Delphine Lallias

Edwige Quillet

Nicolas Dechamp

Jean-Michel Le Calvez

Marjorie Bideau

Lionel Goardon

Laurent Labbé

Mathilde Dupont-Nivet

Analysis of genetic variability of global DNA methylation in response to an early temperature stress in rainbow trout

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ANALYSIS OF GENETIC VARIABILITY OF GLOBAL DNA METHYLATION IN RESPONSE TO AN EARLY TEMPERATURE STRESS IN RAINBOW TROUT

Delphine Lallias*, Edwige Quillet, Nicolas Dechamp, Jean-Michel Calvez, Marjorie Bideau, Lionel Goardon, Laurent Labbé and Mathilde Dupont-Nivet GABI, INRA, AgroParisTech, Université Paris-Saclay 78350 Jouy-en-Josas, France delphine.lallias@inra.fr

We aim to investigate the potential role of epigenetic marks in the expression of phenotypes and their variability in fish, in particular genetic variability of epigenetic marks in response to an environmental stress. In this context, rainbow trout isogenic lines are the material of choice. Within each line, all fish have the same genome i.e. there is no genetic variability. This allows the comparison of epigenetic marks among several individuals with the same genotype. The environmental stress chosen here is temperature because several studies have reported genetic determinism of thermotolerance. Moreover, rainbow trout isogenic lines have recently been characterized for their response to temperature and the existence of a high between-line variability was shown. The aim of this study is to contribute to the understanding of why certain lines are more tolerant to temperature stress than others, by investigating the implication of epigenetic mechanisms in the variability of the response to temperature.

The first objective of this study was to test whether temperature regime experienced during early development leads to epigenetic modifications within and between lines. Nine rainbow trout isogenic lines were chosen. For each line, half of the eggs were incubated at standard temperature (12°C) and the other half at high temperature (16°C), from eyed-stage to hatching. At eyed-stage just before hatching, analysis of global DNA methylation with LUMA (LUminometric Methylation Assay) revealed significant differences between lines but little or no effect of incubation temperature (Figure).

At hatching, no effect of incubation temperature was observed on mortality or malformation rates. After 4 months of rearing at 12°C, mean body weight of batches incubated at 12°C or 16°C was similar.

The second objective of this study was to test whether early temperature regime impacts response to a stress experienced later in life. After tagging fish individually at a mean body weight of 3-4 g, the different batches were grouped into 9 tanks to perform acute temperature stress on 5-month-old juvenile fish. The response was measured in terms of time to equilibrium loss and Upper Thermal Tolerance (UTT). Globally, there was little significant effect of early exposure to high temperatures on the response to a late temperature stress, but tendencies seemed to appear. Thus, in the future, the impact of a longer exposure to high temperatures during early development will be tested.

Funding: This study was carried out within AQUAEXCEL 2020 funded by European Union's Horizon 2020 research and innovation programme under grant agreement No 652831.


Jennifer Bouchenna

Magalie Sénéchal

Hervé Drobecq

Jérôme Vicogne
email: jerome.vicogne@ibl.cnrs.fr

Oleg Melnyk
email: oleg.melnyk@ibl.cnrs.fr

Total Chemical Synthesis of All SUMO-2/3 Dimer Combinations

Keywords: Protein chemical synthesis, convergent, SUMO dimers, SUMO-2, SUMO-3, selective desulfurization

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Protein chemical synthesis is a powerful mean for accessing proteins harboring a large variety of post-traductional modifications. Among the recent achievements in the field, the production of polyubiquitin chains [START_REF] El Oualid | Chemical Synthesis of Ubiquitin, Ubiquitin-Based Probes, and Diubiquitin[END_REF][START_REF] Kumar | Total Chemical Synthesis of Di-Ubiquitin Chains[END_REF][START_REF] Kumar | Total Chemical Synthesis of a 304 Amino Acid K48-Linked Tetraubiquitin Protein[END_REF][START_REF] Pan | Quasi-Racemic X-Ray Structures of K27-Linked Ubiquitin Chains Prepared by Total Chemical Synthesis[END_REF][START_REF] Tang | Practical Chemical Synthesis of Atypical Ubiquitin Chains by Using an Isopeptide-Linked Ub Isomer[END_REF][START_REF] Pan | Chemical Protein Synthesis Enabled Mechanistic Studies on the Molecular Recognition of K27-Linked Ubiquitin Chains[END_REF][START_REF] Qu | A Highly Efficient Synthesis of Polyubiquitin Chains[END_REF] best illustrates the capacity of modern chemical synthesis to address the production of proteins of exceptional size and branching complexity with an atom-by-atom control of their structure. [START_REF] Bondalapati | Expanding the Chemical Toolbox for the Synthesis of Large and Uniquely Modified Proteins[END_REF] Synthetic polyubiquitins open the possibility to investigate precisely how these modifications modulate protein structure and functions. [START_REF] Mcginty | Semisynthesis of Ubiquitylated Proteins[END_REF][START_REF] Chatterjee | Chemical Approaches for Studying Histone Modifications[END_REF][START_REF] Spasser | Chemistry and Biology of the Ubiquitin Signal[END_REF] The chemical synthesis of small ubiquitin-like modifiers (SUMO) [START_REF] Boll | A Novel PEG-Based Solid Support Enables the Synthesis of >50 Amino-Acid Peptide Thioesters and the Total Synthesis of a Functional SUMO-1 Peptide Conjugate[END_REF][START_REF] Wucherpfennig | Traceless Preparation of C-Terminal α-ketoacids for Chemical Protein Synthesis by α-ketoacid-hydroxylamine Ligation: Synthesis of SUMO2/3[END_REF][START_REF] Boll | One-Pot Chemical Synthesis of Small Ubiquitin-Like Modifier (SUMO) Protein-Peptide Conjugates Using Bis(2-Sulfanylethyl)Amido Peptide Latent Thioester Surrogates[END_REF] and conjugates thereof [START_REF] Mcginty | Chemically Ubiquitylated Histone H2B Stimulates hDot1L-Mediated Intranucleosomal Methylation[END_REF][START_REF] Kumar | Highly Efficient and Chemoselective Peptide Ubiquitylation[END_REF][START_REF] Seenaiah | Convergent Versus Sequential Protein Synthesis: The Case of Ubiquitinated and Glycosylated H2B[END_REF][START_REF] Drobecq | A Central Cysteine Residue Is Essential for the Thermal Stability and Function of SUMO-1 Protein and SUMO-1 Peptide-Protein Conjugates[END_REF][START_REF] Chatterjee | Auxiliary-Mediated Site-Specific Peptide Ubiquitylation[END_REF][START_REF] Geurink | A General Chemical Ligation Approach Towards Isopeptide-Linked Ubiquitin and Ubiquitin-Like Assay Reagents[END_REF][START_REF] Weller | Aromatic Thiol-Mediated Cleavage of N-O Bonds Enables Chemical Ubiquitylation of Folded Proteins[END_REF][START_REF] Bouchenna | The Role of the Conserved SUMO-2/3 Cysteine Residue on Domain Structure Investigated Using Protein Chemical Synthesis[END_REF] has been described too but the works in this area are few and far between the reports describing the synthesis of polyubiquitin scaffolds. For example, the chemical synthesis of di-ubiquitin or tetra-ubiquitin chains has been reported by Brik and coworkers in 2011, [START_REF] Kumar | Total Chemical Synthesis of Di-Ubiquitin Chains[END_REF][START_REF] Kumar | Total Chemical Synthesis of a 304 Amino Acid K48-Linked Tetraubiquitin Protein[END_REF] while the chemical synthesis of homogeneous and branched polySUMO chains remains to be addressed.

Like ubiquitin (Ub), SUMO modifiers are attached by their C-terminal glycine residue to the side-chain of exposed lysine residues (Lys), usually located in SUMOylation consensus motifs within the target proteins. Five SUMO isoforms have been identified so far, among which SUMO-1-3 are constitutively expressed in all eukaryotic cells. [START_REF] Matunis | A Novel Ubiquitin-Like Modification Modulates the Partitioning of the Ran-GTPase-Activating Protein Rangap1 between the Cytosol and the Nuclear Pore Complex[END_REF][START_REF] Lapenta | SMT3A,a Human Homologue of the S. Cerevisiae Smt3 Gene, Maps to Chromosome 21qter and Defines a Novel Gene Family[END_REF] SUMO modification modulates the localization and the activity of the target proteins by changing protein-protein interactions and/or by competing with other lysine modifications such as ubiquitination or acetylation. [START_REF] Cappadocia | Ubiquitin-Like Protein Conjugation: Structures, Chemistry, and Mechanism[END_REF][START_REF] Vertegaal | Uncovering Ubiquitin and Ubiquitin-Like Signaling Networks[END_REF] SUMO-2/3 isoforms differ significantly from SUMO-1 by their sequence and by containing an internal SUMOylation site enabling the formation of polySUMO-2/3 chains in vivo (Fig. 1A). Naturally, deciphering the role of polySUMO-2/3 modification stimulates huge efforts worldwide but progress in this area is complicated by the fact that SUMO conjugates and, in particular polySUMO chains, are branched proteins that cannot be precisely programmed using classical recombinant techniques. Therefore, the chemical synthesis of welldefined polySUMO-2/3 scaffolds is a significant goal to pursue. SUMO-2 and SUMO-3 feature a high sequence similarity and differ by only a few amino acids located in the 13-14 AA N-terminal tail (Fig. 1A). However, we recently showed that SUMO-2 and SUMO-3 have different conformational and biochemical properties. [START_REF] Bouchenna | The Role of the Conserved SUMO-2/3 Cysteine Residue on Domain Structure Investigated Using Protein Chemical Synthesis[END_REF] Contrary to SUMO-3, the structure of SUMO-2 is stabilized by a weak interaction occurring between the N-terminal tail and the SUMO core domain (Fig. 1B). Since SUMO-2 and SUMO-3 are not equivalent, polySUMO-2/3 chains might have their structure and function modulated by the proportion of each SUMO isoform within the chain. Another point to consider is the presence into the tail of SUMO-2 of the SUMOylation site, Lys11. Although the exact nature of the SUMO-2 tail-core interaction remains to be established, its existence raise the question of the impact of Lys11 modification on the structure and function of polySUMO-2/3 chains. Indeed, the properties of polySUMO-2/3 conjugates might vary not only with the type of SUMO isoforms that they are made of, but also with the order by which they are concatenated. For example, the properties of SUMO-2-SUMO-3 and SUMO-3-SUMO-2 dimers might not be same because the N-terminal tail of SUMO-2 is unmodified in the former case, while it hosts a SUMO modifier in the latter case (Fig. 1C).

An important step for investigating how the composition of polySUMO-2/3 chains impacts their properties is to access these molecules in homogeneous form and substantial amount, i.e., at mg scale. We describe hereinafter a rapid and robust access to all combination of SUMO-2/3 dimers, which, are challenging to produce due to their size (~20 kDa). This strategy gives also access to C-terminal SUMO-2/3 dimer hydrazides. By being useful protein thioester surrogates, 37-40 SUMO-2/3 dimer hydrazides allow to consider in the future the chemical synthesis of polySUMO scaffolds of even higher complexity.

Results and discussion

Synthetic strategy

The strategy shown in Fig. 2 was adopted for accessing all four SUMO-2/3 dimers (illustrated with the synthesis of SUMO-2-SUMO-3). According to this strategy, the SUMO-2/3 dimers are assembled in one-pot by ligating three peptide segments. Two of these are produced by solid phase peptide synthesis (SPPS) owing to their length (~45AA) and are used to assemble the left SUMO domain highlighted in pink. The third segment in green used in the one-pot process corresponds to the right SUMO domain. It is produced in one-pot too and features an internal Lys(Cys) residue at position 11 to attach the SUMO domain coming from the first ligation step. Therefore, SUMO-2/3 dimers are accessed through two successive one-pot processes. This strategy enables limitating the number of resolutive HPLC purification steps that are known to induce important mass losses. [START_REF] Loibl | Total Chemical Synthesis of Proteins without HPLC Purification[END_REF][START_REF] Raibaut | Solid Phase Protein Chemical Synthesis[END_REF] The SUMO-2/3 dimers produced by this way need to be desulfurized subsequently to remove the thiol function in-between the two SUMO domains. [START_REF] Wan | Free-Radical-Based, Specific Desulfurization of Cysteine: A Powerful Advance in the Synthesis of Polypeptides and Glycopolypeptides[END_REF] Desulfurization is a common post- ligation treatment applied after assembly of Ub conjugates, with the objective of removing the thiol function utilized for assembling the isopeptidic bond. Usually, any Cys residue present in the polypeptide is concomitantly converted to Ala. This can be useful when Cys residues are introduced intentionally in place of Ala residues to facilitate the assembly of the product by an NCL [START_REF] Dawson | Synthesis of Proteins by Native Chemical Ligation[END_REF][START_REF] Kent | Total Chemical Synthesis of Proteins[END_REF] /desulfurization approach. [START_REF] Wan | Free-Radical-Based, Specific Desulfurization of Cysteine: A Powerful Advance in the Synthesis of Polypeptides and Glycopolypeptides[END_REF] In the case of SUMO-2/3 dimers, a global desulfurization is not recommended because we recently showed that the desulfurization of the central Cys residue and its conversion into Ala results in the destabilization of the SUMO-2/3 domains, SUMO-3 being especially sensitive to this modification. [START_REF] Bouchenna | The Role of the Conserved SUMO-2/3 Cysteine Residue on Domain Structure Investigated Using Protein Chemical Synthesis[END_REF] Therefore, the synthesis of SUMO-2/3 conjugates requires selectively removing the thiol amino acid used to form the isopeptidic bond by NCL. The performance of a selective desulfurization of SUMO conjugates featuring one SUMO domain has been described in a few studies. [START_REF] Drobecq | A Central Cysteine Residue Is Essential for the Thermal Stability and Function of SUMO-1 Protein and SUMO-1 Peptide-Protein Conjugates[END_REF][START_REF] Geurink | A General Chemical Ligation Approach Towards Isopeptide-Linked Ubiquitin and Ubiquitin-Like Assay Reagents[END_REF][START_REF] Bouchenna | The Role of the Conserved SUMO-2/3 Cysteine Residue on Domain Structure Investigated Using Protein Chemical Synthesis[END_REF] These reactions are performed in native conditions. The selectivity relies on a difference in accessibility between the thiol to be removed, which is solvent exposed, and the Cys thiol internal to the SUMO domain, which is buried in the hydrophobic core of the folded SUMO domain. However, extending the principle of a selective desulfurization to SUMO dimers for which the isopeptidic bond is located in between two folded domains had to be established. [START_REF] Keusekotten | Multivalent Interactions of the SUMO-Interaction Motifs in Ring Finger Protein 4 Determine the Specificity for Chains of the SUMO[END_REF] Note that the burying of isopeptidic bonds in some polyubiquitin conjugates has been observed by Liu and coworkers. 10

Synthesis of the starting peptide segments

According to the one-pot strategy depicted in Fig. 2, the first ligation step enables the assembly of SUMO-2 or SUMO-3 domains equipped with a C-terminal SEA functionality. The synthesis of the peptide segments used during this step, i.e. SUMO-x N and SUMO-x C (x = 2 or 3), were produced by conventional 9-fluorenylmethyloxycarbonyl (Fmoc) SPPS using bis(2sulfanylethyl)amino (SEA) ChemMatrix resin as already described elsewhere. [START_REF] Boll | A Novel PEG-Based Solid Support Enables the Synthesis of >50 Amino-Acid Peptide Thioesters and the Total Synthesis of a Functional SUMO-1 Peptide Conjugate[END_REF][START_REF] Boll | One-Pot Chemical Synthesis of Small Ubiquitin-Like Modifier (SUMO) Protein-Peptide Conjugates Using Bis(2-Sulfanylethyl)Amido Peptide Latent Thioester Surrogates[END_REF] The one-pot synthesis of the SUMO-2 and 3 domains equipped with a Lys(Cys) residue, i.e.

SUMO-2 Lys(Cys) and SUMO-3 Lys(Cys) (the peptide segment in green in Fig. 2B), required novel developments that are described in Scheme 1. The starting SEA on peptide segment 1a,b was produced from bis(2-sulfanylethyl)amino (SEA) ChemMatrix resin using Fmoc- Lys[Cys(Trt)]-OH for position 11. Such bifunctional peptide cannot be used as such for the assembly of the SUMO-2/3 Lys(Cys) domains because it can cyclize or oligomerize during ligation with segment 4a,b. The SEA on group was inactivated in situ and prior to ligation by adding 4-mercaptophenylacetic acid (MPAA) disulfide to the reaction vessel. MPAA disulfide oxidizes the SEA on group into the corresponding SEA off disulfide by a thiol-disulfide exchange mechanism. The MPAA arylthiol produced during this step contributes to the catalysis of subsequent ligation reactions. [START_REF] Johnson | Insights into the Mechanism and Catalysis of the Native Chemical Ligation Reaction[END_REF] Then, a thioester derivative of acetoacetic acid (AcA) was added to protect the Lys(Cys) residue through an NCL reaction. [START_REF] Boll | Access to Large Cyclic Peptides by a One-Pot Two-Peptide Segment Ligation/Cyclization Process[END_REF] A tight control of the stoichiometry is required during this step as an excess of AcA thioester would inevitably cap the Cys segment introduced in the subsequent step. The AcA-protected segment 3a,b was not isolated and was ligated directly with segment 4a,b by adding an excess of MPAA and tris(2carboxyethyl)phosphine (TCEP). Finally, the AcA group was removed in one-pot by adding two equivalents of hydroxylamine hydrochloride to the ligation mixture. The presence of nonionic detergent N-octylglucoside in the reaction mixture was found to be mandatory to avoid the partial precipitation of the peptides. Peptide segments SUMO-2/3 Lys(Cys) were isolated in good overall yields (58-60% after HPLC purification) and purity (see Supporting Information, Fig. SX). The strategy was also applied successfully to the synthesis of a SUMO-3 Lys(Cys) derivative featuring a C-terminal hydrazide group.

Scheme 1. One-pot synthesis of SUMO-2 or 3 peptide segments equipped with a Lys(Cys) residue at position 11

Assembly of SUMO-2/3 dimers

The successful synthesis of peptide segments 6a,b and 7 set the stage for the assembly of the SUMO-2/3 dimers according to Scheme 2. [START_REF] Ollivier | A One-Pot Three-Segment Ligation Strategy for Protein Chemical Synthesis[END_REF] As for the synthesis of SUMO-2/3 Lys(Cys) domains, the use of N-octylglucoside and 6 M Gn•HCl as additives ensured the solubilization of starting materials and products throughout the process. The different 21 kDa SUMO-2/3 dimers were produced successfully and isolated by HPLC in excellent purity (Fig. 3). They migrate to an apparent molecular weight of 30 kDa by SDS-PAGE (Fig. 4). SUMO-2/3 dimers are composed of 183-185 amino acid residues and as such represent the largest proteins produced so far using N,S-acyl shift thioester surrogates. [START_REF] Agouridas | A Statistical View of Protein Chemical Synthesis Using NCL and Extended Methodologies[END_REF][START_REF] Diemer | Se-Acyl Transfer Devices in Protein Synthesis[END_REF] Scheme 2. Chemical synthesis of SUMO-2/3 dimers Figure 3. LC-MS analysis of isolated SUMO-2/3 dimers 11-14.

Selective desulfurization of SUMO-2/3 dimers 11-14

The successful synthesis of SUMO-2/3 dimers set the stage for the desulfurization experiments.

The TCEP-induced desulfurization of all four dimers in native conditions proceeded with a total selectivity for the Cys thiol in between the two SUMO domains, as demonstrated by extensive proteomic analysis of the desulfurized products (see Supporting Information). In a control experiment, SUMO 2/3 dimer 13 was desulfurized in 6 M Gn•HCl. In this case, all Cys residues were converted to Ala. Thus under native conditions, the Cys thiol used for linking the SUMO domains remains highly accessible to the solvent whenever the composition of the dimer. The efficient protection of internal Cys residues within SUMO domains under native conditions shows that both SUMO domains are properly folded. SUMO-2-SUMO-3 dimer 13 was desulfurized on a preparative scale to produce the desulfurized analog 18 in 61% isolated yield. We further examined the cleavage of SUMO-2-SUMO-3 dimer 18 by Sentrin-specific protease 1 (SENP1 [START_REF] Gong | Differential Regulation of Sentrinized Proteins by a Novel Sentrin-Specific Protease[END_REF] ) and 2 (SENP2 [START_REF] Yeh | Ubiquitin-Like Proteins: New Wines in New Bottles[END_REF][START_REF] Nishida | Characterization of a Novel Mammalian SUMO-1/Smt3-Specific Isopeptidase, a Homologue of Rat Axam, Which Is an Axin-Binding Protein Promoting Β-Catenin Degradation[END_REF] ), which are human SUMO-1, 2 and 3 specific deconjugating enzymes (Fig. 6). [START_REF] Hickey | Function and Regulation of SUMO Proteases[END_REF][START_REF] Sommer | Covalent Inhibition of SUMO and Ubiquitin-Specific Cysteine Proteases by an in Situ Thiol-Alkyne Addition[END_REF] SUMO-2-SUMO-3 dimer 18 was cleaved by both SENP enzymes to produce SUMO-2 and SUMO-3 proteins that migrate by SDS-PAGE analysis at an apparent molecular weight of ~15 kDa. The breakdown of SUMO-2-SUMO-3 dimer 18 into individual SUMO-2/3 proteins was confirmed by LC-MS analysis of the cleavage mixture. Taken together, the CD signature of SUMO-2-SUMO-3 dimer 18 and its cleavage by SENP1 and SENP2 shows that the dimer is properly folded an dfunctional.

CONCLUSIONS

We describe in this report a simple and efficient access to SUMO-2/3 dimers which is compatible with the production of SUMO dimers featuring a C-terminal hydrazide functionality. The preparation of SUMO dimer hydrazides opens potentially the possibility to access more elaborated polySUMO conjugates by exploiting the thioester surrogate properties of the hydrazide group. The desulfurization of the thiol amino acid used to produce the isopeptidic bond has been performed with a high degree of selectivity, regardless the SUMO-2/3 dimer combination examined. The production of SUMO-2/3 dimers at the mg scale is an important step toward further investigations aiming at determining the effect of SUMO dimer composition and order of concatenation on their biophysical and biochemical properties.

Figure 1 .

 1 Figure 1. A) Primary structure of SUMO-2 and SUMO-3 proteins showing the tail and core domain. B) Tertiary structure of SUMO-2 (NMR structure, pdb entry 2N1W). C) Schematic representation of SUMO-2-SUMO-3 and SUMO-3-SUMO-2 dimers.

Figure 2 .

 2 Figure 2. General synthetic strategy toward SUMO dimers taking the synthesis of SUMO-2-SUMO-3 as an example.

Figure 4 .

 4 Figure 4. SDS-PAGE analysis of SUMO-2/3 dimers. A) Commassie staining, 1 µg of each protein. B) Western-blot analysis using anti-SUMO-2/3 polyclonal antibody, 100 ng of each protein. MW: apparent molecular weight markers.

Scheme 3 . 32 wavelength 3 Figure 5 .

 33235 Scheme 3. Selective desulfurization of SUMO-2/3 dimers 11-14

ACKNOWLEDGEMENTS

We thank the Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation for financial support (PhD fellowship to Jennifer Bouchenna). We thank Jean-Jacques Lacapère and Florine Cavelier for useful discussions.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI:

Experimental procedures and characterization data for all peptides and proteins (LC-MS, MALDI-TOF, CD and proteomic analyses) (PDF).


E M Van Grevenhof

J Vandenplas

M P L Calus

Using metafounders to model purebred relationships in genomic prediction for crossbreeding

Selection for feed efficiency in purebred pig and poultry breeding animals should ideally account for the performance of crossbred animals. As part of the Horizon2020 Feed-a-Gene project (grant agreement no. 633531), methodologies to account for crossbred data are being developed and optimized using simulated data. The advantage of using crossbred data instead of purebred data in genomic evaluations for feed efficiency will be evaluated to propose new selection schemes for feed efficiency in monogastric animals. Simulations were set up using a three-way crossbred breeding program, with 10 generations of purebreds (PB), and 5 generations of two-way and three-way crossbred animals. The last generation of PB are validation animals. True breeding values are simulated for each line/cross (5 traits). Genetic correlations between all PB lines were randomly sampled in the range 0.2-0.8. Heritabilities were randomly sampled in the range of 0.2-0.4. Each PB generation exists of 2,000 phenotyped individuals, and all genotyped animals were also phenotyped. Three scenarios will be tested with varying amounts of data available. In the first scenario 2,000 phenotypes and no genotypes will be available, in the second 2,000 phenotypes and 1000 genotypes, and in the third 2,000 phenotypes and 2,000 genotypes. The simulated genotypes follow the size and number of chromosomes of the pig genome (18 chromosomes). The number of SNP simulated is ~60k, with 4,500 QTL in total. Each simulation is replicated ten times. Breeding values of validation animals are predicted using pedigree-based BLUP, or single step GBLUP (SS-GBLUP) that either uses metafounders or not. Metafounders enable to estimate parental relationships between purebred lines using the genotypic information of different lines in the G-matrix (usually no relationship is assumed between PB lines). Results will contain estimated variance components and accuracies of breeding values of purebred selection candidates for crossbred performance. We hypothesize that the use of metafounders will lead to improved accuracies and more unbiased estimated variance components for SS-GBLUP.

Feed restriction effect on progeny of mice selected for birth weight environmental variability N. Formoso-Rafferty 1 , I. Cervantes 1 , J.P. Gutiérrez 1 and L. Bodin 2 1 Universidad Complutense de Madrid. Facultad de Veterinaria, Avda. Puerta de Hierro s/n, 28040, Madrid, Spain, 2 INRA -GenPhySe, CS 52627, 31326, Castanet-Tolosan, France; n.formosorafferty@ucm.es In line with aspects of the H2020 Feed-a-Gene project (grant agreement no. 633531) aiming to understand the genetic relationship between feed efficiency and robustness, we analysed the influence of mice feeding restriction on their offspring birth weights (BW) in two lines divergently selected for birth weight environmental variability. A total of 120 females (four full-sib females from 10 random different litters of the 12, 13 and 14 generations of selection) were chosen within high and low selected lines and split in four groups of feeding type combining restriction or not in two periods: from weaning at 21 to 77 days, and one week before mating to the 2 nd parturition. Restriction consisted of feeding with 75, 90 and 85% of ad libitum consumed feed in the respective three studied generations. The data included 158 litters with 1,275 BW and 4,093 animals in the pedigree. A heteroscedastic model (using ASReml Release 4.1 software) was fitted to ascertain the genetic and environmental factors affecting the BW mean and its residual variance. The model included the diet type of the dam (restricted or not during the growing period and during the reproductive period), its line, generation, litter size where it was born and its parity, as well as the litter size of the progeny and its sex; including also all diet, line and generation interactions. The line (lower BW for the low variability line), and the generation effect for the progeny of dams restricted both during the growing and the reproductive period had significant effects on the progeny BW. Whereas the sex, the interaction diet-line (in dam pregnancy period) and the dam genetic effect have had effect on the BW variability. The interaction dietline produced a decrease in environmental variability of 5 and 18% in low and high variability lines respectively. It seems that selection for BW variability has conferred a lower sensitivity of the dams to the environmental conditions, which could be interpreted as higher robustness.


Zoé Terret

Grégori Bonnet

Laure Didierlaurent

Jean-Luc Gallois

Tospovirus is the only member of the Bunyavirus family which infects plants (the other members infecting animals and humans). Tomato spotted wilt virus (TSWV), the most famous tospovirus, is a major pathogen for tomato and pepper cultures. Because there is no chemical treatment against viruses, the only way to fight them is to develop genetic resistance. Genetic resistances to tospoviruses are available, but are largely overcome. Therefore, there is an urgent need to characterize new sources of resistance. The aim of my PhD is to find new genetic resistances based on susceptibility factors, which are proteins required by the virus to accomplish its cycle and infect the plant. As a first step, I will develop a 3D model of the TSWV RNA-dependent RNA polymerase (RdRp), a key viral protein for its infectious cycle. Based on this model, a part of the RdRp protein will be selected as bait in order to identify plant protein interactors by yeast-two hybrid screening. Finally, I will search for new tomato alleles encoding variant forms of those tomato susceptibility factors. If those variants impair the interaction between the plant factor and the viral protein, those alleles are very likely to be associated with the crop resistance to the pathogen.

Mots-clés :

TSWV, loss-of-susceptibility, resistance, RdRp

loss-of-susceptibility resistance gene toward tospoviruses in Solanaceae

  16eme rencontres de Virologie Végétale, du 15 au 19 janvier 2017, AUSSOIS, France. Poster, Zoé terret Finding Terret Zoé 1 , Bonnet Grégori 2 , Didierlaurent Laure 2 , and Gallois Jean-Luc 1 1 INRA-UR 1052. Génétique et Amélioration des Fruits et Légumes (GAFL) Domaine St

	Maurice -CS 60094 -F-84143 Montfavet cedex 2 Syngenta Seeds SAS -346 Route des
	Pasquiers -F84260 Sarrians
	Résumé :


Olivier Bailleux
email: olivier.bailleux@u-bourgogne.fr

Yacine Boufkhad
email: yacine.boufkhad@irif.fr

Constraint Reductions

context, we outline a classification of Constraints with respect to their deductive power regarding General Arc Consistency (GAC).

Introduction

It is not usual to be asked to write something on a subject on which you have worked fifteen years before and on which you have remained far from subsequent developments. Yet this is the challenge we humbly accepted to undertake in this paper with the limitation that our expertise in this research area have diminished regarding the developments made by many others during the ten previous years.

We begin with the easy part consisting in recalling the context of the paper [START_REF] Bailleux | Efficient cnf encoding of boolean cardinality constraints[END_REF].

In the sequel the word constraint will be used in two meanings: a type of constraints, such as propositional clause, Boolean cardinality constraint, ALLDIFF..., and a constraint instance, i.e., the formal representation of a relation on several variables each having a domain. We will use the word Constraint in the first case and constraint in the second case. For example, CNF is a Constraint that denotes the set of propositional clauses, whereas (a ∨ ¬b ∨ c) is a CNF constraint.

The main result in [START_REF] Bailleux | Efficient cnf encoding of boolean cardinality constraints[END_REF] was twofold: the description of a general method of solving constraints satisfaction problems through translation and the application of this method to the translation of Boolean cardinality Constraint into CNF.

The general method can be quickly described as follows: We have a constraint network based on one or more types of so called source Constraints, and we want to solve this network using a solver dedicated to a type of so called target Constraint. Then we need to translate each source constraint to an equivalent set of target constraints. It is therefore desirable that the problem can be solved at least as effectively with the target solver as it would have been with an up to date source solver. The three most obvious criteria for achieving this objective are:

1. The translation process must be fast compared to the assumed resolution time of the source solver, namely, the translation algorithms must have a polynomial time complexity.

2. The target constraint network must not be of a prohibitive size.

3. All deductions that could be made by an up to date solver from source constraints must be feasible by the target solver.

Let us call for the moment a translation that fulfills the three above criteria a good translation. Regarding the third criterion, almost all modern constraint solvers at least enforce domain consistency, also called generalized arc consistency or GAC. We therefore considered, as [START_REF] Gent | Arc consistency in sat[END_REF] before us, and as many authors thereafter, that it was desirable that enforcing domain consistency on target constraints produces at least the same deductions as enforcing domain consistency on source constraints.

We applied this method to the case of cardinality constraints as a source Constraint and clauses in CNF form as a target Constraint. Most of SAT solvers use unit propagation as a deduction method and therefore we required for the third criterion that the translation restores the generalized arc consistency through unit propagation. At the time, it was known that a direct translation of cardinality constraints to CNF that preserves the power of deduction without adding any new variable requires an exponential number of clauses. Then a linear time translation was proposed in [War98], producing a polynomial number of clauses, but at the cost of a loss of deduction power since the unit propagation does not restore arc consistency.

We proposed then in [START_REF] Bailleux | Efficient cnf encoding of boolean cardinality constraints[END_REF] a good encoding (thus fulfilling the three above criteria) of cardinality constraints to CNF based on boolean adders using the unary representation of integers.

Many developments have been done since : refinements of the translation of cardinality constraints, CNF translation of general arithmetic constraints... It would be difficult to cite them without omitting some. Some papers studied the existence of good translations to CNF as a target Constraint. That is the subject we choose to tackle and generalize in this paper through some incomplete thoughts.

A breakthrough was made in [BKNW09] by giving a necessary and sufficient condition for a source Constraint to have a good translation to CNF. The condition is that a propagator that enforces generalized arc consistency on this source Constraint must be computed by a polynomial size monotone circuit. As a consequence of this result, a superpolynomial lower bound for the monotone circuit that encodes a propagator for some Constraint implies that there is no good translation to CNF for this Constraint. It is the case of ALLDIFF as mentioned [BKNW09] and also for its generalization GCC.

In the same vein, [GK14b] proves that there exists no GAC translation of systems of an arbitrary number of XOR equations. By contrast, it gives a good translation to CNF for XOR systems having a constant number of equations.

These results draw the outlines of classes of Constraints according to the existence of good translations to CNF. We describe in the following a classification that does not consider necessarily CNF as a target Constraint and we discuss it.

Comparing constraints according to their propagation power

Polynomial time constraints translation, in its simplest acceptance, i.e., the target constraint network and the source constraint network must be equiconsistent, is a Karp-reduction in the sense of complexity theory. It allows to polynomialy translate a source problem into an equivalent target problem. We propose to call GAC-reduction any Constraint reduction that preserves the deductive power of domain consistency enforcement. Such a reduction allows to categorize Constraints with respect to their propagation powers.

Let us illustrate the notions of reduction and GAC-reduction with an example involving two Constrains : CNF, namely the propositional clauses, and =, namely the binary difference constraints on finite domains.

Figure 1 shows a reduction from CNF to = in the case where the source constraint is a clause of 3 literals, but which can be generalized to a clause of any length. On the other hand, the reduction from CNF to = presented figure in 2 on the same example is a GAC-reduction.

If the source clause is falsified, then the target network in inconsistent and enforcing domain consistency on its constraints produces an empty domain. In addition to that, in the three cases where unit propagation on the source clause assigns a variable, enforcing domain consistency on constraints of the target network do the same assignation.

Incidentally, if we want to solve SAT instances with a graph coloring solver, it might be more efficient to use the second reduction rather than the first one. 3. The clauses (¬a 1 ∨ ¬b 1 ), ..., (¬a n ∨ ¬b n ).

Here, not only GAC-reduction can introduce auxiliary variables (depending of the encoding of the card[1..1] constraints), but it may also use different representations of the possible restrictions of source domains and the corresponding target domains.

A formal definition of a GAC-reduction -which we will not give here -should express the idea, summarized in figure 3 that if, from a certain source knowledge K, the GAC-propagation of the source constraint produces a deduction D, then from the same knowledge expressed in the target representation, the GAC-propagation of the target constraint network should produce a deduction at least as strong as D. K and D are restrictions of the domains of the source variables. The corresponding target knowledge and deduction are restrictions of domains of target variables. A domain d is a restriction of another domain

k if d ⊆ k.
The main result in [BKNW09] can be reformulated in terms of GAC-reduction this way: for any finite domains Constraint S, the GAC-propagator of S can be implemented by a monotone Boolean circuit if and only if there is a GAC-reduction from S to CNF. We identify here a class of Constraints that we call MPC (for Monotone Polynomially Propagatable Constraints), which is the set of all the Constraints that can be GAC-reduced to CNF. De facto, CNF is a MPC-complete Constraint.

All the generalizations of CNF belonging to MPC, such as Boolean cardinality Constraint (Card) and pseudo-Boolean inequalities (PB > ), are obviously MPC-complete. (Card ∈ MPC follows from the GAC-reduction proposed in [START_REF] Bailleux | Efficient cnf encoding of boolean cardinality constraints[END_REF] and PB > ∈ MPC follows from the one proposed in [START_REF] Bailleux | New encodings of pseudo-boolean constraints into cnf[END_REF]).

It can be noticed that a necessary condition for a type Constraint Q be MPC-complete is that Q is NP-complete -in the sense that the problem of determining the consistency of a constraint network of type Q is NP-completebecause the existence of a GAC-reduction from Q to CNF implies the existence of a Karp-reduction from Q to CNF. So the XOR Constraint, which belongs to MPC but is not NP-complete, is therefore not MPC-complete. Finally, it should be noted that there are Constraints whose satisfaction is verified in polynomial time, but for which enforcing domain consistency is a NP-hard problem. This holds with pseudo-Boolean inequalities (PB = ), for example. Under the assumption P = NP, these Constraints are not in PPC. We propose to call PVC the set of polynomialy verifiable Constraints, in the sense that a finite domain Constraint Q is in VPC if and only if there is a polynomial time complexity algorithm that checks whether a complete assignment satisfies a constraint q of type Q.

Figure 4 shows the classes MPC, PPC and VPC, as well as some Constraints belonging to these classes.

Concluding remarks and questions

In a world where solvers are based on enumeration and domain consistency enforcement, a solver dedicated to a Constraint of the PPC \ MPC class has a higher deductive power than a solver dedicated to an MPC Constraint, such as a SAT solver, a graph coloring solver, or even a pseudo-Boolean solver. And in such a world, CNF is a poor candidate for the role of universal Constraint into which all polynomially propagatable Constraints could be translated without loss of resolution efficiency. If we were to look for a universal solver, we would first have to identify the complete constraints of the PPC class. In the current state of our young reflections, we do not even know if such Constraints exist and so one question that could be addressed would be: are there Constraints complete for the class PPC?

But in a world where solvers use more sophisticated deductive systems, things are becoming more complex. In [GK14a] is addressed the question of power of deduction restricted to the representations of boolean functions but they consider also more sophisticated systems of deduction than GAC. The same can be done with Constraints with general domains. For example, the GAC-propagation of Constraints beyond MPC, such as GCC, cannot be polynomially simulated by unit propagation in a SAT solver or by GAC-propagation in a pseudo-Boolean solver. But what if the SAT solver replaces unit propagation with bounded resolution or if the pseudo-Boolean solver uses cutting planes?

Finally, we think that the study of good practices of constraint translation will have to be strongly connected to the study of solvers in order to progress.

Figure 1 :

 1 Figure 1: A (non-GAC) reduction from the clause (a ∨ ¬b ∨ c) to binary difference constraints.

Figure 2 :

 2 Figure 2: A GAC-reduction from the clause (a ∨ ¬b ∨ c) to binary difference constraints.

Figure 3 :

 3 Figure 3: A schematic representation a GAC-reduction.

Figure 4 :

 4 Figure 4: A classification of Constraints