their gaits [6] [16] [10] [START_REF] Nikolaus F Troje | Person identification from biological motion: Effects of structural and kinematic cues[END_REF]. It also inspired studies in sign language perception, evaluating comprehensibility with this reduced setup [START_REF] Poizner | Perception of American sign language in dynamic point-light displays[END_REF] [START_REF] Vivien | Perception of sign language from an array of 27 moving spots[END_REF].

Relying on passive reflective markers, mocap systems capture equivalent information as point-light displays, and mocap corpora can be used for this kind of studies. Our first analysis of signers motion has been done by computing PL stimuli from mocap data, in order to elaborate an identification task. The aim is to verify first that the identity of a signer can be transmitted through the movement only.

Identification task

In a perceptual experiment, participants are asked to identify signing actors shown as point-light displays. Four different signers describe images in French Sign Language. They are displayed as videos of white moving dots, on a dark background. Three of them are well known from the general public, the fourth is not. Each participant specifies which signer he/her knows before viewing the stimuli.

Stimuli

Point-light stimuli are generated from mocap data. Each mocap sensor representing major joints of the body is displayed, white on black. We use MOCAP1 [START_REF] Benchiheub | Collecting and Analysing a Motion-Capture Corpus of French Sign Language[END_REF], a 3D corpus of motion capture data on French Sign Language (LSF). The 3D body movements of eight LSF native signers have been recorded. From this collection, we selected four signers, two men and two women. A set of 23 reflective markers was attached to their body. We did not include movements of the signer's face. Actors were wearing suits to record markers of the shoulders, the elbows, the wrists, the hands and the chest. Four sensors were attached to a cap and recording the head movements.

Recordings were done with an Optitrack S250e, equipped with 10 cameras with a spatial resolution of 0.7 Mpixels and a temporal resolution of 250 Hz. From the 23 markers, we derived 19 virtual markers which optimally describe the major joints of the body in PL displays. Figure 1 shows the 19 markers in a 3D view and point-light display. All the stimuli are displayed in front view.

Design and procedure

The participants take part in the experiment through an onlinesurvey. Native signers are more likely to identify the actors in the stimuli, however the experiment is also open to non-signers who could interact with signing people. The language level and the degree of interaction with signers are evaluated in the first place.

Before the test sessions, the four signing actors are introduced to the participants with a short video of them using LSF. Unlike the test stimuli, this introducing video includes the person appearance, clothing etc. The participants specify whom of the four signers they know. After one training trial, the test session consists of 20 trials. A trial begins with a 10-sec stimulus display, followed by the presentation of 5 buttons. The task is to identify the signer. Four buttons are illustrated by the four signers (screenshot from the introducing video) and another button enables them to answer that they did not recognize the signer. Each signer is presented five times, with five different contents (each photo is presented only once and by only one signer). In conjunction with this study, we aim at providing a computational framework for the control of signing agent gestural style. The algorithm is developed for analysis and synthesis of the signers motion. Using machine learning techniques, we will be in a position to extract critical features for identification and to control them over the agent.

Gestural identity and machine learning

Proposed methodology based on motion studies

The key hypothesis is that mostly the dynamic part of signing motion accounts for person identification, as it has been shown for walking [START_REF] Nikolaus F Troje | Person identification from biological motion: Effects of structural and kinematic cues[END_REF]. We present here one possible approach developed in biological motion studies, which reduces the motion data to a low-dimensional space. The principal components of this reduced representation are then used to feed a linear classifier. This framework provides a way to investigate critical features for person identification, with no a priori assumption.

Studies assessed candidate features by manipulating motion stimuli and evaluating the effect on recognition through experiments [START_REF] Lynn | Recognizing the sex of a walker from a dynamic point-light display[END_REF] [31] [2] [START_REF] Mather | Gender discrimination in biological motion displays based on dynamic cues[END_REF]. A causal link was then established between the candidate features and the task. Other approaches address the question as a pattern recognition problem, with no a priori hypothesis [START_REF] Nikolaus F Troje | Decomposing biological motion: A framework for analysis and synthesis of human gait patterns[END_REF] [30] [START_REF] Michalak | Embodiment of sadness and depres-sionâĂŤgait patterns associated with dysphoric mood[END_REF] [21] [START_REF] Roether | Features in the recognition of emotions from dynamic bodily expression[END_REF]. Statistical analysis (PCA, Fourier-based decomposition) of the motion data extracts components which are critical for the task (identification, gender classification..). They might be less interpretable than classic features such as velocity, quantity of movement etc. This approach takes its inspiration from eigenfaces, in the face recognition domain [22] [23]. O'Toole et al. demonstrate that identifiable faces can be reconstructed from only a subset of eigenvectors of a covariance matrix of faces. In this study, we propose to extend the idea of eigenpostures and eigenwalkers [START_REF] Nikolaus F Troje | Decomposing biological motion: A framework for analysis and synthesis of human gait patterns[END_REF] to the signers.

Data processing

The proposed methodology consists of working at the sign level, in order to limitate the linguistic complexity that could be a source of variation between signers, allowing the person identification. Isolated signs will be analysed thanks to a mocap system, beginning with periodic signs such as "pédaler" (to cycle) or "marcher" (to walk). Signing data can be seen as a time series of postures described by the 3D coordinates of 19 markers (Figure 1). Each posture refers to a 57-dimensional vector :

p = (x 1 , y 1 , z 1 , ..., z 19 ) (1)
This representation can be reduced to an average posture and eigenpostures for walking data [START_REF] Nikolaus F Troje | Decomposing biological motion: A framework for analysis and synthesis of human gait patterns[END_REF] [30], we will investigate its extent to our signing data. A 57xN (e.g. N=5,000 postures) matrix S representing one signer phrase, can then be reduced to a 57xd matrix F (d << N), depending on the number d of components we use. This value is set so that the components cover the overall variance at the most.

Linear classifier for person identification

The second step of this computational framework is to train a linear classifier to identify signers with the extracted features. A linear discriminant function is computed by regressing the signers labels on their features. The weights of the linear regression w are optimized (minimizing the least-square error) following this relation :

w T F = c (2)
c is the class vector indicating the label to which signer i belongs (c i = 1 if signer 1). This discriminant function w thus optimally separates the feature space according to signers gestural identity.

FUTURE WORK

In this PhD project, we adapted MOCAP1 corpus to the identification purpose and we proposed lines of research for motion analysis and synthesis, using machine learning techniques. At this stage :

• We designed a perceptual experiment to assess the identification of signers shown as point-light displays. It will provide preliminary results and will help to design a second experiment including computational manipulations on specific motion cues. It will also enable us to evaluate the need for the creation of a new mocap corpus, specific to identification. • We are currently developing algorithmic methods for motion analysis. Features are extracted from the mocap data with a data-driven approach, and then feed a linear classifier for person identification. • We evaluated methods for motion synthesis in order to animate the virtual signer and control the extracted features, as presented in the following.

First part of the future work consists of running the perceptual experiment, collecting and analysing data. Second, we will refine the proposed methods for motion decomposition and aim at developing a framework that is invertible (i.e. that enables visualization of the extracted features). A simple Fourier-based decomposition of the time-series postures is one possible solution. If the motion data is trained for person identification based on its Fourier components, we are in a position to manipulate the components and then come back to the time-series representation. Extension of this approach to our dataset of periodic signs is ongoing. For unperiodic sign movements, more complex techniques are needed. We would refer to the notion of spatio-temporal correspondences and morphable models [START_REF] Martin | Morphable models for the analysis and synthesis of complex motion patterns[END_REF]. The idea is to define spatio-temporal differences between prototypes and a reference pattern. New motion can then be generated from a linear combination of these correspondences. Another way to circumvent the problem of temporal description is to normalize the number of frames for each sign. Tilmanne & Dutoit apply PCA to time-normalized data and demonstrate that they can re-generate walking motion in a specific style thanks to Gaussian Modeling [START_REF] Tilmanne | Expressive gait synthesis using PCA and Gaussian modeling[END_REF]. Controlling the gestural style of our virtual signer thanks to Gaussian Mixture Models is another approach that we are evaluating as part of this doctoral project.

INTEREST OF THE DOCTORAL CONSORTIUM TO THIS RESEARCH

This consortium would enable us to get valuable feedback on the chosen approach and methods. The problem we address involves the development of algorithms for gesture analysis and synthesis, but also methods to evaluate the virtual agent. We would be honored to interact with the other participants on this matters. In addition, the Doctoral Consortium would offer us the opportunity to learn from other researchers about person identification in other domains, such as speech or facial expressions.

Figure 1 :

 1 Figure 1: The 19 3D markers (left) provided by our mocap system, then transformed into point-light display (right).

Figure 2 :

 2 Figure 2: A virtual signer developed at LIMSI [4].

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