Quentin Evrard

Cédric Leuvrey

Pierre Farger

Émilie Delahaye

Pierre Rabu

Gregory Taupier

Dodzi Kokou

Jean-Michel Dorkenoo

Nicolas Rueff

Olivier Barrier

Pérez

Emilie Delahaye

Grégory Taupier

Kokou Dodzi Dorkenoo

Jean-Michel Rueff

Nicolas Barrier

Olivier Pérez

Guillaume Rogez

Noncentrosymmetric Cu

Keywords: Synthesis, Crystal Structure, Nonlinear Optical, and Magnetic Properties of Cu 2 Layered Simple Hydroxide, dodecylsulfate, copper, morphology, noncentrosymmetric, non-linear optics

published or not. The documents may come

between Cu(OAc)2•H2O and the layered Cu2(OH)3(C12H25SO4) was isolated and characterized. Xray structure analysis showed that this intermediate presents a ribbon-like structure, of formula Cu3(C12H25SO4)2(CH3COO)2(OH)2(H2O)2. The magnetic properties of the layered Cu2(OH)3(C12H25SO4) have been analyzed in the high-temperature region (T > 20 K) by considering a high-temperature series expansion for a S = ½ Heisenberg 2D triangular lattice. At lower temperature, the compound shows a 3D antiferromagnetic ordering (TN = 10.8 K). The ribbon-like compound Cu3(C12H25SO4)2(CH3COO)2(OH)2(H2O)2 presents an overall antiferromagnetic behaviour, resulting from a combination of ferro and antiferromagnetic interactions between nearest neighbours within the chains.

Introduction.

Layered materials have long proved to be materials of choice in the field of organic-inorganic hybrid systems. [START_REF] Fernandes | Integrative Strategies to Hybrid Lamellar Compounds: An Integration Challenge[END_REF][START_REF]Functional Hybrid[END_REF] Among these materials, one may quote layered oxalate, [START_REF] Clemente-León | Multifunctionality in Hybrid Magnetic Materials Based on Bimetallic Oxalate Complexes[END_REF] Layered Double or Simple Hydroxides (LDH [START_REF] Leroux | Clay Surfaces: Fundamentals and Applications[END_REF] or LSH [START_REF] Rogez | Layered Hydroxide Hybrid Nanostructures: A Route to Multifunctionality[END_REF] ), clays, [START_REF] Ley | Spectroscopic Studies of the Interactions between a Cationic Cyanine Dye and a Synthetic Phyllosilicate: From Photophysics to Hybrid Materials[END_REF][START_REF] Liu | Recent Advances in Synthesis and Applications of Clay-Based Photocatalysts: A Review[END_REF] hexathiohypodiphosphates (MPS3), [START_REF] Lacroix | Stilbazolium-MPS3 Nanocomposites with Large Second-Order Optical Nonlinearity and Permanent Magnetization[END_REF][START_REF] Clément | Magnetism: Molecules to Materials II. Molecule-based Materials[END_REF] layered perovskite [START_REF] Schaak | Perovskites by Design: A Toolbox of Solid-State Reactions[END_REF] or MX4-based layered perovskite-like materials. [START_REF] Mitzi | Hybrid Organic-Inorganic Electronics[END_REF] Hybrid materials based on these systems can have interesting properties in magnetism, [START_REF] Clemente-León | Multifunctionality in Hybrid Magnetic Materials Based on Bimetallic Oxalate Complexes[END_REF][START_REF] Rogez | Layered Hydroxide Hybrid Nanostructures: A Route to Multifunctionality[END_REF][START_REF] Intissar | Trivalent Cation Substitution Effect into Layered Double Hydroxides Co2Fey Al1-y(OH)6Cl•nH2O: Study of the Local Order: Ionic Conductivity and Magnetic Properties[END_REF][START_REF] Coronado | Spontaneous Magnetization in Ni-Al and Ni-Fe Layered Double Hydroxides[END_REF] ferroelectricity, [START_REF] Bristowe | Ferromagnetism Induced by Entangled Charge and Orbital Orderings in Ferroelectric Titanate Perovskites[END_REF] multiferroicity, [START_REF] Pardo | Multiferroics by Rational Design: Implementing Ferroelectricity in Molecule-Based Magnets[END_REF][START_REF] Polyakov | Coexisting Ferromagnetic and Ferroelectric Order in a CuCl4-Based Organic-Inorganic Hybrid[END_REF][START_REF] Kundys | Multiferroicity and Hydrogen-Bond Ordering in (C2H5NH3)2CuCl4 Featuring Dominant Ferromagnetic Interactions[END_REF] magnetoelectricity, [START_REF] Evrard | Layered Simple Hydroxides Functionalized by Fluorene-Phosphonic Acids: Synthesis, Interface Theoretical Insights, and Magnetoelectric Effect[END_REF] luminescence, [START_REF] Ogawa | Photofunctions of Intercalation Compounds[END_REF][START_REF] Abid | Electronic Structure Calculations and Optical Properties of a New Organic-inorganic Luminescent Perovskite: (C9H19NH3)2PbI2Br2[END_REF] trapping of molecular species, [START_REF] Sánchez-Ochoa | Trapping and Diffusion of Organic Dyes inside of Palygorskite Clay: The Ancient Maya Blue Pigment[END_REF][START_REF] Aristilde | Enhanced Interlayer Trapping of a Tetracycline Antibiotic within Montmorillonite Layers in the Presence of Ca and Mg[END_REF] anti-corrosion [START_REF] Stimpfling | Amino Acid Interleaved Layered Double Hydroxides as Promising Hybrid Materials for AA2024 Corrosion Inhibition[END_REF] or catalysis [START_REF] García-González | Evaluation of Fe 3+ Fixation into Montmorillonite Clay and Its Application in the Polymerization of Ethylenedioxythiophene[END_REF] for instance.

In this respect, Layered Hydroxides are particularly interesting because they can be functionalized by various anionic molecules. LDH and LSH possess a similar hydrotalcite structure but they essentially differ in their composition and in the charge of the inorganic layers.

LDHs are synthetic anionic clays, of formula [M II is compensated by anionic species located in the interlayer space. They can be functionalized by exchange of these A n-anions. [START_REF] Leroux | Clay Surfaces: Fundamentals and Applications[END_REF] LSH contains only divalent transition metal ions, with a formula M2(OH)4-nx(A n-)x (M II = Co, Cu, Ni, Mn, … and A n-= carboxylate, sulfate, sulfonate or phosphonate anion). Inserted anion A is coordinated to the inorganic layers, which are thus neutral.

Several strategies have been reported for the synthesis of functionalized LSH: insertiongrafting, [START_REF] Delahaye | New Layered Organic-Inorganic Magnets Incorporating Azo Dyes[END_REF][START_REF] Bourzami | New Metal Phthalocyanines/Metal Simple Hydroxide Multilayers: Experimental Evidence of Dipolar Field-Driven Magnetic Behavior[END_REF][START_REF] Fujita | Reversible Structural Transformation and Drastic Magnetic Change in a Copper Hydroxide Intercalation Compound[END_REF][START_REF] Fujita | Magnetic Properties of Cu2(OH)3(Alkanecarboxylate) Compounds: Drastic Modification with Extension of the Alkyl Chain[END_REF] direct hydrothermal synthesis, [START_REF] Demessence | Optical and Magnetic Properties of Hybrid α,α′-Oligothiophenecarboxylates/Transition Metal Hydroxide Multilayered Compounds[END_REF][START_REF] Kurmoo | Reversible Guest Exchange and Ferrimagnetism (TC = 60.5 K) in a Porous Cobalt(II)-Hydroxide Layer Structure Pillared with Trans-1,4-Cyclohexanedicarboxylate[END_REF] in situ synthesis, [START_REF] Palamarciuc | Microwave-Assisted Post-Synthesis Modification of Layered Simple Hydroxides[END_REF] controlled hydrolysis [START_REF] Fujita | Convenient Crystal Growth, Structural Determination and Magnetic Studies of Layered Copper Hydroxides Containing Aromatic Sulfonates[END_REF] or, very recently, confined condensation. [START_REF] Park | Confined Condensation Synthesis and Magnetic Properties of Layered Copper Hydroxide Frameworks[END_REF] The most widely used method is insertion-grafting, which consists in an anionic exchange between the starting layered hydroxy-acetate and the molecule of interest bearing an anchoring group (carboxylate, sulfonate or phosphonate). [START_REF] Rogez | Layered Hydroxide Hybrid Nanostructures: A Route to Multifunctionality[END_REF][START_REF] Evrard | Layered Simple Hydroxides Functionalized by Fluorene-Phosphonic Acids: Synthesis, Interface Theoretical Insights, and Magnetoelectric Effect[END_REF] A pre-intercalation method has been shown to be very effective to allow the insertion-grafting of large, hydrophobic or prone to hydrolysis molecules, including coordination complexes in Layered Simple Hydroxides. [START_REF] Delahaye | New Layered Organic-Inorganic Magnets Incorporating Azo Dyes[END_REF][START_REF] Bourzami | New Metal Phthalocyanines/Metal Simple Hydroxide Multilayers: Experimental Evidence of Dipolar Field-Driven Magnetic Behavior[END_REF][START_REF] Delahaye | Rational Synthesis of Chiral Layered Magnets by Functionalization of Metal Simple Hydroxides with Chiral and Non-Chiral Ni(II) Schiff Base Complexes[END_REF][START_REF] Eyele-Mezui | Functional Hybrid Materials Based on Layered Simple Hydroxide Hosts and Dicarboxylate Schiff Base Metal Complex Guests[END_REF] This method consists in the insertion-grafting of molecules bearing long-alkyl chains by anion-exchange from the starting layered hydroxy-acetate. In the case of layered copper hydroxide, dodecyl sulfate can be readily inserted into copper hydroxy-acetate, much more easily than less flexible molecules. Compared to copper hydroxy-acetate, copper hydroxy-dodecylsulfate presents a much larger and more hydrophobic interlamellar spacing which enables the subsequent insertion of various molecules.

The precise understanding of the properties of the layered hybrid compounds (optical, magnetic or dielectric for instance) requires a deeper knowledge of their structure. To this aim, it is worth investigating the structures of the starting materials, which appears not to be an easy task. The single-crystal structure of copper hydroxy-acetate Cu2(OH)3(OAc)•H2O was only reported in 2011, whereas research involving this compound has been performed for more than 25 years. [START_REF] Rogez | Layered Hydroxide Hybrid Nanostructures: A Route to Multifunctionality[END_REF][START_REF] Fujita | Reversible Structural Transformation and Drastic Magnetic Change in a Copper Hydroxide Intercalation Compound[END_REF][START_REF] Fujita | Magnetic Properties of Cu2(OH)3(Alkanecarboxylate) Compounds: Drastic Modification with Extension of the Alkyl Chain[END_REF][START_REF] Yamanaka | Anion Exchange Reactions in Layered Basic Copper Salts[END_REF][START_REF] Yamanaka | Anion-Exchange in Basic Copper Acetate[END_REF][START_REF] Rabu | Ferro/Antiferromagnetism Mediated by Interlayer Organic Spacers in Layered Copper(II) Compounds[END_REF][START_REF] Laget | Copper Hydroxide Based Organic/Inorganic Ferromagnets[END_REF][START_REF] Fujita | Controllable Magnetic Properties of Layered Copper Hydroxides, Cu2(OH)3X (X=carboxylates)[END_REF][START_REF] Laget | Hybrid Organic-Inorganic Layered Compounds Prepared by Anion Exchange Reaction: Correlation between Structure and Magnetic Properties[END_REF] Concerning the dodecylsulfate analogue, now widely used as a starting compound for insertion, to the best of our knowledge, no precise description of its structure has ever been reported.

We describe here the synthesis of high crystallinity Cu2(OH)3(C12H25SO4 Cu3(C12H25SO4)2(CH3COO)2(OH)2(H2O)2 presents a combination of ferro and antiferromagnetic interactions between nearest neighbours within the chains, whereas the properties of Cu2(OH)3(C12H25SO4), which presents an antiferromagnetic ordering at TN = 10.8 K, can be interpreted in the high-temperature regime (T > 20 K) using a Heisenberg 2D triangular spin lattice model.

Experimental Section.

Synthesis of Cu2(OH)3(CH3COO)•H2O, (Cu2(OH)3(OAc)•H2O) :

The synthesis is adapted from the one of Švarcová et al. [START_REF] Švarcová | Synthesis and Characterization of Single of the Layered Copper Hydroxide Acetate Cu2(OH)3(CH3COO)•H2O[END_REF] S1).

Powder X-ray diffraction (XRD) patterns of the ribbon-like compounds (compound 1, Figure S2)

were collected with a Bruker D8 diffractometer (Cu Kα1 = 0.1540598 nm) equipped with a LynxEye detector discriminating in energy.

Single crystal X-ray diffraction measurements were performed using Mo K radiation produced with a micro focus Incoatec Iµs sealed X-ray tube on a KappaCCD (Bruker-Nonius) four circles diffractometer equipped with an Apex2 bi-dimensional detector (CCD: charge coupled device).

Crystals of suitable crystalline quality were selected for single crystal XRD; details of the data collection are given in Table 1. Data were corrected from absorption using Sadabs program developed for scaling and absorption corrections of area detector data. [START_REF] Sheldrick | Bruker-Siemens Area Detector Absorption and Other Correction[END_REF][START_REF] Sheldrick | Program for Empirical Absorption Correction[END_REF] The structure was determined with Superflip 46 using charge-flipping algorithm and introduced in the program Jana2006. [START_REF] Petříček | Crystallographic Computing System JANA2006: General Features[END_REF] FT-IR spectra of the hybrid compounds were collected in ATR mode on a SpectrumII spectrometer (PerkinElmer). TGA-TDA experiments were performed using a TA instrument SDT Q600

(heating rates of 5°C•min -1 under air stream, using Pt crucibles). The SEM images were obtained with a JEOL 6700F microscope equipped with a field emission gun, operating at 3 kV in the SEI mode and with a ZEISS GeminiSEM 500 microscope, operating at 1 kV or 5kV in secondary electron imaging mode. The magnetic studies were carried out with a SQUID magnetometer (Quantum Design MPMS3) covering the temperature and field ranges 2-300 K and +/-7 T, respectively. Magnetization versus field measurements at room temperature confirm the absence of ferromagnetic impurities. Data were corrected for the sample holder, and diamagnetism was estimated from Pascal constants.

Non-Linear Optical (NLO) activity was evaluated by detecting the Second-Harmonic Generation (SHG) process. SHG measurements have been performed with an inverted microscope (Olympus IX71). The SHG process is induced by focusing in the sample a pulsed laser beam at 900 nm (Spectra Physics, Tsunami) with ultrashort pulse durations (100 fs at 80 MHz) and input power of 50 mW. Samples in powder form deposited onto a microscope slide are excited by this laser beam using a low-aperture microscope objective (Olympus, SLMPlan, X20, N.A. = 0.35). The SHG signal emitted at 450 nm is separated from the excitation beam by a dichroic mirror and collected during 1 s in reflection mode using a spectrometer (Acton research SP2300) coupled with a CCD camera (Princeton Instruments PIXIS400). For SHG imaging, a micrometric displacement stage is combined with a photon photomultiplier in counting mode (Hamamatsu, H7421).

Results and discussion

Syntheses and crystal structures

Since it is possible to obtain Cu2(OH)3(OAc)•H2O as single crystals, [START_REF] Švarcová | Synthesis and Characterization of Single of the Layered Copper Hydroxide Acetate Cu2(OH)3(CH3COO)•H2O[END_REF] and considering that anionic exchange reactions from Cu2(OH)3(OAc)•H2O have been well studied, [START_REF] Rogez | Layered Hydroxide Hybrid Nanostructures: A Route to Multifunctionality[END_REF] including for the synthesis of Cu2(OH)3(C12H25SO4), [START_REF] Laget | Hybrid Organic-Inorganic Layered Compounds Prepared by Anion Exchange Reaction: Correlation between Structure and Magnetic Properties[END_REF] we first tried to obtain single crystals of Cu2(OH)3(C12H25SO4) by single-crystal to single-crystal modification from Cu2(OH)3(OAc)•H2O.

In order to maximize the chance to keep the crystallinity of the starting material, we performed exchange reaction from Cu2(OH)3(OAc)•H2O without stirring and using softer condition than for the classical exchange (25°C during 48 h instead of 60°C during 72 h). Yet we could obtain only partial exchange (Figure S3) and even though the crystallinity remains very good (Figure S4), the single-crystal character is lost.

Therefore, we adopted another method, derived from the one described by Švarcová et al. which has enabled to obtain single crystals of Cu2(OH)3(CH3COO)•H2O, [START_REF] Švarcová | Synthesis and Characterization of Single of the Layered Copper Hydroxide Acetate Cu2(OH)3(CH3COO)•H2O[END_REF] or from the one used by Fujita to obtain single crystals of copper hydroxides with sulfonates, either with a layer structure or with a distorted diamond chain structure. [START_REF] Fujita | Convenient Crystal Growth, Structural Determination and Magnetic Studies of Layered Copper Hydroxides Containing Aromatic Sulfonates[END_REF][START_REF] Fujita | Crystal Growth, Structures and Magnetic Properties of Copper Hydroxide Compounds with Distorted Diamond Chain Magnetic Networks[END_REF] In the present case, it consists in adding copper acetate to a solution of sodium dodecylsulfate in a water/ethanol mixture heating the solution at 70°C for several days. Despite the relative simplicity of this procedure, several observations can be made.

When the two reactants are mixed (either solid Cu(OAc) This precipitate is filtered after 1 h of stirring at room temperature. Powder X-ray diffraction (Figure S2) and infrared spectroscopy (Figure S5) clearly show that this blueish precipitate is composed of sodium dodecylsulfate and at least one other phase which could not be identified and which corresponds neither to copper acetate nor to copper dodecylsulfate nor to the ribbon-like structure which forms when the suspension is let evaporate (see below).

Indeed, when, instead of being filtered, this suspension is slowly evaporated at room temperature without stirring, crystalline needles form (compound 1) (Figure 1 and the atomic parameters of compound 1 are summarized in Tables S1a andS1b. other by the dodecyl groups, develop along the a direction (Figure 2). Acetate groups are in ( 1 -( 1 -µ2))-µ3 bridging mode are coordinated to one Cu1 in  1 mode and bridge one Cu1 and one Cu2 in  1 -µ2 mode. Finally, the sulfate groups are bridging one Cu1 and one Cu2 in  1 -µ2 mode. One water molecule completes the coordination sphere of Cu2.

If, using the same starting conditions, the solution is heated at 60°C without stirring and with a condenser during 3 days instead of being slowly evaporated, blue platelet-like crystals form with a relatively high yield (around 40%). Despite the very thin plate-like shape, the structure could be solved on a single crystal. The compound is a layered copper hydroxide of formula Cu2(OH)3(C12H25SO4) (compound 2).

Compound 2 crystallizes in the non-centrosymmetric space group P21. The structure determination was performed using Superflip and the charge flipping algorithm using the P1 space group. The determined electron density was then analysed to evidence symmetry operators as described by Palatinus et al. [START_REF] Palatinus | Symmetry Determination Following Structure Solution in P1[END_REF] This method led to the P21 space group. All the attempts of structural determination in a centro symmetric space group (using charge flipping but also direct methods)

were unsuccessful, supporting the assumption of an acentric space group and this despite the lack of high angle diffraction. This is further confirmed by SHG measurements (see below).The crystal structure of compound 2 can be described by 2 Cu, 1 S, 7 O, 12 C independent atoms. All the atomic positions were refined and then atomic displacement parameters (ADP) were considered as anisotropic for copper and sulfur atoms and isotropic for all remaining atoms. In addition, 25 independent hydrogen atoms were further introduced using geometric considerations to fill the carbon environment. As for oxygen atoms, bond valence sum calculations indicated low values for O2, O3 and O7 attributed to the presence of H atoms. Each of these O are surrounded by 3 copper atoms and the hydrogen is building a OCu3H tetrahedron. The position of the H atoms was determined based on these geometrical considerations and restricted in link to their O first neighbour. The model results in the elemental formula Cu2(OH)3(C12H25SO4). Since the space group is non-centrosymmetric, a twin law corresponding to an inversion center has been introduced and the ratio of the possible twin domains (i.e. the Flack parameters) was refined to 0.26(9)/0.74 (9). Final reliability factors and details of the refinement are reported in Table 1 and the atomic parameters of the crystal 2 are summarized in Tables S2a andS2b.

Compound 2 consists in layers of copper hydroxide of botallackite type structure, separated by dodecylsulfate ions, with an interlamellar distance of 26.93 Å (Figure 3). The dodecylsulfate molecules are coordinated to the layers by the sulfate group in  1 -µ3 position. The structure resembles one recently reported with aromatic sulfonate molecules, yet to the best of our knowledge, it is the first time the crystal structure of a sulfate-containing layered copper hydroxide is reported, despite the fact that Cu2(OH)3(C12H25SO4) is often used as a precursor for intercalation compounds. [START_REF] Rogez | Layered Hydroxide Hybrid Nanostructures: A Route to Multifunctionality[END_REF][START_REF] Delahaye | New Layered Organic-Inorganic Magnets Incorporating Azo Dyes[END_REF][START_REF] Bourzami | New Metal Phthalocyanines/Metal Simple Hydroxide Multilayers: Experimental Evidence of Dipolar Field-Driven Magnetic Behavior[END_REF] Structure of the inorganic layer, (ab) plane (right). Cu (purple (Cu1) and blue (Cu2)), O (red), S (green), C (grey), H (white).

One peculiar aspect of the structure of 2 is that it crystallizes in a non-centrosymmetric space group. The non-centrosymmetry comes from the fishbone arrangement of the alkyl chains in the interlamellar spacing. This arrangement is different from the one which was classically and empirically drawn, where the alkyl chains were simply interdigitated in the interlamellar spacing. [START_REF] Laget | Hybrid Organic-Inorganic Layered Compounds Prepared by Anion Exchange Reaction: Correlation between Structure and Magnetic Properties[END_REF][START_REF] Okazaki | A Monolayer Complex of Cu2(OH)3C12H25SO4 Directly Precipitated from an Aqueous SDS Solution[END_REF][START_REF] Park | Layered Copper Hydroxide N-Alkylsulfonate Salts: Synthesis, Characterization, and Magnetic Behaviors in Relation to the Basal Spacing[END_REF] This compound constitutes one relatively rare example of a chiral compound obtained from achiral building blocks, [START_REF] Janiak | Engineering Coordination Polymers towards Applications[END_REF][START_REF] Gil-Hernández | Spontaneous Resolution upon Crystallization of Chiral La(III) and Gd(III) MOFs from Achiral Dihydroxymalonate[END_REF][START_REF] Ma | Enantioselective Catalysis with Homochiral Metal-organic Frameworks[END_REF] even though, as in most of the cases reported in the literature, [START_REF] Ma | Enantioselective Catalysis with Homochiral Metal-organic Frameworks[END_REF] the bulk sample of 2 likely contains both enantiomorphs (i.e. of opposite handedness).

Interestingly, Cu2(OH)3(OAc)•H2O also crystallizes in a non-centrosymmetric space group (P21), [START_REF] Švarcová | Synthesis and Characterization of Single of the Layered Copper Hydroxide Acetate Cu2(OH)3(CH3COO)•H2O[END_REF] with the acetate molecules forming a fish-bone arrangement, contrarily to what was initially inferred by calculations (P21/m). [START_REF] Masciocchi | Characterization, Andab InitioX-Ray Powder Diffraction Study of Cu2(OH)3(CH3COO)•H2O[END_REF] Here, even though it could not be obtained via a crystal to crystal transformation from Cu2(OH)3(OAc)•H2O, Cu2(OH)3(C12H25SO4) crystallizes in the same non-centrosymmetric crystal space group as Cu2(OH)3(OAc)•H2O. It is worth noting here that layered copper hydroxides functionalized by sulfonate molecules, as reported by Fujita et al., crystallize in centrosymmetric space groups, even though the synthetic procedure is similar to the one described here. [START_REF] Fujita | Convenient Crystal Growth, Structural Determination and Magnetic Studies of Layered Copper Hydroxides Containing Aromatic Sulfonates[END_REF] Hence, functionalizing the hydroxide layers with sulfate instead of sulfonate has a significant influence on the structure that can lead to different properties.

Non-Linear Optics

In order to fully ascertain the non-centrosymmetry of the structure of 2, Non-Linear Optical microscopy was performed. Measurements on a single crystal show a clear Second Harmonic Generation signal (Figure S6). To avoid any false-positive signal due to surface Second Harmonic Generation (all the more since the thickness of the crystals is small), we managed to record SHG intensity as a function of thickness on a partially cleaved crystal (Figure 4). The enhancement of the SHG signal with the thickness rules out a surface effect. Since non-centrosymmetry is a necessary condition for Non-Linear Optical activity, the observation of a clear SHG signal for 2 confirms its non-centrosymmetry.

Comparison with classical method and morphology control

The method used to synthesize the compound 2 enables to obtain more than 800 mg for each synthesis, with a yield of about 40%. This synthesis does not involve any pH adjustment like the one used by Okazaki et al. [START_REF] Okazaki | A Monolayer Complex of Cu2(OH)3C12H25SO4 Directly Precipitated from an Aqueous SDS Solution[END_REF] Compared to the « classical » ion-exchange method from Cu2(OH)3(OAc)•H2O, [START_REF] Laget | Hybrid Organic-Inorganic Layered Compounds Prepared by Anion Exchange Reaction: Correlation between Structure and Magnetic Properties[END_REF] this one-step hydrolysis method enables to increase greatly the crystallite size (Figure 5). Finally, it is worth noticing that depending on the water/ethanol ratio and of the reaction temperature, it was possible to control the morphology of the Cu2(OH)3(DS) crystallites. Using up to 30% of ethanol, as described in the experimental part, the crystallites have the classical regular platelet shape. For an ethanol content larger than 40%, associated with a lower reaction temperature (30°C instead of 60°C), the crystallites adopt a "butterfly" morphology (Figure 6).

We checked by Rietveld refinements of the powder X-ray diffraction data that the crystal structure does not change (Figure S1).

Magnetic properties

The magnetic properties of compounds 1 and 2 were recorded in the range 1.8-300 K under a dc magnetic field of 5000 G.

The magnetic properties of compound 1 are presented in or for the related Cu3(OH)2(CO3)2 azurite. [START_REF] Kikuchi | Experimental Observation of the 1/3 Magnetization Plateau in the Diamond-Chain Compound Cu3(CO3)2(OH)2[END_REF] The  = f(T) curve for 1 could be fitted above 7 K, considering isolated chains (separated by the long dodecylsulfate molecules), and the spin topology schematized on figure 8. Below 7 K, the model used is too simplified to be valid, because other intrachain or 3D interchain interactions are likely to be taken into account in this temperature range and because of the finite size of the model. The fit was performed considering the following Hamiltonian for spin-spin interactions :

Ĥ = Σ -Jij Ŝi Ŝj.
We considered a ring of twelve spins to reproduce the chain behaviour without edge effect. The numerical resolution of the Hamiltonian was carried out by using the program SPIN including a refinement routine. 57 A very good adjustment of the experimental data was obtained with the refined values : J1 = 11(6) cm -1 , J2 = -75(1) cm -1 , J3 = -52(2) cm -1 , J4 = 28(2) cm - 1 and g = 2.29(3) (the fit was performed with a single g factor for the two different copper ions to limit over-parameterization). Standard deviations on Ji values are quite high due to important correlations between parameters. Given the fact that several exchange pathways exist between two spin carriers, it is here difficult and beyond the scope of this study to perform a clear correlation between the J values determined and the structure of the compound. Yet it is worth noticing that the J values are moderate, and within the usually observed range for Cu-O-Cu (OH, ( 1 -µ2)-sulfate or ( 1 -µ2)-carboxylate bridges) or Cu-OCO-Cu ((( 1 - 1 )-µ2)-carboxylate) motives. [START_REF] Fujita | Crystal Growth, Structures and Magnetic Properties of Copper Hydroxide Compounds with Distorted Diamond Chain Magnetic Networks[END_REF][START_REF] Gómez-García | Alternating Ferro/Antiferromagnetic Copper(II) Chain Containing an Unprecedented Triple Formato/Hydroxido/Sulfato Bridge[END_REF][START_REF] Crawford | Relation between the Singlet-Triplet Splitting and the Copper-Oxygen-Copper Bridge Angle in Hydroxo-Bridged Copper Dimers[END_REF] In particular, it is noteworthy that the Cu-Cu interaction via the (( 1 - 1 )-µ2)-carboxylate (J4) is ferromagnetic, as expected for a syn-anti carboxylate. [START_REF] Murugesu | Ferromagnetic Interactions Mediated by Syn-anti Carboxylate Bridging in Tetranuclear Copper(II) Compounds[END_REF] Clearly, the peculiar behavior of compound 1 can be explained by the competition between ferromagnetic and antiferromagnetic nearest neighbour exchange interactions.

As for compound 2, the fit of the 1/ = f(T) curve in the high-temperature region (above 200 K) leads to a Curie constant of 0.89 emu•K•mol -1 (i.e. 0.45 emu•K•mol -1 per Cu(II) ion, within the range of expected values 56 ) and very small negative Weiss temperature of -0.3 K, which indicates dominant antiferromagnetic interactions. Approximating the triangular magnetic lattice as being regular, the  = f(T) can be fitted using the high-temperature series expansion for a S = ½ Heisenberg 2D triangular lattice (Figure 9) for T > 20 K. The best fit provides J = -0.40(1) cm -1 and g = 2.17 (1). The exchange interaction is significantly smaller (by two orders of magnitude) than the ones obtained by Fujita for a series of layered hydroxides containing aromatic sulfonates. [START_REF] Fujita | Convenient Crystal Growth, Structural Determination and Magnetic Studies of Layered Copper Hydroxides Containing Aromatic Sulfonates[END_REF] The sharp maximum observed around 11 K in the  = f(T) curve and the very abrupt decrease of T = f(T) (Figure S7), can be associated with the occurrence of a long-range (3D) antiferromagnetic ordering. The ordering temperature can be determined precisely from the maximum of the in-phase susceptibility (Figure S8) leading to TN = 10.8 K. This value is slightly higher than the one determined recently for an analogous compound (synthesized by confined condensation, a totally different approach, and for which no crystal structure could be obtained) (TN = 8 K). [START_REF] Park | Confined Condensation Synthesis and Magnetic Properties of Layered Copper Hydroxide Frameworks[END_REF] The magnetization vs. field curve at 1.8 K shows a clear spin-flop transition for a critical field of 2 T (Figure 10) which supports an antiferromagnetic ordering at low temperature in compound 2.

Conclusion.

Single crystals of 1D and 2D copper hydroxides bearing dodecylsulfate molecules have been obtained by a hydrolysis method from copper acetate. This method has already been employed to obtain single crystals of Cu2(OH)3(OAc)•H2O, [START_REF] Švarcová | Synthesis and Characterization of Single of the Layered Copper Hydroxide Acetate Cu2(OH)3(CH3COO)•H2O[END_REF] various layered copper hydroxides containing aromatic sulfonates [START_REF] Fujita | Convenient Crystal Growth, Structural Determination and Magnetic Studies of Layered Copper Hydroxides Containing Aromatic Sulfonates[END_REF] and copper hydroxide distorted diamond chains bearing sulfonate molecules [START_REF] Fujita | Crystal Growth, Structures and Magnetic Properties of Copper Hydroxide Compounds with Distorted Diamond Chain Magnetic Networks[END_REF] but to the best of our knowledge, it is the first time this method is proved efficient to obtain single crystal of sulfate containing low dimensional copper hydroxide based hybrids.

The structure determination of Cu2(OH)3(C12H25SO4) is particularly noteworthy since this compound is widely used for further functionalization by ion-exchange reaction. Interestingly, Xray structure analysis and NLO measurement clearly indicate that it crystallizes in a noncentrosymmetric space group just like the parent compound Cu2(OH)3(OAc)•H2O, contrarily to what was observed for layered copper hydroxides containing aromatic sulfonates. [START_REF] Fujita | Convenient Crystal Growth, Structural Determination and Magnetic Studies of Layered Copper Hydroxides Containing Aromatic Sulfonates[END_REF] In addition, we isolated and fully characterized a 1D, ribbon-like, copper-hydroxide based compound, which can be considered as an intermediate between the "0D" copper acetate and the 2D Cu2(OH)3(C12H25SO4).

Extension of this hydrolysis approach to the preparation of highly crystalline hydroxide-based low dimensional hybrids networks with other transition metal ions is currently under study.

Supporting

( 1 -

 1 x),M III x(OH)2][A n-(x/n)(H2O)] (M II = Mg, Co, Ni, Zn,…; M III = Al, Cr, V, Ga, Rh,…). The positive charge of the hydrotalcite [M(OH)2] layers

  left). Interestingly, when the reactants are only mixed during 5 min, without full dissolution of Cu(OAc)2•H2O, similar needles appear to grow from the remaining Cu(OAc)2•H2O crystals (compound 1') (Figure 1 right), which suggests that the corresponding compound may be an intermediate between Cu(OAc)2•H2O and Cu2(OH)3(DS).

Figure 1 .

 1 Figure 1. Optical microscopy image of the crystals of compound 1 (left) and of compound 1'

Figure 2 .

 2 Figure 2. View of the structure of Cu3(C12H25SO4)2(CH3COO)2(OH)2(H2O)2 (1) along the a

Figure 3 .

 3 Figure 3. Views of the structure of 2 Cu2(OH)3(C12H25SO4) left: along a; middle: along b.

Figure 4 .

 4 Figure 4. Non-Linear Optical microscopy observation of a partially cleaved crystal of 2. From left

Figure 5 .

 5 Figure 5. SEM image of Cu2(OH)3(C12H25SO4) obtained via ion exchange from

Figure 6 .

 6 Figure 6. Optical images of the regular platelet morphology (left) and of the butterfly morphology

Figure 7 .

 7 The fit of the 1/ = f(T) curve in the high-temperature region (above 200 K) leads to a Curie constant of 1.73 emu•K•mol -1 (i.e. 0.58 emu•K•mol -1 per Cu(II) ion, within the range of expected values56 ) and negative Weiss temperature of -77 K, which indicates dominant antiferromagnetic interactions. The  = f(T) for compound 1 indicates a paramagnetic behaviour on the whole temperature range with short-range interactions. The curve presents a sharp maximum at 10.5 K with a very broad shoulder centered around 70 K. This peculiar shape, with two, more or less defined, peaks in  = f(T) has already been observed in other diamond-like Cu(II) hydroxide chains, with sulfonate and acetate ligands,[START_REF] Fujita | Crystal Growth, Structures and Magnetic Properties of Copper Hydroxide Compounds with Distorted Diamond Chain Magnetic Networks[END_REF]

Figure 7 .

 7 Figure 7.  = f(T) curve at 5000 G for compound 1 (open squares: experimental points, full red

Figure 8 .

 8 Figure 8. Spin topology considered for 1 above 13 K. This topology is identical to the one used by Fujita et al. for related diamond-like chain compounds bearing sulfonate molecules.[START_REF] Fujita | Crystal Growth, Structures and Magnetic Properties of Copper Hydroxide Compounds with Distorted Diamond Chain Magnetic Networks[END_REF]

Figure 9 .

 9 Figure 9.  = f(T) curve at 5000 G for compound 2 (open squares: experimental points, full red

Figure 10 .

 10 Figure 10. M = f(H) (black squares) and dM/dH = f(H) (red squares) at 1.8 K for 2. Full lines are

  Information. Powder X-Ray diffraction diagram of 2 with butterfly morphology. Powder X-Ray diffraction diagram of the blueish precipitate and compound 1. Powder X-Ray diffraction diagram and SEM images resulting from attempts of single-crystal to single-crystal functionalization of Cu2(OH)3(OAc)•H2O. IR spectra of the blueish precipitate and compound 1.

Synthesis of Cu3(C12H25SO4)2(CH3COO)2(OH)2(H2O)2 (1) : Cu

	(OAc)2•H2O is added to 0.5
	equivalent of a solution (0.05 M) of C12H25SO4Na in a water/ethanol mixture (70/30 v:v), stirred
	vigorously during 1 h at room temperature and let slowly evaporated at room temperature without
	stirring. Small crystalline needles grow within a few days (3 days for a total volume of 100 mL).
	Yield: ca. 30%.
	4 g (20 mmol) of Cu(CH3COO)2•H2O are solubilized in 100 mL of a
	mixture water/ethanol (90/10 v:v), then heated under reflux at 60°C during 72 h. Blue-green
	crystals are then collected by filtration and washed with water and ethanol. The filtrate is then
	heated again at 60°C for 48 h, and the blue green crystals are collected, washed with water and
	ethanol and mixed with the first fraction. This procedure is repeated twice. Yield: ca. 4%.

Synthesis of Cu2(OH)3(C12H25SO4), (Cu2(OH)3(DS)) (2) :

	1.33 g (5 mmol) of sodium
	dodecylsulfate are dissolved in 100 mL of a water/ethanol mixture (70/30 v:v). Cu(OAc)2•H2O (2
	g, 10 mmol) are added to the solution which is stirred during 1 h. The mixture is then heated under
	reflux at 60°C for 3 days, without stirring. The blue solid is filtered, washed three times with water,
	twice with a water/ethanol mixture and once with ethanol, then dried under vacuum. Yield: 40%
	(based on NaDS) (885 mg, 2 mmol).
	The Powder X-Ray Diffraction (PXRD) diagram of Cu2(OH)3(C12H25SO4)•(2) was measured in
	transmission geometry on a PANalytical X'Pert PRO diffractometer equipped with a focusing
	mirror (Cu-λKαmoy) and a PIXcel detector. The polycrystalline sample was loaded in a capillary of
	0.3 mm diameter. The PXRD diagram was recorded at room temperature between 3 and 60°(2θ)
	with a step size of ~0.013°(2θ) for 2 hours. The Rietveld refinements were performed with the
	JANA2006 program 43 to check the composition of the polycrystalline sample of
	Cu2(OH)3(C12H25SO4). Assuming the crystal structure model obtained from the single crystal X-
	ray data only the scale, unit cell and profile parameters were refined. The low R factors (Robs =
	7,01 ; RBobs = 13,15 ; Rwp = 8,43, gof = 1,80) and the absence of any extra peaks testify that the
	polycrystalline sample correspond to a single-phase sample of Cu2(OH)3(C12H25SO4) (Figure

Table 1 .

 1 Crystallographic data for 1(1') and 2.Compound 1 adopts a distorted diamond chain structure, analogous to that of azurite Cu3(OH)2(CO3)2.[START_REF] Kikuchi | Experimental Observation of the 1/3 Magnetization Plateau in the Diamond-Chain Compound Cu3(CO3)2(OH)2[END_REF] A similar arrangement has been described by Fujita et al. for sulfonate compounds of general formula Cu3(OH)2(RSO3)2(CH3COO)2(H2O)2,[START_REF] Fujita | Crystal Growth, Structures and Magnetic Properties of Copper Hydroxide Compounds with Distorted Diamond Chain Magnetic Networks[END_REF] but, to the best of our knowledge, it is the first time such a structure is reported with sulfate groups. Although the general diamond-like structure of the chains remains essentially the same, it is worth underlining here that in the present case, the sulfate groups are mono-coordinated to one copper atoms, whereas the sulfonate groups in the compounds described by Fujita et al. are, depending on the nature of the

	1 mm	2 mm

alkyl chain, either coordinated in µ2 bridging mode to two copper ions or not coordinated (instead, water molecules are coordinated in µ2 bridging mode). The chains in 1, well separated from each

Ackowledgements.

The authors thank the CNRS, the Université de Strasbourg, the ENSICAEN and the Agence Nationale de la Recherche (contract N° ANR-14-CE07-0004-01 (HYMN)) and the Labex NIE (ANR-11-LABX-0058_NIE within the Investissement d'Avenir program ANR-10-IDEX-0002-02) for financial support. We thank Dr. T. Buffeteau (CNRS-University of Bordeaux, France) for interesting discussions.

Author Contributions.

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

For Table of Contents Use Only


Arthur Boutillon

Florence A Giger

Nicolas B David

Analysis of in vivo cell migration in mosaic zebrafish embryos

Being optically clear, the zebrafish embryo is a nice model system to analyse cell migration in vivo.

This chapter describes a combination of injection and cell transplant procedures that allows creation of mosaic embryos, containing a few cells labelled differently from their neighbours. Rapid 5D confocal imaging of these embryos permits to simultaneously track and quantify the movement of large cell groups, as well as analyse the cellular or subcellular dynamics of transplanted cells during their migration. In addition, expression of a candidate gene can be modified in transplanted cells.

Comparing behaviour of these cells to control or neighbouring cells allows determination of the role of the candidate gene in cell migration. We describe the procedure, focusing on one specific cell population during gastrulation, but it can easily be adapted to other cell populations and migrating events during early embryogenesis.

Introduction

Cell migration is key to build, shape, repair and defend an organism. It has been extensively studied in vitro, providing invaluable knowledge on its cellular and molecular bases [START_REF] Horwitz | Cell migration[END_REF][START_REF] Vicente-Manzanares | Cell migration: an overview[END_REF]. It, however, clearly appeared in the past few years that a number of cells behave quite differently in vitro and in vivo [START_REF] Lämmermann | Mechanical modes of "amoeboid" cell migration[END_REF][START_REF] Te Boekhorst | Plasticity of Cell Migration In Vivo and In Silico[END_REF]. This likely stems from the more complex environment they encounter (3D extracellular matrix of varying stiffness, neighbouring cells, guidance cues) leading for instance cells that would use only lamellipodia on a flat surface to use a wide array of cell processes (lamellipodia, pseudopodia of varying length and shapes, blebs…) for their in vivo displacements [START_REF] Ridley | Life at the leading edge[END_REF]. Many cells furthermore display collective behaviours, their migration depending on interactions with neighbouring cells [START_REF] Haeger | Collective cell migration: Guidance principles and hierarchies[END_REF][START_REF] Theveneau | Collective cell migrations][END_REF].

Understanding in vivo cell migration thus implies direct analysis of cells moving in their physiological environment.

Doing so obviously requires optically clear systems permitting cell observation without further manipulation or dissection. Cells also need to be labelled, usually through the expression of fluorescent proteins. This can be achieved using transgenic lines expressing reporter constructs in specified cell types. However such a strategy often leads to label a whole cell population, when labelling sparse, isolated cells, is key to good imaging, in particular for analysing cell contours, or membrane protrusions which cannot be seen if neighbouring cells are similarly labelled [START_REF] Row | Completion of the epithelial to mesenchymal transition in zebrafish mesoderm requires Spadetail[END_REF][START_REF] Montero | Shield formation at the onset of zebrafish gastrulation[END_REF].

Creating mosaic embryos, containing only one or few cells differing from surrounding cells, is thus crucial for precise analysis of cell dynamics. Mosaic embryos furthermore permit to test consequences of activation/repression of genes/pathways on migration of individual cells.

Comparing the tracks and behaviour of these cells with surrounding control cells under the same experimental conditions allows determination of the role of a particular gene in cell migration [START_REF] Liang | In vitro scratch assay: a convenient and inexpensive method for analysis of cell migration in vitro[END_REF].

We here describe a procedure, based on injections and cell transplants, to create mosaic zebrafish embryos during gastrulation and image migrating cells.

Gastrulation is the developmental stage during which cells first migrate, to organise the embryo in different germ layers and set up the basis of the future body plan [START_REF] Solnica-Krezel | Gastrulation: Making and Shaping Germ Layers[END_REF]. This involves a wide array of cell migrations, including random walks, directed migrations and collective movements.

The fish embryo, being optically clear, offers direct access to these processes [START_REF] Solnica-Krezel | Transparent things: cell fates and cell movements during early embryogenesis of zebrafish[END_REF]. Among the diverse movements taking place during gastrulation, cells of the organiser (termed 'shield' in zebrafish) internalise and migrate collectively toward the animal pole of the embryo, forming the prechordal plate [START_REF] Montero | Shield formation at the onset of zebrafish gastrulation[END_REF][START_REF] Kai | Sphingosine-1-phosphate receptors regulate individual cell behaviours underlying the directed migration of prechordal plate progenitor cells during zebrafish gastrulation[END_REF][START_REF] Dumortier | Collective mesendoderm migration relies on an intrinsic directionality signal transmitted through cell contacts[END_REF]. We combine injections of RNAs encoding fluorescently tagged proteins, cell transplants and in vivo imaging, to analyse the cellular bases of this migration. We have successfully used the proposed protocol to describe behaviour of wild-type cells, dissect the pathways controlling their motility and orientation, as well as assess the importance of candidate genes in regulating cell migration in vivo [START_REF] Dumortier | Collective mesendoderm migration relies on an intrinsic directionality signal transmitted through cell contacts[END_REF][START_REF] Dumortier | The TORC2 Component, Sin1, Controls Migration of Anterior Mesendoderm during Zebrafish Gastrulation[END_REF][START_REF] Dang | Inhibitory signalling to the Arp2/3 complex steers cell migration[END_REF]. The proposed protocol can be used to test the potential implication of any candidate gene in controlling cell migration in vivo. It can furthermore be easily adapted to analyse other cell types, or other developmental stages. 7. 20 µl microloader tips (Eppendorf), to load injection needles. 8. Plastic Pasteur pipettes for transferring embryos. 9. Embryo Medium (EM, Zebrafish book [START_REF] Westerfield | The zebrafish book. A guide for the laboratory use of zebrafish (Danio rerio)[END_REF]). 10. RNAs: mRNAs are prepared in vitro, using the mMessage mMachine kit (Ambion) to produce fully capped RNAs.

2-Material

11. Sterile-filtered water (Sigma, W3500) for diluting RNAs.

12. Injection needle: needles should be long enough to reach the embryo within its chorion, without creating too large a hole in the chorion. It however should be short enough to keep some rigidity, which is key to piercing the chorion and the embryo. Figure 1b shows a typical injection needle. To prepare a needle, mount a glass capillary (Internal Diameter 0.58 mm) on the needle puller. Adjust temperature and pulling strength (see Note 1). Test different settings until obtaining the desired needle shape (check needles under a dissection scope). Once the puller is correctly set, prepare several dozen injection needles. Carefully store them in a Petri dish, secured on a putty band and seal the dish with parafilm to avoid dust.

13. Injection plate: melt 0.5 g of agarose in 50 ml EM in a microwave to prepare a 1% agarose gel.

Pour it in a 90 mm Petri dish. When the agarose is at 60°C, gently place the injection mould so that it floats. Let the agarose solidify. Remove the mould with forceps, add some EM to prevent the gel from drying and store at 4°C up to a month. 11. Fire-polished glass Pasteur pipettes, to manipulate dechorionated embryos: approach the tip of the pipette close to the flame of a lighter until the glass slightly melts. Be careful not to melt it too much, otherwise the pipette opening may end up too small and embryos will be damaged when drawn into the pipette.

12. Penicillin / Streptomycin (Thermo Fisher Scientific): for transplanted embryos, use at 100 unit/ml Penicillin and 100 µg/ml streptomycin in EM. [START_REF] Kai | Sphingosine-1-phosphate receptors regulate individual cell behaviours underlying the directed migration of prechordal plate progenitor cells during zebrafish gastrulation[END_REF]. Transplant needle: mount a glass capillary (Internal Diameter 0.78 mm) on the needle puller and pull the capillary. The stretched part of the needle should be around 1.5 cm (Figure 1e). Test different settings until obtaining the desired shape and pull several dozen needles (see Note 1).

Mount a needle on the microforge. Position the needle very close to the microforge's filament, at the point where its inside diameter is 25 µm. Briefly heat the filament: upon dilatation the filament touches the needle, the glass locally melts then breaks upon retraction of the filament. Using the microgrinder, grind the tip of the needle for one minute at maximum speed to form a 35° bevel (Fig. 1e; see Note 2). To remove glass residues, mount the needle on a needle holder connected to a syringe (Fig. 1c) and wash the tip by briefly aspiring 2% hydrofluoric acid (toxic and highly corrosive, manipulate under a chemical fume hood) over 5 mm. Repeat three times. Immediately rinse three times by aspiring acetone over 1 cm. Store the needles on a putty band in a parafilm-sealed Petri dish.

14. Transplant plate: melt 0.5 g of agarose in 50 ml EM in a microwave to prepare a 1% agarose gel.

Pour it in a 90 mm Petri dish. When the agarose is at 60°C, gently place the injection mould so that it floats. Let the agarose solidify and remove the mould with forceps.

15. Transplant setup: around the fluorescent stereo-microscope, install the microinjector, connected to a needle holder mounted on the micromanipulator (Fig. 1f). [START_REF] Emmenlauer | XuvTools: free, fast and reliable stitching of large 3D datasets[END_REF].

Mounting and imaging

XuvTool

IMARIS (Bitplane).

5. Matlab (Mathworks).

R (R Foundation for Statistical Computing).

3-Methods

Embryo injection 1-

Warm the injection plate by placing it at 28°C at least 30 minutes before injection.

2-

Once fishes have laid, collect the embryos. Rinse them well to remove all the droppings and scales from the adults and harvest in EM in a 90 mm Petri dish. Transfer 50 embryos in an empty injection plate and squeeze them gently inside the grooves using forceps, without piercing the chorion. Orient the embryos with the animal pole up. Fill the plate with EM.

3-

Wear gloves while manipulating RNA to prevent contamination with RNAse, keep all solutions on ice. Prepare 4 µl of 50 ng/µl Histone2B-mCherry RNA solution by diluting the stock RNA solution in sterile-filtered water. This solution will be injected in embryos used as hosts in the transplant. Prepare 4 µl of 50 ng/µl Histone2B-mCherry RNA and 70 ng/µl LifeAct-GFP RNA. This will be injected in embryos used as cell donors in the transplant. To affect a particular pathway, it is possible to add other compounds to this solution, which will be present only in the transplanted cells. In particular, morpholinos or RNAs encoding dominant-negative or constitutively active forms of proteins can be used.

5-

To prepare host embryos, inject half of the embryos at the 1-cell stage, with the H2B-mCherry solution (Fig. 2a) (see Note 3). To do so, place an embryo close to the injection needle.

Using the manipulator, pierce through the chorion and through the cell membrane so that the needle tip is inside the cell (Fig. 2b). Avoid piercing the yolk and injecting into the yolk. Inject 4 nl (see Note 4) and remove the needle. The embryo should stay in the agarose groove. Repeat for 25 embryos and put the plate at 28°C. To prepare donor embryos, let embryos reach the 4-cell stage (1 hpf), and inject 2 nl of the H2B-mCherry and LifeAct-GFP solution into one of the four cells (Fig. 2c). Repeat for

Dechorionate

1-Coat a 35 mm plate with 1 ml of 1% agarose in EM. When the agarose has solidified, fill the plate with warmed EM (28°C). Transfer embryos to be dechorionated with a plastic Pasteur pipette.

2-

With two fine tweezers, carefully remove the chorion. This is done by pinching the chorion with one tweezer and delicately pulling on the scratch with the second tweezer (see Note 5). Repeat until the embryo is freed from the chorion. Tear the chorion gently and progressively to avoid crushing the embryo. Dechorionated embryos are very fragile and will not survive contact with air or plastic: for further steps, use fire-polished glass pipettes and agarose-coated plates.

3-Clean the plate by removing torn chorions and damaged embryos with a glass pipette then carefully place the plate at 28°C.

Shield to shield transplants

1-Fill a transplantation plate with Penicillin / Streptomycin EM and warm at 28°C.

2-

Wash the eyelash and transplant needle with 70% ethanol. For the transplant needle, mount it on a needle holder connected to a syringe and draw ethanol on 2 cm (Fig. 1c). Empty the needle and dry it by drawing air. Do not dry by blowing, as this may result in dust getting stuck in the needle. 4-Place a donor embryo in front of the needle and delicately insert the needle into the shield.

Be careful not to pierce nor be too close to the yolk. Gently draw up a few cells inside the needle (see Note 8). Using fluorescence, check that cells in the needle are labelled.

5-

Place the corresponding host embryo in front of the needle and delicately insert the needle into the shield. Be careful not to approach the yolk too much. Gently blow the cells into the host, taking care not to add too much liquid with them. However, it may be necessary to keep expelling EM while moving the needle out of the embryo, in order for the cells not to stick to the needle. Be careful not to blow any air as this will damage the embryo. Use fluorescence to check that cells are now in the shield of the host embryo (Fig. 3c).

6-

Repeat steps 4 and 5 until all host embryos have been transplanted. Remove donor and damaged embryos. Carefully place the plate in a 28°C incubator.

7-

Clean transplant needle with water, as described in step 2.

Mounting embryos

Embryos are mounted in a small volume of warm agarose, which cools and thus solidifies rapidly. Being fast is thus crucial: prepare workbench before mounting, so that all required equipment is at hand. Do not mount more than 3 embryos at a time.

1-Prepare 1 ml of 0.2% agarose in Penicillin / Streptomycin EM solution in a small glass vial and place it in a preheated 42°C hot block.

2-

Select one to three embryos and draw them in a fire-polished pipette. While the embryos are in the pipette, put the MatTek plate under the scope and focus on the bottom of the well.

3-

Drop the embryos in the 0.2% agarose solution without adding too much EM. Discard the remaining EM and draw the embryos back into the pipette. Take care to draw enough agarose after the embryos in order to fill the well before the embryos fall out.

4-

Blow a drop of agarose and the embryos into the MatTek well. Take care not to let the embryos touch air or the border of the well. Make sure the well is completely filled with agarose (see Note 9).

5-

Depending on room temperature, the agarose will set in about 1 minute, during which embryos should be oriented using the eyelash. While orienting the embryo, be careful to touch it only on the blastoderm and not on the yolk, which is very fragile. Depending on the type of microscope used for imaging (upright or inverted), place the shield upward or downward, against the glass bottom. In the latter case, use fluorescence to spot transplanted cells and orient the embryo properly.

6-Wait a few minutes for the agarose to set completely, then add a drop of Penicillin /

Streptomycin EM to prevent it from drying.

Imaging

1-Preheat the microscope cage at 28°C at least 30 minutes before starting imaging.

2-

Put the MatTek plate under the spinning-disc microscope and fill it with Penicillin / Streptomycin EM.

3-

Set the hygrometry module to 80% relative humidity. In absence of hygrometry control, place a water-soaked tissue to keep constant moisture. This will prevent the EM from evaporating and the agarose from drying.

4-

Using a 40x long range objective, spot an embryo and focus on labelled cells. Tune the laser power and exposure time to optimise image dynamics for both channels. Specified RNA doses should lead to bright GFP and mCherry signals, so that brief exposure times can be used (<100 ms; see Note 10). This limits photobleaching and toxicity, and allows for high frame rates, compatible with acquiring large z-stacks, at short time intervals (2 minutes). Using bright field, set the X and Y position, then the top and bottom of the z-stack, so that it encompasses the entire shield. Be careful to consider that the embryo is curved and that cells may therefore not migrate in a straight z plane. It may thus be useful to enlarge the z-stack in order to have the whole prechordal plate encompassed in the stack for the duration of the timelapse. To get a larger field of view, image several positions that will be stitched with the XuvTool software [START_REF] Emmenlauer | XuvTools: free, fast and reliable stitching of large 3D datasets[END_REF]. Neighbouring stacks require a 5-10 % overlap.

5-

Repeat step 4 for every embryo in the imaging plate then set the time interval to 2 minutes and z-step to 2 m. Launch the timelapse for two hours. Be careful that total acquisition time at each time step does not exceed 2 minutes.

Data analysis

A. Quantification of actin-rich protrusion orientation 1-Load images in ImageJ using the Bioformat plugin (Fig. 4a).

2-

Using the movement of labelled cells, determine the general direction of migration then rotate the movie using the "Rotate" function of ImageJ to set the direction angle to 0°.

3-

On the green channel, for each time step and each transplanted cell, look for actin-rich protrusions. We consider all protrusions exceeding 5 µm in length. If present, measure their 2D orientation using the "Angle" tool. Draw a straight line from the centroid of the cell toward the stem of the protrusion and measure the angle relative to the general direction of migration (Fig. 4b).

B. Cell tracking 1-

Open the timelapse series with IMARIS. Set the pixel size, depending on the microscope and camera used for imaging (Fig. 4d).

2-

Use the "Spot" function to locate and track nuclei. Set object size to 10 µm, which is the average nucleus size at this developmental stage. Due to lower axial resolution, nuclei may appear elongated in the axial dimension. It is therefore best to allow ellipsoidal shape, with 15 µm in the Z axis. Filter on spot quality to remove false positive. Filter on red intensity to discriminate between ectoderm cells and migrating prechordal plate cells, which, being deeper in the embryo, appear dimmer. Prechordal plate cells migrate at about 3 +/-0.8 µm/min [START_REF] Dumortier | Collective mesendoderm migration relies on an intrinsic directionality signal transmitted through cell contacts[END_REF],

hence allow 9 µm as the maximal distance between consecutive time steps. Allowing gaps over one or two time points provides longer continuous tracks, without introducing too many track errors. Once automatic tracking is done, visually check tracks and manually correct them if necessary (Fig. 4e).

3-

Export the results as a .csv file and process with MatLab. We use custom made Matlab routines to compute instant speed, persistence, coherence, orientation of movement, etc. for each cell. Routines are available on request (Fig. 4f,g).

4-Notes

1-Injections and transplants are technically demanding steps, which highly depend on needles quality. Pulling needles of the right shape (see Fig. 1b,e for reference) requires fine tuning of parameters but generally, to get short and sharp needles for injection, the temperature should be set low and the tension high. On the contrary, for long transplant needles, temperature should be high and tension low.

2-To ease penetration in embryos, which can be difficult at late developmental stages, it is possible to add a barb at the tip of transplant needles. Install a transplant needle on the microforge with the tip 50 µm above the filament. Heat the filament, lower the needle to briefly touch the filament and immediately pull back. By melting the very tip of the bevel, this will stretch a glass barb. If the barb is too long, break it with forceps (Fig. 1e, insert). Pay attention that this procedure may reduce the diameter of the needle opening.

3-Embryos meant to be hosts are injected at the 1-cell stage. Injected RNAs will diffuse in the cytoplasm, leading most cells to be labelled, but with varying intensities, depending on how much RNA they inherited. On the contrary, in donor embryos it is important that all labelled cells have inherited similar levels of RNAs, so that all transplanted cells are similar. Hence, donors are injected at the 4-cell stage, since the RNA will diffuse in a smaller volume and be distributed homogeneously into the daughter cells.

4-Some calibrate injection volume by injecting in an oil drop and measuring the diameter of the created droplet. Although theoretically precise, this technique implies that injection conditions are constant from one embryo to another. Experience proves this to be false, resistance to fluid flow in the needle varying largely from one embryo to another, due to differences in the position of the needle in the embryo, and partial, transient, clogging of the needle. To get reproducible injections, it is thus preferable to visually control the volume of injected liquid, which can be seen as a clearer droplet in the cytoplasm. By comparing the size of the droplet to the rest of the embryo, it is possible to have a good estimation of the injected volume (Fig. 2a,c). Phenol red may be added to the injection solution to better visualise the droplet.

5-While dechorionating, be very careful when first pinching the chorion, since this is when the embryo has the most chance to be crushed. In particular, for injected embryos, the chorion is pierced at the injection spot and embryos have a tendency to squeeze through this hole if chorion is brutally pinched.

6-Oil may be used instead of air in the transplant system. Being inelastic, oil provides a more reactive setup. Entirely fill the microinjector, the tubing and the needle with oil. Use the oil setup as described for the air setup. One drawback is that, to be efficient, the whole system must be purged of any air bubble, which may be difficult. Furthermore, needles filled with oil tend to get dirty and thus cannot be reused as many times as when used with air.

7-Be careful to have the right amount of liquid in your needle: enough to draw and blow cells without contact with air, but not too much, otherwise the system will respond with a delay and sudden jolts. The interface between air and embryo medium must be kept in the stretched part of the needle.

8-Be careful not to draw up yolk in the needle nor to draw up too much liquid after the cells, since injecting yolk or large volumes of liquid appear toxic to the host. Yolk can be seen as a transparent, non-fluorescent mass in the needle. 9-Once embryos have been deposited in the well, and before orienting them, briefly rinse the glass transfer pipette to avoid agarose solidifying into it. Otherwise, although not visible, agarose will partially clog the pipette and likely harm the next embryo that will be mounted. Transplant needle is inserted in a needle holder, mounted on a mechanical micromanipulator. The needle is connected to a microinjector.

2 .

 2 Glass capillaries (Internal Diameter = 0.58 mm, External Diameter = 1 mm).

3 .

 3 Needle puller (KOPF Vertical pipette puller, model 720, David Kopf Instruments, Tujunga, California, USA).

4 .

 4 Injection mould (Figure 1a, 3D model available as a .stl file on request; commercially available from adaptive science tools, model TU1). 5. Injector (Eppendorf, Transjector 5246). 6. Manipulator (Narishige, model M-152).

2. 2

 2 Shield to shield transplant 1. Fluorescent stereo-microscope.

2 .

 2 Glass capillaries (Internal Diameter = 0.78 mm, External Diameter = 1 mm).

3 .

 3 Microforge (Narishige, model MF900). 4. Microgrinder (Narishige, model EG-44).

5 .

 5 Transplant mould (Figure 1d, 3D model available as a .stl file on request; commercially available from adaptive science tools, model PT1). 6. Eyelash mounted on a stick. 7. Micromanipulator (Leica, mechanical micromanipulator).

8 .

 8 Microinjector (Narishige, model IM-9B). 9. Fine tweezers for dechorionation (Dumont Fine Science Tools). 10. 35 mm Petri dishes.

1 .

 1 MatTek chamber (35 mm Dish, No. 1.5 Coverslip, 7 mm Glass Diameter, MatTek Corporation, Ashland, MA). 2. Microscopy: we use a Ti PFS (Nikon) inverted microscope equipped with a CSUX1-A1 (Yokogawa) spinning disc module, a 40x water immersion objective (plan Apo, N.A. = 1.15, Nikon), a Cobolt Calypso laser (491 nm, 100 mW) and a Cobolt Jive laser (561 nm, 100 mW) (Cobolt, 04-01 Series). The microscope is caged and heated using The Cube (Life Imaging Services) to maintain constant temperature and the sample is placed in a The Brick (life imaging Services) chamber to maintain constant hygrometry. Metamorph is used for acquisitions. 2.4 Softwares for imaging and picture analysing 1. Metamorph (Molecular Devices, LLC).2. ImageJ.

4 -

 4 Using microloader tips, fill the injection needle with 2 µL of RNA solution. Insert the needle in a needle holder, mounted on a manipulator and connected to the injector. Under the scope, delicately open the needle using forceps, either by scraping the tip or by breaking the very tip by pinching it. To test whether the needle is open, apply pressure with the injector and check that a drop of RNA solution forms at the tip. Then put the tip of the needle into the EM to prevent it from drying.

3 - 3 -

 33 When embryos have reached the shield stage (6 hpf), select donor and host embryos under a fluorescent stereo microscope. Pick embryos displaying bright and homogeneous fluorescence in the shield. Use the eyelash to manipulate and sort embryos. With a fire-polished glass pipette transfer selected embryos into the wells of the transplantation plate, aligning vertically and side by side hosts and donors. Rotate the embryos with the eyelash in order to place the shield up, slightly tilted toward the needle (Fig.3a,b). Install the transplant needle on the needle holder of the transplant setup (seeNote 6). Under the scope, orient correctly the bevel of the needle: if cells must be transplanted deep, turn the bevel downward; orient it upward to transplant cells superficially. Lower the needle into the EM and aspire EM over half of the stretched part of the needle (seeNote 7).

4 -

 4 Use R and the circular package for data analysis and representation. If angles are measured over 0-180°, classic statistical tests can be used to compare two distributions, like the Kolmogorov-Smirnov test (ks.test). If angles are measured over 0-360°, circular statistical tests, like Watson's two sample test (watson.two.test), should be used. Data are best presented as a rose diagram (rose.diag) (Fig. 4c).

10 -

 10 Laser light and emitted fluorescent light are partially absorbed and diffracted by the sample, leading to signal attenuation when imaging deep. We use a custom Metamorph journal to compensate for this loss of signal. Exposure time is linearly increased while getting deeper in the sample, so that exposure time is doubled over the entire stack.

Figure 1 :

 1 Figure 1: Injection and transplant equipment. (a) 3D model of the injection mould used to prepare

Figure 2 :

 2 Figure 2: Injection procedure. (a) Schematic of the injection procedure at the 1-cell stage. The

Figure 3 :

 3 Figure 3: Shield to shield transplant procedure. (a) Schematic of the transplant procedure. Embryos

Figure 4 :

 4 Figure 4: Data analysis. (a) Transplanted cells expressing LifeAct-GFP. Large actin-rich protrusions are

Acknowledgement

This work was supported by grant PJA 20151203256 for Fondation ARC pour la Recherche sur le Cancer, and grant ANR-15-CE13-0016-02 from Agence Nationale de la Recherche.