Christine Sinoquet
email: christine.sinoquet@univ-nantes.fr

Sylvain Demey

Frédérique Braun

D Laboratoire

A large-scale computational analysis for significance assessment of frequencies relative to potentially strong sigma 70 promoters: comparison between 32 bacterial genomes

published or not. The documents may come

A large-scale computational analysis for significance assessment of frequencies relative to potentially strong sigma 70 promoters -comparison between 32 bacterial genomes -

Introduction

This work addresses potentially high ORF expression related to σ70-like promoters, in bacterial genomes. In these genomes, a single enzyme, the RNA polymerase, is responsible for the synthesis of all RNA types. The core holoenzyme α 2 ββ is competent for transcribing a specific region of the DNA strand into an RNA molecule. However, transcription can only be initiated (at the so-called +1 transcription site) through a temporary biochemical complex. This complex is composed of the four previous sub-units and of a protein, the σ factor, the primary one being σ70. As one of the simplest known bacterial models, E. coli K-12 has been subjected to intensive research, especially with regard to transcription [START_REF] Hawley | Compilation and analysis of Escherichia coli promoter DNA sequences[END_REF][START_REF] Harley | Analysis of E. coli promoter sequences[END_REF][START_REF] Collado-Vides | Control site location and transcriptional regulation in Escherichia coli[END_REF][START_REF] Lisser | Compilation of E. coli mRNA promoter sequences[END_REF][START_REF] Fenton | Escherichia coli promoter opening and -10 recognition: Mutational analysis of sigma70[END_REF][START_REF] Gruber | Multiple sigma subunits and the partitioning of bacterial transcription space[END_REF][START_REF] Pager | The sigma 70 family of sigma factors[END_REF][START_REF] Herring | Immobilization of Escherichia coli RNA polymerase and location of binding sites by use of chromatin immunoprecipitation and microarrays[END_REF]. Knowledge was therefore gained about the E. coli σ70 factor's binding sites. Their consensuses are respectively TTGACA and TATAAT, in the 5' to 3' direction. The optimal fixation of the RNA polymerase requires that the site with the consensus TTGACA should be located between 35 bp and 30 bp or thereabouts upstream of the first transcribed nucleotide. This former site is thus called the -35 box. The Pribnow box, TATAAT, is called -10 box for similar reasons [START_REF] Pribnow | Nucleotide sequence of an RNA polymerase binding site at an early T7 promoter[END_REF]. These sites are separated by 15 to 21 bp in the known functional promoters, the canonical σ70 promoter being characterized by the optimal distance of 17 bp. Various methods and softwares devoted to the prediction of functional promoters in Escherichia coli genome have been developped [START_REF] Huerta | Sigma70 promoters in Escherichia coli: specific transcription in dense regions of overlapping promoter-like signals[END_REF][START_REF] Eskin | Genome-wide analysis of bacterial promoter regions[END_REF][START_REF] Bulyk | A motif co-occurrence approach for genome-wide prediction of transcription-factor-binding sites in Escherichia coli[END_REF][START_REF] Shultzaberger | Anatomy of Escherichia coli σ70 promoters[END_REF] to restrain to a few examples). We do not mention here the numerous softwares designed to uncover a motif common to a set of biological sequences.

Not only is the RNA polymerase conserved through evolution in bacteria, there seems to be a single σ70 factor, responsible for housekeeping gene transcription, across the bacterial kingdom [START_REF] Wosten | Eubacterial sigma-factors[END_REF][START_REF] Mittenhuber | An inventory of genes encoding RNA polymerase sigma factors in 31 completely sequenced eubacterial genomes[END_REF]. Both points legitimate searches for σ70-like binding sites in other prokaryotic genomes [START_REF] Morrison | Streptococcus pneumoniae possesses canonical Escherichia coli (sigma 70) promoters[END_REF][START_REF] Gross | Bacterial sigma factors[END_REF][START_REF] Gralla | Organization and function of transcription regulatory elements. Escherichia coli and Salmonella, Cellular and Molecular Biology[END_REF][START_REF] Li | Identification of the binding sites of regulatory proteins in bacterial genomes[END_REF][START_REF] Martinez-Antonio | Identifying global regulators in transcriptional regulatory networks in bacteria[END_REF]. Furthermore, the number of complete prokaryotic genomes sequenced has increased at a high speed (594 in october 2007), which allows genome-wide computational investigations. In the domain of in silico analyses related to σ70 factor transcription, a reference contribution showed that σ70 promoter-like sequences are present throughout the kingdom of prokaryotic organisms [START_REF] Huerta | Selection for Unequal Densities of sigma70 Promoter-Like Signals in Different Regions of Large Bacterial Genomes[END_REF]. This former study demonstrated that the density of promoter-like sequences is high within regulatory regions, in contrast to coding regions and regions located between convergently transcribed genes. For instance, an average of 38 promoter-like sequences was computed for E. coli, within each 250 bp sub-region located upstream of the start codon. Density differences between regulatory and non-regulatory regions were detected in most of the large genomes analysed.

In vivo, transcriptional regulations are known to compensate for promoter weakness [START_REF] Gross | The functional and regulatory roles of sigma factors in transcription[END_REF][START_REF] Browning | The regulation of bacterial transcription initiation[END_REF]. For example, Huerta and Collado-Vides established that more than 50% of experimentally verified promoters are not the promoters with the highest scores when scoring relies on the proximity to the canonical promoter, both in terms of consensus similarity and optimal bp distances between boxes [START_REF] Huerta | Sigma70 promoters in Escherichia coli: specific transcription in dense regions of overlapping promoter-like signals[END_REF]. This statement was checked on the 111 promoters constituting a training set designed in a former work [START_REF] Gralla | Organization and function of transcription regulatory elements. Escherichia coli and Salmonella, Cellular and Molecular Biology[END_REF]. On the other hand, in E. coli genome, it has been shown that mutations in the -10 box or the -35 box that bring the promoter sequence closer to the σ70 consensus tend to increase the strength of the promoter, and conversely, mutations decreasing homology to the σ70 consensus tend to lower the promoter strength [START_REF] Hawley | Compilation and analysis of Escherichia coli promoter DNA sequences[END_REF]. Thus, the more similar to the canonical σ70 promoter, the more potentially strong this promoter would be, with the noteworthy exception that the consensus promoters may actually be weak because RNA polymerase binds them so strongly that it cannot escape [START_REF] Ellinger | Stalling of Escherichia coli RNA polymerase in the +6 to +12 region in vivo is associated with tight binding to consensus promoter elements[END_REF]. Therefore, it is attractive to study and compare genomes from the point of view of potentially high transcription, allowing for mismatches, under a minimal similarity constraint. This large-scale comparative analysis is feasible through an in silico approach.

No computational method can capture the biological features and environmental conditions involved in vivo, to predict functional strong promoters. Besides, even for the most intensively studied prokaryotic genome, E. coli's, the available repositories of σ70 promoters do not provide annotations about promoter strength. The measurement of promoter activity in cellular or cell-free expression systems cannot be applied on a large scale. ChIP on chip assays allow the identification of transcription factor binding sites, under given environmental conditions, but high-throughput promoter strength measurement cannot be implemented using this technique. Thus, before such large-scale array experimentations may be conducted on the 32 genomes we are interested in, an in silico genome-comparative analysis focused on intrinsically high transcription potentiality is worth being performed.

In our work, we intentionally focus on the subset of putative strong σ70 promoters already potentially favoured by the presence of an optimal Shine-Dalgarno sequence (GGAGG). The presence of the SD sequence has been ascertained for a large number of bacteria [START_REF] Osada | Analysis of base-pairing potentials between 16S rRNA and 5' UTR for translation initiation in various prokaryotes[END_REF] and it was established that the extent to which a SD sequence is conserved relates to its translation efficiency [START_REF] Ma | Correlation between Shine-Dalgarno sequence and gene features such as predicted expression levels and operon structure[END_REF]. Besides, our study also puts emphasis on strength transcription reinforcement through the UP element presence. The Upstream Promoter element is an enhancer for transcription and thus for ORF expression [START_REF] Ross | A third recognition element in bacterial promoters: DNA binding by the alpha subunit of RNA polymerase[END_REF][START_REF] Estrem | Bacterial promoter architecture: subsite structure of UP elements and interactions with the carboxy-terminal domain of the RNA polymerase alpha subunit[END_REF]. In about 3% of E. coli promoters, an UP element has been identified upstream of the -35 region, conferring additional strength to the promoter. The high conservation of the domain of the alpha subunit of the RNA polymerase involved in the interaction with the UP element suggests that the UP element consensus should be valid throughout the bacterial kingdom. To our knowledge, in addition to E. coli genome, the UP element has been experimentally identified in B. subtilis [START_REF] Fredrick | Promoter architecture in the flagellar regulon of Bacillus subtilis: high-level expression of flagellin by the sigma δ RNA polymerase requires an upstream promoter element[END_REF], V. natriegens [START_REF] Aiyar | rRNA promoter activity in the fast-growing bacterium Vibrio natriegens[END_REF] and G. stearothermophilus [START_REF] Savchenko | The Bacillus stearothermophilus argCJBD operon harbours a strong promoter as evaluated in Escherichia coli cells[END_REF]. At the present time, the only other work devoted to in silico identification of putative strong promoters harbouring an UP element is by M. Dekhtyar, A. Morin and V. Sakanyan (Sakanyan, personal communication.).

In this report, we perform a comparison of the frequencies observed for the putative strongest promot-ers over 32 bacterial genomes. We distinguish two strength levels, depending on the relaxation allowed with respect to the canonical σ70 promoter, and combine them with either mandatory or optional UP element presence. Thus, we perform four genome-comparative studies. We discuss the statistical significance of our results through comparisons with randomly generated genomes, highlighting and elucidating the specific case of Firmicutes.

3 System and methods

Genome analysis upon request

For each genome studied, BACTRANS 2 takes as an input the Fasta genome sequence provided by Gen-Bank (http://www.ncbi.nlm.nih. gov/genomes/lproks.cgi) together with the corresponding genome annotation. For each gene encoding a protein, the tool first extracts the sub-region spanning to 350 nucleotides upstream of start codon's first nucleotide. Then, occurrences of the σ70 promoter binding sites are searched for under constraints relative to (i) bp distances between binding sites or distances between binding sites and translation signals playing the role of "anchors" and (ii) the maximal number of mismatches allowed with respect to each consensus. In GenBank files, the only location annotation available is that of the start codon. Hence, for each gene, the start codon (SC) is considered a right anchor and each region upstream of SC is scanned to retrieve in priority the structured motif

[U P element] <3- 18> [-35 box] <15-20> [-10 box] <10-200> [SD] <2-10> [SC] (described in the 5' to 3' direction),
where SD denotes the Shine-Dalgarno sequence and

[box 1 ] <d min -d max > [box 2 ]
states the minimal and maximal bp distances allowed between the two boxes concerned. Actually, the full motif identification is performed in the 3' to 5' direction, successively considering each possible occurrence of the current box as a right anchor. In the absence of any UP element, the structured motif

[-35 box] <15-20> [-10 box] <10-200> [SD] <2-10> [SC] is looked for.
For each genome, the consensuses used have been adapted from E. coli σ70 promoter, relying on the work of Huerta and co-workers [START_REF] Huerta | Selection for Unequal Densities of sigma70 Promoter-Like Signals in Different Regions of Large Bacterial Genomes[END_REF]. These authors first identified a pair of Position-Specific Scoring Matrices (PSSMs), corresponding to the -35 and -10 boxes, associated with an interval of minimal and maximal bp distances, best describing E. coli σ70 functional promoters (see latter reference, Matrix 18 15 13 2 1.5 in Figure 2). Second, for any genome other than E. coli, they normalized the frequencies of the pair of E. coli PSSMs, using the a priori nucleotide probabilities characterizing this genome. Then, they relied on the normalized PSSM pair, to identify a set of promoter-like sequences within each genome. Finally they computed the -10 and -35 consensuses for each genome. In our study, for each genome, the consensuses retained are the subsequences of the consensuses of Huerta and coworkers, corresponding to the locations of the canonical TTGAC and TATAAT E. coli consensuses. We were careful to set accordingly the optimal bp distance between the -10 and the -35 boxes. As a result, the two -10 consensus TATAAT and TAAAAT have been used respectively for 20 and 12 genomes; TTGAC, TTGAA and TTTAA were the three -35 consensuses used to scan 5, 19 ad and 8 genomes respectively. A value of 200 bp was chosen for the maximal distance between start codon and SD; it was selected on the basis of the average 5'UTR region's length (50 or thereabouts, with variations between 0 and 200). The UP consensus used is that of E. coli, AAAWWTWTTTTNNAAAA (The genuine UP element has NN and NNN respectively as 5' and 3' termini).

For each binding site, minimal similarity is described through a maximal number of mismatches allowed. Notation (err(U P ), err(-35 box), err(-10 box)) specifies the maximal numbers of mismatches allowed with regard to the UP element, the -35 box and the -10 box respectively. Given this notation, two mismatch constraints are retained in our study; they are described as follows: (4,2,1) and (4,3,2). From now on, the two mismatch constraints (4,2,1) and (4,3,2) will be respectively denoted CI and CII. CI is more stringent than CII. Finally, four configurations will be considered in our analysis: CI, UP element required; CII, UP element required; CI, UP element optional; CII, UP element optional. The requirement of a greatest specificity for the -10 box compared to the -35 box is modeled after observations relative to functional σ70 promoters.

Hereafter, we denote sp the number of strong σ70 promoter-like sequences obtained from a given genome, when the presence of the UP element is optional. Similarly we define upsp when the UP element is required. From now on, we will refer to sp CI , sp CII , upsp CI and upsp CII .

Scoring function used

In the sequel, err(b) denotes the number of mismatches observed with respect to the consensus box b; d 1 denotes the bp distance observed between the -35 box and the -10 box; d 2 denotes the bp distance observed between the UP element and the -35 box. The score is calculated as follows: score = 0.60 err(-10 box) + 0.40 err(-35 box) + t 1 + err(U P ) + t 2 , where

t 1 = 0 if d 1 belongs to [17-19] else t 1 = 5 * d 1 , and t 2 = 0 if d 2 ranges in interval [6-8] else t 2 = 3 * d 2 .
When no UP element can be identified, the score is merely computed as: score = penalty + 0.60 err(-10 box) + 0.40 err(-35 box) + t 1 . The penalty value is set in order to systematically favour a candidate with an UP element within the regulatory region. This scoring function takes into account the specificity increase of the -10 box with respect to the -35 box. The choice of the coefficients 0.6 et 0.4 may be debatable. The most important point remains that the ratio between these coefficients be consistent with the behaviour of RNA polymerase as observed through functional promoters. Besides, we wished to emphasize the UP element weight, in the case when two promoter candidates harbour an UP-like element. Therefore, we assigned a value of 1 to the coefficient of the UP element. Finally, BACTRANS 2 outputs 0 or 1 putative strong promoter per gene encoding a protein.

The scoring function is one of the six major differences with the approach by Dekhtyar et al. (V. Sakanyan, personal communication). The difference with the algorithm of Dekhtyar et al. and the one presented here lies in six major points (V. Sakanyan, personal communication): (i) the former takes into account genes coding for m-RNAs as well as t-RNAs and r-RNAs; (ii) thus, contrary to ours, the algorithm of Dekhtyar et al. does not benefit from the supplementary clue consisting of the Shine-Dalgarno sequence; (iii) the former algorithm is solely devoted to strong promoters harbouring an UP element; (iv) the scoring function is more sophisticated than ours and emphasizes the similarity requirement with regard to the -10 box; (v) the retrieval of the structured motif is performed in 5' to 3' direction in Dekhtyar et al.'s approach whereas our method scans the regulatory regions in 3' to 5' direction, which allows relying on the most specific "anchors" in priority; (vi) because a dynamic programming alignment algorithm is run to successively retrieve the -35 and -10 boxes, the minimal similarity thresholds regarding these binding sites are specified by the user as minimal alignment scores. Regarding the latter point, we favoured mismatch error specification as being a more intuitive approach for tuning the algorithm.

Comparison with randomly generated genomes

For each bacterial genome considered in this study, we compare the sp value (resp. upsp value) observed with respect to the corresponding value expected on average for a similarly AT-rich genome generated at random. This latter artificial genome is only constrained to have the same following characteristics as the prokaryotic genome considered: same total number of genes coding for proteins and same proportions of A, C, T and G nucleotides in the 350 nucleotide-long region upstream of the start codon. Due to the high bp distance allowed between the -10 box and the SD sequence (200), and the numbers of mismatches allowed, the calculation of the theoretical expected value would not be tractable. Thus, for each genome, and under the four conditions studied, we computed the minimum, maximum, mean and standard deviation for sp and upsp values, over 100 such randomly generated genomes. To evaluate whether two distributions are statistically different when the latter are not of the Gaussian type and when their variances are not in the same order of magnitude, we relied on the Wilcoxon test. The H 0 hypothesis is stated as follows: the populations from which the two distributions are taken have identical median values. This test first ranks all n 1 + n 2 values from both distributions (n 1 and n 2 ) combined, then sums the ranks on each distribution, ws being the smallest sum and ws being computed as n 1 (n 1 + n 2 + 1) -ws. If either ws or ws is smaller than the theoretical value mentioned in Wilcoxon tables for n 1 and n 2 and an a priori level of significance, then hypothesis H 0 is rejected. We also computed the Z-score as the absolute difference between the number of strong promoters obs observed in the prokaryotic genome and the average number M emp of promoters computed from the 100 artificial genomes, divided by the standard deviation σ emp computed over these 100 latter genomes: Z-score =

|obs-Memp| σemp

, where obs is an spCI value (respectively spCII, upspCI, upspCII value). Again, statistical significance will be discussed, this time, with respect to several Z-score thresholds.

Results and discussion

Are potentially strong promoters frequent?

The 32 genomes compared belong to ten Firmicutes, thirteen Proteobacteria, three Actinobacteria, two Spirochaetales, one Chlamydia and three other taxa outside latter phyla. We draw the reader's attention to the case of small genomes: B. burgdorferi (0.91 Mbp), C. pneumoniae (1.22 Mbp), M. genitalium (0.58 Mbp), M. pneumoniae (0.81 Mbp), R. prowazekii (1.11 Mbp) and T. pallidum nichols (1.13 Mbp). All previous six species are either obligate intracellular pathogens, symbionts or animal commensal parasites and have undergone massive gene decay, as well as numerous genomic rearrangements. The presence of functional σ70 promoters is disputable in these genomes. Hereafter the two Firmicutes M. genitalium and M. pneumoniae will be referred to as Mollicutes. Nevertheless, except for R. prowazekii, these genomes were investigated in the reference work of Huerta and co-workers [START_REF] Huerta | Selection for Unequal Densities of sigma70 Promoter-Like Signals in Different Regions of Large Bacterial Genomes[END_REF]. We will follow this line, taking great care regarding the discussion. The total number of genes g encoding proteins in a genome and the size of this genome are proven to be correlated over the 32 genomes studied (linear correlation coefficient: 0.93). To escape the size bias when comparing genomes, we define the percentage p1 (p1 = 100 × sp/g). The top section of Figure 1 ((a) and (b)) depicts the variations of sp values and p1 percentages through genomes (also see Supplementary Data, Appendix 1). For illustration, the output files relative to E. coli genome are provided (see Supplementary Data, Appendix 2).

As a first result, we check that the number of putative strong promoters identified increases when constraints are relaxed from CI to CII. Secondly, we observe that for the AT-rich genomes of Firmicutes, putative strong promoters are over-represented under the two constraints CI and CII. This differentiates Firmicutes from all other genomes studied. Nonetheless, among Firmicutes, the numbers of strong promoters may differ in high proportions (1 to 4 under CI and CII constraints); S. pneumoniae is always characterized by the lowest value whereas B. subtilis, O. ihenyensis and C. perfringens happen to show peaks depending on the constraint. The differentiation between Firmicutes and other genomes holds for p1 percentage. The non Firmicutes genomes pointed out by the highest p1 percentages (over 5%) are A. aeolicus, T. maritima and B. burgdorferi. Thirdly, a more thorough examination shows that the genomes with the highest numbers of genes (g) are not necessarily those with the highest numbers of putative strong promoters (sp). The percentage p1 is variable and no linear correlation can be shown to exist between sp and g. More comments are provided in Supplementary Appendix 3, including a brief report about investigating the nature of genes associated with putative strong promoters.

The high AT-richness of Firmicutes could justifiably be suspected to yield these high numbers of σ70 promoter-like sequences. Indeed, we show that AT-content does not interfere much with p1: over the 32 genomes, the linear correlation coefficient between p1 CI and AT-content is 0.52; the correlation coefficient between p1 CII and AT-content is equal to 0.30, which was expected indeed under relaxed constraints allowing more blurred occurrences of the σ70 promoter model. When we take into account all bacteria but Firmicutes, such coefficients go down to 0.26 (CI) and -0.14 (CII) respectively. When the 10 AT-richest genomes are considered (Firmicutes), the coefficients are 0.27 and 0.20 respectively. Anyway, in the latter case, 10 is a borderline value regarding correlation analysis validity. Along the x-axis, the following phyla and groups are encountered: Actinobacteria, Chlamydia, Firmicutes (among which Mollicutes), "Others" group, Proteobacteria, Spirochaetales. (a) y-axis: number of genes harbouring a Strong Promoter (sp); (b) y-axis: ratio p1 of genes harbouring a strong promoter (sp) to the total number of genes encoding proteins in the genome (g), p1 = 100 × sp/g; (c) y-axis: number of genes identified with an UP element harboured in the Strong Promoter (upsp); (d) y-axis: ratio p2 of the number of genes with an UP element in the strong promoter (upsp) to the number of genes with a strong promoter (sp), p2 = 100 × upsp/sp).

Are potentially strong promoters harbouring an UP element frequent?

We now define percentage p2 as follows: p2 = 100 × upsp/sp. The bottom section of Figure 1 ((c) and (d)) depicts the variations of upsp and p2 among the 32 micro-organisms, under CI and CII constraints (also see Supplementary Data, Appendix 1). The output files relative to E. coli genome are provided (see Supplementary Data, Appendix 4).

Again, detailed complements to the present paragraph may be found in Supplementary Appendix 3. We first show that the differentiation between Firmicutes and other genomes holds, but it is more subdued for p2 percentage than for p1 percentage. Secondly, we observe that σ70 promoter-like sequences of relatively "lesser quality" (constraint CII) are more frequently associated with an UP-like element than sequences of "better quality" (constraint set CI) (Figure 1 ((c) and (d)): the ratio p2CII p2CI is calculable for 24 genomes and its average is 2.13; the average computed for all Firmicutes but Mollicutes is 2.07. Thirdly, we show that some genomes characterized by a low number of strong promoters show in contrast a high (p2) percentage of them harbouring an UP element, whatever the constraint (see Supplementary Appendix 3 for more details).

We calculate a correlation coefficient between p2 CI and AT-content of 0.84 when all 32 genomes are considered; the correlation between p2 CII and AT-content is similarly high (0.87). A high correlation is still observed when Firmicutes are not taken into account (0.82 and 0.86 respectively). In contrast with the case when no UP element was required, the 10 Firmicutes clearly show a correlation between p2 and AT-content (0.87 and 0.65 respectively). As expected, a stronger correlation is observed for p2 with respect to p1, since 7 out of the 17 nucleotides of the UP element consensus are nucleotides A, 5 are nucleotides T and 3 are A or T (W).

We now recapitulate the results obtained regarding AT-richness influence on p1 and p2: (i) depending on the species considered, AT-richness interferes but moderately so long as the UP element is not considered (p1); (ii) on the contrary, AT-content and percentage p2 are highly correlated. A pending question is then: does AT-richness alone entail high upspCI and upspCII values? To answer this question, we will in particular compare Firmicutes' genomes with similarly AT-rich genomes generated at random.

Comparing observations in bacterial genomes with expectations in randomly generated genomes

For each genome, we compare the frequency of putative strong promoters with that obtained for a similarly AT-rich "average" genome generated at random (Figure 2). For comparison purposes, a common scale is used in the four pictures of Figure 2 (The reader interested in details is referred to Supplementary Data, Appendix 5, for a magnification relative to artificial genomes' results).

We start our analysis focusing on the CI case. Figure 2 (a) (CI) shows that strong σ70 promoterlike sequences are significantly more frequent in Firmicutes genomes than in corresponding artificial genomes. From now on, we distinguish the 2 Mollicutes from the other 8 Firmicutes. Given as quadruplets (minimum, maximum, average, standard deviation), Z-scores are as follows: Firmicutes except Mollicutes: (81.3, 308.5, 193.0, 66.1); Proteobacteria: (1.0, 32.4, 16.0, 9.5). We check that the 8 Firmicutes' Z-scores are above threshold 140, except for L. monocytogenes (81.3). Concerning the 12 large Proteobacteria genomes studied, 10 have their Z-scores above threshold 7, among which 6 have their Z-scores above threshold 15. In particular, the Z-score obtained for E. coli genome is 21.7.

When restraining our examination to the 26 species with large genomes, under condition CI, we observe that 24 genomes have their Z-scores over threshold 7, among which 15 have their Z-scores over threshold 15 and finally 10 Z-scores exceed threshold 80. For a detailed description relative to sp CII , upsp CI and upsp CII values (Figure 2,(b),(c) and (d)), the reader is referred to Tables 5.1 through 5.4 in Supplementary Appendix 5. Table 5.3 focuses on E. coli. We recapitulate the main results and conclusions in the following paragraph.

First, we confirm that, except for the slightly more subdued case of L. monocytogenes, Firmicutes clearly show a specific trend, with Z-scores above thresholds 160, 100 and 150 respectively under CII condition (UP optional), and CI and CII conditions (UP required). Yet, under all four conditions, the Z-scores calculated for L. monocytogenes stay rather high (they range in interval [69,93]). Secondly, relaxing the constraint from CI to CII entails no decrease of the Z-score (see Supplementary Appendix 5, Table 5.1). We conclude that relaxing the stringency is not antagonistic to motif significance. This is not a trivial result, as the opposite was expected instead. Besides, the number of putative strong promoters harbouring an UP element, observed in the average random genome under CI condition, drastically decreases down to 0 for 26 species out of 32. Under this latter condition, it is obvious that both observed and expected upsp CI distributions strongly differ from one another. More rigorously, and more generally, the Wilcoxon test successively performed on p1 CI , p1 CII , p2 CI and p2 CII allows us to conclude that the difference between observed values and values expected by chance is statistically significant under all four conditions, for the 0.05 threshold. Thus, the σ70 promoter-like sequences retrieved in bacterial genomes are not due to mere chance. Additionally, Table 5.2 in Supplementary Appendix 5 enables evaluation of the statistical significance for each non Firmicute genome with respect to the Z-score thresholds 7, 15 and 80. Table 5.4 recapitulates the number of large genomes for which statistical significance is ascertained with regard to these thresholds: at least half of them under CI and CII conditions, for threshold 15, which we consider a high threshold; nearly all of them for threshold 7. Finally, since similarly AT-rich average genomes generated at random are far from yielding such high frequencies as those observed for the 8 corresponding Firmicutes genomes, AT-richness is clearly not the reason for the Firmicutes specificity.

Another lead is thoroughly examined to attempt to explain the Firmicutes difference. Due to the lack of space, we refer the reader to Tables 5.5 and 5.6 in Supplementary Appendix 5. We demonstrate therein that the Firmicutes difference is neither explained by genome size bias. Summarizing, in this section, we have characterized the statistical significances for all genomes, under four conditions of stringency, and with respect to three Z-score thresholds. We have proven the existence of a specificity for Firmicutes (large) genomes with regard to our definition of potentially high transcription. Moreover, this specificity is neither an artifact due to high AT-richness nor to differences in gene numbers between genomes.

Discussing the Firmicutes case

To explain the fact that putative strong σ70 promoters appear much more frequently in Firmicutes than in other bacteria, including -paradoxically -E. coli, we recall that we adopted the consensus GGAGG. In E. coli, GGAGG is a very strong SD sequence; more frequent SDs are the submotifs GGAA, GGAG, GAGG, AGGA and AAGG [START_REF] Gold | Posttranscriptional regulatory mechanisms in Escherichia coli[END_REF][START_REF] Ma | Correlation between Shine-Dalgarno sequence and gene features such as predicted expression levels and operon structure[END_REF]. On the other hand, ribosomes from many Gram-positive bacteria depend much more stringently upon a strong SD interaction for initiation [START_REF] Roberts | The effect of Escherichia coli ribosomal protein S1 on the translational specificity of bacterial ribosomes[END_REF]. For instance, in B. subtilis genome, most SD sequences are close to the consensus sequence AAAGGAGG [START_REF] Rocha | Translation in Bacillus subtilis: roles and trends of initiation and termination, insights from a genome analysis[END_REF]. This, we suggest, could be the reason for the abundance of putative strong promoters in Firmicutes genomes. This point has been investigated further. We show that the percentage p bact of genes associated with an optimal SD sequence ranges between 2.21% and 39.8% for the 26 large genomes. Immediately behind T. maritima, which shows the highest ratio, the 8 large Firmicutes genomes rank first with respect to this p bact ratio ([15.3%, 32.6%]). The percentages p rand expected for similarly AT-rich genomes generated at random have been calculated. The calculus is described in Supplementary Appendix 6. The p bact and p rand distributions are proven statistically different through a Wilcoxon test (threshold 0.05). Furthermore, the correlation coefficient between p rand and AT-richness is -0.97, over the 32 artificial genomes. This high negative value was expected since the optimal SD sequence is enriched with four G nucleotides. In contrast, the correlation coefficient between p bact and AT-richness is low when computed over the 32 bacterial genomes (0.22). This point argues in favour of the biological significance of such GGAGG sequences in the close neighbourhood of start codons. Moreover, regarding this criterion, the Wilcoxon test also ascertains the statistical significance of the difference between the 8 Firmicutes and the 18 other species with large genomes. This difference is reflected by the Z-scores. Z-scores range in interval [3.2, 363.9] when all genomes are considered (mean: 86.9, standard deviation: 103.1). The Z-scores calculated for the 8 large Firmicutes genomes range between 86.8 (S. pneumoniae) and 363.9 (C. perfringens). When all large genomes but Firmicutes' are considered, the mean and standard deviation are respectively equal to 41.8 and 40.0. Outside the Firmicutes taxon, T. maritima and A. aeolicus are the only two bacteria showing as outstanding Z-scores as Firmicutes (respectively 168.7 and 106.2). Again, we emphasize that both previous genomes are also characterized with high AT percentages (54.6% and 57.6%), which confirms a bias for the presence of optimal SD sequences in some genomes.

Anyway, such bias exists for all genomes. For example, in the light of the previous explanation, we now explain the scarcity of putative strong promoters associated with optimal SD sequences, in E. coli, through the low p bact percentage of 6.2% observed. Though, the percentage expected is 0.9%. The bias measured through the Z-score is 37.9. Therefore, this point suggests that even in E. coli, hazard would only contribute for 15% ( 0.9 6.2 ) to yield false positive optimal SD sequences. Finally, considering the criteria retained in our analysis (high intrinsic transcription potentiality combined with strong SD interaction), we conclude that Firmicutes would appear as genomes more favoured by nature, especially with respect to other similarly AT-rich genomes.

Putative strong promoters versus experimentally verified functional promoters in Escherichia coli genome

In vivo, activation by various factors is ascertained to compensate for promoter weakness. However, it is not known whether some functional promoters might also be intrinsic strong promoters. So far, data compilations relative to experimentally verified functional promoters are only available for E. coli genome, through two repositories, RegulonDB and PromEC [START_REF] Salgado | RegulonDB (version 5.0): Escherichia coli K-12 transcriptional regulatory network, operon organization, and growth conditions[END_REF][START_REF] Hershberg | PromEC: An updated database of Escherichia coli mRNA promoters with experimentally identified transcriptional start sites[END_REF]. Therefore, we could compare the putative strong promoters identified by BACTRANS 2 in E. coli genome with known E. coli functional promoters. Only few genes of E. coli harbouring the potentially strongest σ70 promoters identified by BACTRANS 2 are also listed in RegulonDB and PromEC databases. Not surprisingly, the distance between the Transcription Start Site (TSS) of the putative strong promoter and the TSS of the functional promoter may vary in a large range. Under CI condition, 96 putative strong promoters are identified by BACTRANS 2 ; 12 out of the corresponding 96 genes are referred to by at least one of the two databases aforementioned. Under CII condition, 20 out of the 254 genes identified with strong promoters are cited in at least one database. For more details and an explanation of the results obtained, the reader is referred to Supplementary Appendix 7. We confirm that in E. coli genome, according to BACTRANS 2 scoring function, when a functional σ70 promoter is known for a gene, it is intrinsically weaker than the putative strong promoter identified by BACTRANS 2 if the latter exists under CI or CII conditions.

Experimental verification of putative strong promoters identified in Thermotoga maritima genome

The hyperthermophilic model Thermotoga maritima has been intensively studied [START_REF] Morin | Hyperthermophilic Thermotoga arginine repressor binding to full-length cognate and heterologous arginine operators and to half-site targets[END_REF][START_REF] Braun | Similarity and divergence between the RNA polymerase alpha subunits from hyperthermophilic Thermotoga maritima and mesophilic Escherichia coli bacteria[END_REF]. In the context of a former study, the activity of thirteen putative strong promoters harbouring an UP element has been measured in E. coli cell free extracts [START_REF] Sakanyan | Method for the identification and isolation of strong bacterial promoters[END_REF]. The present work thereby benefits from these experimentations. The protocol used is described in Supplementary Appendix 8. Seven putative strong promoters harbouring an UP element identified by BACTRANS 2 were thus tested. Four were identified under the most constrained condition CI (T M 1016, T M 0373, T M 0477, T M 1667). The other three were identified under CII condition (T M 0032, T M 1429, T M 1780).

All of them promote protein synthesis, indicating that they are all functional promoters. Moreover, except T M 0032, all provided a higher protein yield than that of the well-studied pTac promoter. T M 0477 has been shown to be twice as strong as others regarding protein yield. Therefore six promoters among the seven tested really favour high expression in E. coli cell free extracts.

Conclusion

Our work contributes to shedding new light on potentially high ORF expression in prokaryotic genomes, focusing on potentially high transcription combined with the presence of an optimal Shine-Dalgarno sequence. Our approach also puts emphasis on transcription initiation potentially enhanced through UPlike elements. In itself, this latter feature introduces originality with respect to other genome-comparative studies devoted to bacterial promoters. Our analysis clearly departs from other works, since it considers four different conditions of stringency and discusses in each framework the statistical significance of the presence of σ70 promoter-like sequences. Under all four conditions, we identified the species showing statistically significant differences between the bacterial genome and an average similarly AT-rich genome generated at random. In particular, Firmicutes would appear as genomes more favoured by nature with respect to other genomes, including the cases when an UP-like element is required. A rigorous discussion allowed us to dismiss AT-richness and genome size bias as determining factors to explain the Firmicutes specificity. To explain this specificity, the hypothesis of the abundance of optimal SD sequences in Firmicutes' large genomes has been checked with success. Besides, so far, the UP element has been identified by experimentation in four genomes. Thus our comparative study also brings novel knowledge about the statistical significance of the presence of putative σ70 promoters enhanced with an UP-like element, in various genomes. The generic software platform BACTRANS 2 currently provides such putative strong promoters for 45 genomes. These data may be of interest to select a subset of promoters for experimental characterization and possible further use in biotechnological applications. In this latter field, inserting in cellular or cell-free expression systems regulatory regions including promoters enhanced with an UP element and an optimal SD sequence may be advocated, instead of inserting artificial binding sites in a synthetic se-

Figure 1 :

 1 Figure 1: Frequencies of genes harbouring a putative strong promoter, under four constraint sets, in 32 prokaryotic genomes. See text, Subsection "Genome analysis upon request" for the definition of CI and CII constraints. (a) and (b): UP element optional; (c) and (d): UP element required.Along the x-axis, the following phyla and groups are encountered: Actinobacteria, Chlamydia, Firmicutes (among which Mollicutes), "Others" group, Proteobacteria, Spirochaetales. (a) y-axis: number of genes harbouring a Strong Promoter (sp); (b) y-axis: ratio p1 of genes harbouring a strong promoter (sp) to the total number of genes encoding proteins in the genome (g), p1 = 100 × sp/g; (c) y-axis: number of genes identified with an UP element harboured in the Strong Promoter (upsp); (d) y-axis: ratio p2 of the number of genes with an UP element in the strong promoter (upsp) to the number of genes with a strong promoter (sp), p2 = 100 × upsp/sp).

  Figure 2: Observed bacterial genome values versus minimal, average and maximal values observed over 100 similarly AT-rich genomes generated at random, for sp and upsp respectively, under 4 constraint sets. See Figure 1 for definition of sp and upsp, and for genome abbreviations. See text, Subsection "Genome analysis upon request" for the definition of CI and CII constraints.

Acknowledgements

S. Demey was supported by the Pays de la Loire Region ("Technological Innovations and Postgenomics" C.P.E.R. program) and by Ouest-Genopole consortium (National Network of Genopoles). The first author is thankful to V. Sakanyan for valuable comments and critically reading the manuscript. Thanks are also due to J. Bourdon for insightful discussions.

A large-scale computational analysis for significance assessment of frequencies relative to potentially strong sigma 70 promoters: comparison between 32 bacterial genomes Christine Sinoquet †, Sylvain Demey †, Frédérique Braun ‡

Abstract

The platform BACTRANS 2 has been designed to help select putative strong σ70-like promoter candidates in prokaryotic genomes. It was run to investigate the importance of σ70-like potentially high transcription in bacteria other than Escherichia coli. We performed a genome-comparative analysis of high ORF expression potentialities over 32 prokaryotic genomes. Besides, we put an emphasis on transcription strength reinforcement through the UP element presence and on translation potentiality enhancement through an optimal Shine-Dalgarno sequence.

We compared frequencies of putative strong promoters between various genomes. We show that in the AT-rich Firmicutes' genomes, frequencies of potentially strong σ70-like promoters are exceptionally high. Besides, though they contain a low number of strong promoters, some genomes may show a high proportion of promoters harbouring an UP element. Putative strong promoters of lesser quality are more frequently associated with an UP element than putative strong promoters of better quality. A meaningful difference is statistically ascertained when comparing frequencies in bacterial genomes with frequencies in similarly AT-rich genomes generated at random; the difference is the highest for Firmicutes. Comparing some Firmicutes genomes with similarly AT-rich Proteobacteria genomes, we confirm the Firmicutes specificity. We show that this specificity is neither explained by AT-bias nor genome size bias but originates in the abundance of optimal Shine-Dalgarno sequences, a typical and significant feature of Firmicutes more thoroughly analysed in our study.

The generic software platform BacTrans2 currently provides such putative strong promoters for 45 genomes. These data may be of interest to select a subset of promoters for experimental characterization and possible further use in biotechnological applications. Finally, BacTrans2's genericity allows the user to analyse genomes with respect to any other super-motif consisting of 3 or 4 boxes.

To our knowledge, this work is the very first genome-comparative study thoroughly analysing the significance of various potentially strong sigma 70-like promoter models, including models harbouring the UP element enhancer.

LINA, Université de Nantes 2, rue de la Houssinière B.P. 92208 -F-44322 NANTES CEDEX 3


Romain Léger
email: romain.leger@mines-ales.fr

Cécile Mattrand
email: cecile.mattrand@sigma-clermont.fr

Ahmed Mooti
email: ahmed.mooti@eleves.ec-nantes.fr

Stéphane Corn

MODELING NATURAL FIBER COMPOSITES MICROSTRUCTURES FOR PREDICTING THEIR WATER AGING

Keywords: Natural fiber composites, realistic microstructure, water diffusion, numerical modeling, durability

The prediction of the in-service behavior and durability of composite materials reinforced with natural fibers is a challenge when they are subjected to simultaneous multi-physical inputs, such as water exposure combined to mechanical loadings. Understanding the response of the material may require an accurate description of its microstructure at different scales. This work proposes an original approach devoted to generate realistic virtual microstructures in order to predict numerically the hygroscopic behavior of composites reinforced with natural fibers.

Yarn scale (single fibres, bundles and resin)

Intra-yarn Composite scale (yarns and resin)

Introduction

Many companies show interest in natural fiber composites (NFC) as a substitute to traditional glass fiber composites. Indeed, natural fibers (NF) present very interesting properties in comparison to glass fibers, such as low density, high specific stiffness and also biodegradability. However, the use of NF in structural applications is still limited by several disadvantages. First, NF exhibit high variability in their dimensions, shapes and mechanical properties. They also require lower processing temperatures which makes it necessary to reconsider existing processes or the choice of a matrix [START_REF] Pickering | A review of recent developments in natural fiber composites and their mechanical performance[END_REF]. Another drawback is the poor durability in humid environment of these composites due to the hydrophilicity of plant fibers [START_REF] Célino | The hygroscopic behavior of plant fibers: a review[END_REF][START_REF] Le Duigou | In-situ evaluation of flax fiber degradation during water aging[END_REF]. Although some authors have shown that fatigue behavior could be improved after humid aging [START_REF] Berges | Influence of moisture uptake on the static, cyclic and dynamic behaviour of unidirectional flax fiber-reinforced epoxy laminates[END_REF], most works demonstrate that static and dynamic behavior of NFC is impaired by moisture [START_REF] Testoni | Effects of water aging on the mechanical properties of flax and glass fiber composites : Degradation and reversibility[END_REF][START_REF] Le Duigou | Long term immersion in natural seawater of Flax/PLA biocomposite[END_REF]. Therefore, the prediction of the mechanical strength of NFC in humid environment and the comprehension of the underlying phenomena remain challenging. The experimental exploration of the sensitivity of the diffusional and mechanical behavior of NFCs to variations of microstructural features such as fibers shapes and dispersion would lead to a gigantic work. Thus, parametric numerical simulations based on a finite element modeling are a more reasonable and efficient alternative. This work proposes a modeling strategy of unidirectional NFC microstructures based on relevant morphological parameters. Numerical predictions of the diffusive and mechanical behavior of NFCs are subsequently performed and the influence of the microstructural features is assesed.

Materials and Methods

Composite Materials

The resin used for the studied composite is an Enydyne® dicyclopentadiene isophthalic unsaturated polyester (Cray Valley -Rouvroy, France), polymerized with 1.8% w/w of methyl ethyl ketone peroxide Luperox K1S® (Arkema -Colombes, France). Quasi-unidirectional flax fabrics were manufactured by Fiber Recherche Developpement (Troyes, France) for a weight of 390 g/m2 (Weft: 360 g/m2 / Warp: 30 g/m2). Four layers of flax fabrics were vacuum infused with the resin to obtain 300 x 250 mm flax fiber reinforced composite (FFRC) sheets. A constant pressure of 100 mbar was maintained during the 24 hours curing of the resin at room temperature. A subsequent 24h post-curing in an oven at 60°C was necessary to obtain a polyester crosslinking rate of 88%. Thickness ranged from 2.7 to 3.4 mm for the FFRC. Beam samples were cut to size of 250 mm x 25 mm using a diamond blade. FFRC of 32% vol. of fibers were obtained. Small samples of polyester (15 x 8 x 3 mm) were also produced for this study. All specimens were stored in a climatic room, at 23°C and 50% H.R., before testing. The cross-sectional multiscale microstructure of the composite is displayed in Fig. 1. Two scales can be observed: the yarn scale, which contains 46% areal fraction of uniformly dispersed reinforcement that can be divided in single elementary fibers and fibre bundles, and the composite scale with yarns arranged in staggered rows into the matrix [START_REF] Léger | A multiscale finite element model to predict the diffusional behavior of biocomposites dedicated to structural applications[END_REF]. As a first approach, only the intra-yarn microstructure is considered in this work.

Image analysis and microstructure modeling

The synthesis of virtual but statistically representative microstructures was endeavoured in order to assess the sensitivity of the composite to its microstructural features. Here, the procedure is based on a three steps sequence. Firstly, images obtained by scanning electron microscopy of the polished FFRP cross-sections, see section 2.1, are analysed with a semi-automated procedure using Aphelion®, which quantifies elementary fibers and bundles on the basis of their morphological parameters (surface, elongation and convexity measurements). Then, each elementary fiber and bundle cross-section is described by means of its complex coordinates z n (i) which stands for the n th complex coordinate of the i th elementary fiber or bundle, see Fig. 2. Each complex function is analyzed in the frequency domain by performing a Fourier transform. (i) per fiber, k={1,2,…, N (i) }, with N (i) the number of pixels composing the contour of the i th fiber or bundle. As N e , resp. N b , elementary fibers, resp. bundles, have been featured in the database, each real and imaginary part of Fourier coefficients can be modeled as a random variable, see Fig. 3.

Figure 3. Fourier analysis of a fiber

By identifying the distributions and the correlations of the first random variables of the Fourier decomposition, one can capture the main dispersion in the elementary fiber and bundle shapes. The inverse Fourier transform of the random Fourier coefficients sampled from their probabilistic distributions allows an easy generation of virtual shapes statistically representative of the observed ones. More details are available in [8,9]. The last step lies in arranging the previously simulated fibers in a given Volume Element (VE). A specific algorithm has been been developed for this purpose. It is assumed that the fibers are randomly spaced, i.e. no spatial correlation is taken into account. The proposed algorithm merges two existing strategies, namely LS-RSA (Level Set controlled Random Sequential Adsorption) [START_REF] Sonon | A unified level set based methodology for fast generation of complex microstructural multi-phase RVEs[END_REF] and RSE (Random Sequential Addition) [START_REF] Yang | A new method for generating random fibre distributions for fibre reinforced composites[END_REF]. They are slightly modified here to incorporate the constraints linked to the complex and arbitrary shapes of the fibers, which has never been done to the best authors' knowledge. This allows us to simulate unidirectional NFC with reinforcement volume ratio up to 60%, see Fig. 4 and5 for illustration with V f =46%.

Diffusion and swelling modeling

In order to predict the water diffusion and the swelling of this FFRP, a numerical finite element model (FEM) based on the generated microstructures has been implemented in Comsol Multiphysics®. Five virtual statistically representative microstructures (1.5mm x 0.4mm) have been generated (Fig. 4c).

They are compared with two other type of microstructures (Fig. 4a and4b) with the same ratio but composed of regularly and randomly dispersed cylindrical fibers (uniform diameter of 20 µm) in order to assess the impact of morphology and distribution on diffusion, swelling and stress fields. The studied composite is unidirectionally (UD) reinforced and a preferential diffusion is expected in the permeable fiber direction since their diffusion coefficient D f and water uptake at saturation M sf are usually higher than that of the matrix [START_REF] Gueribiz | Diffusion modeling of composite with permeable fiber[END_REF][START_REF] Célino | Characterization and modeling of the moisture diffusion behavior of natural fibers[END_REF]. However, because the high length-to-thickness and width-to-thickness ratios of the UD beam samples induce for every cross-section water diffusion fluxes that are mostly in-plane oriented, a 2D diffusion was considered and modeled (Fig. 5) [START_REF] Peret | Numerical transient hygro-elastic analyses of reinforced Fickian and non-Fickian polymers[END_REF][START_REF] Joliff | Modified water diffusion kinetics in an unidirectional glass/fiber composite due to the interphase area : Experimental, analytical and numerical approach[END_REF]. In a first approach, the diffusion law in both matrix and fibers is supposed to follow the Fick's law. Diffusion coefficients D c and D m , water uptakes M Sc and M Sm of composite and matrix respectively and matrix swelling coefficient  m have been measured during an aging in distilled water at 30°C (see Table 1). Note that the swelling of the composite is not isotropic, with an increase in thickness 3 times greater than the increase in width (and length swelling is negligible). Swelling of matrix is isotropic. Diffusion and swelling coefficients are supposed to not depend on the local water uptake. Diffusion coefficient and water uptake of flax fibers have been determined (see Table 1) according to the work of Gueribiz et al [START_REF] Gueribiz | Diffusion modeling of composite with permeable fiber[END_REF]. Note that the diffusion coefficient and the water uptake of flax fibers in the composite calculated with this method are about 10 times lower than classical values directly measured on fiber samples. This could be attributed to the fact that fibers are partially penetrated by the matrix and become less sensitive to water. Fiber swelling coefficient has been taken from the literature [START_REF] Le Duigou | Hygroscopic expansion : A key point to describe natural fiber/polymer matrix interface bond strength[END_REF] and is supposed to be isotropic (see Table 1). Let C w be the local water concentration, then, with the assumption of uniform diffusivity D, the Fickian diffusion is described by equation 2 :

(2)

Obviously, water concentration is discontinuous across the interface between permeable fiber and matrix. To solve this numerical problem a normalized field variable, namely the relative water uptake, has to be introduced and should be continuous across the interface. Such variable W has been introduced by some authors [START_REF] Wong | Moisture diffusion and vapour pressure modeling for electronic packaging[END_REF][START_REF] Yoon | On moisture diffusion modeling using thermal-moisture analogy[END_REF] :

(3)
where C ws is the water concentration at saturation. Let M be the local water uptake in percent :

(

) 4
where m is the local mass of humid composite around a point and m 0 its initial value. m w represents the local mass of absorbed water. If one considers the volume to remain constant during diffusion, then W can be rewritten :

(5)

with M s the water uptake at saturation. Then, W is following a Fickian law, as long as M s for matrix and fiber is constant during the simulation :

(6)
W and its flux should also be continuous at the interface [START_REF] Wong | Moisture diffusion and vapour pressure modeling for electronic packaging[END_REF][START_REF] Yoon | On moisture diffusion modeling using thermal-moisture analogy[END_REF].

The mechanical behaviour is assumed elastic for this first study : [START_REF] Léger | A multiscale finite element model to predict the diffusional behavior of biocomposites dedicated to structural applications[END_REF] where is the stress tensor, the stiffness matrix and the elastic tensor which depends on swelling coefficient  :

where represents the swelling tensor :

Elastic properties have been measured on the matrix, and taken from the literature for flax fiber (transverse modulus estimation) [START_REF] Baley | Transverse tensile behavior of unidirectional plies reinforced with flax fibers[END_REF].

In terms of boundary conditions, the blue line (Fig. 5) represents the edge subjected to water (W=1) and free to swell. Symmetry conditions are imposed on the other edges (red solid lines), which correspond to zero water flow for diffusion and no orthogonal displacement for mechanics [START_REF] Peret | Numerical transient hygro-elastic analyses of reinforced Fickian and non-Fickian polymers[END_REF][START_REF] Joliff | Modified water diffusion kinetics in an unidirectional glass/fiber composite due to the interphase area : Experimental, analytical and numerical approach[END_REF]. A sensitivity study to the mesh fineness has led to a 150000 elements model (with smallest elements area of 1µm 2 ).

First results

Composite global water uptake M C (%) and swelling in the thickness direction (%) are calculated (eq. 10 and 11) for each of the 3 simulated microstructures and plotted in Fig. 6. [START_REF] Sonon | A unified level set based methodology for fast generation of complex microstructural multi-phase RVEs[END_REF] where M Sm , M Sf and S indicate the water uptake at saturation for the matrix, water uptake at saturation of the fibers, and the FEM surface which is divided in S m the matrix surface and S f the fiber surface. [START_REF] Yang | A new method for generating random fibre distributions for fibre reinforced composites[END_REF] u is the displacement of a node which is integrated along the left edge of the FEM. e/2 is the thickness of the FEM, b its width (Fig. 5). It can be observed from our results that the influence of the microstructure (dispersion and shape of fibers) is negligible on both the global sorption kinetics and swelling of the free edge. The overall diffusion behavior of the composite is Fickian, thus its kinetics could be modeled by one homogeneous diffusion coefficient (which can be a tensor in order to account for anisotropy) and one water uptake at saturation for the composite, like it is frequently done in the litterature with a Fickian law [START_REF] Hadi | Assessment of 3D moisture diffusion parameters on flax/epoxy composites[END_REF]. Concerning the stress distribution, really, high Von Mises stress values are obtained at saturation (Fig. 7) but this is consistent with the modeling choices made in this first approach of the problem. Indeed, matrix and fibers have been modeled as elastic materials and their properties do not depend on the local water uptake, which is obviously a limit in this model. At saturation, both matrix and fibers could behave like viscoelastoplastic materials [START_REF] Poilâne | Polymer reinforced by flax fibres as a viscoelastoplastic material[END_REF], leading to decrese their apparent stiffness and, as a consequence, actual stresses should be lower than those simulated and actual swelling should be higher. Nevertheless, the impact of dispersion and shape of fibers on stress distribution can be analyzed on the basis of these results. It can be observed that the random dispersion of fibers has a strong impact on the stress distribution in matrix which is shifted towards higher levels (Fig. 8). The closest the fibers, the higher the Von Mises stresses in the matrix. The impact on stresses in fiber is moderated with slightly higher values. The shape of NF is responsible for local stress concentration, but seems to be of second order by comparison with the spatial arrangement of fibers in the matrix (Fig. 8).

Conclusions

The prediction of NFC durability is a technical and scientific challenge as they can be submitted to multiple simultaneous solicitations. Modeling a realistic microstructure can help understanding the behavior of such composite at a local scale and subsequently at a global scale. Here, an efficient method has been developed to create realistic numerical microstructures on the basis of simple morphological parameters. Modeling of the diffusion of water and of the swelling of this composite have been first attempted with some hypotheses. It appears that both arrangment and shape of fibers has no real impact on the overall diffusion kinetics, nor on the swelling behavior. Stress distributions resulting from the differential swelling of matrix and fibers are mostly impacted by the arrangement of fibers. The influence of fibers contour was found to be of second order in that study but additional simulations should be performed to confirm those results.

Figure 1 -

 1 Figure 1 -Multiscale microstructure of the unidirectional flax fiber reinforced polyester

Figure 2 .

 2 Figure 2. Definition of an elementary fiber or bundle contour This leads us to a collection of Fourier coefficients Z k(i) per fiber, k={1,2,…, N (i) }, with N (i) the number of pixels composing the contour of the i th fiber or bundle. As N e , resp. N b , elementary fibers, resp. bundles, have been featured in the database, each real and imaginary part of Fourier coefficients can be modeled as a random variable, see Fig.3.

Figure 4 .

 4 Figure 4. Examples of generated microstructures (V f =46-47%)a) Regularly dispersed circular fibers b) Randomly dispersed circular fibersc) Randomly dispersed statistically representative fibers.

Figure 5 .

 5 Figure 5. Mechanical and hydric boundary conditions.

Figure 6 .

 6 Figure 6. Water uptake and thickness swelling of the 3 FEM models.

Figure 7 .

 7 Figure 7. Stress distribution in MPa at saturation (7000h) of 3 flax/polyester composites FEM.

Figure 8 .

 8 Figure 8. Stress distribution in matrix and fibers at saturation (7000h) of 3 flax/polyester composites FEM.

Table 1 .

 1 Diffusion, swelling and elastic properties of composite, fibers and matrix.

		Diffusion coefficient D (mm 2 /s)	Water uptake at (%) saturation M s	Swelling coefficient  	Modulus E (GPa)	Poisson coefficient 	Density of dry matter (g/cm 3 )
	Matrix	1.28e-6	0.9	4.3e-3	3.1	0.35	1.12
	Composite	1.64e-6	6	-	-	-	1.27
	Flax fiber	1.34e-7	14.5	11.4e-3	7	0.4	1.54