Sara Dendene

Shuanghong Xue

Quentin Nicoud

Odile Valette

Angela Frascella

Anna Bonnardel

Romain Le Bars

Mickaël Bourge

Peter Mergaert

Matteo Brilli

Benoît Alunni

Emanuele G Biondi
email: emanuele.biondi@i2bc.paris-saclay.fr

Sinorhizobium meliloti FcrX coordinates cell cycle and division during freeliving growth and symbiosis

Sinorhizobium meliloti is a soil bacterium that establishes a symbiosis within root nodules of legumes (Medicago sativa, for example) where it fixes atmospheric nitrogen into ammonia and obtains in return carbon sources and other nutrients. In this symbiosis, S. meliloti undergoes a drastic cellular change leading to a terminal differentiated form (called bacteroid) characterized by genome endoreduplication, increase of cell size and high membrane permeability. The bacterial cell cycle (mis)regulation is at the heart of this differentiation process. In free-living cells, the master regulator CtrA ensures the progression of cell cycle by activating cell division (controlled by the tubulin-like protein FtsZ) and simultaneously inhibiting supernumerary DNA replication, while on the other hand the downregulation of CtrA and FtsZ is essential for bacteroid differentiation during symbiosis, preventing endosymbiont division and permitting genome endoreduplication. Little is known in S. meliloti about regulators of CtrA and FtsZ, as well as the processes that control bacteroid development. Here, we combine cell biology, biochemistry and bacterial genetics approaches to understand the function(s) of FcrX, a new factor that controls both CtrA and FtsZ, in free-living growth and in symbiosis. Depletion of the essential gene fcrX led to abnormally high levels of FtsZ and CtrA and minicell formation.

Using multiple complementary techniques, we showed that FcrX is able to interact physically with FtsZ and CtrA. Moreover, its transcription is controlled by CtrA itself and displays an oscillatory pattern in the cell cycle. We further showed that, despite a weak homology with FliJlike proteins, only FcrX proteins from closely-related species are able to complement S. meliloti fcrX function. Finally, deregulation of FcrX showed abnormal symbiotic behaviors in plants suggesting a putative role of this factor during bacteroid differentiation. In conclusion, FcrX is the first known cell cycle regulator that acts directly on both, CtrA and FtsZ, thereby controlling cell cycle, division and symbiotic differentiation.

INTRODUCTION

Sinorhizobium meliloti belongs to the class of Alphaproteobacteria and is known for its dual lifestyle: as a free-living bacterium in the soil and as a symbiotic endophyte within legumes of the genera Medicago, Melilotus and Trigonella 1 . Free-living S. meliloti cells thrive in the soil and divide asymmetrically to produce two physiologically and morphologically different cell types (Figure 1A): a smaller cell, unable to replicate its DNA and a larger cell able to replicate its DNA once per cell cycle. The small cell first has to differentiate into the large cell type, upon suitable nutrient conditions, before it can undergo genome replication 2 .

To ensure a normal progression of the cell cycle, it has to be tightly regulated. In Alphaproteobacteria the response regulator CtrA plays a central role in this process by binding to the DNA, mostly activating or inhibiting transcription of more than a hundred target genes [START_REF] Laub | Genes directly controlled by CtrA, a master regulator of the Caulobacter cell cycle[END_REF][START_REF] Brilli | The diversity and evolution of cell cycle regulation in alphaproteobacteria: a comparative genomic analysis[END_REF] . The function of CtrA has been mainly studied in Caulobacter crescentus, an aquatic bacterium that divides asymmetrically, as S. meliloti, giving two morphologically and physiologically different daughter cells [START_REF] Hughes | Caulobacter crescentus[END_REF] ; a stalked cell, able to replicate immediately after division, and a non-replicative motile cell that is blocked at the G1 phase. CtrA is under a strict control, as its levels oscillate during the cell cycle, reaching a maximum in two moments: i. at the G1 phase (motile cell), when it inhibits DNA replication by binding to specific sites that prevent origin binding of DnaA, the initiation factor of DNA replication, and ii. at the end of S-phase/G2, when CtrA also activates the cell division process [START_REF] Quon | Negative control of bacterial DNA replication by a cell cycle regulatory protein that binds at the chromosome origin[END_REF] . To permit this pattern, regulation mechanisms at the transcriptional and post translational (by phosphorylation and proteolysis) levels are involved [START_REF] Ryan | Recruitment of a cytoplasmic response regulator to the cell pole is linked to its cell cycle-regulated proteolysis[END_REF][START_REF] Biondi | Regulation of the bacterial cell cycle by an integrated genetic circuit[END_REF] . An homolog of CtrA is present in S. meliloti, where it has a similar function [START_REF] Barnett | A homolog of the CtrA cell cycle regulator is present and essential in Sinorhizobium meliloti[END_REF][START_REF] Pini | Cell Cycle Control by the Master Regulator CtrA in Sinorhizobium meliloti[END_REF] . In S. meliloti, CtrA inhibits indirectly the DNA replication by a yetunknown process and activates the cell division by repressing the transcription of the minCDE system [START_REF] Pini | Cell Cycle Control by the Master Regulator CtrA in Sinorhizobium meliloti[END_REF] , which ultimately inhibits the polymerization of the tubulin-like FtsZ responsible of cell constriction at the septum [START_REF] Rowlett | The bacterial Min system[END_REF] . The FtsZ protein is composed by a N terminal core region, containing a GTPase domain, involved in the polymerization activity, and a C terminus responsible for the interaction to other actors [START_REF] Sogues | Essential dynamic interdependence of FtsZ and SepF for Z-ring and septum formation in Corynebacterium glutamicum[END_REF] . In S. meliloti, FtsZ is present in two copies, FtsZ1 and FtsZ2, however only FtsZ1 is essential for the Z ring formation, while the second copy lacks the C-terminal domain and its deletion is not lethal [START_REF] Margolin | FtsZ and the division of prokaryotic cells and organelles[END_REF] . As many cell cycle actors, FtsZ1 is expressed at the predivisional phase of the cell cycle [START_REF] De Nisco | Global analysis of cell cycle gene expression of the legume symbiont Sinorhizobium meliloti[END_REF] .

In symbiosis with Medicago plants, S. meliloti colonizes special root organs, called nodules.

There, it fixes atmospheric nitrogen into ammonium that is assimilated by the plant, while it receives in return dicarboxylic acids and other nutrients [START_REF] Long | Rhizobium-legume nodulation: life together in the underground[END_REF] . In nodules, after a stage of multiplication, S. meliloti undergoes a drastic cellular change into a terminally differentiated form called bacteroid. This process takes place intracellularly, inside the nodule plant cells, where differentiated bacteroids are characterized by genome endoreduplication, cell enlargement and high membrane permeability [START_REF] Mergaert | Eukaryotic control on bacterial cell cycle and differentiation in the Rhizobium-legume symbiosis[END_REF] . Previous studies have shown an implication of the bacterial cell cycle regulation in this differentiation process (Pini et al., 2013-2015; Kobayashi et al., 2009). Indeed, CtrA and FtsZ are absent in bacteroids [START_REF] Pini | The DivJ, CbrA and PleC system controls DivK phosphorylation and symbiosis in Sinorhizobium meliloti[END_REF][START_REF] Farkas | Medicago truncatula symbiotic peptide NCR247 contributes to bacteroid differentiation through multiple mechanisms[END_REF] and mutants that overexpress CtrA are characterized by a symbiotic defect [START_REF] Pini | The DivJ, CbrA and PleC system controls DivK phosphorylation and symbiosis in Sinorhizobium meliloti[END_REF] . Interestingly, the depletion of ctrA in S. meliloti, similarly to C. crescentus, leads to a cell elongation/enlargement and endoreduplication phenotype that is strikingly similar to bacteroids formed in nodules. The mechanism leading to the downregulation of CtrA and FtsZ in bacteroids is not known yet but studies showed the involvement of plant-produced Nodule-specific Cysteine-Rich (NCR) peptides [START_REF] Van De Velde | Plant peptides govern terminal differentiation of bacteria in symbiosis[END_REF][START_REF] Penterman | Host plant peptides elicit a transcriptional response to control the Sinorhizobium meliloti cell cycle during symbiosis[END_REF] (Figure 1A). Legumes such as Medicago truncatula produce a wide spectrum of NCR peptides (about 600) that are implicated in the disruption of several cellular processes including the cell cycle, thus resulting in the terminal differentiation of S. meliloti (Mergaert et al., 2006; Van de Velde et al., 2010; Alunni & Gourion, 2016). Indeed, the treatment of a wild type strain of S. meliloti with the NCR247 showed a down regulation of CtrA and its regulon.

Farkas and colleagues also highlighted a physical interaction between this NCR and FtsZ (Farkas et al., 2014). Overall these data strongly suggest that the regulation of bacterial cell cycle and cell division are playing a major role in the symbiosis process [START_REF] Xue | Coordination of symbiosis and cell cycle functions in Sinorhizobium meliloti[END_REF] .

Here we characterized the role of a new cell cycle regulator, named FcrX, elucidating its role with respect to CtrA and FtsZ1 and FtsZ2, its regulation by transcription, its conservation across the class Alphaproteobacteria and finally, its role during symbiosis.

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RESULTS

The fcrX gene is essential and controls cell cycle in Sinorhizobium meliloti

The fcrX gene (SMc00655, 351 bp ORF coding for a 116 aa predicted protein) is adjacent to ctrA in the S. meliloti chromosome in a head-to-head orientation, with a ca. 500 bp long intergenic sequence that controls the transcription of both genes. The fcrX gene appears essential in free-living conditions, based on Tn-seq results (Figure S1A). In order to study the function of fcrX, we constructed a depletion strain by deleting the chromosomal copy of fcrX and expressing an extra copy of fcrX on a plasmid under the control of an IPTG-inducible lac promoter [START_REF] Pini | The DivJ, CbrA and PleC system controls DivK phosphorylation and symbiosis in Sinorhizobium meliloti[END_REF][START_REF] Khan | Broad-host-range expression vectors with tightly regulated promoters and their use to examine the influence of TraR and TraM expression on Ti plasmid quorum sensing[END_REF] . This conditional depletion strain of FcrX grew best in a medium supplemented with 100 µM IPTG (Figure S1B) and showed upon removal of IPTG dramatic growth defects (Figure 1B and Figure S1B), as well as a reduced capacity to form colonies (Figure 1C), indicating that fcrX is essential for the viability of S. meliloti. To gain more insights in FcrX function(s), we investigated the FcrX-depleted cells by microscopy and flow cytometry.

Interestingly, the absence of FcrX induced the production of DNA-free small cells, referred to as minicells, as revealed by DNA staining by Syto9 and microscopy observation (Figure 1D).

The accumulation of minicells in an FcrX-depleted suspension was confirmed by DNA/membrane double staining with DAPI/Potomac Gold dyes and flow cytometry analysis (Figure S2-S3B, 14.99% of total events with IPTG against 36.91% of total events without IPTG). Thus upon depletion of fcrX, an accumulation of small cells with no DNA was observed.

We monitored the depletion of FcrX by time-lapse microscopy in order to understand the development of minicells at the cellular level. Minicells tend to form only in daughter cells (small cell) while the mother (large) cell remains able to divide efficiently producing daughter cells, until two additional cycles and then completely stops dividing (Figure 1E). This minicell phenotype can be interpreted as the consequence of an imbalanced cell cycle, with an excess of division and a block of DNA replication, suggesting that FcrX may coordinate these two processes in S. meliloti. Consistently, the absence of FcrX led to increased levels of CtrA, FtsZ1 and FtsZ2 proteins, as shown by western blot analysis (Figure 2A), indicating that FcrX indeed negatively controls the accumulation of CtrA and FtsZ1/2. This result strengthens our hypothesis of the implication of FcrX in the regulation of cell cycle and cell division.

FcrX interacts with CtrA and FtsZ1/2

The 3D structure prediction of FcrX performed with the Alphafold 2 algorithm showed that the The structure did not reveal the presence of a DNA binding domain, suggesting that its putative mode of action on CtrA and FtsZ1/2 may be by a direct interaction at the protein level. To verify this hypothesis, an affinity column experiment was realized using His6-FcrX loaded nickel columns in order to identify potential FcrX-interacting proteins. The presence of FtsZ1/2 and FcrX itself, together with other proteins listed in Table S1 was detected in the affinity column eluate by mass spectrometry (Figure S5). The presence of CtrA on the other hand was only detected by western blot (Figure 2B), as its low abundance makes it hardly detectable by mass spectrometry. In order to confirm this result, we carried out a bacterial two-hybrid (BACTH) experiment using the Escherichia coli carrier (Figure 2C) (Karimova et al., 1998). FcrX, CtrA and FtsZ1/2 proteins were fused to domains 18 and 25 of the adenylate cyclase from Bordetella pertussis in C-and N-terminal orientations and all possible combinations of prey and bait were introduced in the E. coli strain HB101. In this system, FcrX interacts with CtrA and with both copies of FtsZ (1 and 2). FtsZ2 lacks the C-terminal domain that is usually implicated in proteinprotein interactions and recruitment of FtsZ partners [START_REF] Xiao | Redefining the roles of the FtsZ-ring in bacterial cytokinesis[END_REF] . Thus, the observed interaction between FcrX and FtsZ2 may be explained by either an unusual interaction between the N-terminal domain or by the presence of a functional full-length FtsZ homolog in E. coli (FtsZEc), which could promote the formation of a FcrX-FtsZEc-FtsZ2 ternary complex. We also tested the interaction of FcrX with itself to verify the possible dimerization of the protein, as observed with the affinity column. As shown in the (Figure 2C) a strong FcrX-FcrX interaction was observed, which is consistent with a putative oligomeric FcrX structure.

Subcellular localization of FcrX and its interactors

To gain more insights about the function of FcrX we decided to investigate its subcellular localization and whether it colocalizes with its interactors, FtsZ being shown to have a mid-cell localization and CtrA potentially being polarly localized in S. meliloti as it has been shown previously in C. crescentus [START_REF] Ma | Interactions between heterologous FtsA and FtsZ proteins at the FtsZ ring[END_REF][START_REF] Wheeler | Protein localization during the Caulobacter crescentus cell cycle[END_REF] . We constructed a strain expressing a C-terminal translational fusion of FcrX with a yellow fluorescent protein (YFP) and further deleted the chromosomal copy of fcrX by transduction using a DfcrX::tetR M12 phage lysate. This approach was used in order to avoid all possible competitions of the wild-type FcrX with the tagged version and it confirmed that the fusion protein retained its function. FcrX localized at the septum, as observed by epifluorescence microscopy (with a less frequent localization at the cell pole, presumably after cell division) (Figure 2D). Image analysis in predivisional phase cells confirmed that FcrX is localized at the septum in the majority of these cells (Figure 2E). We wanted to correlate this constructed a C-terminal translational fusion of FtsZ1 with a cyan fluorescent protein (CFP), which despite the loss of its functionality retained its native localization [START_REF] Ma | Interactions between heterologous FtsA and FtsZ proteins at the FtsZ ring[END_REF] . Using a similar approach, we tagged FtsZ2 with CFP. CtrA localization investigation appeared more complex as N-or C-terminal tags strongly stabilized its levels, which is a lethal condition in S. meliloti [START_REF] Pini | Cell Cycle Control by the Master Regulator CtrA in Sinorhizobium meliloti[END_REF] . Therefore, we added a sequence coding for the last 15 amino acids of CtrA that constitute the degradation motif, downstream of CFP to ensure the timely degradation of the fusion protein by proteolysis, then deleted the chromosomal copy of ctrA by transduction using a DctrA::tetR M12 phage lysate. Tagged proteins were observed under the microscope. FtsZ1 and FtsZ2

showed as expected a midcell localization while CtrA showed a localization at the cell pole, consistently with FcrX localization (Figure S6). Together, these results indicate that FcrX may interact with both CtrA and FtsZ1/2 in vivo but at distinct subcellular localizations.

Transcription of fcrX is positively regulated by CtrA

In order to define and characterize the fcrX promoter, we made a promoter deletion analysis by introducing in S. meliloti wild-type cells an extra copy of fcrX with different putative promoter lengths located on a plasmid downstream of the IPTG-regulated lacZ promoter (Figure S7).

Then, the obtained clones were transduced using a phage M12 lysate produced from the strain DfcrX::tetR + Plac-fcrX and selected in the presence or absence of IPTG. All clones should give viable colonies with IPTG while only the constructs containing a functional promoter of fcrX should support viability without IPTG (Figure S7). Constructs with PfcrX-fcrX fragments containing at least the region between -1/-287 were viable, while a shorter promoter fragment (-1/-224) was not active, suggesting that the promoter region of fcrX resides within the -287 region and that the -224/-287 contains a critical promoter element.

To confirm these results, we used the plasmid pOT1em [START_REF] Meyer | Regulation of Hydroxycinnamic Acid Degradation Drives Agrobacterium fabrum Lifestyles[END_REF] , which contains genes encoding mCherry and EGFP in opposite directions. Several derivatives of the fcrX promoter, described in Figure S7, as well as the full intergenic region between fcrX and ctrA, were cloned between the ATGs of mCherry and EGFP. The full intergenic region between fcrX and ctrA was able to express both mCherry (fcrX) and EGFP (ctrA) (Figure 3A). Analysis of the other constructs containing different versions of the upstream region of fcrX confirmed that only clones with at least -1/-287 expressed mCherry (fcrX) (data not shown). The ctrA gene is also controlled by the same intergenic region, suggesting that these two genes may share the same transcriptional regulation. The analysis of the region -224/-287 revealed several interesting characteristics.

First, in this region the ctrAP1 promoter [START_REF] Schlüter | Global mapping of transcription start sites and promoter motifs in the symbiotic α-proteobacterium Sinorhizobium meliloti 1021[END_REF] and the estimated pfcrX are overlapping with RNA-seq determined putative TSSs (transcriptional start site) separated only by 20/25 bp (Figure S7).

Second, the promoter of fcrX contains a CtrA binding box within the 50 bp region upstream the putative TSS [START_REF] Brilli | The diversity and evolution of cell cycle regulation in alphaproteobacteria: a comparative genomic analysis[END_REF][START_REF] Pini | Cell Cycle Control by the Master Regulator CtrA in Sinorhizobium meliloti[END_REF] . These observations suggest that the activation of the fcrX promoter may depend on CtrA. In order to test this hypothesis, we mutated the CtrA-binding box by replacing the 5'-TTAA-3' half box with 5'-GCGC-3' in a pOT1em plasmid carrying the full intergenic region between ctrA and fcrX (Figure 3A). It was shown that this mutation prevents the fixation of CtrA on the box and therefore affects its transcriptional activity on the downstream gene (Figure 3A) (ref). Microscopy observation showed that the strain containing the mutated CtrAbinding box didn't express the mCherry fluorescence, implicating that CtrA may activate fcrX transcription by binding to its box. On the other hand, the mutated CtrA binding box didn't change the EGFP expression noticeably, excluding the implication of this box in the regulation of ctrA transcription (Figure 3A).

To confirm the positive regulation of fcrX expression by CtrA, we tested the steady state levels of FcrX upon depletion of CtrA by western blot using antibodies directed against FcrX. In the absence of CtrA, we observed a significant decrease of FcrX (Figure 3B). Since CtrA is a DNAbinding protein implicated in transcriptional regulation, we also performed a qRT-PCR in the same conditions. Consistently, fcrX expression decreased upon CtrA depletion, confirming the previous observation (Figure S8). These results build up a regulatory model involving a negative feedback loop between CtrA and FcrX.

Cell cycle regulators are known to be dynamically regulated over the cell cycle, consistent with the oscillatory nature of this biological phenomenon. Because FcrX is closely linked to cell cycle regulation, we wanted to check whether FcrX was subject to oscillation. Therefore, a synchronization of a wild type culture of S meliloti was made as described before (Figure 3C) [START_REF] De Nisco | Global analysis of cell cycle gene expression of the legume symbiont Sinorhizobium meliloti[END_REF] . Samples were recovered every 30 minutes over a full cell cycle and the corresponding total RNA was used to perform a qRT-PCR analysis while cell lysates were used for Western blot experiments using antibodies directed against FcrX. Both transcription and translation of FcrX increased at 90 min of the cell cycle, meaning that FcrX is not only a regulator of the cell cycle but it is also subject to cell cycle oscillation. These data are consistent with previous analyses on the ensemble of cell cycle regulated genes [START_REF] De Nisco | Global analysis of cell cycle gene expression of the legume symbiont Sinorhizobium meliloti[END_REF] .

FcrX is essential for the establishment of the legume symbiosis

The terminal bacteroid differentiation that S. meliloti undergoes during its interaction with us to test the involvement of FcrX in the symbiotic process. We tested the importance of FcrX by inoculating M. sativa plants with the FcrX depletion strain and watered the plants with a range of concentrations of IPTG in order to obtain different levels of FcrX expression. We also inoculated plants with the wild type strain of S. meliloti carrying an empty plasmid as a reference. At 28 days post inoculation (dpi) we checked nodule colonization using confocal microscopy (Figure 4A), measured the plant dry weight (Figure 4B) and assessed bacteroid differentiation by measuring the bacterial DNA content with flow cytometry (Figure S9). Plant weight decreased when FcrX expression was reduced with respect to the condition with the highest IPTG concentration (Figure 4B). The confocal microscopy images showed a clear nodule colonization defect, with much less plant cells containing bacteroids in the plants watered with 0µM, 10µM and 100µM IPTG compared to the plants watered with 1mM IPTG and the references, implying that FcrX is essential to the establishment of a fully functional symbiosis. However, the nodules from the condition watered with 1mM IPTG were still less colonized and the bacteroids did not show a similar extent of terminal differentiation as observed in the reference conditions, an observation that can be explained by the IPTGregulated expression of FcrX which may not mimic the natural cell cycle-regulated expression.

Considering our results showing that FcrX inhibits the accumulation of CtrA, FtsZ1 and FtsZ2 (Figure 2A), we wondered if an overexpression of FcrX may promote CtrA and FtsZ1/2 disappearance inside nodule cells and thereby boost the symbiotic process. To do so, we inoculated plants of M. sativa with a S. meliloti strain containing a second copy of fcrX expressed on a pSRK plasmid under the control of the Plac promoter, which has a weak transcriptional leakage in S. meliloti, even in the absence of IPTG [START_REF] Khan | Broad-host-range expression vectors with tightly regulated promoters and their use to examine the influence of TraR and TraM expression on Ti plasmid quorum sensing[END_REF] . The upregulation of FcrX resulted in a significant plant biomass gain at 28 dpi, as compared to the controls (Figure 4C). However, no increase in the bacteroid differentiation level was noticed, suggesting that the increase in symbiotic efficiency is likely related to the speed up of the differentiation process rather than to a larger extent of differentiation (data not shown). Finally, we investigated whether fully differentiated bacteroids contained FcrX by using anti-FcrX antibodies. Unlike CtrA and FtsZ1/2 that are absent from mature bacteroids, FcrX remained detectable (Figure 4D), supporting a role of FcrX during the establishment of bacteroid differentiation and maintenance.

FcrX is a conserved factor in several species of the class Alphaproteobacteria

We further wanted to investigate the presence and functionality of FcrX in other bacteria. First, the S. meliloti FcrX protein sequence was used to search in the Microbes Online database 28 for similar proteins. Orthologs defined by Bidirectional Blast Hit (BBH) of FcrX were found in several rhizobia (Bradyrhizobium japonicum, Rhizobium leguminosarum), the human pathogen Brucella abortus and the phytopathogen Agrobacterium vitis. Except for A. vitis for which no information is available, previous Tn-seq data on all those species revealed that the putative FcrXs were all essential in the organism of origin [START_REF] Perry | The Use of Transposon Insertion Sequencing to Interrogate the Core Functional Genome of the Legume Symbiont Rhizobium leguminosarum[END_REF][START_REF] Sternon | Transposon Sequencing of Brucella abortus Uncovers Essential Genes for Growth In Vitro and Inside Macrophages[END_REF][START_REF] Baraquet | Transposon sequencing analysis of Bradyrhizobium diazoefficiens 110spc4[END_REF] . Those orthologs were tested for their capacity to complement fcrX deletion in S. meliloti. We also tested a distant homolog of fcrX from C. crescentus, which codes for the flagellar protein FliJ, located in the same genomic context as fcrX. Interestingly, the fcrX-ctrA synteny is widely preserved among these bacteria suggesting a possible conservation of fcrX function (Figure 5A). In order to test our hypothesis, we constructed S. meliloti strains expressing a copy of these orthologs and we deleted by transduction the chromosomal copy of fcrX. Results of this experiment showed that the expression of the orthologs from R. leguminosarum and B. abortus were able to support S. meliloti growth in a fcrX deletion background, implying functional conservation of FcrX. A western blotting experiment was carried out confirming that the overexpression of these orthologs is able to down regulate the accumulation of FtsZ and CtrA (Figure S10). However, the orthologs from B. japonicum, A. vitis and the FliJ homolog from C. crescentus were not able to complement the fcrX deletion. This functional complementation analysis, although still limited in the number of tested species, revealed that from a functional point of view each FcrX has acquired specific functions independently from the phylogenetic distance from S. meliloti, as for example A. vitis (a species close to S. meliloti) is not able to complement while the more distant B. abortus does. In order to have a broader view of FcrX conservation, we searched for FcrX/FliJ orthologs/homologs in other alphaproteobacterial species (Figure 5B, Table S2).

Significantly similar sequences to either the S. meliloti FcrX or the C. crescentus FliJ, were only found in the Caulobacterales and Rhizobiales. However, the two queries retrieved sequences in complementary sets of species; for example, in C. crescentus FcrX retrieved no results (Table S2). This can be consequent to a functional diversification of the same ancestral gene in the Caulobacterales and Rhizobiales, which is however difficult to demonstrate because of the short length and variability of these sequences, even if a phylogenetic tree of all homologs found seems to suggest an orthology relationship as the topology is largely congruent with the RecG tree (data not shown). In parallel we checked the distance between fcrX/fliJ and ctrA genes, discovering that the ctrA gene is in proximity to fcrX orthologs (or fliJ in observed that orthologs able to complement the S. meliloti fcrX deletion belong to the phylogenetic group of Brucella-rhizobia (excluding bradyrhizobia). However, the functional complementation of fcrX is not a conserved feature of specific clades, as for example A. vitis does not complement. Finally the functional diversification between FcrX and FliJ is also supported by the fact that, to the best of our investigations, FcrX has no role in the control of motility.

DISCUSSION

In every organism, important functions of the cell are controlled by key factors (master regulators) coordinating many related elements. This is the case, for example, of the cell cycle in eukaryotes, based on cyclins [START_REF] Wang | Cell Cycle Progression and Synchronization: An Overview[END_REF] , the sporulation process of Bacillus subtilis, controlled by Spo0A [START_REF] Kovács | Bacterial differentiation via gradual activation of global regulators[END_REF] and the cell cycle regulation in some alphaproteobacterial, such as C. crescentus, where it is controlled by the master regulator signal transduction protein CtrA [START_REF] Poncin | Learning from the master: targets and functions of the CtrA response regulator in Brucella abortus and other alpha-proteobacteria[END_REF] . In this work we identified in S. meliloti a new one key factor of cell cycle and cell division that we named FcrX.

FcrX is a surprisingly small protein with no homology to other, so far characterized, regulators.

We predicted that FcrX is an alpha helix-rich protein that can oligomerize, and shares ancestry with a previously characterized chaperon involved in flagellum physiology, named FliJ. In C. crescentus, this small protein is specifically required for flagellum functioning through the stabilization of another protein FliI, an ATPase involved in the export of flagellar subunits across the membrane using a dedicated type III protein secretion system [START_REF] Stephens | Identification of the fliI and fliJ components of the Caulobacter flagellar type III protein secretion system[END_REF] . The analysis of synteny of FcrX orthologs clearly underlined this association between FcrX and FliJ-FliI, as many orthologs of FcrX are still organized in a fliIJ operon. Another striking feature of the analysis of the fcrX locus in many alphaproteobacteria is its proximity to the ctrA gene. As previously hypothesized, CtrA is considered as an ancestral flagellum regulator in many alphaproteobacterial species, including those in which CtrA also plays a role as cell cycle regulator [START_REF] Brilli | The diversity and evolution of cell cycle regulation in alphaproteobacteria: a comparative genomic analysis[END_REF][START_REF] Greene | Analysis of the CtrA pathway in Magnetospirillum reveals an ancestral role in motility in alphaproteobacteria[END_REF] . This conserved characteristic may suggest that FcrX evolved from FliJ, extending or changing its targets from flagellar components to the divisome protein FtsZ and the cell cycle regulator CtrA. Indeed we showed here that FcrX binds directly CtrA in an unknown way and its presence plays a negative role on the steady state levels of CtrA. Conversely, CtrA in addition to many cell cycle genes 10 also controls fcrX transcription in the second half of DNA replication phase.

From this point of view, CtrA-FcrX forms an essential negative feedback loop contributing to the oscillation of CtrA levels during cell cycle (Figure 5C). The presence of an essential genetic negative feedback loop has been also demonstrated in C. crescentus, in which DivK and CtrA are the main components of the feedback loop of this species 8 . It is tempting to speculate that although the architecture of cell cycle regulation may change between different organisms, CtrA-DivK (linked by a transcriptional relationship) in C. crescentus and CtrA-FcrX in S. meliloti, the logical principles behind the regulation remain similar.

In addition, this CtrA-related crucial regulatory function of FcrX is not its only role, as this novel master regulator of cell cycle also negatively controls the main component of the divisome, FtsZ (FtsZ1 and FtsZ2 in S. meliloti), by direct protein-protein interaction. However, at this stage it cannot be excluded that FcrX interaction with FtsZ2 (both in BACTH and affinity columns) may involve a ternary complex with FtsZ1 (either from E. coli in BACTH or endogenous one in affinity columns) and FcrX, as FtsZ2 lacks a protein interaction domain found in FtsZ1. This dual activity of FcrX makes this factor a novelty in the knowledge of cell cycle regulation in alphaproteobacteria. Although cell division has been shown to be usually regulated by CtrA at the transcriptional level in S. meliloti, but also in C. crescentus or B. abortus [START_REF] Poncin | Learning from the master: targets and functions of the CtrA response regulator in Brucella abortus and other alpha-proteobacteria[END_REF] , this is the first time that a negative regulator of cell cycle is able to connect directly to both cell cycle regulation and the divisome itself. This dual activity of FcrX is responsible of its severe depletion phenotype, leading to a block of cell cycle producing minicells that contain no DNA, but also keeping a mother cell with the genome able to produce new minicells.

Considering potential applications that need minicells to perform specific functions [START_REF] Yu | Minicells from Highly Genome Reduced Escherichia coli: Cytoplasmic and Surface Expression of Recombinant Proteins and Incorporation in the Minicells[END_REF][START_REF] Kim | Escherichia coli minicells with targeted enzymes as bioreactors for producing toxic compounds[END_REF] , the depletion of fcrX represents a miniatured minicell factory, which may be exploited in the future for biotechnological purposes.

Another important aspect of FcrX functionality is related to symbiosis and bacteroid differentiation. It has been shown previously that bacteroids in S. meliloti, in order to become functionally mature, must eliminate CtrA and FtsZ, leading consequently to elongated cells with multiple copies of DNA. The discovery of a single regulator that is able to control negatively both CtrA and FtsZ suggests that FcrX may play a role during bacteroid differentiation. Indeed we have shown that FcrX is present in mature bacteroids and its function is required for a correct establishment of symbiosis. Accordingly, a strain constitutively expressing FcrX was able to increase plant biomass with respect to the wild-type situation, suggesting that promoting CtrA and FtsZ downregulation can increase the efficiency of the symbiosis, possibly by predisposing bacteria to terminal differentiation and making this process take place earlier rather than increasing it to a higher level. This will open new frontiers of sustainable agriculture by the use of improved bacterial inoculants based on FcrX deregulation.

Even more interestingly, FcrX appears as a conserved factor in several rhizobial species further suggesting that this approach of plant growth amelioration may be extended to other agronomically-important legumes symbionts.

In conclusion, FcrX is a novel global factor controlling two essential key functions of the cell, regulation of cell cycle progression (CtrA) and cell division (FtsZ) (Figure 5C). This central physiology may rely on FcrX regulation in order to perform higher levels of coordination of cell cycle. In the future, the investigation should move towards exploring how FcrX is regulated and what is the actual mechanism of CtrA and FtsZ1/2 inhibition by FcrX. FcrX indeed represents a small protein with capacities to interact with very diverse targets that may be a tool or a target for antibiotic therapies.

MATERIALS AND METHODS

Growth conditions

The strains used in this study are listed in the Table S3. S. meliloti 1021 and E. coli strains were grown in YEB medium (0.5% beef extract, 0.1% yeast extract, 0.5% peptone, 0.5% sucrose, 0.04% MgSO4⋅7H2O, pH 7.5) at 30°C and LB medium (1% tryptone, 1% NaCl, 0.5% yeast extract) at 37°C, respectively. Media were supplemented with appropriate antibiotics: Kanamycin (50µg/ml), Tetracycline (10µg/ml), Gentamicin (20µg/ml) for E. coli, Streptomycin (200µg/ml), Kanamycin (200µg/ml), Tetracycline (2µg/ml), Gentamicin (20µg/ml) for S. meliloti. Depletion strains of S. meliloti were grown in a medium supplemented with IPTG (100µM for fcrX and 1mM for ctrA); the depletion was accomplished by washing three times the culture and resuspending it in a medium lacking IPTG at OD600nm = 0.3. The synchronization experiment was performed as described previously (De Nisco et al., 2014).

Strain constructions

The two-step recombination procedure was used to perform the fcrX deletion using the integrative plasmid pNPTS138 as previously described (Pini et al., 2013). Deletions were verified by PCR using primers flanking the recombination locus (see primers in Table S4).

To construct the fusion between the protein of interest and the fluorescent proteins (CFP or YFP), the Gateway procedure (Thermo Fisher) was used. First, the gene was amplified by PCR (see primers in Table S4) then introduced in the pENTR vector. Then, the vectors were mixed with the destination plasmid carrying the gene coding for the fluorescent protein, to perform the LR reaction as recommended by the manufacturer. The final product was amplified by PCR and cloned in the pSRK vector downstream the Plac promoter (Khan et al., 2005) and electroporated in S. meliloti as previously described [START_REF] Ferri | Plasmid electroporation of Sinorhizobium strains: The role of the restriction gene hsdR in type strain Rm1021[END_REF] .

To transduce the fcrX::tetR deletion the phage M12 was used 40 . To do so, the bacteria were grown in LB containing 2.5 mM CaCl2 and 2.5 mM MgSO4 then mixed with the phage to give a multiplicity of infection of 0.5. The mixture was incubated at room temperature for 45 min and subsequently plated on LB plates with the appropriate antibiotics.

In order to identify the fcrX promoter, six different PfcrX-fcrX constructions were cloned into the Plac inducible plasmid pSRK and were electroporated in S. meliloti wild type cells. All S. meliloti clones containing an extra plasmid-encoded copy of fcrX with different promoter lengths were transduced using a phage M12 lysate produced from the strain DfcrX::tetR + Plac-fcrX and selected in presence or absence of IPTG. To verify the fcrX promoter sequence and its regulation by CtrA, the different constructions were introduced in pOTem1 26 vector using the RF cloning procedure [START_REF] Ent | RF cloning: A restriction-free method for inserting target genes into plasmids[END_REF] .

S. meliloti 1021 (wild type) Tn-seq data of the fcrX gene during growth in YEB medium was obtained from a previous study [START_REF] Travin | Dual-Uptake Mode of the Antibiotic Phazolicin Prevents Resistance Acquisition by Gram-Negative Bacteria[END_REF] .

Nodulation assays and analysis

M. sativa cultivar Gabès seeds were scarified with pure sulfuric acid for 8 min. After several washes with distilled water, the seed surface was sterilized with bleach (150ppm) for 30 min and seeds were washed again. Finally, seeds were soaked overnight under agitation in sterile water and then transferred onto a Kalys agar plate for one day at 30°C in the dark to allow the germination. The seedlings were planted in perlite/sand (2:1 vol/vol) in 1.5L pots in the greenhouse (24°C, photoperiod 16 h of light and 8 h of dark, humidity 60%) and were inoculated 7 days after planting with 50 ml per pot of the appropriate bacteria at OD600nm = 0.05. Plants were watered every three days, alternating tap water and a commercial N-free fertilizer (Plant Prod solution [N-P-K, 0-15-40; Fertil] at 1 g per liter). Plants were harvested at 6 weeks post inoculation (42 dpi) to analyze bacteroid colonization and nodule development by confocal microscopy, level of bacteroid differentiation by flow cytometry and plant dry mass measurement [START_REF] Nicoud | Sinorhizobium meliloti Functions Required for Resistance to Antimicrobial NCR Peptides and Bacteroid Differentiation[END_REF] .

Electron microscopy

Bacteria were prefixed by adding an equal volume of fixative (2% glutaraldehyde in HEPES buffer 200mM, pH 7.2) to the culture medium. After 20 min, the medium was replaced by 1% glutaraldehyde in HEPES buffer for at least 1 h at 4°C. Bacteria were then washed with HEPES buffer, concentrated in 2% agarose (LMP Agarose, Sigma A9414), washed again with HEPES buffer and post-fixed in 1% osmium tetroxide (EMS 19150) for 1h at 4 °C. Samples were washed again in distilled water and treated with 1% uranyl acetate (EMS 22400) for 1 h at 4°C in the dark. Subsequently, samples were dehydrated in a graded series of acetone and embedded in Epon resin. Ultrathin sections (60-90 nm) were cut, stained with uranyl acetate and lead citrate and were analyzed using a Tecnai 200kV electron microscope (field electron interference or FEI). Digital acquisitions were made with a numeric camera (Oneview, Gatan).

Confocal and wide field microscopy

Nodule imaging was performed on a SP8X confocal DMI 6000 CS inverted microscope (Leica) equipped with hybrid and PMT detectors, a 10x dry (Plan Apo + DIC (NA: 0.4, Leica)) and a 63x oil immersion (Plan Apo + DIC (NA: 1.4, Leica)) objectives. For each condition, multiple z-stacks were acquired (excitation: 405 nm; collection of fluorescence: 520-580 nm for calcofluor excitation: 488 nm; collection of fluorescence: 520-580 nm for Syto9 and excitation: 561 nm; collection of fluorescence: 520-580 nm for Propidium iodide). Stacks were transformed into maximum intensity projections using ImageJ software.

Time lapse experiments were performed on depleted cells deposited on agarose/YEB (with appropriate antibiotics and inducers) and observed every 10 minutes (up to 16h) on a Nikon

Eclipse Ti E microscope equipped with a Yokogawa CSU-X1-A1 spinning disk system.

qRT-PCR experiment

RNA was extracted from bacterial culture samples using Maxwell® 16 LEV miRNA Tissue Kit (Promega). cDNA was produced using random hexamers as primers and the GoScriptTM Reverse Transcription kit from Promega. Amplification of 16S rRNA and fcrX cDNA was made using SsoFast EvaGreen Supermix 2X kit (Bio-Rad, France) on a CFX96 Real-Time System (Bio-Rad) instrument and the results were analyzed by Bio-Rad CFX Maestro version 1.1 software (Bio-Rad). For each sample, a biological duplicate was realized. Primers are listed in Table S4.

Flow cytometry

Cells were heated 10 minutes at 70°C and then stained, depending on the experiment, with DAPI (300µM), Syto9 (2.5nM), Propidium iodide (2.5nM) and Potomac Gold (1mM). After 10 minutes of incubation at room temperature, the cells were processed with Cytoflex benchtop cytometer (Beckman-Coulter) and the data analyzed with CytExpert 2.5 software.

Western blot experiment

The bacterial pellets were prepared and frozen at OD600nm = 0.6. Western blot was performed as previously described (Pini et al., 2013). Anti-GroEL are commercial antibiodies against E. coli GroEL (Abcam). For anti-FcrX antibodies, fcrX was cloned into a pET derivative with Nterminal His6 tag using a Gateway cloning procedure as previously described (Skerker et al., 2005). His6-FcrX was purified on a nickel column and rabbits were injected using a 28 days protocol (Pini et al., 2013). Purified plasma was then used for western blots.

Protein interaction experiments

For the Bacterial Two Hybrid experiment [START_REF] Karimova | A bacterial two-hybrid system based on a reconstituted signal transduction pathway[END_REF] , the recommendations by the supplier (Euromedex) were applied. To construct recombinant proteins, vectors available from Euromedex were used.

These vectors enable the in frame fusion of the proteins subunits of adenylate cyclase from Bordetella pertussis (T18, T25) at the C and N terminus. To test protein putative interactions, each appropriate combination of vectors was electroporated into the E. coli strain βHT101, deleted of the gene coding for the endogenous adenylate cyclase (cya strain). Positive control corresponds to the Tol-Pal from E. coli [START_REF] Wojdyla | Structure and Function of the Escherichia coli Tol-Pal Stator Protein TolR[END_REF] .

For biochemical protein-protein interaction analysis, a nickel affinity column was used. Cells of E. coli BL21 (D3A) expressing His6-FcrX and E. coli BL21 (D3A) with no expression vector were induced 3h with 100µM IPTG at 30°C. Cells were harvested, sonicated as previously described (Skerker et al, 2005) and soluble lysate of both strains was loaded onto prepacked nickel columns. After several washes of extraction buffer (Tris 100mM, NaCl 500mM, imidazole 30mM, pH 7.5), an S. meliloti sonicated lysate was loaded on the columns, washed as previously described, followed by elution at increasing concentrations of imidazole (5%, 10% and 30%), collecting the eluates. Samples were loaded on SDS-PAGE gels and analyzed by mass spectrometry (details in Table S1) or western blot using antibodies direct against CtrA and FtsZ1 or 2 (the same polyclonal antibody is able to detect both copies).

FcrX conservation analysis

Homologs of RecG, FcrX and CtrA were identified by first blast [START_REF] Camacho | BLAST+: architecture and applications[END_REF] hits, with an e-value cutoff of 10 -4 . Proteomes for all alphaproteobacteria considered were downloaded from NCBI. Only complete genomes were considered for the analysis. Genomic distances were calculated by using coordinates in the corresponding ".gff" file; the distance dividing two genes was defined as the minimum distance in both directions, i.e. taking the circularity of the genome into account. Ancestral state reconstruction of distances was performed and mapped on trees with function contMap from R-package phytools [START_REF] Revell | phytools: an R package for phylogenetic comparative biology (and other things)[END_REF] . Alignments were performed with Muscle 48 and refined by hand in AliView 49 ; maximum likelihood phylogenetic reconstructions were performed with iqTree 50 , with options -nt AUTO -alrt 1000 -bb 1000, which combines ModelFinder, tree search, ultrafast bootstrap and SH-aLRT test. (A) Western blot using Anti-FtsZ, CtrA, FcrX and GroEL on the fcrX depletion strain in comparison with wild type (WT) and a strain containing the empty vector used in the fcrX depletion strain (Empty). For the depletion strain of fcrX, a depleted culture was reincubated with IPTG for 2h (IPTG 2h) or without for 2h (2h) or 3h (3h).

Figure 1 :

 1 Figure 1: fcrX is an essential gene in S. meliloti. (A) Scheme representing the cell cycle progression of S. meliloti in free-living condition and in symbiosis with legume plants. The green color refers to CtrA concentration, which is low at the beginning of S-phase and after cell division in large cells. During bacteroid differentiation CtrA is removed in order to induce morphological changes. (B) Transmission contrast (T) and electron microscopy (EM) of a depletion strain of fcrX in presence and absence of the inducer (IPTG). In particular, in no IPTG conditions, the depletion of fcrX is causing the formation of small cells (red asterisks). (C) Viability test on S. meliloti containing empty plasmid and a depletion strain of fcrX. Cells of fcrX depletion strain or wild type strain carrying an empty plasmid were grown with IPTG and then washed before plating. From left to right, non-diluted to 1/10 6 diluted cell suspensions were spotted on an agar plate with or without IPTG. (D) Electron microscopy of a depletion strain of fcrX (EM) and overlay of transmission contrast (T) and epifluorescence microscopy of a depletion strain of fcrX labeled with Syto9. (E) Time lapse microscopy on a depletion strain of fcrX. Orange dots represent the mother cells and the blue dots represent the daughter cells. Only daughter cells are able to produce abnormal mini cells. Scale bar corresponds to 2 μm.

Figure 2 :

 2 Figure 2: FcrX down regulates and interacts directly with the master regulator CtrA and the Z ring proteins (FtsZ1, FtsZ2).

(

  B) Affinity column western blot using CtrA, FcrX and FtsZ antibodies. Percentages represent imidazole concentration (see Materials and Methods for details). Membrane stained with Ponceau Red shows His6-FcrX. (C) Bacterial Two hybrid (BACTH) testing FcrX interaction with FtsZ1, FtsZ2, CtrA and itself. Upper right box shows negative and positive controls provided by the supplier. 25 and 18 are the two subunits of adenylate cyclase of the BACTH (see Materials and

Figure 5 :

 5 Figure 5: FcrX is conserved among alphaproteobacteria (A) Typical organization of fcrX genomic loci in model alphaproteobacteria. The presence and the relationship between locations of fcrX and ctrA genes in those alphaproteobacterial species is highlighted with a blue asterisk in figure 5B. (B) Phylogenetic tree of FcrX orthologs-containing species (as described in Materials and Methods). The color code of the tree marks the distance between the fcrX and ctrA genes (values are bp). Species used in Figure 5A are marked with a blue asterisk, tree based on RecG sequences. (C) Model of FcrX role in cell cycle regulation with respect to main functions of cell cycle and CtrA/DivK/ClpXP essential regulators.

Figure 1 :

 1 FIGURE 1 A

Figure 4 :

 4 FIGURE 4 A B

Figure 5 :

 5 FIGURE 5

ACKNOWLEDGMENTS

Sara Dendene and Quentin Nicoud were supported by a PhD fellowship from the Université Paris-Saclay. Shuanghong Xue benefited from a PhD fellowship from the Chinese Scholarship Council. The present work has benefited from the core facilities of Imagerie-Gif (http://www.i2bc.paris-saclay.fr), a member of IBiSA (http://www.ibisa.net), supported by France-BioImaging (ANR-10-INBS-04-01) and from the support of Saclay Plant Sciences-SPS (ANR-17-EUR-0007). We thank the IMM Transcriptomic facility for the RNA preparation and the qRT-PCR experiment; we also thank Artemis Kosta and Hugo le Guenno from the IMM Microscopy platform for Electron Microscopy acquisition and analysis. This work was funded by the Agence Nationale de la Recherche, grants no. ANR-17-CE20-0011 and ANR-21-CE20-0040. The authors thank Corine Foucault, Armelle Vigouroux, Solange Morera and Roza Mohammedi for technical help.

(D) Functional FcrX-YFP C-terminal fusion observed by transmission (T) and epifluorescence microscopy (EM) in a fcrX deletion genetic background (see text for details). Bar corresponds to 1 μm. Cells showing mid-cell localization are marked with an orange asterisks, while the cell with polar localization is marked with a blue asterisk.

(E) Heatmap of YFP-FcrX subcellular localization in a synchronized cell population (predivisional phase, 150 minutes). Analysis performed on >300 cells (56 with foci). (A) S. meliloti strain containing the intergenic region between fcrX and ctrA fused with mCherry and EGFP, respectively. Lower panels correspond to the same intergenic region mutated in the CtrA box (see text for details). This mutation doesn't affect the expression of ctrA but it completely abolishes the expression of fcrX.

(B) Western blot using Anti FcrX antibodies using FcrX depletion and CtrA depletion samples. First lane is purified His6-FcrX. M = Marker (sizes are reported).

(C) qRT-PCR of fcrX and Western blot using anti-FcrX antibodies on a synchronized population of S. meliloti. Bottom part represents a timeline of cell cycle phases. (A) S. meliloti strain containing the intergenic region between fcrX and ctrA fused with mCherry and EGFP, respectively. Lower panels correspond to the same intergenic region mutated in the CtrA box (see text for details). This mutation doesn't affect the expression of ctrA but it completely abolishes the expression of fcrX. (B) Western blot using Anti FcrX antibodies using FcrX depletion and CtrA depletion samples.

First lane is purified His6-FcrX. M = Marker (sizes are reported). (C) qRT-PCR of fcrX and Western blot using anti-FcrX antibodies on a synchronized population of S. meliloti. Bottom part represents a timeline of cell cycle phases.


K Rajamanickam

A Mahuthannan

S Idlahcen

B Lecordier

C Lacour

A Cessou

D Honoré

Multi-Scalar Measurements in Hydrogenated Bluff-Body Stabilized Turbulent Flames Using 1D Spontaneous Raman Scattering and OH -PLIF

This paper examines the effect of H2 enrichment in a primary fuel (CH4) using 1D spontaneous Raman scattering (SRS) and OH-PLIF measurements. The experiments are conducted in a canonical non-premixed bluff body burner operating under typical central fuel jet-dominated flow mode. Downstream of the bluff body, the flow exhibits complex patterns, and it can be globally categorized into three successive zones: recirculation, neck, and jet-like zones. The flame undergoes local extinction in the neck zone, where the local flow-induced hydrodynamic strain rate (𝜅 ) is much higher than the flame extinction strain rate (𝜅 ). It is well known that H2 enrichment increases (𝜅 ), and thus modifies the probability of localized flame extinctions in the neck zone. To understand this phenomenon, four H2 enrichment levels are considered: 0%, 10%, 30%, and 50% (in vol.). The OH-PLIF measurements reveal the presence of local extinctions in the cases of H2 enrichment ≤ 30%, while local extinctions are not witnessed for H2 = 50%. 1D SRS measurements are implemented at different axial heights above the burner to identify the interlink between H2 addition, local extinction, and scalar structure. The evolution of instantaneous and simultaneous distributions of multiple species (C.O., CO2, N2, O2, CH4, H2, H2O) concentrations and temperature are meticulously analyzed using various conditional statistics to gain insights into the non-premixed bluff-body stabilized hydrogenated turbulent flames.

Introduction

Hydrogen (H2) is a promising energy source in decarbonizing combustion systems, as it can be readily produced on large scales from renewables. However, a significant difference in the thermophysical properties of H2 in comparison with conventional fuels (e.g., CH4) causes several operational challenges. For instance, the higher reactivity and higher flame temperature of H2 lead to flashback and NOx emissions. Besides, the increased extinction strain rate (𝜅 ) due to H2 enrichment [START_REF] Shanbhogue | Flame macrostructures, combustion instability and extinction strain scaling in swirl-stabilized premixed CH4/H2 combustion[END_REF], [START_REF] Zhang | Dynamics of premixed hydrogen/air flames in unsteady flow[END_REF] is expected to alter the flame shape significantly. (Chterev and Boxx, 2021) highlighted the transition from an M-shaped flame to a shear-layer stabilized Vflame with H2 enrichment in the swirl-stabilized flames. Furthermore, several studies (Barbosa et al., 2007) [START_REF] Indlekofer | The effect of hydrogen addition on the amplitude and harmonic response of azimuthal instabilities in a pressurized annular combustor[END_REF] reported modifications in the combustion instabilities with H2 addition.

Hence, more profound insights into the turbulencechemistry interactions in H2 flames are essential. For these reasons, canonical burner configurations are often employed, which provide access to investigation on various proportions of H2 addition. In the present study, experiments are carried out in a canonical nonpremixed bluff body burner with three different levels (10%, 30%, and 50% in vol.) of H2 enrichment to the CH4. Simultaneous measurements of the flow field and flame fronts are performed using time-resolved PIV & OH PLIF systems. Besides, 1D Spontaneous Raman Scattering (SRS) is implemented across various axial heights above the burner. The trends in the local extinction and subsequent evolution of local flame structure with the H2 enrichment are explained based on the instantaneous temperature profile in mixture fraction space.

Canonical Burner Configuration and Operating Conditions

The schematic of the non-premixed canonical bluff body burner employed in this study is illustrated in Figure 1. It comprises of annular air passage and a central fuel injection port embedded with the cylindrical bluff body. The fuel flow rates of CH4 and H2 are varied in reference to the critical experimental parameter, namely, the volumetric concentration proportions of H2 (𝜶 𝑯𝟐 ). All the fluid flow rates are precisely controlled using thermal mass flow meters (Bronkhorst). Throughout all the test conditions, the thermal output of the burner (Table 1) and annular airflow rate have been maintained constant; the latter allowed us to keep the same aerodynamic features close to the burner exit.

Diagnostic Techniques a. 1D Spontaneous Raman Scattering (SRS)

A simplified schematic of the 1D SRS diagnostics tool employed in this study is shown in Figure 2. A detailed schematic can be found in (Ajrouche et al., 2015). A high-power (~1.8 mJ/pulse at 532 nm) laser (second harmonic of Nd: YAG) pulsing at 10 Hz is used. A spherical lens (f=1000mm) focuses the laser beam into the desired probe volume. Raman signal in the orthogonal direction is collected and refocused on a slit (S) using two achromatic lenses (L1 & L2). The slit allows lights only from the region of interest (ROI). Lens (L3) is used to collimate the light, and L4 is used to focus the light on the entrance slit of the spectrometer. Electro-Optic Shutter (EOS) consists of two polarizers and a Pockels cell between L3 and L4. The readout time of the eMCCD (PIXIS 400) camera used with the spectrometer (Princeton Instruments, IsoPlane SCT 320) is much larger than the laser pulse width (1000 ns). Thus, EOS minimizes the flame luminosity during such long exposure. The eMCCD has a resolution of 1340*400 pixels. The vertical 400 pixels are binned (hardware level before readout) into 8 ROIs covering 3.44 mm of probe length. The edge ROIs are removed during the post-processing due to the poor signal, which brings down the effective probe length to 2.58 mm in 6 simultaneous neighbored measurement locations with 430 µm spatial resolution each.

Furthermore, the horizontal 1340 pixels covered the spectrum range from 567nm to 694nm. One thousand shots are recorded for each measurement location. The final post-processing convergence is slightly lower due to poor signal in some instantaneous shots. Measurements are carried out above the burner at six axial heights (y = 5mm; 10 mm; 20 mm; 35 mm; 45 mm; 60 mm). For each axial height, radial profiles are acquired at x = -6mm to 30 mm with the steps of 2 mm. A robotic traverse system is employed to control the measurement positions precisely.

b. Flow field and OH -PLIF measurements

The velocity field and OH fluorescence have been measured simultaneously using time-resolved PIV & OH -PLIF systems at 5 kHz. More details on the system and post-processing can be found in [START_REF] Rajamanickam | On the relationship between H2 addition, local extinction and hydrodynamic instability in non-premixed bluff-body stabilized flames[END_REF].

Global Flow Field and Flame Structures

Figure 3 compares the mean flow fields of the test cases investigated in this study. Due to the axisymmetric nature of mean quantities, only the positive side of the radial coordinate is shown in Figure 3. Interestingly, despite a significant rise in the central fuel jet velocity (𝑈 ) from 12 m/s to 20 m/s between 𝛼 = 0 to 𝛼 = 0.5, the global topology of mean flow field is (relatively) similar across all the test cases. This is because the low-density property of hydrogen and constant annular airflow rate keeps the momentum ratio (M.R.) approximately the same (Table 1). Thus, the flow topology remains relatively unaltered even with a high-velocity jump in a central fuel jet due to H2 enrichment. 3 This is referred as neck zone (Zone B). Finally, zone C resembles a jet-like flow structure downstream of Zone B. The obtained flow structure is classically referred to as "central jet-dominated flow" in the non-premixed bluff body flame literature [START_REF] Roquemore | A study of a bluff-body combustor using laser sheet lighting[END_REF]. This corresponds to typical aerodynamic conditions ensuring turbulent flame stabilization thanks to the R.Z. obtained in our study for all hydrogen proportions. 4). For instance, the mean reaction zones of 𝛼 = 0, 0.1 are found to be shorter and located within R.Z. On the other hand, for 𝛼 = 0.3, 0.5, reaction zone is extended beyond the RZ. Interestingly, for all the cases, within RZ (i.e., Zone A), the flame is located in the shear layer formed between the outer and inner boundaries of RZ and the annular air jet, respectively (i.e., ISL1). This can be explained as follows, (i) First, part of the fuel from the central jet mixes with the air inside the RZ; (ii) The formed mixture is then convected radially outwards by strong air-driven RZ; (iii) Finally, the reaction is established in the ISL1, probably due to the local establishment of stoichiometry (or 𝜙 = 1) in that region. This is consistent with the observation made by (Dally et al., 1998) in a similar bluff body burner configuration. Furthermore, in line with the abovemade discussions concerning different flow regimes, the flame switches its path from ISL1 to ISL2 in the neck zone (i.e., zone B) and then resembles a jet-like flame configuration in zone C.

Figure 5a compares the radial profiles of mean and RMS temperature and mixture fraction obtained at different axial heights above the burner exit. Mixture fraction (𝜉) is calculated based on Brigler's formulation (Bilger, 1989).

𝜉 = 2(𝑌 -𝑌 , ) 𝑊 + (𝑌 -𝑌 , ) 2𝑊 - (𝑌 -𝑌 , ) 𝑊 2(𝑌 , -𝑌 , ) 𝑊 + (𝑌 , -𝑌 , ) 2𝑊 - (𝑌 , -𝑌 , ) 𝑊
Where 'Y' represents elemental mass fractions of Carbon (C), Oxygen (O), and Hydrogen (H); 'W' represents atomic weights. The subscripts F and Ox denote fuel and oxidizer, respectively. Inside the RZ, the mean mixture fraction is found to be overall lean in the radial region span of x = 10 -20 mm (Figure 5a). Across all the test cases, the largest gradients of mean mixture fraction (𝜉 ) occur at ISL2. Furthermore, the maxima of 𝜉 is also found to be aligned with the region where the 𝜉 exhibits a steep gradient. The 𝜉 shows nearly zero fluctuations in the central fuel jet within zone A. However, in zones B and C, it does fluctuate due to an increase in the 𝑈 , 𝑉 in that region (Figure 5b) because of strong air-fuel jet interactions. For all the H2 enrichment levels, the mean temperature (𝑇 ) inside the RZ exhibits a broader high-temperature region of 7 < 𝑥 < 25 mm due to the recirculation of hot combustion products. On the other hand, 𝑇 become progressively narrower in zone B and zone C (i.e., 𝑦 ≥ 35 𝑚𝑚) due to the jet-like flame structure. In line with the mean OH profiles shown in Figure 4, a decrease in the 𝑇 is noticed at 𝑦 = 45 mm; 60 mm (i.e., downstream to the RZ) for 𝛼 = 0, 0.1 (marked with arrows in Figure 5a). The physical interpretation behind this will be explained in more detail in the next section. As the fluctuations of 𝜉 increased in the zone B and C (Figure 5a; y =35mm; 45 mm; 50mm) due to an increased 𝑈 and 𝑉 which eventually causes high fluctuations in the temperature (𝑇 ).

Instantaneous Flame Structures and Scalar Profiles

This section presents instantaneous OH profiles and scatter plots of scalars in mixture fraction space to gain further insights into the spatial evolution of temperature relative to the H2 enrichment. Attention is focused on the neck zone, where a drastic difference in 𝑇 is observed between 𝛼 = 0, 0.1and 𝛼 = 0.3, 0.5. Previous studies (Dally et al., 1998) [START_REF] Masri | Turbulent nonpremixed flames of methane near extinction: mean structure from Raman measurements[END_REF] highlighted the occurrence of local extinctions in the neck zone as the flame undergoes excessive stretch due to the larger radial velocity gradients associated with the annular airflow in that region (convective centripetal influx). Figure 6 illustrates the instantaneous OH profiles of different H2 enrichment cases in the neck zone. The overlaid black contours represent the flame topology from OH PLIF images, and the color contours denote the 2D hydrodynamic strain rate (𝜅 -norm of the strain rate obtained from the PIV velocity field) acquired at the same time instant. The flame undergoes local extinction as a consequence of interaction with a high strain of 5000 s - 1 in the ISL2 (Figure 6; 𝛼 = 0 -t = 0.4 ms; 𝛼 = 0.3-t = 0.2 ms). On the contrary, as illustrated in (Figure 6 𝛼 = 0.5), local extinctions are no longer witnessed despite the strong interaction of flame fronts with the high strain rate in the ISL 2. The increased H2 content intensifies the extinction strain resistance of flame (𝜅 ) [START_REF] Shanbhogue | Lean blowoff of bluff body stabilized flames: Scaling and dynamics[END_REF] dynamic strain (𝜅 ) and thereby prevents local extinction. Furthermore, following the flame branches are witnessed for the test case 𝛼 = 0.3 (Figure 6). On the other hand, failure of the reconnection of flame branches is noticed for nonhydrogenated flame (Figure 6; 𝛼 = 0). Two reignition mechanisms, edge flame propagation and turbulence mixing by adjacent vortices, are widely reported in non-premixed turbulent jet flames. (Briones et al., 2008) and [START_REF] Frouzakis | From diffusion to premixed flames in an H2/air opposed-jet burner: the role of edge flames[END_REF] have shown that H2 enrichment to the methane leads to a progressive rise in the edge flame speed due to enhanced reactivity and preferential diffusion. Thus, an increase in the edge flame speed with H2 enrichment leads to quicker reconnection of the broken branches that formed due to the local extinction. Figure 7a illustrates the scatter plots of instantaneous temperature and oxygen mass fractions (𝑌 ) colored relatively to the burner's radial positions. The vertical solid (blue) line on the temperature scatter plot represents the stoichiometric mixture fraction (𝜉 ). Here, x = 6 -12 mm (colored with green) is the radial region where the local extinctions are majorly observed (see Figure 7). As discussed earlier, for the test cases of 𝛼 = 0, 0.1, failure of reconnection of the broken flame branches following the local extinction resulted in the distribution of samples in the low-temperature region (green-colored dots in Figure 7a; 𝛼 = 0, 0.1). The increase in 𝑌 in the same region Figure 7b; 𝛼 = 0, 0.1) further supports this observation. On the other hand, quicker reconnection of the flame branches following local extinction and the absence of local extinction leads to higher temperatures in the region x = 6 12 mm 𝛼 = 0.3 and 𝛼 = 0.5, respectively (Figure 7a). It is interesting to note that, even for 𝛼 = 0.3,0.5, small fraction of samples (marked with dotted circles in Figure 7a; 𝛼 = 0.3,0.5) exhibits low temperature in the region of x = 6 -24 mm. This is attributed to the radial flapping of flame caused by increased 𝑈 (Figure 5b) in that region.

Furthermore, conditional statistics are implemented to quantify the degree of local extinctions. This is done by conditioning the temperature data in the small mixture fraction window of 0.05 < 𝜉 < 0.06 (these values lie close to the stoichiometric mixture fraction). Figure 7c compares the conditional pdfs of temperature distribution across different axial heights above the burner. Within zone A, i.e., RZ (Figure 7c; y= 5mm, 20 mm), the obtained temperature exhibits unimodal distribution across all the test cases. This is due to the absence of local extinctions inside the RZ. However, a bimodal distribution is witnessed in the axial heights of Y ≥ 35mm (i.e., zones B and C), which is attributed to the two phenomena: local extinctions and flame flapping. The probability of hightemperature samples is progressively reduced, and it possesses broadened distribution of T = 1250 -2250 K for 𝛼 = 0,0.1 (Figure 7c; y > 35 mm). For the same cases, it should also be noted that there is a drastic increase in distribution in the low-temperature region of T = 400-600 K. In particular, this is more pronounced for 𝛼 = 0 due to the high degree of local extinctions and failure of reconnection of flame branches after the local extinction, as illustrated in Figure 7 (𝛼 = 0). For the cases of 𝛼 = 0.3, 0.5, although there is reduction in the probability of samples (Figure 7c) in the high-temperature region, unlike, 𝛼 = 0,0,1, distribution still peaks at T ~ 2100 K. As illustrated in Figure 7 (𝛼 = 0.3,0.5), the absence of local extinctions/ quicker reconnection of broken flames due to increase in the edge flame speed leads to high temperature in the downstream regions, i.e., y = 45 mm, 60 mm.

Figure 1 .

 1 Figure 1. Configuration of a canonical nonpremixed bluff-body burner.

Figure

  Figure 2. Schematic of Spontaneous Raman Scattering (L1 = 150 mm; L2 = 300 mm; L3 =200 mm; L4=300 mm)

Figure 3 .

 3 Figure 3. Time-averaged flow field across different H2 enrichment levels. Three distinct flow zones are identified based on the height above the burner (Figure 3; 𝛼 = 0). The first zone (Zone A) comprises a strong air Recirculation Zone (R.Z.) induced immediately downstream of the bluff body exit. Here, the length of R.Z. (𝑳 𝑹𝒁 ) is marked based on the average location of the stagnation point at the end of R.Z. Furthermore, three shear layers are witnessed in Zone A (see Figure 3;𝛼 = 0), (i) Outer shear layer (OSL) formed between the outer boundary of annular air jet and ambient air; (ii) Inner shear layer 1 (ISL1) separates the inner and outer boundaries of the annular air jet and R.Z., respectively. (iii) Inner shear layer 2 (ISL2) is induced between the inner boundary of R.Z. and the central fuel jet. Next to R.Z., the annular airflow converges towards the central fuel jet in the small region of 40 𝑚𝑚 ≤ 𝑦 ≤ 55 𝑚𝑚.

Figure 4 .

 4 Figure 4. Mean flame structures of different H2 enrichment cases obtained from OH -PLIF Despite similar global flow topologies (Figure4) across all the values of 𝛼 , there exists strong variations in the mean reaction zone height (𝒉 𝑹 ) obtained from OH PLIF (Figure4). For instance, the mean reaction zones of 𝛼 = 0, 0.1 are found to be shorter and located within R.Z. On the other hand, for 𝛼 = 0.3, 0.5, reaction zone is extended beyond the RZ. Interestingly, for all the cases, within RZ (i.e., Zone A), the flame is located in the shear layer formed between the outer and inner boundaries of RZ and the annular air jet, respectively (i.e., ISL1). This can be explained as follows, (i) First, part of the fuel from the central jet mixes with the air inside the RZ; (ii) The formed mixture is then convected radially outwards by strong air-driven RZ; (iii) Finally, the reaction is established in the ISL1, probably due to the local establishment of stoichiometry (or 𝜙 = 1) in that region. This is consistent with the observation made by(Dally et al., 1998) in a similar bluff body burner configuration. Furthermore, in line with the abovemade discussions concerning different flow regimes, the flame switches its path from ISL1 to ISL2 in the neck zone (i.e., zone B) and then resembles a jet-like flame configuration in zone C.Figure5acompares the radial profiles of mean and RMS temperature and mixture fraction obtained at different axial heights above the burner exit. Mixture fraction (𝜉) is calculated based on Brigler's formulation(Bilger, 1989).

  Figure 5. a. Radial profiles of the mean (+) and RMS (solid lines) temperature, mean (o), and RMS (dots) mixture fraction [Top row -Zone A; Bottom row -Zone B, C]; b. RMS contours of axial and radial velocity (𝜶 𝑯𝟐 = 𝟎. 𝟏).

Figure 6 .

 6 Figure 6. Time sequences of superimposed PIV strain field (color contours) and OH-PLIF (black contours) images illustrating the flame's interaction with high strain in the neck zone.

Figure 7

 7 Figure 7. a. and b. Scatter plots of temperature and oxygen mass fraction (𝑌 ) in mixture fraction space at y = 45 mm; c. Conditional pdfs of the temperature in the small fraction window (𝟎. 𝟎𝟓 < 𝝃 < 𝟎. 𝟎𝟔) for different 𝜶 𝑯𝟐 values.

Table 1 . Operating conditions (𝜶 𝑯𝟐

 1 ) 𝑹𝒆 𝒇𝒖𝒆𝒍 𝑹𝒆 𝒂𝒊𝒓 𝑷𝒐𝒘𝒆𝒓

					𝑴𝑹
			(kW)	=	𝟐 𝝆 𝒂𝒊𝒓 𝑼 𝒂𝒊𝒓 𝝆 𝒇 𝑼 𝒇 𝟐
	0	4370 10575	16.8		0.25
	0.1	4300 10575	16.8		0.26
	0.3	4123 10575	16.8		0.31
	0.5	3872 10575	16.8		0.38

Conclusions

This work discusses the impact of H2 enrichment to the primary fuel CH4 on the local flame structures in a canonical non-premixed bluff body burner. 1D SRS and simultaneous time-resolved PIV and OH-PLIF are employed to provide deeper insights into the turbulence-chemistry interactions. The evolution of radial profiles of temperature and scalars relative to different H2 enrichment levels are presented across various axial heights above the burner. The scatter plots of temperature and oxygen mass fraction (𝑌 ) in the mixture fraction space highlighted the presence of localized flame extinctions in the neck zone and subsequent reduction of temperature in the downstream region for the 𝛼 = 0,0.1 flames. The results also revealed the absence of local extinctions for 𝛼 = 0.5 due to the increased extinction strain rate over the local flow-induced hydrodynamic strain rate (𝜅 > 𝜅 ).

Acknowledgments

This research work is supported by Normandie Regional Council and European Union through European Regional Development Fund (ERDF) in the framework of the RAPHYD project (RIN 2018). A. Mahuthannan's stay at the CORIA laboratory was part of a research collaboration with SINTEF and NTNU, funded by the OXYFUN project under the Research Council of Norway (grant number 268369).


Thomas Guyet

Declarative Sequential Pattern Mining in ASP Enhance sequential patterns mining with background knowledge

Keywords: /michael-fuchs-python, netlify, app

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

a versatile encoding that ease the trials and error approach a sufficiently efficient approach to experiment on mid-size datasets

∃(ei ) i∈[p-1] such that pi ⊆ te i for all i ∈ [p -1] and px ⊆ tp.
1 item( I ) :-seq(T,P,I) .

3 slot (1). 4 { slot (X+1) } :-slot (X); X<max. 5 1{ pat(X,E) : item(E) } :slot (X). T. Guyet ILP@IJCLR -11/2023 31 / 42 q q q q q q q -2 0 CPSM fg sg ASP-Mining/FIFA q q q q q q q q q q q q q q q q q q q q q q q q 0 2 4 CPSM fg sg ASP-Mining/IPRG q q q q q q q q q q q q q q q q q -3 CPSM fg sg ASP-Mining/JMLR q q q q q q q q q q q q q q q q q q q q q q q q q q q q -4 Realworld dataset experiments -Memory consumption q q q q q q q q q q q q q q q q q q q q q q q q q q q q 2000 4000 6000 8000

Threshold #atoms+#rules heuristic dom none option q closure maximal none prog q q q CPSM fg sg ASP-Mining/FIFA q q q q q q q q q q q q q q q q q q q q q q q q q q 14.6 CPSM fg sg ASP-Mining/IPRG q q q q q q q q q q q q q q q q q q q q q q q q q q q q 100 200 300 Threshold #atoms+#rules heuristic dom none option q closure maximal none prog q q q CPSM fg sg ASP-Mining/JMLR q q q q q q q q q q q q q q q q q q q q q q q q q q q q 12 13 14 100 200 300

  Representing the pharmaco-epidemiology tool-chain in ASP ⟨D, S, K, M, C⟩ D (facts): raw-administrative data base encoding K (facts): knowledge-base (ontology, guidelines, etc) S: rules for prior patient selection and feature selection M: efficient ASP encodings of sequence mining C: pattern selection constraints Answer Set Programming (ASP) sequence mining framework a unified formalism to represent the entire processing chain (in few lines)

⇒

  T,P,1) :-seq(T,P,E):pat(1,E); seq(T,P,_). 10 occ(T,P,X+1) :-occ(T,Q,X); seq(T,P,_); Q<P; 11 seq(T,P,E):pat(X+1,ESeveral alternative encodings were implemented and evaluated [GMQS16] Alternative strategies to evaluate pattern covering skip-gaps vs fill-gaps embedding evaluations Efficient additional rules Early filtering out infrequent items Using projected databases principle: extend patterns only with potentially frequent items (fill-gap basis) item(1, I ) :-item( I ) , #count{ T: seq(T,_,I) } >= th. item(Ip+1,I) :-item(Ip , I ) , #count{ T: seq(T,Is, I ) , occ(T,Ip , Is ) } >= th. 1 { pat(Ip , I ) : item(Ip , I ) } 1 :-slot (Ip) pattern constraints (efficient and easy to implement constraints) :-pat(X,I ) , forbidden_item(I ) .more practical examples on the use-case Most of the constraints only require the addition of rules easy to modify a pattern mining task by (des)activate rules sequences, 100 different items mean length of sequences: 30 items 20 simulated patterns of mean length 5 and with a frequency of 10% probability of occurrence of an item: a normal distribution (µ = .5is slightly more efficient (especially for large memory requirement problems) CPSM is 1 to 2 order of magnitude faster than ASP encoding reduces significantly the required memory length of the sequences is a very sensitive dataset characteristic very low threshold will not increase the memory requirements maximal and closed encoding require more memory T. Guyet ILP@IJCLR -11/2023

s}| Frequent pattern mining: Given

	SPM-ASP SPM-ASP SPM-ASP SPM-ASP SPM-ASP	Integrated toolchain Integrated toolchain Integrated toolchain Integrated toolchain Integrated toolchain	ASP-SMT ASP-SMT ASP-SMT ASP-SMT ASP-SMT	CCL CCL CCL CCL CCL
	Sequential pattern mining Sequential pattern mining Sequential pattern mining Integrating knowledge into pattern mining Basic ASP encoding of frequent sequential pattern mining
	T. Guyet T. Guyet T. Guyet T. Guyet T. Guyet supp(p) = |{s ∈ D|p ⪯ T. Guyet ILP@IJCLR -11/2023 Introduction Sequential pattern mining in ASP Frequent sequential pattern mining ASP encodings Experiments Partial conclusions Integrated pharmaco-epidemiology toolchain GENEPI study Toolchain encoding Partial conclusions Implementation of ASP propagator ASP-MT motivation and principles Sequence covering propagator Experiments Conclusions and Perspectives ILP@IJCLR -11/2023 SID sequence 10 ⟨a(abc)(ac)d(cf )⟩ 20 ⟨(ab)c(bc)(ae)(ad)⟩ 30 ⟨(ef )(ab)(df )cbc⟩ 40 ⟨eg(af )cbc(de)⟩ 50 ⟨aa(ad)b⟩ ILP@IJCLR -11/2023 ⟨1, 3, 5⟩) SID sequence 10 ⟨a(abc)(ac)d(cf )⟩ 20 ⟨(ab)c(bc)(ae)(ad)⟩ 30 ⟨(ef )(ab)(df )cbc⟩ 40 ⟨eg(af )cbc(de)⟩ 50 ⟨aa(ad)b⟩ ILP@IJCLR -11/2023 Let D be a set of sequences, the support of pattern p in D is the 2, 4⟩, number of sequences in D that contain p: supp(p) = |{s ∈ D|p ⪯ s}| Frequent pattern mining: Given a support threshold σ, find the complete set of sequential patterns with support above σ SID sequence 10 ⟨a(abc)(ac)d(cf )⟩ 20 ⟨(ab)c(bc)(ae)(ad)⟩ 30 ⟨(ef )(ab)(df )cbc⟩ 40 ⟨eg(af )cbc(de)⟩ Some frequent patterns: ⟨abd⟩ (but not ⟨a(bc)d⟩) ⟨(ab)c⟩ ILP@IJCLR -11/2023 Let D be a set of sequences, the support of pattern p in D is the Atom Meaning number of sequences in D that contain p: ILP@IJCLR -11/2023 Embedding constraints: specification of the embedding relation ⪯ item(e) item e belongs to some t ∈ D examples: exclude items, super-pattern, cost → extract only frequent patterns that do not contain the b item slot (x )	7 / 42 8 / 42 9 / 42 9 / 42 10 / 42 10 / 42

A sequence s is an ordered set of events (or itemsets)

A sequence s is an ordered set of events (or itemsets) A sequential pattern is a subsequence example: pattern p = ⟨a(bc)d⟩ containment relation: p ⪯ s → inclusion of itemsets → gaps are allowed embedding: is a mapping of a pattern to a sequence (⟨1, a support threshold σ, find the complete set of sequential patterns with support above σ SID sequence 10 ⟨a(abc)(ac)d(cf )⟩ 20 ⟨(ab)c(bc)(ae)(ad)⟩ 30 ⟨(ef )(ab)(df )cbc⟩ 40 ⟨eg(af )cbc(de)⟩ Some frequent patterns: ⟨abd⟩ (but not ⟨a(bc)d⟩) ⟨(ab)c⟩ → Algorithms are based on an anti-monotonicity property p ⪯ p ′ =⇒ supp(p ′ ) ≤ supp(p) Too many "useless patterns" pattern mining algorithms generate a deluge of patterns ... it is not reasonable to present this deluge of patterns to a data analyst a challenge of pattern mining: extract fewer but meaningful patterns. Constrained(sequential) pattern mining A user defines constraints to specify the expected patterns based: Pattern constraints: expressed on an individual pattern p examples: gap constraint, span constraint, number of embeddings → p ⊑ s iff p ⊑ s with at most two items in-between successive embedding positions (⟨(a)(bc)(ae)(e)(ad)⟩) Dataset constraints: expressed on the set of sequences matching a pattern {s | s ⪯ p} examples: frequency constraint (frequent, rare), discriminant, contrastive 1 ≤ x ≤ m refers to the position x of an item sx in p pat(x ,e) px = e is the item at position x in p cover(t) ⟨p1 . . . pm⟩ ⪯ ⟨t1 . . . tn⟩, that is, p ⪯ t occ(t,p,x )

cover(T) :-patlen (L); occ(T,_,L). 16 :-not k { cover(T) }.T. Guyet ILP@IJCLR -11/2023

Basic ASP encoding

Database encoding seq(t,x ,e): sequence t, at position x holds the item e seq(0,1,20). seq (0,2,19). seq(0,3,2). seq (0,4,18). seq(1,1,5). seq (1,2,6). seq (1,3,6). seq (1,4,14). seq(2,1,13). seq (2,2,12). seq (2,3,9). seq (3,1,15). seq(3,2,7). seq (3,3,17). seq (3,4,17). seq (4,1,11). seq(4,2,2). seq (5,1,14). seq (5,2,[START_REF] Guyet | Declarative Sequential Pattern Mining of Care Pathways[END_REF]. seq (5,3,13). seq(5,4,1).

Raw database of patients (D) in FOL

Patient raw database Patient information (e.g. sex, age, chronic long-term illness) Care events (timestamped):

hospital stays (including diagnosis codes) drugs deliveries medical consultations (general practitioners, specialists)

Facts encoding: patient(0). sex(0,m). birthYear (0,1960). delivery(0,1,3585053,1). delivery(0,1,3599730,1). delivery(0,154,3599730,1). delivery(0,346,3599730,1). delivery(0,350,3599730,2). disease(0,380,g409). disease(0,380,k700).

Data preparation S

Sequence of AED deliveries within the 3 months before the first seizure firstseizure(P,T) :-disease(P,T,D), is_a(D,g40;g41), #count{Tp: disease(P,Tp,Dp), is_a(Dp,g40;g41), Tp<T}=0.

seq(P,T,delivery(AED,1)):-delivery(P,T,CIP,Q), aed(CIP,AED), generic(CIP), T<Ts, T>Ts-90, firstseizure(P,Ts).

seq(P,T,delivery(AED,0)):-delivery(P,T,CIP,Q), aed(CIP,AED), not generic(CIP), T<Ts, T>Ts-90, firstseizure(P,Ts).

G40 and G41 are disease codes for epileptic seizures (CIM-10 ) aed/2: classifies a drug code in one of the 5 ATC classes of AED dates are numbers of days (integers)

Are ASP pattern mining ready for practical use?

Partial conclusions

ASP enables to encode sequential pattern mining tasks in an "intuitive" way Different encodings have been proposed

easy implementation/(des)activation of a wide range of pattern mining constraints ⇒ versatility and readability of encodings Evaluation of the efficiency, ASP encoding of FSM is not competitive with state of the art algorithms comparable with "fairly-versatile" other declarative frameworks (SAT/CP) Some limitations ⇒ memory requirement is the hardest constraint ⇒ the most efficient encodings are not the most "intuitive" T. Guyet ILP@IJCLR -11/2023

Declarative pattern mining approach (reminder ) ⇒ evaluation of pattern's embeddings is memory consuming 1 item( I ) :-seq(T,P,I) .

3 slot (1). 4 { slot (X+1) } :-slot (X); X<max. 5 1{ pat(X,E) : item(E) } :slot (X).

7 patlen (L) :-pat(L,_);

8 not pat(L+1,E):item(E). 9 occ(T,P,1) :-seq(T,P,E):pat(1,E); seq(T,P,_). 10 occ(T,P,X+1) :-occ(T,Q,X); seq(T,P,_); Q<P; { slot (X+1) } :-slot (X), X<maxlen-1. patlen (L+1) :-slot (L), not slot (L+1).

1 { pat(X,I ) : item( I ) } 1 :-slot (X).

% is the pattern covers the sequence S or not?? { cover(S) } :-seq(S,_,I ) , pat(_,I ) .

:-#count{ S : cover(S) } < th.

Role of the theory propagator

→ detect conflicts with the theory constraint in a partial model → identify no goods: a small subset of atoms that "explains" a conflict

The "smallest" the no good, the more informative ⇒ detect conflicts from partial models

Early detection of conflicts in partial models

Partial model: describe a pattern q s.t. q ⪯ p cover(s) ∧ q ̸ ⪯ s, then p ̸ ⪯ s: an early no-good is send to the solver ¬cover(s) ∧ q ⪯ s, ...: can not but used as no good to discard p ⪯ s

Comparison between propagators and pure ASP ⇒ it is compatible with (most of) the end-to-end toolchains