Shingo Akita

Christophe Vieira

Takeaki Hanyuda

Florence Rousseau

Corinne Cruaud

Arnaud Couloux

Svenja Heesch

J Mark Cock

Hiroshi Kawai

Providing a phylogenetic framework for trait-based analyses in brown algae: phylogenomic tree inferred from 32 nuclear protein-coding sequences

Keywords: Sphacelariales, Syringodermatales, Dictyotales, Onslowiales Ectocarpales, Genomics, Heterokontophytes, Phaeoexplorer, Phaeophyceae, Stramenopiles

In the study of the evolution of biological complexity, a reliable phylogenetic framework is needed. Many attempts have been made to resolve phylogenetic relationships between higher groups (i.e., interordinal) of brown algae (Phaeophyceae) based on molecular evidence, but most of these relationships remain unclear. Analyses based on small multi-gene data (including chloroplast, mitochondrial and nuclear sequences) have yielded inconclusive and sometimes contradictory results. To address this problem, we have analyzed 32 nuclear protein-coding sequences in 39 Phaeophycean species belonging to eight orders. The resulting nuclear-based phylogenomic trees provide virtually full support for the phylogenetic relationships within the studied taxa, with few exceptions. The relationships largely confirm phylogenetic trees based on nuclear, chloroplast and mitochondrial sequences, except for the placement of the Sphacelariales with weak bootstrap support. Our study indicates that nuclear protein-coding sequences provide significant support to conclusively resolve phylogenetic relationships among Phaeophyceae, and may be a powerful approach to fully resolve interordinal relationships with increased taxon sampling.

Introduction

Brown algae or Phaeophyceae represent a large class of multicellular photosynthetic marine eukaryotes distributed in cold to tropical marine waters with major ecological and economical functions [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF]. Brown algae include about 2000 species classified into 340 genera, 59 families and 19 orders (Guiry and Guiry, 2021). In contrast to land plants, our understanding of brown algal evolution remains quite limited [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF]. The Phaeoexplorer project (https://phaeoexplorer.sb-roscoff.fr/home/) was initiated in 2016 with the objective of exploring the evolution of biological complexity in brown algae by generating genomic data for a broad range of brown algal species. A fully resolved backbone phylogeny for brown algae is required to investigate questions in evolution, ecology and conservation. Initial efforts to elucidate phylogenetic relationships among brown algae were based on nuclear ribosomal DNA sequences [START_REF] Bhattacharya | Algae containing chlorophylls a+ c are paraphyletic: molecular evolutionary analysis of the Chromophyta[END_REF][START_REF] Druehl | Molecular and morphological phylogenies of kelp and associated brown algae[END_REF][START_REF] Rousseau | Phylogenetic relationships within the Fucales (Phaeophyceae) based on combined partial SSU+ LSU rDNA sequence data[END_REF][START_REF] Tan | Phylogeny of the Northeast Pacific brown algal (Phaeophycean) orders as inferred from 18S rRNA gene sequences[END_REF], followed by studies adding RuBisCO genes [START_REF] Bailey | Analysis of clonal cultures of the brown tide algae Aureococcus and Aureoumbra (Pelagophyceae) using 18S rRNA, rbcL, and rubisco spacer sequences[END_REF][START_REF] De Clerck | A revised classification of the Dictyoteae (Dictyotales, Phaeophyceae) based on rbcL and 26S ribosomal DNA sequence analyses[END_REF][START_REF] Draisma | A reassessment of phylogenetic relationships within the Phaeophyceae based on RUBISCO large subunit and ribosomal DNA sequences[END_REF][START_REF] Peters | Molecular phylogeny of small brown algae, with special reference to the systematic position of Caepidium antarcticum (Adenocystaceae, Ectocarpales)[END_REF][START_REF] Phillips | Resolving evolutionary relationships among the brown algae using chloroplast and nuclear genes[END_REF]. More recently, significant attempts were made to produce multi-gene datasets but with a limited number of genes (less than 15), mainly from chloroplast and mitochondrial genomes with nuclear DNA still represented only by ribosomal markers [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF][START_REF] Cho | Molecular systematic reassessment of Sargassum (Fucales, Phaeophyceae) in Korea using four gene regions[END_REF][START_REF] Kawai | Molecular phylogeny of two unusual brown algae, Phaeostrophion irregulare and Platysiphon glacialis, proposal of the Stschapoviales ord. nov. and Platysiphonaceae fam. nov., and a re-examination of divergence times for brown algal orders[END_REF][START_REF] Lane | A molecular assessment of northeast Pacific Alaria species (Laminariales, Phaeophyceae) with reference to the utility of DNA barcoding[END_REF][START_REF] Silberfeld | A multi-locus time-calibrated phylogeny of the brown algae (Heterokonta, Ochrophyta, Phaeophyceae): investigating the evolutionary nature of the "brown algal crown radiation[END_REF]. While contributing considerably to our understanding of brown algal evolutionary history, these previous phylogenies only partially resolved relationships at some taxonomic levels, in particular for interordinal relationships within the Fucophycideae. Furthermore, in some cases, multi-gene molecular phylogenies based on chloroplast and mitochondrial genes indicated contradictory relationships [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF][START_REF] Kawai | Molecular phylogeny of two unusual brown algae, Phaeostrophion irregulare and Platysiphon glacialis, proposal of the Stschapoviales ord. nov. and Platysiphonaceae fam. nov., and a re-examination of divergence times for brown algal orders[END_REF][START_REF] Kawai | Taxonomic revision of the Agaraceae with a description of Neoagarum gen. nov. and reinstatement of Thalassiophyllum[END_REF][START_REF] Kawai | Ancestral reproductive structure in basal kelp Aureophycus aleuticus[END_REF]. Whole genome data are gradually emerging for brown algae [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF], and several studies based on mitochondrial or chloroplast genomes, focused mainly on Laminariales and Fucales members, produced strong evidence supporting the merit of genome data in resolving phylogenetic relationships (e.g., [START_REF] Zhang | Characterization of the complete chloroplast genome of Sargassum fusiforme and its phylogenomic position within phaeophyceae[END_REF]. However, so far, whole genome data are available for only six of the 19 orders of brown algae [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF]. More recently, two studies made use of nuclear transcriptomic data to deduce brown algal evolutionary relationships [START_REF] Jackson | Kelp transcriptomes provide robust support for interfamilial relationships and revision of the little known Arthrothamnaceae (Laminariales)[END_REF][START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF]. The latter study, which was based on 108 orthologous genes from 18 Phaeophyceae species belonging to six orders (i.e., Desmarestiales, Dictyotales, Ectocarpales, Fucales, Ishigeales, Laminariales), produced mixed results [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF]. Overall, phylogenomic trees provided strong to full support for infraordinal relationships and for the relationship between Ectocarpales and Laminariales, but less strong support for other interordinal relationships (e.g., bootstrap (BS) = 55 for Dictyotales-Ishigeales node) [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF]. A second nuclear-transcriptome-based phylogenomic study conducted at the infraordinal level, employed 152 genes from 15 Laminariales species and yielded a nearly fully resolved tree, which enabled relationships between various genera to be revised [START_REF] Jackson | Kelp transcriptomes provide robust support for interfamilial relationships and revision of the little known Arthrothamnaceae (Laminariales)[END_REF]. Family-level relationships were similar to those previously established based on a dataset of eight chloroplast and mitochondrial genes [START_REF] Kawai | Ancestral reproductive structure in basal kelp Aureophycus aleuticus[END_REF]. These two transcriptome-based studies effectively resolved lower taxonomic-level phylogenetic relationships (infraordinal), but further studies are needed to improve resolving power at a higher level (i.e., interordinal level).

The objective of the study presented here was twofold: (1) to test the power of nuclear genome-based datasets for resolving inter and infraordinal phylogenetic relationships in brown algae and (2) to provide a reliable phylogenetic framework for trait-based phylogenetic analyses in the context of the Phaeoexplorer project.

Maximum likelihood and Bayesian phylogenomic trees were constructed based on the predicted amino-acid sequence data of 32 nuclear protein-coding genes in 39 brown algal species and two outgroup taxa selected in the Phaeoexplorer project.

Materials and methods

Taxa sampling

A total of 39 species of brown algae representing 24 genera, 16 families and eight orders (i.e., Desmarestiales, Discosporangiales, Dictyotales, Ectocarpales s.l., Fucales, Laminariales, Sphacelariales, Tilopteridales), in addition to two outgroup taxa, Schizocladia ischiensis E.C.Henry, K.Okuda & H. Kawai (class Schizocladiophyceae) and Phaeothamnion wetherbeei R.A.Andersen, L.Graf & H.S.Yoon (class Phaeothamniophyceae), selected in the Phaeoexplorer project, were used in the present study for the phylogenetic reconstructions (Table S1).

Culture conditions, DNA extraction, genome sequencing and assembly

Genomic DNA was extracted from laboratory-housed culture strains (Roscoff Culture Collection, Bezhin Rosko Culture Collection, Kobe University Macroalgal Culture Collection, Culture Collection of Algae at Göttingen University) or from specimens collected in the field (Table S1). For species with diplohaplontic life cycles, the gametophyte generation was grown in culture either in 140 mm Petri dishes or in 2-10 L bottles, the latter aerated by bubbling with sterile air. Standard growth conditions were sterile, Provosoli-enriched [START_REF] Starr | Utex-The culture collection of algae at the University of Texas at Austin 1993 List of Cultures[END_REF] natural seawater (ES medium) under fluorescent white light (10-30 µM photons/m 2 •s) at 13°C. The freshwater species Pleurocladia lacustris A.Braun and Heribaudiella fluviatilis (Areschoug) Svedelius were grown in natural seawater that had been diluted to 5% with distilled water (i.e., 95% distilled water / 5% seawater) before addition of ES medium (http://sagdb.uni-goettingen.de/culture_media/01%20Basal%20Medium.pdf) micronutrients, at 20°C for P. lacustris. Phaeothamnion wetherbeei was grown in MIEB12 (medium 7 in [START_REF] Schlösser | SAG-Sammlung von Algenkulturen at the University of Göttingen Catalogue of Strains[END_REF]). Material for fucoid species was collected on the seashore, and extractions used either dissected meristematic regions or released male gametes. DNA was extracted with either the Nucleospin Plant II midi DNA Extraction Kit (Macherey-Nagel, Düren, Germany) or the OmniPrep Genomic DNA Purification Kit (G Biosciences, St. Louis, MO, USA). DNA quality was assessed using a Qubit fluorometer (Themo Fisher Scientific, Waltham, MA, USA), and fragment length was assessed by migration on a 1% agarose gel for some of the samples. DNA (30-100 ng) was sonicated to a 100 to 800 bp size range using a Covaris E220 sonicator (Covaris, Woburn, MA, USA). Fragments were end-repaired, 3′-adenylated and Illumina adapters (Bioo Scientific, Austin, TX, USA) were then added using the NEBNext Sample Reagent Set (New England Biolabs, Ipswich, MA, USA). Ligation products were purified using Ampure XP (Beckmann Coulter Genomics, Danvers, MA, USA), and DNA fragments (>200 bp) were PCR amplified using Illumina adapter-specific primers and the KAPA HiFi HotStart polymerase (KapaBiosystems, Wilmington, MA, USA). Libraries were quantified by qPCR using the KAPA Library Quantification Kit for Illumina Libraries (KapaBiosystems), and library profiles were assessed using a DNA High Sensitivity LabChip kit on an Agilent Bioanalyzer (Agilent Technologies, Santa Clara, CA, USA). Some samples were prepared according to the same protocol but with less DNA input (10-25ng) and using the NEBNext Ultra II DNA Library Prep Kit for Illumina (New England Biolabs).

Illumina short read sequence data (150 bp paired end sequence) was generated on either a HiSeq4000 or a NovaSeq6000 platform. The sequence data was first assembled with Megahit [START_REF] Li | MEGAHIT: an ultra-fast single-node solution for large and complex metagenomics assembly via succinct de Bruijn graph[END_REF], and eukaryotic contigs were separated from the bacterial contigs using a gene detection strategy based on Metagen and Blastp. The bacterial contigs were then used to filter the initial dataset by mapping Illumina reads to the contigs with BWA and then removing these reads, which were not of eukaryotic origin. The set of filtered Illumina reads were then assembled with SPAdes [START_REF] Bankevich | SPAdes: a new genome assembly algorithm and its applications to single-cell sequencing[END_REF] using the standard protocol.

Identification of orthologous single-copy genes

Genomes were predicted from Schizocladia ischiensis and 23 Phaeophycean species that belong to various orders (Table S1). Predicted genomes were analyzed with OrthoFinder v.2.3.11 [START_REF] Emms | OrthoFinder: solving fundamental biases in whole genome comparisons dramatically improves orthogroup inference accuracy[END_REF] to detect orthologous single-copy genes. The program detected a total of 32 single-copy genes, which were used in the phylogenetic analyses. Table S2 presents a list of the 32 orthologues in the reference Ectocarpus sp.7 strain Ec32 genome. For Phaeothamnion wetherbeei and the other 16 species, orthologous amino acid sequences were retrieved using the "tblastn" function of BLAST+ 2.6.0 [START_REF] Camacho | BLAST+: architecture and applications[END_REF].

Phylogenetic analyses

Amino acid sequences of the thirty-two single-copy genes were aligned manually using the alignment software AliView v.1.26 [START_REF] Larsson | AliView: a fast and lightweight alignment viewer and editor for large datasets[END_REF]. The aligned sequences were concatenated (41 OTUs, 15,597 amino acids (aa)) and subjected to Maximum likelihood (ML) and Bayesian (BI) analysis. For ML analysis, 10,000 Rapid Bootstrap searches and the subsequent ML search with gamma model were conducted using RAxML v.8.2.9 [START_REF] Stamatakis | RAxML version 8: a tool for phylogenetic analysis and post-analysis of large phylogenies[END_REF]. Bayesian analyses were performed using MrBayes v.3.2.2 [START_REF] Ronquist | MrBayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space[END_REF]. The best-fit evolutionary models for each gene were determined on the basis of AIC for ML and BIC for BI using Kakusan4 [START_REF] Tanabe | Kakusan4 and Aminosan: two programs for comparing nonpartitioned, proportional and separate models for combined molecular phylogenetic analyses of multilocus sequence data[END_REF] (Table S2). The Bayesian analyses were initiated with a random starting tree, and four chains of Markov chain Monte Carlo iterations were run simultaneously for 10,000,000 generations, keeping one tree every 100 generations.

The first 10,000 trees sampled were discarded as 'burn-in', based on the stationarity of log-likelihood as assessed using Tracer v.1.7.1 [START_REF] Rambaut | Posterior summarisation in Bayesian phylogenetics using Tracer 1.7[END_REF]. A consensus topology and posterior probability values were calculated from the remaining trees.

Results

Data Characteristics

We assembled a 41-species dataset based on 32 nuclear genes (Tables S2,S3) from 39 species of Phaeophyceae, belonging to 24 genera, 16 families and eight orders (Desmarestiales, Discosporangiales, Dictyotales, Ectocarpales, Fucales, Lamiariales, Sphacelariales, Tilopteridales), together with one species from the Schizocladiophyceae (Schizocladia ischiensis) and one species from the Phaeothamniophyceae (Phaeothamnion wetherbeei), which served as outgroups (Table S2). The gene matrix was 95.6% complete and the dataset contained 15,597 aa (Table S2).

Phylogenetic relationships

ML and BI analyses of the 32-nuclear concatenated genes in the 41-species dataset produced trees with identical topology except for the placement of the Sphacelariales in relation to the Dictyotales (Figs 1, S1). In both analyses, placement of the Sphacelariales was poorly supported with a BS of 53 % and a Bayesian posterior probability (BPP) of 59 %. Eighty-two percent of the 38 brown algal nodes were fully supported in the ML analysis (i.e., 100 % BS) and 95 % in BI analysis (i.e., 100 % BPP). Five nodes within the genus Ectocarpus yielded BS values of 81 to 99 %. The seven inter-family relationships presented 99 -100 % BS and BPP support, and the seven interordinal relationships were fully supported for both BS and ML analyses with the exception of the Sphacelariales. Porterinema fluviatile (H.C.Porter) Waern (SAG 2381) positioned among the Ectocarpales as a sister to the Chordariaceae.

Discussion

Morphology and gene-based studies of higher-level brown algal phylogeny have a long history [START_REF] De Reviers | Classification of the Phaeophyceae from past to present and current challenges[END_REF][START_REF] Draisma | A reassessment of phylogenetic relationships within the Phaeophyceae based on RUBISCO large subunit and ribosomal DNA sequences[END_REF][START_REF] Silberfeld | A multi-locus time-calibrated phylogeny of the brown algae (Heterokonta, Ochrophyta, Phaeophyceae): investigating the evolutionary nature of the "brown algal crown radiation[END_REF][START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF]. However, many higher-level relationships remain problematic, even with the major improvements that have resulted from multi-gene methodologies [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF][START_REF] Silberfeld | A multi-locus time-calibrated phylogeny of the brown algae (Heterokonta, Ochrophyta, Phaeophyceae): investigating the evolutionary nature of the "brown algal crown radiation[END_REF]. Recent studies have demonstrated the value of studies based on multi-gene data from organellar [START_REF] Cui | The complete chloroplast genome of Sargassum horneri and its phylogenetic analysis[END_REF]Liu and Pang, 2015a, b;[START_REF] Liu | Understanding the evolution of mitochondrial genomes in Phaeophyceae inferred from mitogenomes of Ishige okamurae (Ishigeales) and Dictyopteris divaricata (Dictyotales)[END_REF][START_REF] Liu | The complete chloroplast genome of Sargassum fusiforme[END_REF][START_REF] Wu | The complete chloroplast genome of Sargassum hemiphyllum var. Chinense (Sargassaceae, Phaeophyceae) and its phylogenetic analysis[END_REF][START_REF] Zhang | Characterization of the complete chloroplast genome of Sargassum fusiforme and its phylogenomic position within phaeophyceae[END_REF] and nuclear genomes [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] for solving higher-level relationships in the Phaeophyceae. The current study was based on higher ordinal coverage of protein-coding nuclear genes to assess the resolving power of protein-coding nuclear genes in brown algae at this taxonomic level.

The approach used for the current study significantly improves on previous analyses. With the exception of Sphacelariales, interordinal relationships were fully resolved in the current study. [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] used a similar approach to resolve interordinal relationships, but it is difficult to compare our results with this earlier study, as it was based on different nuclear genes and taxon sampling. However, some conclusions can still be drawn. First, our study included a smaller number of nuclear genes (32 vs. 108 genes), but comprised a higher number of taxa (39 vs. 18 species, 24 vs. 10 genera, 16 vs. seven families, and eight vs. six orders) than that of [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF]. The strong branch support obtained by our phylogenetic analyses indicates that the nuclear genes selected in this study are sufficient to generate a robust molecular higher-level phylogeny, although the number of genes are lower than that used by [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF]. Testing the quantity of sequence data required for strong node support (e.g., [START_REF] Wortley | How much data are needed to resolve a difficult phylogeny? Case study in Lamiales[END_REF] will facilitate targeted inclusion of additional taxa in future studies. Second, a better taxonomic representativity of the different orders seems to increase node robustness in our study. Five of the orders analyzed by [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] were also analyzed in our study, but we did not include any members of the Ishigeales.

Another important difference with [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] concerns the choice of outgroup.

In their study, they used a distant outgroup, i.e., the diatom Phaeodactylum tricornutum (Bacillariophyceae), which caused a very long branch and may have affected the ingroup taxa relationships and caused lower bootstrap supports [START_REF] Li | Long-branch attraction and the phylogeny of true water bugs (Hemiptera: Nepomorpha) as estimated from mitochondrial genomes[END_REF], while we used closely related outgroups, i.e., Scizocladiophyceae and Phaeothamniophyceae, which is recommended, when distantly related ingroup taxa are poorly sampled [START_REF] Li | Long-branch attraction and the phylogeny of true water bugs (Hemiptera: Nepomorpha) as estimated from mitochondrial genomes[END_REF], as it is the case in [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] and our studies.

The taxa analyzed by [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] were biased towards Fucales and Ectocarpales, and our study mainly towards Ectocarpales. The [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] analysis included four brown algal crown radiation (BACR) orders and our study five. In line with previous multi-gene studies, both studies conclusively resolved the sister relationship between the Ectocarpales and the Laminariales. The [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] analysis did not fully resolve relationships among the BACR orders (Desmarestiales, Ectocarpales, Fucales, Laminariales), but interordinal relationships were fully resolved in our analyses (Desmarestiales, Ectocarpales, Fucales, Laminariales, Tilopteridales). Our analyses conclusively positioned the Desmarestiales as first divergence within the BACR with almost full support (BS = 99, BPP = 100). This stands in contrast with previous nuclear-and mitochondrial-based analyses (Liu and Pang, 2015a, b;Liu et al., 2019;[START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF], which positioned the Fucales basally in relation to the Desmarestiales. Nevertheless, in the mitochondrial-based analyses (Liu and Pang, 2015a, b;[START_REF] Liu | Understanding the evolution of mitochondrial genomes in Phaeophyceae inferred from mitogenomes of Ishige okamurae (Ishigeales) and Dictyopteris divaricata (Dictyotales)[END_REF], the ordinal taxon coverage was very limited, and in the nuclear-based analysis [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF], placement of the Desmarestiales and the Fucales was supported by lower BS values of 95 and 90, respectively. These low support values in [START_REF] Sun | Transcriptome-wide evolutionary analysis on essential brown algae (Phaeophyceae) in China[END_REF] may be explained by the long branch of the outgroup. Overall, these results indicate a beneficial effect of increased taxon sampling for phylogenetic inference in brown algae using protein-coding nuclear data. Since our dataset only encompassed eight of the 19 Phaeophyceae orders, we assume that increasing taxon sampling may further resolve the placement of Sphacelariales.

Interordinal relationships retrieved in this study were nearly identical to those established by [START_REF] Bringloe | Phylogeny and evolution of the brown algae[END_REF] based on 12 plastid, mitochondrial and nuclear markers (18S, 5.8S, 28S, atpB, psbA, psaB, psaA, rbcL, psbC, cox1, cox3, nad1), with the exception of the relationship between the Dictyotales and the Sphacelariales. The phylogenetic position of the Sphacelariales, associated to the monophyly of the Dictyotophycidae, was found to be unstable in previous studies. The weak support and unstable position of the Sphacelariales in most studies is possibly associated with incongruence among markers, with a weak phylogenetic signal and/or methodological bias. We assume that adding the missing orders for the Sphacelariales, Syringodermatales, Dictyotales, Onslowiales (SSDO) clade (i.e., Onslowiales and Syringodermatales) may help improving the resolution.

Our dataset included five out of the seven families of Ectocarpales, and relationships within Ectocarpales sensu lato were fully resolved. The Acinetosporaceae were positioned as a sister group to the Chordariaceae. Familial relationships within the Laminariales were fully supported and identical to the most up-to-date phylogeny of this order based on genomic data [START_REF] Starko | A comprehensive kelp phylogeny sheds light on the evolution of an ecosystem[END_REF]. For Porterinema fluviatile, it should be noted that strain SAG 2381 differs genetically from strain SAG 124.79 [START_REF] Mccauley | Taxonomic reappraisal of the freshwater brown algae Bodanella, Ectocarpus, Heribaudiella, and Pleurocladia (Phaeophyceae) on the basis of rbcL sequences and morphological characters[END_REF], which are both from the Culture Collection of Algae at Göttingen University (SAG). SAG 2381 was positioned within the Ectocarpales in this study, while SAG 124.79 was positioned basally among the brown algae [START_REF] Draisma | A revised classification of the Sphacelariales (Phaeophyceae) inferred from a psb C and rbc L based phylogeny[END_REF][START_REF] Mccauley | Taxonomic reappraisal of the freshwater brown algae Bodanella, Ectocarpus, Heribaudiella, and Pleurocladia (Phaeophyceae) on the basis of rbcL sequences and morphological characters[END_REF]. Molecular and morphological analyses of the culture strains of SAG 2381, SAG 124.79, and Pilinia rimosa collected from various localities worldwide indicated that SAG 2381 is the true P. fluviatile displaying the characteristic plurilocular zoidangia, whereas SAG 124.79 is in fact P. rimosa [START_REF] Kawai | Transfer of Pilinia from Ectocarpales to Ishigeales (Phaeophyceae) with proposal of Piliniaceae fam. nov., and taxonomy of Porterinema in Ectocarpales[END_REF].

Conclusions

In conclusion, this study provides a valuable phylogenetic framework for the Phaeoexplorer project, which focuses on the study of the evolution of biological complexity in brown algae, and further evidence supporting the resolving power of protein-coding nuclear genes at inter-ordinal level in brown algae, demonstrating the interest of nuclear multi-gene analysis as a complementary tool to analysis of mitochondrial and chloroplast organellar genome data. Since the current study only included eight of the 19 orders of brown algae, much effort is still needed to provide a comprehensive phylogeny robustly resolving inter-ordinal relationships in brown algae. By comparing our results with previous studies, taxonomic sampling appears to be a major element in resolving interordinal relationships. In the data vs. taxa trade-off, it would therefore be better to give priority to taxonomic sampling. Given the satisfactory results based on the 32 nuclear genes included in the present study, we recommend that future studies make use of the same set of genes as a standard approach using whole-genome sequencing data.

Acknowledgements

We would like to thank the following colleagues for contributions to data production and treatment: Akira Peters (Behzin Rosco), Zofia Nehr, Olivier Godfroy, Delphine Scornet, Susana Coelho, Loraine Guéguen, Erwan Corre, Chloé Jollivet (Station Biologique de Roscoff), France Denoeud (Genoscope). We are grateful to Line Le Gall for her helpful comments on the manuscript. The authors thank the Japan Society for the Promotion of Science (JSPS) for financial support to SA and CV.

Funding

This work was supported by the France Génomique National infrastructure project Phaeoexplorer (ANR-10-INBS-09), the ERC grant SEXSEA (638240) and the JSPS Grant-in-Aid for Scientific Research (19F19796).

Figure legend

 S1. Algal specimens used in this study.

Table S2. List of strains and single-copy genes analyzed in this study with the coverage (%) for each species and for each of the single-copy genes. The new phylogeny provides a valuable tool for the study of the evolution of biological complexity in brown algae.


Lamtahri

Julien Chuquet
email: julien.chuquet@univ-rouen.fr

Prolonged deficit of gamma oscillations in the peri-infarct cortex of mice after stroke

Days and weeks after an ischemic stroke, the peri-infarct area adjacent to the necrotic tissue exhibits very intense synaptic reorganization aimed at regaining lost functions. In order to enhance functional recovery, it is important to understand the mechanisms supporting neural repair and neuroplasticity in the cortex surrounding the lesion. Brain oscillations of the local field potential (LFP) are rhythmic fluctuations of neuronal excitability aimed at synchronizing neuronal activity to organize information processing and plasticity. Although the oscillatory activity of the brain has been probed after stroke in both animals and humans using electroencephalography (EEG), the latter is ineffective to precisely map the oscillatory changes in the periinfarct zone where synaptic plasticity potential is high. Here, we worked on the hypothesis that brain oscillatory system is altered in the surviving peri-infarct cortex, which may slow down functional repair and reduce the capacity to recovery. In order to document the relevance of this hypothesis, oscillatory power was measured at various distances from the necrotic core at 7 and 21 days after a permanent cortical ischemia induced in mice. Delta and theta oscillations remained at a normal power in the peri-infarct cortex, in contrast to gamma oscillations that displayed a rapid decrease, the closer we get to the lesion core. A broadband increase of power was also observed in the homotopic contralateral sites. Thus, the proximal peri-infarct cortex could become a target of therapeutic interventions aimed at correcting the oscillatory regimen. These results argue for the usefulness of therapeutic intervention aimed at boosting gamma oscillations in order to improve post-stroke functional recovery.

Introduction

Stroke remains the most frequent cause of disability stemming from the lack of efficient therapy to increase the magnitude of functional recovery. In the chronic stage following a focal brain ischemia, neuronal plasticity possibly leads to a regain of lost functions. The wiring of new circuits uses both established and de novo cellular materials, from spinogenesis to axonal sprouting [START_REF] Brown | In Vivo Voltage-Sensitive Dye Imaging in Adult Mice Reveals That Somatosensory Maps Lost to Stroke Are Replaced over Weeks by New Structural and Functional Circuits with Prolonged Modes of Activation within Both the Peri-Infarct Zone and Distant Sites[END_REF][START_REF] Carmichael | New patterns of intracortical projections after focal cortical stroke[END_REF][START_REF] Florence | Large-scale sprouting of cortical connections after peripheral injury in adult macaque monkeys[END_REF][START_REF] Murphy | Plasticity during stroke recovery: from synapse to behaviour[END_REF]Nudo and Milliken, 1996;Nudo et al., 1996;[START_REF] Stroemer | Enhanced neocortical neural sprouting, synaptogenesis, and behavioral recovery with D-amphetamine therapy after neocortical infarction in rats[END_REF][START_REF] Ueno | Intraspinal rewiring of the corticospinal tract requires target-derived brain-derived neurotrophic factor and compensates lost function after brain injury[END_REF]. The reorganization of neuronal networks potentially occurs in any structure involved in the relearning of a behavior. Intense plastic changes take place especially in the cortex adjacent to the ischemic lesion, the so-called peri-infarct cortex, where neurons are well alive but neural circuits are partially damaged [START_REF] Brown | Extensive turnover of dendritic spines and vascular remodeling in cortical tissues recovering from stroke[END_REF][START_REF] Murphy | Plasticity during stroke recovery: from synapse to behaviour[END_REF][START_REF] Stroemer | Neocortical neural sprouting, synaptogenesis, and behavioral recovery after neocortical infarction in rats[END_REF]. There is an increasing number of studies showing how the somatosensory-motor cortical activities of the affected limbs are progressively transferred and reorganized in the peri-infarct area [START_REF] Brown | In Vivo Voltage-Sensitive Dye Imaging in Adult Mice Reveals That Somatosensory Maps Lost to Stroke Are Replaced over Weeks by New Structural and Functional Circuits with Prolonged Modes of Activation within Both the Peri-Infarct Zone and Distant Sites[END_REF][START_REF] Carmichael | Brain Excitability in Stroke[END_REF][START_REF] Dijkhuizen | Correlation between tissue depolarizations and damage in focal ischemic rat brain[END_REF][START_REF] Sharma | Recovery of motor function after stroke[END_REF][START_REF] Tombari | A longitudinal fMRI study: in recovering and then in clinically stable sub-cortical stroke patients[END_REF][START_REF] Wang | Involvement of Notch1 signaling in neurogenesis in the subventricular zone of normal and ischemic rat brain in vivo[END_REF]. Progress from basic research also suggests that cellular and molecular mechanisms aimed at assembling neurons after stroke are similar to those identified during learning and memory formation in physiological context (e.g. long-term change of synaptic strength) [START_REF] Chervyakov | Possible Mechanisms Underlying the Therapeutic Effects of Transcranial Magnetic Stimulation[END_REF][START_REF] Cooke | Plasticity in the human central nervous system[END_REF][START_REF] Yu | Optochemogenetic Stimulation of Transplanted iPS-NPCs Enhances Neuronal Repair and Functional Recovery after Ischemic Stroke[END_REF]. However, the peri-infarct cortex is under the influence of various pathophysiological processes such as chronic inflammation and glial reactivity. It is not yet clear how and to what extent these micro-environmental conditions interfere with neuronal reconnection [START_REF] Skaper | An Inflammation-Centric View of Neurological Disease: Beyond the Neuron[END_REF][START_REF] Sochocka | Inflammatory Response in the CNS: Friend or Foe?[END_REF]. For instance, neuronal excitability, a determining factor for neuronal communication and synaptic plasticity, is reduced in the peri-infarct area, which has author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.03.05.978593 doi: bioRxiv preprint been demonstrated to limit functional recovery [START_REF] Clarkson | Reducing excessive GABA-mediated tonic inhibition promotes functional recovery after stroke[END_REF][START_REF] Carmichael | Brain Excitability in Stroke[END_REF]. Thus, a therapeutic goal to optimize recovery after acute brain damage is to normalize the conditions of neuronal communication.

Neural oscillations are rhythmic fluctuations of the brain electrical field potential (including membrane potential of neurons) that can be measured with extracellular electrodes placed into the cortex (local field potential, LFP) or with external electrodes placed over the scalp (electroencephalography, EEG). Several discrete frequency bands generated by different oscillators have been identified, from slow rhythms (e.g. delta band, 1-3 Hz) to fast rhythms (e.g. gamma band, 30-80 Hz). Each rhythm is more or less expressed depending on the brain state (i.e. wake vs. sleep) and the ongoing sensory, motor or cognitive activity. The fundamental role of these rhythmic fluctuations of neuronal excitability is to regulate action potentials trafficking by synchronizing the firing of multiple neuronal assemblies distributed across brain regions (Buzsáki 2007). Interestingly, an increasing number of studies show the potential importance of oscillations in neuronal plasticity [START_REF] Womelsdorf | Latent Connectivity: Neuronal Oscillations Can Be Leveraged for Transient Plasticity[END_REF][START_REF] Zarnadze | Cell-specific synaptic plasticity induced by network oscillations[END_REF]. For instance, reduction of theta (3-7 Hz) and gamma (30-80 Hz) activity has been correlated with decreased long term potentiation (LTP) [START_REF] Huerta | Heightened synaptic plasticity of hippocampal CA1 neurons during a cholinergically induced rhythmic state[END_REF][START_REF] Kalemaki | Mice With Decreased Number of Interneurons Exhibit Aberrant Spontaneous and Oscillatory Activity in the Cortex[END_REF][START_REF] Kalweit | Changes in Neuronal Oscillations Accompany the Loss of Hippocampal LTP that Occurs in an Animal Model of Psychosis[END_REF][START_REF] Stephan | Dysconnection in schizophrenia: from abnormal synaptic plasticity to failures of self-monitoring[END_REF][START_REF] Wespatat | Phase sensitivity of synaptic modifications in oscillating cells of rat visual cortex[END_REF][START_REF] Huerta | Heightened synaptic plasticity of hippocampal CA1 neurons during a cholinergically induced rhythmic state[END_REF][START_REF] Wespatat | Phase sensitivity of synaptic modifications in oscillating cells of rat visual cortex[END_REF][START_REF] Stephan | Dysconnection in schizophrenia: from abnormal synaptic plasticity to failures of self-monitoring[END_REF][START_REF] Kalweit | Changes in Neuronal Oscillations Accompany the Loss of Hippocampal LTP that Occurs in an Animal Model of Psychosis[END_REF][START_REF] Kalemaki | Mice With Decreased Number of Interneurons Exhibit Aberrant Spontaneous and Oscillatory Activity in the Cortex[END_REF]. Indeed, theta and gamma wave-bands are precisely tuned to dictate a timing of collective neuronal discharges that match the temporality of synaptic plasticity mechanisms, such as LTP or spike timing dependent plasticity (STDP) [START_REF] Bi | Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type[END_REF][START_REF] Buzsáki | Neuronal oscillations in cortical networks[END_REF][START_REF] Engel | Why does the cortex oscillate?[END_REF][START_REF] Harris | A role for lateral hypothalamic orexin neurons in reward seeking[END_REF][START_REF] Harris | Organization of cell assemblies in the hippocampus[END_REF][START_REF] König | Integrator or coincidence detector? The role of the cortical neuron revisited[END_REF][START_REF] Magee | A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons[END_REF][START_REF] Wespatat | Phase sensitivity of synaptic modifications in oscillating cells of rat visual cortex[END_REF]Nishiyama et al., 2010). Logically, the modification of network connections allowing functional recovery after a stroke requires that homeostatic mechanisms such as the maintenance of neuronal oscillatory activity stick to their operating range [START_REF] Buzsáki | Rhythms of the Brain[END_REF][START_REF] Llinás | Rhythmic and dysrhythmic thalamocortical dynamics: GABA systems and the edge effect[END_REF] author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.03.05.978593 doi: bioRxiv preprint [START_REF] Schnitzler | Normal and pathological oscillatory communication in the brain[END_REF]. Several tools are tested with the aim to precisely tune the oscillatory spectrum of the pathological brain by the mean of pharmacologic, optogenetic, transcranial magnetic, direct current or rhythmic sensory stimulation methods [START_REF] Guerra | Boosting the LTP-like plasticity effect of intermittent theta-burst stimulation using gamma transcranial alternating current stimulation[END_REF][START_REF] Lozano-Soldevilla | On the Physiological Modulation and Potential Mechanisms Underlying Parieto-Occipital Alpha Oscillations[END_REF]. Therefore, it is important to document the oscillatory conditions of the repairing cortex after stroke. In human, measuring the rhythmic activity of the post-stroke cortex is not new [START_REF] Carino-Escobar | Longitudinal Analysis of Stroke Patients' Brain Rhythms during an Intervention with a Brain-Computer Interface[END_REF][START_REF] Giaquinto | EEG recordings in the course of recovery from stroke[END_REF][START_REF] Zhang | EEG patterns from acute to chronic stroke phases in focal cerebral ischemic rats: correlations with functional recovery[END_REF] and in most cases the purpose was to find an early biomarker able to predict the quality of recovery [START_REF] Laaksonen | Alterations in spontaneous brain oscillations during stroke recovery[END_REF][START_REF] Nicolo | Coherent neural oscillations predict future motor and language improvement after stroke[END_REF][START_REF] Pfurtscheller | Central beta rhythm during sensorimotor activities in man[END_REF][START_REF] Tecchio | Rhythmic brain activity at rest from rolandic areas in acute mono-hemispheric stroke: a magnetoencephalographic study[END_REF][START_REF] Van Huffelen | Quantitative electroencephalography in cerebral ischemia. Detection of abnormalities in "normal[END_REF][START_REF] Zhang | EEG patterns from acute to chronic stroke phases in focal cerebral ischemic rats: correlations with functional recovery[END_REF][START_REF] Rabiller | Perturbation of Brain Oscillations after Ischemic Stroke: A Potential Biomarker for Post-Stroke Function and Therapy[END_REF]). But these studies were carried out with EEG or magnetoencephalography (MEG), whose spatial resolution is too low to probe the ~2 mm peri-infarct boundary extending from the edge of the core [START_REF] Ohab | A neurovascular niche for neurogenesis after stroke[END_REF][START_REF] Brown | Extensive turnover of dendritic spines and vascular remodeling in cortical tissues recovering from stroke[END_REF]. Therefore, little is known about the spatial extent of neural oscillatory changes around the necrotic neuronal mass. The aim of the present work was thus to describe how the oscillatory activity of the peri-infarct cortex evolves, one and three weeks after a focal cortical ischemia in mice.

Material and Methods

Study approval

Experiments, approved by the Ethics Committee for Animal Research of Normandy (CENOMEXA) and the French ministry of higher education, research and innovation, were conducted by authorized investigators in accordance with the recommendations of the European Community Council Directive 2010/63/UE of September 22.2010 on the protection of animals used for scientific purposes.

Stroke model

For these studies, 8-12-week-old (20-25g) male C57BL/6J mice were purchased from Janvier Laboratories. Anesthesia was induced with 5% isoflurane in an induction chamber. Following the loss of righting reflex, the mouse was rapidly transferred to a nose cone mask, and maintained with isoflurane (2-2.5%) delivered at 1 L/min in oxygen enriched air and 0.15 mg/kg of buprenorphine (Par Sterile Products) was injected i.p. Spontaneous breathing frequency was kept over 0.5 Hz and body temperature was strictly maintained at 37 ± 0.2°C throughout the surgery.

Focal ischemia was induced by the permanent occlusion of the left middle cerebral artery as reported previously [START_REF] Nawashiro | TNF-alpha pretreatment induces protective effects against focal cerebral ischemia in mice[END_REF][START_REF] Welsh | Effect of lactacidosis on pyridine nucleotide stability during ischemia in mouse brain[END_REF]. Briefly, a skin incision was made between the orbit and ear. Under an operating microscope, an incision was made, dividing the temporal muscle, and the left lateral aspect of the skull was exposed by reflecting the temporal muscle and surrounding soft tissue. The distal course of the middle cerebral artery was then visible through the translucent skull. A small burr-hole craniectomy was performed with a dental drill. The left middle cerebral artery was electrocoagulated by bipolar diathermy. The muscle and soft tissue were replaced, and the incision was sutured. In this model, ischemia is restricted to the neocortex. An analgesic (bupreorphine) was administered on the day of the surgery (0.015 mg/kg, s.c.) and on subsequent 2 days.

In vivo electrophysiology

Seven or 21 days after the occlusion of the middle cerebral artery, anesthesia was induced with 5% isoflurane in an induction chamber. Following the loss of righting reflex, the mouse was rapidly transferred to a nose cone mask and maintained with isoflurane (2-2.5%) delivered at 1 L/min in oxygen enriched air. A calibrated isoflurane dispenser with consistent and constant oxygen pressure was used to ensure reliable and reproducible delivery of specific isoflurane concentrations.

Animal was placed in a stereotaxic frame (Kopft Instrument), and 0.15 mg/kg of buprenorphine (Par Sterile Products) was injected i.p. and the eyes were protected with ophthalmic gel. Breathing frequency was maintained over 0.5 Hz and body temperature was strictly maintained at 37 ± 0.2°C throughout the surgery using a feedback-controlled heating pad. The head was shaved and disinfected with iodine, the cranium was exposed, and 3 small holes were drilled in the parietal bone and the dura-matter was incised with care to leave the cortex intact. Three Teflon-coated silver wire electrodes, 100 µm in diameter, were lowered into the cortex until layer 4.

Two electrodes were placed in the ischemic ipsilateral hemisphere at varying distances (<2.5mm) from the putative lesion border. The third electrode was placed in the contralateral hemisphere in homotopic position with the distal ipsilateral electrode. The 3 electrodes were secured to the skull with some dental cement (Paladur, DentalMedical). Two other electrodes were implanted in the cerebellum for reference and ground readings. After the surgical procedure, isoflurane was reduced to 1.1 ± 0.1% for a resting period of 45-60 min followed by the recording period.

Fifteen minutes of recording were performed twice with each electrode resulting in 6 different readings overall. At the end, anesthesia was elevated to 5% for a 5 min period followed by an intracardiac injection of saturated KCl solution inducing heart arrest.

Data acquisition and analysis

All in vivo recordings were done in a Faraday chamber and used an amplifier

Measurement of Infarct-electrodes distance

After the recording, under deep anesthesia, mice were killed, and 1 µL of black ink was slowly injected using a micropipette into the site of each ipsilateral electrode.

The brains were removed rapidly and frozen in cooled isopentane at -65°C for 10 seconds. Whole brains were cut in 20-μm-thick sections with a cryostat (Leica CM3050), and 1/5 serial sections were collected on a glass slide and stained by thionine. Thionine stained slides were scanned at a high resolution and imported into ImageJ. The Euclidian distance between ink spots and the closer lesion border was calculated.

Immunofluorescent labeling of GFAP

Reactive astrogliosis was assessed by immunofluorescent labeling for GFAP at 7 and 21 days post stroke. Brains were sectioned and every 5 th section (20 μm thick) was collected and stored in cryopreservation solution until used. Sections were rinsed in buffered saline and transferred to 1% BSA in tris-buffered saline (TBS) for 10 min at room temperature, followed by a second TBS rinse. The sections were blocked for 30 min in TBS containing 2% donkey serum with 0.3% Triton X-100 before being incubated in TBS with 2% donkey serum and 0.3% triton X-100 containing the primary antibody rabbit GFAP, 1:600 (ref Z033401-2, Agilent Dako) for 24 hours at 4°C. Ensuing incubation with primary antibody, sections were washed three times in TBS followed by incubation for 2 hours at room temperature in TBS with 2% normal donkey serum and 0.3% triton X-100 containing the fluorescent secondary antibody (Donkey anti rabbit Alexa-488, 1:300, A-21206, Invitrogen) and finally by the nuclear counter stain DAPI (1:1000, Sigma-Aldrich) in TBS for 5 min at room temperature. Images were taken with a Leica SP8 microscope, where two sections from each animal (n = 3) were included in the analysis.

Statistics

Data are presented as mean ± SEM. All statistics were performed using Prism software (Graphpad). A paired Student's t-test was used for pairwise comparisons.

Results

Cerebral ischemia was induced in mice using a variation of the well-characterized Tamura model [START_REF] Tamura | Focal cerebral ischaemia in the rat: 1. Description of technique and early neuropathological consequences following middle cerebral artery occlusion[END_REF] consisting in a permanent occlusion of a distal trunk of the middle cerebral artery. This procedure generated a reproducible focal lesion (8.5 ± 0.8 mm 3 at 48 h, n = 20 mice) representing about 12% of the volume of the entire ipsilateral cortex. Sham operated animals didn't present any lesion. In order to visualize the extent of the pathophysiological alteration of the surviving cortex adjacent to the necrotic core, the cellular reactivity of astrocytes, an endogenous biomarker for brain diseases, was investigated. Upregulation of GFAP is generally considered as a reliable maker for reactive astrocytes [START_REF] Escartin | Questions and (some) answers on reactive astrocytes[END_REF]. The immunostaining of GFAP showed a gradual decrease in intensity as we move away from the stroke border (Figure 1). At day 7 post-stroke, the upexpression of GFAP was most intense in a 315 ± 12 µm (n = 6 mice) zone surrounding the necrotic core, where a long leading process of each astrocyte was extended in the direction of the infarct (Figure 1A). Further away, a second peripheral area of 1552 ± 52 µm was defined by intense GFAP staining with protoplasmic shape astrocytes without preferred orientation of their processes (Figure 1A). Beyond, GFAP expression was no more different from its expression in the contralateral cortex (Figure 1Aa). At day 21, the glial scar was narrower (163 ± 3 µm) but overall, the glially-defined peri-infarct area was more extended (2320 ± 40 µm) (Figure 1B).

To test the hypothesis of an alteration of neural oscillatory activity around the cortical infarction, 3 electrodes were implanted in the cortex of the mouse brain, 7 or 21 days after MCAO. Two electrodes (E1 and E2) were placed in cortical layer 4 at various distances (< 4 mm) from the expected location of the lesion border (Figure 2A). The third electrode (E3) was placed in the layer 4 of the contralateral hemisphere, in mirror position with the nearest electrode from the lesion. In sham animals, two electrodes were place in mirror position, in the layer 4 of the barrel field cortex. After 45-60 min of rest under isoflurane anesthesia (1.1 ± 0.1%) and during which body temperature was strictly kept at 37 ± 0.2°C, each recording was done twice during 15 min at 7 days or 21 days. In such condition, the whitened power spectrum of LFP activity shows 3 distinct peaks at 1.8 ± 0.8 Hz, 4.5 ± 0.9 Hz and 36.4 ± 1.1 Hz, corresponding respectively to the delta (1 -3 Hz), the theta (4 -7 Hz) and the gamma (30 -50 Hz) waveband (Figure 2B). The other wavebands (alpha, beta, high gamma) were considered inactive. Sham operated animals didn't show any LFP spectrum power difference between the ipsilateral and the contralateral hemisphere (P > 0.05 for the three wavebands at both 7 and 21 days post-stroke, n = 4 animals, Figure 2B). Irrespective to their distance from the infarct border, averaging the power spectrum recorded by all ipsilateral electrodes showed a slight depression of the broadband cortical oscillatory power at day 7 post-stroke, compared with sham animal, albeit not significant (P > 0.05 for the 3 wavebands studied; n = 8 ipsilateral electrodes from 4 mice, Figure 2B). In contrast, the contralateral hemisphere showed a global increase in power, relative to sham animal. As a result, at 7 days, there was a significant difference of the theta and the gamma waveband power between the contralateral and the ipsilateral (66.8 ± 0.5 dB vs. 63.3 ± 1.8 dB for theta, P < 0.01; 72.5 ± 1.1 vs. 67.3 ± 1.5 for gamma, P < 0.05; n = 8 ipsilateral electrodes from 4 mice Figure 2B). At day 21 post-stroke, the ipsilateral power spectrum (irrespective to electrodes position) moved toward normalization relative to sham (Figure 2C), while the LFP power of the contralateral cortex remained significantly increased for the delta (P < 0.01), the theta (P < 0.05) and the gamma wavebands relative to the ipsilateral LFP power (P < 0.05; n = 5 contralateral electrodes and n = 10 ipsilateral electrodes from 5 mice, Figure 2C andD).

To investigate the spatial relation between the oscillatory activity and the extent of the glially defined peri-infarct area, the scar border-to-electrodes distances were measured precisely by histological analysis, using ink labeling as a marker of the electrode sites. No significant correlation between the ipsilateral LFP power and the distance from the infarct border was found for the delta and the theta waveband at 7 or 21 days post-stroke (7 days: P > 0.05, n = 8 electrodes from 4 mice; 21 days: P > 0.05, n = 10 electrodes from 5 mice; Figure 3A andB). However, for the gamma waveband (30-50 Hz), there was a significant positive relationship between LFP power and distance to the infarct border at both 7 and 21 days post-stroke (7 days: r(6) = 0.912; P < 0.05, n = 8 electrodes from 4 mice; 21 days: r(8) = 0.752; P < 0.05, n = 10 electrodes from 5 mice; Figure 3A andB). The relationship was best described by a power function which equation was used to build a visual model showing the spatial extent of the gamma depression relative to the average location and size of the ischemic lesion (Figure 4).

Discussion

The main finding of this study is that the cortex surrounding an ischemic lesion undergoes a long-lasting deficit in gamma (30-50 Hz) oscillatory power, the latter being an emerging neurophysiological determinant of neural communication and plasticity.

In human, the highest potential for recovery is observed within the first 3 months after stroke [START_REF] Biernaskie | Efficacy of rehabilitative experience declines with time after focal ischemic brain injury[END_REF]. In rodent models of focal cerebral ischemia, this critical period of plasticity corresponds to the first 4 weeks, after which functional recovery gains are no more significant [START_REF] Brown | Extensive turnover of dendritic spines and vascular remodeling in cortical tissues recovering from stroke[END_REF][START_REF] Dijkhuizen | Functional magnetic resonance imaging of reorganization in rat brain after stroke[END_REF].

We chose to study the spontaneous oscillatory activity of the repairing cortex under anesthesia to avoid the stochastic changes of the oscillatory pattern associated with the awake state and favor the stability and the reproducibility of an internally driven regimen [START_REF] Lustig | Oscillatory patterns in hippocampus under light and deep isoflurane anesthesia closely mirror prominent brain states in awake animals[END_REF]. Isoflurane is a well-known depressor of cortical activity [START_REF] Land | Auditory Evoked Bursts in Mouse Visual Cortex during Isoflurane Anesthesia[END_REF], however at ~1%, we systematically observed a LFP oscillation pattern composed of three peaks reminiscent of the delta, theta and gamma frequencies in the awake mice.

We found no clear differences with control animals for delta and theta power at 7 and 21 days post-stroke in the neighborhood of the lesion. Neither the necrotic environment nor the loss of proximal afferent fibers seems to prevent peri-infarct neural networks to oscillate at these frequencies. A similar conclusion could have been drawn for gamma oscillations when averaging their power over the entire periinfarcted zone. However, our detailed analysis revealed an accelerating collapse of gamma power the closer we get from the lesion. The extent of the deficit spanned 2 mm away from the glial scar, a distance matching many previous measurement of the peri-infarct cortex in the rodent brain [START_REF] Brown | Extensive turnover of dendritic spines and vascular remodeling in cortical tissues recovering from stroke[END_REF]. In the human brain, the extent is not proportionally bigger, but it represents an important volume of grey matter with high plasticity potential (Funck et al., 2016). As for the relevance of 2 mm of cortex, it represents the equivalent distance of 5 to 6 cortical columns in mice [START_REF] Tischbirek | In Vivo Functional Mapping of a Cortical Column at Single-Neuron Resolution[END_REF]. Moreover, cortical motor microcircuits are functional units organized in territory of 100 µm receiving local inputs from ~500 µm away (Amirikian and Georgopoulos 2003). Of note, plastic reorganization of neurons starts readily after the edge of the glial scar, that is, in the present case, ~160 µm from the necrotic core [START_REF] Brown | Extensive turnover of dendritic spines and vascular remodeling in cortical tissues recovering from stroke[END_REF]. These topological considerations emphasize the potential importance of this 2 mm strip of cortex for post-stroke functional recovery.

What is the origin of the selective depression of cortical gamma rhythm around the consolidated lesion? Seven and 21 days after stroke, peri-infarct neurons are still under the influence of inflammatory processes and glial reactivity. It could be argued that cell swelling or water content in the tissue changes its conductance in a magnitude such as gamma oscillations are less detected. This is however unlikely as several studies verified that the cortical tissue conductivity tested with an intracortical electrode show weak frequency dependence similar to cerebrospinal fluid [START_REF] Logothetis | Interpreting the BOLD signal[END_REF][START_REF] Miceli | Impedance Spectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level[END_REF]. Moreover, as suggested by Miceli et al. (2018) the filtering properties of the tissue itself should be a minor factor in shaping the LFP. Therefore, the origin of gamma depression in the periphery of the stroke lesion should be searched in the light of cell and neural network properties. Gamma oscillations are generated sporadically by local groups of cortical neurons spatially confined into the volume of a putative column [START_REF] Steriade | Synchronization of fast (30-40 Hz) spontaneous cortical rhythms during brain activation[END_REF] that is approximately 250 µm in diameter [START_REF] Tischbirek | In Vivo Functional Mapping of a Cortical Column at Single-Neuron Resolution[END_REF] beyond which the amplitude of a gamma oscillation decreases rapidly with distance [START_REF] Sirota | Entrainment of neocortical neurons and gamma oscillations by the hippocampal theta rhythm[END_REF]. Possibly, and in agreement with several studies suggesting patchy selective neuronal death into the surviving cortex, long after the consolidation of the ischemic lesion, the number of neurons required to generate enough gamma power is not met in this zone [START_REF] Baron | How healthy is the acutely reperfused ischemic penumbra?[END_REF][START_REF] Guadagno | Selective neuronal loss in rescued penumbra relates to initial hypoperfusion[END_REF].

Two other considerations can serve as food for thought regarding the origin of gamma deficit. Firstly, gamma oscillations are known to emerge from the interaction of parvalbumin interneurons and principal cells [START_REF] Buzsáki | Mechanisms of Gamma Oscillations[END_REF]. A selective reduction of these interneurons in the ipsilateral perilesional cortex has been associated with an improved plasticity and training-induced functional recovery [START_REF] Alia | Reducing GABA A -mediated inhibition improves forelimb motor function after focal cortical stroke in mice[END_REF][START_REF] Zeiler | Medial Premotor Cortex Shows a Reduction in Inhibitory Markers and Mediates Recovery in a Mouse Model of Focal Stroke[END_REF]. Future studies on the specific survival of these interneurons [START_REF] Baron | How healthy is the acutely reperfused ischemic penumbra?[END_REF] and the integrity of their perineuronal net (Härtig et al., 2017), will help to interpret the present observation. Secondly, several demonstrations have been made in the last decade showing that the hypoexcitability of peri-lesional neurons can be corrected by antagonists of GABA A R tonic inhibition to boost functional recovery [START_REF] Clarkson | Reducing excessive GABA-mediated tonic inhibition promotes functional recovery after stroke[END_REF]. Whether this excess of tonic inhibition can dampen the power of gamma oscillations is not clear (ref?). Outside of the cortex at least, reducing tonic inhibition leads to the emergence of gamma oscillations in hippocampal CA3 slices (ref?).

Little is known about gamma oscillation changes after stroke, since most studies have been done using EEG or EcoG with low spatial resolution and poor detection of frequencies above 30 Hz [START_REF] Lake | Functional magnetic resonance imaging in chronic ischaemic stroke[END_REF][START_REF] Rabiller | Perturbation of Brain Oscillations after Ischemic Stroke: A Potential Biomarker for Post-Stroke Function and Therapy[END_REF]. Here we found that gamma power is strongly and persistently depressed in a cortical area that closely matches with the peri-infarct zone described as a primary reservoir of neuronal plasticity. Since gamma abnormalities have been associated with many brain disorders of very different pathophysiologic background [START_REF] Woo | Gamma oscillation deficits and the onset and early progression of schizophrenia[END_REF], it is tempting to consider that it is simply an epiphenomenon resulting from perturbation of cerebral cortical network functions, only useful as a good sensitive clinical readout [START_REF] Woo | Gamma oscillation deficits and the onset and early progression of schizophrenia[END_REF]. However, the role of gamma oscillations in synaptic plasticity is increasingly suggested. Synaptic strengthening or weakening required to build new neuronal networks as a result of learning -and most likely of re-learning after a brain lesion-is an activity-dependent process driven by the principle of temporal coincidence of pre-and post-synaptic firing (Hebb, 1949). Oscillation of neuronal membrane potential at the gamma frequency allows synchronized neuronal firing within a temporal window that is optimal for STDP process [START_REF] Engel | Why does the cortex oscillate?[END_REF][START_REF] König | Integrator or coincidence detector? The role of the cortical neuron revisited[END_REF][START_REF] Magee | A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons[END_REF][START_REF] Bi | Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type[END_REF][START_REF] Buzsáki | Neuronal oscillations in cortical networks[END_REF][START_REF] Wespatat | Phase sensitivity of synaptic modifications in oscillating cells of rat visual cortex[END_REF][START_REF] Harris | Organization of cell assemblies in the hippocampus[END_REF][START_REF] Harris | A role for lateral hypothalamic orexin neurons in reward seeking[END_REF]. In other words, under a gamma rhythm of oscillation, the probability to associate pertinent information to assemble a neuronal circuit, increases. In support of the role of gamma oscillation in plasticity, several studies have demonstrated that the power of hippocampal gamma oscillation during learning predicts the quality of the recall (Sederberg et al., 2003(Sederberg et al., , 2007;;Headley and Paré, 2017). More compelling demonstrations are certainly necessary to prove a causal role of gamma oscillations in cortical synaptic plasticity and it remains to be shown that gamma deficit is actually associated with poor plasticity and functional recovery. But based on this concept, a lot of efforts are being carried out to stimulate the human brain with transcranial alternative electric current (tACS) at a specific frequency supposed to entrain natural oscillations and boost network plasticity (see [START_REF] Bland | Current challenges: the ups and downs of tACS[END_REF] for a recent update). While many challenges are still ahead to understand the neurobiology behind the observed effect, encouraging data suggest that tACS delivered at gamma frequency can be used to improve motor performance in humans [START_REF] Guerra | Boosting the LTP-like plasticity effect of intermittent theta-burst stimulation using gamma transcranial alternating current stimulation[END_REF].

The cease of inputs originating from the necrotic cortex causes a functional imbalance in many regions of the brain, not necessarily directly connected to dead neurons. This phenomenon named diaschisis, describes changes of neuronal activity that will positively or negatively contribute to the reorganization of brain circuits [START_REF] Reggia | Neurocomputational models of the remote effects of focal brain damage[END_REF]. One of the most obvious expressions of diaschisis after a cortical stroke is the activity change of the homotopic contralateral area. Both clinical and pre-clinical studies have shown hyperactivity in the contralateral cortex due to disinhibition [START_REF] Andrews | Transhemispheric diaschisis. A review and comment[END_REF][START_REF] Brown | In Vivo Voltage-Sensitive Dye Imaging in Adult Mice Reveals That Somatosensory Maps Lost to Stroke Are Replaced over Weeks by New Structural and Functional Circuits with Prolonged Modes of Activation within Both the Peri-Infarct Zone and Distant Sites[END_REF][START_REF] Dijkhuizen | Functional magnetic resonance imaging of reorganization in rat brain after stroke[END_REF][START_REF] Tombari | A longitudinal fMRI study: in recovering and then in clinically stable sub-cortical stroke patients[END_REF][START_REF] Cramer | Harnessing neuroplasticity for clinical applications[END_REF]. However, this increase in "activity", whether measured by an increase of firing rate, excitability or neurovascular signaling is not necessarily accompanied by an increase of neuronal synchronization and therefore of oscillatory power. In the present study, we found an increase of the broadband LFP power of the contralateral cortex, mostly 3 weeks after stroke. The origin of this power increase is unlikely due to a genuine enhancement of the activity of each frequency-band oscillator but most likely due to an enlargement of the neuronal population entrained into these rhythms, because 1/ while the homotopic contralateral cortex displays an increased power in delta and theta wavebands, the peri-infarct cortex displays no change in delta and theta power at 21 days, irrespective to the distance with the lesion, suggesting that theta and delta subcortical oscillators deliver stable inputs; 2/ it is well known that a stroke induced transcallosal disinhibition is amplified by a downregulation of GABA receptor [START_REF] Buchkremer-Ratzmann | Electrophysiological transcortical diaschisis after cortical photothrombosis in rat brain[END_REF][START_REF] Kokinovic | Loss of GABAB -mediated interhemispheric synaptic inhibition in stroke periphery[END_REF] and a concomitant up regulation of NMDA receptor [START_REF] Qü | Bihemispheric reduction of GABAA receptor binding following focal cortical photothrombotic lesions in the rat brain[END_REF] in the contralesional cortex.

Whether the increase of oscillatory power in the contralateral hemisphere is associated with favorable or unfavorable recovery, remains to be clarified [START_REF] Kokinovic | Loss of GABAB -mediated interhemispheric synaptic inhibition in stroke periphery[END_REF][START_REF] Marshall | Evolution of cortical activation during recovery from corticospinal tract infarction[END_REF][START_REF] Silasi | Stroke and the Connectome: How Connectivity Guides Therapeutic Intervention[END_REF].

In conclusion, the present work leads to the hypothesis that gamma deficit may slow down the process of synaptic reorganization occurring during the period of poststroke recovery. Accordingly, this result argues for the usefulness of therapeutic intervention aimed specifically at boosting gamma oscillations in order to enhance post-stroke functional recovery.

Legends

  PowerLab 8/35 (AD-Instrument). Raw data were acquired with Labchart software (AD Instrument). The extracellular signals were amplified (10000×), bandpass filtered (0.1 Hz to 100 Hz) for the local field potential (LFP) and acquired continuously at 4 kHz. In addition, a notch filter was added to eliminate the 50 Hz band noise. For spectral analysis of oscillatory patterns (epoch of 15 min), a modified version of the multitaper FFT MATLAB package by Mitra and Pesaran (1999) was used: FFT window size of 4 s, three to five tapers, frequency bins = 0.15 Hz, no overlap between successive windows, time bandwidth = 3 (Mitra and Pesaran, 1999; Quilichini et al., 2010).

Figure 1 .

 1 Figure 1. Astroglial identification of the peri-infarct cortex. GFAP immunostaining of a coronal section of the mouse brain 7 days (A) and 21 days (B) after MCAO. Four regions of interest were identified: a. the contralateral cortex where GFAP immunoreactivity is low; b. the distal ipsilateral cortex where the level of GFAP expression is as low as in the contralateral cortex; c. the proximal ipsilateral cortexwhere astrocytes are strongly GFAP-positive; d. the border of the infarction, the glial scar, where astrocytes express high level of GFAP with a long leading process oriented toward the lesion (or the cavity). Hence, 3 distinct zones were define, the extent of which is reported in the horizontal stacked bar down to panel A and B (average Euclidian length of each zone ± SEM; n = 3 mice per time point).

Figure 2 .

 2 Figure 2. Spectral analysis of the LFP activity of the peri-infarct cortex. A. Left: experimental arrangement. Three electrodes were implanted for sequential recordings of 15 min in the ipsilateral cortex (E1 and E2) and in the contralateral cortex (E3); R: reference electrode. Right: a representative ischemic lesion 48h after the MCAO procedure. Whitened power spectrum (1-80 Hz) obtains at 7 days (B) and 21 days (C) in sham and ischemic animal. Note the three distinct peaks

Figure 3 .

 3 Figure 3. Analysis of LFP power change relative to the distance from the cortical infarct. At each time point, (A: 7 days; B: 21 days) LFP power and the distance between peri-infarct electrodes and the lesion border where plotted to test the hypothesis of a correlation. No correlation where found for delta and theta.However, the power of gamma oscillation (30-50 Hz) showed a strong correlation with the distance from the infarct border. The green background indicates the limits of the astroglial scar (dark green) and the peri-infarct zone (light green) as reported in figure 1.

Figure 4 .

 4 Figure 4. Model of gamma deficit in the cortical environment of an ischemic lesion. Based on the 2 power functions best describing the significant correlations obtained in Figure 3, a spatial modelization of gamma power deficit in the periinfarcted cortex was drawn. Top: three examples of raw LFP band-pass filtered (30-50Hz) recorded at various distances from the infarction, 7 days after MCAO.

  Figure1

Acknowledgment

This work was supported by INSERM (U1239), Rouen University, the Fondation pour la Recherche sur les AVC, the Normandy Region and the European Union (3R project). Europe gets involved in Normandy with European Regional Development Fund (ERDF).


Amani Abdallah

Hassina Kada

Toufik Kanit

Abdelwaheb Amrouche

DETERMINATION OF THE MECHANICAL PROPERTIES OF CEMENTITIOUS MIXTURES WITH SEDIMENTS: EXPERIMENTAL AND NUMERICAL APPROACHES

Keywords: Dredged sediments, Mechanical properties, SEM, Indentation, Homogenization

Sediment management is increasingly oriented towards valorization processes in several fields. Many researches have been conducted on the characterization of sediments and the possibility to be used as raw materials in the field of civil engineering. The overall objective of this contribution is to set-up a numerical modeling strategy with a validation on the basis of experimental results. The mechanical strengths (flexural and compressive) and the elastic modulus were investigated. Five mortars were formulated with different substitution of sand by sediments (from 0% to 40%). A numerical model was built using the finite element method (FEM) based on homogenization technique. This model allows the prediction of the global mechanical behavior of the mortars based on the knowledge of the mechanical behavior of each phase constituting these samples. The model was validated through an example of a microstructure of a BOF (Basic Oxygen Furnace) slag from literature work. The microstructure has been observed using Scanning Electron Microscope SEM in order to identify the major phases in presence. Besides, the elastic properties of these phases have been determined using an instrumented indentation technique coupled with SEM. The obtained results show a good agreement between numerical and experimental. The model is validated and can then be applied on the mortars. The mechanical properties of the formulated mortars decrease with the increase of sediment substitution similarly to the obtained results in literature.

INTRODUCTION

The accumulation of sedimentary particles at the bottom and on the edges of watercourses and shipping lanes as well as in seaports leads to their clutter. For navigable waterways, it slows the flow and prevents activities of transportation. In order to maintain and restore these accesses, it is necessary to dredge or clean up regularly from coast and estuarine lines throughout the world. Currently, the French, European and international legislation aim to preserve the environment. In this context, due to the shortages of natural resources and the sustainable development approach adopted by several countries, sediment management is increasingly oriented towards valorization processes by respecting technical, environmental and economic criteria. Many studies on the reuse of sediments in mortar or concrete were investigated [START_REF] Meyer | The greening of the concrete industry[END_REF][START_REF] Aoual-Benslafa | Durability of mortars made with dredged sediments[END_REF][START_REF] Couvidat | Feasibility of the reuse of total and processed contaminated marine sediments as fine aggregates in cemented mortars[END_REF][START_REF] Wang | Solidification/stabilization of dredged marine sediments for road construction[END_REF]. Some authors investigated the possibility of using sediments as replacement of sand in the cement-based materials while others as a replacement of cement.

All the previous researches on the valorization of sediments lies on experimental work. High number of tests should be performed in order to assess the influence of sediments on the formulated materials.

The aim of this study is to provide a new approach for valorization based on a numerical model. This approach is very challenging due to the different techniques needed for the developed model. Besides an experimental approach is conducted on five formulations of mortars with different substitution percentages of sand by uncontaminated marine sediments.

MATERIALS AND EXPERIMENTS

Cement

For the formulation of mortars, a Portland cement CEM I 52.5N has been used. It is composed of over 95% of clinker and less than 5% of secondary components. It is a rapid hardening cement for early strength or higher strength class. It has a density of 3.14 g/cm 3 .

Sand

CEN siliceous sand (according to EN 196-1), with rounded grains was used (Class 0/5). This sand has a density of 2.6g/cm 3 .

Sediments

The used marine sediments were dredged in the port of Dunkirk (GPMD) located in the North of France. Leaching tests of the raw sediments were conducted in accordance with the European standard EN 12457-2 (2002). These tests allow the determination of the proportions of heavy metals and pollutants leached. The results are shown in Table 1. The values obtained are compared with the inert waste reference thresholds ISDI (Decree of October 28, 2010 concerning inert waste storage facilities). They are also served to evaluate the degree of sediment's pollution. For the used sediments, the determined values are below the threshold values with the exception of antimony (Sb) and molybdenum (Mo). Thus, the studied raw sediments are categorized as nonhazardous waste according to the French legislation.

Experiments

Formulation

Five mortars were formulated for which the siliceous sand being replaced by the same volume of sediment at replacement percentage of 0%, 5%, 15%, 30% and 40%. In the following, the mortars will be referred to MT, MT5, MT15, MT30 and MT40 respectively. Table 2 presents the composition of the various formulations investigated in 1L of volume. Note that the sediments were pre-saturated before any mixing. The effective water-to-cement (W/C) ratio was kept constant (0.49) for all formulations. These formulations were prepared according to the mixture procedure described in the European standard EN 196-1. For each mixture, three prismatic samples of 4×4×16cm 3 were prepared and cured until 28 days.

Mechanical strength

The mechanical strength of the prismatic mortar samples (4×4×16cm 3 ) were determined in accordance with the European standard EN 196-1. Flexural and compressive tests were carried out using a mechanical INSTRON testing machine. These tests were performed on the sediment-based mortars after being cured in water for 28 days. Results are the averages of three samples.

Elastic modulus

A method has been developed to determine the elastic modulus of the sediment-based mortars. It consists in recording the deformation of the tested specimen when subjected to a compression imposed by the INSTRON testing machine (with a displacement control). The elastic modulus E (MPa) is obtained from the slope of the elastic part of the stress-strain curve. The deformation was measured using a strain gage (SG) installed at one side of the tested specimen using an adequate glue (X60). The length of the strain gage as well as the displacement rate imposed by the compression machine were optimized in order to determine an accurate value of the elastic modulus.

Note that in order to compensate the effect of the temperature on the deformation result, a dummy gage (identical to the active strain gage) was installed on an unstrained sample of the same material as the tested specimen. In this way, the deformation caused by the temperature change in the dummy gage can be calculated and then subtracted to that given by the active gage to obtain at the end the real representative deformation of the material. The elastic modulus results are the averages of three measurements.

NUMERICAL MODEL

The mechanical behavior of the sediment-based mortars can be predicted numerically, avoiding the complicated and costly experiments. The mortar is a complex material with a variety of heterogeneities. The determination of the macroscopic response of such heterogeneous materials is of a great interest in engineering applications and large number of researches have been made in the last years [START_REF] Zohdi | Computational micromacro material testing[END_REF]. The method consists in determining the macroscopic elastic behavior through the knowledge of the mechanical behavior of each phase that constitutes the tested sample. A numerical model is built using the finite element method (FEM). This model is based on the homogenization technique (theory of effective properties), by which the heterogeneous material is replaced by an equivalent homogeneous continuum [START_REF] Fan | Concrete microstructure homogenization technique with application to model concrete serviceability[END_REF]. The latter should respond globally to any load in the same way as the heterogeneous original material. This technique is applied on a statistically representative sample of material, referred to as a representative volume element (RVE) [START_REF] Aboudi | Mechanics of Composite Materials: A Unified Micromechanical Approach[END_REF], [START_REF] Hill | Elastic properties of reinforced solids: some theortical principles[END_REF]. The main objective of this numerical homogenization is to predict the effective properties on the RVE. This approach has not been yet performed on sedimentbased mortars.

The microstructure of the mortar sample is obtained using a Scanning Electron Microscope (SEM) coupled with an Energy Detector Spectrometer (EDS). The major phases constituting the heterogeneous mortar can then be identified. The inputs of the finite element FE model are the elastic properties of each phase: elastic modulus E i and Poisson's ratio ν i . The Poisson's ratio was assumed as 0.2. The elastic modulus E i of each phase can be determined by means of a coupled system combining a Scanning Electron Microscope (SEM) and an instrumented indentation equipment [START_REF] Olivier | An improved technique for determining hardness and elastic modulus using load displacement sensing indentation experiments[END_REF], [START_REF] Betrancourt | Instrumented indentation study of slag in view of a better valorization[END_REF]. This step is the key to the developed model. The main advantage of this system is the capability of performing indentation tests in a specific area (a particular phase). A pre-treatment of the image representing the microstructure of the studied sample is necessary. The microstructure was segmented into scales of grey color using conventional image analysis/processing. Filters were used to eliminate the noise produced by the microscope. FE meshing was then performed using multi-phase element method. [START_REF] El Moumen | A multiscale approach and microstructure design of the elastic composite behavior reinforced with natural particles[END_REF]. This method consists of superimposing a regular FE mesh on each microstructure image. The obtained meshes were then introduced in the computation code. The image of the microstructure was used to attribute at each integration point, the mechanical behavior associated to the phases. Different density of meshes were applied to study the mesh sensitivity on the results. The mesh density is defined as the number of FE required to mesh the volume of heterogeneous material. For numerical simulations, a simple uniaxial compression test has been applied, defining the boundary conditions. A displacement is applied to one face of the microstructure while the opposite one is fixed. All the other faces are free. These conditions can be illustrated in Eq. ( 1):

  0 x) 0, face(y u     0 ) x 0, face(y v   (1)   d   ) x L, face(y v
where u and v are the applied displacements in x and y-directions, L is the numerical model length, and d is the imposed displacement in y-direction (Fig. 1).

Fig. 1 Boundary conditions for the numerical approach

The homogenized effective elastic modulus can then be determined. The algorithm of the numerical model is presented in Fig. 2.

RESULTS AND DISCUSSION

Experimental

The flexural and compressive strengths of the sediment-based mortars are presented in Fig. 3 and Fig. 4. Average values obtained by three measurements for flexural strength and six measurements for compressive strength are shown with the corresponding standard deviation. Both the flexural and compressive strength of mortars decreased with the proportion increase of sediment.

This result highlights the influence of sediments on the mechanical behavior of cemented-materials. The mechanical strength comes foremost from the formation of cemented products. The use of marine dredged sediments as aggregates, compared to sand, may alter the hydrating processes. Organic matter which is contained in sediments are especially known to interfere with the hydration process of cement [START_REF] Tremblay | Influence of the nature of organic compounds on fine soil stabilization with cement[END_REF]. The marine sediments contain also chloride salts. Their high salinity has a negative effect on the mechanical strength development of cement-based materials [START_REF] Siham | Marine dredged sediments as new materials resource for road construction[END_REF]. Besides, traces of metals are presented in these sediments (Table 1). All of them even with small concentrations can influence the quality of the obtained mortars. They might affect adversely the mechanical strength by changing the mortar's average porosity. The influence of sediments can be refined by presenting the percentage of the compressive strength of sediment-based mortars with respect to the unsubstituted reference mortar (MT) as a function of sediment percentage (Fig. 5). The compressive strengths of mortars decrease linearly with the amount of substitution of sand by sediment up to 30% of replacement. Between 30% and 40%, the decrease is barely noticed. For MT5, the compressive strength attains 87% with respect to MT while 62% for MT15, 31% for MT30 and 28%. For MT40. Substituting more than 30% of sand by sediment has no additional effect on the mechanical behaviour of mortars. This result can be explained by the repartition of particles in the microstructure of the cemented-materials. The average elastic modulus and the standard deviation of three measurements for each mixture of sediment-based mortars are presented in Table 3. The errors on the measurements are less than 5%. The percentage of the elastic modulus of mortars with respect to the unsubstituted reference mortar (MT) is also shown. The elastic modulus E decreases when the percentage of replacement of sand by sediment increase. The variation of E with respect to MT is s similar to the results obtained in Fig. 5. The Young modulus decreases approximately by 80% when substituting 40% of sand by sediments.

The Young modulus depends heavily on the modulus of the aggregates that compose the cemented-materials as well as on their form and texture [START_REF] Carlos | Influence of coarse aggregate on concrete's elasticity modulus[END_REF]. This decrease with the sediment substitution can be explained by two reasons. In general, sediments have high porosity which generate an increase of the mortars porosity and thus the diminution of the elastic modulus. Besides, sediments have low resistance compared to natural aggregates. Substituting sand by sediments leads to low values of the young modulus.

Numerical

The microstructures images of the sedimentsbased mortars were not performed yet. Thus, the numerical approach was validated through an example of a microstructure of a BOF (Basic Oxygen Furnace) slag studied experimentally by D. Betrancourt et al [START_REF] Betrancourt | Instrumented indentation study of slag in view of a better valorization[END_REF]. Five phases constituting the slag were identified (Fig. 6) with the corresponding proportion and elastic modulus E i obtained from the nano-indentation technique. Table 4 resumes the different phases characteristics. The treatment of the image was performed (segmentation, filtering) and six different densities of meshes were studied (from 2500 to 250000 elements). FE meshing was performed using the multi-phase element method (Fig. 7). The homogenized elastic property of the material was then determined after numerical computations. A value of E= 109 GPa was obtained regardless the mesh density. The sensibility of the mesh is considered negligible on the macroscopic result. This value is in conformity of what has been obtained by D. Betrancourt et al. [START_REF] Betrancourt | Instrumented indentation study of slag in view of a better valorization[END_REF] who have estimated the global elastic property by the application of mixtures law (Table 5). The numerical approach was validated. The influence of each phase on the global property can be studied. Additional neglected phases can be introduced on the microstructure as well, such as pores phase, to optimize the results.

This approach can be applied on 3D images which can be obtained by performing X-ray computed Tomography (XCT).

CONCLUSIONS

The present study aimed to minimize the tests required for evaluating the mechanical behavior of sediment-based mortars. Five formulations of mortars were prepared with different substitution percentages of sand by uncontaminated marine sediments. Compressive and flexural tests were performed on the formulated mortars. The elastic modulus was also investigated using specific strain gages.

A numerical model was developed to assess the global mechanical property of the mortars. This model was built using the finite element method based on the homogenization technique. The main key for this approach is the knowledge of the elastic property of each phase constituting the sample in study. For this purpose, an instrumented indentation technique coupled with SEM should be performed.

The results show that the flexural and compressive strengths of mortars decrease when the substitution of sediment increases. This decrease is linear up to 30% of replacement. The elastic modulus decreases as well with the percentage of substitution of sand by sediment. This property depends mainly on the modulus of the aggregates composing the cemented-materials. The numerical model was validated on a slag microstructure. The macroscopic elastic property was in conformity with the value obtained experimentally by the authors of the mentioned work. This approach was not applied on the mortars. It will be the object of another detailed study.

Fig. 2

 2 Fig. 2 Algorithm of the numerical model

Fig. 5

 5 Fig. 5 Compressive strength percentage as function of the amount of sand substituted by sediment

Fig. 6

 6 Fig.6Phase identification in the slag[START_REF] Betrancourt | Instrumented indentation study of slag in view of a better valorization[END_REF]

Fig. 7 :

 7 Fig. 7: Multi-phase element method: (a) Microstructure image after treatment process, (b) 2D FE-grid (one mesh type) and (c) Mesh of microstructure (colors here only for illustration purpose)

Table 1

 1

	Contaminant percentage in raw sediments
	(mg/kg)
	Element	Element	Percentage	ISDI
	symbol	name	(%)	limits
	Sb	Antimony	0.066	0.06
	As	Arsenic	<0.08	0.5
	Ba	Barium	0.370	20
	Cd	Cadmium	<0.008	0.04
	Cr	Chromium	<0.03	0.5
	Cu	Copper	0.192	2
	Hg	Mercury	0.004	0.01
	Pb	Lead	<0.03	0.5
	Mo	Molybdenum	0.618	0.5
	Ni	Nickel	<0.03	0.4
	Se	Selenium	<0.07	0.1
	Zn	Zinc	<0.06	4

Table 2

 2 Composition of the mortars (in 1L)

	Mortar	MT	MT5	MT15	MT30 MT40
	Cement (g)	507	507	507	507	507
	Sand (g)	1526	1450	1298	1068	916
	Water (g)	249	249	249	249	249
	Sediment (g)	0	95	285	570	760
	W/C	0.49	0.49	0.49	0.49	0.49

Table 3

 3 Elastic modulus of mortars

	Mortar	MT	MT5	MT15 MT30 MT40
	E (MPa)	35076	31554 22710 12417	7678
	Standard
	deviation	1524	1049	2125	396	229
	(MPa)
	E Percentage	100	90	65	35	22

Table 4

 4 Characteristics of slag's phases[START_REF] Betrancourt | Instrumented indentation study of slag in view of a better valorization[END_REF]

	Phase	Compound	Area	E (GPa)
	Phase 1 (pink)	C2F	30.5	127±22

Table 5

 5 Estimation of global elastic modulus by mixture law models, from the estimated values in Table4

	Voigt	Reuss	Voigt-Reuss-
			Hill
	E (GPa) 115 ± 12	111 ± 11	113