Ethienne Routhier

Edgar Pierre

Alexandra Joubert

Astrid Lancrey

Jean-Baptiste Boulé
email: jean-baptiste.boule@mnhn.fr

Julien Mozziconacci
email: julien.mozziconacci@mnhn.fr.cor-respondence

In silico design of DNA sequences for in vivo nucleosome positioning

The computational design of synthetic DNA sequences with desired in vivo properties is gaining traction in the field of synthetic genomics. We propose here a computational method which combines a kinetic Monte Carlo framework with a deep mutational screening based on deep learning predictions. We apply our method to build regular nucleosome arrays with tailored nucleosomal repeat lengths (NRL) in yeast. Our design is validated in vivo by successfully engineering and integrating thousands of kilobases long tandem arrays of computationally optimized sequences which could accommodate NRLs much larger than the yeast natural NRL. This method delineates the key sequence rules for nucleosome positioning in yeast and is readily applicable to other sequence properties and other genomes.

Introduction

Recent biotechnology techniques such as CRISPR/Cas9 and DNA oligonucleotide in vivo assembly have opened ways to precisely and extensively modify genomes. Taking advantage of these technologies, several projects have been launched with the aim to partially or completely design and assemble synthetic genomes [START_REF] Ostrov | Technological challenges and milestones for writing genomes[END_REF]. Nevertheless, controlling chromatin assembly and gene expression on a synthetic genome remains a challenge. Decisive efforts have been recently made for designing promoter sequences that produce controlled levels of mRNA in yeast [START_REF] Hossain | Automated design of thousands of nonrepetitive parts for engineering stable genetic systems[END_REF][START_REF] De Boer | Deciphering eukaryotic gene-regulatory logic with 100 million random promoters[END_REF] or the activity of enhancers in a Drosophila cell line [START_REF] De Almeida | Deepstarr predicts enhancer activity from dna sequence and enables the de novo design of synthetic enhancers[END_REF]. While the control of gene expression is now within our grasp, there is yet no efficient way to control by sequence design the positioning of nucleosomes along a synthetic DNA cassette inserted in an eukaryotic genome. Nucleosome positioning is however of crucial importance as it influences DNA accessibility to DNA binding factors involved in DNA replication and transcription, thus adding a supplementary level of control on top of the DNA sequence [START_REF] Tsankov | The role of nucleosome positioning in the evolution of gene regulation[END_REF][START_REF] Hughes | A functional evolutionary approach to identify determinants of nucleosome positioning: a unifying model for establishing the genome-wide pattern[END_REF]. In a seminal experiment, Lowary and Widom used a SELEX approach to isolate a DNA sequence with the highest affinity to a histone octamer among a set of more than 5 × 10 12 sequences [START_REF] Lowary | New dna sequence rules for high affinity binding to histone octamer and sequence-directed nucleosome positioning[END_REF]. The resulting 147 bp sequence, known as the 601-sequence, has been extensively used to reconstruct regular nucleosomal arrays in vitro (e.g. [START_REF] Robinson | Em measurements define dimensions of the "30-nm" chromatin fiber: evidence for a compact, interdigitated structure[END_REF]). Given the success in using the 601 sequence for nucleosome positioning in vitro, we recently addressed the affinity of nucleosomes to the 601 sequence in vivo using insertions in the S. cerevisiae genome of three long arrays of approximately 50 nucleosomes, with three different spacing between nucleosomes (167,197 and 237 bp), also known as nucleosomal repeat length (NRL). In this study we found that in sharp contrast with the in vitro experiments, the affinity of nucleosomes to the 601 sequence was very low in vivo [START_REF] Lancrey | Nucleosome Positioning on Large Tandem DNA Repeats of the '601' Sequence Engineered in cerevisiae[END_REF] suggesting that this sequence is not an adequate tool to control nucleosome positions in synthetic genomics approaches. Computational tools are a good alternative to optimize the design of synthetic sequences from in vivo data. Among the available computational methods, deep learning has been widely applied to building predictive models that relate DNA sequences to genomic functions [START_REF] Zou | A primer on deep learning in genomics[END_REF][START_REF] Routhier | Genomics enters the deep learning era[END_REF]. The ability of deep neural networks to predict annotations resulting from variations of a sequence is now used for de novo design of genomic sequences, including tailored alternative poly-adenylation sites [START_REF] Bogard | A deep neural network for predicting and engineering alternative polyadenylation[END_REF][START_REF] Linder | A generative neural network for maximizing fitness and diversity of synthetic dna and protein sequences[END_REF] or human 5'UTR sequences [START_REF] Cuperus | Deep learning of the regulatory grammar of yeast 5 ′ untranslated regions from 500,000 random sequences[END_REF][START_REF] Sample | Human 5 ′ utr design and variant effect prediction from a massively parallel translation assay[END_REF].

Building on these previous studies, we use here a nucleosome density predictor [START_REF] Routhier | Genome-wide prediction of dna mutation effect on nucleosome positions for yeast synthetic genomics[END_REF] together with a kinetic Monte-Carlo framework in order to design three sequences (of 167 bp, 197 bp and 237 bp) that lead to a regular nucleosome positioning when assembled into tandem repeated arrays in vivo (Fig. 1). The three NRL chosen encompassed the natural NRL of S.cerevisiae (167 bp) and the longest NRL known in eukaryotic species (237 bp, found in the sea urchin sperm [START_REF] Zalenskaya | Nucleosomal structure of sea urchin and starfish sperm chromatin. Histone H2B is possibly involved in determining the length of linker DNA[END_REF]). 2

MATERIALS AND METHODS

Synthetic sequence initialization

The initial sequences were determined at random. Each of the four (A,T,G,C) nucleotides is sequentially picked N times with a probability proportional to its abundance within the genome. This procedure insures that starting sequences have a GC content similar to the natural GC content of S.cerevisiae.

Synthetic sequence mutation

Our mutation and selection strategy for optimizing the sequence is inspired from the kinetic Monte-Carlo (k-MC) method originally designed for Ising spin systems ( [START_REF] Bortz | A new algorithm for monte carlo simulation of ising spin systems[END_REF]). Once the sequence of length N is initialized, it is duplicated 3 × N times in order to create 3 × N new sequences which will each harbor one of the 3 × N single mutations of the sequence (Fig. 1a). We then associate an energy term with each of the mutated sequences (see below). For every sequence i a selection probability Γ i is then defined as follow:

Γ i = 1 Z e -∆Ei/T (1)
with Z being the normalisation factor (Z = Σ i e -∆Ei/T ) and T the temperature, a broadening factor chosen by the user and corresponding to a classical temperature in a Maxwell-Boltzmann distribution. The next sequence is then randomly chosen according to this distribution of probability. The i th configuration is selected -with a probability Γ i -and the process continues for a given number of steps (10 4 in our case). Each chosen configuration is saved at each step, and the configuration with the minimal energy is chosen at the end.

Synthetic sequence energy term

An energy is associated to every sequence, representing how far the sequence is from having the desired characteristics. The energy can be divided into four parts (Fig. 1 b), described below.

Nucleosome density energy on the direct strand E reg In a former work we used a convolutional neural network (CNN) to predict the nucleosome density at the center nucleotide of a 2001 bp long DNA sequence [START_REF] Routhier | Genome-wide prediction of dna mutation effect on nucleosome positions for yeast synthetic genomics[END_REF]. In order to evaluate the nucleosome density over our synthetic array, we first create a 2001 + N bp long sequence by repeating the monomeric synthetic sequence. Then, this sequence is cut in N sequences of 2001 bp long used as inputs of the network thus providing the predicted nucleosome density over the whole synthetic sequence. The nucleosome density related energy is the distance between the predicted nucleosome density on the synthetic sequence and a target density. It forces the predicted density to converge to the target density (Fig. 1 c) The distance is defined as :

d(x, y) = 1 -corr(x, y) + 1 N Σ i |x i -y i | (2)
where corr stands for the Pearson correlation and N is the length of the sequence. The target signal y target is a combination of a gaussian distribution in the nucleosome region and a uniform distribution in the linker region:

y target i = a.e -(i-73) 2 2σ 2 + b if i ≤ 147 y target i = a.e -(147-73) 2 2σ 2 + b if i > 147 (3)
The parameters a, b and σ are chosen in order to create a realistic target (i.e which shape is similar to canonical nucleosomal densities found on the genome). The results are shown for a = 0.4, b = 0.2 and σ = 147 4 .

GC content related energy E GC As said previously, there are 4 N different sequences of a given length N . The CNN learned to position nucleosomes for sequences within the genome of saccharomyces cerevisiae. As a result, one wants to get a synthetic sequence which has a rather similar GC content as natural yeast. In order to do so, a first constrain energy is calculated as follow:

E GC = (GC synt -GC nat ) 2 (4)
with GC synt the GC content of the synthetic sequence and GC nat the GC content of the natural yeast (in that case, GC nat ≈ 0.38).

Enhanced sampling mutation energy E mut

It is common that such monte carlo procedure can get stuck into a local minimum of the energy, for instance flipping between the same two mutations. To avoid this potential pitfall, we added a term to the energy term that penalizes sequences that were already generated during the optimization process.

Nucleosome density energy on the reverse strand E rev

This energy is calculated in the same way as the nucleosome density related energy on the direct strand, but using the reverse complement strand instead. On most sequences this term is not relevant since the nucleosomal density predicted by the network is, due to the training process, the same for both strands.

However, we added this term to add an extra penalty to sequences for which the network would not work as expected and predict different densities for the two strands.

As a result, Eq.1 can be rewritten as:

Γ i = Σe -(α∆E GC +β∆Ereg+γ∆Erev+δ∆Emut)/T (5)
with α, β, γ and δ the relative weights for each energy component, chosen to get the same order of magnitude (e.g. = 1) for each energy term.

Interpretation of the mutations selected during the optimization process.

Positions of the mutations along the sequence A thousand independent k-MC optimization processes were executed and stopped after 20 steps. At each time step, the energy associated with each possible mutation is computed and stored. To quantify the importance of a given nucleotide in the positioning capacity of the sequence, the average absolute energy variation created by a mutation at this specific position is computed.

Typical mutation logos For each length (167, 197 and 237 bp), we collected all the 5-bp long motifs centered at each mutation site during 1000 independent optimization processes stopped after 20 steps. We then selected motifs for which a mutation induces an absolute energy variation higher than 0.5 (see Supplementary Figure S1 for the distribution of the absolute energy changes). We then regrouped the collected motifs into four categories depending on the sign of the energy modification and on their position, located in the linker region or in the dyad region (respectively after 147 bp and between 50 bp and 100 bp). We ended up with 14938 negative mutations in the linker, 16165 negative mutations in the dyad, 52603 positives mutations in the dyad and 158422 positive mutations in the linker. For each of these four categories we extracted significant logos of 5 bp using STREME [START_REF] Bailey | Meme suite: tools for motif discovery and searching[END_REF][START_REF] Bailey | Streme: accurate and versatile sequence motif discovery[END_REF] with the argument w=5. We also provided a list of control sequence to STREME by passing the list of 5 bp motifs associated to a mutation that modify the energy by less than 0.03. Finally, we selected logos that matched more than 10 % of the input sequences and represented them before and after the mutation.

In vivo assembly of the computationally designed sequences

Strains, plasmids, reagents and media In vivo genomic assembly of synthetic sequences nucleosome positioning (SSNP, Supplementary Table 1) DNA repeats was performed in the yeast strain YPH499. Strains derived from this study are listed in Supplementary Table 2. Plasmids used for the in vivo expression of spCas9 and the guide RNA targeting the YMR262 gene have been previously described [START_REF] Lancrey | Locus specific engineering of tandem dna repeats in the genome of saccharomyces cerevisiae using crispr/cas9 and overlapping oligonucleotides[END_REF] and are listed in Supplementary Table 3. Strains were grown at 30°C in yeast extract Peptone Dextrose 2% media (YPD) or in the appropriate synthetic complete Dextrose 2% media (SCD), media minus relevant amino acids necessary to maintain plasmid borne auxotrophic markers. All media reagents were purchased from Formedium and used as recommended. Oligonucleotides used in this study were synthetized by Eurogentec. Enzymes for nucleic acids modification were purchased from New England Biolabs. Zymolyase 20T was purchased from Amsbio.

Assembly of synthetic sequences nucleosome positioning DNA repeats in the yeast genome In vivo assembly using CRISPR/Cas9 and overlapping oligonucleotides in the Chromosome XIII of S. cerevisiae strain YPH499 was performed as previously described [START_REF] Lancrey | Locus specific engineering of tandem dna repeats in the genome of saccharomyces cerevisiae using crispr/cas9 and overlapping oligonucleotides[END_REF][START_REF] Lancrey | Nucleosome Positioning on Large Tandem DNA Repeats of the '601' Sequence Engineered in cerevisiae[END_REF] 4. YPH499 was transformed with the Cas9 expressing plasmid pRS413-Cas9-His (AJ-P1). The resulting strain was transformed using the LiAc technique [START_REF] Hill | DMSO-enhanced whole cell yeast transformation[END_REF] DraI, which cut at each side of the insertion locus. Digested DNA was electrophoresed in 1% agarose and transferred by capillarity onto a nylon membrane (Hybond N+, GE healthcare). Membranes were hybridized in Church buffer at 68°C with Cy5-probe ( [START_REF] Church | Genomic sequencing[END_REF]). The genomic probe was a 1 kb DNA fragment amplified by PCR from genomic DNA using primers O-33/O-34 and Cy5-dCTP. Membranes were scanned using a FLA 9500 GE healthcare.

Mononucleosome preparation using Micrococcal Nuclease digestion and sequencing (Mnase-Seq) Each strain was grown to an OD600 of 0.8 in 250 mL SCD media at 30°C with 200 rpm shaking. Cultures were treated with a final concentration of 1.85 % formaldehyde for 30 min at 30°C. Cross-linking was stopped by addition of 105 mM Glycine (final concentration). Cell pellets (6500g, 10 min) were washed and resuspended in 50 mL of 1 M Sorbitol, 10 mM Tris pH 7.5 supplemented with 10 mM ß-mercaptoethanol and 15 mg of Zymolyase 20T, and incubated 1h at 30°C with 50 rpm shaking. Spheroplasts were pelleted (6500g, 10 min), and resuspended in 2.4 mL solution containing 1M Sorbitol, 50 mM NaCl, 10 mM Tris pH 7.5, 5 mM MgCl2, 1 mM CaCl2 and 0.75 % Igepal CA630 freshly supplemented 6 with 1 mM ß-mercaptoethanol, 500 µM spermidine and 1000 units of MNase. The spheroplasts/MNase mixture was then incubated at 37°C for 30 min and stopped by adding 600 µL of 1% SDS, 10 mM EDTA. Reversal of crosslink and protein removal was achieved by adding 0.6 mg of Proteinase K (ThermoFisher) and overnight incubation at 65°C. DNA was purifed using phenol/chloroform precipitation method. Mononucleosomal DNA was isolated on a 1.8 % agarose electrophoresis gel and purified using QIAquick Gel extraction Kit. After DNA concentration determination using a Qubit Fluorometer, samples were treated and sequenced on a NovaSeq 6000 S4 PE150 XP by the Eurofins sequencing platform (NGSelect Amplicons).

Construction of synthetic reference genomes

For the three synthetic sequences we constructed a reference genome carrying two tandem repeats plus 65 bp of a third one. Indeed, the construction of the reference genome is required to take into account all possible alignments of a reads. Reads for which one mate overlaps the linker and the beginning of the following synthetic sequence justify the use of a second repeat in our reference genome. Extreme cases where the 2 mates of a read overlap two linkers justify the use of the beginning on a third repeat (65 bp is the length of our read -1 bp).

Reads alignment

the removal of barcodes, paired-end reads of 66 nt each were mapped against the appropriate (167, 197 or 237 bp) reference genome using Bowtie 2 (version 2.3.1) [START_REF] Langmead | Ultrafast and memoryefficient alignment of short dna sequences to the human genome[END_REF][START_REF] Langmead | Fast gapped-read alignment with bowtie 2[END_REF] allowing at most 2 alignments per read (-k m) and fragments length ranging 100 to 200 bp for 167 and 197 strains, and 120 to 250 bp for 237 strains (-I and -X parameters). Concordant reads were specifically selected using samtools (version 1.10).

Reconstruction of sequence coverage over DNA repeats

By choosing a reference genome with two repeats and 65 bp of an additional repeat, a large proportion of the reads of interest should be able to map twice justifying the allowing of 2 hits per reads using bowtie 2. Reads presenting multiple hits were filtered to select the most 5'-end alignment. Then, the density of nucleosome (i.e DNA fragments) on the specific reference genome is reconstructed using bedtools (version 2.29.2). Finally, the density on a unique repetition of a synthetic sequence was calculated by adding the density on every repeats in the synthetic reference genome. such arrays within a yeast chromosome [START_REF] Lancrey | Nucleosome Positioning on Large Tandem DNA Repeats of the '601' Sequence Engineered in cerevisiae[END_REF]. Our results unambiguously showed that the ability of the 601 sequence to strongly position nucleosomes is lost in S.cerevisiae (Fig. 2 b). We used our nucleosome density predictor [START_REF] Routhier | Genomics enters the deep learning era[END_REF] on the 601 sequence arrays used in this previous study and questioned whether it is able to predict the nucleosome density on a completely exogenous sequence, namely the Widom-601 sequence. In agreement with the experimental nucleosome densities, the predictor anticipates that the Widom-601 sequence is unable to position nucleosomes in vivo (Fig. 2 b). The predicted density is relatively flat over the 167 bp long sequence, showing no evidence of nucleosome localization on the first 147 bp where the Widom-601 sequence is placed. Moreover, for both the 197 bp and the 237 bp long sequence, the predictor anticipated that the preferential position of the nucleosomes is around the linker, in agreement with the experimental results (Fig. 2 c). The ability of our model to predict correctly the position of nucleosomes on exogenous sequences prompted to use it for a design purpose.

RESULTS AND DISCUSSION

Optimization of the monomer sequences for regular nucleosome positioning in tandem arrays

Starting from a random sequence, we computed the effect that would have on the predicted density all possible single mutations (Fig. 1). We then selected one of these mutations in order to obtain a nucleosomal density corresponding to one nucleosome precisely occupying the first 147 bp and being excluded from the rest of the linker region. We devised an energy function (Fig. 1 b) based on the distance between the predicted nucleosomal density on the tandem array sequence and a target density (in grey on Fig. 1c). The k-MC methodology optimisation process typically converged after 20 to 50 steps, starting from a DNA sequence (Methods and Fig. 1). The distance to the target was rapidly divided by a factor 3 during the 5 first mutations steps, then slowly converged and finally stabilised around a value of 0.6. The predicted nucleosome densities corresponding to three time points sampled during the optimisation process illustrate the convergence of the predicted density towards the target function (Fig. 1 c, right panels).

Quite surprisingly, for all initial random sequences we used, 5 to 20 changes out of 167 197 or 237 bp are always sufficient to provide a strong nucleosome po-9 sitioning sequence (Supplementary figure S2). Starting from random DNA seeds and after many round of sequence optimisation, we could produce hundreds of positioning sequences with a predicted nucleosome at the desired dyad position (Supplementary figure S3). Three sequences corresponding to the three NRLs we wished to impose on our tandem arrays were selected for further study.

Experimental validation of the positioning capabilities of the synthetic sequences

In order to compare the positioning efficiency of our three in silico optimized sequences with the in vitro optimized Widom's 601 sequence, we performed MNase-seq experiments on three S.cerevisiae strains in which repeated arrays containing 167 bp, 197 bp or 237 bp long monomers were engineered into the non essential YMR262 gene in chromosome XIII (Supplementary Figure S4, Online Methods and [START_REF] Lancrey | Nucleosome Positioning on Large Tandem DNA Repeats of the '601' Sequence Engineered in cerevisiae[END_REF]). We obtained mono-nucleosomal fragments both in the genomic sequences (Supplementary figure S5a,b,c) and in the synthetic repeated regions (Supplementary Figure S5d,e,f ). The experimental nucleosomal densities over the arrays as well as the corresponding predicted densities are shown on Fig. 2. Our results unambiguously show that our sequence optimisation framework enables the generation of non-natural sequences that are able to produce such arrays for 167, 197 and 237 bp (Fig. 2 d,e). For the 167 and 197 bp repeat, we observed a global preferential positioning of the nucleosome in the first 147 bp of the synthetic sequence with a flat peak which indicates that the nucleosome dyads (i.e. the fragments mid-points) are sharply distributed around the center of the first 147 bp (Supplementary Figure S6a). For the 197 bp long synthetic sequence, we also find a nucleosome well positioned on the first 147 bp of the sequence and a precisely positioned dyad (Supplementary Figure S6b). For the 237 bp long synthetic sequence tandem repeats, the experimental density exhibited a peak on the first 150 bp followed by a constant low density over 90 bp. Indicating that most of the nucleosomes were correctly positioned on the sequence. The central position of sequenced fragments distribution (Supplementary Figure S6c) also showed a strong enrichment in the first 147 bp although with a broader distribution, potentially resulting from several nucleosome preferred positions. The linker regions were as expected strongly depleted in nucleosomes.

Analysing the optimisation process of the synthetic sequences

In order to better understand how the sequence was designed to position the nucleosomes we made a quantitative analysis of the mutations that arise during the optimisation process. We first identified which regions of the sequence are the most important to design a positioning sequence by performing 1000 k-MCMC independent, 20 steps long, optimisations and recording at each step the energy changes associated with each of the possible mutation. The more important a given mutation is, the more is the associated change in energy, either positively or negatively. The absolute value of the average ∆E along the sequence suggests that the most important regions for nucleosome positioning are the linker region (in blue in Fig. 3 a) and the 50 bp region surrounding the dyad axis of the nucleosome (in red in Fig. 3). In order to go further into the sequence rules that define nucleosomes positions, we studied the motifs corresponding to the most important mutations (Online Methods). We split mutations into four groups: positioned either in the linker or in the dyad region and either increasing or decreasing the energy term. We then searched for typical 5 bp long DNA motifs within each group using STREME [START_REF] Bailey | Streme: accurate and versatile sequence motif discovery[END_REF]. Two types of mutations could be extracted: mutations that construct one of the two known nucleosome repelling motives (poly(dA-dT) and poly(dCG)) and mutations that destruct these motives [START_REF] Routhier | Genome-wide prediction of dna mutation effect on nucleosome positions for yeast synthetic genomics[END_REF]. The sign of the resulting energy change is dictated by the position of the nucleotide within the monomer sequence: in the linker region, destructive mutations increase the energy while constructive mutations decrease the energy. In the dyad region the opposite occurs. These results are consistent with previous studies suggesting that nucleosome attractive sequences do not 11 exist in S.cerevisiae genome and explain the inefficiency of the 601 sequence to position nucleosomes in vivo [START_REF] Tsankov | The role of nucleosome positioning in the evolution of gene regulation[END_REF][START_REF] Routhier | Genome-wide prediction of dna mutation effect on nucleosome positions for yeast synthetic genomics[END_REF].

CONCLUSION

In this study, we used the k-MC heuristic combined with a deep learning nucleosome density predictor to design an array of nucleosome positioning sequence. By assembling DNA tandem repeats of those synthetic sequence in S.cerevisiae genome, we validated that they were able to position a nucleosome on their first 147 bp and lead to the formation of regular arrays of various NRLs, including non-natural ones. The experimental control of the local NRL will enable the study of the structure of the nucleosomal fiber in vivo to decipher the causal link between nucleosome positioning, epigenetics marks, transcription or other related processes linked to chromatin structure. Our method, which combines a deep learning predictive method and the k-MCMC methodology, can be adapted to design DNA sequences with other designer characteristics and we expect it to play a growing role in the emerging field of synthetic genomics.

  . In summary, donor DNA containing the left (YMR/SSNP) and right (SSNP/YMR) genomic junction were amplified by PCR using primers couples O-1/O-2(O-3/O-4/O-5) and O-10/O-6(O-7/O-8/O-9) respectively. This donor DNA results, upon recombinational assembly in the deletion of the region -129 to 232 bp of the YMR gene. All oligonucleotides used for in vivo repeat assembly are listed in Supplementary Table

  with 1 µg of gRNA expressing plasmid targeting YMR262 (AJ-P2), 100 pmol of each of the four or six appropriate SSNP-oligonucleotides, and 10 pmol of both YMR/SSNP left and right junction PCR. After transformation cells were plated on SCD-His-Ura to select cells carrying both CAS9 and gRNA expressing plasmids. The in vivo assembly of synthetic sequences repeated arrays was verified by left and right junction PCR amplification (O-1/O-2 ; O-3 ; O-4 ; O-5 and O-10/O-6 ; O-7 ; O-8 ; O-9) and Sanger sequencing. The correct locus and the size of the SSNP assembly was confirm by analyzed recombinant clones by southernblotting. Genomic DNA from recombinant strains were digested with BamHI

3. 1

 1 Our computational model predicts the inefficiency of the Widom-601 sequence in vivoIn order to test the in vivo ability of the Widom-601 sequence to form regular nucleosome arrays of various NRLs we recently synthesize and integrated 7

Figure 1 :

 1 Figure 1: Sequence optimization via kinetic Monte-Carlo. (a) General principle of the method. (b) The energy associated to a sequence is the sum of four terms: (1) the distance between the nucleosome density predicted by the model and the target nucleosome density (2) the distance between the GC content of the sequence and the natural GC content of the yeast DNA (3) a penalty if the sequence has been already sampled (4) the distance between the density predicted on the reversed complemented sequence and the target density. (c) Evolution of the predicted nucleosome density (blue densities on the right) and of the corresponding energy (surrounded in blue) during the optimization process. The target density is displayed at the top (grey).

8 densityFigure 2 :

 82 Figure 2: Target, predicted and experimental nucleosome densities on a 1000 bp long subset of Widom-601 repeats and of synthetic sequence repeats. (a) Target nucleosome densities corresponding (from left to right) to one nucleosome every 167 bp, 197 bp and 237 bp. (b,c) Normalized predicted (b) and experimental (c) nucleosome densitiy on a 1000 bp region of 601 repeats. (d,e) Normalized predicted (d) and experimental (e) nucleosome density on the 1000 bp subset of our synthetic sequence repeats. Densities are normalized so that the area under the curve is equal to the area under the curve of the target densities

10 positionFigure 3 :

 103 Figure 3: Positions on the sequence and typical motifs around important mutations during the optimisation process. (a) Average absolute change in energy due to mutations at each position along the 167 bp, 197 bp and 237 bp monomer sequence (from left to right). (b) DNA motifs enriched around important mutations before and after the mutation (respectively on the left and right of the black arrows).

ACKNOWLEDGEMENTS

We thank members of the Structure and Instabilités des génomes and LPTMC laboratories for constructive comments during the realization of this work. Work was supported by core funding from CNRS, INSERM and MNHN. ALJ and ER were supported by a doctoral fellowship from the french ministry for Education, Research and Technology. EP was funded by grant ANR-15-CE11-0023-03 (HiResBac).

Availability of data and materials

Synthetic strains developed in this work are available upon request to JBB or AJ. Raw sequencing reads for Mnase-Seq experimentsare available at the following address: https://dataview.ncbi.nlm.nih.gov/object/ PRJNA863754?reviewer=c8p620eemjlo6r3dvv6kcjoip

The code developed in this work is available on github at the following address: https://github.com/etirouthier/nuc sequence design 6.0.1 Conflict of interest statement.

None declared.


MIVEGEC Antonio A Vázquez

Emeline Sabourin

Pilar Alda

Clémentine Leroy

Carole Leray

Eric Carron

Stephen Mulero

Céline Caty

Sarah Hasfia

Michel Boisseau

Lucas Saugné

Olivier Pineau

Thomas Blanchon

Annia Alba

Dominique Faugère

Marion Vittecoq

Sylvie Hurtrez-Boussès

Genetic diversity and relationships of the liver fluke Fasciola hepatica (Trematoda) with native and introduced definitive and intermediate hosts

Keywords: Domestic and wildlife infection, Fasciolosis, Lymnaeid snails, Population genetics

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

Among the trematode species affecting domestic and wild mammals with major impacts in human populations worldwide, the liver fluke Fasciola hepatica displays the largest known altitudinal and latitudinal distribution [START_REF] Mas-Coma | Human fascioliasis infection sources, their diversity, incidence factors, analytical methods and prevention measures[END_REF]. This parasite presents a heteroxenous life cycle including freshwater snails of the family Lymnaeidae as intermediate hosts (around 30 verified species; review in [START_REF] Correa | Bridging gaps in the molecular phylogeny of the Lymnaeidae (Gastropoda: Pulmonata), vectors of Fascioliasis[END_REF][START_REF] Vázquez | Lymnaeid snails hosts of Fasciola hepatica and Fasciola gigantica (Trematoda: Digenea): A worldwide review[END_REF] and a wide range of mammals as definitive hosts [START_REF] Hurtrez-Boussès | Dynamics of host-parasite interactions: The example of population biology of the liver fluke (Fasciola hepatica)[END_REF]. At a global scale, F. hepatica is responsible for fasciolosis, a food and waterborne disease affecting an estimated range between 35 and 72 million people annually and over 180 million at risk of infection [START_REF] Nyndo | Fascioliasis: An ongoing zoonotic trematode infection[END_REF]). Yet, it remains among the most Neglected Tropical Disease [START_REF] Who | Report of the WHO Informal Meeting on use of triclabendazole in fascioliasis control[END_REF]. This disease is also prevalent in temperate countries such as France where several outbreaks are usually linked to the consumption of contaminated watercress [START_REF] Mailles | Commercial watercress as an emerging source of fascioliasis in Northern France in 2002: Results from an outbreak investigation[END_REF] from cattle-rearing areas [START_REF] Rondelaud | Changes in human fasciolosis in a temperate area: About some observations over a 28-year period in central France[END_REF]. At veterinary level, fasciolosis infects around 600 million domestic animals and directly affects the national economies with about US $3 billion losses annually worldwide [START_REF] Khan | The global burden of fasciolosis in domestic animals with an outlook on the contribution of new approaches for diagnosis and control[END_REF][START_REF] Toet | Liver fluke vaccines in ruminants: Strategies, progress and future opportunities[END_REF]. Although wild species are much less studied, some of them may maintain the circulation in non-domestic and domestic environments (e.g. Wild Red Deer and Wild Nutria: [START_REF] French | Prevalence of liver fluke (Fasciola hepatica) in wild red deer (Cervus elaphus): Coproantigen ELISA is a practicable alternative to faecal egg counting for surveillance in remote populations[END_REF][START_REF] Kim | A case of fascioliasis in a wild nutria, Myocastor coypus, in Republic of Korea[END_REF]. In any case, the risk of fasciolosis transmission usually relates to areas with some degree of anthropic incidence (e.g. management of hydrographic networks, husbandry practices using sensible breeds, introduction of exotic species; [START_REF] Sabourin | Impact of human activities on fasciolosis transmission[END_REF]. Such facts bring forward the need of knowing precisely the infective capacity of the circulating strains and the hosts they infect along with the circumstances that actually promote their infection.

For instance, the analysis of the population genetic structure of parasites helps to understand their circulation among their hosts [START_REF] De Meeûs | Population genetics and molecular epidemiology or how to ''de´busquer la bête[END_REF]. Recent genetic studies using microsatellites markers on F. hepatica from different regions present most populations as highly diverse [START_REF] Beesley | Fasciola hepatica demonstrates high levels of genetic diversity, a lack of population structure and high gene flow: Possible implications for drug resistance[END_REF][START_REF] Cwiklinski | Characterisation of a novel panel of polymorphic microsatellite loci for the liver fluke, Fasciola hepatica, using a next generation sequencing approach[END_REF]. These results are usually explained through different hypothesis: (1) F. hepatica is hermaphroditic but adults usually reproduce by cross-fertilization (Hurtrez-Boussès et al., 2004); (2) flukes infecting domestic animals (particularly bovines) are passively introduced into distant regions because of poor cattle managerial activities [START_REF] Vázquez | Genetic and infective diversity of the liver fluke Fasciola hepatica (Trematoda: Digenea) from Cuba[END_REF]; and (3) introduction of non-native intermediate and definitive hosts in natural environments may prompt the transmission bridging the infecting wildlife genotypes with common domestic flukes [START_REF] Beesley | Fasciola hepatica demonstrates high levels of genetic diversity, a lack of population structure and high gene flow: Possible implications for drug resistance[END_REF]. Although there has been a handful of studies addressing F. hepatica variability within domestic animals [START_REF] Beesley | Fasciola hepatica demonstrates high levels of genetic diversity, a lack of population structure and high gene flow: Possible implications for drug resistance[END_REF][START_REF] Vázquez | Genetic and infective diversity of the liver fluke Fasciola hepatica (Trematoda: Digenea) from Cuba[END_REF][START_REF] Vilas | Contrasting patterns of population genetic structure of Fasciola hepatica from cattle and sheep: Implications for the evolution of anthelmintic resistance[END_REF], to our knowledge none has considered a detailed analysis of its diversity within wild hosts. Here, we propose a study that allows to explore precisely how the dynamics of a host-parasite system may rapidly evolve from a natural complexity (heteroxenous life cycle, multiple hosts, combination of sexual and asexual reproduction according to the host) increasing through local human activities (cattle management and introduction of invasive species).

Understanding host-parasite relationships is fundamental in the attempt of preventing and controlling the transmission of infection diseases [START_REF] Hawley | Disease ecology meets ecological immunology: Understanding the links between organismal immunity and infection dynamics in natural populations[END_REF]. However, laboratory approaches can only approximate reality to a certain point (e.g. revealing alleles or genotypes will rely upon the number of sampled individuals and the random probability of having higher or lower diversity). Moreover, field studies oblige to deal with some undesirable constraints (e.g. finding infected snails has proved to be challenging due to usually low prevalence; [START_REF] Sabourin | Impact of human activities on fasciolosis transmission[END_REF][START_REF] Vázquez | Natural prevalence in Cuban populations of the lymnaeid snail Galba cubensis infected with the liver fluke Fasciola hepatica: Small values do matter[END_REF]. In an attempt to have a closer glance to the genetics and infection patterns in this system, we have combined field and experimental approaches in order to study different intermediate and definitive hosts susceptible to F. hepatica. To this end, we carried out our study within the Camargue Regional Park. In this region, fasciolosis transmission is long reported (de Rivière, 1826) and largely affected by human activities [START_REF] Pnrc | Gestion du parasitisme bovin et faune coprophage[END_REF] and thus, ideal to the study of this system. The objective is to provide a better knowledge on the epidemiology of F. hepatica in wild and domestic animals and its ability to infect different lymnaeid species.

We characterized the population genetic structure of the parasite within each host using microsatellite markers in order to unveil the potential roles of each species as reservoirs and disseminators. Finally, we conducted experimental infections to test the compatibility of the circulating strain of F. hepatica with some native and introduced lymnaeid species and to assess the risks of transmission beyond the study area.

| MATERIALS AND METHODS

| Study area and F. hepatica sampling in domestic and wild definitive hosts

The study was carried out in the domain of Tour du Valat (TdV), a territory within the Regional Natural Park of Camargue (ProvenceAlpes-Côte d'Azur region, France) including lands classified as Regional Natural Reserve (Figure 1). The domain covers about 2,650 ha intended for the study and protection of wetlands including the typical natural habitats of Camargue such as temporary marshes, dunes and extensive halophile meadows. Although being a protected area, the territory has some managed resource activities including cattle farming. Cattle in this place belongs to the rustic race 'Raço di Biòu' (Bos taurus) adapted to the harsh conditions of Camargue. Because of the natural reserve regulations, the use of anthelmintic drugs definitively stopped in 2005 in all animals belonging to the TdV herd (hereafter considered as 'non-treated cattle'). However, some private cattle farms rent the surrounding lands off the limits of the Natural Reserve within TdV and use the flukicide Nitroxinil as anthelmintic drug (hereafter considered as 'treated cattle'). Treatment in this case occurs every once a year in November/ December. Among wild mammals, the domain harbours the native wild boar (Sus scrofa) and the introduced nutria (Myocastor coypus). Both species are known to be susceptible to F. hepatica infection [START_REF] Ménard | Myocastor coypus as a reservoir host of Fasciola hepatica in France[END_REF][START_REF] Mezo | The wild boar (Sus scrofa Linnaeus, 1758) as secondary reservoir of Fasciola hepatica in Galicia (NW Spain)[END_REF].

We explored the infection with F. hepatica in the domestic and the two wild species from 2013 to 2019. Cattle from TdV (non-treated, n = 210) and surrounding farms (treated, n = 15) were slaughtered for meat consumption in the nearby abattoirs of Tarascon (Bouches-duRhône) and Pézenas (Hérault). Veterinary authorities kindly allowed us to exhaustively dissect the livers and sample adult flukes from recently slaughtered cattle strictly following the particular hygiene and best practice guidelines of the abattoir. Liver examination was performed by cutting the whole liver in 2-cm perpendicular slices and pressing the biliary ducts. Concomitantly with liver examination, the content of the bile vesicle was examined (see exact methodology in Section 2.3) and either recovering the adults from the ducts or the eggs from the bile confirmed the prevalence. Wild boar samples (n = 156) were kindly donated by private hunters during the hunting season whereas nutrias (n = 42) were obtained through the conservation programme carried out to reduce this invasive species in the area (order approving the departmental hunting management scheme for Bouches-du-Rhône, 2014 -available at: http://www. bouch esdu-rhone.gouv.fr/conte nt/downl oad/9416/57472/ file/ ARRETE_SDGC.pdf). As with cattle, all received wild individuals were also thoroughly dissected and their liver examined following the same methodology as in cattle. All liver-infecting trematodes were recovered and stored in ethanol 80% for further molecular analysis. Parasite prevalence and intensities were noted following [START_REF] Reiczigel | Biostatistics for parasitologists -A primer to quantitative parasitology[END_REF]. Data on sex and age were also recorded for non-treated cattle from TdV herd.

| Molecular studies of F. hepatica (DNA extraction, microsatellite amplification, genotyping and data analysis)

We used a random sample of adult flukes from each definitive host (range 1-30 upon availability according to individual intensities) for molecular studies in an attempt to include a maximum number of infected individuals. A small piece of tissue (2 mm 2 ) from the posterior end of each adult F. hepatica (n = 1,148) was used for DNA extraction using the Chelex extraction technique adapted for 96well plates after [START_REF] Estoup | Marqueurs microsatellites: Isolement à l'aide de sondes non-radioactives, caractérization et mise au point[END_REF]. Briefly, the tissue was dried and placed in a well (one well per individual) containing a mix of 5 µl of proteinase K (Promega) and 100 µl of 5% Chelex® (Bio-Rad Laboratories). The plates were vortexed and incubated overnight at 56°C followed by vortex again and incubated 10 min at 95°C. Afterwards, the plates were centrifuged at 10,000 g for 5 min and the supernatant containing the DNA was collected and stored at -20°C until use.

Individual DNA extracts were diluted 1:10 for PCR amplification of nine microsatellite loci following the protocols of Hurtrez-Boussès et al. (2004) and [START_REF] Cwiklinski | Characterisation of a novel panel of polymorphic microsatellite loci for the liver fluke, Fasciola hepatica, using a next generation sequencing approach[END_REF]. Used markers (GenBank accession numbers) were FH15 (AJ508371), FH25 (AJ508373), FH222CBP (AJ003821), Fh_2 (LN627942), Fh_5 (LN627876), Fh_6 (LN629193), Fh_7 (LN635535), Fh_10 (LN628015) and Fh_12 (LN628360). Each locus was amplified using 1 µl of diluted DNA (1:10) in a 10 µl final reaction volume containing 2 µl buffer 5X (Promega), 1.2 µl 25 mM MgCl2, 2 µl 2 mM deoxynucleoside triphosphates (dNTPs) (Invitrogen/Life Technology), 1 µl of each primer (10 pmol) and 0.2 µl of 1 U Taq DNA polymerase (Promega). Thermocycling was performed in a 96-well MJ-Research PTC 100 (MJ Research) and consisted of an initial denaturation at 94°C for 4 min; 30 cycles of 94°C for 35 s, annealing temperature (FH15 = 48°C; Fh_2, Fh_5, Fh_6, Fh_7, Fh_10, FH222CBP = 55°C; FH25 = 57°C; Fh_12 = 60°C) for 30 s and 30 s at 72°C; and a final elongation step of 72°C for 10 min. Primers were fluorescently labelled to be used in an ABI automated sequencer (ABI-Prism 310 Genetic Analyzer, Applied Biosystems, Perkin-Elmer). Each PCR product was diluted 1:100, and 1 µl was used to prepare a mix containing 0.5 µl of internal size standards (GENESCAN 500 LIZ, Applera France) and 15 µl of Hi-Di Formamide (20 µl qsp) for the automated electrophoreses. All allele lengths were read using GeneMapper® v. 4.0 software (Applied Biosystems).

We estimated current parameters of population genetics such as mean number of alleles (Ar), observed (HO) and expected (HE) heterozygosities, departure from Hardy-Weinberg equilibrium (FIS) and pairwise differentiation between populations (FST). We considered all individuals sampled within a particular host group (non-treated cattle, treated cattle, nutria and wild boar) as different F. hepatica populations. Estimations were computed using the software FSTAT v2.9.3.2 [START_REF] Goudet | FSTAT, a program to estimate and test gene diversities and fixation indices (Version 2.9[END_REF], and Bonferroni corrections were applied for multiple tests [START_REF] Rice | Analyzing tables of statistical tests[END_REF]. We identified identical multilocus genotypes (MLGTs) only in flukes with all nine loci amplified and tested the probability of observing n copies of a given MLGT as the result of random mating (Psex values) using RCLone [START_REF] Bailleul | RClone: A package to identify MultiLocus Clonal Lineages and handle clonal datasets in R[END_REF]. Individuals with statistically significant Psex values (p < .05) were considered the result of clonal amplification [START_REF] Vilas | Contrasting patterns of population genetic structure of Fasciola hepatica from cattle and sheep: Implications for the evolution of anthelmintic resistance[END_REF]. Genotypic diversity (D) was also calculated using the Simpson index. The average number of migrants between populations (Nm) was estimated with GENEPOP v. 4.2.1 [START_REF] Rousset | Genepop'007: A complete reimplementation of the Genepop software for Windows and Linux[END_REF] using the private allele (Apriv) method developed by [START_REF] Slatkin | Rare alleles as indicators of gene flow[END_REF] for which parasites were grouped by definitive hosts. We used a Bayesian algorithm to determine the most appropriate number of genetic clusters (K). Twenty independent iterations of 200 000 burn-in length were followed by 100,000 Markov chain Monte Carlo repeats at each level for K = 1-30. ΔK was determined using the method proposed by [START_REF] Evano | Detecting the number of clusters of individuals using the software STRUCTURE: A simulation study[END_REF] computed in Structure Harvester [START_REF] Earl | STRUCTURE HARVESTER: A website and program for visualizing STRUCTURE output and implementing the Evanno method[END_REF]. We performed a discriminant analysis of principal components (DAPC) using the package adegent in R [START_REF] Jombart | Discriminant analysis of principal components:A new method for the analysis of genetically structured populations[END_REF] to explore the relatedness of MLGTs observed in each population F. hepatica. All MLGTs were reduced to one instance for the DAPC analysis and for the construction of the genetic distance matrix.

| Experimental infection of lymnaeid snails

Six populations of four lymnaeid species (two introduced and two native in Europe; see details in Table 1) were exposed to the circulating F. hepatica isolate from TdV collected during the 2019 campaign (Camargue) and served as experimental models.

From these field populations, we reared two successive generations in the laboratory using plastic cages. Snails were fed with boiled minced lettuce ad libitum and maintained at constant temperature (22°C) and relative humidity (55%) conditions.

Threeweek-old snails were used for experimental infections. A pool of F. hepatica eggs from non-treated cattle (n = 25) was selected to obtain miracidia (the larvae that infect the intermediate host) to expose the snails as it resulted the most genetically diverse parasite isolate (see Section 3.2). Briefly, we collected the content of the bile vesicle from cattle obtained in the abattoir (see Section 2.1) for mass egg retrieval. The bile was sift using pore size-decreasing set of sieves and continuous washing with saline solution (0.85%) to isolate the eggs that were stored in tubes containing saline solution at 4°C in the dark until use [START_REF] Vázquez | Reviewing Fasciola hepatica transmission in the West Indies and novel perceptions from experimental infections of sympatric vs. allopatric snail/fluke combinations[END_REF]. When the snails were one week old, we changed the eggs to spring water and incubated for 15 days in darkness at 27°C. The experimental infection methodology was followed as in [START_REF] Vázquez | Reviewing Fasciola hepatica transmission in the West Indies and novel perceptions from experimental infections of sympatric vs. allopatric snail/fluke combinations[END_REF] individually exposing 30 snails of each population to a dose of five F. hepatica miracidia.

Mortality was recorded daily. All snails that died after the first week post-exposure were dissected and those individuals that showed the intramolluscan stage of F. hepatica, the rediae, were marked as infected. Those snails dying during the first week post-exposure were considered as non-infected since the early stages are very difficult to detect and would introduce uncontrollable bias. After 30 days post-exposure, all remaining snails were dissected under a stereoscope following [START_REF] Caron | The detection and quantification of a digenean infection in the snail host with special emphasis on Fasciola sp[END_REF] and all living F. hepatica rediae (irrespective of their size or generation; [START_REF] Rondelaud | Redial generations of Fasciola hepatica: A review[END_REF] were counted. We kept 30 individuals of each population unexposed but submitted to the same experimental manipulation as negative controls.

Compatibility was evaluated using three parasitological variables according to [START_REF] Reiczigel | Biostatistics for parasitologists -A primer to quantitative parasitology[END_REF]: (1) prevalence (%), that is proportion of infected individuals from all the exposed within the host sample; (2) mean parasite intensity as the average of intensity values-rediae/snail-calculated for a sample with 95% confidence intervals (CI); and (3) survival (%) as the percentage of alive individuals in the sample (exposed or unexposed population). To that end, a one-way ANOVA followed by a post hoc Tukey test was used to compare parasite intensities among trials after normality and homogeneity of variance were verified by the Shapiro-Wilk and Levene tests. Differences in survivorship among trials were statistically assessed through a log-rank test of Kaplan-Meier curves built from day 0 to day 30 post-exposure. All statistical tests were performed in Statistica v.12 (StatSoft. Inc., Tulsa, OK, USA 2014), and differences were considered significant at values of p < .05.

| RESULTS

| Trematode liver infections in domestic and wild definitive hosts

The total prevalence of F. hepatica in cattle (domestic definitive hosts; N = 225) was 60% but with higher values in non-treated cattle (85%; mean intensity 15.7 ± 2.3 CI) than in treated cattle (67%; mean intensity 16.3 ± 7.4 CI), although non-significant (chi-square = 3.36, p = .06) (Table 2). Intensities among all combinations of non-treated (young/adult/male/female) and treated cattle (ANOVA results: F = 0.583; p = .67) were not significant. In non-treated cattle, prevalence was higher in females (91.6%) than in males (81%) (χ 2 = 5.06, p = .02). Both sexes combined, prevalence in young individuals (1-3 years old), were higher than in adults (χ 2 = 4.03, p = .04). We observed a slight trend of increasing intensity with age, but it was nonsignificant (p = .24). Prevalence was lower in wild definitive hosts with 19% in nutria (N = 42) and 4.5% in wild boars (N = 156) (Table 2).

During liver dissection, we also noted the infection with the trematode Dicrocoelium dendriticum (Lancet liver fluke) in some individuals from all examined host species. Overall D. dendriticum prevalence was higher in non-treated cattle (76%) and nutria (50%) compared with treated cattle (25%) and wild boars (11%). Co-infection occurred in cattle (non-treated, 70%; treated 25%) and in nutria (38%), but it was not detected in wild boars.

| Genetic diversity and population structure of F. hepatica from definitive hosts

We attempted the genetic characterization at nine microsatellite loci for 1,148 recovered adult liver flukes from non-treated cattle (949), treated cattle (100), nutria (81) and wild boar (18). The characterization of all examined loci among the four definitive host species of F. hepatica from TdV is presented in Table 3. We did not find significant associations (Spearman correlation) between the number of analysed flukes and the number of alleles per locus for all loci among the parasites found in the definitive host species.

Overall, all loci resulted polymorphic with non-significant deviations from the Hardy-Weinberg equilibrium in any of the examined groups of hosts (Table 4). Globally, F. hepatica populations from domestic hosts presented significantly higher values of allelic richness (5.7 alleles per locus; range: 4-25 alleles) and expected heterozygosity (p < .05) than those from wild hosts (mean: 5 alleles per locus; range: 2 -19) (p < .001, Wilcoxon rank-sum test). The populations from the four definitive host species shared 42 alleles (32%, N = 131). However, private alleles (Apriv) were observed only in cattle populations (Table 4). These unique alleles attained a maximum of six per locus.

| Genetic differentiation in F. hepatica

All populations from the four definitive host species appeared slightly differentiated but still differed significantly (overall FST = 0.024 ± 0.013 SD; p < .05). Actually, we detected a number of migrants among populations (mean 13.9 ± 7.4) particularly between non-treated cattle and nutria (Table 5).

Overall, we found 729 different MLGTs among 783 liver flukes with the nine loci amplified and 47 MLGTs repeated across the sample. However, the number of MLGTs found in each definitive host species was dependent of the sample size (Pearson correlation r = 1, p < .001). All identical MLGTs were the result of clonal amplification (Psex < 0.05) with a global high genotypic diversity (Table 5). We found 41 MLGTs repeated in two flukes, five MLGTs repeated in three flukes and only 1 MLGT repeated in four flukes. Overall, 21 MLGTs were shared by different host individuals but only in nontreated cattle and five were recovered at different years (2014)(2015). None MLGT was found shared by different host species.

The ΔK values were very low indicating low structuration among the analysed flukes but still three clusters (K = 3) were found. To gain deeper insight into the genetic structure of F. hepatica populations and obtain a clearer view of the genotypic variation, we performed a DAPC that identifies clusters of genetically related individuals only for individuals with the nine loci amplified. Although most MLGTs are closely related, we still are able to observe three clusters separating treated cattle, nontreated cattle/nutrias and wild boars. MLGTs from nutrias and non-treated cattle could not be differentiated (Figure 2); however, it should be noted that only individuals with all nine loci amplified were kept for this analysis.

| Infection of different lymnaeid species with F. hepatica

All four snail species and populations were susceptible to F. hepatica infection (Figure 3a). Overall, the introduced species presented higher values of prevalence (G. truncatula from TdV, 70%; P. columella, 57%) than native lymnaeids. The allopatric population of G. truncatula from Rieu Massel attained 30% prevalence with lower values of parasite intensities and survival than the rest of analysed populations. Overall, parasite intensities were significantly different (ANOVA results: F = 20.3; p < .001), particularly G. truncatula from Pesquier (TdV) with the highest values (mean 36 ± 6 CI) (Figure 3b). However, similar values were observed among P. columella, L. stagnalis and G. truncatula (Anciennes Vignes, TdV) after the post hoc Tukey test. The species with the lowest values of prevalence and parasite intensities was R. balthica. Survival was globally higher than 60% (Figure 3c) for most species and populations, reaching 100% in G. truncatula from TdV. Only G. truncatula from Rieu Massel attained low survival rate (13.3%). All control groups attained zero mortality (data not shown).

| High transmission of liver trematodes in domestic and wild definitive hosts in TdV

The overall prevalence of F. hepatica in cattle from TdV (>60%) is considerably higher than in other regions such as central France (13% to 25%; [START_REF] Mage | Fasciola hepatica and Paramphistomum daubneyi: Changes in prevalences of natural infections in cattle and in Lymnaea truncatula from central France over the past 12 years[END_REF] but similar to certain endemic regions elsewhere (Nepal > 70%; Yadav, Ahaduzzaman, Sarker, Sayeed, & MA, 2015; Cuba > 70%; [START_REF] Vázquez | Genetic and infective diversity of the liver fluke Fasciola hepatica (Trematoda: Digenea) from Cuba[END_REF]Zambia > 60%, Nyirenda et al., 2019). The absence of differences in prevalence or intensity between treated and non-treated cattle may suggest a failure of grazing management and/or treatment strategy by either wrong appliances or the existence of resistance to the used flukicide Nitroxinil. In this region, cattle is treated once a year in November-December (breeder's communication) and the exposure to the fluke would be potentially all-year-round. Given that flukes from the non-treated herd were recovered usually in late December, a failure of the drug can be a plausible explanation. Elsewhere, Nitroxinil has been used successfully in Triclabendazole-resistant flocks [START_REF] Romero | Flukicide efficacy against Fasciola hepatica of Triclabendazole and Nitroxynil in cattle of the central valley of Chile[END_REF] but it is known to lower its efficacy in 7-to 9-week-old liver fluke's juveniles [START_REF] Martínez-Valladares | Efficacy of nitroxynil against Fasciola hepatica resistant to triclabendazole in a naturally infected sheep flock[END_REF].

Although the probability of infection may increase with age (i.e. definitive hosts have more time to encounter the parasite cysts in the field; [START_REF] Khan | The global burden of fasciolosis in domestic animals with an outlook on the contribution of new approaches for diagnosis and control[END_REF], we found no direct link between age and parasite intensity (calculated as the burden of flukes within a single host). Our non-significant trend (analysed individuals ranged from 1 to 18 years old) could be understood as a similar risk of infection every year associated with a natural parasite turnover during the lifespan of the host (flukes usually live for less than 2-3 years in cattle). This maintained risk of infection could be supported by a very high prevalence of field-occurring cysts of F. hepatica supporting reinfection. Given that females and males graze together in the studied area, the proportionally more infected females could be due to a lower immune competence by stress during pregnancy and parturition [START_REF] Spithill | Fasciola gigantica: Epidemiology, control, immunology and molecular biology[END_REF], or by a differential pattern of grazing areas because of particular management practices in this region.

The infection observed in wild hosts was not negligible and agrees with studies elsewhere. [START_REF] Ménard | Myocastor coypus as a reservoir host of Fasciola hepatica in France[END_REF] found an overall 8.7% prevalence in nutria from Loire-Atlantique (western France) although it increased up to 40% when nutria were sampled from areas containing farms with infected cattle. In the case of wild boars, a study from Galicia (Spain) recorded over 11% prevalence suggesting a role as secondary reservoir of fasciolosis [START_REF] Mezo | The wild boar (Sus scrofa Linnaeus, 1758) as secondary reservoir of Fasciola hepatica in Galicia (NW Spain)[END_REF]. In addition to cattle, both wildlife species are particularly interesting in fasciolosis epidemiology. Nutrias are, however, probably more relevant in maintaining fasciolosis in a given small area due to their territoriality [START_REF] Carter | A review of the literature on the worldwide distribution, spread of, and efforts to eradicate the coypu (Myocastor coypus)[END_REF] and typical habitats that usually overlaps with those of intermediate host snails (e.g. irrigation and drainage channels). On the contrary, wild boars are known to use over 100 ha of effective territory [START_REF] Boitani | Spatial and activity patterns of wild boars in Tuscany, Italy[END_REF], and thus would be able to use different non-connected biotopes. For instance, both species would be key players in disseminating different liver fluke's genotypes among intermediate hosts that could entangle the genetic background of the overall metapopulation. This hypothesis is supported by the fact that all alleles observed in both wild hosts were shared in domestic hosts, particularly between non-treated cattle and nutrias. Whatever the case may be, we should note that transmission in the studied area is mainly due to cattle (higher prevalence and genetic diversity) and that they are generally responsible for raising the probability of infection in wildlife or eventually humans [START_REF] Vázquez | Genetic and infective diversity of the liver fluke Fasciola hepatica (Trematoda: Digenea) from Cuba[END_REF].

On the other hand, the observed co-infection between F. hepatica and D. dendriticum (e.g. 70% in non-treated cattle) is particularly interesting as both trematode species target the liver of definitive hosts. In fact, this particular co-infection event is commonly reported [START_REF] Ducommun | Prevalence and distribution of Dicrocoelium dendriticum and Fasciola hepatica infections in cattle in Switzerland[END_REF][START_REF] Khanjari | Prevalence of fasciolosis and dicrocoeliosis in slaughtered sheep and goats in Amol abattoir, Mazandaran, northern Iran[END_REF]. The observed prevalence in this study reveals that D. dendriticum is also highly prevalent in both domestic and wild mammals. Contrary to F. hepatica, D. dendriticum uses land snails and ants as first and second intermediate hosts, respectively, and the existence of humid conditions or lasting waterbodies is not needed for transmission to occur. Indeed, alkaline and carbonate-rich soils are the most important conditions for their intermediate hosts [START_REF] Manga-González | Contributions to and review of dicrocoeliosis, with special reference to the intermediate hosts of Dicrocoelium dendriticum[END_REF] whilst parasite eggs can last long periods in pastures [START_REF] Taylor | Emerging parasitic diseases of sheep[END_REF]. These facts would suggest that the infection by D. dendriticum might be higher than that by F. hepatica and that it might affect the establishment of F. hepatica. Notwithstanding, this was not the case here and a plausibly explanation could be that the studied territory is a wetland harbouring lymnaeid populations highly compatible with the local strains of F. hepatica (see Section 3.4). In a potential scenario of strong interspecific competition inside the definitive hosts, F. hepatica seems able to resist and survive. Future studies should model the outcome of such competition by examining the intensities of both interacting trematode species since it could overall affect the transmission epidemiology.

| High polymorphism in F. hepatica populations from different hosts

The allelic sizes found in this study fall within the reported range elsewhere [START_REF] Cwiklinski | Characterisation of a novel panel of polymorphic microsatellite loci for the liver fluke, Fasciola hepatica, using a next generation sequencing approach[END_REF]Hurtrez-Boussès et al., 2004). However, here we found less alleles per locus for most explored loci (except Fh_7) compared with those observed by [START_REF] Beesley | Fasciola hepatica demonstrates high levels of genetic diversity, a lack of population structure and high gene flow: Possible implications for drug resistance[END_REF]. In Cuba, for example, where F. hepatica is endemic in cattle [START_REF] Alba | Assessment of the FasciMol-ELISA in the detection of the trematode Fasciola hepatica in field-collected Galba cubensis: A novel tool for the malacological survey of fasciolosis transmission[END_REF], a population genetic study using FH15, FH25 and FH222CBP markers from eight different cattle isolates showed similar values with a mean of 7.5 alleles per locus and up to 30 alleles among the three loci [START_REF] Vázquez | Genetic and infective diversity of the liver fluke Fasciola hepatica (Trematoda: Digenea) from Cuba[END_REF]. Other studies that have attempted to explore F. hepatica using haplotype diversity also show high variability. For instance, studies using Nad1 gene found 24 haplotypes from 79 individuals in Brazil [START_REF] Schwantes | Fasciola hepatica in Brazil: Genetic diversity provides insights into its origin and geographic dispersion[END_REF] and 37 haplotypes from 130 individuals in Iran [START_REF] Bozorgomid | Genetic diversity and distribution of Fasciola hepatica haplotypes in Iran: Molecular and phylogenetic studies[END_REF].

We found an absence of deviations from the Hardy-Weinberg equilibrium and high genetic diversity of F. hepatica that could be explained by cross-fertilization among parasites and high migration rate thanks to definitive host movements. In fact, private alleles were only found in non-treated (14%) and treated (3%) cattle. In Spain, a study showed that structuration might occur between flukes from sheep and cattle [START_REF] Vilas | Contrasting patterns of population genetic structure of Fasciola hepatica from cattle and sheep: Implications for the evolution of anthelmintic resistance[END_REF]. Here, after analysing three different host species we can only think of an established flow of parasites among them, particularly in non-treated cattle and nutrias that may explain the results observed in the DAPC analysis. In the case of the more evident differentiation between treated and non-treated cattle, we should keep in mind that although farms are adjacent to one another, cattle from both herds never mix. However, we still observe some overlaps indicating that genetic distances are not very high. This raises concerns on breeding and managing practices that may promote year-round infections and the encountering of distant flukes through passive dissemination by definitive hosts. Host movements may act as 'bridging agents' playing an important role in homogenizing the metapopulation of F. hepatica. As a result, the random emergence of resistant genes to anthelmintic treatment may mix in the metapopulation through these migration events and complicate the eventual control of fasciolosis. For instance, clonal expansion of resistant genotypes to the flukicide Triclabendazole within the snails has been highlighted in G. truncatula [START_REF] Hodgkinson | Clonal amplification of Fasciola hepatica in Galba truncatula: Within and between isolate variation of triclabendazole susceptible and -resistant clones[END_REF]. Usually, important genetic bottlenecks are expected in populations routinely treated with anthelmintic [START_REF] Vázquez | Genetic and infective diversity of the liver fluke Fasciola hepatica (Trematoda: Digenea) from Cuba[END_REF]) but here we still find a high genotypic diversity. It would be nevertheless interesting to develop tests aimed at exploring the existence of resistant genes to the different used anthelminthic drugs. Such genes would explain the prevalences observed in treated cattle or expose hazardous management of grazing patterns here and elsewhere.

| Field transmission and risks of fasciolosis expansion in Camargue

We should note that 40 repeated genotypes were observed in cattle. Some of these genotypes were recovered not only from different host individuals but also from different years. Two different explanations can be given: (1) F. hepatica may live at least over two years inside their mammal host [START_REF] Takeuchi-Storm | Patterns of Fasciola hepatica infection in Danish dairy cattle: Implications for on-farm control of the parasite based on different diagnostic methods[END_REF]; and (2) metacercariae cysts are capable of resisting for several months before being ingested by the definitive hosts [START_REF] Andrews | The life cycle of Fasciola hepatica[END_REF]. In either case, the field contamination with metacercarie should be sufficiently large to infect different individuals with the same MLGT.

Overall, we found 687 MLGTs in cattle of which 647 were recorded once. Although snails are susceptible to be infected with more than one miracidium (see [START_REF] Rondelaud | Fasciola hepatica: The developmental patterns of redial generations in naturally infected Galba truncatula[END_REF], if we accept, theoretically, that one MLGT equals one infected lymnaeid snail (infection more commonly occur by only one miracidium that will expand asexually), there should had been up to as many infected snails as observed MLGTs in the studied period. This result suggests the existence of multiple sources of field infection for the definitive hosts allowing for such high genotypic diversity. This is particularly important if we understand that natural prevalence in the snails is usually low [START_REF] Dreyfuss | Natural infections of Omphiscola glabra (Lymnaeidae) with Fasciola hepatica in central France[END_REF][START_REF] Mekroud | Preliminary studies on the prevalences of natural fasciolosis in cattle, sheep, and the host snail (Galba truncatula) in north-eastern Algeria[END_REF][START_REF] Vázquez | Natural prevalence in Cuban populations of the lymnaeid snail Galba cubensis infected with the liver fluke Fasciola hepatica: Small values do matter[END_REF]. Susceptible populations of lymnaeid snails should then be scattered throughout the grazing areas at TdV, and managerial activities should recognize the location of intermediate host populations as a predictor for fasciolosis infection.

Here, we proved that the isolate of F. hepatica from TdV is capable of infecting several species of lymnaeid snails. Overall, we found differences in compatibility regarding their susceptibility, capacity of the parasite to expand inside the snails and survival of the latter after the exposure. The compatibility showed by sympatric G. truncatula is in agreement with the existence of local adaptation in this system [START_REF] Vázquez | Reviewing Fasciola hepatica transmission in the West Indies and novel perceptions from experimental infections of sympatric vs. allopatric snail/fluke combinations[END_REF]. Inversely, the allopatric population of G. truncatula showed low compatibility with F. hepatica. This population was recovered from a non-transmission region in a commonly droughtfloodable habitat (side route ditch). Genetic drift might have rendered those individuals highly incompatible through a continuous series of genetic bottlenecks that make them impossible to sustain the infection. Similar results were obtained by [START_REF] Dreyfuss | Local adaptation of the trematode Fasiola hepatica to the snail Galba truncatula[END_REF] when testing local adaptation in G. truncatula to F. hepatica.

Anyhow, although G. truncatula appears as the best suitable intermediate host (at least the sympatric populations), we should not disregard the results from the other species, even if we did not allowed for cercarial shedding in our experiments. This is particularly the case of P. columella, an invasive species known for its ability of inserting itself into the epidemiological scenario of fasciolosis after recent incidental introductions worldwide [START_REF] Lounnas | Self-fertilization, long-distance flash invasion and biogeography shape the population structure of Pseudosuccinea columella at the worldwide scale[END_REF]. In a world-changing climate, conditions may shift to render more suitable the establishment of this species in southern Europe and consequently promote fasciolosis transmission. For instance, P. columella is already introduced into many artificial habitats in many European countries [START_REF] Glöer | The freshwater gastropods of the West-Palaearctis. Volume I. Fresh-and brackish waters except spring and subterranean snails[END_REF] and has already been found living in the wild in France [START_REF] Pointier | Pseudosuccinea columella (Say 1817) (Gastropoda, Lymnaeidae), snail host of Fasciola hepatica: First record for France in the wild[END_REF]. Moreover, native species such as those tested here (L. stagnalis and R. balthica) would be capable of facilitating the transmission in nearby areas not yet colonized by G. truncatula or P. columella. In fact, both lymnaeids species are known to transmit F. hepatica in several European countries [START_REF] Vázquez | Lymnaeid snails hosts of Fasciola hepatica and Fasciola gigantica (Trematoda: Digenea): A worldwide review[END_REF].

| Concluding remarks

These results highlight the importance of studying the epidemiology of an infectious trematode disease by taking into account the diversity of occurring definitive and intermediate hosts. Indeed, this kind of approach helps in the implementation of efficient integrated management programmes to prevent and/or control the transmission. For instance, in the case of fasciolosis, human activity has proved to be a key factor in promoting the transmission [START_REF] Sabourin | Impact of human activities on fasciolosis transmission[END_REF]. Herd density and grazing management coupled with topographic features and environmental conditions that favour the occurrence of snail hosts would influence prevalence and parasite intensity of F. hepatica. Thus, limiting access to high-risk pastures and implementing good anthelmintic treatments are key aspects in reducing the transmission in regions such as Camargue. In addition, addressing the epidemiological risks cannot be limited to a single host-parasite system, but should focus on understanding the diversity of hosts in the heterogeneous environment through space and time. The existing polymorphism of compatibility in the snail host and F. hepatica has revealed that different species may play different roles and that certain combinations are particularly dangerous [START_REF] Vázquez | Reviewing Fasciola hepatica transmission in the West Indies and novel perceptions from experimental infections of sympatric vs. allopatric snail/fluke combinations[END_REF]. Although not very well studied, something similar may occur at the definitive host level. For example, rapid evolution can take place through human activities and the introduction of new host species or the replacement of rustic breeds may facilitate the transmission. Surveillance is, therefore, mandatory if we are to meet the challenge of tackling the emergence or re-emergence of such infectious diseases.

FIGURE 1 FIGURE 2 FIGURE 3

 123 FIGURE 1 Map of Tour du Valat within the Camargue Regional Park with details of cattle farms and sampled wild host infected with Fasciola hepatica [Colour figure can be viewed at wileyonlinelibrary.com]

ACKNOWLEDGEMENTS

We are in debt to veterinary authorities and technical personnel from the abattoirs of Tarascon and Pézenas, as well as hunters and farmers from the domain of Tour du Valat and T. Noëll for their help in obtaining fluke samples. These studies have been partially supported by Muse (project REPAS: grant n°170544IA, n°ANR-IDEX-0006), Labex CeMeb, Tour du Valat, INEE CNRS through the Ecosan funding programme and Peps Ecomob, IRD, and University of Montpellier.

MUSE, Grant/Award Number: 170544IA and ANR-IDEX-0006; INEE CNRS; Labex CeMeb; Université de Montpellier; Tour du Valat; Ecosan; IRD

DATA AVAILABILITY STATEMENT

All data are available upon direct request to the authors.

CONFLICT OF INTEREST

The authors declare that they have no competing interests.

ETHICAL STATEMENT

The study was conducted in compliance with ethical standards.


domain: chim spi

text:
Jakob Langenbach
email: jakob.langenbach@espci.fr

Antonia Georgopoulou

Frank, Clemens b , François, Tournilhac a , Sophie Norvez

SELF-HEALING VITRIMER COMPOSITES FOR SOFT ROBOTICS

Keywords: soft robotics, matrix-sensor fiber laminates, deformation gradient, stiffness matching

Hybrid networks (i.e. including physical and chemical crosslinks) were synthesized from bio-sourced fatty acids, linked to each other by a controlled number of non-exchangeable ether bonds, exchangeable ester bonds and non-covalent hydrogen bonds. Mechanical properties are tuned by the acid/epoxy ratio. Their thermo-stimulated weldability was exploited to incorporate stretchable strain sensors by embedding electrically conductive fibers into the vitrimer matrix. The efficiency of welding at 80 °C and the tunability of mechanical properties are both attractive assets for effective incorporation of thermo-degradable conductive fibers while preserving their mechanical and electrical integrity. Mechanical and electrical behavior of the sensor composites were simultaneously tested in cyclic tensile experiments at 50 °C. The stress concentration in dog-bone shaped samples was investigated by observations in polarized light and shear stress calculations. The study emphasizes the importance of matching the Young's moduli of components in deformable composite samples, which is important for soft robotic applications.

Introduction

Soft robots have many advantages over conventional robots made of rigid materials, such as their high deformability (up to several hundred percent strain) and adaptability to their environment. However, soft materials are also intrinsically prone to damage, leading to an increasing research of self-healing elastomers for soft robots [START_REF] Terryn | A review on self-healing polymers for soft robotics[END_REF]. Self-healing (SH) polymers can heal damage due to dynamic bonds in the network. In order to detect possible damage or to measure the robot's deformation, stretchable strain sensors have to be integrated into the robotic devices [START_REF] Georgopoulou | Piezoresistive Elastomer-Based Composite Strain Sensors and Their Applications[END_REF]. Different manufacturing techniques are possible for the sensor integration, while self-healing polymers take advantage of exchangeable bonds in the network to promote the adhesion [START_REF] Chabert | Multiple welding of long fiber epoxy vitrimer composites[END_REF][START_REF] Roels | Processing of Self-Healing Polymers for Soft Robotics[END_REF].

The strain sensors often consist of an elastomeric material with incorporated conductive fillers like carbon black particles, carbon nanotubes, etc. The electrically conductive filler modifies the mechanical properties of the strain sensor, which results in a stiffness mismatch between the elastic matrix and the integrated sensor fiber. The mismatch induces shear stresses at the fibermatrix interface which has negative effects up to the rupture of the sensor fiber inside the matrix. Herein, we report the integration of thin strain sensor fibers into hybrid networks (i.e., including physical and chemical crosslinks) with tunable mechanical properties. The matrix stiffness is adapted to reduce the shear stress at the fiber-matrix interface. Calculations and observations under polarized light suggest that small stiffness changes can significantly decrease the shear stress to prevent a fiber rupture, especially in areas with changing cross-section.

Results

The hybrid network materials (including physical hydrogen bonds and possibly exchangeable ester bonds) were synthesized in a facile two step synthesis (5) and the crosslinking density was adapted by the initial feed ratio acid/epoxy. An epoxy excess leads to homo-polymerization and the formation of non-exchangeable ether bonds [START_REF] Tangthana-Umrung | Epoxy homopolymerisation as a tool to tune thermo-mechanical properties and fracture toughness of vitrimer[END_REF]. Nevertheless, the vitrimer nature of the materials was preserved, as indicated by creep and solubility measurements [START_REF] Langenbach | Adhesion and Stiffness Matching in Epoxy-Vitrimers/Strain Sensor Fiber Laminates[END_REF]. The sensorfiber composites (SFCs) were produced by cutting pairs of dog-bone shaped specimens and placing the thin sensor fiber (diameter 0.3 mm) in between (Figure 1). The sensor-fiber composite was assembled by using the thermally stimulated weldability, leading to a good integration of the thermo-degradable sensor fiber between the two laminates (7).

Figure 1. Scheme for the integration of electrically conductive sensor fibers in tunable hybrid networks by sandwich-welding. Sensor fibers are sandwiched between two dog-bones and sensor-fiber composite is welded at 80 °C for 1 h. Reprinted with permission from [START_REF] Langenbach | Adhesion and Stiffness Matching in Epoxy-Vitrimers/Strain Sensor Fiber Laminates[END_REF]. Copyright 2022 American Chemical Society.

The SFCs were tested under cyclic tensile experiments (0 -20 % strain) at 50 °C, measuring simultaneously the tensile stress and electrical resistance of the sensor fiber. The glass transition temperature (Tg) of the hybrid networks is slightly below room temperature (12 -16 °C), so the speed of elastic return at temperatures T around 25 °C is highly influenced by the distance T-Tg.

The samples with 0 mol%, 5 mol% and 10 mol% epoxy excess are named C_0epoxy, C_5epoxy and C_10epoxy, respectively. Figure 2 displays 20 cycles of tensile stress of the composites and the relative resistance, which is the ratio of the change in resistance (R-R0) divided by the resistance at rest (R0):

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑅 -𝑅 0 𝑅 0 (1)
All SFCs show buckling during cyclic tensile loading at room temperature due to the vicinity of glass transition. Nevertheless, the sensor fibers withstand the deformation without break. Of note, at this temperature, the stiffnesses of matrix and fiber are similar (see Young's moduli of sensor fiber and matrices in Figure 5a) [START_REF] Langenbach | Adhesion and Stiffness Matching in Epoxy-Vitrimers/Strain Sensor Fiber Laminates[END_REF].

Composites Meet Sustainability -Proceedings of the 20 th European Conference on Composite Materials, ECCM20. 26-30 June, 2022, Lausanne, Switzerland At 50 °C, the hybrid networks get softer due to the increased distance from the Tg whereas the stiffness of the strain sensor remains almost the same. During cyclic testing at 50 °C, the sensor fiber in the matrix C_0epoxy breaks after 3 tensile cycles (shown by the dashed line of the relative resistance increasing abruptly in Figure 2a) and the fiber in C_5epoxy after 5 cycles (Figure 2b). However, the sensor fiber in C_10epoxy (Figure 2c) shows a linear response with only a small drift for all 20 tensile cycles. Consequently, an increase of the matrix stiffness correlates with extended cyclability before rupture of the sensor fiber inside the composite. Images of stretched specimens are shown in Figure 3. The sensor rupture appeared in the shoulder region of the dog-bone samples in several cases (C_5epoxy in Figure 3a,b). For investigation of the stress concentration, a constant force of 1 N (to the bottom direction) was applied on a pristine sensor-fiber composite. When crossed polarizers are oriented at 45° with respect to the stretching direction, the darker area reflects the stress gradient in the lower part of the shoulder region (Figure 3c). When crossed polarizers are oriented along the stretching direction (Figure 3d), orange areas appear in both shoulders. Consequently, the dark spots in both images with polarized light show the region of highest stress concentration during tensile stretching (Scheme in Figure 3e). As described by G'sell et al. in the case of neck formation during bar stretching, the stress concentration in the region of changing cross-section depends on the area of convex or concave curvature [START_REF] G'sell | Effect of stress triaxiality on neck propagation during the tensile stretching of solid polymers[END_REF]. At the root of the shoulder, in the concave part, the triaxial stress is in tension in all directions, causing a phenomenon of cavitation that possibly initiates rupture (see Figure 4a).

To describe quantitatively the situation of rupture in our samples, the difference of stiffness between fiber and matrix must be considered, in addition to triaxiality effects appearing in the shoulder region of the dog-bone sample. Indeed, as the dog-bone is made of components having different stiffnesses, a shear stress τ is generated along the interface ST between fiber and matrix in the shoulder region. τ may be written as the difference of forces Δf applied on the fiber in the narrow (f1) and large (f'1) parts divided by the interfacial surface ST in the shoulder region (Figure 4b):

𝜏 = 𝛥𝑓 𝑆 𝑇 (2)
The overall force f applied to the dog-bone bar may be decomposed into partial forces f1 and f2, f'1 and f'2, applied to the fiber and to the matrix, in both extremities of the shoulder:

𝑓 = 𝑓 1 + 𝑓 2 = 𝑓 ′ 1 + 𝑓 ′ 2 (3)
and the variation Δf expressed as:

𝛥𝑓 = 𝑓 1 -𝑓 ′ 1 = 𝑓 2 -𝑓 ′ 2 (4)
Introducing strains ε and ε' in narrow and large parts of the bar, (3) may be written as:

𝑓 = 𝑆 1 𝐸 1 𝜀 + 𝑆 2 𝐸 2 𝜀 = 𝑆 ′ 1 𝐸 1 𝜀 ′ + 𝑆 ′ 2 𝐸 2 𝜀 ′ ( 5
)
Composites Meet Sustainability -Proceedings of the 20 th European Conference on Composite Materials, ECCM20. 26-30 June, 2022, Lausanne, Switzerland Assuming the fiber cross-section remains constant during stretching, S1 = S'1 implies:

𝑓 = (𝑆 1 𝐸 1 + 𝑆 2 𝐸 2 )𝜀 = (𝑆 1 𝐸 1 + 𝑆 ′ 2 𝐸 2 )𝜀 ′ (6)
and:

∆𝑓 = 𝑓 1 -𝑓 ′ 1 = 𝑆 1 𝐸 1 𝜀 -𝑆 1 𝐸 1 𝜀 ′ = 𝑆 1 𝐸 1 (𝜀 -𝜀 ′ ) (7)
Combining ( 6) and ( 7) leads to:

∆𝑓 𝑓 = 𝑆 1 𝐸 1 ( 1 𝑆 1 𝐸 1 + 𝑆 2 𝐸 2 - 1 𝑆 1 𝐸 1 + 𝑆 ′ 2 𝐸 2 ) = 𝛼 ( 8
)
where α describes the relative variation of the force when the composite sensor is under strain. Plotting α against E2 clearly shows that this ratio passes through a maximum value for a Young's modulus of the matrix around 0.025 MPa and drops rapidly with softer or stiffer matrices (Figure 5b). This extremum corresponds also to a maximum of the shear stress τ. The E2 values measured for the three matrices at 50 °C were 0.07 MPa, 0.085 MPa and 0.13 MPa for 0 %, 5 %, and 10 % epoxy excess, respectively. Those matrix moduli may seem quite similar and far from the one of the fiber (9 MPa at 50 °C). However, their difference makes them more or less close to the maximum of α values, as shown in the plot of Figure 5b. The sample C_0epoxy experiences the highest shear stress, with decreasing shear for raising epoxy excess. This may explain why samples C_0epoxy and C_5epoxy broke at 50 °C while C_10epoxy sample did not, as the formers suffered much more shear stress during cyclic experiments.

Composites Meet Sustainability -Proceedings of the 20 th European Conference on Composite Materials, ECCM20. 26-30 June, 2022, Lausanne, Switzerland 4b). Reprinted with permission from [START_REF] Langenbach | Adhesion and Stiffness Matching in Epoxy-Vitrimers/Strain Sensor Fiber Laminates[END_REF]. Copyright 2022 American Chemical Society.

The dog-bone shape of the specimen, useful to apply strong elongation while avoiding break in the clamps, has underlined the importance of matching the Young's moduli of matrix and fiber.

This problem is important to integrate sensors in soft robotics grippers whose shapes are rarely rectangular. This also raises the question of matrix glass transition temperature. A glass transition temperature well below room temperature is desirable for improving the mechanical properties of the matrix (faster return, less drift, in particular), but meanwhile possibly worsens the Young's moduli mismatch with a fiber of high stiffness.

Conclusions

In this work, the integration of strain sensor fibers into self-healing matrices is reported. The stiffness mismatch of hybrid network material and sensor fiber induces shear stresses at the fiber-matrix interface. Moreover, the stiffness of the matrix is highly temperature dependent, which causes a premature rupture of the softest matrix, C_0epoxy at 50 °C. A slight epoxy excess leads to a stiffness increase of the matrix and avoids early fiber rupture (C_10epoxy). Moreover, the shear stress is concentrated in the concave shoulder region of the SFC, shown by images between crossed polarizers. The calculations show that even a slight change of matrix stiffness may have a significant impact on the interfacial shear stress. The matching of Young's moduli of matrix and integrated sensor fibers is thus an essential requirement for the development of long-lasting soft robots made of self-healing materials.

Experimental section 4.1 Hybrid network synthesis

The hybrid networks C_nepoxy were synthesized in the form of flat sheets. Desired quantities of DGEBA, TGMDA and supramolecular polymer precursor SP50 were introduced in a PTFE beaker, that was heated to 100 °C while mixing with a metallic stirrer until phase miscibility took place. 2-Methylimidazole (2-MI) was then added, and the mixture was stirred for two minutes before casting into a rectangular PTFE mold. After degassing under vacuum, the mold was put

Strain sensor fiber synthesis

For the piezoresistive strain sensor fiber, a styrene-based triblock copolymer by Kraiburg TPE (Waldkraiburg, Germany) was combined with carbon black obtained from TIMCAL (Bodio, Switzerland). The two components were mixed in a 1:1 mass ratio (50 wt% carbon black), using torque rheometer HAAKE Polylab Rheomix 600 from Thermofisher (Karlsruhe, Germany). Sensor fibers with a diameter of 0.3 mm were extruded using a capillary rheometer RH7 from NETZSCH (Selb, Germany). The temperature used for the mixing and the extrusion was 190 °C. The sensor fiber fabrication and properties have been reported elsewhere [START_REF] Melnykowycz | Comparison of Piezoresistive Monofilament Polymer Sensors[END_REF]. The sensing mechanism is based on rotation of the conductive particles, as well as on tunneling and hopping.

Figure 2 .

 2 Figure 2. Cyclic tests (20 cycles at 0 -20 % strain) for the three SFCs at a deformation rate of 50%.min -1 . Solid lines represent the stress values and dashed lines the relative resistance. a) C_0epoxy, b) C_5epoxy and c) C_10epoxy at 50 °C.

Figure 3 .

 3 Figure 3. a) Image of stretched C_5epoxy sample showing two spots of fracture of the sensor fiber. b) Zoom-in on the point of rupture in the shoulder region observed with a binocular magnifier. c, d) A SFC sample bearing with 1 N weight observed in polarized light between crossed polarizers oriented at 45° or parallel to the stretching direction. e) Scheme of dog-bone region with area of highest stress concentration due to extensive deformation.

Figure 4 .

 4 Figure 4. a) Scheme of stress profile (dark arrows) in shoulder region of a dog-bone sample. Biaxial stress profile in convex (extensive and compressive) and in concave (all tensile) areas. b)Parameters for calculation of shear stress during stretching: E1, E2, Young's moduli of fiber, matrix, respectively; S1, S2, cross-sections of fiber, matrix. The projection of fiber-matrix surface ST is underlined in red; f1, f2 partial strengths applied to fiber, matrix. The (') symbol accounts for parameters in the large part of the specimen.

Figure 5 .

 5 Figure 5. a) Compared Young's moduli of the sensor fiber and the three vitrimer matrices, at 20 °C and 50 °C. b) Dependence of the ratio α= Δf /f at the sensor-matrix interface on E2, the Young's modulus of the elastomer matrix. E1 = 10 MPa, S1 = 0.07 mm 2 , S2 = 16 mm 2 and S'2 = 48 mm 2 (Figure4b). Reprinted with permission from[START_REF] Langenbach | Adhesion and Stiffness Matching in Epoxy-Vitrimers/Strain Sensor Fiber Laminates[END_REF]. Copyright 2022 American Chemical Society.

  Composites Meet Sustainability -Proceedings of the 20 th European Conference on Composite Materials, ECCM20. 26-30 June, 2022, Lausanne, Switzerland

  Proceedings of the 20 th European Conference on Composite Materials, ECCM20. 26-30 June, 2022, Lausanne, Switzerland

Composites Meet Sustainability -

Table 1 :

 1 Composites Meet Sustainability -Proceedings of the 20 th European Conference on Composite Materials, ECCM20. 26-30 June, 2022, Lausanne, Switzerland in an oven and flushed with an inert atmosphere during curing at 130 °C for 3 h. Table1summarizes the hybrid network samples synthesized, with the different total quantities of di-(DGEBA) and tetra-(TGMDA) epoxide introduced. The molar quantity of the total epoxides in the network is shown in the last column. The crosslinking accelerator 2-MI was used at 6 mol%/COOH group for all formulations. Quantities of reactants for the preparation of hybrid network sheets.

	Name	SP50 [g] DGEBA [g] TGMDA [g] COOH [mmol] Epoxy [mmol]
	C_0epoxy 15.00	2.85	0.589	22.3	22.3
	C_5epoxy 15.00	2.99	0.619	22.3	23.5
	C_10epoxy 15.00	3.13	0.648	22.3	24.5

239/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

240/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

241/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

242/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

243/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

244/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

245/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

246/448 ©2022 Langenbach et al. doi:10.5075/epfl-298799_978-2-9701614-0-0 published under CC BY-NC 4.0 license ToC

Acknowledgements

This work was funded by the European Union's Horizon 2020 FET Open Project Self-Healing Soft Robotics [grant agreement no. 828818]. The authors thank ESPCI-PSL, CNRS, and EMPA for the supportive financial environment, as well as Arkema for kindly gifting UDETA.