Zhongwei Zhang

Yangyu Guo

Marc Bescond

Masahiro Nomura

Sebastian Volz
email: volz@iis.u-tokyo.ac.jp

Jie Chen

Assessing Phonon Coherence Using Spectroscopy

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Coherence is a fundamental characteristic of the wavelike behavior of elementary particles and quasi-particles [1][2][3][4]. Due to the wave nature of lattice vibrations, phonon coherence has been established as the dominant source of various unique thermal transport phenomena, such as coherent thermal transport (including minimum thermal conductivity in nanophononic crystals [1,2,[5][6][7][8] and phonon Anderson localization in disordered nanophononic crystals [9][10][11][12][13]), band folding [5,14,15] and phonon confinement [16][17][18]. Furthermore, recent studies [19][20][21][22][23] have uncovered the significant impact of phonon coherence on phonon-phonon scattering [19][20][21], phonon modal correlations [20,22,23] and interfacial phonon propagation [12], leading to clear discrepancies with the predictions obtained from the particle picture and also to promote coherence as a critical phonon attribute.

Phonon coherence is usually quantified by the physical quantity of coherence time [START_REF] Snoke | Solid state physics: Essential concepts[END_REF]. However, most of the experimental demonstrations of coherence for thermal phonons are qualitatively inferred from the variation of measured thermal conductivity [1,2,10,[START_REF] Hu | [END_REF]. For instance, the existence of coherent phonons is indirectly evidenced by the experimental observation of the non-monotonic variation of superlattice thermal conductivity with decreasing superlattice period [2]. On the other hand, phononic quantities, including phonon number, eigenfrequency and scattering rate, can be measured from the well-established time-domain thermoreflectance approach [26][27][28] or various spectroscopies [29][30][31][32][33][34], which are boosting the exploration of phonon physics and thermal transport in different matters. Clearly, the experimental characterization of the coherence of thermal phonons is lagging behind, due to the lack of an adequate theory, which impedes the scientific understanding and practical application of phonon physics and thermal transport.

In this Letter, we develop a theoretical model for experimentally investigating phonon coherence using spectroscopy measurements. The predictions of the model disclose that in the case of confined nanostructures, such as nanowires (NWs) and nanomembranes (NMs), the coherence time for different modes can be efficiently extracted. Because of the substantial phonon confinement, modes have a prominent wavelike characteristic and exhibit a significant dimensionality-dependent coherence. Furthermore, the phonon coherence times and lifetimes detected from spectroscopy agree qualitatively well with the outcomes from the direct molecular dynamic (MD) simulations. The proposed theory reassesses mainstream spectroscopies to quantify mode coherence having a general impact on the understanding and the estimation of phonon and thermal properties.

Phonon lifetime is conventionally measured from the Lorentzian fitting of experimental spectra, such as inelastic neutron scattering, inelastic x-ray scattering and Brillouin-Mandelstam light scattering [17,32,[35][36][37]. The underlying physics of a Lorentzian fit is based on the hypothesis of an exponential decay of phonon dynamics in time, assuming phonons as particles governed by diverse scattering processes [38,39]. In the frequency domain, the Lorentzian function is expressed as [38,40,41] Φ ks (ω) = I 0

4 (ω -ω ks ) 2 τ p ks 2 + 1 , (1)
where Φ ks (ω) is the spectral mode energy and I 0 is the peak intensity. The physical quantities of eigenfrequency (ω ks ) and lifetime (τ p ks ) are simultaneously evaluated by matching the experimental measurements as implemented in Refs. [17,32]. The Eq. ( 1) can also be expressed in terms of the modal linewidth (γ ks ) according to the expression of τ p ks = 1 2γ ks . Using the normal mode decomposition method, the spectral energy Φ ks (ω) can also be calculated from MD simulations, making of Eq. ( 1) a widely used model for studying the phonon lifetimes and thermal transport in theoretical and numerical simulation works [38,[41][42][43][44].

Recent studies [21,23,45] demonstrated the significance of coherence on the phonon dynamics and thermal transport in various solids. By taking into account the coherence effects, a pioneering work [21] established that the time-dependent phonon number should be corrected as follows

N ks (t) = N ks (0) e -γ ks t e -4ln2•Ω 2 ks t 2 , (2)
where N ks (0) denotes the phonon number of mode ks at the initial time of decay. γ represents the corrected linewidth for this mode and Ω ks denotes the inverse of the temporal extension of the wavepacket. The corrected phonon lifetime from Eq. ( 2) writes τ p ks = 1 2γ ks and the temporal coherence time τ c ks = 1 Ω ks . On the other hand, the phonon number can also be defined from the normal mode coordinate q ks as

N ks (t) hω ks = 1 2 qks (t) q * ks (t) + 1 2 ω ks q ks (t)q * ks (t), (3)
where * indicates the complex conjugate. Based on Eqs.

(2) and (3), we can further infer the expression of the normal mode coordinate as [START_REF] Snoke | Solid state physics: Essential concepts[END_REF] q ks (t) ≈ q 0 e -iω ks t e -γ ks

2 t e -2ln2•Ω 2 ks t 2 , (4)
where q 0 denotes the amplitude and e -iω ks t corresponds to the natural oscillation of the lattice wave. In a further step, the mode energy can be obtained from the Fourier transform of Eq. ( 4) as

Φ ks (ω) = 2 × 1 2 ω ks ∞ 0 q ks (t)e iωt dt 2 . ( 5
)
The coefficient 2 accounts for the summation of the kinetic and the potential terms. Finally, the spectroscopy model that includes both lifetime and coherence time is obtained as 1) and the proposed one in Eq. ( 6). The experimental data were previously published by Kargar et al. [17]. (c) The MD spectral analysis of Si nanowires with a diameter D = 1.5 nm at the specific wavevector k = (0,0,0) µm -1 . (d) The fitting of the MD calculated spectral energy with the classical Lorentzian model of Eq. ( 1) and the one of Eq. ( 6).

Φ ks (ω) = Icos 1 16ln2

τ c2 ks τ p ks (ω -ω ks ) e -(ω-ω ks ) 2 τ c2 ks 8ln2
, (6) where I denotes the peak intensity. In contrast to the Lorentzian model of Eq. (1), our theory can simultaneously provide the information of eigenfrequency (ω ks ), coherence corrected phonon lifetime (τ p ks ) and coherence time (τ c ks ). As previously discussed, the spectral energy can be measured by experimental spectroscopy as implemented by many different techniques, and can also be calculated from the normal mode decomposition with inputs from MD simulations. However, Eq. ( 6) reveals that τ p ks and τ c ks are coupled in the spectral domain, making the fitting for these two quantities non-unique.

A previous study [21] showed that the lifetimes fitted by Eq. ( 1) are close to the coherence corrected ones, i.e., τ p ks ≈ τ p ks . Following this approximation, the lifetimes and coherence times can be estimated from the spectral energy via a two-step fitting: 1) the lifetime and eigenfrequency can be obtained by fitting the spectral energy with Eq. (1); 2) the second fitting is performed to extract the coherence time from Eq. ( 6) based on 1). The fitting code has been implemented in our open-source WPPT package [46], which is originally designed to study the coherence of phonons and the thermal conductivity of solids.

To support the proposed model, we further investigate the coherence of phonons in the confined nanostructures. Previous studies [16-18, 47, 48] demonstrated that phonon confinement appears along the non-periodic direction as reducing the structure dimensionality to one or two. In one-dimensional NWs, for example, phonons are confined in the diameter direction as standing waves and exhibit a diameter-dependent confinement [17,27,49]. For instance, Kargar et al. [17] have measured the phonon subbands in GaAs NWs using the Brillouin-Mandelstam light scattering spectroscopy. Figure 1(a) reports the experimental spectrum from Ref. [17] at a specific wavevector for a GaAs NW with a diameter D = 122 nm. Peaks corresponding to different phonon modes clearly appear. The fitting of a specific mode is shown in Fig. 1(b). The proposed model displays a better agreement with the spectroscopy data than the Lorentzian fit does. To provide further comparison, we also calculate the spectral energy of Si NWs with smaller diameters, from MD simulations. The details about MD simulations and the normal mode decomposition are provided in Supplementary Material [START_REF]See Supplemental Material [url] for (1) direct MD simulations; (2) normal mode decomposition; (3) phonon coher[END_REF]. Figure 1(c) reports the spectral energy at wavevector k = (0,0,0) for a Si NW with a diameter D = 1.5 nm. The fitting is carried out for a specific mode in Fig. 1(d) and the proposed model was found to provide a high accuracy as found in the experimental spectroscopy data of Fig. 1(b), when the coherence effects are considered in the full phonon dynamics. The same model is also applied to study the phonon coherence in two-dimensional NMs, as reported in Sec. S3 of the Supplementary Material [START_REF]See Supplemental Material [url] for (1) direct MD simulations; (2) normal mode decomposition; (3) phonon coher[END_REF]. Figure S2 illustrates how our model can satisfactorily fit the measured Raman scattering data of Si NMs [18].

The estimated phonon lifetimes and coherence times of GaAs NWs are reported in Figs. 2(a) and 2(b), respectively. Lifetimes and coherence times are always close to each other and gradually decrease when frequency increases, which agrees qualitatively well with the general frequency dependence observed in various solids [21,23,42,45]. The acoustic modes (AC) have higher characteristic times than those of confined optical modes (CO) at high frequencies.

We further evaluate the coherence of different modes through the ratio of coherence times to lifetimes, τ c /τ p . This ratio compares the degree of the wavelike behavior to the particlelike one for a specific mode. Figure 2(b) highlights that when comparing the acoustic modes to the confined ones, the wavelike behavior of phonons gradually intensifies. As experimentally confirmed by Kargar et al. [17], those GaAs NWs modes are resulting from a confinement effect, which clearly exhibit a more pronounced coherence as compared to the bulk optical and the low-frequency AC modes. For CO modes, the size of the phonon wavepackets, i.e., the spatial coherence length of phonons l c [23,[START_REF] Latour | [END_REF], along the radial direction is comparable or even larger than the non-periodic dimension, as indicated in Fig. 2(c). Consequently, phonon modes are confined along the diameter direction as stand-ing waves with strong phonon coherence. Constratingly, the wavepackets of AC modes can tilt along any direction and the lengthes l c remain significantly smaller than the size of the non-periodic dimension D, yielding a predominant particlelike behaviour of those modes.

A further implementation of the proposed model to MD simulations is presented in Figs. 2(d) and 2(e). The decreasing trend of phonon lifetimes and coherence times as a function of frequency in the full Brillouin Zone is also obtained in Si NWs as a first validation. For phonons with frequencies below 2 THz, where the acoustic modes are predominant (See Fig. 3(c)), the values of τ c /τ p exhibit an increasing trend with frequency, indicating an enhanced coherence as approaching the confined modes frequency. This outcome qualitatively agrees with the results obtained from the spectroscopy of GaAs NWs.

Note that the full phonon dispersion in Fig. 3(c) contains a large range of modes which yields the scattered data of Fig. 2(e). The average (black line, averaged over frequency intervals) clearly discloses the enhanced wavelike behavior for confined modes in the middle frequency range. In addition, at frequencies above 6 THz, the ratio decreases with frequency, demonstrating that the high- frequency optical phonons resembles to bulk and weakly confined modes, as expected from modes with very small wavelengths.

The phonon confinement effect weakens when size in the confined direction increases, i.e. when diameter and thickness increase in NWs and NMs, respectively. The weakened confinement is also accompanied by a frequency reduction of the confined modes as observed in spectroscopy measurements [17,18] and phonon dispersions of Figs. 3(c) and3(d).

With the spectroscopy data of the GaAs NWs [17], we further estimate the dependence of the wavelike behavior on the diameter from the ratio τ c /τ p . Figure 3(a) reports the decrease of the ratio τ c /τ p with increasing diameter for a confined mode, indicating the suppressed wavelike behaviors due to the weakened phonon confinement effect. The suppressed confinement with increasing thickness is also observed in two-dimensional Si NMs (See Sec. S3 in Supplementary Material [START_REF]See Supplemental Material [url] for (1) direct MD simulations; (2) normal mode decomposition; (3) phonon coher[END_REF]).

We further study the size-dependent wavelike behavior using the MD spectral energy. Figure 3(b) highlights a pronounced impact of the diameter on the times ratio in Si NWs. The increase of τ c /τ p below 2 THz is shifted to a lower frequency as increasing the diameter due to the red-shift of the confined mode frequency (See Figs. 3(c) and 3(d)). Besides the suppression of the wavelike behavior around the frequency of the confined modes, a larger diameter substantially reduces the times ratio in the high frequency range, which might be caused by the stronger boundary scattering [52], yielding the simultaneous decrease of the two characteristic times.

To demonstrate phonon coherence, we further investigate the modal wave information of Si NWs from Lattice Dynamics calculations [53] in Figs. 3(c-e). Figs. 3(cd) indicate that the confined modes around the region of lowest optical modes shift to lower frequencies as the diameter increases from 1.5 nm to 4 nm. In Fig. 3(e), we further compare the eigen-displacements of two kinds of optical modes at different frequencies (See the symbols in Figs. 3(c) and 3(d)), i.e., the confined optical modes in the low frequency region with high coherence, and the bulk optical modes with strong particlelike behavior. The eigen-displacements of the confined modes of the ultra-thin NWs (i.e., D = 1.5 nm) reveal a strong confinement effect (See Fig. 3(e1)), in which the atoms at the four corners are collectively vibrating in phase and clearly interact with the boundary (See Video 1). However, for the D = 4 nm NWs reported in Fig. 3(e3), the in-phase vibrations of the NW lattice cell are still maintained but the interaction with boundary has been partially suppressed (See Video 2), resulting in a weakened confinement effect. The reduced wavelike behavior expressed by the eigen-displacements are well consistent with the estimated lifetimes and coherence times.

On the other hand, the eigen-displacements of the bulk optical modes are also shown in Figs. 3(e2) and 3(e4). Random and disordered vibrations are found for these optical modes which are located in the high frequency Our formalism of mode energy delivers a description of phonon coherence and provides the measurable physical quantity of coherence time using conventional phonon spectroscopy. In the context of previous studies on nanostructures, we have demonstrated the general applicability of our theory in assessing phonon coherence from both experimental measurements and numerical simulations. As a general framework, the developed model is an effective approach for studying phonon coherence in diverse solids and provides a new metric to interpret broadly used spectroscopies.

FIG. 1 .

 1 FIG. 1. (a) The experimental spectrum of GaAs nanowires with a diameter D = 122 nm at the specific wavevector k = (21.8,0,0) µm -1 . (b) The fitting of experimental spectroscopy data with the classical Lorentzian model of Eq. (1) and the proposed one in Eq. (6). The experimental data were previously published by Kargar et al.[17]. (c) The MD spectral analysis of Si nanowires with a diameter D = 1.5 nm at the specific wavevector k = (0,0,0) µm -1 . (d) The fitting of the MD calculated spectral energy with the classical Lorentzian model of Eq. (1) and the one of Eq. (6).

FIG. 2 .

 2 FIG. 2. (a) The estimated lifetimes (τ p ) and coherence times (τ c ) versus frequency obtained from the experimental spectroscopy of GaAs NWs with diameter D = 122 nm. (b) The ratio τ c /τ p versus frequency for GaAs NWs. The AC and CO in (a) and (b) denote normal acoustic and confined optical modes, respectively. (c) A schematic of the different behaviors of AC and CO modes in NWs. lc is the size of the phonon wavepacket along the radial direction. D refers to the nonperiodic (diameter) dimension of NWs. (d) The estimated lifetimes (τ p ) and coherence times (τ c ) versus frequency obtained from the MD spectral energy of Si NWs with diameter D = 1.5 nm. (e) The ratio τ c /τ p versus frequency for Si NWs. The black line in (e) corresponds to the averaged ratio at a given frequency.

FIG. 3 .

 3 FIG. 3. (a) The ratio τ c /τ p versus diameter for the mode of lowest frequency in GaAS NWs. (b) The average ratio τ c /τ p versus frequency for Si NWs with different diameters. The arrow in (b) denotes an increasing trend with diameter. Phonon dispersion of Si NWs with diameters D = 1.5 nm (c) and D = 4 nm (d). (e1-4) Perspective views of the atomic eigen-displacements that correspond to the specific modes in (c) and(d) referred to as symbols. Arrows in (e1-4) denote the atomic vibrational directions.

S3.

  FIG. S2. The fitting of experimental spectroscopy with the classical Lorentzian model of Eq. (1) and with the proposed model of Eq. (6). The experimental spectroscopy data of a Si nanomembrane with thickness 8 nm were previously published by Lee et al.[4].

ACKNOWLEDGMENTS

We would like to thank Prof. Alexander A. Balandin and Prof. Fariborz Kargar of the University of California, Riverside for providing us the experimental spectroscopy data. This project is partially supported by the grants from the National Natural Science Foundation of China (Grant No. 12075168 and 11890703), and Science and Technology Commission of Shanghai Municipality (Grant No. 19ZR1478600 and 21JC1405600). This work is also supported in part by CREST JST (No. JP-MJCR19I1 and JPMJCR19Q3).

Supplementary Material for 'Assessing Phonon Coherence Using Spectroscopy' Zhongwei Zhang, 1, 2 Yangyu Guo, 3 Marc Bescond, 4 Masahiro Nomura, 2 Sebastian Volz, 1, 5, * and Jie Chen All MD simulations are carried out using the LAMMPS package [1] with a time step of 0.35 fs. The Si-Si interactions in silicon systems are modeled by the Stillinger-Weber potential [2]. For the NWs, a sufficient vacuum space (15 Å) is added to the y and z directions, and x direction is simulated with a periodic boundary condition as shown by Fig. S1(a). For the NMs, z direction contains 15 Å additional vacuum space, and x and y directions are simulated with a periodic boundary condition (See Fig. S1(b)). A 100×1×1 and 100×20×1 supercells are, respectively, applied to the MD simulations. After the structure relaxation and thermal equilibration in the isothermal-isobaric (NPT) ensemble for 500 ps, EMD simulations with the microcanonical (NVE) ensemble are performed to record the atomic trajectories.

S2. Normal mode decomposition

The phonon modal velocity υ (k, s) can be expressed as [3]

where ubl (t) is the velocity of the bth atom in the lth unit cell at time t, a is the number of cell, e * (λ) the complex conjugate of the eigenvector of mode λ, and R 0l is the equilibrium position of the lth unit cell. Here, k and s correspond to the mode λ. The spectral energy can be further calculated as

where m is the mass of the Si atom.


David Ropartz

Lery Marion

Mathieu Fanuel

Jasna Nikolic

Murielle Jam

Robert Larocque

Elizabeth Ficko-Blean

Gurvan Michel

Helene Rogniaux
email: helene.rogniaux@inrae.fr

In-depth structural characterization of oligosaccharides released by GH107 endofucanase MfFcnA reveals enzyme subsite specificity and sulfated fucan substructural features

Keywords: Brown algae, GH107, Mass spectrometry, Pelvetia canaliculata, Sulfated fucans

: complete list of oligofucans released at different reaction times with MfFcnA; the species correspond to those plotted on Figures 2 and 3 of the main manuscript.

Figure S1: C-PAGE profile of the digestion products by MfFcnA of FCSPs originating from different sources.

Figure S2: He-CTD spectra recorded for the DP4 and DP6 corresponding to the species: (2.Fuc + 3.S)2 and (2.Fuc + 3.S)3. Figures S3, S4 and S5: Postulated structures for, respectively, the most abundant pure fuco-oligosaccharides (from DP2 to DP6), the most abundant oligofucans containing one hexose (DP6, DP10 and DP12) and containing one pentose (from DP7 to DP13), as well as their possible production by MfFcnA.

Introduction

The extracellular matrix of brown algae represents a rich and abundant source of fucosecontaining sulfated polysaccharides (FCSPs). FCSPs include two families of polysaccharides: sulfated fucans and fucoidans. Sulfated fucans are homopolymers of L-fucose displaying numerous substitutions (e.g. sulfate esters, acetyl groups), while fucoidans are heteropolymers containing sulfated L-fucose but whose main chains are constituted by various neutral and/or uronic monosaccharides [START_REF] Deniaud-Bouët | A review about brown algal cell walls and fucose-containing sulfated polysaccharides: Cell wall context, biomedical properties and key research challenges[END_REF], 2014). The FCSPs extracted from brown algae are heterogeneous and their structure remains mostly uncharacterized. The majority of the available structural knowledge on brown algal FCSPs concerns sulfated fucans. In most Fucales species (including P. canaliculata), sulfated fucans have backbones containing long stretches of alternating α-(13) and α-(14)-L-fucose residues, bearing one sulfate group on the carbon at position C2 and/or C3 [START_REF] Bilan | Structure of a fucoidan from the brown seaweed Fucus evanescens C[END_REF][START_REF] Chevolot | A disaccharide repeat unit is the major structure in fucoidans from two species of brown algae[END_REF][START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF] (Figure 1). In Laminariales, sulfated fucan backbones are only based on α-(13) linked L-fucose residues bearing one or two sulfate groups at C2 and C3 [START_REF] Anastyuk | Structural analysis of a highly sulfated fucan from the brown alga Laminaria cichorioides by tandem MALDI and ESI mass spectrometry[END_REF][START_REF] Nagaoka | Structural study of fucoidan from Cladosiphon okamuranus TOKIDA[END_REF][START_REF] Nishino | Studies on Polysaccharides from Ecklonia-Kurome .2. Structural Characterization of a New Anticoagulant Fucan Sulfate from the Brown Seaweed Ecklonia-Kurome[END_REF][START_REF] Sakai | Structures of oligosaccharides derived from Cladosiphon okamuranus fucoidan by digestion with marine bacterial enzymes[END_REF]. As described by [START_REF] Ale | Fucoidans from brown seaweeds: an update on structures, extraction techniques and use of enzymes as tools for structural elucidation[END_REF] the structure of the polysaccharide strongly varies depending on the seaweed species. The backbone is also subject to modifications such as acetyl groups and/or sidechains of distinct lengths, as well as to variations in the bonding positions or changes in the sugar compositions [START_REF] Yuguchi | Primary structure, conformation in aqueous solution, and intestinal immunomodulating activity of fucoidan from two brown seaweed species Sargassum crassifolium and Padina australis[END_REF].

Because of their chemical diversity, FCSPs have an impressive range of biomedical activities, including anti-oxidative and anti-inflammatory properties [START_REF] Deniaud-Bouët | A review about brown algal cell walls and fucose-containing sulfated polysaccharides: Cell wall context, biomedical properties and key research challenges[END_REF][START_REF] Guerra Dore | A sulfated polysaccharide, fucans, isolated from brown algae Sargassum vulgare with anticoagulant, antithrombotic, antioxidant and anti-inflammatory effects[END_REF][START_REF] Wang | Biological Activities of Fucoidan and the Factors Mediating Its Therapeutic Effects: A Review of Recent Studies[END_REF]. However, the lack of in-depth knowledge of FCSPs structure and the scarce availability of enzymes leading to their deconstruction hamper the full exploitation of those properties. The first fucanase gene (fcnA) was cloned from the marine flavobacterium Mariniflexile fucanivorans [START_REF] Barbeyron | Mariniflexile fucanivorans sp nov., a marine member of the Flavobacteriaceae that degrades sulphated fucans from brown algae[END_REF][START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF]. Its corresponding gene product, referred to as MfFcnA, was shown to be an endo-acting glycoside hydrolase and is the founding member of the GH107 family of the CAZy classification (http://www.cazy.org/) [START_REF] Lombard | The carbohydrate-active enzymes database (CAZy) in 2013[END_REF]. NMR analyses of the major products released from the action of MfFcnA, on the sulfated fucan from Pelvetia canaliculata (Fucales order) revealed that MfFcnA specifically hydrolyses α(14)-glycosidic linkages within the repeating motifs [4)-α-L-fucopyranosyl-2,3-disulfate-(13)-α-L-fucopyranosyl-2-sulfate-(1]n [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF]. The crystal structure of this endo-α-1,4-fucanase (EC 3.2.1.212) was recently determined, revealing a complex modular architecture [START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. The GH107 family catalytic module adopts a (α/β)8-barrel fold and its active site has an open groove topology, consistent with the endolytic character of MfFcnA. The subsites -1 and +1 of MfFcnA are respectively specific for L-fucopyranose-2-sulfate and L-fucopyranose-2,3-disulfate [START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. However, only the most abundant products have been successfully resolved in these two studies [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF][START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF], which is probably an incomplete view of the products actually released.

In this context, the present work used a highly sensitive approach based on ion-pair reversedphase liquid chromatography (IP-RP-LC) hyphenated to high-resolution mass spectrometry (MS) in order to elucidate the low abundance products released by MfFcnA from the sulfated fucan of P. canaliculata. This in-depth structural characterization intended to better describe the structure of sulfated fucans in Fucales. In secondary intention, it allowed to complete the structural knowledge on the substrate specificity of MfFcnA. Hydrolysis kinetics were performed to highlight different potential deconstruction patterns. Some of the products were characterized by tandem MS (MS/MS), using an activation method based on an ion/ion interaction between ionized products and a highly energetic helium cations [START_REF] Li | Charge Transfer Dissociation (CTD) Mass Spectrometry of Peptide Cations: Study of Charge State Effects and Side-Chain Losses[END_REF]. This approach, called Helium charge transfer dissociation (He-CTD), has indeed proven to outperform the more conventional collision activated dissociation (CID) by efficiently fragmenting complex oligosaccharides and preserving labile modifications such as sulfations (Akoumany et al., 2019;[START_REF] Ropartz | Negative Polarity Helium Charge Transfer Dissociation Tandem Mass Spectrometry: Radical-Initiated Fragmentation of Complex Polysulfated Anions[END_REF]Ropartz et al., , 2016b)).

Results

Enzymatic hydrolysis of sulfated fucans by MfFcnA in MS-compatible conditions

Optimal condition for the activity of MfFcnA was previously determined by Colin and coworkers to be the following: 20 mM Tris-HCl pH 7.5; temperature: 20°C (i.e., room temperature) [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF].

However, the production of oligofucans in the above buffer would require a desalting step for subsequent MS analysis, which would cause possible loss of oligosaccharides. Therefore, ammonium bicarbonate was chosen as a buffer solution, since its volatility is compatible with mass spectrometry and its pH value (pH=8) with the enzymatic activity of MfFcnA. The activity of MfFcnA in 50 mM ammonium bicarbonate has been tested on sulfated fucans of P. canaliculata, as well as on sulfated fucans from other sources: the Fucales brown algae Ascophylum nodosum and Fucus vesiculosus, the Laminariales brown alga Laminaria japonica and the sea urchin Paracentrotus lividus. The C-PAGE profiles of the released oligofucans are provided in Supplementary Data (Figure S1). Under these conditions, the oligofucans released by MfFcnA from P. canaliculata have a profile similar to that previously obtained in Tris-HCl buffer [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF]. As expected, MfcnA is also active on the mixed-linked sulfated fucans from other Fucales (A. nodosum and F. vesiculosus) but is inactive on pure α-1,3-linked fucans (L japonica and P. lividus) [START_REF] Berteau | Sulfated fucans, fresh perspectives: structures, functions, and biological properties of sulfated fucans and an overview of enzymes active toward this class of polysaccharide[END_REF][START_REF] Deniaud-Bouët | A review about brown algal cell walls and fucose-containing sulfated polysaccharides: Cell wall context, biomedical properties and key research challenges[END_REF].

Exploration of the oligofucans released at different digestion times by MfFcnA

The oligofucans from P. canaliculata released by MfFcnA were analysed in depth by IP-RP-LC-MS.

In order to explore the kinetics of the enzymatic reaction, four time points were chosen for the digestion: T=0H, 1H, 16H and 5 Days. The longer times of reaction (i.e., T=16H and 5 Days) aimed to maximise the degradation of the sulfated fucans by MfFcnA, including cleavage of "non-ideal" patterns-in other words, not strictly composed of an alternation of [4)-α-L-fucopyranose-2,3disulfate-(13)-α-L-fucopyranose-2-sulfate-(1] motif-that possibly exist in the heterogeneous polysaccharide. Thus, the aim was to increase the chemical diversity of the released oligofucans. The time point T=0H, in which the boiled enzyme was introduced with the sulfated fucans, was used as a control. As expected, no oligofucans were detected for T=0H (data not shown), meaning that all products detected for other time points were produced by the action of MfFcnA.

With the aim to provide an efficient representation of the results, that keeps the comprehensiveness of the data while allowing an easy comparison of samples, results are presented in the form of graphs. The graphs plot the degree of sulfation (DS) divided by the degree of polymerization (DP) (i.e., DS/DP) as a function of the DP. This allows visualizing the oligosaccharide structures of a given family (in term of monosaccharide composition) independently of the sulfation degree. The surface area of the sphere in the graph is proportional to the ion intensity measured in MS for the different species, and has been normalized so that areas can be compared among graphs of a same figure. The complete list of the reaction products identified by MS is available in Supplementary Data (Tables S2, S3 andS4). At this stage, structure assignment was made solely based on the mass measured for the molecular species and knowledge of the most common building blocks composing oligofucans (Figure 1). Eventual isomers have been grouped under the same bubble.

Ideal structural patterns among oligofucans

In a first step, we focused on the "ideal" structures described in the literature as composing the backbone of sulfated fucans from Fucales species, i.e., a repeating unit of [4)-α-L-fucopyranose-

(13)-α-L-fucopyranose-(1]
. This is expected to lead to three possible disaccharide moieties (A-, Bor C-type) depending on the number of sulfates brought by the fucosyl residues, as represented in S2.

After one hour of enzymatic degradation, the major products correspond to oligosaccharides built from the ideal C-type moiety (2.Fuc + 3.S), with DP ranging from 4 to 20 (Figure 2). The most intense species corresponds to a molecule with 10 fucoses and 15 sulfates (DP of 10 and DS/DP of 1.5) and has a measured intensity of 1.67e6. This intensity accounts for about 30% of the total intensity measured for the oligofucans, after one hour of digestion with MfFcnA. The ionic species detected in MS, at a mass-to-charge ratio (m/z) of 1296.12, was a triply charged ion of the type [M-15.H+12.HxA] 3-, where HxA stands for hexylammonium (C6H16N + , 102.13 Da) and comes from the ion-pairing agent used for the LC separation. A very small amount of DP2 with DS/DP of 1.5 (pure C-type motif) was also detected (measured intensity of 3.38e3), as well as small amounts of oligofucans with DS/DP < 1.5 (DP4 to DP8, with an intensity of the magnitude order of 1e3), which likely derive from a combination of typical building blocks (for example, 1.B + 1.C leads to DP4 with DS/DP=1.25).

The structural patterns of the oligofucans released after 16H and after 5 Days are rather similar, but differ significantly from the situation at 1H. The species with a DS/DP = 1.5 have all shifted towards lower DPs. The major species now corresponds to a DP4, composed of two C-type moieties (i.e., 4.Fuc + 6.S). The intensity of the DP2 species corresponding to the pure C-type motif notably increased and reached 4% of the total species after 5 Days. Finally, several species with more heterogeneity in terms of degree of sulfation became significantly present (all with DS/DP < 1.5). Some may correspond to pure motifs, although it cannot be excluded that they encompass a combination of other blocks. For instance, the DP8 with DS/DP =1 may arise from pure B-type pattern [(2.Fuc + 2.S)4], but may also be formed by two A-type moieties and two C-type moieties [(2.Fuc + 1.S)2-(2.Fuc + 3.S)2]. Notably, no species could be detected corresponding to pure A-type pattern (2.Fuc + 1.S, DS/DP = 0.5) and most of the species detected can be explained by combining only B-type and C-type moieties. The species with a DP of 4 and a DS/DP of 1.75 contains 7 sulfates, necessitating that one moiety (2.Fuc) bears 4 sulfates, which does not correspond to an "ideal" block.

Oligofucans with divergent structures

Beyond the ideal moieties of A-, B-and C-type discussed above, the LC-MS analysis demonstrated the production, in the digested samples, of some oligofucans containing non-fucosyl residues.

Precisely, these oligofucans contain glycoside residues whose masses correspond to regular hexosyl (i.e., not deoxyhexosyl) or to pentosyl residues. The interpreted results are presented in Figure 3 for the three time points of the kinetics. Supplementary Tables S3 andS4 At the time point T=1H (Figure 3), only a few species were apparent, all with a low intensity: two species bore one pentose, DP11 and DP13, while seven contained an additional hexose other than fucose, DP6, DP10 and DP12. Two of the identified species with one hexose have a DS/DP between 1.2 and 1.5. For instance, the species of DP10 with a DS/DP of 1.5 encompass 9.Fuc + 1.Hex + 15.S. In other words, this species could fit with five C-type blocks, in which the hexose would replace the fucose in one block and bear one to two sulfate groups. Species that contain a pentose are less sulfated (DS/DP < 1.2). At T=16H, more species containing hexose or pentose in the oligofucans appeared, in the range of DP6 to DP14.These species had increased intensity compared to the 1H time point, especially those corresponding to the less sulfated species (DS/DP < 1.4). Conversely, the species which contain one hexose and a higher DS/DP (between 1.4 and 1.5) remained more or less stable in intensity between T=1H and T=5 Days. For the products containing a pentose, the species identified at T=1H showed an enhanced intensity and many species with low sulfation degrees emerged (DS/DP < 1.1). At T=5 Days, intensities of the released products from both families (hexose or pentose) did not evolve compared to T=16H, with the exception of two species of DP10 (DS/DP = 1.3 and DS/DP = 1.2). Interestingly, all species with one hexose exhibit an even DP while all species with one pentose exhibit uneven DPs and relatively low DS/DP ratios.

In the next stage, a deeper characterization of selected representative structures of oligofucans produced by MfFcnA was performed using He-CTD MS/MS.

Structural study of released oligofucans

In order to determine the exact structure of some oligofucans and refine the substrate specificity of MfFcnA, four representative structures produced from MfFcnA digest of sulfated fucans were structurally studied by He-CTD MS/MS, without and with 18 O-labelling of the reducing end, as well as in positive and negative ionisation modes. The 18 O-labelling specifically targets the hydroxyl group at the reducing end of the oligosaccharide. It intends to break the glycoside symmetry and thus, leads to the differentiation of the non-reducing and reducing ends isobaric fragments (since all reducing end fragments will be shifted by 2 Da). This strategy allows for directional sequencing of the oligosaccharides and thereby, is a means of consolidating the interpretation of the fragments observed and of assembling the full-length oligosaccharide structure. Only the results obtained on the 18 O-labelled structures in positive ionisation mode are presented. MS/MS fragmentation by He-CTD is favoured for its ability to obtain an extended fragmentation of oligosaccharides above DP8 and, importantly, to preserve labile functions-including sulfate groups-as established previously in our group (Akoumany et al., 2019;[START_REF] Ropartz | Negative Polarity Helium Charge Transfer Dissociation Tandem Mass Spectrometry: Radical-Initiated Fragmentation of Complex Polysulfated Anions[END_REF]Ropartz et al., , 2016b)). The latter is a key point for the structural analysis of complex sulfated carbohydrates, such as those in algae, which overcomes the limitation of collisionally induced MS fragmentation (CID) (Ropartz et al., 2016b).

Four selected candidates for He-CTD MS/MS investigation were chosen. Two from the oligofucans composed of pure C-type moieties in order to confirm those structures, which have been previously characterized by NMR [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF][START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. Two from the oligofucans exhibiting a pentose or a regular hexose (i.e., a non deoxy-hexose), to investigate whether these monosaccharides are found in the backbone or on lateral branch points and if they bear a sulfate group.

Concerning the C-type structural patterns, we isolated one DP4 (4.Fuc + 6.S) as [M-6.H+8.HxA] 2+ ion at m/z 947.5, and one DP6 (6.Fuc + 9.S) as [M-9.H+11.HxA] 2+ ion at m/z 1365.2. Figure 4 gives the structures that could be deduced for both DPs from the He-CTD spectra, with an annotation of the fragments that led to unambiguously establish those structures (the spectra are available in Supplementary Data, Figure S2). For the DP4, we obtained a complete series of 1,5 Xn, Yn and Zn and of Cn and Bn fragments. The Yn and Zn fragments, which contain the reducing end, were shifted by 2 Da due to the heavy oxygen labelling and could thus be differentiated from possible isobaric Bn and Cn fragments. For the DP6, the fragmentation pattern was less comprehensive than for the DP4. However, at least one specific fragment could be identified between each subunit. In both cases, the reducing end consisted of a mono-sulfated fucosyl residue while a di-sulfated fucose was found at the nonreducing end. The result showed a strict alternation between mono-and di-sulfated fucoses along the backbone. Thus, the fragmentation profiles of both oligosaccharides were in agreement with the ideal pattern of C-type disaccharides, as well as with the expected enzyme specificity, described as cleaving the α(14)-glycosidic linkages within the repeating motifs [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF].

[4)-α-L-fucopyranosyl-2,3-disulfate- (13)-α-L-fucopyranosyl-2-sulfate-(1]n
The next representative structure of oligofucans released by MfFcnA that was selected for a deeper structural investigation by He-CTD was a DP6 bearing one hexose (5.Fuc + 1.Hex + 8.S). It was isolated as [M-8.H+10.HxA] 2+ ion at m/z 1282.6. Figure 5 shows the fully interpreted He-CTD spectrum as well as the annotated structure. For clarity, only the specific fragments discussed below were annotated on the structure. The fragmentation spectrum highlighted different interesting features.

Considering the 1,5 X1 (m/z 477.2) and Y1 (m/z 449.2), it could be deduced that the structure has a monosulfated fucose at the reducing end. From the other end, two ions (m/z 628.1 and m/z 610.1) were identified as C1 and B1 fragments and placed a di-sulfated fucose residue at the non-reducing end. Two fragments at m/z 809.2 and 791.2 were found to be specific of this species (i.e., not measured for the C-type structures solved before). Their masses correspond to a trisulfated fucose with four HxA counter-ions. These ions did not shift upon 18 O labelling, which indicates that they do not include the reducing end. In parallel, the 18 O-labelled fragments at m/z 1447.5 and 1463.6, attributed respectively to a Z2 and Y2" fragments, included the trisulfated fucose while the Y1 fragment (m/z 449.2) did not.

The mass difference between these two series correspond to two fucoses, four sulfates and four HxA.

Overall, these fragments positioned a trisulfated fucose as a laterally branched moiety on the second residue from the reducing end. One sulfate group is found as well on the same fucosyl residue.

Nonetheless, the exact positioning of the trisulfated fucose and of the sulfate group remains uncertain (either C2 or C3). The two fragments at m/z 809.2 and 791.2 were indicated with a Greek letter α in the mass spectrum (Cα and Bα, respectively).

Concerning the hexose, a set of fragments lead us to propose that the hexose is laterally branched on the second residue from the non-reducing end (Figure 5). These fragments are the following: m/z 1116.5 (2.Fuc + 3.S + 1.Hex + 4.HxA) and m/z 628.1 (1.Fuc + 2.S + 3.HxA). Both contain the non-reducing end, as they do not shift upon 18 O-labelling, and were interpreted as C2 and C1 fragments. In accordance with the proposed structure, losses of 162 Da (corresponding to the loss of a hexose) are clearly visible on the mass spectrum from C2 (and also C3) but not from C1. The m/z 1953.8 (4.Fuc + 6.S + 1.Hex + 7.HxA) and the corresponding doubly-charged ion at m/z 1028.4, and the m/z 1463.6 (3.Fuc + 5.S + 6.HxA) were interpreted as Y3 • , Y3 2+ and Y2" and all corroborated the above hypothesis; in particular, a loss of 162 Da was observed for Y3 2+ but not for Y2". For clarity, the complementary Z and B fragments were not mentioned above although they were observed on the mass spectrum and confirmed the proposed structure. Notably, the concomitant observation of 162 Da losses from the m/z 1936.8 (Z3) and m/z 1116.5 (C2) cannot be explained if the hexose is in the backbone. Due to significant noise in the low mass region, the He-CTD acquisition started at m/z 300 and thus, the m/z 282.2 corresponding to [1.Hex + 1.HxA] + could not be detected. The interpreted fragments leaves an ambiguity on the exact positioning of the hexose, either on the C2 or on the C4 of the second fucosyl residue from the nonreducing end.

The last structure selected for fragmentation was a DP9 oligofucan with one pentose (8.Fuc + 1.

Pen + 8.S), isolated as [M-8.H+10.HxA] 2+ ion at m/z 1486.76. (m/z 1587.6) and B2 (m/z 1260.6) show that the third and fourth residues from the reducing end correspond to two singly sulfated fucans, thus typically a B-type block. On the other end of the structure, two doubly charged fragments (Y5 2+/• at m/z 1232.5 and Z5 2+ at m/z 1223.6) and two singly charged fragments (C1 at m/z 628.4 and B1 at m/z 610.4) indicate the presence of a doubly sulfated fucose at the non-reducing end. This leaves three fucoses, one pentose and one sulfate group to be positioned in-between this fucosyl residue and the "B-type block -C-type block" sequence of the reducing end. Two fragments, at m/z 725.2 and m/z 707.4, were found to be specific of this structure (i.e., not observed in the He-CTD spectra of other structures). These fragments match with the singlycharged trisaccharide: [2.Fuc + 1.S + 1.Pen + 1.HxA] + . Our hypothesis is that this chain is branched laterally on the second fucose residue from the non-reducing end, which led us to annotate the aforementioned fragments as being Cα and Bα. This interpretation is corroborated by the observation of the fragments at m/z 1918.5, 1428.5, 1101.6, 1083.5, 774.4, 766.4, which all fit with a loss of 605.2 Da (corresponding to 2.Fuc + 1.S + 1.Pen + 1.HxA) from the B5, C4, C3, B3, C2, B2 ions respectively. In addition, the Y5 fragment, detected at m/z 1232.5 as a doubly charged ion, exhibited a loss of 605.2 Da, as evidenced by the singly charged fragment at m/z 1656.9. The exact positioning of the trisaccharidic lateral chain may be on the C2 or C4 position of the fucosyl subunit.

Discussion

The present work provides an in-depth structural characterization of the oligosaccharide products released by MfFcnA from sulfated fucans extracted from P. canaliculata. The primary goal of this study was to improve the structural knowledge of sulfated fucans in Fucales. In secondary intention, our results allowed to refine the fine substrate specificity and mode of action of MfFcnA, first member of the GH107 family. The study was performed at different kinetics time points: from 1H to 5 Days. Longer kinetics aim to promote the degradation of the polymer, including that of non-preferential patterns.

At short times of reaction (T=1H), MfFcnA produces a majority of oligosaccharides with a DS/DP of 1.5, which fit with the pure C-type motif (α-L-fucopyranose-2,3-disulfate-(13)-α-L-fucopyranose-2sulfate). These species represent 99% of the released oligofucans at 1H. When the reaction goes further (T=16H and more), the prominent product in the mixture is the DP4 with a DS/DP=1.5, corresponding to two C-type units. This structure was also the major product found in previous studies using NMR [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF][START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. It confirms the strong preference of MfFcnA for cleaving the α-(14)-glycosidic linkage within repeating motifs of the type:

[4)-α-L-fucopyranosyl- 2,3-disulfate-(13)-α-L-fucopyranosyl-2-sulfate-(1]n.
The main oligofucan species produced by MfFcnA (referred to as "classical species") contain 47 % (w/w) of sulfate groups, which is in agreement with previous results [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF]. Previous research on intact fucans from P. canaliculata have shown that different fucan fractions from this species contain between 29-40 % (w/w) of sulfate groups [START_REF] Descamps | Isolation and Culture of a Marine Bacterium Degrading the Sulfated Fucans from Marine Brown Algae[END_REF][START_REF] Mabeau | Fractionation and analysis of fucans from brown algae[END_REF][START_REF] Ponce | A Comprehensive and Comparative Analysis of the Fucoidan Compositional Data Across the Phaeophyceae[END_REF]. Thus, the main oligofucan species produced by MfFcnA are significantly more sulfated compared to the intact fucan fractions. This suggests that MfFcnA degrades in priority the highly sulfated domains in the sulfated fucan chain.

The sensitivity of the analytical method employed in the present study, as well as its capacity of resolving a high molecular complexity, revealed a much wider chemical diversity of products released by MfFcnA, especially for longer times of reaction. Our analyses revealed a variety of oligofucans that do not match with pure C-type motifs (DS/DP < 1.5). Overall, these species contribute to a significant proportion of the released products, representing approximately 25% of the oligofucan products after 5 Days of degradation. Most of them can be explained by combining C-and B-type blocks, although a contribution of A-type block cannot be excluded. Notably, many species are less sulfated in comparison to pure C-type motifs (i.e., they contain less than three sulfate per two fucose residues), suggesting a tolerance of MfFcnA for substrates with lower sulfation degrees. Mass spectrometry is known to promote desulfation in the gas phase. However, this effect is reduced here thanks to the protecting effect of the ion-pairing reagent (HxA) which binds to each sulfate group. Also, species differing by their sulfation status exhibited different retention times in LC, which proves that the difference in their number of sulfates was not induced by the mass spectrometry process.

One striking result of this study concerns the complex, branched structures, which were evidenced among the released oligofucans. These structures are not composed solely of sulfated fucoses, i.e., of deoxyhexoses. Their mass indicates that they also include either one pentose or one "regular" hexose. These species were mostly produced after long reaction times with MfFcnA (T=16H and longer). Even if they exhibit a lower abundance than the pure fucose-containing oligosaccharide products (about 10 to 50-fold on average), they are diverse in terms of DP and DS and are significantly represented in the reaction medium. Indeed, they account for 5% and 9% and of the oligofucans released by MfFcnA after 5 Days, for the pentose and "regular" hexose containing species, respectively. The presence of hexoses (Gal and Man) and pentoses (Xyl), was corroborated by a compositional analysis of the starting material and represents around 20% in dry weight (data not shown). It also agrees with previous research on P. canaliculata sulfated fucans. Notably, intact sulfated fucans contained 81% Fuc, 9% Xyl, 7% Gal, 2% Man and 1% Glc [START_REF] Mabeau | Fractionation and analysis of fucans from brown algae[END_REF]. The oligofucans released by the extracellular enzymatic fraction from M. fucanivorans contained about 84% Fuc, 6% Xyl, and 10% Gal, as well as traces of Man and Glc (Descamps, 2006). These data suggest that the hexose detected in the present study corresponds most likely to Gal, while the detected pentose corresponds to Xyl, which is the only pentose found so far in P. canaliculata sulfated fucans [START_REF] Descamps | Isolation and Culture of a Marine Bacterium Degrading the Sulfated Fucans from Marine Brown Algae[END_REF][START_REF] Mabeau | Fractionation and analysis of fucans from brown algae[END_REF].

Interestingly, all species bearing one hexose display even DPs, whereas species bearing one pentose have odd DPs. Furthermore, the oligosaccharides bearing one hexose have higher DS/DP than the ones bearing one pentose. Prima facie, this initially suggested that the pentose might be a nonsulfated laterally branched residue, whereas the hexose might replace one of the fucosyl residues in the backbone and be sulfated. The structural examination of two selected structures using He-CTD tandem MS has discarded this interpretation. In fact, both the hexose and the pentose are branched laterally on the fucosyl main chain. The hexose was established as a single residue branched on a mono-sulfated fucose (Figure 5). The pentose was found to be part of a longer trimeric chain, which comprises two fucosyl residues along with one pentose (Figure 6). This trisaccharide branched on the backbone leads to an oligosaccharide of uneven DP. Another finding of these structural analyses is the existence, in the hexose-containing species, of a trisulfated fucosyl residue branched laterally on a nearby backbone fucose (Figure 5). The two laterally linked residues (i.e., the hexose and the trisulfated fucose) restore parity in the number of residues, leading to even DPs of hexose-containing oligofucans. The occurrence of such trisulfated fucose has been evidenced in the context of fucoidans isolated from the brown alga Saccharina latissimi (formerly Laminaria saccharina) [START_REF] Bilan | Further studies on the composition and structure of a fucoidan preparation from the brown alga Saccharina latissima[END_REF].

Overall, our results suggest a much wider tolerance of MfFcnA than previously described (Colin et al., 2006;[START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. The large amount of DP4 produced (4.Fuc + 6.S) leads us to propose that the active site of MfFcnA is symmetric and comprises eight subsites. This hypothesis is consistent with the length and the topology of the active site identified in the crystal structure of MfFcnA [START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. Also, there seems to be a strong constraint for a pure C-type motif in subsites -1/-2 and +1/+2 as all the species produced with a DP of 4 have at least one C-type moiety. This finding agrees with the specificity of subsites -1 and +1 of MfFcnA for L-fucopyranose-2-sulfate and L-fucopyranose-2,3-disulfate, as described earlier [START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. Subsites -3/-4 would have tolerance for lesssulfated moieties while subsites +3/+4 could be left empty. This corresponds well with the observation of a DP4 with a DS/DP=1.25, which would correspond to a "B-type block -C-type block" sequence, as well as with the observation of the DP2, which is produced only as a pure C-type unit. The above hypothesis on the subsite tolerance of MfFcnA fits well, for instance, with all the DP6 oligofucans observed in Figure 2. The DP6 with DS/DP=1.5, which is made of pure C-type units, would place a Ctype block in subsites -1/-2 and a C-type unit in subsites -3/-4 (Supplementary Data, Figure S3). The DP6 with DS/DP=1.33 (8.S), which fits with two C-type blocks and one B-type block, would have the Ctype block in subsites -1/-2, and either a B-or a C-type unit in subsites -3/-4. The DP6 with DS/DP=1.17 (7.S), which fits with two B-type blocks and one C-type block, would have a C-type block in subsites -1/-2 and a B-type block in subsites -3/-4. Finally, the DP6 with DS/DP=1 (6.S), which fits with one A-, one B-and one C-type block, would have the C-type block occupying subsites -1/-2 while the B block would be in subsites -3/-4. A synthesis of the above discussion about MfFcnA subsites is presented in Considering the oligofucan structures containing one hexose, the DP10 forms are produced first (T=1H) and become prominent at longer times of reaction (T=16H and longer). They represent 56% of the oligofucans with one hexose after 5 Days. From the structure resolved by tandem MS for the DP6, we postulate the following structure for the most abundant species (DP10, 12.S) from the nonreducing end: one C-type block with a laterally branched hexosyl residue, one A-type block with a laterally branched trisulfated fucose, one B-type block and one C-type block (Supplementary Data, Figure S4). This would place the C-type unit in subsites -1/-2 and a B-type block in subsites -3/-4. This structure makes any further degradation by MfFcnA difficult, which fits with the fact that it becomes the prominent product after 16 hours of reaction. The DP8 species, which are detected after longer reaction times (T=16H and longer) and with lower abundance (they account for 8% of the oligofucans with one hexose after 5 Days), are relatively more sulfated (9.S, 10.S, 11.S; DS/DP of 1.12, 1.25 and 1.37, respectively) compared to the DP10. One hypothetical structure of the DP8 with 10 sulfates, which fits with the subsites specificities of MfFcnA, is proposed in Figure S3. This structure could arise from a DP12 (16.S) from a cleavage between two C-type moieties. The DP6 (8.S), which has been resolved structurally by He-CTD MS, suggests that the trisulfated fucose, and possibly the fucosyl with a lateral hexose, could be accommodated in the active site of MfFcnA (Supplementary Data, Figure S4). However, these DP6 species are much less abundant than the DP10 or DP8 described above.

Finally, the species bearing one pentose are detected after longer reaction times. They remain at a stable but relatively low abundance between T=16H and 5 Days. Altogether, these species represent 5% of the oligofucans released by MfFcnA after 5 Days. The smaller DP observed for these species is a DP7. In contrast to the structure resolved for the DP9, in which the pentose was linked to the fucosyl backbone as part of a trimeric chain (see Figure 6), structural analysis of the DP7 showed branching of the pentose as a single residue on the backbone (data not shown). We postulate that the pentosecontaining species that are detected in Figure 3 share a backbone of six to eight fucosyl residues. The pentose is linked directly to the second fucosyl residue from the non-reducing end of the oligofucan either as a single residue, or as part of a longer chain. The different DPs observed in Figure 3 would arise from this lateral chain elongating by further addition of di-fucosyl blocks (i.e., 0 for DP7, 1 block for DP9, 2 blocks for DP11) (Supplementary Data, Figure S5). All the species detected with one pentose can be rationalized considering the subsite specificities proposed for MfFcnA in Figure 7. Precursors are sulfated fucans with a side chain containing the pentose, the pentose being the branching point.

The side chain can be relatively short and composed of A-type, B-type or C-type di-fucosyl units (Supplementary Data, Figure S4). It could also be much longer and itself constitute another polysaccharide chain. In any case, our data suggests that the side chain containing the pentose must be located at the non-reducing end of the precursor polymer.

In conclusion, a fine structural analysis on the products released from the sulfated fucans of P. canaliculata by the endo-α-1,4-fucanase MfFcnA, the first characterized member of the GH107 family, has been undertaken. The analytical strategy used mass spectrometry coupled with ion-pair reversedphase liquid chromatography (IP-RP-LC) and tandem MS by Helium-Charge Transfer Dissociation (He-CTD). This very sensitive and comprehensive approach revealed greater complexity in the structures released by MfFcnA than the expected strict alternation of ideal patterns, consisting of single and double sulfated fucosyl residues [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF][START_REF] Vickers | Endo-fucoidan hydrolases from glycoside hydrolase family 107 (GH107) display structural and mechanistic similarities to -l-fucosidases from GH29[END_REF]. In particular, the analyses showed the presence of glycosyl-residues other than fucose in the reaction products; more precisely, we found oligofucans containing either one hexose (probably Gal or Man) or one pentose (probably Xyl). Structural determination demonstrated a lateral branching for these non-fucosyl residues. The hexosyl residue is always found with a neighbouring trisulfated fucose, which could suggest that this motif serves a signalling function for the alga. The pentose appears to be the branching point of a lateral chain made of sulfated fucoses. Our data suggests that this chain is located at the non-reducing end of the polymer and we hypothesize it develops as a fucan chain itself.

The heterogeneity found in sulfated fucans of P. canaliculata agrees with some recently published extensive analyses of the composition of sulfated fucans from brown algae of the order Fucales [START_REF] Ponce | A Comprehensive and Comparative Analysis of the Fucoidan Compositional Data Across the Phaeophyceae[END_REF]. The specialized fucan structures discovered in the present study contribute to the complexity of the polymer and are likely important in protection against degradation by marine microbial pathogens. In addition, our study revealed the interesting ability of MfFcnA to recognize different patterns within sulfated fucans. This flexibility suggests an adaptation of marine bacteria to the significant heterogeneity of sulfated fucans. The result, as shown here, is the release of structurally diverse oligofucans that potentially could be screened for bioactivities.

Materials and Methods

a. Chemicals

Hexylamine 99% (HxA) was purchased from Sigma-Aldrich Co. (Saint Quentin Fallavier, France).

Acetic acid 98% was from Fluka (purchased by Sigma-Aldrich Co., Saint Quentin Fallavier, France). HPLC-grade acetonitrile (ACN) was purchased from Carlo-Erba Reagents (Val de Reuil, France).

Ultrapure water was obtained from a Milli-Q apparatus (Millipore).

b. Preparation of sulfated fucans from P. canaliculata Multiple individuals of P. canaliculata were collected from rocky shore of Moguériec, France.

Collected algae were washed with tap water, and dried overnight at 50˚C. Dry algal material (430 g) was milled into powder. Afterwards, alcohol insoluble residue (AIR) was prepared according to the modified protocol by Salmeán and coworkers [START_REF] Salmeán | Double blind microarray-based polysaccharide profiling enables parallel identification of uncharacterized polysaccharides and carbohydrate-binding proteins with unknown specificities[END_REF]. AIR was soaked during 75 min at RT in water acidified with H2SO4 (pH 2.9) (1:15, w/v). Sulfated fucans extraction and purification were performed according to the modified protocol by Kloareg and co-workers (KLOAREG et al., 1979).

Briefly, extraction was done for 30 min at 98˚C under mechanical stirring. Raw algal extract was centrifuged (30 min, 14000 g, RT), and the supernatant was collected. Remaining precipitate was used for one re-extraction, and the raw re-extract was clarified under the same conditions. Raw extract and re-extract were treated separately. The pH was adjusted to 6.25, and co-extracted alginate was precipitated by the addition of 2M CaCl2 to a final concentration of 2% CaCl2 (w/v). Alginate was removed by centrifugation (20 min, 14000 g, RT) and the supernatant was collected. Cold 96 % (w/w) ethanol was added to obtain a final ethanol concentration of 70% (w/w) and left overnight at 4˚C. Precipitated sulfated fucans were pelleted by centrifugation (20 min, 14000 rpm, 4˚C). The pellet was solubilized in a minimal volume of water and dialyzed against water using CO 12-14 kDa (Sigma Aldrich) to remove remaining salts, oligosaccharides and any low-molecular weight compounds. Desalted samples were freeze-dried. The sulfated fucans from the first extraction and the re-extraction were denoted as E and R fractions, respectively. The current study used the sulfated fucans from the R fraction only.

c. Cloning and overproduction of the recombinant endo-fucanase MfFcnA

For production of MfFcnA, the fcnA gene [START_REF] Colin | Cloning and biochemical characterization of the fucanase FcnA: definition of a novel glycoside hydrolase family specific for sulfated fucans[END_REF] Escherichia coli BL21 (DE3) expression strain. Protein production was done at 20°C in 1 L of autoinduction ZYP 5052 medium [START_REF] Studier | Protein production by auto-induction in high-density shaking cultures[END_REF] supplemented with 100 µg/ml ampicillin. Cells were harvested after 72 hours by centrifugation (15 min, 8000 g, 4˚C). Cell harvesting was followed by chemical lysis [START_REF] Ficko-Blean | Biochemical and structural investigation of two paralogous glycoside hydrolases from Zobellia galactanivorans: novel insights into the evolution, dimerization plasticity and catalytic mechanism of the GH117 family[END_REF]. Clarified cell lysate was loaded onto an immobilized metalaffinity chromatography (IMAC) column (5 ml His Trap GE Healthcare) and unbound protein fraction was removed by washing with binding buffer (20 mM Tris-HCl, 500 mM NaCl, 20 mM Imidazole, pH 7.6). Bound proteins were eluted using a linear gradient 0 to 100 % of elution buffer (20 mM Tris-HCl, 500 mM NaCl, 500 mM Imidazole, pH 7.5). Collected MfFcnA purified protein fractions were pooled and further purified by size-exclusion chromatography (125 ml Superdex 200) using an isocratic gradient (20 mM Tris-HCl, 500 mM NaCl, pH 7.5). Purity of the protein was confirmed by SDS PAGE analysis on a 12 % polyacrylamide gel.

d. Hydrolysis of sulfated fucans using MfFcnA

Prior to enzymatic digestion, the purification buffer solution of MfFcnA was exchanged against 50 mM ammonium bicarbonate using Amicon ultra device (cut-off at 30 kDa were done overnight (16H) in 50 mM ammonium-bicarbonate at room temperature (R.T., 20˚C).

MfFcnA concentration in each of the reaction mixtures was 0.05 mg/mL. Following the digestion, 1 µL of each digestion mixture was applied onto carbohydrate polyacrylamide gel electrophoresis (C-PAGE) according to the protocol of Zablackis and Perez [START_REF] Zablackis | A Partially Pyruvated Carrageenan from Hawaiian Grateloupia-Filicina (cryptonemiales, Rhodophyta)[END_REF], with 4 % stacking and 27 % resolving polyacrylamide gels. For mass spectrometry analyses, digestions of 2 % (w/v) fucans from P. canaliculata (R fraction) were done in 50 mM ammonium bicarbonate at 20 °C (R.T.). MfFcnA concentration in the reaction mixture was 0.05 mg/mL. Released products were recovered at different times: T=0H corresponds to incubation with the boiled enzyme; 1H; 16H; and 5 Days. Enzymatic digestions were stopped using thermal denaturation (10 min at 95°C).

e. Heavy oxygen labelling of oligofucans

Prior to tandem MS experiments, samples at 0.2% (w/v) in 50 mM ammonium bicarbonate were vacuum dried at room temperature in using a speed vacuum concentrator system. The reducing ends set at 10 ms. The CTD beam at 6 kV was pulsed during 100 ms per scan. Data were recorded for 5 min, over m/z range of 300 -2200. The sample were infused at a flow rate of 10 µL/min. Raw data were converted into mzML format using MSConvert and processed with mMass 5.5.0 [START_REF] Niedermeyer | mMass as a Software Tool for the Annotation of Cyclic Peptide Tandem Mass Spectra[END_REF]. Peak picking was performed using a signal-to-noise threshold of 5 and a minimum relative intensity of 1%. Fragment peaks were annotated according to the nomenclature of Domon and Costello [START_REF] Domon | A systematic nomenclature for carbohydrate fragmentations in FAB-MS/MS spectra of glycoconjugates[END_REF]. Legend :

Figure 1 .

 1 Figure 1. Figure 2 displays the LC-MS results after 1H, 16H and 5 Days of degradation by MfFcnA. All

  provide the complete list of species with their measured intensities. The additional pentosyl or hexosyl residues have been included in the computation of the DP. Note that the species represented in Figure 3, on average, exhibit a 10-fold lower intensity than the "ideal" oligofucans represented in Figure 2. After 5 Days, the oligofucans bearing non-fucosyl residues represent 14% of the oligofucans released by MfFcnA from P. canaliculata sulfated fucans.

Figure 6

 6 shows the fully interpreted He-CTD spectrum as well as the annotated structure. The 1,5 X1 (m/z 477.2), Y1 (m/z 449.2) and Y2 (m/z 957.5), demonstrate the presence of a classical C-type moiety at the reducing end (α-L-fucopyranose-2,3-disulfate-(13)-α-L-fucopyranose-2-sulfate). The C5 2+ and B4 fragments (respectively at m/z 1323.2 and m/z 1914.6) validate this part of the structure. Considering the series of B fragments, B3

Figure 7 .

 7 Figure 7.

Figure 1 .

 1 Figure 1. Typical building blocks found in FCSPs from Fucales (including P. canaliculata), bearing one,

Figure 2 .

 2 Figure 2. Oligofucans released by MfFcnA represented by their DS/DP as a function of their DP, for

Figure 3 .

 3 Figure 3. Oligofucans released by MfFcnA represented by their DS/DP as a function of their DP, for

Figure 4 .Figure 5 .

 45 Figure 4. Annotated structures of two oligofucans released by MfFcnA, which masses fitted with an

Figure 6 .

 6 Figure 6. He-CTD mass spectrum of the 18 O-labelled DP9 oligofucan with one pentose (8.Fuc + 1. Pen + 8.S) isolated for fragmentation as [M-8.H+10.HxA] 2+ at m/z 1486.8. Lower panel (left): annotated

Figure 7 .

 7 Figure 7. Schematic representation of the subsite-binding specificity in the catalytic cleft of MfFcnA.

  Figure 2.

  Figure 3.

  Figure 4.

  Figure 5.

  was cloned as described by Groisillier

	and	coworkers	(Groisillier	et	al.,	2010)		using	the	forward	primer
	AAAAAAAGATCTCAAGTACCAGATCCAAACCAAGGA	and	the		reverse	primer
	TTTTTTCAATTGTTAATTTCCATCACTAATAATAGTTGCAATT.	Plasmid DNA was transformed into

Acknowledgements

This work was supported by the French National Research Agency with regard to the investment expenditure program Breaking Alg (grant ANR-18-CE43-0003-01). We would also like to thank Prof.

Patrick Cormier for his kind gift of P. lividus fucans.

of the oligosaccharides were 18 O-labeled by suspending the dried material in 50 µL of H2 18 O. Incubation was allowed for one week at 70°C, in the dark.

f. UHPLC-MS analyses of the oligofucans Ion-pair reversed-phase (IP-RP) separation was run on an ultrahigh performance liquid chromatography system (UHPLC, Acquity H-Class plus® Waters, Wilmslow, UK), equipped with a BEH C18 column (100 mm x 1 mm, packed with 1.7 µm porosity particles) (Waters, Wilmslow, UK). The flow rate was 0.15 mL.min -1 and the column was heated at 45°C. A ternary gradient was used with A, pure water; B, pure acetonitrile; and C, 20 mM HxA dissolved in water (pH value adjusted to 6 by addition of acetic acid). The gradient was from 16.6% to 35% of solvent B in 10 min, then up to 63.4% at 20 min and maintained at 73.4% for 4.5 min. Solvent C was kept constant at 25% (Ropartz et al., 2016a).

Acquisitions were performed through direct coupling of the UHPLC system with a Select Series Cyclic IMS mass spectrometer (Waters, Wilmslow, UK) [START_REF] Giles | A Cyclic Ion Mobility-Mass Spectrometry System[END_REF]. Spectra were acquired in negative electrospray ionization (ESI) mode on the m/z range 300 -2000, with the TOF (Time-of-flight) analyser operating in the V-mode. The source parameters were the following: Capillary voltage 2.5 kV; Cone Voltage: 40V; Source temperature: 100°C; Desolvation temperature: 280°C; Desolvation gas: 500 L/hour; Nebulization gas: 5.5 bar. Data were recorded with the Quartz software (Waters embedded software, release 5) and processed using Mass Lynx 4.2 (from Waters, Wilmslow, UK) and MzMine software [START_REF] Pluskal | MZmine 2: Modular framework for processing, visualizing, and analyzing mass spectrometry-based molecular profile data[END_REF]. MzMine was used to produce a database of annotated structures (m/z; retention time; intensity) that can be exported in a tabulated format. Parameters used in MzMine are described in the Supplementary Data, Table S1.

g. He-CTD MS/MS analysis of the oligofucans

The 18 O-labeled samples were diluted 4-fold in a solution of H2 16 O/20 mM HxA pH6 in H2 16 O /ACN (1:1:2, in volume) right before the analysis. Helium-Charge Transfer Dissociation (He-CTD) spectra were obtained on a modified AmaZon 3D ion trap (Bruker Daltonics, Billerica, MA, USA) with helium as the CTD reagent gas as described by [START_REF] Ropartz | Negative Polarity Helium Charge Transfer Dissociation Tandem Mass Spectrometry: Radical-Initiated Fragmentation of Complex Polysulfated Anions[END_REF][START_REF] Ropartz | Negative Polarity Helium Charge Transfer Dissociation Tandem Mass Spectrometry: Radical-Initiated Fragmentation of Complex Polysulfated Anions[END_REF]. Doubly charged precursor ions were isolated in positive mode using an isolation window of 6 Da. Ion accumulation times were