Michel Hosny

Jacques Yaacoub

Bou Khalil

Aurelia Caputo

Rita Abou Abdallah

Anthony Levasseur

Philippe Colson

Nadim Cassir

Bernard La Scola
email: bernard.la-scola@univ-amu.fr

Multidisciplinary evaluation of Clostridium butyricum clonality isolated from preterm neonates with necrotizing enterocolitis in South France between 2009 and 2017

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

Multidisciplinary evaluation of Clostridium butyricum clonality isolated from preterm neonates with necrotizing enterocolitis in South France between 2009 and 2017

Michel Hosny, Jacques Yaacoub Bou Khalil, Aurélia Caputo, Rita Abou Necrotizing enterocolitis (NEC) is a multifactorial intestinal disease that occurs in 4-12% of preterm neonates, with a high attributable mortality especially in patients with very low birth weight (i.e. 500-1000 g) [START_REF] Cassir | Gut microbiota and the pathogenesis of necrotizing enterocolitis in preterm neonates[END_REF][START_REF] Seeman | Infant and maternal risk factors related to necrotising enterocolitis-associated infant death in the United States[END_REF] . Recent studies propounded the idea of bacteriological etiology, mostly microbiota dysbiosis during NEC episodes, leading to the generation of inflammatory process [START_REF] Neu | Pathogenesis of NEC: Impact of an altered intestinal microbiome[END_REF][START_REF] Hosny | Updating on gut microbiota and its relationship with the occurrence of necrotizing enterocolitis[END_REF] . In recent years, several bacterial species have been suspected of being associated with NEC outbreaks, especially Clostridia like Clostridium butyricum, Clostridium perfringens and Clostridium neonatale [START_REF] Hosny | Updating on gut microbiota and its relationship with the occurrence of necrotizing enterocolitis[END_REF][START_REF] Roze | Nutritional strategies and gut microbiota composition as risk factors for necrotizing enterocolitis in very-preterm infants[END_REF] . Zhao-Fleming et al. also reported a significantly higher frequency of strictly anaerobic species by using 16S rRNA sequencing to identify bacteria from patients with necrotizing infections [START_REF] Zhao-Fleming | Are anaerobes a major, underappreciated cause of necrotizing infections?[END_REF] . Cassir et al. described a relationship between the presence of C. butyricum in stool samples from preterm neonates and the occurrence of NEC, using a combination of three techniques (16S rRNA pyrosequencing, culturomics and qPCR). However, neither the pathogenicity nor the epidemiology of this relationship have yet been totally resolved [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . In addition to Clostridia, Gram-negative bacterial species were also identified especially, K. pneumoniae, E. cloacae and Uropathogenic Escherichia coli [START_REF] Boccia | Nosocomial necrotising enterocolitis outbreaks: Epidemiology and control measures[END_REF][START_REF] Ward | Metagenomic sequencing with strain-level resolution implicates uropathogenic E. coli in necrotizing enterocolitis and mortality in preterm infants[END_REF] .

In present work, we conducted a multidisciplinary study on a cohort of NEC and control preterm neonates stool samples that we investigated for C. butyricum in stool by qPCR, a small fraction of samples only being previously tested by culture [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . The main objective of the current investigation on this cohort was to isolate the qPCR-detected C. butyricum in order to perform strain typing by whole genome sequencing on isolates and to correlate it with the date of sampling as the geographical origin of the isolates. Indeed, in a preliminary work done on 16 strains, we suspected isolates to have a clonal origin isolates [START_REF] Benamar | Multi-spacer typing as an effective method to distinguish the clonal lineage of Clostridium butyricum strains isolated from stool samples during a series of necrotizing enterocolitis cases[END_REF] . For this, we used a heat-shock selective culture protocol that allowed us also to isolate C. butyricum but also some other Clostridia previously also suspected to be associated to NEC. We took the opportunity in the present work to add additional cases received between 2015 and 2017. Then, the association between C. butyricum and the occurrence of NEC was reassessed and typing data were analysed together.

Results

evaluation of Clostridium species community in samples from preterm neonates. Combination of culture and qPCR results allowed the identification of a strong association between the presence of C. butyricum in stool samples from preterm neonates and the occurrence of NEC, when compared to controls (66/88; 75% vs. 8/71; 11%; p < 0.001 respectively) (Table 1). Overall, 58 strains of C. butyricum were isolated including 52 (59.1%; n = 88) from NEC patients and 6 (8.45%; n = 71) from controls (p < 0.001) (Table 2). By comparing means of cycle thresholds (Ct), the density of C. butyricum was lower in controls stool samples than in NEC (32.938 and 29.182 respectively, p value = 0.0344). The frequency of C. butyricum in this later seems to be associated with the administration of antibiotics (p value = 0.027), which is not the case in controls (p value = 0.838) (Supplementary Table S1). As for the other previously proposed NEC-associated Clostridium species, we isolated four strains (4.5%) of C. neonatale from NEC patients and one (1.14%) from controls (p = 0.26). Clostridium perfringens was detected equally in patients with NEC and controls (respectively 8; 9% and 6; 8.4%). This was also the case for Clostridium paraputrificum (1; 1.1% and 1; 1.4% respectively). Finally, we identified other Clostridia from the stools of patients with NEC: Clostridium sardiniense (1; 1.1%), Clostridium tertium (1; 1.1%) and Clostridium difficile (2; 2.3%). In particular, 7/8 and 1/6 of C. perfringens from the NEC patients and controls, respectively, were co-isolated with C. butyricum in the same sample.

Core-genome and core-genome single-nucleotide polymorphism phylogenetic analysis. The average length of genomes included in this study was 4,676,116 bp. The greatest genome size was 5,214,902 bp (strain NEC23), the smallest genome size was 4,014,159 bp (strain DORA). An average of 4,363 open reading frames was predicted (Supplementary Table S2). Although strains isolated from Marseille (NICU-1 and NICU-2) were over-represented in this study, the eBURST analysis of core-SNP enabled the identification of three main C. butyricum clonal groups (a, b, c): group (b) included one cluster; cluster (b), thus both group (a) and (c) included two clusters; respectively cluster (a1, a2) and cluster (c1, c2) (Figs 1, 2 and Supplementary Figure S1-S3). The majority of NEC-associated C. butyricum (28/52, 54%) were clustered within the group (b). Genomic relationships were identified between NEC and control isolates, also grouped depending on geographic source of isolation. Strains isolated from the same NICUs were close to each other i.e. cluster (a1), (a2), (b), (c1) isolates detected from NICU-1 and 2 in Marseille, also, C. butyricum strains from NICU-3 and NICU-4 on the other hand in cluster (a1) and (b) (Fig. 1). Core-SNP temporal clustering revealed that highly-related strains were identified between 2009 and 2010 in group (b) (73.5%; 25/34), also, during 2010 in cluster (c1) (Fig. 2). Nearly all strains were grouped in clusters revealing their clonality whereas strains from other origin were dispersed and far from each another. The comparative analysis allowed the identification of hemolysin-encoding genes (hemolysin A, B, C and beta) in NEC and control isolates from all clusters.

Genotyping using multispacer sequence typing phylogeny. MST phylogeny identified four sequence types (ST) where the strains had the same MST: NEC1, NEC3, NEC10 and NEC17 (Supplementary Figure S4 andS5). We compared the eBURST analysis of MST with that of core-SNP. Isolates were clustered into three groups centered on the Kwashiorkor strain (KW10): Group a' included the same cluster as Group a, except for NEC1, NEC8, NEC35, NEC72 and NEC74; Group b' included the same strains as Group b except for NEC29, NEC52, NEC64, NEC65 from Group (a) and NEC88 from Group (c); finally, Group c' included NEC50.

Discussion

Inclusion of additional cases and the use of a selective culture procedure for Clostridium isolation confirmed our previous results showing a significant association between C. butyricum and NEC in preterm neonates [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF][START_REF] Benamar | Multi-spacer typing as an effective method to distinguish the clonal lineage of Clostridium butyricum strains isolated from stool samples during a series of necrotizing enterocolitis cases[END_REF] . Indeed, 75% of NEC were positive using qPCR and culture, while this rate was only 11% in controls (p < 0.001). Culture technique emphasizes the specificity of qPCR, as 3.4% of NEC-associated C. butyricum were negative by qPCR and positive by culture. Reciprocally, qPCR validated the culture by detection of C. butyricum in 75.75% (50/66) from all positive samples. The advantage of this selective culture protocol allowed easy isolation of C. butyricum during NEC outbreaks as compared to culturomics technique which is highly fastidious [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . The drawback of included culture method was the possibility to skip isolation of in vivo non-spore-form of Clostridia species. As well, the density of C. butyricum was higher in NEC than in controls (p value = 0.0344). The association between C. butyricum-linked NEC with antibiotics administration (p value = 0.027), suggested a mechanism of pathogenicity comparable to that of C. difficile, where cases of pseudomembranous colitis were significantly associated with previous antibiotic administration, especially lincosamides, third generation cephalosporins and fluoroquinolones. It would be interesting, in future studies, to evaluate the influence of antibiotics families in the occurrence of NEC. Additionally, culture enabled the isolation of other Clostridia (n = 25) previously suggested in linked with NEC that were not evaluated by Cassir et al. [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . Among these, C. neonatale and C. perfringens were specifically suspected to be associated with NEC [START_REF] Hosny | Updating on gut microbiota and its relationship with the occurrence of necrotizing enterocolitis[END_REF][START_REF] Roze | Nutritional strategies and gut microbiota composition as risk factors for necrotizing enterocolitis in very-preterm infants[END_REF][START_REF] Dittmar | Necrotizing enterocolitis of the neonate with Clostridium perfringens: Diagnosis, clinical course, and role of alpha toxin[END_REF][START_REF] Heida | A necrotizing enterocolitis-associated gut microbiota is present in the meconium: results of a prospective study[END_REF][START_REF] Haque | Necrotizing enterocolitis -Some things old and some things new: A comprehensive review[END_REF][START_REF] De La Cochetière | Early intestinal bacterial colonization and necrotizing enterocolitis in premature infants: The putative role of Clostridium[END_REF][START_REF] Alfa | An Outbreak of necrotizing enterocolitis associated with a novel Clostridium species in a neonatal intensive care unit[END_REF] . These species were infrequently isolated, the most where the authors used a metagenomic approach to detect C. perfringens type A (3/12; 25%) from NEC samples [START_REF] Sim | Dysbiosis anticipating necrotizing enterocolitis in very premature infants[END_REF] .

It has been demonstrated that early colonization by C. perfringens affected the onset of NEC [START_REF] De La Cochetière | Early intestinal bacterial colonization and necrotizing enterocolitis in premature infants: The putative role of Clostridium[END_REF] . Furthermore, unbalanced gut microbiota in Lebanese neonates suffering from NEC have been reported, including C. perfringens widely identified in patients, despite the limited number of samples tested in this study [START_REF] Itani | Preterm infants with necrotising enterocolitis demonstrate an unbalanced gut microbiota[END_REF] . C. neonatale was less prevalent than C. butyricum and C. perfringens and not significantly associated with NEC (NEC and controls, n = 4, 4.5% versus n = 1, 1.4% respectively, p = 0.5). However, it is difficult to draw conclusion from a limited number of isolates. C. neonatale was first identified by Alfa et al., during a NEC outbreak in a Canadian NICU. However, no control neonates were tested, and its pathogenicity was not fully investigated [START_REF] Alfa | An Outbreak of necrotizing enterocolitis associated with a novel Clostridium species in a neonatal intensive care unit[END_REF] , only its microbiologic features were studied [START_REF] Ferraris | One-step multiplex PCR assay for differentiating proposed new species 'clostridium neonatale' from closely related species[END_REF] , particularly through comparative phenotypic features with C. butyricum [START_REF] Schönherr-Hellec | Comparative phenotypic analysis of "Clostridium neonatale" and Clostridium butyricum isolates from neonates[END_REF] . Genomic relations were previously reported by Benamar et al. on a limited number of strains (n = 32) including 16 isolated from NEC and controls [START_REF] Benamar | Multi-spacer typing as an effective method to distinguish the clonal lineage of Clostridium butyricum strains isolated from stool samples during a series of necrotizing enterocolitis cases[END_REF] . Three clonal clades were identified. In the present work, 42 additional preterm neonates' strains isolated from different geographic origin and time of isolation were analysed. Core-genome, core-SNP and MST phylogenetic analysis on an exceptional collection of C. butyricum strains (n = 81) confirmed genomic relationship between NEC-associated and controls isolates as the discrimination of the prior identified clades. Therefore, three main epidemic clonal groups were identified, including a large clonal cluster occurring between 2009 and 2010 (cluster (b)). This last clustered the majority of NEC-associated C. butyricum (28/52, 54%) identified as clade C in Benamar et al. [START_REF] Benamar | Multi-spacer typing as an effective method to distinguish the clonal lineage of Clostridium butyricum strains isolated from stool samples during a series of necrotizing enterocolitis cases[END_REF] . In some cases, especially during September/ October 2010, NEC occurred as an outbreak (n = 10) with highly related isolates. Other small epidemics clusters were detected with a limited number of strains (Groups a1, a2, c1 and c2). Additionally, strains isolated from the same NICU were highly related suggesting the existence of geographic-associated C. butyricum clonal lineages and epidemic transmission. This was confirmed by similarities observed between controls and NEC-associated isolates and highlighted a C. butyricum asymptomatic carriage of these genetically-related strains. Clusters (a2) and (c2) were not observed in Benamar et al. [START_REF] Benamar | Multi-spacer typing as an effective method to distinguish the clonal lineage of Clostridium butyricum strains isolated from stool samples during a series of necrotizing enterocolitis cases[END_REF] and corresponded to strains isolated after 2015. This finding confirms the temporal clustering.

The first NEC-associated C. butyricum outbreak was reported by Howard et al. in 1977, based on clinical examination and microbiologic analysis, since no genotyping methods were employed [START_REF] Howard | Outbreak of necrotising enterocolitis caused by Clostridium butyricum[END_REF] . Gorham et al. reported 152 cases of C. butyricum hand-carriage isolated from 152 healthcare workers during a NEC outbreak [START_REF] Gorham | Clostridial hand-carriage and neonatal necrotising enterocolitis[END_REF] . Several studies showed that C. butyricum is a beneficial microorganism, especially MIYAIRI 588 strain, that prevents entero-hemorrhagic E. coli, C. difficile infections and gastric ulcers [START_REF] Cassir | Clostridium butyricum: from beneficial to a new emerging pathogen[END_REF] . Conversely, other strains might contribute to the pathogenesis of several infectious diseases, such as botulism and NEC [START_REF] Cassir | Clostridium butyricum: from beneficial to a new emerging pathogen[END_REF][START_REF] Aureli | Two cases of type e infant botulism caused by neurotoxigenic Clostridium butyricum in Italy[END_REF] . Recently, Wydau-Dematteis et al. reported the importance of the dlt operon of C. butyricum associated NEC by establishing the resistance of C. butyricum to antimicrobial peptides, lysozymes and vancomycin [START_REF] Wydau-Dematteis | Anaerobe The functional dlt operon of Clostridium butyricum controls the D-alanylation of cell wall components and influences cell septation and vancomycin-induced lysis[END_REF] . A high dose of butyric acid has also been demonstrated to have a cytotoxic effect on diverse cell lines, notably Caco-2 cells monolayers [START_REF] Peng | Effects of butyrate on intestinal barrier function in a caco-2 cell monolayer model of intestinal barrier[END_REF] . Genomic identification in C. butyricum of a toxin comparable to β-hemolysin secreted by Brachyspira hyodysenteriae 7 suggests a similar possible mechanism for cytotoxicity [START_REF] Hsu | Cloning of a beta-hemolysin gene of Brachyspira (Serpulina) hyodysenteriae and its expression in Escherichia coli[END_REF] . Moreover, we previously reported a cytotoxic activity of C. butyricum supernatant tested by flow cytometry on Jurkat cells [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . Such a toxigenic mechanism of Clostridia in NEC disease is supported by the findings of Heida et al., who observed a low density of Clostridia by fluorescent in situ hybridization [START_REF] Heida | Identification of bacterial invasion in necrotizing enterocolitis specimens using fluorescent in situ hybridization[END_REF] . Other toxins-related NEC cases have been suggested in association with different bacterial species such as toxigenic E. coli, Pseudomonas aeruginosa, Serratia spp., delta toxin-producing strains of coagulase-negative Staphylococci, S. aureus and pore-forming type A toxin Clostridium perfringens [START_REF] Scheifele | Role of bacterial toxins in neonatal necrotizing enterocolitis[END_REF][START_REF] Gohari | A novel pore-forming toxin in type A Clostridium perfringens is associated with both fatal canine hemorrhagic gastroenteritis and fatal foal necrotizing enterocolitis[END_REF] .

The picture observed in C. butyricum-associated NEC resembles that of C. difficile-associated pseudomembranous colitis [START_REF] Janoir | Virulence factors of Clostridium difficile and their role during infection[END_REF] . Similarly to C. butyricum-associated NEC, C. difficile hospital-associated isolates were found to be highly related with asymptomatic carriage, supporting the idea of a plausible transmission amongst hospitals as from environmental reservoirs [START_REF] Curry | Use of multilocus variable number of tandem repeats analysis genotyping to determine the role of asymptomatic carriers in Clostridium difficile transmission[END_REF][START_REF] Eyre | Diverse sources of C. difficile infection identified on whole-genome sequencing[END_REF] . This work is the first to note that the WGS was used to investigate probable C. butyricum-associated NEC outbreak, during a period of 8 years using SNP analysis. WGS is a revolutionizing large-scale genomic-based technique, highlighting the clonal transmission between reservoirs and patients [START_REF] Price | Transmission of Staphylococcus aureus between health-care workers, the environment, and patients in an intensive care unit: a longitudinal cohort study based on whole-genome sequencing[END_REF] , as the identification of virulence factors [START_REF] Samore | Clinical and molecular epidemiology of sporadic and clustered cases of nosocomial Clostridium difficile diarrhea[END_REF] . In addition, we observed that MST techniques represent an alternative method as clusters were approximately validated by core-SNP analysis, but due to continuous reduction of costs, WGS will be probably preferred for routine use in future diagnosis.

Conclusion

The key findings of this study were first, the confirmation of significant association between C. butyricum strains and the occurrence of NEC, then the genetic correlation between NEC and non-NEC-associated strains of C. butyricum. This suggested that cases emerge from a small number of genetically heterogeneous sources, validated the possibility of asymptomatic carriage and confirmed that most strains are hospital-acquired. These findings and significant association with the administration of antibiotics in NEC patients resembles epidemiology of C. difficile in adults.

Methods

study design and patients. One hundred and fifty-nine preterm neonates with NEC and matched controls were enrolled, including neonates from the study of Cassir et al. (NEC n = 82, control n = 67) [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] , and 10 (NEC n = 6, control n = 4) received between 2015 and 2017 (Supplementary Table S3). The stool samples collected from 88 NEC and 71 controls were from four south-eastern regions of France (Marseille, Nice, Nîmes and Montpellier), including five neonatal intensive care units (NICUs) (Table 2, Supplementary Table S2 and Figure S6). Cases were defined as patients with suspected, definite or advanced NEC corresponding to Bell stages I, II or III. When feasible, stool samples were collected on the day of symptoms onset and stored at -80 °C. Controls were matched with patients by sex, gestational age, birth weight, days of life, feeding strategies, mode of delivery, and previous antibiotic therapy and NICU. All patients with NEC and controls were preterm neonates (under 37 weeks completed weeks of gestation). Since the dates of antibiotic administration were not recorded, patients were not distinguished for the duration of antibiotic therapy. None of the selected patients had received probiotics or been included in therapeutic protocols prior to stool collection and all were negative for routine microbial investigation. Agreements from the ethics committee of the "Institut Fédératif de Recherche, IFR48" and the "Institut Hospitalo-Universitaire, IHU-2017-007" were obtained to confirm the study procedure, as well as a written informed consent from parents of all patients [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . All methods were performed in accordance with the relevant guidelines and regulations.

Clostridium species isolation, C. butyricum qpCR detection. Stools were cultured for Clostridium species isolation using HS treatment based on the thermal resistance of spores [START_REF] Marler | Comparison of five cultural procedures for isolation of Clostridium difficile from stools[END_REF] . Briefly, samples were suspended (v/v) in sterile phosphate-buffered saline by vortexing and heated for 20 minutes at 80 °C. Stools were then cultured on 5% Columbia sheep blood agar (Becton Dickinson ® , USA) at 37 °C for 48 hours in an anaerobic atmos- phere inside an anaerobic chamber. Provisional identification of all strains was performed by MALDI-TOF, then the amplification and sequencing of 16S rRNA gene was used to confirm this identification, as previously described [START_REF] Hosny | Description of Clostridium phoceensis sp. nov., a new species within the genus Clostridium[END_REF] . Simultaneously, specific detection of C. butyricum qPCR was performed on DNA extracts obtained from stool samples of cases received after 2015, as described previously [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . Data of qPCR and culture-based technique were analysed, the same 30 stool samples tested by culturomics method in Cassir et al. study being used as positive controls to validate the ability of spore-based method in the isolation of C. butyricum [START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] .

Core-genome and core-genome single-nucleotide polymorphism analysis. The genomic DNA of isolated C. butyricum was sequenced on MiSeq sequencer (Illumina, San Diego, CA, USA) using the paired-end strategy. Reads were assembled and scaffolded using SPAdes version 3.4.0 [START_REF] Bankevich | SPAdes: a new genome assembly algorithm and its applications to single-cell sequencing[END_REF] . Overall, 81 genomes were analysed, including 42 from strains isolated and sequenced in this study, 16 from previous isolates 7 , 5 strains isolated in our laboratory from humans as part of gut microbiota analysis [START_REF] Lagier | Current and past strategies for bacterial culture in clinical microbiology[END_REF] and 18 from the Genbank database. Analysed genomes and their references are summarized in Supplementary Table S2. Protein sequences and nucleotide coordinates were predicted using the GeneMarkS platform (Genemark ™ , USA) 39 . Orthologous proteins analysis were performed using the ProteinOrtho software [START_REF] Lechner | Proteinortho: Detection of (Co-) orthologs in large-scale analysis[END_REF] . Core-genome coding DNA sequences were inferred from the pan-genome, concatenated and aligned using a Python script. SNPs were obtained from the core-genome using SNP-sites software [START_REF] Keane | SNP-sites: rapid efficient extraction of SNPs from multi-FASTA alignments[END_REF] . Phylogenetic trees were generated using the maximum-likelihood method within PhyML 42 and edited by Treegraph 2 software [START_REF] Stöver | TreeGraph 2: Combining and visualizing evidence from different phylogenetic analyses[END_REF] . PHYLOViZ version 2.0 was used to generate a core-SNP eBURST phylogenetic tree based on expected numbers of nucleotide substitutions per variable site [START_REF] Nascimento | PHYLOViZ 2.0: Providing scalable data integration and visualization for multiple phylogenetic inference methods[END_REF] . Scaled phylogenetic trees were procured using Adobe Photoshop CC 2018. BLASTP was retrieved to allow the identification of potential hemolysin sequences within the draft genomes of C. butyricum, their protein sequences are in Supplementary Material 1.

  Abdallah, Anthony Levasseur, Philippe Colson, Nadim Cassir, Bernard La Scola To cite this version: Michel Hosny, Jacques Yaacoub Bou Khalil, Aurélia Caputo, Rita Abou Abdallah, Anthony Levasseur, et al.. Multidisciplinary evaluation of Clostridium butyricum clonality isolated from preterm neonates with necrotizing enterocolitis in South France between 2009 and 2017. Scientific Reports, 2019, 9 (1), 10.1038/s41598-019-38773-7. hal-02263577

Figure 1 .

 1 Figure 1. Clostridium butyricum geographic relationship based on core-genome single-nucleotide polymorphism phylogenetic analysis. The color of strain names represents the geographic zone of isolation.(Marseille: NICU-1, NICU-2; Nice: NICU-3; Montpellier: NICU-4). Red strain names represents the 16 isolates sequenced Cassir et al.[START_REF] Cassir | Clostridium butyricum Strains and Dysbiosis Linked to Necrotizing Enterocolitis in Preterm Neonates[END_REF] . NEC: necrotizing enterocolitis, NICU: neonatal intensive care units.

Figure 2 .

 2 Figure 2. Clostridium butyricum temporal relationship based on core-genome single-nucleotide polymorphism phylogenetic analysis. The color of strain names represents the timing of isolation. Red strain names represents the 16 isolates sequenced Cassir et al. 7 . NEC: necrotizing enterocolitis, C: control.

Table 1 .

 1 Detection of Clostridium butyricum by qPCR and Heat-shock. NEC: necrotizing enterocolitis, qPCR: quantitative real-time polymerase chain reaction.

								C. butyricum
		C. butyricum qPCR		C. butyricum culture	qPCR + culture
			Controls			Controls	NEC	Controls
		NEC (n = 88)	(n = 71)	NEC (n = 88)	(n = 71)	(n = 88)	(n = 71)
	Positive	63 (71.6%)	8 (11.3%)	52 (59.1%)		6 (8.4%)	66 (75%)	8 (11%)
	Negative	25 (28.4%)	63 (88.7%)	36 (40.9%)		65 (91.6%)	22 (25%)	63 (89%)
	P value	p value < 0.001			p value < 0.001		p value < 0.001
				NEC (n = 88)	Controls (n = 71)
	Characteristics		No. (%)		No. (%)	p value
	Gestational age +/-SD (weeks)	28.36 (+/-2.82)	28.24 (+/-2.93)	0.7864
	Days of life +/-SD (days)		25.99 (+/-13.16) 23.99 (+/-11.61) 0.3166
	Birth weight mean +/-SD (g)	1179 (+/-380)	1174 (+/-432)	0.950
	Male sex			49 (55.7)	43 (60.5)	0.594
	Very low birth weight (≤1500 g)	69 (78.4)	58 (81.7)	0.617
	Pasteurized breast milk		59 (67)	49 (69)	0.372
	Formula fed			9 (10)	13 (18)	0.139
	Vaginal delivery		32 (36)	37 (52)	0.023
	Antibiotics before collection		64 (73)	40 (56)	0.092

Table 2 .

 2 Clinical Characteristics of necrotizing enterocolitis and controls preterm neonates. NEC: necrotizing enterocolitis.

Scientific RepoRts | (2019) 9:2077 | https://doi.org/10.1038/s41598-019-38773-7

Scientific RepoRts |

Acknowledgements

We are grateful to the medical teams of the Assistance publique -Hôpitaux de Marseille (AP-HM), CHU Nîmes, CHU Montpellier and CHU Nice for providing us the stool samples. We thank the genomics platform at the Institut Hospitalo-Universitaire (IHU) -Méditerranée Infection for technical assistance. This work was supported by the French Government under the "Investissements d'avenir" program managed by the Agence Nationale de la Recherche (ANR), [reference: Méditerranée-Infection 10-IAHU-03], by Région Provence-Alpes-Côte d' Azur and European funding FEDER PRIMI. M. Hosny was supported by the Fondation de Coopération Scientifique, Méditerranée-Infection [Infectiopole Sud 2016].

Genotyping using multispacer sequence typing. MST was performed as described by Benamar et al. [START_REF] Benamar | Multi-spacer typing as an effective method to distinguish the clonal lineage of Clostridium butyricum strains isolated from stool samples during a series of necrotizing enterocolitis cases[END_REF] . Briefly, DNA from patients' isolates was extracted and amplified by standard PCR and then sequenced using 16 capillary sequencer 3130 XL (Applied Biosystems ® , USA) and the BigDye Terminator v1.1 Cycle Sequencing kit (Applied Biosystems ® , USA). For C. butyricum genomes available online, intergenic spacers were extracted by in Silico BLASTn. statistical analysis. Statistical analysis was performed using the SPSS ® statistics software 2016 (IBM, NY, USA). Mean and standard deviation were used to describe continuous variables. Percentage and number of events were used for quantitative variables. Student t-test or Mann-Whitney U test was used to perform two-group comparisons for quantitative variables. The chi-square (Mantel-Haenszel) test was used to perform two-group comparisons for qualitative variables.

Author Contributions

Additional Information

Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-019-38773-7.

Competing Interests:

The authors declare no competing interests.

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Julien Flamant Cran
email: julien.flamant@univ-lorraine.fr

Sebastian Miron
email: sebastian.miron@univ-lorraine.fr

David Brie
email: david.brie@univ-lorraine.fr

Quaternion Non-negative Matrix Factorization: a new tool for spectropolarimetric imaging

Keywords: quaternion non-negative matrix factorization (QNMF), Stokes parameters, spectropolarimetry

Quaternion non-negative matrix factorization (QNMF) is a new tool which generalizes usual non-negative matrix factorization (NMF) to the case of polarized signals.

The approach relies on two key features: (i) the algebraic representation of polarization information, namely Stokes parameters, thanks to quaternions and (ii) the exploitation of physical constraints linked to polarization generalizing non-negativity constraints. QNMF improves NMF model identifiability by revealing the key disambiguating role played by polarization information. A simple and numerically efficient algorithm is introduced for practical resolution of the QNMF problem. Numerical experiments on synthetic data validate the proposed approach and illustrate the potential of QNMF as a generic spectropolarimetric image unmixing tool.

I. INTRODUCTION

Polarization information is essential to many imaging applications ranging from astrophysics [START_REF] Antonucci | Optical spectropolarimetry of radio galaxies[END_REF] to biology [START_REF] Zhao | Spectropolarimetric imaging for pathological analysis of skin[END_REF]. It simultaneously carries a strong natural discriminative power as well as numerous physical and morphological attributes of the observed scene which are unaccessible to conventional intensity imaging. Recent years have seen a booming interest in pairing polarization diversity together with conventional hyperspectral imaging systems [START_REF] Mu | Static hyperspectral imaging polarimeter for full linear stokes parameters[END_REF]. Such spectropolarimetric imaging technique consists in acquiring, for every pixel u and wavelength λ, a Stokes vector x(λ, u) ∈ R 4 describing the polarization properties of the measured light. Importantly, these energetic parameters obey to structural constraints that reveal the physics of polarization. These constraints generalize classical non-negativity: only one Stokes parameter is nonnegative, whereas the 4 Stokes parameters are linked all together by an inequality constraint.

Spectropolarimetric images can be represented as a 3D data array gathering the spatial, spectral and polarization diversities. For narrow-band sources with constant polarization, usual low-rank tensor approximation techniques (e.g. CPD with constraints [START_REF] Veganzones | Nonnegative tensor cp decomposition of hyperspectral data[END_REF]) -adapted to the specificities of polarization -permit an efficient unmixing of spectropolarimetric images. However, the general wideband sources case is much more challenging, notably due to wavelength-dependent polarization Research supported by Région Grand Est and project ANR-15-CE10-0007 OPTIFIN.

properties. The latter case thus requires the development of new, generic and interpretable signal processing tools for spectropolarimetric data.

To this aim, we introduce quaternion non-negative matrix factorization (QNMF). This new tool extends to the case of polarized signals the concept of non-negative matrix factorization (NMF), widely used for hyperspectral unmixing [START_REF] Ma | A signal processing perspective on hyperspectral unmixing: Insights from remote sensing[END_REF]. QNMF relies on two ingredients: (i) the algebraic representation of the Stokes vector x(λ, u) using quaternions and (ii) the exploitation of physical constraints related to polarization, which generalize the usual non-negativity constraint. Focusing on practical purposes, we give a simple yet numerically efficient algorithm that solves the QNMF problem using a quaterniondomain alternated least square optimization strategy. A first theoretical analysis of QNMF can be found in [START_REF] Flamant | Quaternion non-negative matrix factorization: definition, uniqueness and algorithm[END_REF], where it is shown that QNMF greatly improves NMF in terms of model identifiability, by having less strict uniqueness conditions on the sources. Numerical experiments on synthetic data demonstrate the potential of QNMF as a generic low-rank approximation tool for polarized signals.

II. BACKGROUND A. Polarization

Polarization is a fundamental property of waves (electromagnetic, elastic, gravitational) which describes the geometric nature of oscillations. Consider for instance light in vacuum: in the transverse plane, i.e. perpendicular to the direction of propagation, the electric field vector usually describes an elliptical trajectory; hence one says that the wave is elliptically polarized. Intensity and polarization properties of light are characterized by 4 Stokes parameters S 0 , S 1 , S 2 , S 3 . This set of energetic, experimentally measurable quantities is widely used in many applications, including optics [START_REF] Born | Principles of Optics[END_REF]. The first Stokes parameter S 0 ≥ 0 measures the total intensity, i.e. the sum of intensities of the polarized part and unpolarized part of light. The relative contribution of these two parts is ruled by the degree of polarization Φ Φ = polarized intensity total intensity

= S 2 1 + S 2 2 + S 2 3 S 0 , (1)
where by definition Φ ∈ [0, 1]. When Φ = 1, light is said to be fully polarized, whereas for Φ = 0 light is said to be unpolarized. For 0 < Φ < 1, it is said to be partially polarized. The three remaining Stokes parameters S 1 , S 2 , S 3 define the polarization state fo the wave: S 1 and S 2 encode linear polarization states, while S 3 gives circularly polarized states.

B. Quaternion representation

A Stokes vector (S 0 , S 1 , S 2 , S 3 ) ∈ R 4 can be algebraically represented by the quaternion

w = S 0 + iS 3 + jS 1 + kS 2 ∈ H , (2)
where H = Span{1, i, j, k} is the set of quaternions, i, j, k are roots of -1 (i 2 = j 2 = k 2 = -1) such that ij = k and ij = -ji. Eq. ( 2) can be geometrically rewritten as:

w = I + IΦµ (3)
where

I = S 0 ≥ 0 is the total intensity, Φ ∈ [0, 1]
is the degree of polarization. The polarization axis µ is a pure quaternion (i.e. such that µ 2 = -1) which can be identified with a unit vector of R 3 on the Poincaré sphere of polarization states [START_REF] Flamant | Spectral analysis of stationary random bivariate signals[END_REF]. Eq. ( 3) illustrates one of the benefits of the quaternion approach, as it enables a natural separation between purely energetic information (the real part of w, Rew = I) and polarization / geometric content (the imaginary part of w, Imw = IΦµ).

C. Polarization constraint and non-negativity

A Stokes vector (S 0 , S 1 , S 2 , S 3 ) ∈ R 4 is said to be admissible when the following constraints (S) are satisfied:

S 0 ≥ 0 and S 2 1 + S 2 2 + S 2 3 ≤ S 2 0 . (S)
The first constraint S 0 ≥ 0 is classical and indicates that the total intensity is a non-negative real quantity. The second constraint is specific to polarization: it stipulates that the intensity of the polarized part cannot exceed that of the total intensity. From a mathematical viewpoint, (S) extends the usual non-negativity constraint of univariate signals to the case of bivariate signals. To see this, consider the coherency matrix J [9, Section 1.4], i.e. the spectral covariance matrix of the bivariate electric field such that

J = 1 2 S 0 + S 1 S 2 + iS 3 S 2 -iS 3 S 0 -S 1 ∈ C 2×2 . (4)
By definition, J is a positive semidefinite (or simply nonnegative) Hermitian matrix. Non-negativity of J is characterized by tr J ≥ 0 and det J ≥ 0, two conditions which yield directly to (S). The proposed approach relies on exploiting the constraint (S) through the quaternion representation (2) of Stokes parameters. By extension, we define the set of nonnegative quaternions H S ⊂ H such that

H S {q ∈ H|Req ≥ 0 et |Imq| ≤ Req} . (5)
This formal identification between a quaternion q ∈ H S and a Stokes vector is used throughout the paper.

III. QUATERNION NON-NEGATIVE MATRIX

FACTORIZATION

This section introduces quaternion non-negative matrix factorization (QNMF), a new tool which generalizes NMF to the case of polarized signals. QNMF relies on two key distinctives aspects: (i) the polarization constraints (S), which encodes non-negativity for polarized signals and (ii) the algebraic representation (2) of Stokes parameters using quaternions.

A. Definition

Consider for simplicity the case of spectropolarimetric imaging, where the four Stokes parameters x(λ, u) ∈ H S are measured for every wavelength λ and pixel u. The following linear mixing model permits to decompose spectropolarimetric data into P sources like

x(λ, u) = P p=1 w p (λ)h p (u) (6)
where h p (u) ≥ 0 is the activation coefficient of the p th source at pixel u, and w p (λ) ∈ H S is the corresponding Stokes vector at wavelength λ. Eq. ( 6) describes a blind wideband polarized source separation problem. This model is very general: no hypotheses on the frequency dependence of polarization properties are introduced, unlike other existing approaches based on narrow-band modeling [START_REF] Raimondi | Wideband multiple diversity tensor array processing[END_REF]. Solving ( 6) can be formulated as the resolution of the following quaternion non-negative matrix factorization (QNMF) problem X = WH

where X ∈ H M ×N S is the spectropolarimetric data matrix, i.e. X mn = x(λ m , u n ). The source matrix W ∈ H M ×P S has coefficients W mp = w p (ν m ), while H ∈ R P ×N + is the activation matrix such that H pn = h p (u n ). Given X, the QNMF (7) relies on exploiting the polarization onstraint (S) for the sources W, together with the usual non-negativity constraint for the activations H. As a result, for a given P ≤ M, N , the product WH defines a structured low-rank approximation of X.

B. Relation with NMF

The QNMF problem (7) can be rewritten using the decomposition of any quaternion into the sum of its real and imaginary part like

X = WH ⇔ ReX = [ReW] H (NMF) ImX = [ImW] H (polarization) . (8)
Eq. [START_REF] Flamant | Spectral analysis of stationary random bivariate signals[END_REF] shows that QNMF can be interpreted as a matrix cofactorization problem, where activation matrix H stands as a common factor. The first problem ReX = [ReW] H is a standard NMF one on the real part of X, i.e. on intensity data only (first Stokes parameter S 0 ≥ 0). The second problem Im X = [Im W] H searches for a factorization of the imaginary part of X, which describes polarization properties of the sources (Stokes parameters S 1 , S 2 , S 3 ). Importantly, these two matrix factorization problems are not independent, for two reasons: (i) the activation matrix H is a common factor and (ii) the very nature of the polarization constraint (S) links the real and imaginary parts of the source matrix W. In full generality, QNMF greatly improves NMF model identifiablity by taking advantage of supporting polarization informationfundamental properties that can be measured in most optical imaging setups. From a theoretical perspective, we derive in [START_REF] Flamant | Quaternion non-negative matrix factorization: definition, uniqueness and algorithm[END_REF] sufficient conditions (for P = 2 sources) and necessary uniqueness conditions (for P ≥ 2 sources). Compared to their NMF counterparts [START_REF] Huang | Non-negative matrix factorization revisited: Uniqueness and algorithm for symmetric decomposition[END_REF]- [START_REF] Fu | Nonnegative matrix factorization for signal and data analytics: Identifiability, algorithms, and applications[END_REF], these conditions appear far less restrictive -in particular, one may recover QNMF uniqueness even when sources never vanish, a case where NMF is known to be not unique.

IV. ALGORITHM

A. Optimization problem formulation

The practical resolution of the QNMF problem can be formulated as an optimization problem, which aims at minimizing the following Euclidean quadratic cost

min W∈H M ×P S H∈R P ×N + X -WH 2 F (9) where X -Y 2 F = m,n |X mn -Y mn | 2
is the Frobenius norm between quaternion matrices X and Y. Note the similarity between ( 9) and the standard Euclidean cost NMF. However, the QNMF setting raises two specific issues that subtend any algorithm attempting to solve [START_REF] Gil | Polarized Light and the Mueller matrix approach[END_REF], namely: 1) can we implement the constraint (S) on W in an efficient way? and 2) can we optimize directly with respect to the quaternion matrix W? Fortunately, the key link between (S) and the set of non-negative Hermitian 2-by-2 matrices allows to answer positively to 1). For 2), recent advances in the theory of quaternion-domain derivatives [START_REF] Xu | The theory of quaternion matrix derivatives[END_REF]- [START_REF] Mandic | A quaternion gradient operator and its applications[END_REF] (also called generalized HR calculus), enable to perform optimization of (9) directly in the quaternion domain, as described below.

B. Quaternion alternating least squares

Since the objective function ( 9) is biconvex, i.e. it is convex in each W and H, but not in (W, H), we adopt a popular strategy based on the alternated constrained minimization of (9) w.r.t. H and W. To this aim, a first approach consists in the following. At a given iteration r, for each factor, one solves the unconstrained least-squares problem and project the obtained solution onto the corresponding constraint. This approach is called quaternion alternating least squares (QALS) due to its resemblance with the usual ALS algorithm [START_REF] Paatero | Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values[END_REF] for the NMF. QALS is written symbolically as

H r+1 ← Π R+ arg min H X -W r H 2 F (10) W r+1 ← Π H S arg min W X -WH r+1 2 F (11)
where Π R+ and Π H S denote element-wise projections onto constraints R + and (S), respectively. Projection onto R + is simply obtained by keeping non-negative values, i.e. Π R+ (H pn ) = max(0, H pn ). The projection of elements of W onto (S) is performed by projecting the associated 2-by-2 Hermitian matrix onto the subspace spanned by its nonnegative eigenvalues, see [START_REF] Flamant | Quaternion non-negative matrix factorization: definition, uniqueness and algorithm[END_REF] for details.

Detailed derivations of explicit updates for unconstrained least-squares problems are provided in [START_REF] Flamant | Quaternion non-negative matrix factorization: definition, uniqueness and algorithm[END_REF]. It requires special care due to the quaternion nature of X and W. For H, it involves a cautious handling of quaternion non-commutativity. Optimization over W is performed thanks to the recently introduced theory of quaternion derivatives [START_REF] Xu | The theory of quaternion matrix derivatives[END_REF]- [START_REF] Mandic | A quaternion gradient operator and its applications[END_REF]. It yields updates expressions that are very much alike the standard ALS algorithm for the NMF [START_REF] Berry | Algorithms and applications for approximate nonnegative matrix factorization[END_REF]. At iteration r > 0, one gets

H r+1 ← Π R+ Re W r W r -1 Re W r X (12)
W r+1 ← Π H S XH r+1 H r+1 H r+1 -1 (13)
where X and X are the transpose and element-wise conjugate of the quaternion matrix X, respectively. Note that in ( 12)-( 13), matrix inverses are computed for real matrices only. The proposed QALS algorithm is thus remarkably simple and cheap. Its numerical complexity is similar to that of the ALS algorithm, which scales as O(M N P ) for small values of P . This heuristic algorithm provides a first baseline for the resolution of QNMF, and paves the way to the development of more sophisticated algorithms in the near future.

V. NUMERICAL VALIDATION

A. Illustration

To illustrate the potential of QNMF, we consider a data example X 0 = W 0 H 0 constructed from synthetic quaternion non-negative sources W 0 and activation maps H 0 . We generate P = 3 sources with realistic spectral signatures (S 0 parameter) for M = 64 wavelengths together with N = 16 × 16 = 256 spatial locations. For simplicity, each source is fully polarized (Φ = 1) with constant polarization properties distinct from one another. Activation maps are chosen such that the pure pixel condition is satisfied. Such conditions guarantee that the QNMF X 0 = W 0 H 0 satisfies the necessary uniqueness condition given in [START_REF] Flamant | Quaternion non-negative matrix factorization: definition, uniqueness and algorithm[END_REF]Prop. 3].

Additive noise was added to X 0 , resulting in observations X = X 0 + N where N has i.i.d. quaternion circular Gaussian entries, i.e. N mn = n 0 mn + n 1 mn i + n 2 mn j + n 3 mn k with i.i.d. n i mn ∼ N (0, σ 2 ). Signal-to-noise ratio is defined as SNR = X 0 2 F /(4M N σ 2 ) and we note SNR dB = 10 log SNR. Fig. 1 depicts reconstruction results for sources and corresponding activation maps obtained using the QALS algorithm for SNR dB = 0 dB. We performed 100 independent runs of the QALS algorithm. Convergence of the algorithm is monitored by the relative reconstruction error at iteration r, ε r = X -W r H r 2 F / X 2 F . The algorithm stops whenever |ε r -ε r-1 | goes below some predefined threshold. Out of 100 runs, it took on average 8 iterations for the QALS algorithm to converge. Fig. 1 displays the best of all runs in terms of final reconstruction error. Overall, the excellent match between theoretical values and reconstructed sources and activations indicates the good practical performances of the proposed QALS algorithm.

B. Reconstruction performance

To quantify the performances of QALS in terms of reconstruction accuracy, we consider a second experiment where we monitor the total reconstruction error H 0 -H 2 F + W 0 -W 2 F = ε H +ε W for SNR values ranging from SNR dB = -40 dB to SNR dB = 40 dB. For each SNR value, 100 independent noisy observations were simulated and QALS reconstruction was performed.

Fig. 2 displays the evolution of the average total reconstruction error with respect to the SNR. As expected, the total reconstruction error ε H + ε W decreases as the SNR increases. These results illustrate the good numerical properties of QALS, which provides, despite the lack of convergence guarantees, a good baseline for practical resolution of the QNMF problem.

VI. CONCLUSIONS

This paper has introduced QNMF, a new low-rank approximation tool which generalizes the usual NMF to the case of polarized signals. A first algorithm named QALS provides an efficient and simple resolution of the QNMF problem. These first results, together with unicity results provided in [START_REF] Flamant | Quaternion non-negative matrix factorization: definition, uniqueness and algorithm[END_REF] appear very promising and herald many further theoretical and methodological developments on QNMF. These future works will bring fundamental tools essential to the generalization of spectropolarimetric imaging modalities.

3 Fig. 1 .Fig. 2 .

 312 Fig. 1. QALS reconstruction example for the P = 3 sources case with SNR dB = 0 dB. Reconstructed activations and Stokes parameters are given row-wise. Results display excellent match with theoretical values (solid black lines).