Vanessa Soldan

Irma Custovic

Sara Castaño-Cerezo

Stéphanie Balor

Miguel Fuentes-Cabrera

Gilles Truan

Eric Lesniewska

David Reguera

Luis F Garcia-Alles

Inferring assembly-curving trends of bacterial micro-compartment shell hexamers from crystal structure arrangements

Keywords: bacterial micro-compartments, shell, hexamer, assembly curvature, crystal structure, microscopy, nanotube

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INTRODUCTION

Bacterial micro-compartments (BMC) are complex macromolecular protein assemblies that confine specialized enzymatic activities within shells and participate to processes like carbon fixation in cyanobacteria or metabolite degradation related to bacterial growth and pathogenesis [START_REF] Prentice | Bacterial microcompartments and their role in pathogenicity[END_REF] . According to a recent genomic survey, about 70 BMC types can be found in nature, all differing by sort of cargo contents 2 . In contrast, all shell protomers belong to two structural families. The first one adopts the Pfam 00936 fold, which associate as hexamers (BMC-H) or trimers of bidomain proteins (BMC-T). These proteins can be further sub-classified depending on structural details such as for instance the permutation of secondary elements or the capacity to further dimerize [START_REF] Melnicki | Evolutionary relationships among shell proteins of carboxysomes and metabolosomes[END_REF][START_REF] Ochoa | Recent structural insights into bacterial microcompartment shells[END_REF] . Members of the second family (Pfam 03319) assemble as pentamers (BMC-P) and occupy shell vertices [START_REF] Sutter | Assembly principles and structure of a 6.5-MDa bacterial microcompartment shell[END_REF] . Accordingly, BMC-P are stoichiometrically very minor in shells.

The structure of reconstituted minimalist shells proved that BMC-H are endowed with a considerable assembly versatility, being capable of establishing contacts with themselves in at least two different dispositions (planar or bent), but also with BMC-T and BMC-P shell partners [START_REF] Sutter | Assembly principles and structure of a 6.5-MDa bacterial microcompartment shell[END_REF] . Noteworthy, the same set of residues basically ensured interactions with all different partners, irrespective of the precise local symmetry environment, something that is reminiscent of viral capsids, where a single protein often occupies different structural environments. Yet, BMC shells were demonstrated in atomic-force microscopy (AFM) nano-indentation experiments to be considerably less rigid than capsids or encapsulins 6 .

Despite impressive advances in the structural characterization of BMC, our understanding of shell assembly is progressing slowly. A major milestone was the characterization of the biogenesis of carboxysomes from Synechococcus elongatus PCC 7942 (Syn7942) [START_REF] Chen | The bacterial carbon-fixing organelle is formed by shell envelopment of preassembled cargo[END_REF] . Colocalization experiments with fluorescently-labelled RuBisCO and shell proteins evidenced that -carboxysome assembly is a two-step process, shells appearing only after the emergence of pre-organized procarboxysome "grains" of coalesced RuBisCO, carbonic anhydrase and scaffolding proteins (cargo-first mechanism, see below). The presence of less organized/compact encapsulated contents in other BMC types, when compared to hexadecameric RuBisCO [START_REF] Iancu | structure, and assembly of alpha-carboxysomes determined by electron cryotomography of intact cells[END_REF] , and the observation of compartment formation in the absence of cognate cargo [START_REF] Menon | Halothiobacillus neapolitanus carboxysomes sequester heterologous and chimeric RubisCO species[END_REF][START_REF] Parsons | Synthesis of empty bacterial microcompartments, directed organelle protein incorporation, and evidence of filament-associated organelle movement[END_REF] , pointed to the existence of other assembly pathways for other BMC types. In line with this, a recent study on Pdu BMC biogenesis proved that cargo-first and shell-first assembly pathways are both feasible, even when cargo-enzymes coalesce following a hierarchical organization mode [START_REF] Yang | Biogenesis of a bacterial metabolosome for propanediol utilization[END_REF] .

A compelling understanding of assembly is being provided by theoretical simulations using coarse-grained (CG) models to describe simplified cocktails of shell components, cargo proteins and even scaffolding factors [START_REF] Perlmutter | Many-molecule encapsulation by an icosahedral shell[END_REF][START_REF] Mohajerani | Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control[END_REF] . These studies indicated that assembly pathway, as well as the morphology and cargo-loading extent will be function of the precise balance of interaction strengths between the components and of their stoichiometries. For instance, strong scaffold-mediated cargo-cargo interactions would favour twostep mechanisms, whereas weaker interactions would lead to concomitant scaffold-cargo coalescence and shell assembly. These studies also highlighted that, albeit BMC size is relatively insensitive to hexamerhexamer or scaffold-hexamer affinities, it was critically impacted by the assignment of spontaneous shell curvature and scaffold length [START_REF] Mohajerani | Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control[END_REF] . Curvature would result from an imbalance of attractive and repulsive forces established above and below the planes of each interacting pair of hexamers.

Although expected to be critical in driving BMC closure, studies of spontaneous curvature are scarce. To the best of our knowledge, only the assembly of PduA was investigated with this intention [START_REF] Li | Computational and Experimental Approaches to Controlling Bacterial Microcompartment Assembly[END_REF] . All-atom molecular dynamics (MD) performed on a pair of interacting hexamers revealed a preference to remain planar. Notwithstanding, coarse-grained simulations were parametrized with 25° curvature between hexamers, a choice based on angles observed in the cryo-electron microscopy (EM) structure of Hal. ochraceum (HO) BMC shells [START_REF] Sutter | Assembly principles and structure of a 6.5-MDa bacterial microcompartment shell[END_REF] . Globally, it is still unknown whether BMC-H are endowed with properties required to induce spontaneous shell curvature or not.

In this study we present experimental evidences that support the existence of two major BMC-H assembly behaviors, depending on the preference to form curved-implying or flat objects, and the possibility that this could be inferred from the kind of organization adopted in crystal structures exhibiting piled planar subunit arrangements. Indeed, all-atom MD performed on hexamer ensembles extracted from these structures closely reproduced experimental trends. Thus, BMC-H that form curved objects and display the first organization mode in crystals, bent rapidly and reliably, evolving towards similar dispositions to those characterized in objects formed by purified proteins belonging to this group [START_REF] Pang | Structural insights into higher order assembly and function of the bacterial microcompartment protein PduA[END_REF] or in structures of minimalist reconstituted BMC shells [START_REF] Sutter | Assembly principles and structure of a 6.5-MDa bacterial microcompartment shell[END_REF][START_REF] Sutter | Structure of a Synthetic β-Carboxysome Shell[END_REF] . On the contrary, hexamers adopting other assembly types were more reluctant to bend. Although interaction energy profiles along the hexamer interface were shallow, indicating that assembly is cooperative, an ionic interaction was found to contribute to hold a BMC-H subset away from the disposition that precedes shell formation.

RESULTS

BMC-H propensity to assemble

Individual BMC-H have been shown to form varied structures in vivo, generally after recombinant expression in E. coli (a compilation of literature data is given in Table S1). EM and AFM studies on purified proteins from this family also highlighted an extraordinary assembly plasticity. Thus, apart from predicted 2D organizations, filaments/nanowires, nanotubes, swill-rolls and even spherical structures could be characterized. With the intention to contribute more data and complete the vision, we programmed the characterization of several purified oligohistidine-tagged BMC-H, which were not covered in previous studies, or only partly: CcmK1, CcmK2 and CcmK4 from Syn6803, CcmK2 and CcmK4 from Syn7942, CsoS1A from H. neapolitanus, PduA and PduJ from S. enterica, EutM from E. coli, BMC-H from H. ochraceum and RMM-H from M. smegmatis [referred hereafter with the notation: Protein name species abbreviation (e.g.

CcmK1 6803 )].
Two types of data permitted to get a glance of BMC-H relative assembly potential. First, the alteration of cell size induced upon BMC-H overexpression was assayed using phase contrast microscopy (Fig. S1A).

When compared to controls, a significant number of PduA Sent and PduJ Sent expressing cells exhibited increased length, something that also occurred at lower extent with RMM-H Msm and BMC-H Hoch . Size alterations were considerably weaker than those reported [START_REF] Kennedy | Self-assembling Shell Proteins PduA and PduJ have Essential and Redundant Roles in Bacterial Microcompartment Assembly[END_REF] , something possibly related to the different induction methods. Expression of Syn6803 proteins also led to a moderate increase of length, in comparison to empty pET15b controls. Although data collected for CcmK3 6803 , an insoluble protein when expressed in E. coli, invite to caution, collectively these results suggest that nanotubes or 2D-assemblies form inside cells, as previously reported for PduA and PduJ [START_REF] Kennedy | Self-assembling Shell Proteins PduA and PduJ have Essential and Redundant Roles in Bacterial Microcompartment Assembly[END_REF] or other assembly-prone proteins [START_REF] Lederer | Heterologous expression of the surface-layer-like protein SllB induces the formation of long filaments of Escherichia coli consisting of protein-stabilized outer membrane[END_REF] . In the second approach, BMC-H remaining soluble after IPTG induction was compared with amounts of potential assemblies retained in pellets. The latter was inferred using an experimental setup that pursued the solubilization by disassembly with a chaotropic agent, urea, at sufficiently low concentrations as to avoid the recovery of misfolded proteins forming inclusion bodies (IB). Experiments with CcmK3 6803 , an insoluble protein that only becomes soluble when co-expressed with CcmK4 [START_REF] Garcia-Alles | Occurrence and stability of hetero-hexamer associations formed by β-carboxysome CcmK shell components[END_REF] , indicated that resolubilization of IB required at least 2 M urea concentrations.

With the exception of C-ter Histagged CsoS1A Hneap , all other tested BMC-H were correctly expressed in E. coli (Fig S1B). Globally, BMC-H distributed between soluble fractions (SF) and the urea solubilized fraction (USF), the latter being most prominent for most of proteins. PduA Sent , CcmK1 6803 , CcmK4 6803 and CcmK4 7942 were almost exclusively recovered in urea fractions. On the opposite side, EutM Ecol and CcmK2 6803 were more abundant in soluble fractions. Noteworthy, urea purified fractions (UPF) remained soluble after removal of urea and gave similar results in AFM and transmission EM (TEM) as the PF. The pentameric CcmL 6803 was also found at relatively high amounts in urea fractions, suggesting potential assembly, as reported [START_REF] Gao | A prototype protein nanocage minimized from carboxysomes with gated oxygen permeability[END_REF] .

Overall, these data indicated a common strong propensity of BMC-H to form big macro-molecular entities during expression inside bacteria.

Two general BMC-H assembly behaviors

To complete published data compiled in Table S1, we investigated the assembly of CcmK from Syn6803 and Syn7942 inside E. coli by TEM (Fig S2). Only CcmK1 6803 and CcmK3 6803 images differed from those obtained for the control strain (empty vector). Although unclear, stripped motifs might occur with CcmK1 6803 . With CcmK3 6803 , homogenous spherical patches suggestive of IB were often present at cellular poles. The lack of noticeable observations for CcmK proteins contrasts with nanotubes, filaments and spherical structures reported for many other BMC-H (Table S1).

Assembly potential was also assessed by AFM and TEM taking purified proteins conditioned at comparable concentrations in the presence of a phosphate buffer. 2D flat-organizations were recurrently imaged by AFM with all CcmK proteins (see Fig. S3A-F), although CcmK1 6803 gave rise to the reported honeycomb mosaics consisting of laterally-collapsed cup-like motifs [START_REF] Garcia-Alles | Spontaneous non-canonical assembly of CcmK hexameric components from β-carboxysome shells of cyanobacteria[END_REF] . Less clear-cut and difficult to reproduce data were obtained for the rest of BMC-H, pointing to difficulties expected if rounded objects formed, since these would establish weak contacts with the planar mica support. 2D patches were seen rarely with PduJ Sent (Fig. S3M,N), and with BMC-H Hoch (Fig. S3O), in agreement with reported data collected for the untagged protein [START_REF] Sutter | Visualization of Bacterial Microcompartment Facet Assembly Using High-Speed Atomic Force Microscopy[END_REF] . With PduA Sent or EutM Ecol , mica was sometimes covered with material that attained relatively homogenous heights (less than 6 nm, Fig S3J ,S3P). Notwithstanding, patches remained small, suggesting difficulties to grow in 2D. Spheroids insinuated in occasions with CsoS1A Hneap and PduA Sent (Fig. S3G,I,K). Similar spherical entities were also imaged as protrusions/incrustations with RMM-H Msm or EutM Ecol (Fig. S3Q). Linear arrangements evocative of bundles of nanotubes were monitored for PduA Sent in a buffer supplemented with MgCl2 (Fig. S3L), but could not be reproduced in independent experiments. Among all CcmK imaged by TEM, assemblies were only evident for CcmK1 6803 (Fig. S4A-B): flat 2D patches with irregular edges, occasionally also polygonal-like tiles. Roughness was noticed inside some assemblies, which could reflect abovementioned honeycomb mosaics. Flat assemblies also occurred with PduA Sent (Fig. S4F-G), PduJ Sent (Fig. S4H-I) or BMC-H Hoch (Fig. S4L-M). Hexamers were more evident with the latter, in virtue of spacing close to the 7.5 nm distances reported before [START_REF] Lassila | Assembly of robust bacterial microcompartment shells using building blocks from an organelle of unknown function[END_REF] . Patches had remarkable sharp edges and almost polygonal shapes in the case of the two Pdu proteins. However, the most recurrent structures imaged for PduA and PduJ were nanotubes, in agreement with the literature (see Table S1). Frequently appearing straight, with 22-30 nm diameters in the case of PduA, wider with PduJ, their darker interior suggested the access of TEM contrast agent to their lumen. PduA and, especially, PduJ nanotubes stuck sometimes on 2D tile-edges (e.g. Fig. S4I), suggesting a potential 2D-growth mechanism. Indeed, although not studied here, we noticed that the probability of observing flat tiles with PduA augmented with prolonged incubations in saline phosphate buffer. For PduJ, some images suggested the possibility that large nanotubes, apparently opened along the longitudinal axis, were in fact partly rolled 2D-assemblies (e.g. structure pointed by the arrow in Fig. S4H). Spheroids and narrow curved filaments/nanowires (16-20 nm diameters) were sporadically detected with PduA Sent , CsoS1A Hneap (detected in only one out of three independent preparations, Fig. S4C-E) and EutM Ecol (Fig. S4J-K). Indeed, EutM Ecol more often resulted in skinny and aggregated material without evident organization, as judged by FT treatments. Amorphous fibers were seen in few occasions for RMM-H Msm , which might be reminiscent of bundles of nanotubes observed at significantly higher RMM concentrations [START_REF] Noël | Purification and Characterization of Protein Nanotubes Assembled from a Single Bacterial Microcompartment Shell Subunit[END_REF] . Formation of varied types of assemblies was confirmed in cryo-EM experiments, both for PduA and PduJ (Fig. S5A-F), whereas large and dense nanotubes with rough edges were observed with CsoS1A (Fig. S5G-I).

These data and reported observations, apart from highlighting an extraordinary assembly plasticity, point to the manifestation of two major trends: some proteins are prone to build curved-implying objects (PduA Sent , CsoS1A Hneap , RMM-H Msm and possibly PduJ Sent ); -carboxysome CcmK proteins and possibly BMC-H Hoch more easily organize as (quasi)flat assemblies. Less clear-cut, EutM Ecol might figure among curving BMC-H, according to published data.

Different 2D-assembly modes identified in BMC-H crystals

Our intention was to investigate BMC-H assembly behavior by MD simulations taking advantage of crystallographic data. By the time of the realization of this study, there existed about 60 BMC-H structures deposited in the Protein Databank (plus 8 entries from reconstructed shells published in the course of this work, see Table S2). Thirty-four structures were from wild-type (WT) proteins. Within this group, we focused our work on the 18 crystal structures that displayed hexamers organized as piled 2D layers (see below). These structures could be categorized in four groups according to the BMC-H disposition, which differed by lateral displacements and distances between interacting hexamers (Fig. 1 and Table S2). The first assembly type (hereafter called Ass-A) is characterized by a short distance between the two key Lys residues from interacting hexamers. A representative case is the PduA Sent 3NGK structure, with measured 7.2-8.4 Å distances between Lys26 C from hexamer counterparts (Fig. 1A). Ass-A is the only assembly mode observed for WT PduA Sent , CsoS1A Hneap , CsoS1C Hneap and BMC-H Ahyd (Fig. 1B). Ass-A also reflects closely the disposition of BMC-H noticed in all reconstituted shells. The second assembly mode (Ass-B) is adopted by all CcmK proteins, EutM Ecol and BMC-H Hoch (Fig. 1C-D). Here, the inter-lysine distance is considerably longer (14.9-17.6 Å). An intermediate organization (Ass-C), with distances of about 10 Å, is seen in CcmK2 6803 3DNC and CcmK4 7942 4OX6 structures, whereas CcmK2 7942 4OX7 is the only case displaying a fourth assembly type (Ass-D). Assembly occurrence did not seem to be defined by crystallization conditions. Thus, the organization mode is reproduced in crystals of the same protein prepared under variable conditions (e.g. Ass-A for structures 2EWH and 2G13 from CsoS1A Sent , or in the 3H8Y structure of the close CsoS1C Sent homolog; Ass-B for 3BN4 or 3DN9 structures of CcmK1 6803 or 3MPW and 3MPY from EutM Ecol ).

Globally, a parallel seem to exist between experimental assembly behavior and the way BMC-H tile in crystals. Ass-A would be the preferred crystallization mode for proteins endowed with curving propensity, whereas flat-behaving BMC-H would mostly adopt Ass-B arrangements.

Variable curving trends supported by all-atom molecular dynamics

The last hypothesis was challenged by means of all-atom MD. We followed the approach described in a previous study [START_REF] Garcia-Alles | Spontaneous non-canonical assembly of CcmK hexameric components from β-carboxysome shells of cyanobacteria[END_REF] , in which MD runs were launched on ensembles of three interacting hexamers, extracted from crystal structures showing tiled BMC-H (PDB codes indicated in Table S3). Tri-hexameric ensembles were selected as best compromise to describe the situation in BMC shells while keeping reasonable computational costs. After energy minimization, MD were run (AMBER forcefield) with proteins embedded in explicit hydration boxes under quasi-physiological conditions (see M&M). All different assembly types mentioned in the previous section were covered. Hexamer tilting and bending angles were monitored for intermediate structures extracted in the course of each trajectory (250 ps snapshots), as well as interhexamer distances calculated from the hexamers center of mass in the MD average structure. Rather than long single simulations, we opted by performing several independent simulations on each case (20 ns each), which differed by the attribution of random initial atom velocities. This parameter is known to impact MD trajectories more profoundly than time length [START_REF] Wan | Uncertainty quantification in classical molecular dynamics[END_REF] , something that we indeed confirmed (see below).

MD behavior seemed to be defined by the kind of assembly. Thus, strong and reproducible bending was noticed for all Ass-A-deriving cases, tilting remaining close to values measured for the crystal (Fig. 2, Fig. S6 -S7, and Table S3). For instance, PduA Sent and CsoS1A Hneap (2G13) bent by about -25°, something reproduced in 4 independent runs. Among Ass-A cases, the less pronounced effect occurred for PduJ Sent (starting ensemble taken from the K25A mutant 5D6V entry, after manual reintroduction of interfacial K25 side-chains). As expected for bending, inter-hexamer separation decreased slightly (not to be confused with edge to edge inter-hexamer separation) (Table S3). Data dispersion for all Ass-A BMC-H was low, even smaller than those measured for EutL Ecol , a BMC-T that basically remained flat in two MD runs. Induction of curvature was rapid, reaching dispositions close to the MD average during the first nanosecond (Fig. 2D), explaining the narrow data dispersion. Importantly, negative bending values corresponded to the orientation described for full BMC shells. Indeed, root-mean-square deviations (RMSD) of 1.3 Å were measured (on 1392 backbone atoms) when comparing interacting pairs of monomers in the average structure of two independent MD PduA Sent (3NGK) with corresponding interacting monomers of bent BMC-H in the H. ochraceum BMC shell structure (5V74). Worth-mentioning, the results were reproduced using CHARMM as forcefield in similar independent simulations launched on PduA Sent (average bending of -23°) and CsoS1A Hneap (-16°).

Assembly fate was more uncertain for non-Ass-A organizations. Bending and tilting were variable (Fig. 3), the reproducibility between runs being considerably poorer than with Ass-A, as illustrate strong data dispersion (Table S3). With some cases, the tri-hexamer remained close to flat independently of the run [e.g. CcmK1 6803 (3BN4) or CcmK4 7942 ]. But for most other cases, behavior was instable, even conducting to inversions of bending orientation (e.g. EutM Ecol or BMC-H Hoch ). As possible exception, CcmK2 6803 (3DNC) evolved from its Ass-C dispositions in the two runs much like Ass-A assemblies. Yet, the overall trend for non-Ass-A dispositions seemed to be to remain planar.

Theoretical behavior of shell assembled BMC-H substructures

The possibility that Ass-A configurations were responsible of BMC-H curving was evaluated in simulations launched on ensembles of 2 interacting BMC-H extracted from BMC shells (tri-hexamers are not found so far in shells), since BMC-H always adopted Ass-A-like dispositions in characterized structures (Table S2).

The two hexamer configurations observed for the BMC-H Hoch 5V74 shell were assayed [START_REF] Sutter | Assembly principles and structure of a 6.5-MDa bacterial microcompartment shell[END_REF] , which correspond to either bent or flat organizations, as well as an ensemble of two bent CcmK 7418 hexamers from the 6OWF shell structure [START_REF] Sutter | Structure of a Synthetic β-Carboxysome Shell[END_REF] .

MDs trajectories clearly showed a preference for curved dispositions: bent BMC-H Hoch or CcmK 7418 remained close to the starting angle, while the planar BMC-H Hoch evolved towards a curved configuration (Fig. S7).

Atomic determinants for triggering BMC-H bending

Our most challenging aim was the identification of atomic determinants implied in curvature. We selected for such study PduA Sent , because of its demonstrated experimental trend to form nanotubes and robust MD behavior. First, we sought to establish key interactors that clamp hexamers together. Two analytical approaches were followed: i) side-chain RMSD with regard to the MD average structure were monitored over the MD run (Fig. S8 andS9). For each residue, the different 18 positions in the tri-hexamer were plotted together. A clamping residue was expected to result in a relatively fixed conformation, and thus in lower RMSD, but only when located at the interface. In that manner, Lys26 and Arg79 always occurred with lowest RMSD at interfaces, for two independent MDs. Interfacial Glu19, Asp22, Asn29, Pro78 and His81 were often, but not always, lowest; ii) the contribution to the interaction energy of each residue was evaluated. The snapshot with lowest RMSD to the average structure of each MD was selected and energyminimized. We considered as contributor to the interaction those residues that resulted in maximal interval of values, when comparing values for the 18 monomers (Fig. S10A), and at the same time presented highest stabilization when at the interface, when compared to exposed positions (Fig. S10B). In that manner, Lys26, Arg79 were again confirmed to be key contributors. Surprisingly, the only additional identified residue was Ser27.

The role of above-pinpointed residues for assembly fate was investigated by in silico MD of single-residue alanine mutants. We extended the exploration to other interfacial residues to anticipate unforeseen possibilities, also to positions known to establish contacts between hexamers in characterized BMC shells, such as Asn67 that replaces Arg66 of CcmK 7418 [START_REF] Sutter | Structure of a Synthetic β-Carboxysome Shell[END_REF] . In total, the next 21 residues were scanned: K12, E19, D22, K26, S27, N29, R48, D50, V51, K55, D59, R66, N67, H75, P78, R79, H81, T82, D83, E85 and K86 (mutations were introduced 6 or 9 times in the tri-hexamer, depending on whether the residue was close to the center or edge of the interface, respectively). Notably, curvature was only impacted by the K26A mutation (Fig. S11), which completely abolished bending and led to 1-2 Å larger hexamer separation. The result was reproduced in four independent 20 ns MDs (only two shown). All other mutations were without effect, including the R79A. None of 6 side-chains tested replacing the interfacial K26 was able to restore bending (Fig. S12), a result that agrees with the full conservation of this residue among BMC-H 3 .

The importance of the two key interfacial residues was evaluated in other BMC-H (Fig. S13). CsoS1A Hneap behavior was not perturbed by either K29A or R83A mutations. Bending extent of K25A BMC-H Ahyd diminished slightly, depending on MD run, whereas the R78A mutation was again without consequence.

Multiple energy minima in lateral contacts between planar BMC-H

MD results combined with the structures of all recomposed shells (Table S2) concur to prove that Ass-A is the ready-to-curve disposition. That most other BMC-H tiling BMC-H adopted a second organization (Ass-B) could therefore point to a structural trap delaying shell closure. To verify this hypothesis, two approaches were envisioned. First, we evaluated the interaction energy profile after gradually displacing the relative lateral disposition of hexamers. Umbrella sampling all-atom MD [START_REF] Hub | g_wham-A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates[END_REF] were performed on hexamer couples extracted from PduA Sent (3NGK), CcmK1 6803 (3BN4) or CcmK4 7942 (4OX6) structures, taken as representative of Ass-A, Ass-B, and Ass-C organizations, respectively (Fig. 4). Preliminarily, we measured the potential of mean force (PMF) that results from pulling apart the two partners (Fig. 4A). Despite comparable to calculations on CcmK2 6803 27 , CcmK1 6803 binding energy was very weak, about 2 to 4 times smaller than for CcmK4 or PduA, respectively. When the PMF was screened along the reaction coordinate that leads from Ass-A to Ass-B (further extended on both sides), while hexamers were constrained flat, the highest stability was attained around crystal dispositions, supporting a preference of PduA Sent for Ass-A, or of CcmK4 7942 for Ass-B/C arrangements (Fig. 4B). Although CcmK1 6803 did not manifest a clear preference, globally these data supported that arrangements occurring in 2D-tiling crystals represent energy minima.

Besides, shallow profiles fitted with the high plasticity of BMC-H interfaces, indicating that transitions between different assemblies, separated by small energetic barriers (few kBT), should be feasible.

Behavior of reconfigured assemblies

The second approach consisted in launching MDs simulations on tri-hexamers of CcmK, EutM Ecol and BMC-H Hoch (remaining flat in crystal dispositions), after artificially repositioning each hexamer in Ass-A configuration. For that, each hexamer was superimposed individually on the different hexamers of the template PduA Sent (3NGK) and potential clashes relaxed (see M&M). We decided to include RMM-H Msm in the study, in view of its demonstrated potential to form nanotubes [START_REF] Noël | Purification and Characterization of Protein Nanotubes Assembled from a Single Bacterial Microcompartment Shell Subunit[END_REF] .

MD launched on reconfigured assemblies revealed significantly more stable than when starting from crystal dispositions, and collectively confirmed that Ass-A likely represents an arrangement competent for shell closure for most, if not all BMC-H (Fig. S14). Thus, BMC-H Hoch and RMM-H Msm behaved much like CsoS1A Hneap or PduA Sent in dynamics of Fig. 3. Also remarkable was CcmK4 7942 curving trend, contrasting with the reproducible flatness of this protein when arranged as in the crystal. An exception was CcmK4 6803 , which remained flat. However, the inter-hexamer separation increased by almost 2 Å, similarly to CcmK2 7942 (Table S4), something that could point to insufficiently relaxed starting structures. Since several bulky residues lie at the junction of the three CcmK4 6803 hexamers and might hamper bending, we assessed a mutant with several residues replaced by corresponding residues from PduA Sent : R30N, Q53G, E54A, E85T and N86D. This mutant bent, albeit still less pronouncedly than other cases (Fig. S14).

Experimental assembly of selected PduA mutants

Structural analysis (Fig. 1) and sequence alignments (Fig. S15A) indicate that ionic interactions mediated by residues corresponding to Arg28 and Asp49 of CcmK1 6803 could contribute to hold some BMC-H in non-Ass-A organizations. The consequence of mutating the Asn29 of PduA Sent into Arg was therefore evaluated.

Similarly, the ionic bridge was disrupted in CcmK4 7942 and BMC-H Hoch via R29N or K28N mutations, respectively. In this chapter, we also investigated the effect of substituting Ala for the two key interfacial residues of PduA Sent : Lys26 and Arg79.

Overexpression of any of the three PduA Sent mutants in BL21(DE3) caused a significant reduction of the proportion of elongated cells, when compared to the WT protein (Fig. S15B). The K26A mutation induced the strongest effect, when compared to R79A and N29R. On the contrary, disruption of the presumed ionic bridge led to a significant increase with both CcmK4 7942 and BMC-H Hoch mutants. SDS-PAGE analysis supported that all mutants continued to assemble inside cells, since most of protein was recovered after resolubilisation with 1M urea for all cases (Fig S15C ).

Assembly of mutants recovered in UPF was then investigated by TEM. Only small patches were observed with K26A PduA Sent , structures that could not be unequivocally attributed to protein assemblies (Fig. S16A).

The R79A mutant gave rise to compact 2D-patches (Fig. S16B). Structures resembling 40-80 nm amorphous nanotubes were seen, albeit rarely, together with a single sharp nanotube that could not be reproduced.

With the N29R mutant, 2D-patches grew abundantly, sometimes accompanied by nanotube-like bundles (Fig. S16C). Differing from observations on the WT protein, hexamers were well defined inside the 2Dplateforms, appearing as strips arranged with approximately 120° angles, with long inter-hexamer separations (from 7.1 up to 9 nm, depending on direction), overall fitting to the occurrence of Ass-B arrangements with N29R PduA. Possibly due to higher compactness, hexamer definition decreased at platform edges, in nanotube bundles too. Also differing from WT, individual nanotubes were seen only once, and mixtures of motifs seem to coexist within the bundles. These data might point to assembly transitions that would be favored by subunit exchange and could trigger for instance wrinkling of 2Dpatches towards nanotube-like bundles. On the other hand, 2D patches imaged for the R29N CcmK4 7942 or K28N BMC-H Hoch , appeared more compact than those characterized by AFM for the respective WT proteins (Fig. S16D,E). However, nanotubes were not detected with any of the two mutants.

Intrigued by the profiles of cellular elongation, we decided to monitor assembly formation inside cells (Fig. 5, see also Fig. S17). Overexpression of WT PduA Sent resulted in patterns compatible with 22-24 nm-wide nanotubes, although transverse sections failed to reveal described honeycomb motifs [START_REF] Parsons | Synthesis of empty bacterial microcompartments, directed organelle protein incorporation, and evidence of filament-associated organelle movement[END_REF][START_REF] Pang | Structural insights into higher order assembly and function of the bacterial microcompartment protein PduA[END_REF] . The K26A and R79A mutants gave rise to very similar compact assemblies, which almost filled up the cytosol. Stripped motifs, which were more evident with R79A PduA, were spaced by about 7 to 9 Å, suggesting the presence of piled sheets, as proposed before [START_REF] Chowdhury | Selective molecular transport through the protein shell of a bacterial microcompartment organelle[END_REF] . Most interesting, the R29N PduA Sent mutant did not form nanotubes (Fig. 5D andS17D). Instead, fingerprint-like arrangements, possibly single layered, were detected.

Intriguingly, most of cells displayed zebra-like patterns, something that might arise from 2D-layer wrinkling. While reported rolled layers were reproduced with BMC-H Hoch 22,[START_REF] Young | Visualizing in Vivo Dynamics of Designer Nanoscaffolds[END_REF] (Fig. 5E) and the structures were affected by replacement of Lys28 by Asn (Fig. 5F,S17F), the mutation did not cause appearance of nanotubes. However, structures reminiscent of nanotubes or nanowires accompanied other compact patches in a majority of cells overexpressing the R29N CcmK4 7942 mutant (Fig. 5G-H andS17G).

Discussion

Understanding how macromolecular structures as complex as BMC or BMC shells form is challenging.

Implying the controlled assembly of hundreds to thousands of oligomeric subunits [START_REF] Sun | Decoding the Absolute Stoichiometric Composition and Structural Plasticity of α-Carboxysomes[END_REF] deriving from several components, such processes are thought to rely in cooperativity phenomena. Relatively weak interactions, in the low kBT regime, normally govern contacts between pairs of shell components [START_REF] Mahalik | Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome's Facet[END_REF] . That explains why coarse-grained models are precious tools to investigate parameters governing these processes [START_REF] Perlmutter | Many-molecule encapsulation by an icosahedral shell[END_REF][START_REF] Mohajerani | Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control[END_REF] , in spite of being unsuitable for predictive work aiming to engineer new assemblies.

With the intention to contribute to this effort, this study sought to investigate global relationships between BMC-H experimental assembly behavior and predictions from all-atom MD simulations. Compiled experimental data pointed to a segregation of BMC-H in two major groups (Table S1), depending on trends to form flat assemblies (basically -carboxysome CcmK) or rounded objects (e.g. Pdu or CsoS1 proteins).

Within the first group could be included cases like BMC-H Hoch , found here or before to assemble flat in vitro 22, 23 , and leading to rosette structures inside E. coli that are assumed to derive from spooling of quasi-flat carpets [START_REF] Sutter | Visualization of Bacterial Microcompartment Facet Assembly Using High-Speed Atomic Force Microscopy[END_REF][START_REF] Young | Visualizing in Vivo Dynamics of Designer Nanoscaffolds[END_REF][START_REF] Young | Engineering the Bacterial Microcompartment Domain for Molecular Scaffolding Applications[END_REF] . Nanotubes/spheroids and planar structures are not necessarily mutually exclusive, as demonstrate for example data presented here for PduA or PduJ (e.g. Fig. S4G-I), or before for several EutM homologs assembled at variable temperatures [START_REF] Schmidt-Dannert | Building a toolbox of protein scaffolds for future immobilization of biocatalysts[END_REF] . Transitions between flat and curved structures might be one of the consequences of the relatively shallow interaction energy profiles calculated here for several BMC-H.

A notable discovery was that BMC-H experimental assembly behavior appears to be related to the type of organization found in crystals that exhibit internal 2D-layered organizations. Bending cases like PduA Sent , PduJ Sent or CsoS1A Hneap exhibited Ass-A dispositions, whilst other arrangements are noticed in structures of CcmK, EutM Ecol , EutM Cdif or BMC-H Hoch . Most often, assembly units were laterally displaced by approximately 8-10 Å (Ass-B), when compared to Ass-A. If such relationship was correct, crystal data would indicate that proteins like CsoS1C Hneap , CsoS1 Pmar and BMC-H Ahyd should form rounded structures, temptingly also BMC-H that attained Ass-A states even when mutated: CmcB Ecol (7MN4, K25A-E55G mutant), CmcC Ecol (7MPX, K25A-E35G) or CutR Sint (6XPI, K66A). However, this rule is not obeyed by all BMC-H, since EutM is prone to form rounded structures but adopts Ass-B configurations in crystals. EutM complex behavior is illustrated by the varied types of structures formed depending on the homolog selected [START_REF] Schmidt-Dannert | Building a toolbox of protein scaffolds for future immobilization of biocatalysts[END_REF] .

That hexamers could organize differently within 2D-layered crystals was already known since the early report of CsoS1A Hneap crystal structure [START_REF] Tsai | Structural analysis of CsoS1A and the protein shell of the Halothiobacillus neapolitanus carboxysome[END_REF] . At that time, side-to-side hexamer packing differences between CsoS1A (66.4 Å inter-hexamer separation) and CcmK structures (69.7 or 70.5 Å for CcmK1 6803 or CcmK4 6803 , respectively) was argued to reflect means to attain compatibility among shell constituents or to regulate the porosity of the shell. The availability of many more structures nowadays rules out that differences were coincidental or induced by crystallization conditions, which spread considerably by pH (4.2 to 9.5) or additives within each group (Table S2), and occasionally overlapped between the two classes (compare for instance conditions with 4OX8 vs 4OX6). Indeed, PMF profiles estimated here supported that highest stabilization is attained in different flat dispositions of PduA Sent and CcmK4 7942 hexamers. Although CcmK1 6803 profile was unexpectedly shallow, that CcmK never reached an Ass-A disposition in crystals (10 PDB entries) solidly points to global minima different from Ass-A. Yet, the structures of all reconstituted BMC shells prove that Ass-A is the mode of organization that conducts to closed assemblies (Table S2), also for shells composed of CcmK proteins [START_REF] Sutter | Structure of a Synthetic β-Carboxysome Shell[END_REF] .

All-atom MDs robustly demonstrated the experimental curving capabilities of Ass-A-organized BMC-H. Not only PduA Sent , but also all other Ass-A BMC-H rapidly and robustly bent. The known bending orientation was reproduced, i.e. the convex face lying towards the inner side of the compartment. In fact, structures averaged over the MD were strikingly similar to those found in minimalist shells, which all appear to derive from Ass-A arrangements. Comparison with data published for PduA Sent bi-hexamers [START_REF] Li | Computational and Experimental Approaches to Controlling Bacterial Microcompartment Assembly[END_REF] indicate that assembly might be better simulated on tri-hexamer ensembles, although in our hands a preference for curved dispositions was even demonstrated on bi-hexamers extracted from minimalist BMC-H Hoch and CcmK 7418 shells. BMC-H with Ass-B, Ass-C or Ass-D organizations behaved less clear-cut, bending and even tilting values being much dispersed over the MD trajectories. Globally, however, Ass-B or Ass-C trihexamers seem to fluctuate around flat dispositions. This was seen for individual MD runs [e.g. CcmK4 7942 (4OX6)], or was concluded from independent MDs [e.g. CcmK2 6803 behavior in assemblies prepared from crystals 2A1B and 3CIM]. However, curving capabilities could be also demonstrated for these BMC-H when reconfigured in Ass-A dispositions, suggesting that transitions between assembly modes might be a means to control BMC closure.

The ionic pair between Arg/Lys at position 28 and Asp49 (CcmK1 6803 ) likely contributes to maintain some BMC-H in Ass-B arrangements. This is supported by hexamer interspacing in 2D-patches imaged by TEM for the purified N29R PduA Sent , or conversely by the compact patches formed by R29N CcmK4 7942 , possibly by K28N BMC-H Hoch too. Similarly, 2D-patches were seen in cells overexpressing N29R PduA Sent , contrasting with nanotubes typically observed with WT PduA, whereas structures compatible with nanotubes/nanowires occurred in cells expressing the R29N CcmK4 7942 . However, the latter, and K28N BMC-H Hoch continued to assemble flat when purified, while nanotube-like bundles happened with N29R PduA Sent , suggesting that the mutations increased the chances of observing the inversed arrangements, but did not suffice to fully alter BMC-H assembly behavior. Also challenging were efforts to clarify the atomic determinants behind spontaneous curvature. Difficulties are illustrated by the striking failure to disrupt the assemblies when key residues are mutated. This is the case of K26A, N29R and R79A PduA Sent mutants studied here or before [START_REF] Pang | Structural insights into higher order assembly and function of the bacterial microcompartment protein PduA[END_REF] , of K28A and R78A BMC-H Hoch 22,[START_REF] Young | Visualizing in Vivo Dynamics of Designer Nanoscaffolds[END_REF] , or K25A, R28A, D49A and R80A CcmK1 6803 21 . Assemblies continued to grow, in spite of the fact that interactions between constituting subunits are weak. One of these residues, corresponding to K26 of PduA Sent , is conserved at the interface of all BMC-H. Its mutation into Ala or Asp in PduA Sent led to Ass-B arrangements in crystals (Table S2), while flat patches were imaged in E. coli (Fig. 5B), further reinforcing the link between crystal arrangements and curving trend. Energetic calculations proved that this residue and R79 are key interactors (Fig. S10). These data might match with the important role for curvature proposed for R79 [START_REF] Li | Computational and Experimental Approaches to Controlling Bacterial Microcompartment Assembly[END_REF] . In that study, the mutation of PduA R79 in a PduJ strain was shown to hamper the formation of nanotubes or even of Pdu BMC. TEM data presented here confirms this effect in vitro. Yet, mutation of other positions was known to have similar consequences [e.g. for K26A PduA 15 or K25A PduJ 17 ], as also demonstrated here for K26A and even N29R PduA Sent mutants, altogether inviting caution before concluding on cause/effect relationships. In our hands, R79A did not exert any significant effect on curvature in silico. Among 21 mutants tested, only the interfacial K26 (PduA) completely and reproducibly abolished bending, but the effect was weaker in other BMC-H. The prediction was supported by the neat drop of the proportion of abnormally elongated BL12(DE3) with the K26A mutant, as compared to WT PduA, and by the direct observation of 2D organizations and absence of nanotubes within these cells.

Interestingly, Pdu compartments were not recovered from S. enterica when the K26 of chromosomal PduA or K25 of PduJ were mutated into alanine, whereas compartments still formed with the R79A mutant and the protein was even co-purified with the BMC [START_REF] Sinha | Alanine scanning mutagenesis identifies an asparagine-arginine-lysine triad essential to assembly of the shell of the Pdu microcompartment[END_REF] . Piled 2D sheets were also imaged by TEM for a K26A mutant of a variant of PduA from Cit. freundii expressed in E. coli [START_REF] Pang | Structural insights into higher order assembly and function of the bacterial microcompartment protein PduA[END_REF] . However, in this last study the R79A mutation elicited similar results, likewise in our study. Accordingly, the two residues might be proposed to play a concerted role. K26 side-chain is often modeled in crystals with a stretched conformation, lying antiparallel with regard to the same residue of the counter-interacting hexamer. Asp22, also fully conserved, contributes to hold such conformation. A consequence is that the positively-charged groups of K26 and R79 are brought closer, something that might impose an extended conformation to R79 sidechain and facilitate its insertion in a small pocket of the facing hexamer in Ass-A dispositions. Alternatively, PduA curvature might be only directly defined by the electrostatics around the K26 ammonium group. The R79A would exert its effect indirectly, for instance if the mutant was incapable of reaching the required Ass-A disposition, similarly to the N29R mutant. These processes would be out of reach for short MD simulations.

Irrespective of the mechanisms that trigger curvature, our observations have implications for the interpretation of BMC biogenesis. -carboxysome formation was proven to be two-step process in Syn. elongatus PCC 7942, the presence of pre-organized cargo preceding shell assembly [START_REF] Chen | The bacterial carbon-fixing organelle is formed by shell envelopment of preassembled cargo[END_REF] . A similar study on Pdu Sent compartments pointed instead to a less synchronized mechanism, with coexistence of cargo-first and shell-first events [START_REF] Yang | Biogenesis of a bacterial metabolosome for propanediol utilization[END_REF] . A similar model could operate with -carboxysomes, as indicate the gathering of CsoS2 scaffolding protein to portion of shells, which would precede recruitment of RuBisCO and final BMC closure [START_REF] Oltrogge | Multivalent interactions between CsoS2 and Rubisco mediate α-carboxysome formation[END_REF] , or the multiple layers of RuBisCO attached to the inner surface of partial -carboxysome shells 8, 36 . In view of that, and considering that BMC-H are the most abundant shell components, Ass-B might be seen as a structural trap that would delay premature shell closure of some BMC such as -carboxysomes.

Transit towards Ass-A dispositions would be triggered by contacts with motifs on cargo/scaffold components or, alternatively, upon intervention of auxiliary proteins such as CcmO or CcmP. Indeed, BMC-T co-expression was required to induce the formation of Halothece sp. PCC 7418 or BMC-H Hoch empty shells, both inside cells [START_REF] Sutter | Structure of a Synthetic β-Carboxysome Shell[END_REF][START_REF] Hagen | Programmed loading and rapid purification of engineered bacterial microcompartment shells[END_REF] or in vitro [START_REF] Hagen | In Vitro Assembly of Diverse Bacterial Microcompartment Shell Architectures[END_REF] , while BMC-T presence was dispensable for the formation of RMM-H Msm nanotubes [START_REF] Hagen | In Vitro Assembly of Diverse Bacterial Microcompartment Shell Architectures[END_REF] , minimalist -carboxysomes [START_REF] Tan | Structure of a Minimal α-Carboxysome-Derived Shell and Its Utility in Enzyme Stabilization[END_REF] or Klebsiella pneumoniae GRM2 shells [START_REF] Kalnins | Encapsulation mechanisms and structural studies of GRM2 bacterial microcompartment particles[END_REF] . In the last study, cmcC from GRM2 was proposed to be a component endowed with high spontaneous curvature, in agreement with the crystal Ass-A organization of the E. coli K25A cmcC homolog [START_REF] Ochoa | Structural characterization of hexameric shell proteins from two types of choline-utilization bacterial microcompartments[END_REF] . Future studies will be required to address the possible implication of BMC-T in mediating BMC-H assembly transitions, also to investigate the physiological consequences of altering the natural biogenesis pathway of a given BMC.

MATERIALS AND METHODS

Cloning, Expression, and Protein Purification

DNA sequences permitting the expression of the different BMC-H studied here are given in the excel Table S5, including flanking regions. These segments were integrated in between XbaI and BlpI sites of a pET26b vector using standard cloning methods. Plasmids for studies of Synechocystis sp. PCC8603 based on pET15b were described before [START_REF] Garcia-Alles | Occurrence and stability of hetero-hexamer associations formed by β-carboxysome CcmK shell components[END_REF][START_REF] Garcia-Alles | Spontaneous non-canonical assembly of CcmK hexameric components from β-carboxysome shells of cyanobacteria[END_REF] . After transformation of BL21(DE3) cells, protein expression was carried out in ZYM-5052 auto-induction media (4 mL) overnight at either 25°C or 37°C, following a described protocol [START_REF] Garcia-Alles | Occurrence and stability of hetero-hexamer associations formed by β-carboxysome CcmK shell components[END_REF] . Cells pellets collected by centrifugation (4000 g) were lysed with 0.5 mL BugBuster extraction reagent (Sigma), supplemented with PMSF (1 mM, final conc.). Small aliquots were withdrawn and prepared for SDS-PAGE analysis (denatured at 95°C), corresponding to cellular fractions (CF). Soluble fractions (SF) were prepared similarly from material remaining in supernatants after centrifugation at 21000 g, 4°C for 15 min (pellets were kept at 4°C for studies of protein disassembly). Purification was performed on Vivapure 8 96-well cobalt-chelate microplate columns, following provider (VivaScience) instructions. Elution was effected with 300 L of a 20 mM NaPi/300 mM NaCl/300 mM imidazole (pH 8.0) solution. EDTA (5 mM final conc.) was added immediately after elution and purified fraction (PF) aliquots withdrawn and denatured for SDS-PAGE analysis. Material remaining in pellets were re-treated with BugBuster, sonicated for 20 sec at 4°C and centrifuged at 21000g. After discarding supernatants, pellets were supplemented with 600 L of a 20 mM NaPi/300 mM NaCl/10 mM imidazole (pH 8.2) solution containing 1 M urea. After resuspension with vigorous vortexing, the suspension was shaken for 3-5 hours at 4°C, with two interspersed rounds of 20 sec sonication. After 21000 g, urea-solubilized fraction (USF) aliquots were prepared for SDS-PAGE as other fractions, and the material was purified as indicated above on microplate columns. In that manner urea-purified fractions (UPF) were prepared.

The remaining of material eluted from the purification columns, which permitted to prepare PF and UPF, was dialyzed at 4°C against 10 mM NaPi/150 mM NaCl (pH 6.5) using 3500 Da MWCO Pure-A-Lyzer devices.

Two steps were carried out, theoretically permitting a > 10 4 fold decrease of initial buffer and urea concentrations. When necessary, proteins were concentrated to 1-2 mg/mL using Vivaspin 500 centrifugal concentrators (PES, 10 kDa MWCO).

Phase contrast microscopy

Cells growing in LB supplemented with the corresponding antibiotic were induced at exponential phase (OD 280nm = 0.6-0.8) with IPTG (200 M). Growth was pursued at 37°C for 6 h before visualization under an oil immersed 100x objective lens with a DM4000B Leica microscope (DFC 450C caméra and EF6000 laser).

Image analysis was carried out with ImageJ using an automated procedure that consisted in i) subtracting signal background, ii) setting-up a common threshold, and iii) rejecting small objects, well below the cell size.

Atomic Force Microscopy imaging

AFM experiments were carried out exactly as previously described [START_REF] Garcia-Alles | Spontaneous non-canonical assembly of CcmK hexameric components from β-carboxysome shells of cyanobacteria[END_REF] , after diluting protein samples in 10 mM NaPi, 300 mM NaCl pH 6.5 (Buffer P). When indicated, this solution was supplemented with 1 mM MgCl2 (final conc.) with the intention to inverse mica surface charge.

Transmission electron microscopy

Specimens were prepared for electron microscopy using the conventional negative staining procedure.

After diluting proteins in Buffer P to 0.05-0.15 mg/mL, 10 µL drops were deposited on parafilm for 20 min.

After absorbing material on glow-discharged Formvar carbon-coated grids for 2 min, grids were blotted and negatively stained with uranyl acetate (1%) for 1 min.

For analysis of cell contents, induction was effected with IPTG as indicated above. After 6h, cells were pelleted and resuspended in 2,5% glutaraldehyde and 2% paraformaldehyde in cacodylate buffer (0.1 M, pH 7.2). After 2 h at RT, cells were post-fixed with 1% OsO4 in the same buffer. After pelleting and concentrating in agarose, cells were treated for 1 h with 2% aqueous uranyl acetate. The samples were then dehydrated in a graded acetone series and embedded in Epon. After 48 h of polymerization at 60 °C, ultrathin sections (80 nm thick) were mounted on 200 mesh Formvar-carbon-coated copper grids. Sections were stained with Uranyless and lead citrate.

A JEM-1400 electron microscope (JEOL Inc, Peabody, MA, USA) operating at 80 kV, equipped with a Gatan Orius digital camera (Gatan Inc, Pleasanton, CA, USA) was used for imaging at different magnifications.

Cryoelectron microscopy (Cryo-EM)

3.5µL sample drops were deposited on parafilm for 20 min. Glow-discharged lacey carbon grids were then placed onto the drops and incubated for 1min. Grids were transferred to the thermostatic chamber of a Leica EM-GP automatic plunge freezer, set at 20°C and 95% humidity. Excess solution was removed by blotting with Whatman n°1 filter paper for 0.2-0.6 seconds, and the grids were immediately flash frozen in liquid ethane at -185°C. Frozen specimens were placed in a Gatan 626 cryo-holder, and cryo EM was carried out on a Jeol 2100 microscope, equipped with a LaB6 cathode and operating at 200 kV, under low dose conditions. Images were acquired with SerialEM software, with defocus of 1.5-2.5 μm, on a Gatan US4000 CCD camera. This device was placed at the end of a GIF Quantum energy filter (Gatan, Inc.), operated in zero-energy-loss mode, with a slit width of 25 eV. Images were recorded at a nominal magnification of 4,000 corresponding to calibrated pixel sizes of 1.71Å.

All-atom Molecular Dynamics Simulations

Assemblies composed of three hexamers were prepared from available crystallographic structures (PDB ID indicated in Table S2) after applying translation and symmetry operations. Glycerol and other crystallographic ligands were removed (sulfate ions associated to CsoS1A were deleted, or not, without evident difference). Ensembles were embedded in cuboid cells with dimensions extending 20 nm around all protein atoms, which were filled with explicit solvent. Each system was neutralized with NaCl (0.9 % final concentration). Periodic boundary conditions were applied and unless otherwise mentioned the YASARA AMBER14 force field was selected. The cut-off for the Lennard-Jones potential and the short range electrostatics was 8 Ǻ. Long-range electrostatics were calculated using the Particle Mesh Ewald (PME) method with a grid spacing <0.1 nm, 4th order PME-spline, and PME tolerance of 10 -5 for the direct space sum. YASARA's pKa utility was used to assign pKa values at pH 7.0. The entire system was energy-minimized using steepest descent minimization, followed by a simulated annealing minimization until convergence (<0.05 kJ/mol/200 steps). The equations of motions were integrated with a multiple time step of 2.5 fs for bonded interactions and 5.0 fs for non-bonded interactions at a temperature of 298K and a pressure of 1 atm (NPT ensemble). At least two simulations were launched on each case, with attribution of random initial atomic velocities (20 ns/run, unless otherwise indicated). Intermediate MD snapshots were recorded every 250 ps. Simulations were carried out in a 16-core CPU PC exploiting GPU capabilities (NVIDIA GeForce GTX 1080), and lasted typically 50 to 60 hours per 20 ns run.

For simulations of Ass-A reconstituted assemblies, hexamers extracted from target PDB structures were superimposed individually on the different hexamers of the template PduA Sent (3NGK) tri-hexamer. For most cases, sterical clashes around R30, the D51-E54 segment and the R82-N86 region (CcmK4 6803 numbering) were alleviated by adapting the side-chain conformation to reproduce those present in the corresponding residue of PduA (3NGK). Special attention was given to the CcmK conserved Arg30. Its sidechain conformation was adapted to reproduce the orientation observed for Arg28 in the cryo-EM structure of the CcmK 7418 shell (6OWF). In CcmK4 6803 , the Arg30, Gln53 and Glu54 collapse close to the C3 axes of symmetry of the tri-hexamer. These side-chains were therefore adapted manually.

Dihedral angle and distance analysis was performed with adapted Python scripts executed under Pymol (https://www.pymol.org/). Tilting was measured among main-chain C atom positions of M24 and Ile18 (PduA Sent , corresponding residues in other BMC-H) from two monomers of a given hexamer with regard to same symmetric residues of the interacting hexamer counterpart, as described [START_REF] Garcia-Alles | Spontaneous non-canonical assembly of CcmK hexameric components from β-carboxysome shells of cyanobacteria[END_REF]

CORRESPONDING AUTHOR

To whom correspondence should be addressed: Luis F. Garcia-Alles, phone + 33 561-048-807. E-mail: lgarciaa@insa-toulouse.fr

Figure S17 .

 S17 Figure S17. Characterization of assemblies formed by BMC-H single point mutants inside E. coli.

symmetric monomer of the opposite hexamer. For plane representations, structures averaged over the MD were first superimposed on the corresponding crystal structure. Only main-chain atoms from one of the hexamers was used for the superimposition. Next, each hexamer was represented by the plane containing V54 C atom (PduA Sent ) of the three monomers of the given hexamer that compose the interface. In other representations, each hexamer was represented by its center of mass, calculated considering only main-chain atoms of core residues (res 1 to 90) from the six monomers. Structural figures were also prepared with Pymol.

Data from MD trajectories snapshots, either in YASARA .sim format or as pdb files, as well as AFM or TEM data presented in this study are available upon request.

Umbrella Sampling Molecular Dynamics Simulations

Assemblies of two hexamers of PduA Sent (3NGK), CcmK1 6803 (3BN4), and CcmK4 7942 (4OX6) were prepared at pH 7.0 from the available crystal structure using ProteinPrepare (https://playmolecule.com/proteinPrepare/). All atom MD simulations were performed using GROMACS (version 2021.1), with Amber ff99SB-ILDN force field. All other conditions were as mentioned above, with the difference that the cut-off for the Lennard-Jones potential and the short-range electrostatics was established at 10 Ǻ. The entire system was energy-minimized using steepest descent minimization, followed by a constant volume, constant temperature (NVT) equilibration at T=298 K for 100 ps with the backbone of both hexamers restrained with a force constant of 1000 kJ/mol/nm 2 .

Umbrella sampling simulations were performed with translation and rotation of the first hexamer prevented with harmonic restraints (force constant of 1000 kJ/mol/nm 2 ) applied to six Cα atoms (one per monomer, near its COM). Binding energies were evaluated using the distance between the two hexamers COM as reaction coordinate. A steered simulation pulling on the second hexamer with a force constant of 1000 kJ/mol/nm 2 at a rate of 10 nm/ns was used to generate configurations at 1 Å steps along the reaction coordinate. A total of 15 windows per case were therefore processed through 2 ns of NPT equilibration at 1 atm and 10 ns of production simulations to finally calculate the PMF between the two hexamers using the Weighted Histogram Analysis Method (WHAM) [START_REF] Hub | g_wham-A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates[END_REF] . The error was estimated using bootstrapping. The PMF as a function of the hexamer lateral displacement as reaction coordinate was calculated similarly, with the difference that the second hexamer was progressively displaced using UCFS Chimera from the crystal disposition, at 1 Å steps in a range between -15 Å and + 15 Å. In those simulations the bending, tilting, and z-rotation angles were restrained to zero with harmonic potentials with a force constant 1000 kJ/mol/rad 2 to keep the two hexamers planar.

SUPPORTING INFORMATION

Next files are provided as supplementary data: Table S1

FUNDING SOURCES

The French ANR supported financially this work: ANR-19-CE09-0032-01. The Spanish MICINN is also acknowledged for funding D.R. work (project PGC2018-098373-B-I00).

NOTES

The authors declare no conflict of interest


Samory Houzangbe
email: samory.houzangbe@ensam.eu

David Antonio

Gómez Jáuregui

Sylvain Fleury

Loïc Huet

Léo Berdon

Baptiste Manusset

Paul Subert

Jean-Baptiste Pigrée

Nadine Couture

Simon Richir

Étude de l'Influence du Stress sur la Créativité dans un Scénario en Réalité Virtuelle

Keywords: Réalité Virtuelle, Créativité, Stress centered computing~User studies, Virtual Reality, • Computing methodologies~Cognitive science

Whether it is for evolution, competitiveness or problem solving, innovation is necessary to a company's survival. Thus, it is essential to understand this process and what affect them to improve innovation. In this paper we focus on the ideation steps (generating ideas and proposing new concepts). We developed an experimental protocol in Virtual Reality, as it has been demonstrated to be a useful medium for creativity. We conducted the experiment following two conditions, one with an induction of stress and one without, to evaluate the effect of stress on the level of creativity. The levels of stress, creativity and physiological signals have been monitored. Our early results did not show significant differences between the two groups, however, as supported by previous studies, we have successfully used the Empatica E4 physiological wearable in our experimental context and observed a general rise in electro-dermal activity (EDA) among our participants. We suggest that our experiment was able to elicit an emotional response in our participants that is observable in the physiological data. This preliminary study will help us shape the next steps of our research on the understanding of the creativity experience depending on different parameters.

Introduction

La capacité d'innovation d'une entreprise est cruciale pour son développement et sa compétitivité. Ses processus d'innovation sont souvent complexes car reposent sur des capacités stratégiques, humaines, techniques, organisationnelles. Dans le cadre de ce projet, nous nous intéressons aux étapes d'idéation de ces processus qui consistent à la génération d'idées et à la proposition de nouveaux concepts. Ces étapes reposent sur des capacités et des activités de créativité. La créativité est généralement définie comme la capacité à proposer de nouveaux concepts adaptés au contexte dans lequel elle est réalisée [START_REF] Lubart | Psychologie de la créativité-2e édition[END_REF]. Bien que les composantes temporelles, matérielles et humaines soient importantes [START_REF] Amabile | The dynamic componential model of creativity and innovation in organizations: Making progress, making meaning[END_REF], certains leviers peuvent être de nature à moduler la créativité, comme par exemple en influençant les schémas de raisonnement et de résolution de problèmes [START_REF] Teresa M Amabile | The social psychology of creativity: A componential conceptualization[END_REF][START_REF] Todd | An investment approach to creativity: Theory and data[END_REF]. Il a été démontré que de nombreux éléments de l'environnement peuvent influencer la créativité [START_REF] Goldschmidt | Variances in the impact of visual stimuli on design problem solving performance[END_REF][START_REF] Baird | Inspired by Distraction: Mind Wandering Facilitates Creative Incubation[END_REF].

Les outils de réalité virtuelle ont montré leur pertinence pour stimuler la créativité des utilisateurs dans le cadre de tâches d'idéation, en comparaison à d'autres outils d'esquisses tels que le papier/crayon [START_REF] Yang | Examining creativity through a virtual reality support system[END_REF], Photoshop [START_REF] Jee | Design Cognitive Actions Stimulating Creativity in the VR Design Environment[END_REF] ou encore des outils de conception assistée par ordinateur (CAO) [START_REF] Feeman | Exploration and evaluation of CAD modeling in virtual reality[END_REF]. Mille et al. [START_REF] Mille | Effects of digital tools feature on creativity and communicability of ideas for upstream phase of conception[END_REF] ont aussi démontré que la génération d'idée par l'esquisse en réalité virtuelle offre une meilleure expérience utilisateur que la CAO et le papier/ crayon. Les études précédemment citées indiquent que l'activité d'esquisse en réalité virtuelle est propice à l'état de flow, qui conduit les participants à générer des idées plus élaborées.

Plusieurs chercheurs ont étudié la relation entre les états émotionnels et la créativité. En effet, en 2008 de Dreu et al. [START_REF] Dreu | Hedonic tone and activation level in the mood-creativity link: toward a dual pathway to creativity model[END_REF] proposent une voie double à la créativité. Ils présentent les résultats de quatre expériences consécutives. Ils indiquent que la valeur d'excitation stimule la créativité. De plus, ils précisent qu'une excitation positive peut améliorer la performance au travers d'une plus grande flexibilité et inclusivité, tandis que l'excitation négative amène un meilleur niveau de créativité au travers d'une plus grande persévérance et persistance. Ils insistent sur le fait que les effets des états émotionnels ne peuvent être attribués uniquement à la valeur d'excitation, la valence de l'émotion doit aussi être prise en compte en fonction du type de tâches.

Une autre étude par Hao et al. [START_REF] Hao | Enhancing creativity: Proper body posture meets proper emotion[END_REF] approfondi les études précédentes. Ils essayent d'observer si une adéquation entre l'état émotionnel et la posture amène à une meilleure performance créative. Ils conduisent deux expériences, la première en induisant des émotions négative ou positive aux participants et en leur faisant prendre une posture ouverte ou fermée. Les participants réalisent un test d'usage alternatif (Alternative Uses Task, AUT) [START_REF] Guilford | Measurement and Creativity[END_REF]. Pour la seconde expérience ils utilisent le même protocole que la première expérience mais les participants réalisent un exercice de résolution de problème réaliste (Realistic Presented Problem, RPP) pour mesurer leur pensée divergente et potentiel créatif. Ils concluent que la performance créative n'est pas uniquement liée à l'état émotionnel, mais plutôt à une adéquation entre l'émotion et la posture. Ils précisent qu'une association des deux pourrait amener à de meilleurs résultats créatifs.

Selon Lazarus et Folkman [START_REF] Richard | Stress, appraisal, and coping[END_REF], le stress est un processus bilatéral : il implique la production d'éléments stressant par l'environnement et la réponse d'un individu sujet à ces facteurs stressant. Plusieurs études ont montré que les données physiologiques, tel que le rythme cardiaque et la variabilité du rythme cardiaque sont liées au stress [START_REF] Joachim Taelman | Influence of Mental Stress on Heart Rate and Heart Rate Variability[END_REF]. De plus, des études ont montré un lien entre l'activité électrodermale et les niveaux de stress [START_REF] Joshi | An experimental analysis to monitor and manage stress among engineering students using Galvanic Skin Response meter[END_REF][START_REF] Islam | Measuring User Responses to Driving Simulators: A Galvanic Skin Response Based Study[END_REF]. Ces réactions physiologiques peuvent être recoupées avec les études que nous avons présentées plus tôt et donc la question peut poser de l'effet du stress sur la performance créative.

Le stress est présent dans la vie quotidienne et professionnelle notamment, en 1992 Talbot et al. [START_REF] Talbot | Creativity and Stress[END_REF] ont donc étudié sa relation avec la créativité. Dans leur recherche ils ont trouvé qu'il existe une forte corrélation négative entre le stress et le climat créatif, provenant principalement des relations aux autres et à la structure organisationnelle. Cependant, Byron et al. [START_REF] Byron | The relationship between stressors and creativity: a meta-analysis examining competing theoretical models[END_REF] ont indiqué que la relation entre le stress et la créativité pourrait ne pas être simplement capturée en la qualifiant comme négative ou positive. Somaz et Tulgan [START_REF] Sormaz | Performance Under Pressure: Managing Stress in the Workplace[END_REF] suggèrent que, dans le cadre professionnel, un stress aigu induit une montée d'adrénaline dans le corps, et donc alimentant la performance, augmentant la concentration et servant de catalyseur pour la créativité et l'innovation. De plus, des études [START_REF] Karel | Recall performance, plasma cortisol and plasma norepinephrine in normal human subjects[END_REF][START_REF] Heather | Endogenous cortisol elevations are related to memory facilitation only in individuals who are emotionally aroused[END_REF] ont démontré qu'un stress aigu semble améliorer la mémoire dans un contexte d'apprentissage.

Cela contraste avec plusieurs études qui suggèrent qu'une exposition répétée au stress ou un stress chronique bloque généralement le traitement d'informations et entraîne des problèmes de mémoire chez des adultes en bonne santé [START_REF] Clemens Kirschbaum | Stress-and treatment-induced elevations of cortisol levels associated with impaired declarative memory in healthy adults[END_REF]. Ainsi, le stress dans ces cas pourrait inhiber la créativité [START_REF] Shanteau | Environmental Stressor Effects on Creativity and Decision Making[END_REF] et avoir un impact négatif [START_REF] Selye | Stress and disease[END_REF].

Il existe donc des aspects positifs dû au stress et des aspects négatifs, qui sont dépendant des individus et des situations. Dans le cadre de notre étude nous souhaitons explorer l'influence du stress sur la créativité lors d'un scenario en réalité virtuelle (RV), qui est un outil puissant pour la créativité. Nous émettons l'hypothèse que s'il y a une induction de stress, via un facteur environnemental négatif, le participant est moins créatif et qu'il est possible d'observer des changements physiologiques. Pour vérifier cette hypothèse nous proposons un protocole composé de deux groupes qui vont réaliser la même tâche de créativité en RV. L'un des groupes subira une induction de stress avant l'exercice. Pour essayer de détecter le niveau de stress en nous utilisons des marqueurs physiologiques (rythme cardiaque et micro-sudation) ainsi que des échelles subjectives. Les résultats de cette étude nous donneront des indices sur les effets du stress sur la créativité en RV. Des perspectives sur l'adaptation de l'environnement créatif à l'utilisateur en temps réel pour permettre d'améliorer la qualité de l'expérience créative et des résultats produits pourrons être envisageables. Cette étude préliminaire s'inscrit dans le cadre de travaux plus large sur la compréhension des effets de la réalité virtuelle sur l'expérience créative et de l'utilisation des données physiologiques pour la détection et l'anticipation des états créatifs.

Dispositif expérimental

La tâche de créativité en RV se passe dans une application d'esquisse en 3D. Cette application permet à l'utilisateur de dessiner en 3D grâce au système de suivi de mouvements. Dans l'application l'utilisateur peut dessiner grâce aux manettes. Il a le choix entre différentes tailles de pinceaux et de couleurs via une palette de couleurs. Il a aussi l'option d'effacer des parties du dessin, de sélectionner et redimensionner ou encore dessiner des formes symétriques en utilisant un plan de symétrie. L'utilisateur peut sauvegarder un dessin et créer une nouvelle scène pour repartir à zéro.

Nous avons décidé d'utiliser un visiocasque HTC Vive, pour sa qualité d'image et la qualité de son système de suivi de mouvements. Il permet à l'utilisateur de se mouvoir naturellement autour de son dessin. Ce système de RV est associé avec un ordinateur haute performance (Intel Core i7 Coffee Lake, 16GB of RAM, NVIDIA GeForce RTX 2070) pour s'assurer de la fluidité de l'expérience.

Pour mesurer les données physiologiques nous avons décidé d'utiliser le bracelet Empatica E4 1 [START_REF] Garbarino | Empatica E3 -A wearable wireless multi-sensor device for real-time computerized biofeedback and data acquisition[END_REF]. Ce bracelet connecté a été designé pour la recherche et permet d'avoir accès aux données brutes, pour la photopléthysmographie, l'intervalle inter-battement, la température de la peau, les données d'accéléromètre et 1 https://www.empatica.com/en-eu/research/e4/ l'activité électrodermale. Plusieurs études se sont concentrées sur la fiabilité de l'E4 pour la reconnaissance des émotions, le comparant à des outils médicaux. En effet, Ollander et al. [START_REF] Ollander | A comparison of wearable and stationary sensors for stress detection[END_REF] compare l'E4 à un outil médical pour la détection du stress dans une situation stationnaire. Dans leur étude ils font passer aux participants le Test de Stress Sociale Trier [START_REF] Birkett | The Trier Social Stress Test protocol for inducing psychological stress[END_REF], qui consiste à simuler un entretien d'embauche. Van Lier et al. [START_REF] Hendrika G Van Lier | A standardized validity assessment protocol for physiological signals from wearable technology: Methodological underpinnings and an application to the E4 biosensor[END_REF] propose une méthode standardisée de validation de la fiabilité des outils de mesure physiologique connectés. Les participants réalisent une tâche inductrice de stress pour déterminer si l'E4 est capable de détecter les changements physiologiques de manière fiable. Ces auteurs ont conclu que l'E4 est un capteur valide pour détecter les réponses physiologiques aux facteurs de stress.

Protocole expérimental

Dans un premier temps les participants doivent lire et s'il l'accepte, signer un formulaire de consentement stipulant qu'ils acceptent que leurs données physiologiques soient enregistrées et utilisées pour cette étude. Ils remplissent ensuite un questionnaire pré-expérimental renseignant des données démographiques. Les participants complètent le State-Trait Anxiety Index (STAI-Y) [START_REF] Spielberger | State-Trait Anxiety Inventory[END_REF] pour mesurer leur niveau de stress.

Une fois que les participants ont complété les questionnaires, ils sont équipés de l'Empatica E4 et du visiocasque Vive. Ils réalisent une phase de tutoriel pour se familiariser avec l'application de dessin (apprendre à dessiner, effacer, changer la taille du pinceau et la couleur, enregistrer son dessin et créer une nouvelle scène). La phase de tutoriel dure 3 minutes. Une fois celle-ci terminée, le scénario de créativité est présenté aux participants. La tâche proposée est un exercice de pensée divergente, basée sur les travaux de Guilford (Alternative Uses, GAU) [START_REF] Guilford | Measurement and Creativity[END_REF]. Le scénario est le suivant, une entreprise de production de porte manteau en a produit trop et l'objectif des participants est d'imaginer autant de manières détournées d'utiliser les portes manteau. Durant cette tâche les participants doivent dessiner autant d'idées que possible en utilisant l'outil 3D. Un modèle 3D du porte manteau est présent dans l'environnement virtuel, il sert de base pour le dessin (voir les figures 1). Une fois qu'un dessin est terminé, les participants l'enregistre et passe à l'idée suivante. La tâche de créativité dure 7 minutes.

Pour cette expérience les participants ont été séparé en deux groupes : un groupe avec induction de stress et un groupe sans induction de stress. Les deux groupes suivent la procédure décrite précédemment. Cependant, pour le groupe avec induction de stress l'expérimentateur introduit aux participants (avant le début de la tâche de créativité) un jury non-répondant, présent dans la pièce. La présence d'un jury a déjà été utilisée avec succès pour induire du stress dans différents scénarios [17]. Le jury ne possède pas de double virtuel présent dans l'environnement. Nous avons pris cette décision car la méthode du jury a déjà démontré son efficacité et que nous ne voulons pas rajouter de facteurs distrayant dans l'environnement virtuel qui pourrait altérer l'exercice créatif. Nous avons décidé d'utiliser un design inter-sujet pour comparer la même tâche de créativité. Proposer deux scénarios de créativité différents pouvant être évalués séparément mais en restant comparable en termes de niveaux de créativité produit par les participants était excessivement complexe dans le cadre de notre étude.

À la fin de la tâche de créativité les participants retirent le visiocasque et l'E4 et il leur est demandé de compléter une fois de plus le questionnaire STAI-Y.

Mesures

Pour mesurer le niveau de stress et l'anxiété générale des participants, nous avons utilisé le STAI-Y. De plus, nous avons mesuré l'activité électrodermale (EDA) des participants, il a été démontré que cette donnée était liée au niveau de stress [START_REF] Joachim Taelman | Influence of Mental Stress on Heart Rate and Heart Rate Variability[END_REF][START_REF] Joshi | An experimental analysis to monitor and manage stress among engineering students using Galvanic Skin Response meter[END_REF][START_REF] Islam | Measuring User Responses to Driving Simulators: A Galvanic Skin Response Based Study[END_REF].

Le niveau de créativité est mesuré pour chaque participant en fonction d'un score combiné en utilisant les méthodes de Guilford [START_REF] Guilford | Measurement and Creativity[END_REF], comme décrites par Fleury et al. [START_REF] Fleury | Studying the effects of visual movement on creativity[END_REF]. Le GAU permet la création d'une collection d'idées pour chaque participant. Chaque idée est analysée est caractérisée sur la base de 4 critères qui vont constituer un score total. Ces critères sont l'originalité (qui détermine si l'idée du participant est unique comparée aux autres participants), la fluidité (le nombre d'idées ou de caractéristiques générées), la flexibilité (le nombre d'idées provenant de différents domaines ou catégories) et l'élaboration (la quantité de détails ajoutés pour chaque idée).

Participants

Cette expérience a été menée avec 16 étudiants en Master, spécialisé en Réalité Virtuelle, ceux-ci étant donc habitués à l'utilisation du média et des techniques d'interactions. Il y avait 10 hommes et 6 femmes, âgés de 22 à 33 ans (M=23,56). Les participants ont été répartis dans deux groupes de 8 (un groupe avec induction de stress et un sans induction de stress). Le jury non-répondant était un membre récent du laboratoire peu connu par les étudiants.

Résultats préliminaires et travaux futurs

Pour analyser les niveaux de stress nous avons utilisé des t-tests appairés, le test de normalité de Shapiro-Wilk n'étant pas significatif (p=0,141). Une première analyse des résultats n'a pas retourné de différence significative pour le niveau de stress (avant-après) pour le groupe sans induction de stress (p=0,320, M-Avant=33,13, M-Après=29,75). Le t-test n'a pas retourné de différence significative pour le niveau de stress (avant-après) pour le groupe avec induction de stress (p=0,377, M-Avant=35,63, M-Après=33,13). Nous avons utilisé une analyse ANOVA pour comparer les niveaux de créativité entre les deux groupes. Les résultats n'ont pas retourné de différence significative entre les deux groupes (p=0,442, F=0,627, M-NoStress=14,13, M-Stress=15,50).

Concernant les données physiologiques nous n'avons pas trouvé de corrélations entre le niveau moyen d'activité électrodermale et le niveau de créativité, ni avec le niveau de stress rapporté par les participants. Nous avons réalisé une analyse qualitative de l'activité électrodermale. Nous n'avons pas trouvé de de changement significatif du niveau d'activité cardiaque chez les participants du groupe avec induction de stress. Le rythme cardiaque est constant tout au long de l'expérience (voir la figure 2). Ces résultats semblent cohérents avec les retours des participants concernant leur niveau de stress perçu. Nous ne relevons que très peu de données aberrantes et aucune déconnexion durant l'expérience. Pour obtenir une représentation visuelle de l'évolution de l'activité électrodermale, nous avons normalisé les données (utilisant un algorithme min-max), calculé la moyenne des données et tracé un graphique des données (voir la figure 3). Nous pouvons observer pour chaque groupe que l'activité électrodermale augmente tout au long de l'expérience. L'activité électrodermale étant liée à la valeur d'excitation [START_REF] Siqueira | Estimating Player Experience from Arousal and Valence Using Psychophysiological Signals[END_REF], nous pouvons supposer que la tâche de créativité en réalité virtuelle a provoqué une réponse émotionnelle chez nous participants. Ce qui est intéressant car, comme nous l'avons discuté plus tôt, les émotions sont essentielles dans le processus créatif [START_REF] Dreu | Hedonic tone and activation level in the mood-creativity link: toward a dual pathway to creativity model[END_REF].

Nous avions émis l'hypothèse, après notre analyse de la littérature, que l'induction de stress, via un facteur environnemental négatif, a une influence négative sur la performance créative. Au vu des réponses des participants à l'induction de stress nous ne sommes pas en mesure de vérifier cette hypothèse. En effet, les participants n'ont pas rapporté une augmentation du stress qui était différente entre les deux conditions. Nous supposons que le cadre trop familier pour les participants couplé avec l'absence d'un facteur stressant dans l'environnement virtuel, n'ont pas permis de générer un facteur stressant suffisant pour que le comportement des participants en soit altéré.

Cependant, si nos résultats ne présentent pas de différences significatives, cette expérience nous donne des perspectives intéressantes sur l'utilisabilité des objets connectés portables, tel que l'Empatica E4, dans des applications de réalité virtuelle impliquant des mouvements sans pour autant limiter l'expérience. Cette expérience combinée avec les résultats présents dans la littérature valide l'utilisation de l'E4 comme outil de captation de données physiologique durant une tâche de créativité en réalité virtuelle. Si nous sommes en mesure de détecter certains modèles de réponses physiologiques, nous pourrions être en mesure de

Figure 1 :

 1 Figure 1 : Exemple d'idées produites par les participants (Un arrosoir, une lampe et un perchoir à oiseau)

Figure 2 :

 2 Figure 2 : Graphiques d'exemple d'évolution du rythme cardiaque de participants (Exemple d'évolution du rythme cardiaque d'un participant du groupe sans induction de stress (BPM/s) ; Exemple d'évolution du rythme cardiaque d'un participant du groupe avec induction de stress (BPM/s)).

Figure 3 :

 3 Figure 3 : Graphiques des moyennes normalisées de l'activité électrodermale. (Moyenne normalisée des valeurs d'activité électrodemrale pour les participants du groupe sans induction de stress (moyenne normalisée d'EDA/secondes) ; Moyenne normalisée des valeurs d'activité électrodemrale pour les participants du groupe avec induction de stress (moyenne normalisée d'EDA/secondes)).

Remerciements

Nous souhaitons remercier tous les étudiants ayant participé à cette expérience. Nous voulons aussi remercier les ingénieurs de l'équipe AM Valor qui nous ont aidé à mettre en place l'environnement de dessin 3D. Enfin nous voulons remercier Olivier Christmann et Geoffrey Gorisse qui ont coordonné ce projet de recherche et avoir permis le développement de cette étude.


A V Isaev

A V Yeremin

N I Zamyatin

I N Izosimov

A A Kuznetsova

O N Malyshev

R S Mukhin

A G Popeko

Yu A Popov

B Sailaubekov

A I Svirikhin

E A Sokol

M.S Tezekbayeva

D A Testov

M L Chelnokov

V I Chepigin

S Antalic

P Mosat

P Brionnet

B Gall

O Dorvaux

K Kessaci

A Sellam

A Lopez-Martens

K Hauschild

Study of Spontaneous Fission Using the SFiNx System

Keywords: numbers: 25.85.Ca, 25.70.-z, 27.90.+b, 29.40.Cs, 29.40.Gx

A new detector system consisting of 116 3 He neutron counters and DSSSD array was created. This system can be used to study spontaneous fission properties of short-lived heavy isotopes. The single neutron registration efficiency of the counter assembly was measured as 54.7±0.1% with 248 Cm-source. Using the setup, new data were obtained for prompt neutron yields of 252 No isotope.

Introduction

The spontaneous fission process defines the boundaries of the existence of heavy elements. At present, there is no complete nuclear fission model, and new experimental data are needed more than ever to improve the theoretical approaches.

Our group has accumulated significant experience in the study of the decay properties of heavy isotopes using VASSILISA [START_REF] Yeremin | The electrostatic separator VASSILISSA Performance and experimental results[END_REF] and SHELS [START_REF] Popeko | Separator for Heavy ELement Spectroscopy -velocity filter SHELS[END_REF] recoil separators. Important data were obtained for neutron deficient isotopes of Fm [START_REF] Svirikhin | The emission of prompt neutrons from the spontaneous fission of 252 No and 244 Fm[END_REF][START_REF] Svirikhin | Neutron multiplicity at spontaneous fission of 246 Fm[END_REF], No [START_REF] Svirikhin | Characteristics of spontaneous fission of 250 No[END_REF][START_REF] Isaev | Comparative Study of Spontaneous-Fission Characteristics of 252 No and 254 No Isotopes[END_REF] and Rf [START_REF] Svirikhin | Prompt neutrons from spontaneous 254 Rf fission[END_REF][START_REF] Svirikhin | Spontaneous fission of 256 Rf, new data[END_REF] using a detector [START_REF] Svirikhin | A detector for studying the characteristics of spontaneous fission of short-lived heavy nuclei[END_REF].

The detector consisted of 54 3 He neutron counters and a silicon detector array with a 60×60 mm 2 focal plane detector. To increase the collection of [START_REF] Yeremin | The electrostatic separator VASSILISSA Performance and experimental results[END_REF] recoil nuclei by a factor of 3, we decided to install a new DSSSD assembly [START_REF] Chakma | Gamma and conversion electron spectroscopy using GABRIELA[END_REF] inside the neutron detector with a large 100×100 mm 2 focal plane detector. It was necessary to completely change the counter's geometry. The new detection system was named SFiNx (Spontaneous Fission, Neutrons and x-rays, fig. 1). The system consists of 116 3 He-counters of neutrons that surround the vacuum chamber with DSSSD. The characteristics and number of 3 He counters are given in the table 1.

Detector

The counters are placed in a polyethylene moderator in the form of a regular octagonal prism (height 630 mm, circumscribed circle diameter 762 mm). The outer side of the detector is covered with a 5%-borated polyethylene shield (thickness from 30 to 50 mm) to protect against background neutrons.

The single neutron registration efficiency measured with 248 Cm-source is 54.7±0.1% (nonlinear least-squares method error). The average neutron lifetime in the setup is 18.4±0.2 µs (exponent fitting error).

An array of DSSSD detectors inside the vacuum chamber is represented by a focal plane 128×128-strip detector (100×100 mm 2 area, 500 µm thickness) and 8 side 16×16-strip detectors (50×60 mm 2 area, 700 µm thickness) [START_REF] Chakma | Gamma and conversion electron spectroscopy using GABRIELA[END_REF]. Silicon detectors allow registering α-, β-particles and fission fragments. Energy resolutions were measured using 8 MeV α-particles as 20 keV and 30 keV for the focal and side silicon detectors respectively.

Experiment

An experiment to study 252 No spontaneous fission was carried out on a velocity filter SHELS [START_REF] Popeko | Separator for Heavy ELement Spectroscopy -velocity filter SHELS[END_REF]. The complete fusion reaction of accelerated 48 Ca 18+ ions with 206 Pb target nuclei was used. The thickness of the 206 PbS target was 350 µg/cm 2 (on 1.5 µm Ti backing) and the 206 Pb enrichment was about 97%. The beam energy in the middle of the target was about 215±2 MeV (2n-evaporation channel maximum ∼ 800 nb).

After passing through the separator, the recoil nuclei were implanted into the focal plane large DSSSD. The spontaneous fission branching fraction for 252 No is about 32%. When a fission fragment was detected in the focal DSSSD, the coincidence with the recoil nucleus that fell into the same pixel of the detector in the time window 1 ms -25 s (∼ 10 T 1/2 ) was checked. After that, a search for neutrons was carried out in the time window of 128 µs. A total of 3260 reliable events of 252 No spontaneous fission were found.

The half-life of 252 No was determined as 2.44±0.05 s (exponential fitting error) based on recoil nucleus -fission fragment correlations. The received half-life is in good agreement with the already measured values 2.44±0.04 s [START_REF] Yu | Measurements of cross sections for the fusionevaporation reactions 204,206,207,208 Pb+ 48 Ca and 207 Pb+ 34 S : Decay properties of the even-even nuclides 238 Cf and 250 No[END_REF] and 2.30±0.22 s [START_REF] Bemis | Fragment-mass and kinetic-energy distributions from the spontaneous fission of 252 No[END_REF].

The prompt neutron multiplicity distribution of 252 No was measured and then true distribution was restored by using the Tikhonov statistical regularisation method [START_REF] Turchin | Solution of the Fredholm equation of the first kind in a statistical ensemble of smooth functions[END_REF][START_REF] Turchin | THE USE OF MATHEMATICAL-STATISTICS METHODS IN THE SOLUTION OF INCORRECTLY POSED PROBLEMS[END_REF][START_REF] Mukhin | Reconstruction of Spontaneous Fission Neutron Multiplicity Distribution Spectra by the Statistical Regularization Method[END_REF] (fig. 3). The dispersion of the measured neutron multiplicity distribution is σ 2 ν = 2.1, whereas the dispersion of restored distribution is σ 2 νr = 2.2. The average number of neutrons per spontaneous fission act of 252 No was obtained as ν = 4.25±0.09 (contains the statistical error and the efficiency error of the neutron detector) and is in good agreement with previously measured values 4.15±0.30 [START_REF] Yu | Multiplicity of prompt neutrons from spontaneous fission of the isotope 252 102[END_REF], 4.43±0.45 [START_REF] Yeremin | Neutron detector at the focal plane of the set up VASSILISSA[END_REF], and 4.51±0.25 [START_REF] Isaev | Comparative Study of Spontaneous-Fission Characteristics of 252 No and 254 No Isotopes[END_REF]. The restored average number of neutrons per fission act is ν r = 4.27±0.15.

Conclusion

The SFiNx setup contains 116 3 He-filled proportional counters of neutrons and a DSSSD array has been created.

The new large focal plane DSSSD (100×100 mm 2 ) allowed to significantly increase the speed of statistics collection in comparison with our old neutron detector [START_REF] Svirikhin | A detector for studying the characteristics of spontaneous fission of short-lived heavy nuclei[END_REF]. At the same time, the higher neutrons registration efficiency (54.7±0.1%) of counter assembly allows us to better reconstruct the neutron multiplicity distributions by the statistical regularisation method.

As a result of the first experiment, new data were obtained on the prompt neutron yields from 252 No spontaneous fission.

The system currently has no analogs in the study of the spontaneous fission properties of short-lived heavy nuclei.

Fig. 1 .

 1 Fig. 1. Photograph of the SFiNx system. A schematic front view of the assembly is shown in the inset image.

Fig. 2 .

 2 Fig. 2. Measured (squares) and restored (circles) prompt neutron multiplicity distributions of 252 No and background neutron spectra (triangles). Lines that connect the points have been added for clarity.

Table 1 . The main properties and number of the different types of counters used in the detector. Layers are numbered relative to the central axis of the detector.

 1

	Layer Number	Diameter, mm	Active length, mm	Operating voltage, V	3 He pressure, atm
	1	20	32	530	1400
	2 3	24 28	32	460	1775	7
	4	44	30	585	1500

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (project №18-52-15004).