Marine Blondeau

Yohan Guyodo

François Guyot

Christophe Gatel

Nicolas Menguy

Imène F Chebbi

Bernard Haye

Mickaël Durand-Dubief

Edouard F Alphandéry

Roberta Brayner

Edouard Alphandery

Thibaud Coradin
email: thibaud.coradin@upmc.fr

Magnetic-field induced rotation of magnetosome chains in silicified magnetotactic bacteria

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Introduction

Since their discovery more than 30 years ago, magnetotactic bacteria have received much attention in the fields of geological, chemical, physical and biological sciences [START_REF] Blakemore | Magnetotactic Bacteria[END_REF][START_REF] Faivre | Magnetotactic bacteria and magnetosomes[END_REF][START_REF] Komeili | Molecular mechanisms of compartmentalization and biomineralization in magnetotactic bacteria[END_REF][START_REF] Lefèvre | Ecology, diversity, and evolution of magnetotactic bacteria[END_REF][START_REF] Prozorov | Novel magnetic nanomaterials inspired by magnetotactic bacteria: Topical review[END_REF] . However, the processes by which they synthesize iron oxide (or sulphide) magnetic nanoparticles and organize them into chains allowing the cell to orient itself along the geomagnetic field are still far from being fully understood [START_REF] Frankel | Magnetic guidance of organisms[END_REF][START_REF] Frankel | How magnetotactic bacteria make magnetosomes queue up[END_REF][START_REF] Mao | Magnetotaxis and acquisition of detrital remanent magnetization by magnetotactic bacteria in natural sediment: First experimental results and theory[END_REF][START_REF] Popp | Polarity of bacterial magnetotaxis is controlled by aerotaxis through a common sensory pathway[END_REF][START_REF] Zhu | Angle sensing in magnetotaxis of Magnetospirillum magneticum AMB-1[END_REF] . It is well-admitted that production of the nanocrystals occurs in specialized organelles, called magnetosomes, formed by a membrane invagination at multiple sites in the cell. However, identifying the proteins controlling nucleation, size, shape and arrangement in chains of the nanocrystals, as well as the mechanisms of action of these proteins, remains a challenging task [START_REF] Gorby | Characterization of the bacterial magnetosome membrane[END_REF][START_REF] Bazylinski | Magnetosome formation in prokaryotes[END_REF][START_REF] Komeili | Magnetosome vesicles are present before magnetite formation, and MamA is required for their activation[END_REF][START_REF] Nudelman | Structure prediction of magnetosome-associated proteins[END_REF][START_REF] Uebe | Magnetosome biogenesis in magnetotactic bacteria[END_REF] .

Phenotypic divergences between different species were evidenced [START_REF] Richter | Comparative Genome Analysis of Four Magnetotactic Bacteria Reveals a Complex Set of Group-Specific Genes Implicated in Magnetosome Biomineralization and Function[END_REF] . In some Magnetospirillum sp. strains, the chain is stabilized along the longitudinal axis of the cell by an organic filament, MamK protein, while the connection of magnetosomes to this structure is provided by a protein MamJ [START_REF] Scheffel | An acidic protein aligns magnetosomes along a filamentous structure in magnetotactic bacteria[END_REF][START_REF] Komeili | Magnetosomes Are Cell Membrane Invaginations Organized by the Actin-Like Protein MamK[END_REF] . The deletion of MamK gene in Magnetospirillum gryphiswaldense MSR-1 leads to short chains separated by gaps devoid of magnetosomes, while the deletion of MamJ induces aggregation of magnetosomes within the cell with observable filaments not attached to the biogenic particles [START_REF] Scheffel | The Acidic Repetitive Domain of the Magnetospirillum gryphiswaldense MamJ Protein Displays Hypervariability but Is Not Required for Magnetosome Chain Assembly[END_REF][START_REF] Katzmann | Loss of the actin-like protein MamK has pleiotropic effects on magnetosome formation and chain assembly in Magnetospirillum gryphiswaldense[END_REF] . In Magnetospirillum magneticum AMB-1, additional MamJ-like and MamK-like proteins were identified that are involved in the dynamic of the filament and the magnetosome organization in chain [START_REF] Rioux | A Second Actin-Like MamK Protein in Magnetospirillum magneticum AMB-1 Encoded Outside the Genomic Magnetosome Island[END_REF][START_REF] Draper | a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ[END_REF][START_REF] Abreu | Interplay between two bacterial actin homologs, MamK and MamK-Like, is required for the alignment of magnetosome organelles in Magnetospirillum magneticum AMB-1[END_REF] .

The capacity of the magnetosome chain to act as a compass is not only related to the spatial arrangement of nanocrystals, but also to their crystallographic and magnetic alignment.

In some magnetotactic bacteria (e.g., Magnetospirillum sp.), the biogenic magnetite nanoparticles have a cubo-octahedral morphology with a magnetic easy axis [111] aligned along the chain axis [START_REF] Mann | Structure, morphology and crystal growth of bacterial magnetite[END_REF][START_REF] Bazylinski | Electron microscopic studies of magnetosomes in magnetotactic bacteria[END_REF] . The magnetization of a given single domain crystal is also oriented parallel with respect to the others in the chain thus forming a larger-scale magnetic dipole [START_REF] Dunin-Borkowski | Magnetic Microstructure of Magnetotactic Bacteria by Electron Holography[END_REF] . It could be expected that an external magnetic field present during the formation of magnetosomes, or once the chains are formed, could affect the organization of these biogenic structures. Few reports are available on the effect of an external magnetic field on the biomineralization process itself [START_REF] Wang | Sinusoidal magnetic field stimulates magnetosome formation and affects mamA, mms13, mms6, and magA expression in Magnetospirillum magneticum AMB-1[END_REF][START_REF] Wang | Magnetosome formation and expression of mamA, mms13, mms6 and magA in Magnetospirillum magneticum AMB-1 exposed to pulsed magnetic field[END_REF][START_REF] Wang | Effects of static magnetic field on magnetosome formation and expression of mamA, mms13, mms6 and magA in Magnetospirillum magneticum AMB-1[END_REF][START_REF] Pan | Effects of pulsed magnetic field on the formation of magnetosomes in the Magnetospirillum sp. strain AMB-1[END_REF] . The interactions between already-formed magnetosomes and an external magnetic field have been so far mainly studied on free-moving bacteria [START_REF] Blakemore | Magnetotactic Bacteria[END_REF][START_REF] Ērglis | Dynamics of Magnetotactic Bacteria in a Rotating Magnetic Field[END_REF][START_REF] Nadkarni | A Comparison of Methods to Measure the Magnetic Moment of Magnetotactic Bacteria through Analysis of Their Trajectories in External Magnetic Fields[END_REF] or cell-extracted magnetosomes [START_REF] Körnig | Magnetite Crystal Orientation in Magnetosome Chains[END_REF] . In one report, magnetotactic bacteria were immobilized in agarose gels, allowing for the observation a field-induced re-orientation of the chains without rotation of the whole bacterial cell [START_REF] Körnig | Probing the Mechanical Properties of Magnetosome Chains in Living Magnetotactic Bacteria[END_REF] . Importantly the chain deviation was shown to be reversible when the field was turned off, suggesting that the assembly of proteins involved in the nanocrystal organization had a dynamic character.

These intriguing observations opened many additional questions such as the effect of chain re-orientation on cell viability as well as its impact on the crystallographic and magnetic orientation of the nanoparticles. Aiming to go further in the understanding of these processes, we have used here a mineral matrix, made of hydrated silica, as an encapsulation host for the AMB-1 magnetotactic bacteria, in order to prevent their motility in presence of an external magnetic field. This mineral matrix can be obtained in water, near neutral pH and at room temperature [START_REF] Depagne | How to design cell-based biosensors using the solgel process[END_REF] . It is transparent, chemically-stable and not biodegradable by most living organisms. Such cellular hosts have been previously shown to be compatible with the longterm viability of several strains of bacteria and many other living cells [START_REF] Blondeau | Living materials from sol-gel chemistry: current challenges and perspectives[END_REF] . In these environments, bacteria are confined in a cavity adapted to their size, preventing their motility, and cell division is hindered to insure that the population remains constant over the whole experiment [START_REF] Nassif | Living bacteria in silica gels[END_REF] .

In these conditions, it was possible to observe the stable reorientation of magnetosome chains within living magnetotactic bacteria exposed to an external magnetic field. The detailed study of the resulting crystallographic and magnetic structures pointed out the dynamic character of the protein set involved in the organization of the magnetosome chains.

Results

Bacterial encapsulation and viability. Initially, AMB-1 cells were cultivated in presence of 20 µM of ferric quinate allowing for the production of magnetosomes. According to the transmission electron microscopy (TEM) observations, these bacteria had as expected biogenic nanoparticles aligned into one or more chains (Fig. 1a). After one day of encapsulation of a bacterial suspension (in phosphate buffer 10 wt% glycerol) in an aqueous silica gel, the ultrastructure of the bacteria remained well preserved (Fig. 1b) and scanning electron microscopy (SEM) images showed that the cells were well dispersed in the porous mineral network (Fig. 1c). Within the encapsulated bacterium in Fig. 1b, magnetosomes with a size typical of 40-50 nm were aligned in chain located on average at 34 nm away from the cytoplasmic membrane. The distance between individual nanoparticles was ca. 7 nm. These values were typical of this type of cells, suggesting that the encapsulation process did not impact magnetosome organization [START_REF] Gorby | Characterization of the bacterial magnetosome membrane[END_REF][START_REF] Bazylinski | Magnetosome formation in prokaryotes[END_REF] . In order to evaluate the viability of the magnetotactic bacteria encapsulated in gels, a colorimetric Alamar Blue test was used to directly quantify the whole viable cells comprising also non-cultivable bacteria. This test allows for the monitoring of the oxygen-consuming metabolism of the cells and was shown to fully correlate with the plate count technique for bacterial viability quantification in the case of silica-encapsulated bacteria. [START_REF] Blondeau | Correlating biological methods to assess Escherichia coli bacteria viability in silica gels[END_REF] The Alamar Blue test indicated that after 7 days of encapsulation, 28 % (+/-4 %) of bacteria were alive in gels (Fig. S1). In parallel, the bacterial gels were exposed to an external static magnetic field of 80 mT by means of two parallel magnets placed on either side of flasks containing cells (Fig. S2). A nearly identical viability rate of 27 % (+/-4 %) was obtained after 7 days, indicating that the magnetic field did not significantly affect the viability of the bacteria over this period (Fig. S1).

Magnetic properties of bacteria encapsulated in silica gel. Direct current (DC) induced magnetizations and backfield demagnetizations of the bacteria encapsulated in silica aerogel after 1 day were acquired at room temperature. The hysteresis loop displayed a magnetic behavior typical of a mixture between diamagnetic (negative slope of the curve, noticeable at high fields) and ferro-or ferri-magnetic (open hysteresis) materials (Fig. 2a). Mathematical subtraction of the diamagnetic contribution allowed us to isolate the ferrimagnetic contribution of the nanocrystals (Fig. 2b). The sample was characterized by saturation magnetization (Ms) and saturation remanent magnetization (Mrs) values of 0.065 and 0.030 Am 2 .kg -1 , respectively. The saturation magnetization was very low due to the dispersion of the cells within the silica matrix. The sample coercivity (Bc) and coercivity of remanence (Bcr) obtained from backfield measurements were 32 and 38 mT, respectively. The Bcr/Bc and Mrs/Ms ratios were 1.19 and 0.46, respectively. These values are close to those previously reported for whole cell AMB-1. [START_REF] Li | Magnetic anisotropy, magnetostatic interactions and identification of magnetofossils[END_REF][START_REF] Li | A comparative study of magnetic properties between whole cells and isolated magnetosomes of Magnetospirillum magneticum AMB-1[END_REF][START_REF] Moskowitz | Rock magnetic criteria for the detection of biogenic magnetite[END_REF][START_REF] Pan | Rock magnetic properties of uncultured magnetotactic bacteria[END_REF] Thermal demagnetization curves of low-temperature saturation remanent magnetization (acquired in 2.5 T at 10 K) after cooling from room temperature in zero magnetic field (zero field cooling, ZFC) or in a 2.5 T magnetic induction (field cooling, FC) displayed a drop in magnetization around 100-110 K characteristic of the Verwey transition, in agreement with previous other AMB-1 samples [START_REF] Li | Magnetic anisotropy, magnetostatic interactions and identification of magnetofossils[END_REF] (Fig. 2c). The Verwey transition was also clearly visible on the cooling and warming curves of the room temperature (acquired at 300 K in 2.5 T), attesting that bacterial nanocrystals corresponded to magnetite (Fig. 2d). [START_REF] Dunlop | Rock Magnetism: Fundamentals and Frontiers[END_REF] In addition, the rather flat aspect of the cooling curve above the transition indicated that our samples were not oxidized. δ FC and δ ZFC ratios [START_REF] Moskowitz | Rock magnetic criteria for the detection of biogenic magnetite[END_REF] were equal to 0.14 and 0.09, respectively.

The δ FC /δ ZFC ratio of 1.5 was below the commonly accepted cut-off value of 2 for intact chains of magnetosomes. This suggests that: (i) some chains were disrupted during the CO 2 supercritical drying for aerogel preparation or (ii) bacteria were encapsulated at different stages of magnetosome chains formation [START_REF] Li | Magnetic anisotropy, magnetostatic interactions and identification of magnetofossils[END_REF][START_REF] Moskowitz | Rock magnetic criteria for the detection of biogenic magnetite[END_REF][START_REF] Carter-Stiglitz | Low-temperature remanence in stable single domain magnetite[END_REF] .

Effect of the magnetic field on magnetosome orientation. The bacteria entrapped in silica matrix without further iron supply (to limit the production of new magnetosomes) were observed after 7 days of exposition or not to an external magnetic field of up to 80 mT (Fig. 3). Whereas the orientation of the magnetosome chains parallel to the bacterial longitudinal axis was preserved in the absence of magnetic field (Fig. 3a), some of the bacteria exposed to the 80 mT field presented several chains of magnetosomes disposed parallel between them but inclined relative to the longitudinal axis of the bacteria (Fig. 3b). Noticeably, those two orientations were sometimes observed within one cell (Fig. 3c). The length of magnetosomes chains oriented transversely to the cell body varied from one bacterium to another (chains of 3 to 6 nanocrystals) (Fig. 3b, 3c andS3). Importantly, bacteria in suspension after 7 days in presence of a magnetic field presented the same magnetosome orientations as in the initial bacterial suspension, indicating that these unusual chain orientations were due to the combination of cell immobilization and external magnetic field. Further information was obtained using off-axis Electron Holography (EH), a powerful interferometric TEM method to correlate morphological microscopy information and local magnetic measurements of nanomaterials [START_REF] Dunin-Borkowski | Off-axis electron holography of patterned magnetic nanostructures[END_REF][START_REF] Dunin-Borkowski | Off-axis electron holography of magnetic nanowires and chains, rings, and planar arrays of magnetic nanoparticles[END_REF][START_REF] Gatel | Size-Specific Spin Configurations in Single Iron Nanomagnet: From Flower to Exotic Vortices[END_REF][START_REF] Reyes | Magnetic Configurations in Co/Cu Multilayered Nanowires: Evidence of Structural and Magnetic Interplay[END_REF][START_REF] Galindo-Gonzalez | Magnetic and microscopic characterization of magnetite nanoparticles adhered to clay surfaces[END_REF] . This technique allows a quantitative mapping of the magnetic properties of magnetosome chains at the nanoscale [START_REF] Dunin-Borkowski | Magnetic Microstructure of Magnetotactic Bacteria by Electron Holography[END_REF][START_REF] Dunin-Borkowski | Off-axis electron holography of magnetotactic bacteria: magnetic microstructure of strains MV1 and MS1[END_REF][START_REF] Li | Crystal growth of bullet-shaped magnetite in magnetotactic bacteria of the Nitrospirae phylum[END_REF][START_REF] Simpson | Magnetic induction mapping of magnetite chains in magnetotactic bacteria at room temperature and close to the Verwey transition using electron holography[END_REF][START_REF] Devouard | Magnetite from magnetotactic bacteria; size distributions and twinning[END_REF][START_REF] Pósfai | Characterization of Bacterial Magnetic Nanostructures Using High-Resolution Transmission Electron Microscopy and Off-Axis Electron Holography[END_REF] . Here, bacteria with pre-existing magnetosomes in suspension and unexposed to the external magnetic field were first observed after 7 days (Fig. 4a). The contour map of the magnetic flux inside and outside the magnetosomes chains suggests that the biogenic particles were coupled parallel and that the magnetization of each magnetosome was aligned forming a magnetic dipole as usually observed in magnetotactic bacteria [START_REF] Dunin-Borkowski | Magnetic Microstructure of Magnetotactic Bacteria by Electron Holography[END_REF] (Fig. 4b andc). Encapsulated bacteria were observed after 7 days of exposure to a magnetic field (Fig. 4d andg). In bacterium containing only chains deviated off the cell longitudinal axis (Fig. 4d), off-axis EH images displayed anti-parallel coupling between the magnetosomes (Fig. 4e) whereas for bacterium exhibiting both parallel and deviated chains off the cell longitudinal axis (Fig. 4g), two magnetic configurations were observed: (i) an anti-parallel coupling in deviated chain (Fig. 4h) and (ii) a parallel coupling in parallel chain (Fig. S4). Complementary experiments were performed to determine how the magnetosomes reoriented in the applied magnetic field. High-resolution TEM (HRTEM) analyses were used to determine the crystallographic axes in nanoparticles from different chains previously studied by electron holography. In the magnetosome chain of the bacterium not exposed to the magnetic field, the [111] axes were aligned parallel to the bacterial longitudinal axis (Fig. 4c; S5), as already observed for Magnetospirillum sp. [START_REF] Mann | Structure, morphology and crystal growth of bacterial magnetite[END_REF][START_REF] Dunin-Borkowski | Magnetic Microstructure of Magnetotactic Bacteria by Electron Holography[END_REF] . The same crystallographic orientation was observed for the bacterium containing only chains deviated off the longitudinal cell axis (Fig. 4f; S6) and for the bacterium where both chain orientations coexisted (Fig. 4i; S7). Some [111] axes in deviated chains in both bacteria (Fig. 4f; 4i) were oriented in the direction or close to the direction of the particles magnetization (Fig. 4e;4h). In the chain placed along the longitudinal axis of the cell (Fig. 4g; S4 and S8), the [111] axes of magnetosomes preserved their orientations parallel to the magnetization and in the chain direction.

Discussion

So far, the influence of a magnetic field on magnetosome within magnetotactic bacteria has been mainly studied on cell suspensions, showing noticeable effects on magnetosome size, morphology and rate of production [START_REF] Wang | Sinusoidal magnetic field stimulates magnetosome formation and affects mamA, mms13, mms6, and magA expression in Magnetospirillum magneticum AMB-1[END_REF][START_REF] Wang | Magnetosome formation and expression of mamA, mms13, mms6 and magA in Magnetospirillum magneticum AMB-1 exposed to pulsed magnetic field[END_REF][START_REF] Wang | Effects of static magnetic field on magnetosome formation and expression of mamA, mms13, mms6 and magA in Magnetospirillum magneticum AMB-1[END_REF][START_REF] Pan | Effects of pulsed magnetic field on the formation of magnetosomes in the Magnetospirillum sp. strain AMB-1[END_REF] . One study by Körnig et al. reported the effect of a magnetic field on MSR-1 bacteria entrapped within an agarose hydrogel [START_REF] Körnig | Probing the Mechanical Properties of Magnetosome Chains in Living Magnetotactic Bacteria[END_REF] . At sufficiently high magnetic field (35 mT and above), a rotation of the nanocrystals to align along the field direction was reported. When these cells were fixed with paraformaldehyde (i.e. preserving the intracellular organization when the field is turned off), short chains were observed that were also aligned along the field direction. Such a disruption of the chain organization was further evidenced by application of a second field that could re-orientate the chains only if the first field had an intensity above 35 mT. Interestingly, if the first field was turned off without cell chemical fixation, the initial chains were recovered. Such reversibility would suggest that the assembly of MamK/MamJ proteins responsible for chain integrity had a strong dynamic character, allowing for chain reconstruction after the field-induced disruption.

Compared to this study, our system has several specificities. First it must be pointed out that the magnetotactic bacteria strain we used, AMB-1, does not show the exact same set of proteins as MSR-1, [START_REF] Richter | Comparative Genome Analysis of Four Magnetotactic Bacteria Reveals a Complex Set of Group-Specific Genes Implicated in Magnetosome Biomineralization and Function[END_REF][START_REF] Scheffel | An acidic protein aligns magnetosomes along a filamentous structure in magnetotactic bacteria[END_REF][START_REF] Komeili | Magnetosomes Are Cell Membrane Invaginations Organized by the Actin-Like Protein MamK[END_REF][START_REF] Scheffel | The Acidic Repetitive Domain of the Magnetospirillum gryphiswaldense MamJ Protein Displays Hypervariability but Is Not Required for Magnetosome Chain Assembly[END_REF][START_REF] Katzmann | Loss of the actin-like protein MamK has pleiotropic effects on magnetosome formation and chain assembly in Magnetospirillum gryphiswaldense[END_REF][START_REF] Rioux | A Second Actin-Like MamK Protein in Magnetospirillum magneticum AMB-1 Encoded Outside the Genomic Magnetosome Island[END_REF][START_REF] Draper | a bacterial actin, forms dynamic filaments in vivo that are regulated by the acidic proteins MamJ and LimJ[END_REF][START_REF] Abreu | Interplay between two bacterial actin homologs, MamK and MamK-Like, is required for the alignment of magnetosome organelles in Magnetospirillum magneticum AMB-1[END_REF] which could at least explain some of the differences between the two systems. Contrary to some magnetotactic bacteria which are difficult to isolate, cultivate [START_REF] Schüler | Manual of Environmental Microbiology[END_REF] or are obligate microaerophile, [START_REF] Blakemore | Isolation and pure culture of a freshwater magnetic spirillum in chemically defined medium[END_REF][START_REF] Maratea | Aquaspirillum magnetotacticum sp. nov., a magnetic spirillum[END_REF] AMB-1 bacteria grow in liquid culture medium and on agar plates in presence of oxygen. [START_REF] Matsunaga | Magnetite formation by a magnetic bacterium capable of growing aerobically[END_REF] This strain is not obligate microaerophile and can therefore be easily manipulated for various applications.. [START_REF] Faivre | Magnetotactic bacteria and magnetosomes[END_REF][START_REF] Yang | Effects of growth medium composition, iron sources and atmospheric oxygen concentrations on production of luciferase-bacterial magnetic particle complex by a recombinant Magnetospirillum magneticum AMB-1[END_REF][START_REF] Matsunaga | Biotechnological application of nano-scale engineered bacterial magnetic particles[END_REF] The incubation of these oxygen-tolerant bacteria in culture medium bottle without stirring and air exchange at 30°C permitted to obtain microaerophilic conditions favoring the magnetosomes productions. In our experiments, the oxygen tolerance of AMB-1 bacteria limited the stress of the encapsulation in an air atmosphere. Compared to M. gryphiswaldense, M. magneticum possess additional proteins (MamK-like and MamJ-like) acting in the chain magnetosomes organization and dynamic of the filament. [START_REF] Rioux | A Second Actin-Like MamK Protein in Magnetospirillum magneticum AMB-1 Encoded Outside the Genomic Magnetosome Island[END_REF][START_REF] Abreu | Interplay between two bacterial actin homologs, MamK and MamK-Like, is required for the alignment of magnetosome organelles in Magnetospirillum magneticum AMB-1[END_REF] Consequently, the cell response to a magnetic environment may depend on the strain and phenotypic divergences. [START_REF] Moisescu | The effect and role of environmental conditions on magnetosome synthesis[END_REF] Second, whereas in the previous study, the MSR-1 cells were initially aligned by a magnetic field before their immobilization in agarose, the AMB-1 cells were here randomly distributed within the silica gel when it formed and trapped the bacteria. In other words, if the observed magnetosome and/or chain orientation was strictly reflecting the external field direction, all organizations within a single bacterium should be the same, in contradiction with our observations. Finally, and more importantly, the chains deviated off the longitudinal cell axis were here observed when the external magnetic field was turned-off without the need for cell fixation. This calls for the examination of alternative mechanisms.

It seems crucial to first consider magnetosome nanocrystals and chains of magnetosomes independently. Electron microscopy studies on bacteria-containing gels after 1 and 7 days in the absence of external field indicated that the intracellular content of the initial magnetotactic bacteria was well-preserved within the silica network. In this situation, single domain magnetite nanoparticles were arranged in chains oriented parallel to the longitudinal axis of the cell. When the magnetic field was applied on the encapsulated bacteria, we observed that (i) some chains were no longer parallel to the cell longitudinal axis and remained so even if the field is turned-off, (ii) in these chains, the magnetosomes interacted via an anti-parallel magnetic coupling, (iii) they preserved their relative crystallographic coalignment, (iv) these modifications did not seem to have a significant detrimental effect on cell viability (as compared to encapsulated cells aged without external field). Some studies of M. gryphiswaldense MSR-1, have suggested that the magnetosome vesicles form a distinct compartment detached from the cytoplasmic membrane [START_REF] Scheffel | An acidic protein aligns magnetosomes along a filamentous structure in magnetotactic bacteria[END_REF] . The nucleation of magnetite crystals would take place in invagination of the cytoplasmic membrane, favoring iron transfer from the external medium; the vesicles would then detach at some stage of the biomineralization process [START_REF] Faivre | Intracellular magnetite biomineralization in bacteria proceeds by a distinct pathway involving membrane-bound ferritin and an iron(II) species[END_REF][START_REF] Raschdorf | Genetic and Ultrastructural Analysis Reveals the Key Players and Initial Steps of Bacterial Magnetosome Membrane Biogenesis[END_REF] . A dynamic filamentous protein MamK would play a role in the maintenance of chain continuity by reducing gaps between magnetosomes in M. magneticum AMB-1 [START_REF] Komeili | Magnetosomes Are Cell Membrane Invaginations Organized by the Actin-Like Protein MamK[END_REF][START_REF] Cornejo | Dynamic Remodeling of the Magnetosome Membrane Is Triggered by the Initiation of Biomineralization[END_REF] . Note that some remaining contact between the magnetic chain and the membrane is necessary to permit the alignment of the cell in the geomagnetic field [START_REF] Komeili | Molecular mechanisms of compartmentalization and biomineralization in magnetotactic bacteria[END_REF] . From this starting situation (Fig. 5a), the effect of the magnetic field can occur according to two hypothetical mechanisms: (i) the integrity of the whole chain is lost, allowing for the motion of individual magnetosomes in the magnetic field, that could be then collected and reassembled by the dynamic structural proteins MamK and MamJ (Fig. 5b). It has been suggested that the formation of magnetosome chains was a step-by-step process in which each particle is synthesized consecutively so that the orientation of the growing one is imposed by those already present [START_REF] Frankel | Magnetic guidance of organisms[END_REF][START_REF] Körnig | Magnetite Crystal Orientation in Magnetosome Chains[END_REF][START_REF] Frankel | Navigational compass in magnetic bacteria[END_REF][START_REF] Schüler | Magnetoreception and Magnetosomes in Bacteria[END_REF] . Here, as each magnetite nanocrystal would respond individually to the magnetic field before being reassembled, their relative crystallographic and magnetic orientation is difficult to predict.

(ii) the structures connecting magnetosomes to the cytoplasmic membrane would be disrupted to the exception of some possible anchoring sites and the protein filament insuring the chain integrity would be preserved. Then the whole chain would turn to align its global magnetic dipole along the external field (Fig. 5c). In this situation the crystalline orientation of the magnetosomes should be preserved whereas modification in the magnetic interactions can occur.

Here, we found out that the crystalline orientation within deviated chains after the field is turned off can be similar to non-deviated chains (i.e.

[111] axis parallel to the chain direction).

It is important to point out that compared to Körnig et al., 2014 [START_REF] Körnig | Probing the Mechanical Properties of Magnetosome Chains in Living Magnetotactic Bacteria[END_REF] , the cells were still alive (not chemically fixed) when the field was turned-off so that they could preserve their ability to synthesize the proteins involved in chains organization, orientation and interaction with the inner membrane. Turning to magnetic interactions, anti-parallel coupling has been observed in deviated chains of magnetosomes whereas parallel coupling was present in non-deviated ones. Overall, the magnetic field exposure has favored the destructuration of magnetosome chains organization In conclusion, our results shade new light on the mechanisms by which magnetotactic bacteria are able to control the assembly of magnetic nanocrystals within magnetosome chains. Our observation of a stable deviation of the chain orientation within living cells suggests that the assembly of cytoskeletal proteins regulating the nanocrystal organization would have a significant dynamic character, echoing recent evidences of the role of actin in iron oxide biomineralization in honeybees [START_REF] Hsu | Magnetoreception System in Honeybees (Apis mellifera)[END_REF] . Some other proteins could also have a role in maintaining stable deviated chains by interacting with magnetosomes and the cytoplasmic membrane. Of significance for the field of magnetotactic bacteria is the fact that the underlying process, and therefore the associated set of proteins, may be specific to AMB-1, providing an additional evidence of phenotypic divergence in this group of biomineralizing bacteria. The here-demonstrated possibility to manipulate chain orientation without impacting cell viability may also open opportunities for the use of encapsulated magnetotactic bacteria within functional devices. seconds, 1 mL of bacterial suspension (OD=5) was added and the assemblage was stirred for 5 minutes. The gels were formed after 5-6 min at room temperature and were then kept at 20 °C for up to 7 days.

Methods

The encapsulated bacteria were exposed to an external static magnetic field created by two parallel magnets. The magnets were placed in a set-up realized with Plexiglas TM and were spaced of 5 cm that permitted to have a field of 55 mT in the center of the set-up and 80 mT at each magnet (see Fig. 2b).

Characterization of bacteria-silica aerogels. In order to obtain dried material, AMB-1 containing silica gels were converted into aerogels via supercritical drying as described thereafter. Shortly, the bacterial gels are first fixed with a glutaraldehyde solution (2.5 %) for 1 hour and washed 3 times in a buffer. Then the samples are dehydrated in different baths of ethanol and dried by using a CO 2 supercritical point dryer.

The aerogel magnetization was first measured as a function of the applied field magnetic intensity at 300 K using a Vibrating Sample Magnetometer (VSM) model 3900 from Princeton Measurements Corporation. Low-temperature measurements were performed using a Superconducting Quantum Interferference Device (SQUID) magnetometer MPMS XL-5 from Quantum Design.

Scanning electron microscopy (SEM) was performed using a Zeiss Ultra 55 SEM-FEG microscope on a carbon-coated aerogel crushed sample.

Characterization of silica-extracted bacteria. Bacterial gels were dispersed in 5 ml of phosphate buffer, then broken with 4 mm glass beads under stirring for 15 minutes. The resuspended gels were then diluted in phosphate buffer before performed viability tests using the Alamar Blue method [START_REF] Blondeau | Correlating biological methods to assess Escherichia coli bacteria viability in silica gels[END_REF] .

For TEM observations, the resuspended gels were centrifuged at 600 x g at 10°C during 15 min to sediment the gel aggregates. The supernatant containing bacteria was collected and diluted in phosphate buffer. All diluted suspensions were washed by centrifugation at 6000 x g at 10°C during 15 min. The supernatant was removed and 3 ml of the bottom were kept and homogenized. 10 µL of concentrated bacterial suspension were placed on copper grids covered with thin carbon film and dried at 30°C during 3 hours to permit sedimentation of cells on the carbon film. Then the bacteria were fixed with 10 µL of glutaraldehyde (2.5 %) for 1 hour at 4°C. The samples were then washed with ultrapure water and dried before the observation by TEM using a JEOL TEM 2100 equipped with an LaB6 crystal gun, with an accelerating tension of 200 kV. The high-resolution TEM (HRTEM) has been performed on the same samples by using a TEM JEOL-2100F operating at 200 kV and equipped with a field emission gun (FEG). The in-plane crystallographic direction and observed zone axes have been determined by using the Fast Fourier transform on the twodimensional HRTEM images and have permitted to deduce then the corresponding stereographic projection for each particle. Off-axis electron holography (EH) was carried out using Hitachi HF3300C microscope, following previously described protocols 26,45,46,68,,69 .

Ultrathin sections of bacterial gels were prepared according to the following protocol. The bacterial gels were first fixed with a glutaraldehyde solution (2.5 %) for 1 hour and washed 3 times in a buffer, then fixed with osmium tetroxide solution (2 %) for 1 hour before washed 3 times in a buffer. The samples were then dehydrated in different baths of ethanol and embedded in Araldite ® resin.

Figure 1 .

 1 Figure 1. Electron microscopy imaging of free and silica-encapsulated magnetotactic bacteria. (a) TEM observation of M. magneticum AMB-1 in the initial bacterial suspension (magnetosome chains are indicated by black arrows). Bacteria encapsulated in silica gel observed by (b) TEM after ultrasectionning and (c) SEM using backscattered electrons after 1 day of encapsulation (bacteria are indicated by white arrows in silica gel).

Figure 2 .

 2 Figure 2. Magnetic properties of silica-encapsulated magnetotactic bacteria. Magnetization curves for the AMB-1 cell-containing aerogel after 1 day acquired at 300 K (a) between -1.5 T and +1.5 T and (b) between -0.5 T and +0.5 T with correction of the diamagnetic component. (c) Field Cooling (FC) and Zero Field Cooling

Figure 3 .

 3 Figure 3. TEM images of silica-encapsulated magnetotactic bacteria exposed, or not, to an external magnetic field. AMB-1 cells kept in (a) absence or (b, c) presence of an 80 mT magnetic field during 7 days of encapsulation. (Black arrows show undeviated chains and white arrows show deviated chains).

Figure 4 .

 4 Figure 4. Electron microscopy observations of magnetic and crystallographic orientations in magnetosomes. (a) TEM image of an AMB-1 cell in suspension observed after 7 days of incubation in absence

Figure 5 :

 5 Figure 5: Schematic representation of the possible mechanisms involved in deviated magnetosome chains. (a) AMB-1 bacteria with magnetosome chains connected to the cytoplasmic membrane via an invagination and stabilized by the molecular complexe MamK / MamJ. (b) Magnetosome chains disrupted during the magnetic field exposition. Each magnetosome responds individually to the field and arranges again in chain thanks to the molecular complex MamK / MamJ. (c) Whole magnetosome chains as one entity orient directly in the magnetic field direction.

Acknowledgements

M.B. thanks the Région Ile-de-France for funding in the framework of C'Nano IdF. C'Nano-IdF is the nanoscience competence center of Paris Region, supported by CNRS, CEA, MESR and Région Ile-de-France. We thank Corine Illoul and Jean Michel Guigner for their help in the ultramicrotomy samples preparation and microscopy observations.

Data Availability

Authors Contribution


Florian Beaugnon

Gianluca Gariani

Emmanuelle Gouillart

Anne Bouquillon

Marc Bormand

Gilles Wallez

Microstructure imaging of Florentine stuccoes through x-Ray tomography: a new insight on ancient plaster-making techniques

Keywords: Gypsum, Plasters, Renaissance stuccoes, X-Ray microtomography, Porosity Highlights

Gypsum-based plasters or stuccoes, in spite of their importance and diffusion, received little attention in cultural heritage materials studies. This work introduces a new, non-destructive methodology, using micro-tomography to measure the water/plaster ratio and the morphology of the hemihydrate powder used to make plasters on < 1mm 3 samples. This methodology give insight in both the raw material (and ultimately provenance) and the technique used to make plaster. The methodology was tested first on mock-up samples of known composition, then in a case study on 13 low-relief cast plaster sculptures from 15 th century Florentine artists. Preliminary conclusions on this limited corpus show relative uniformity across most reliefs in terms of raw materials and techniques. The casts of one model (Nativity, attributed to Donatello and B. Bellano) were made with a different raw material, in line with prior geochemical analyses ; these results support the previous attribution to a North Italian rather than Florentine origin. The casts of a second model (Virgin and Child, type of Saint Petersburg, attributed to Antonio Rossellino) were prepared with a different technique. This surprising result was not expected from Art History or previous studies.

Introduction

Gypsum (CaSO 4 -2H 2 O), formed as an evaporite mineral, is the raw material used in the manufacture of plasters. When heated above 100-120 °C [START_REF] Oetzel | Einfluss von Umbegungsfeuchte und Temperatur auf die Phasenumwandlungen im System CaSO 4 -H 2 O -Ein Betrag zur Herstellung von phasenreinen Bindemitteln aus REA-Gips[END_REF] it releases part of its water as vapor and forms calcium sulfate hemihydrate, the main constituent of the reactive plaster powder (eq. 1).

CaSO 4 ⋅2 H 2 O → CaSO 4 ⋅0.5 H 2 O+ 1.5 H 2 O( g ) (1) Mixed with water in a slurry, hemihydrate dissolves and recrystallises to set as secondary gypsum crystals (eq. 2).

CaSO 4 ⋅ 0.5 H 2 O+1.5 H 2 O (l )→ CaSO 4 ⋅2 H 2 O (2) Other phases can appear during or after the calcination of primary gypsum: when exposed to a wet atmosphere, hemihydrate turns to CaSO 4 -0.625H 2 O [START_REF] Schmidt | Water channel structure of bassanite at high air humidity: crystal structure of CaSO 4 -0.625H 2 O[END_REF]; soluble anhydrite (γ-CaSO 4 ) forms if the calcination is run in a dry atmosphere or at a slightly higher temperature [START_REF] Oetzel | Einfluss von Umbegungsfeuchte und Temperatur auf die Phasenumwandlungen im System CaSO 4 -H 2 O -Ein Betrag zur Herstellung von phasenreinen Bindemitteln aus REA-Gips[END_REF]. Both these soluble subhydrates behave like hemihydrate when mixed with water. However, at higher temperatures of 250-350 °C, γ-anhydrite transforms into insoluble anhydrite (β-CaSO 4 ) [START_REF] Jacques | Structural evolution during the dehydration of gypsum materials[END_REF]. This unreactive phase behaves as a charge that does not take part in the setting, thus lowering the mechanical properties of the final material. For these reasons, the β-CaSO 4 is generally unwanted and is only present as a result of excessive heating or from impurities in the raw gypsum.

The setting of the plaster is a two-step process. The dissolution of hemihydrate grains is quickly halted by the saturation of the solution, and gypsum seeds slowly appear during an activation period of several minutes. In a second step, the growth of the gypsum crystals depletes the solution and the hemihydrate grains are completely dissolved [START_REF] Joiret | Submicrometric Picture of Plaster Hydration: Dynamic and Space-Resolved Raman Spectroscopy versus Kinetic Monte Carlo Simulations[END_REF]. As for any hydraulic binder, the proportion of water and hemihydrate is an important parameter as it affects the rheology of the slurry and the density of the final material. It is quantified through the waterto-plaster ratio (W/P), based on the masses of the ingredients mixed to make the slurry. As only a small amount of water takes part in the re-hydration reaction (eq. ( 2)), most of it is left at the end of the reaction. Pores can be observed at several scales after drying. Macropores (typical size of a few hundreds of microns up to several millimeters in diameter) result from the trapping of air bubbles. The excess water that dries off leaves pores in the plaster at two additional scales : micropores of small size (under 10 µm) are found between crystals of secondary gypsum. Finally, the two-step reaction leads to the formation of mesopores (ranging in size from a few dozens to a few hundreds of microns). Their morphology results from the chronology of the setting of plaster, as secondary gypsum grows from seeds that form outside of hemihydrate grains, leaving "ghost pores" of identical shape after their dissolution (fig. 1) [START_REF] Adrien | In-situ X-ray tomographic monitoring of gypsum plaster setting[END_REF].

Figure 1 : Setting of plaster. The dissolution of hemihydrate and growth of gypsum is a two-step process: at first, gypsum seeds appear in the saturated solution with no significant dissolution of hemihydrate grains (1-2); gypsum crystals then grow while hemihydrate grains are dissolved until the reaction is complete [START_REF] Jacques | Structural evolution during the dehydration of gypsum materials[END_REF][START_REF] Joiret | Submicrometric Picture of Plaster Hydration: Dynamic and Space-Resolved Raman Spectroscopy versus Kinetic Monte Carlo Simulations[END_REF][START_REF] Adrien | In-situ X-ray tomographic monitoring of gypsum plaster setting[END_REF]. Excess water then dries off leaving pores behind [START_REF] Ma | Mercury intrusion porosimetry in concrete technology: tips in measurement, pore structure parameter acquisition and application[END_REF]. Drawn after J. Adrien et al. [START_REF] Adrien | In-situ X-ray tomographic monitoring of gypsum plaster setting[END_REF].

Both the total porosity and the morphology of the mesopores are of interest for the study of ancient plasters. The total porosity can be used to asses the W/P ratio. This ratio is adjusted depending on the casting technique, additives and intended use of the plaster. This makes it an important indicator of workshop practices. The morphology of the mesopores depends on the microstructures of the plaster powder; they are in turn affected by the crystal habitus of the primary gypsum and processing [START_REF] Adrien | In-situ X-ray tomographic monitoring of gypsum plaster setting[END_REF]. The morphology of the mesopores can thus be an indicator of the raw gypsum's crystal morphology and its transformation into a plaster powder.

Mercury intrusion porosimetry (MIP) is the go-to technique for the measurement of porosity in mineral materials, but can not be used with precious cultural heritage samples. The drying of the material prior to the measurement (common methods involve oven-, freeze-, or solvent-drying [START_REF] Ma | Mercury intrusion porosimetry in concrete technology: tips in measurement, pore structure parameter acquisition and application[END_REF]) as well as the trapping of mercury make it a destructive technique. This is often not acceptable with cultural heritage samples. In addition, while MIP provides a measurement of the total porosity and the distribution of pores size, it is only sensitive to the open, interconnected porosity. Bottlenecks in pores also result in an in-/extrusion hysteresis that only allows to measure the smallest section. X-ray tomography has been proposed as a better alternative for the study of porous rocks [START_REF] Kovarova | Comparison of mercury porosimetry and X-Ray microtomography for porosimetry study of sandstones[END_REF] as it is not subject to these limitations. It also allows the additional characterisation of the pores' shape in three dimensions whith no damage to the sample, unlike the more traditional micrography on thin sections. Tomography is routinely used for the characterisation of inorganic building materials, including gypsum plasters [START_REF] Bentz | The visible cement data set[END_REF][START_REF] Bouterf | Digital volume correlation applied to X-ray tomography images from spherical indentation tests on lightweight gypsum[END_REF][START_REF] Fusseis | Pore formation during dehydration of polycrystalline gypsum observed and quantified in a time-series synchrotron radiation based X-ray micro-tomography experiment[END_REF][START_REF] Bedford | A 4D view on the evolution of metamorphic dehydration reactions[END_REF]. It has also been applied to various cultural heritage topics. However, its application to the characterisation of ancient gypsum plasters has only been attempted from the angle of macrostructures [START_REF] Badde | Three dimensional computerized microtomography in the analysis of sculpture[END_REF][START_REF] Parisi | The conservation project of a liturgical object : the case of Infant Jesus of Prague in the church of Saint Mary of Providence at Macchia Giarre (Italy)[END_REF] and not from material sciences on a microscopic scale.

Research aims

This article reports on an exploratory work in which we researched a novel methodology for the analysis of ancient gypsum plasters, through a case study on samples taken from 15 th century Florentine reliefs. This effort was motivated by the need to find non-destructive protocols to extract information on both the raw material and workshop practices of the past. In this contribution, we adress two questions: 1. Is it possible to measure the W/P ratio and the morphology of the reactive powder used to make plaster, on the basis of synchrotron X-ray microtomography data? Can this method be validated with mock-up samples of small (1 mm 3 ) size, as required for the characterisation of valuable works of Art? 2. Are these analysis useful for the study of ancient plasters, i.e. do they allow a meaningful comparison on a test corpus of a dozen sampled reliefs from the Renaissance and do they bring new insights in the study of these reliefs? 2. Materials 2.1 Historical artworks 13 cast plaster low-reliefs from the 15 th century were sampled (fig. 2,table 1). They are part of a large production of artworks depicting religious scenes -almost exclusively compositions of the Virgin and Child -that were intended to be used as supports of private devotions in the homes of wealthy families [START_REF] Palmer | The Walters' Madonna and Child Plaquette and Private Devotional Art in Early Renaissance Italy[END_REF]. They were originally painted, gilded and framed in wood or plaster. Some of the original models survive as marble, terracotta or bronze sculptures from which the plaster casts were most likely moulded [START_REF] Pope-Hennessy | The interaction of painting and sculpture in Florence in the fifteenth century[END_REF][START_REF] Gentilini | Scultura dipinta o pittura a rilievo? Riflessioni sulla policromia nel quattrocento fiorentino[END_REF]. The reliefs, cast in gypsum-based plaster (often described using the more generic "stucco" in artistic litterature), were manufactured in multiples after models by Florentine artists such as Lorenzo Ghiberti, Donatello, Luca Della Robbia, Antonio Rossellino, Desiderio da Settignano or Mino da Fiesole. While these artists spent most of their working life in Florence, some are known to have been active in other cities [START_REF] Vasari | The lives of the artists[END_REF]. The original reliefs are expected to have been produced in the bottegha of the masters but might have been replicated in other workshops on the models they supplied. In addition, there is a possibility they were imitated in other places and at a later time. This is especially true for the 19 th century when a resurgence of interest from collectors and academies could have prompted the making of forgeries [START_REF] Gentilini | Scultura dipinta o pittura a rilievo? Riflessioni sulla policromia nel quattrocento fiorentino[END_REF][START_REF] Natale | L'art d'imiter[END_REF]. This work is part of a larger project that aims at understanding the manufacturing techniques and sourcing of the raw material of these low-relief sculptures, including studies of the geology and chemistry of the binder [START_REF] Gariani | First insights on the mineral composition of "stucco" devotional reliefs from Italian Renaissance Masters: investigating technological practices and raw material sourcing[END_REF] and of organic additives [START_REF] Aksamija | Investigation of organic additives in Italian Renaissance devotion stucco reliefs from French collections[END_REF].

Recreation samples

In order to test the proposed methodology, mock-up samples were prepared with different hemihydrate powders (industrial vs. hand made). These were used for comparison of the mesopores morphologies; some were also prepared with different W/P ratio for the calibration of W/P measurements. Three samples were made from hemihydrate plaster (plaster 1) supplied by Saint-Gobain Research Paris. They were each prepared from 100 g of plaster powder and W/P = 0.50, 0.70 and 1.00. The plaster powders and water were mixed for 30 seconds in a plastic cup where they were left to set.

A fourth mix of plaster was made starting with acicular crystals of gypsum heated at 120 °C for 6 h in a muffle furnace. The calcined plaster (plaster 2) was then ground up to a powder using a mortar and pestle and mixed with water at W/P = 0.6. The plaster powder was again mixed for 30 s in a plastic cup and left to set; two samples were analysed to check the repetability of measurements.

No additives are included in either plaster 1 or plaster 2. Nethertheless, naturally occuring impurites were searched for using quantitative Rietveld phase analysis. None were detected in plaster 2, while CaCO 3 (3.0(8) % by mass) was found in plaster 1.

Samples preparation

The plaster samples, a few mm 3 in size, were taken using a surgical scalpel from the surface of both historic and recreation plasters. Historic samples were extracted from the back and sides of the reliefs in places hidden to comply with deontological concerns.

To fit the 1.2 mm X-ray beam size, a 1 mm internal diameter polyimide tubing transparent to X-Rays was used as a sample holder. Most samples (both historical and recreations) were wider than 1 mm and broken into up to five fragments to fit inside the sample holder tubing. All of them were analyzed for a better measurement statistics.

Methods 3.1 Images acquistion

Our experiments were done on the ESRF synchrotron micro-tomography beamline ID19 [21,[START_REF] Weitkamp | Parallel-beam imaging at the ESRF beamline ID19: current status and plans for the future[END_REF]. The choice of the source was motivated by the intense, quasi-monochromatic pink-beam that only synchrotron radiation can provide. It is neccessary for an accurate measurement of the absorption coefficient regardless of the sample's thickness, in order to avoid beam hardening effects which are unavoidable with a polychromatic beam.

For each 3-D volume, 3000 radiographies were acquired over 180° with a sCMOS PCO Edge camera, corresponding to a pixel size of 0.65 micrometer and a scan time of two minutes. A 19.6 keV pink beam was used, and a 10 µm GGG scintillator converted the transmitted X-ray beam to visible light. X-ray absorption maps were reconstructed in three dimensions from the raw data using the PyHST algorithm [START_REF] Mirone | PyHST2 Hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilites[END_REF] and processed using the python package Scikit image [START_REF] Der Walt | Scikit-image: image processing in Python[END_REF][START_REF] Gouillart | Analyzing microtomography data with Python and the scikit-image library[END_REF] (fig. 3).

Figure 3: reconstructed X-Ray absorption images (slices).

The samples can be seen inside sample holder tubes [START_REF] Oetzel | Einfluss von Umbegungsfeuchte und Temperatur auf die Phasenumwandlungen im System CaSO 4 -H 2 O -Ein Betrag zur Herstellung von phasenreinen Bindemitteln aus REA-Gips[END_REF]. In the secondary gypsum matrix ( 2) are primary gypsum inclusion (3) as well as pores. Mesopores ( 4) and trapped air bubbles ( 5) can be differentiated by the round shape of the latter.

Measurement of water-to-plaster ratio 3.2.1 Calculations

The W/P ratio is defined as the mass of water m W divided by the mass of plaster powder (hemihydrate) m H mixed in the plaster slurry. After the reaction, the stoechiometric part of the water is structurally bound in the gypsum while the rest, left in excess, is liquid and fills the pores of the gypsum.

W / PR= m W m H = m W ,excess +m W , gypsum m H (1)
The masses of structurally bound water and hemihydrate can be infered from the mass of gypsum in the set plaster and the molar masses of water, gypsum and hemihydrate (M W , M G , M H ):

W / PR= m W , excess + 1,5 M W M G * m G M H M G * m G ( 2
)
The masses of water in excess and gypsum can be replaced in the formula by the multiplication of the respectives densities (d W , d G ) and volumes; the volume occupied by excess water is equal to the measured porosity V porosity (3):

W / PR= d W * V Porosity + 1,5 M W M G * d G * V G M H M G * d G * V G ( 3
)
As it is a ratio, the volumes can be replaced by volumic fractions. Their sum is equal to one as the samples only contain gypsum and air, which mean that the W/P ratio can be expressed from the sole volumic fraction of gypsum v G [START_REF] Joiret | Submicrometric Picture of Plaster Hydration: Dynamic and Space-Resolved Raman Spectroscopy versus Kinetic Monte Carlo Simulations[END_REF].

W / PR= d W * ( 1-v G )+ 1,5 M W M G * d G * v G M H M G * d G * v G (4).
In addition, as X-ray absorption in air is negligible, the X-ray coefficient of linear absorption of the sample ρ S only depends on v G and the absorption coefficient of gypsum ρ G : ρ S =v G ρ G .

Image analysis

We segmented the samples from the background on the images using the absorption contrast between gypsum and air, with Otsu automated thresholding [START_REF] Otsu | Threshold selection methods from gray histograms[END_REF] and mathematical morphology operations such as dilation and /erosion filters features from Scikit-Image. The X-ray absorption coefficient was then averaged over the segmented sample volume.

Conditions for application

The W/P measurement relies on three assumptions :

1) The samples are only made up of secondary gypsum and air. Inclusion of materials with a different X-Ray absorption coefficient, such as mineral charges or unwanted β-CaSO 4 . will skew the measurement of the total porosity. If impurities were present in significant amounts, corrections depending on their proportion and chemical nature would be neccessary.

2) The reactive plaster powder is pure hemihydrate (CaSO 4 -0.5H 2 O). Soluble anhydrite (γ-CaSO 4 ) or CaSO 4 -0.625H 2 O are sometimes produced by the calcination of gypsum instead of hemihydrate. In plaster manufacture they will lead to slightly different results. However, they are not stable and quickly revert to hemihydrate when exposed to ambiant conditions of temperature and humidity [START_REF] Schmidt | Water channel structure of bassanite at high air humidity: crystal structure of CaSO 4 -0.625H 2 O[END_REF][START_REF] Bezou | Étude des caractéristiques cristallographiques, thermodynamiques et microstructurales des produits de déshydratation du gypse[END_REF].

3) There are no air bubbles. Air can be trapped in the slurry when mixing plaster powder and water. Unlike modern plasters that often include foaming agents though, ancient plasters typically show few bubbles that will not affect the measurement of W/P significantly.

Experimental validation

The X-ray linear absorption coefficient measured on recreation samples and plotted against the gypsum volumetric fraction (calculated in reverse from the known W/P) shows good linearity (fig. 4). The slope of the linear fit is found to be near the linear absorption coefficient of gypsum. ρ G = 13.21 cm -1 , somewhat higher than the theoretical value of 11.31 cm -1 at an incident energy of 19.6 keV. Concievably, the difference results from the moderate energy dispersion of the incident beam.

Figure 4: X-ray absorption and gypsum volumic fraction of recreation samples. Measured average X-ray absorption coefficient vs calculated gypsum volumic fraction in recreation samples of known water-to-plaster ratio. The good linearity of our measurements can be seen with the regression line in black.

The measurement of the W/P ratio proved to be reliable, with only limited deviation from calculated values. This deviation is acceptable considering the small size of the studied sample.

Measurement of pores size and morphology 3.3.1 Image analysis

Pores were segmented using Otsu's thresholding and dilation/erosion tools. An arbitrary lower cutoff of 10000 voxels was taken to make sure that only the significant mesopores were selected. The sizes of the pores were recorded. Their irregular shapes (fig. 5) were approximated as ellipsoids of identical moment of inertia using Scikit image. The diameters d 1 < d 2 < d 3 of the ellipsoids were divided to obtain aspect ratios r 1 = d 1 / d 3 and r 2 = d 2 / d 3 that describe the shape of the pores, independently of their size.

For each sample, we plotted both the normalized histogram of sizes and the unweighted average of aspect ratios r 1 and r 2 .

Figure 5: segmented pores. Three dimensional visualisation of segmented mesopores (grid cube 260 x 260 x 260 µm). The highly irregular shapes were approximated as ellipsoïds for comparison purposes.

Conditions for application

Only one assumption is neccesary for the measurement of pores morphology: the absence of trapped air bubbles. These are pores that will be measured accordingly, but their (spherical) shape is obviously not related to the morphology plaster powder. As seen in 3.2.3, trapped air bubbles are a rare occurence in ancient plaster samples.

Experimental validation

The measurement of pore size showed no significant difference in the distribution of sizes between the mock-up samples prepared with industrial plaster and those with plaster made in the lab using a mortar and pestle for grinding (fig 6). From this we can conclude that the distribution of pores sizes is not a relevant indicator of manufacturing processes. The measurement of pores aspect ratios (fig. 7) was consistent across mock-up samples prepared with the same plaster powder while making a difference between those prepared with a different powder. In addition, the samples made from industrial plaster powder were prepared with different W/P and showed that the W/P ratio had no effect on the recorded pores shapes.

Case study

In light of the results of Part 3, the W/P ratio as well as the average aspect ratios of pores were measured in historic samples, while the size distribution of the mesopores was not recorded. From these measurements an attempt was made to establish groups of artworks showing a material of similar W/P and pores shape, and to compare these groups with the models and historical backgrounds of the reliefs.

Results

Verification of the conditions of application

The chemical analysis of samples taken from the reliefs [START_REF] Gariani | First insights on the mineral composition of "stucco" devotional reliefs from Italian Renaissance Masters: investigating technological practices and raw material sourcing[END_REF] shows that they are mainly made up of gypsum, even if the ratio between calcium and sulfate shows that there is a small fraction of calcium carbonate. Traces amounts of Na, Mg, Al, Si, P, Cl, K and Fe suggest the presence of dolomite, clays and halite in smaller amounts.

Bubbles due to trapped air are supposed to exhibit a roughly spherical shape. A quantitative assessment was made by counting those pores which exhibited aspect ratios higher than 0.9 (including bubbles but also regular shaped mesopores). Only faint amounts were found, ranging from 0 to 0.48% of all pores. This result is in agreement with the common opinion that ancient plasters were prepared without foaming agents.

Water-to-plaster ratio

The results of the W/P measurement are shown in fig. 8. W/P ranged from 0.43 to 0.97. We observed a wide dispersion among fragments of the same sample with an overall standard deviation of 0.06 (and as high as 0.11 for individual relief Inv. 247). We found that our samples could be divided in two groups: the first and larger one includes the reliefs made on models attributed to Donatello, Bartolomeo Bellano, Desiderio da Settignano and Antonio Rossellino (Virgin and Child, types of Vienna, type of the candelabra, and type of Santa Maria Nova). Works of this group were manufactured with W/P ratios over a wide range between 0.4 and 0.7.

Unfortunately the small number of samples and their high dispersion prevent any finer analysis.

The two reliefs 1937-3 and Camp. 24 (both Virgin and Child, type of St Petersburg) stood apart with W/P = 0.97 and 0.88 respectively. They constitute a second group. Finally, we investigated the cast of a Virgin and Child after Luca della Robbia (Inv. 247). It exhibits a W/P of 0.80, but with individual fragments ranging from 0.68 to 0.96, overlapping both ranges: considering this high dispersion, we did not allocate it to either group.

Pores morphology

The aspect ratios r 1 and r 2 of our pore data set are shown in fig. 9. They range from 0.25 to 0.40 and 0.48 to 0.60 respectively. Two groups can be identified: the first is constituted of reliefs D488 and RF1191, both cast on a model of the Nativity attributed to Donatello and Bartolomeo Bellano. Averaged aspect ratios of this group were significantly lower than those of the other reliefs we sampled, gathered together in a second group.

Discussion

Even if the studied corpus of a dozen reliefs is limited (especially considering the large diffusion of these models), interesting first hypotheses can be made. The study of porosity allowed a first attempt at differentiating reliefs by crossing the information obtained through the measurement of W/P and pores morphologies. The majority of the artworks, (8 reliefs out of the 13) present common features: 0.4 < W/P < 0.7 and a pore shape characterised by averaged aspect ratios 0.31 < r 1 < 0.40 and 0.52 < r 2 < 0.61. These results support previous research led on these artworks [START_REF] Gariani | First insights on the mineral composition of "stucco" devotional reliefs from Italian Renaissance Masters: investigating technological practices and raw material sourcing[END_REF][START_REF] Aksamija | Investigation of organic additives in Italian Renaissance devotion stucco reliefs from French collections[END_REF] that report similar chemical and mineralogical composition of the plaster binder across these 8 reliefs. Moreover, all those reliefs belong to models attributed to Donatello, Desiderio da Settignano and Antonio Rossellino as they lived in Florence and suggest a certain continuity in the manufacture of 15 th century Florentine reliefs. Two pairs stand out. They differ either in the morphology of their mesopores (D488 RF119), or in their W/P ratio (1937-3, Camp 24). Both correspond to a particular model: this observation invites a more detailed discussion of each pair.

Nativities

According to previous [START_REF] Gariani | First insights on the mineral composition of "stucco" devotional reliefs from Italian Renaissance Masters: investigating technological practices and raw material sourcing[END_REF] and ongoing studies, two reliefs D488 and RF1191 (Nativity model, the attributed to Donatello and B. Bellano) exhibit distinguishing features based on compositional and geochemical analyses. The two specimens show a W/P in line with the main group. However, the average aspect ratios of their pores are lower at r 1 = 0.25, 0.26 and r 2 = 0.48. This difference in the morphology of the pores is indicative of more elongated hemihydrate grains in the plaster powder. This has been interpreted as a possible difference in the raw material used for plaster manufacture that can point to several possibilities. A first and most simple hypothesis is that gypsum was excavated from outcrops in the same area but showing different morphologies. The second hypothesis is that it is significative of gypsum from various sources, but supplied to the same city. Finally, they could be an indicator of the different gypsum supplies available in different cities.

Comparing the pores morphology with the center of production of these reliefs makes for an interesting case. Indeed the third relief of our corpus, cast on a model attributed to Donatello (Inv. 242, Virgin and Child, Pazzi type), falls within the main group. The attribution of the Madonna Pazzi (the marble sculpture, kept in the Bode Museum, after which relief Inv. 242 is patterned) to Florentine context is undisputed amongst art historians. The casts of the Nativity on the other hand were most likely produced in northern Italy, based on the number of reliefs of this type reported in the area [START_REF] Fava | La Madonna del prescepe, da Donatello a Guercino, Una devozione antica e nuova nella terra di Cento, cat. expo[END_REF].

The third hypothesis seems therefore likely. Additional work, including morphological as well as chemical analyses on other casts of this model, is necessary in order to reach solid conclusions.

Virgins and Child, type of Saint Petersburg

The two reliefs 1937-3 and Camp. 24 (Virgin and Child, type of Saint Petersburg attributed to Antonio Rossellino), show a higher W/P ratio (respectively 0.97 and 0.89), while the morphology of their pores is in line with that of the main group. This difference in W/P indicates a difference in plaster preparation. Indeed W/P is used to control the viscosity of the plaster slurry, and the density of the set plaster (important both for weight and for mechanical properties). Two hypotheses can therefore be made to explain the higher W/P: the first one is that W/P was adjusted because of constraints in weight and durability. However all artworks in our corpus were cast in low relief, with comparable dimensions and purpose, ruling out this hypothesis. The second possibility is that W/P differs because of a different manufacturing technique. Indeed, different casting methods require slurries of different viscosity. The viscosity of the slurry can also be affected by additives, and W/P changed to compensate.

What is interesting here is that the six other reliefs, cast on four models attributed to A. Rossellino fall with the main group. Of the sampled corpus, only the two reliefs of the St. Petersburg type show a higher W/P. The difference between casts attributed to A. Rossellino could be due to an experiment with an original technique, or to craftsmen tasked with the serial manufacture of plaster casts working with different practices, either in A. Rossellino's workshop or in several Florentine ones. Ultimately it also can not be ruled out that these two casts are later imitations of 15 th century reliefs. Again, additional work with a larger corpus is required to get a better grasp of the technical variations existing in historical artworks.

Conclusion

We determined the water-to-plaster ratio and characterized the morphology of the reactive plaster powder for the first time on set plaster samples. These measurements were conducted on samples smaller than 1 mm 3 , small enough for the characterisation of precious artworks, using synchrotron Xray microtomography. They can give insight into both the raw material and the techniques used in the manufacture of ancient plasters. The methodology was tested through the analysis of mock-up samples, showing consistent results in spite of the limited amount of material.

A first case study was conducted on a corpus of thirteen 15 th century low-relief cast plaster sculptures.

A main group of eight reliefs, all attributed to a Florentine context, was found to show similarity in both the raw material and the W/P ratio. Two casts of the Nativity, on a model attributed to Donatello and B. Bellano and most likely made in northern Italy, were differenciated by their raw material morphology. Finally, two casts of the Virgin and Child, type of St Petersburg (a model attributed to A. Rossellino) were differenciated by their higher W/P ratio. This discrepency in the casting technique could suggest variation among 15 th century plaster-making practices or that the reliefs are later imitations. These promising results show that the method introduced in this work is adequate for the investigation of ancient gypsum plasters. Its application is particularly promising for the study of Renaissance serial production of low-relief plasters, including provenance studies and the detection of possible forgeries.

Images captions:

Figure 1: illustration of the two-step setting of gypsum plasters. Figure 2: photographies of four 15th century low-relief cast sculptures, part of the corpus under study. Figure 3: reconstructed tomography slices, showing pores and inclusions in the samples. Figure 4: results of the measurement of W/P ratios in mock-up samples. Figure 5: 3D visualisation of segmented pores. Figure 6: results of the measurement of the size distributions of pores in mock-up samples. Figure 7: results of the measurement of the morphologies of pores in mock-up samples. Figure 8: results of the measurement of W/P ratios in historical samples. Figure 9: results of the measurement of the morphologies of pores in historical samples.

Figure 2 :

 2 Figure 2: historical reliefs sampled. From left to right : Nativity, 77x79 cm (RF 1191), Virgin and Child, type Pazzi, 68x52 cm (Inv. 242), Virgin and Child, type of the Candelabra, 78x52 cm (Camp. 20), Virgin and Child, type Saint Petersburg, 82x51 cm (Camp. 24). (c) C2RMF / J.-Y. Lacôte.

Figure 6 :

 6 Figure 6: Pores sizes distribution of mock-up samples. Histograms of pores sizes measured in mockup samples, shown as a normalized frequency. Some variation is seen but is not correlated with the plaster powder used; it should rather be ascribed to statistical noise.

Figure 7 :

 7 Figure 7: Averaged aspect ratios of the pores found in mock-up samples. Averaged values computed from the aspect ratios of individual pores of historic samples. Cast made with industrial plaster 1 show higher aspect ratios r 1 > 0.37 and r 2 < 0.60 compared to r 1 < 0.35 and r 2 < 0.55 for plaster 2. Plaster 2 showing more elongated pores is consistent with the acicular habitus of the raw gypsum it was made from.

Figure 8 :

 8 Figure 8 : Water-to-plaster ratio of historic samples. Values for each fragment of sample are represented by grey crosses, the averaged W/P by colored markers. The ranges in blue and pink show the two main groups separated by their W/P: respectively the majority of the corpus (0.4 < W/P < 0.7) and the two reliefs of the Virgin and Child, type of St Petersburg (0.85 < W/P < 1). Relief Inv. 247 with its high dispersion overlaps both ranges.

Figure 9 :

 9 Figure 9 : averaged aspect ratios of the pores found in historic samples. Averaged values computed from the aspect ratios of individual pores of historic samples. Reliefs of the nativity (attributed to Donatello and B. Bellano, figured in red) show low aspect ratios r 1 <0.26 and r 2 <0.48 compared to 0.31<r 1 <0.40 and 0.52<r 2 <0.60 for the rest of the corpus. The lower ratios indicate mesopores, and in turn hemihydrate grains, of a more elongated shape.

Table 1 : historical reliefs sampled.

 1 Inventory numbers, models and attributed authorship and cities of production of the models.

	Attribution			Model	Production centre Inventory
	(after/workshop of)				number
	Donatello	(Florence,	Nativity	Northern	Italy	RF 1191
	1378-1455)				(Padua?)
	Donatello			Nativity	Northern	Italy	D 488
						(Padua?)
	Donatello			Virgin and Child, Pazzi type	Florence	Inv 242
	Luca	della	Robbia	Virgin and Child, Massimo type	Florence	Inv 247
	(Florence, 1399/1400-
	1482)
	Desiderio da Settignano	Virgin and Child, Turin type	Florence	RF 897
	(Settignao,	1430	-
	Florence, 1464)
	Antonio		Rossellino	Virgin and Child, Vienna type	Florence	Camp 16
	(Settignano, 1427/1428-
	Florence, 1479)
	Antonio Rossellino		Virgin and Child, Madonna of the	Florence	Camp 20
					Candelabra type
	Antonio Rossellino		Virgin and Child, Madonna of the	Florence	1937-4
					Candelabra type
	Antonio Rossellino		Virgin and Child, Madonna of the	Florence	DS 534
					Candelabra type
	Antonio Rossellino		Virgin and Child, Madonna of the	Florence	MBA 587
					Candelabra type
	Antonio Rossellino		Virgin and Child, Santa Maria Nova	Florence	Inv 362
					type
	Antonio Rossellino		Virgin and Child, Saint Petersburg type Florence	1937-3
	Antonio Rossellino		Virgin and Child, Saint Petersburg type Florence	Camp 24

Acknowledgements:

The authors gratefully thank Elodie Boller and the staff at ESRF ID19 as well as APS 2-BM for the help with tomography experiments (during Beamtime IN1072). We also thank Florian Fusseis (University of Edinburgh) for the beamtime used in preparatory research and enlightening discussions. We finally thank Sara Quiligotti for providing samples of industrial gypsum. Financial support was received from the LabEx MATISSE, the Fondation des Sciences du Patrimoine (LabEx PATRIMA) and Saint-Gobain Recherche. This work was conducted in the framework of project ESPRIT (Étude des Stucs Polychromés de la Renaissance ITalienne), led by Marc Bormand (Musée du Louvre) who supervised the sampling campaign.