Nathalie Beaujean
email: nathalie.beaujean@inserm.fr

Epigenetic features of animal biotechnologies

Keywords: DNA methylation, histone post-translational modifications, reprogramming, in vitro culture, in vitro maturation

Epigenetic mechanisms play a crucial role in many biological processes, such as regulation of gene expression especially after fertilization and during early embryonic development. Indeed, the parental genomes that carry special epigenetic signatures, undergo important chromatin remodelling through epigenetic modifications during the first embryonic cleavages, some of which are crucial for the production of healthy embryos.

It is therefore very important for breeders and embryologists to understand how parentally inherited genomes may be epigenetically altered by animal biotechnologies as it could affect embryo quality and further development. This chapter introduces some of the basic epigenetic parameters underpinning early embryonic development and how they could be affected during the processes of embryo in vitro production, somatic cell nuclear transfer or stem cells derivation.

Introduction

Epigenetics include heritable changes of the phenotype, which do not involve changes in the DNA sequence itself [START_REF] Kouzarides | Chromatin modifications and their function[END_REF][START_REF] Greally | A user's guide to the ambiguous word "epigenetics[END_REF]. Epigenetic control is usually based on chemical modifications, which can be transmitted to daughter cells through mitosis and sometimes through meiosis. Epigenetic modifications alter the chromatin structure and nuclear architecture to enable control of the "accessibility" to the DNA (genes) [START_REF] Schneider | Dynamics and interplay of nuclear architecture, genome organization, and gene expression[END_REF]. The major epigenetic modifications of the genome include histone post-translational modifications, DNA methylation and remodelling of the chromatin. These modifications, by causing structural changes of the chromatin, affect the expression or silencing of genes and thereby the access of transcription factors controlling gene expression [START_REF] Kouzarides | Chromatin modifications and their function[END_REF]. This kind of epigenetic regulation takes place in all types of cells, including gametes and embryosd It is now well established that epigenetic reprogramming of gametes and preimplantation embryos is crucial for normal development into a new organism (Beaujean 2014;Beaujean 2015;[START_REF] Sepulveda-Rincon | Early epigenetic reprogramming in fertilized, cloned, and parthenogenetic embryos[END_REF]. Moreover, epigenetic modifications seem to be important factors in driving cell fate in mammalian embryos [START_REF] Graham | The Acquisition of Cell Fate in Mouse Development: How Do Cells First Become Heterogeneous?[END_REF][START_REF] Wu | The Molecular Harbingers of Early Mammalian Embryo Patterning[END_REF]. Due to the intensity of epigenetic reprogramming that occurs during preimplantation development, this period in particular is very sensitive (El Hajj and Haaf 2013;Anckaert and Fair 2015). Disruption of these control mechanisms can cause aberrant gene expression or silencing which could lead to epigenetic related diseases. In the case of animal biotechnologies, such as embryo in vitro production (IVP), somatic cell nuclear transfer (SCNT) or stem cells derivation, several steps of the procedures may exert environmental stress on these epigenetic controls. Importantly, it is known that these modifications are dynamic and are rapidly changing within minutes when responding to an arriving stimulus [START_REF] Kouzarides | Chromatin modifications and their function[END_REF]. In this chapter, the potential epigenetic alterations that may/have been encountered in animal biotechnologies will be discussed.

Chromatin compaction & epigenetic mechanisms

In eukaryotes, the DNA is packaged with histone proteins to form the chromatin [START_REF] Margueron | Chromatin structure and the inheritance of epigenetic information[END_REF]. Originally described largely as a method of compaction, the structure of chromatin is now understood to direct and respond to gene expression patterns in a highly dynamic manner. Chromatin can be broadly divided into two categories. Euchromatin is the one with a more relaxed structure and therefore more accessible for transcription mechanisms. This permissive chromatin is usually related with a high gene expression activity although not all genes are necessarily expressed. On the other hand, heterochromatin is considered as repressive because it has a very compact structure which is hard to access and few genes are expressed [START_REF] Grewal | Heterochromatin revisited[END_REF][START_REF] Jost | Heterochromatin and gene positioning: inside, outside, any side?[END_REF][START_REF] Saksouk | Constitutive heterochromatin formation and transcription in mammals[END_REF].

The histone proteins family consists of the core histones H2A, H2B, H3 and H4, and the linker histone H1. Histones are organized in octamers to form the so called nucleosome, a structure around which linear DNA is wrapped. The different core histones have a similar structure consisting of a globular, hydrophobic internal region and the N-terminal histone tail. Histone tails are protruded from the nucleosome core particle and can be targeted by various enzymes to modify the histone characteristics of particular residues [START_REF] Kouzarides | Chromatin modifications and their function[END_REF]. These post-translational modifications (PTM) include acetylation, methylation, ubiquitination and phosphorylation. Histone PTMs may exert their effects on chromatin by changing the relationship between DNA strands and the nucleosome. Acetylation for instance decreases the affinity of the histones for DNA by neutralising the basic charge of the lysine residues and is generally associated with chromatin "unfolding" [START_REF] Hasan | Histone acetyl transferases: a role in DNA repair and DNA replication[END_REF]. This open chromatin conformation is often more accessible for transcriptional factors (in other words "permissive") leading to gene expression (Figure 1). On the other hand, histone methylation usually acts on chromatin through the recruitment of other proteins, such as the chromatin-containing CBX-protein family, that are capable of condensing the chromatin structure (Beaujean 2014). Histone methylation is therefore frequently found in condensed chromatin areas together with hypoacetylated histones [START_REF] Schneider | Dynamics and interplay of nuclear architecture, genome organization, and gene expression[END_REF][START_REF] Woodcock | Chromatin higher-order structure and dynamics[END_REF]. However, histone methylation may also promote gene expression depending on which residues are methylated [START_REF] Kouzarides | Chromatin modifications and their function[END_REF]. Histone methylation has indeed been identified on multiple lysine (K) and arginine (R) residues of histones H1b, H3, and H4; depending on the position of the modified residue, lysine methylation can be associated with transcriptional repression (H3K9, H3K27, H4K20) or activation (H3K4, H3K36, and H3K79). Arginine (R) methylation is also associated with regulation of transcription. Additional complexity is introduced by the possibility of mono-, di-or tri-methylation at lysine residues, and mono-or di-methylation at arginine residues. Correlation of these histone PTMs with the gene expression status led to the proposal of a "histone code", with different combinations PTMs leading to the recruitment of specific co-factors, with distinct downstream effects in various biological tasks [START_REF] Turner | Cellular memory and the histone code[END_REF].

Each one of these histone PTMs is catalysed by specific enzymes, capable of "writing" or "erasing" the modification. The acetylation status for instance is determined by a balance of enzymatic activity between histone acetyltransferases (HATs) and histone deacetylases (HDACs). More than a dozen HDACs have been discovered and several classes of HDACs can be distinguished: class I (HDAC 1-3 and 8), class IIa (HDAC 4,5,7,[START_REF] Wu | The Molecular Harbingers of Early Mammalian Embryo Patterning[END_REF], class IIb (HDAC 6 and 10), class III (SIRT 1-7), and class IV (HDAC 11) [START_REF] Narlikar | Cooperation between complexes that regulate chromatin structure and transcription[END_REF]. Their importance has been reported in several studies, in particular in cell proliferation control. For this reason many researchers started to be interested in their mechanism of action and in the use of HDAC inhibitors (HDACi), such as trichostatin A (TSA) that induce hyperacetylation of histones by blocking the access of HDAC to their active site [START_REF] Kretsovali | Histone Deacetylase Inhibitors in Cell Pluripotency, Differentiation, and Reprogramming[END_REF]. Similarly, histone methyltransferases (HMTs) are predominantly catalysing methylation of histones H3 and H4: histone lysine methyltransferases (KMTs) target lysine residues whereas protein arginine methyltransferases (PRMTs) target arginine residues. There are two main families of KMTs: with a SET domain (Su(var)3-9, Enhancer of Zeste, Trithorax) or without (Dot1 lysine methyltransferases). In all cases, cofactor S-Adenosyl methionine (SAM) serves as a cofactor and methyl donor group. On the other hand, the enzymes that promote histone demethylation can be broadly classified into the jmjC (jumonji) demethylases, the LSD1-type KDMs, and the PAD-type arginine demethylases (Cyr and Domann 2011).

Apart from histone PTMs, DNA methylation is the other most studied and well-characterized epigenetic modification. Methylation has been observed on cytosine, adenine and guanine, with cytosine methylation being the most abundant and widely studied modification (Auclair and Weber 2012). Cytosine methylation at CpG nucleotides has been well studied, but it is now clear that methylation also occurs in other contexts [START_REF] Ramsahoye | Non-CpG methylation is prevalent in embryonic stem cells and may be mediated by DNA methyltransferase 3a[END_REF], including at CpA at specific loci on the embryonic genome [START_REF] Haines | Allelespecific non-CpG methylation of the Nf1 gene during early mouse development[END_REF]. DNA methylation inhibits transcription initiation and removes the engaged transcriptional machinery from active templates (Auclair and Weber 2012). Transcriptional repression depends on methylation density; and even 7% of methylation on CpG sites can cause dramatic transcriptional repression. Low levels of methylation were found to inhibit gene expression by 67 -90% whereas higher levels of methylation were able to completely abolish gene expression. In one specific case, called "imprinting", only one parental allele is silenced, usually by hypermethylation, leading to expression from the other nonmethylated parental allele [START_REF] Reik | Genomic imprinting: parental influence on the genome[END_REF]. The enzymes responsible for DNA methylation, the DNA methyltransferases (DNMT) include DNMT1 that is mainly involved in the maintenance of DNA methylation through replication and DNMT3A, DNMT3B as well as the cofactor DNMT3L known as the de novo methyltransferases. Mechanisms leading to active demethylation have been extensively studied recently [START_REF] Ficz | New insights into mechanisms that regulate DNA methylation patterning[END_REF]. One of them involves the oxidation of methylated DNA by enzymes of the Ten Eleven Translocation (TET) family. During this reaction, a hydroxymethyl group replaces the hydrogen atom at the C5 position in cytosine, thereby transforming the 5-Methylcytosine (5mC) into to 5hydroxymethylcytosine (5hmC) [START_REF] Tahiliani | Conversion of 5-methylcytosine to 5-hydroxymethylcytosine in mammalian DNA by MLL partner TET1[END_REF].

Epigenetic changes & development: the mouse example

Prior to fertilization, the gametes carry the parental germline epigenetic signature. Interestingly, the spermatozoa nucleus exhibits a highly compacted chromatin stemming from the replacement of histones by protamines and the high acetylation of residual histones associated with methylation of lysine residues (H4K20, H3K27 & H3K9me3; Beaujean 2014), plus eventually with other new posttranslational modifications such as crotonylation [START_REF] Tan | Identification of 67 histone marks and histone lysine crotonylation as a new type of histone modification[END_REF]) and high DNA methylation [START_REF] Reik | Genomic imprinting: parental influence on the genome[END_REF]. During follicular maturation, the growing oocytes show a dynamic profile of the methylation with a clear increase of methylation level (from 0.5% in young oocytes to 15.3% in ovulated metaphase II oocytes) that remains lower than in sperm (24.9%) [START_REF] Smallwood | Dynamic CpG island methylation landscape in oocytes and preimplantation embryos[END_REF]. Histone deacetylation (H4K12), removal of arginine methylation from histones H3/H4 and methylation of H3K9 are also important for the epigenome of female gametes (Bonnet-Garnier et al. 2012;Beaujean 2014).

From fertilisation, both the incoming paternal DNA complement and that of the oocyte itself are reprogrammed in a number of steps, resetting chromatin to the embryonic form capable of undergoing further changes required during development (Figure 2) (Beaujean 2014;Beaujean, 2015;Sepulveda-Ricon et al., 2016). This results in a series of epigenetic modifications that start during the formation of the paternal and maternal pronuclei (PN) at the 1-cell stage (or zygote). These steps are particularly dramatic for the paternally inherited genome. The protamines associated with the haploid paternal genome in the sperm head are rapidly replaced with histones, including histones H3 and H4 forms that are more acetylated than those associated with the maternal genome (Adenot et al. 1997). Within few hours, there is a widespread intense demethylation of both the paternal and the maternal genome, although both genomes are not similarly affected (Figure 3): methylation is retained on intergenic regions such as constitutive heterochromatin in the paternal genome vs. intragenic regions in the maternal genome [START_REF] Mayer | Demethylation of the zygotic paternal genome[END_REF][START_REF] Salvaing | 5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote[END_REF][START_REF] Okamoto | DNA methylation dynamics in mouse preimplantation embryos revealed by mass spectrometry[END_REF][START_REF] Guo | Single-cell multi-omics sequencing of mouse early embryos and embryonic stem cells[END_REF]. The mechanism responsible for this rapid removal remains unclear: it is suggested that the dioxygenase Tet3 catalyses the oxidation of 5mC to 5hmC in this context [START_REF] Gu | The role of Tet3 DNA dioxygenase in epigenetic reprogramming by oocytes[END_REF] but other recent data suggest that the initial loss of paternal 5mC does not require 5hmC formation (Amouroux et al. 2016). Imprinted genes are not affected during this wave of genome-wide DNA demethylation, and parental imprints are maintained in the somatic tissues of the fets throughout life [START_REF] Reik | Genomic imprinting: parental influence on the genome[END_REF].

In addition to the aforementioned asymmetry in histone acetylation, the profiles of several other histone modifications differ between maternally and paternally inherited genomes. In mouse, the paternal genome is initially associated with mono-methylation of H3 and H4 (H3K9me1 and H4K20me), while the maternal genome is characterised by di-and tri-methylation marks including H3K9me3, H3K27me2/3, H3K4me3 and H4K20me3. After fertilisation, H3K9me3 is one of the modifications characterising the maternal genome, with little H3K9me3 detected on the paternal genome. This asymmetry persists until the 4-cell stage [START_REF] Liu | Regulation of histone H3 lysine 9 methylation in oocytes and early preimplantation embryos[END_REF]. All these histones/DNA methylation changes are believed to participate in the onset of the embryonic genome activation (EGA). Indeed, EGA is characterized by a typical chromatin organization that is not observed in somatic cells or at later stages of development. It is believed that these special epigenetic features of the embryo lead to specific changes of gene expression during preimplantation development.

Trimethylation of lysine 27 of histone H3 (H3K27me3) is another histone modification associated with gene repression, but that does not seem to play a major role prior to EGA. In mouse embryos, H3K27me3 is found only on the maternal genome at fertilisation, with accumulation on the paternal genome occurring by the late pronuclear stage (Albert and Peters 2009). H3K27me3 is maintained until the morula stage, when a significant drop in levels has been observed [START_REF] Zhang | Defective chromatin structure in somatic cell cloned mouse embryos[END_REF]). This is followed by an increase at the blastocyst stage, in the inner cell mass (ICM) cells only (Bogliotti and Ross 2012). Differential H3K27me3 levels at the promoters of several key transcription factors have recently been shown to be functionally significant in determining whether cells assume an ICM or trophectoderm fate [START_REF] Saha | EED and KDM6B Coordinate the First Mammalian Cell Lineage Commitment To Ensure Embryo Implantation[END_REF]). Immunostaining has shown H3K27me3 at the inactive X chromosome in extra-embryonic and embryonic cells [START_REF] Plath | Role of histone H3 lysine 27 methylation in X inactivation[END_REF], and whole genome analyses have indicated that its accumulation at the promoters of key developmental genes coincides with their repression during differentiation [START_REF] Pan | Whole-genome analysis of histone H3 lysine 4 and lysine 27 methylation in human embryonic stem cells[END_REF][START_REF] Hawkins | Distinct epigenomic landscapes of pluripotent and lineagecommitted human cells[END_REF]. Another epigenetic mark seems to play a key role in late preimplantation stages: analysis of the expression of Carm1, an enzyme mediating methylation of arginine residues on H3, has shown overexpression in the ICM of mouse blastocysts [START_REF] Torres-Padilla | Histone arginine methylation regulates pluripotency in the early mouse embryo[END_REF], suggesting an epigenetic bias of the cell fate at the blastocyst stage [START_REF] Parfitt | Epigenetic Modification Affecting Expression of Cell Polarity and Cell Fate Genes to Regulate Lineage Specification in the Early Mouse Embryo[END_REF][START_REF] Wu | The Molecular Harbingers of Early Mammalian Embryo Patterning[END_REF]. Indeed H3R26 methylation regulates Sox2 transcription factor binding to DNA as early as the 4-cell stage thereby modulating the balance between pluripotency (ICM cells) and differentation (trophectoderm cells) [START_REF] Goolam | Heterogeneity in Oct4 and Sox2 Targets Biases Cell Fate in 4-Cell Mouse Embryos[END_REF][START_REF] White | Long-Lived Binding of Sox2 to DNA Predicts Cell Fate in the Four-Cell Mouse Embryo[END_REF]. Similarly, high levels of 5meC colocalize with the ICM in blastocysts [START_REF] Ruzov | Lineage-specific distribution of high levels of genomic 5-hydroxymethylcytosine in mammalian development[END_REF]) and knockdown of Tet1 in pre-implantation embryos results in a bias towards trophectoderm differentiation, suggesting a role of TET1 protein in ICM specification [START_REF] Ito | Role of Tet proteins in 5mC to 5hmC conversion , ES-cell self-renewal and inner cell mass specification[END_REF]. Knockdown of Set1a, one of the H3K4 methyltransferase, also demonstrated that H3K4 methylation is not only required for early embryonic development but also for the emergence of the ICM (Fang et al. 2016).

Such knockdowns of enzymes catalysing histone PTMs confirm that these histone modifications are essential regulators of chromatin remodeling after fertilization that modulate the maternal-to-embryonic transcriptional transition. Both histones methyltransferases and demethylases are crucial for pre-implantation development. For example, without Setdb1, an HMT that controls H3K9me2, embryos do not develop properly and exhibit severe cell cyle defects (Eymery et al. 2016;Kim et al. 2016). However, embryonic development is also disrupted after knockdown of KDMs targeting H3K9me2/me3 such as KDM4A or KDM1A (Ancelin et al. 2016;Sankar et al. 2017) underlying the requirement of a good epigenetic balance.

Remarkably, the sames changes in histones PTMs / DNA methylation have been shown to regulate embryonic development by knockdowns or over-expression of regulating enzymes in other species such as pig (Cao et al. 2017;[START_REF] Huan | Trichostatin A Rescues the Disrupted Imprinting Induced by Somatic Cell Nuclear Transfer in Pigs[END_REF]Ding et al., 2017) and bovine (li 2015; chung 2018 fu 2017). However, in these cases, embryos are often produced after superovulation, in vitro maturation and in vitro culture (Figure 4). All these biotechnologies have been shown to affect the epigenetic profile of the derived embryos/offspring that will be described hereafter.

Embryo in vitro production (IVP)

Oocyte supply

In the female germ line, methylation patterns are established predominantly during the last steps of oocyte development. Hormonal stimulation of the follicles (superovulation) during this period to obtain oocytes used for embryo IVP has been suggested to affect the completion of this epigenetic event. Superovulation seems associated with reduced oocyte quality and delayed embryonic development, but it has been also shown in the mouse to affect DNA methylation remodelling in the resulting embryo [START_REF] Shi | Aberrant methylation patterns at the two-cell stage as an indicator of early developmental failure[END_REF], that would correlate with altered gene expression at later stages. Superovulation has been shown to be associated with aberrant imprinted methylation profiles, especially at high hormone dosage: loss of methylation was observed in maternally imprinted genes Snrpn, Peg3, and Kcnq1ot1 and gain of methylation at the maternal allele in paternally imprinted H19 gene altered its expression (Denomme and Mann 2012). The transcriptomic profile divergences between bovine oocytes collected from stimulated vs. non-stimulated donors suggests that epigenetic changes may contribute to the reduced developmental competence of oocytes under certain conditions (high dosages of gonadotropins, prepubertal cattle), but only minor changes have been observed and further studies are still required [START_REF] Urrego | Epigenetic disorders and altered gene expression after use of assisted reproductive technologies in domestic cattle[END_REF].

In livestock species, in vitro maturation (IVM) is often used to obtain oocytes prior to embryo IVP. In the mouse, IVM has been shown to down-regulate the expression of key epigenetic modifiers such as HDAC1 both in the oocyte and in the 2-cell embryo [START_REF] Wang | Effects of in vitro maturation on histone acetylation in metaphase II oocytes and early cleavage embryos[END_REF]. Imprinted genes also are affected: IVM resulted under some conditions in a loss of methylation at the Igf2r and Mest loci and a gain of methylation at the H19 imprinted region. However, improved culture conditions (e.g. with different metabolic compounds present in the media) yielded fewer epigenetic abnormalities. Similarly, oocyte culture in bovine and ovine species does not seem to have significant effects on imprinted genes (Anckaert et al. 2012). However, other epigenetic mechanisms may be affected (e.g. histone methylation or acetylation) that could contribute to differences in the transcriptomic profile of those in vitro matured oocytes with various developmental competence.

Sperm quality

Spermatogenesis is a long process of cellular differentiation requiring a well orchestrated series of epigenetic modifications to obtain a stably packed chromatin, facilitating all sperm functions (motility, energy production, capacitation, acrosomal reaction…) and thus ultimately fertilization. DNA methylation, histone/protamine exchange, histone PTMs and non coding RNAs have important, but so far underestimated, roles in the production of fertile sperm and for subsequent embryo development (Boissonnas et al. 2013). Any aberrations in the sperm epigenetic landscape may indeed have detrimental consequences for early embryo development.

Literature suggests that stochastic, environmentally and genetically induced deviation in the genome-wide epigenetic reprogramming process during germ-cell development may lead to epigenetic aberrations impacting spermatogenesis, semen quality and the male fertility as a whole [START_REF] Laurentino | On the origin of sperm epigenetic heterogeneity[END_REF]. Identifying sub-fertile males is thus a major issue that has stimulated research on sperm characteristics associated with poor or successful fertilization events. Much progress has been made in this area, especially in dairy cattle due to the extensive use of artificial insemination. Current factors such as motility, chromatin structure or seminal proteins help in identifying defects mainly associated with fertilization. Recently, the epigenetic impact of DNA methylation on embryonic development and pregnancy has been addressed in bovine [START_REF] Kropp | Male fertility status is associated with DNA methylation signatures in sperm and transcriptomic profiles of bovine preimplantation embryos[END_REF], showing a link between spermatozoa DNA methylation and fertility, as in human.

In vitro Culture of preimplantation embryos

It was shown already 20 years ago that embryo culture can alter the imprinted H19 locus in mouse (Anckaert et al. 2012). The impact of embryo culture, especially the presence of fetal calf serum in the media, on imprinted gene methylation and expression was then confirmed in several studies, both in mouse and in other species. In general, imprinting errors appeared to occur during the preimplantation period in culture and persisted during gestation, most probably because the trophectoderm is directly in contact with the culture medium, which can potentially affect placental development. The 'Large Offspring Syndrome' (LOS) was the first obvious incidence of abnormal development following transfer of in vitro culture (IVC) ruminant embryos into surrogate mothers. This syndrome is characterized by an overgrowth phenotype and appeared to be linked to culture conditions (serum-containing; coculture) [START_REF] Van Soom | An Introduction to Epigenetics as the Link Between Genotype and Environment: A Personal View[END_REF]. Indeed, LOS sheep foetuses exhibited aberrant hypomethylation and reduced expression of the imprinted IGF2R gene (insulin-like growth factor receptor), a gene known to influence body size and carcass traits [START_REF] Young | Epigenetic change in IGF2R is associated with fetal overgrowth after sheep embryo culture[END_REF].

In 2002, W. Shi and T. Haaf demonstrated by 5mC staining of mouse 2-cell embryos cultured in vitro that suboptimal culture media can lead to disturbances of the genome-wide DNA demethylation process and concomitantly to developmental arrest. Similar results were obtained in the rabbit although timing and the degree of DNA demethylation differ between these species (Figure 5) emphasising the importance DNA methylation in preimplantation development (e Silva et al. 2012;[START_REF] Salvaing | Assessment of "one-step" versus "sequential" embryo culture conditions through embryonic genome methylation and hydroxymethylation changes[END_REF]. Using a similar immunostaining approach for histone PTMs such as H3K9 methylation, H4 acetylation or H3S10 phosphorylation no differences were observed between in vitro fertilized/IVC mouse embryos and their in vivo counterparts (Beaujean 2015), only H3K4me3 levels were significantly lower in the IVC embryos [START_REF] Wu | Differences in H3K4 trimethylation in in vivo and in vitro fertilization mouse preimplantation embryos[END_REF]. A gene candidate approach based on chromatin immunoprecipitation (ChIP) has also enabled studies of several PTMs in embryos after IVC and confirmed few chromatin configuration changes and histone PTMs alterations [START_REF] Urrego | Epigenetic disorders and altered gene expression after use of assisted reproductive technologies in domestic cattle[END_REF]. The importance of this IVC step has led (and is still leading) numerous laboratories worldwide to improve culture conditions in order to reduce the deficiencies that might lead to epigenetic alterations and changes in gene expression. Some culture media have been tested in mouse and bovine that seem to have lower impact on the DNA methylation and histone acetylation levels, resembling quite closely the in vivo situation (El Hajj and Haaf 2013;[START_REF] Rollo | Histone 3 lysine 9 acetylation is a biomarker of the effects of culture on zygotes[END_REF]Canovas et al. 2017).

Cryopreservation and vitrification of gametes & embryos

Storage of gametes and embryos is a routine procedure in all animal biotechnologies, but few studies analysed the impact on epigenetic marks. In mouse, it was shown that epigenetic reprogramming of H3K4me3 and H4K12ac up to the blastocyst stage was similar in embryos derived from frozen sperm (at -20°C) and in fertilized embryos derived from fresh sperm (Chao et al. 2012). Reversely, oocytes can be preserved, either by cryopreservation or vitrification. In the mouse, histone PTMs alterations have been observed after vitrification with vitrified oocytes showing abnormally high levels of H4K12ac and low HDAC1 expression [START_REF] Suo | Effect of cryopreservation on acetylation patterns of lysine 12 of histone H4 (acH4K12) in mouse oocytes and zygotes[END_REF]) that correlated with lower developmental rates. Similar results were obtained in ovine and bovine vitrified oocytes (Chen et al. 2016;[START_REF] Shirazi | The effect of ovine oocyte vitrification on expression of subset of genes involved in epigenetic modifications during oocyte maturation and early embryo development[END_REF]. In cryopreserved bovine embryos, DNMT3 expression and global DNA methylation levels also seem to be affected. However, such studies are also quite rare in livestock animals, with no evaluation of the potential impact on later development.

Somatic Cell Nuclear transfer (SCNT or "cloning")

Differentiated cells can be reprogrammed back to a pluripotent state through somatic cell nuclear transfer (SCNT). This technique consists of a single cell nucleus being injected into an enucleated oocyte in order to produce a viable embryo [START_REF] Ogura | Recent advancements in cloning by somatic cell nuclear transfer[END_REF]). However, the efficiency of SCNT is very low. The first evidence for reprogramming was shown by Briggs and King when tadpoles were produced from transplanting the nuclei of blastula cells into enucleated frog oocytes in 1952 [START_REF] Gurdon | Nuclear transfer to eggs and oocytes[END_REF]. In 1997, Wilmut et al. were able to produce a healthy cloned sheep, the first mammal to be cloned from an adult cell [START_REF] Wilmut | Viable offspring derived from fetal and adult mammalian cells[END_REF]. Since then, features of cloning techniques have been improved in order to get more accurate and reproducible procedures for generating live mammalian offspring. The importance of the type and age of the nucleus donor cell, as well as the strain and genotype of the oocyte that will receive this nucleus have been demonstrated. Reasons to explain why some cells are more suitable for cloning than others include epigenetic reprogramming problems. Nuclear epigenetic reprogramming is known to be an essential mechanism needed for embryonic development, both after fertilization (as described earlier) but even more after nuclear transfer (Figure 2). The somatic donor nucleus will need to be reprogrammedthe expression profile of the differentiated donor cell needs to be replaced by an embryo-specific one-in order to give rise to a totipotent embryo (Beaujean 2015; Sepulveda-Rincon 2016). It is now clear that reprogramming errors may accumulate during this process and that reprogramming of DNA methylation and histone PTMs profiles of the donor nucleus is a critical step. The removal of the epigenetic profile associated with the donor cell type, and its replacement by the epigenetic profile of the embryo has been widely suggested to be incomplete or incorrect, thereby limiting the success of SCNT.

A comparison of H3K27me3 levels in normal and cloned mouse embryos for example failed to detect any H3K27me3 in the ICM of cloned embryos [START_REF] Zhang | Defective chromatin structure in somatic cell cloned mouse embryos[END_REF]). This work indicated a role for H3K27me3 in repressing expression of genes associated with differentiation, allowing cells to maintain pluripotency during development. The authors suggested that in cloned embryos, decreased H3K27me3 levels resulted in faulty expression of such genes, resulting in arrest of development [START_REF] Zhang | Defective chromatin structure in somatic cell cloned mouse embryos[END_REF]. Several other histone PTMs levels, such as H3K9me3 and H3K4me3, are also abnormal in SCNT embryos as compared to in vivo produced embryos. Remarkably, the degree of reprogramming of these levels correlates with the developmental potential of these clones into adult offspring [START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF][START_REF] Kallingappa | Quiescence Loosens Epigenetic Constraints in Bovine Somatic Cells and Improves Their Reprogramming into Totipotency[END_REF].

Similarly, DNA methylation reprogramming has been shown to be critical for the success of SCNT (Beaujean et al. 2004). DNA methylation is usually associated with repression of gene expression and is found at higher levels in somatic cells than in embryos. Successful nuclear reprogramming involves genome wide removal of DNA methylation, profiles with observations suggesting that demethylation is necessary for gene expression after reprogramming [START_REF] Simonsson | demethylation is necessary for the epigenetic reprogramming of somatic cell nuclei[END_REF]). Persistent cytosine methylation after nuclear transfer has been suggested as a factor contributing to the low efficiency of cloning, and to the high incidence of abnormalities observed in cloned animals [START_REF] Kang | Aberrant methylation of donor genome in cloned bovine embryos[END_REF]. Indeed, several studies in cloned embryos suggest that most cloned animals do not develop because of hypermethylation changes in their genome, both at a gene-specific level but also genome-wide. This retention of 5mC is thought to be responsible for the so-called "persistent cellular memory" after SCNT. Genome-wide methylation analyses of cloned mouse embryos revealed that the DNA demethylation process normally observed after fertilization also occurs after SCNT. However, this demethylation was less drastic and the resulting DNA methylation profile was more similar to the donor fibroblast one than to a fertilized embryo. This aberrant demethylation is concomitant with aberrant nuclear reorganization of the heterochromatin that forms somatic-like clusters usually not observed after fertilization (Figure 6). In ovine, bovine and mouse, a clear correlation was found between the efficiency of nuclear heterochromatin reorganization and the percentage of SCNT embryos surviving the first embryonic cleavages, up to embryonic genome activation (Beaujean et al. 2004;[START_REF] Zink | Architectural reorganization of the nuclei upon transfer into oocytes accompanies genome reprogramming[END_REF].

Importantly, the kinetics of DNA demethylation/remethylation in SCNT cloned embryos clearly differs from that in fertilized embryos, leading to an awkward situation at the blastocyst stage. Indeed, most SCNT blastocysts do not present the typical asymmetry of DNA methylation between ICM and trophectoderm cells (Beaujean et al. 2004). In fact, most SCNT derived blastocysts present a hypermethylation of the trophectoderm cells that might potentially be associated with developmental abnormalities in cloned foetus. This hypothesis is particularly sustained by the high frequency of the large offspring syndrome after SCNT. It has indeed been confirmed that several imprinted regions of the genome, which should remain methylated, are in fact demethylated after SCNT [START_REF] Niemann | Epigenetic reprogramming in mammalian species after somatic cell nuclear transfer based cloning[END_REF]. Several researchers have produced data on SCNT cloned foetuses or offspring showing that the aberrant phenotypes described after SCNT bear strong similarities to abnormalities associated with deletion/mutations in imprinted regions. Aberrant proper expression of genes such as IGF2 gene and other members of this gene family (IGF2R and H19) is critical for normal embryonic and fetal development [START_REF] Young | Epigenetic change in IGF2R is associated with fetal overgrowth after sheep embryo culture[END_REF]. The maintenance of such high DNA methylation levels in SCNT embryos has been related to the presence of the somatic form of the DNA methyltransferase brought by the somatic donor cell that probably interferes with the genome-wide demethylation process that normally takes place after fertilization. Similarly, the NDN (Necdin; paternally expressed) and XIST (paternally expressed) imprinted genes were found to be aberrantly expressed in cloned bovine embryos (compared to fertilized ones), and this aberrant expression was at least partially associated with histone aberrant H4K5 acetylation [START_REF] Wee | Inheritable histone H4 acetylation of somatic chromatins in cloned embryos[END_REF].

Because these abnormal gene expression profiles observed during preimplantation development often persist throughout fetal development up to birth in some cases [START_REF] Koike | DNA Methylation Errors in Cloned Mouse Sperm by Germ Line Barrier Evasion[END_REF], it suggests that very early epigenetic modifications can have very late impact and that preimplantation development is a very sensitive period in this regard.

Use of epigenetic inhibitors to improve SCNT

As epigenetic reprogramming clearly plays a key role in the development of SCNT derived embryos, many researchers have chosen to use HDAC inhibitors (HDACi) -such as TSA-to correct epigenetic errors and improve cloning efficiency [START_REF] Ogura | Recent advancements in cloning by somatic cell nuclear transfer[END_REF]. They examined the efficiency of SCNT with TSA treatments, demonstrating that TSA enhances the pool of acetylated histones in SCNT embryos as well as DNA demethylation. They also reported that the optimal concentration of TSA to obtain development to the blastocyst stage was 5-50 nM for a few hours after nuclear transfer, during the first embryonic cycle (usually 6 to 10 hours post-activation). Toxicity was shown at 500 nM and when the treatment was extended for more than 10 hours. One study using TSA, demonstrated that this inhibitor can assist with reprogramming of Oct4, a major factor for pluripotency maintenance: while SCNT embryos often showed aberrant expression of this gene in the trophectoderm cells of mouse blastocysts, TSA treatment helped embryos to express Oct4 in the correct number cells during development [START_REF] Hai | Pluripotency maintenance in mouse somatic cell nuclear transfer embryos and its improvement by treatment with the histone deacetylase inhibitor TSA[END_REF]. The nuclear reorganization of heterochromatin was also clearly improved in SCNT embryos treated with HDAC inhibitors (Figure 6) [START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF]. In most species studied so far it has been shown that histone acetylation can be enhanced by TSA and other HDACi (e.g. scriptaid, valproic acid -VPA), even in inter-species (porcinebovine) cloned-embryos [START_REF] Opiela | In vitro development and cytological quality of interspecies (porcine→bovine) cloned embryos are affected by trichostatin A-dependent epigenomic modulation of adult mesenchymal stem cells[END_REF].

They have now been demonstrated to play a similar beneficial role on cloned embryo development, albeight with different efficiencies and outcomes [START_REF] Ono | Inhibition of class IIb histone deacetylase significantly improves cloning efficiency in mice[END_REF]. It was demonstrated that scriptaid can indeed increase transcriptional activity in SCNT embryos, but could not support full-term development of inbred cloned embryos in contrast to TSA. It also appears that SAHA (suberoylanilide hydroxamic acid) and oxamflatin -but not valproic acid-could reduce apoptosis in SCNT derived blastocysts and thus improve full-term development of the clones. Since valproic acid inhibits HDAC classes I and IIa and the rest of HDACi's act on HDAC classes IIa / b, this suggests that the inhibition of HDAC class IIb is an important step for reprogramming mouse cloning efficiency. Analyses performed on imprinted genes also showed improved reprogramming after HDACi treatments: in the porcine SCNT protocols, scriptaid treatment of the donor cells rescued disrupted methylation at H19 imprinted region after SCNT and oxamflatin treatment improved the DNA methylation profile at the imprinted XIST locus that lead to higher in vitro developmental rates and offspring rates [START_REF] Xu | Effects of DNMT1 and HDAC inhibitors on gene-specific methylation reprogramming during porcine somatic cell nuclear transfer[END_REF][START_REF] Hou | Effects of histone deacetylase inhibitor oxamflatin on in vitro porcine somatic cell nuclear transfer embryos[END_REF]. Similar results were obtained on developmental key genes Oct4, Nanog and Sox2 [START_REF] Huan | Trichostatin A Rescues the Disrupted Imprinting Induced by Somatic Cell Nuclear Transfer in Pigs[END_REF][START_REF] Jin | Quisinostat treatment improves histone acetylation and developmental competence of porcine somatic cell nuclear transfer embryos[END_REF][START_REF] Sun | Suberoylanilide hydroxamic acid, a novel histone deacetylase inhibitor, improves the development and acetylation level of miniature porcine handmade cloning embryos[END_REF].

Other histone PTMs abnormal levels have also been targeted : removal of H3K9me3 by overexpression of the lysine demethylase Kdm4d has been proven to restore transcriptional reprogramming in mouse cloned embryos and to efficiently improve blastocysts rates both in mouse and human cloning experiments [START_REF] Matoba | Embryonic Development following Somatic Cell Nuclear Transfer Impeded by Persisting Histone Methylation[END_REF]Chung et al. 2015). Similarly, treatment with a DOT1L inhibitor to reduce H3K79 methylation improved cloning efficiency in pig [START_REF] Tao | DOT1L inhibitor improves early development of porcine somatic cell nuclear transfer embryos[END_REF]) and overexpression of USP21 in cloned mouse embryos improved their transcriptional reprogramming [START_REF] Jullien | Gene Resistance to Transcriptional Reprogramming following Nuclear Transfer Is Directly Mediated by Multiple Chromatin-Repressive Pathways[END_REF]. Combinations of several approaches are now being explored. Recently, the very first SCNT monkeys were obtained by a combined treatment with TSA and Kdm4D overexpression [START_REF] Liu | Cloning of Macaque Monkeys by Somatic Cell Nuclear Transfer[END_REF].

Strategies directing DNA methylation have also been reported. In the mouse and pig, the removal of DNA methylation in donor cells by knockout of the DNMT3l or Dnmt1s genes, respectively, was associated with significant changes of the epigenetic profile of the cloned embryos and significant improvements of the SCNT process with regard to blastocyst rates, indicating that modulation of DNMTs activity could indeed be beneficial [START_REF] Liao | Dnmt3l-knockout donor cells improve somatic cell nuclear transfer reprogramming efficiency[END_REF][START_REF] Song | Dnmt1s in donor cells is a barrier to SCNT-mediated DNA methylation reprogramming in pigs[END_REF]. Similarly, helping the cloned embryos to remove DNA methylation by overexpression of the AID (Activation-induced cytidine deaminase, on of the demethylation mechanism) significantly improves the cleavage and blastocyst rates in the bovine (Ao et al. 2016).

These findings provide clues towards more efficient cloning protocols by modulating epigenetic reprogramming. However, it remains to be shown whether this yields to more healthy live cloned offspring as only few studies have been performed so far on this subject.

Stem cells derivation

Embryonic stem (ES) cells can be derived from the ICM of mammalian blastocysts. They are pluripotent and have the ability to differentiate into cells of all three germ layersmesoderm, endoderm and ectoderm [START_REF] Rossant | Stem Cells and Early Lineage Development[END_REF]. All specialized cells are derived from one of these three germ layers, which implies that pluripotent cells can differentiate into any type of cell in the body. ES cells also have a high capacity for renewal and can be expanded indefinitely in culture. These properties have led to expectations that ES cells could be useful for research into understanding disease mechanisms, screening for safe and effective drugs and treating diseases and injuries. Pluripotent cells have indeed the potential to be cultured and differentiated in the lab to make specialized cell types that could be used to replace damaged cells and tissues in the organisms. However, ES cells production is limited by embryo availability.

On the other hand, induced pluripotent stem (iPS) are somatic cells that can be reprogrammed to a pluripotent state by overexpressing certain transcription factors (initially Oct4, Sox2, Myc and Klf4) [START_REF] Takahashi | Induction of pluripotent stem cells from mouse embryonic and adult fibroblast cultures by defined factors[END_REF]. They are able to function similarly to ES cells and are more readily available for use in research and therapeutics than ES cells. When mouse iPS cells are transplanted into blastocysts, they are able to give rise to adult chimeras, which are competent for germline transmission. This has introduced the opportunity to develop custom-made cells in order to study and treat many diseases.

Animal stem cells play an important role as a research model in testing research theories before human clinical trials and clinical use. Animal pluripotent stem cells could also serve for agricultural purposes: such stem cells could be used for genetic engineering to generate livestock with superior genes that are important for economic and disease-resistant traits; they could also be used for studying functional genomics in those mammals. As a result, monkey, bovine, pig, sheep, goat, horse and rabbit iPS cells have been successfully established although there is a lack of research on stem cells from farm animals (Nowak-Imialek and Niemann 2013; [START_REF] Ogorevc | Cellular reprogramming in farm animals: an overview of iPSC generation in the mammalian farm animal species[END_REF]. However, those non-human/non-murine stem cells are often unable to colonize embryos after injection into blastocysts; they do not show all the attributes of pluripotent stem cells and lacked some of the key features of pluripotency compared to mouse stem cells. Consequently, it has been proposed that most of these stem cells are not in a " naïve" pluripotency status like in mouse ES cells but rather in a more "primed" status with less flexibility [START_REF] Piedrahita | Perspectives on transgenic livestock in agriculture and biomedicine: an update[END_REF].

Studies have shown that mouse iPS cells have a higher ratio of euchromatin to heterochromatin when compared to differentiated cells such as somatic cells [START_REF] Mattout | Global epigenetic changes during somatic cell reprogramming to iPS cells[END_REF]. This is similarly seen in ES cells, which display an even more opened and hyperdynamic chromatin structure in comparison to somatic cells. These characteristics resemble the ones observed in vivo in the ICM of mouse blastocysts, which are the source of ES cells (Ahmed et al. 2010). It has been hypothesized that an open chromatin structure allows rapid switching of transcriptional programmes when differentiation is induced [START_REF] Meshorer | Chromatin in pluripotent embryonic stem cells and differentiation[END_REF]. As these stem cells have the ability to differentiate into many different cells, a broad spectrum of differentiation opportunities is indeed necessary. In agreement with this hypothesis, the ES cell genome is transcriptionally globally hyperactive, a hallmark that seems to be characteristic of ES cell pluripotency and contributes to their plasticity. On the other hand, it has been proposed that reduction of pluripotency potential in primed pluripotent cells correlates with a reduction of the actively transcribed portion of the genome and that, similarly to the situation observed after SCNT, abnormal reprogramming of DNA and histones involved in the removal of the original somatic cell epigenetic landscape [START_REF] Savatier | Pluripotency of embryo-derived stem cells from rodents, lagomorphs, and primates: Slippery slope, terrace and cliff[END_REF].

DNA

demethylation and cytosine hydroxymethylation appeared to be key elements in the reactivation of pluripotency genes in mice stem cells as they are hypermethylated and silenced in somatic cells [START_REF] Mikkelsen | Dissecting direct reprogramming through integrative genomic analysis[END_REF]. Indeed, the TET family of enzymes, which promote the conversion of 5mC to 5hmC, are highly expressed in embryonic stem cells [START_REF] Tahiliani | Conversion of 5-methylcytosine to 5-hydroxymethylcytosine in mammalian DNA by MLL partner TET1[END_REF][START_REF] Ito | Role of Tet proteins in 5mC to 5hmC conversion , ES-cell self-renewal and inner cell mass specification[END_REF]. Moreover, DNA methylation deficient ESCs are unable to differentiate [START_REF] Jackson | Severe Global DNA Hypomethylation Blocks Differentiation and Induces Histone Hyperacetylation in Embryonic Stem Cells[END_REF]. In humans, it has been shown that DNA methylation patterns in iPS and ES cells were similar but exhibited different methylated regions in which 55% of methylated regions in iPS cells are not found in the somatic cell of origin or in ES cells. Finally, it has been found that iPS cells retain a methylation signature of their tissue of origin [START_REF] Kim | Epigenetic memory in induced pluripotent stem cells[END_REF]. Histone PTMs also seem involved: histone acetylation (particularly H3K9ac) is increased in undifferentiated human ES cells [START_REF] Krejcí | Genome-wide reduction in H3K9 acetylation during human embryonic stem cell differentiation[END_REF]) and H3K9me3/H3K27me3 was shown to increase from 4% in ES cells to 12-16% coverage in differentiated cells [START_REF] Hawkins | Distinct epigenomic landscapes of pluripotent and lineagecommitted human cells[END_REF]. Moreover, H3K9me is associated with Oct4 inactivation suggesting that this mark could indeed act as a barrier for reprogramming [START_REF] Feldman | G9a-mediated irreversible epigenetic inactivation of Oct-3/4 during early embryogenesis[END_REF]). Those observations have been confirmed by genomewide analysis of H3K9ac, H3K27me3 and H4K3me3 (ChIP-sequencing technology) (Bernstein et al. 2006;Azuara et al. 2006). In rabbbits, clear histone PTMS/DNA methylation differences can be observed between highly "primed" iPS cells and more "naïve" ones [START_REF] Tapponnier | Reprogramming of rabbit induced pluripotent stem cells toward epiblast and chimeric competency using Krüppel-like factors[END_REF].

There have been studies conducted on iPS cells that focus on particular chromatin treatments in order to decondense and open the chromatin , similar to the chromatin structure of ES cells. Treatment with agents that promote chromatin decondensation has been shown to increase the efficiency of iPS cell generation [START_REF] Szablowska-Gadomska | Treatment with small molecules is an important milestone towards the induction of pluripotency in neural stem cells derived from human cord blood[END_REF]. It was shown that even at low doses, the histone deacetylase inhibitor TSA was able to stabilize expression of pluripotent genes. Similarly, VPA was found to stabilize histone acetylation and the expression of pluripotent gene in bovine iPS cells [START_REF] Mahapatra | Valproic acid assisted reprogramming of fibroblasts for generation of pluripotent stem cellsin buffalo (Bubalus bubalis)[END_REF]. It was also shown that the use of such chemicals to increase reprogramming efficiency could also replace one or more of the key factors found to induce reprogramming [START_REF] Ma | Reprogramming cell fates by small molecules[END_REF]. Removal of the barrier imposed by H3K9me also leads to better reprogrammed iPS cells (Chen et al. 2013;[START_REF] Wei | KDM4B-mediated reduction of H3K9me3 and H3K36me3 levels improves somatic cell reprogramming into pluripotency[END_REF]. Interestingly, studies decreasing H3K9me2 via inhibition of the histone methyltransferase G9a can replace Oct4 during pluripotency induction [START_REF] Shi | Induction of pluripotent stem cells from mouse embryonic fibroblasts by Oct4 and Klf4 with small-molecule compounds[END_REF]. Similarly, studies have shown that it is possible to decrease the retention of DNA methylation and increase pluripotency using chromatinmodifying compounds [START_REF] Kim | Epigenetic memory in induced pluripotent stem cells[END_REF].

Conclusions & Perspectives

Epigenetic reprogramming naturally occurs in gametes and embryos and is essential criteria for undisturbed development. However, during this vulnerable time window of the lifespan environmentally-induced epigenetic defects may occur, some of which may have long term effects leading to subsequent changes in gene expression. In this chapter, several stress factors leading to such defects in animal biotechnologies have been mentioned, but other factors such as environmental exposures to toxic compounds, nutrients or infectious agents may also interfere and should be taken into account (Doherty et al. 2014). Some of these phenotypic modifications can be seen during preimplantation development but also during gestation, at birth or shortly after, or even during adult life. This concept called DOHaD (Developmental Origin of Health and Diseases) has attracted much attention recently and numerous reviews can be found in the literature (Dupont et al. 2012;[START_REF] Lucas | The long-term effects of the periconceptional period on embryo epigenetic profile and phenotype; The paternal role and his contribution, and how males can affect offspring's phenotype/epigenetic profile[END_REF]. Finally, it should be remembered that many studies have shown that such environmental changes alter epigenetic modification not only in the animals studied but also in the descendants as epigenetics can be passed from one generation to the next [START_REF] Jammes | Epigenetic control of development and expression of quantitative traits[END_REF][START_REF] Feil | Epigenetics and the environment: emerging patterns and implications[END_REF]Feeney et al. 2014). This improved is correlated with an improved development to term [START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF]).

Figure 1 :

 1 Figure 1: The impact of permissive and repressive epigenetic modifications will influence the equilibrium between chromatin unfolding and chromatin condensation thereby leading either to gene expression or gene repression.

Figure 2 :

 2 Figure 2:After fertilization of the oocyte by the sperm as well as after somatic cell nuclear transfer, important epigenetic reprogramming events will take place before EGA, involving epigenetic modifications as well as nuclear 3D reorganization. Further epigenetic changes will also occur at the blastocyst stage, either in the ICM or in the trophectoderm leading to cell fate bias. All these events will influence the potential of later development of the embryo.

Figure3:

  Figure3: DNA methylation immunofluorescent detection at the 1-cell (zygote) stage in mouse and rabbit embryos showing the paternal and maternal genome in separated pronuclei. Due to the rapid replacement of histones by protamines, the paternal genome is always more decondensed and the pronucleus bigger than the maternal one. The remnant chromosomes expulsed from the oocyte at the end of the meiosis for the so-called polar body (PB) that can often be observed. In both species DNA demethylation is observed on both the paternal and maternal genomes although not to the same extent. In particular, pericentromeric constitutive heterochromatin that surrounds the nucleolar precusor forming rings (white arrows) clearly maintains DNA methylation even in the paternal genome even just before the first mitosis.

Figure 4 :

 4 Figure 4: Animal biotechnologies are mostly based on the quality and the development of embryos that may be affected either at the level of the gametes used (oocyte & sperm) or during embryo production by various protocols. On the other hand, once obtained, these embryos may then be used to produce stem cells that are also very interesting both for biomedical and veterinarian applications.

Figure 5 :

 5 Figure5: DNA methylation immunofluorescent detection in rabbit embryos from the 2-cell to the morula stages. To evaluate the impact of in vitro culture, embryos were fertilized in vivo but were either collected at 2-cell and cultured or left in vivo and collected just before being processing. DNA demethylation during pre-implantation development was observed in both cases, but with different kinetics (quantification was performed to confirm this obseration:[START_REF] Salvaing | 5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote[END_REF]. Unexpectedly, the level of DNA methylation increased between the 16-cell and morula stages after in vitro culture.

Figure 6 :

 6 Figure 6: H3K9me3 immuno-fluorescent detection in mouse SCNT embryos at the 1-cell stage. The upper panel corresponds to a single focal plan through the nucleus and the lower panel to the 3Dreconstructions obtained from the confocal scanning that was performed through the nucleus. Clusters of heterochromatin usually not observed after fertilization actually accumulating at the periphery (arrow) in the nucleus of cloned embryos. However, treatment of the embryos just after nuclear transfer with an HDAC inhibitor (scriptaid) improves the reprogramming of H3K9me3 and the density as well as the number of heterochromatin clusters clearly decreases.This improved is correlated with an improved development to term[START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF]).

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Olivier Jamet

Dimitrios Tsoulis

A line integral approach for the computation of the potential harmonic coefficients of a constant density polyhedron

A novel approach for the computation of the spherical harmonic coefficients of the gravity field of a constant density polyhedron is presented. Based on the expression of the solid harmonics involved in the integrals in term of a gradient of the same function of higher degree, and on the homogeneity and harmonicity of theses functions, the approach leads, after subsequent application of the divergence theorem in 3D and the Stokes theorem on the plane, to explicit line integrals defined along each polyhedral face, which are then summed for all faces of the polyhedral source. In contrast to previous approaches that involved recurrent relations for the integrals of the same functions, the proposed algorithm concludes to a numerical computation of line integrals linked directly to the coefficients. The performed numerical implementation revealed the stability of the proposed algorithm up to degree 360 for a prismatic test source.

Introduction

The problem of computing the spherical harmonic coefficients of the gravity field of a constant density polyhedral source has been considered by many contributions in the past.

First computations, based on the series expansion of the surface of the body itself were implemented as early as 1989 [START_REF] Chao | The gravitational field of phobos[END_REF][START_REF] Martinec | The phobos gravitational field modeled on the basis of its topography[END_REF][START_REF] Balmino | Gravitational potential harmonics from the shape of an homogeneous body[END_REF]. Their approach is efficient by poorly adapted to isolated bodies away from from the origin of the reference frame, such as geological layers. The problem of the numerical computation of the coefficient through explicit integration has also be tackled very early. The first solution was proposed by [START_REF] Werner | Spherical harmonic coefficients for the potential of a constant-density polyhedron[END_REF]. His stategy was based on the decomposition of the body into tetrahedra, and of the integrands into homogeneous monomials that can be integrated analytically. Recent works proposed also a generalized algorithm for integrating homogeneous polynomials inside a space of any dimension [START_REF] De Loera | Software for exact integration of polynomials over polyhedra[END_REF].

However, the complexity of this family of approaches, which is in the order of n 4 to compute all the coefficients at degree and order n, do not allow very high degree expansions.

Another family of approaches was initiated by [START_REF] Jamet | A linear algorithm for computing the spherical harmonic coefficients of the gravitational potential from a constant density polyhedron[END_REF] who proposed a linear reccurent scheme, of complexity n 2 for the computation of all the coefficients at degree and order n. Their algorithms was also based on the division of the polyhedron into tetrahedra. In each tetrahedron, the volume integrals were transformed into surface integrals thanks to the divergence theorem, and the surface intergals at degree n were expressed as function of the surface integrals at degree n -1 and of line integrals. This method was implemented by [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF], who proved that it was unstable, but that it allowed the computation of the coefficients up to degree 60 for a test asteroid model.

Recently, the work of [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF] was further developed by [START_REF] Chen | Evaluation of the spherical harmonic coefficients for the external potential of a polyhedral body with linearly varying density[END_REF], who stabilized the recurrent computation by choosing a specific frame for each face and extending the approach to linearly varying densities.

The aforementioned works take benefit from the fact that the involved integrands are homogeneous functions. The application of the divergence theorem to theses functions in 3 dimensions is indeed a particular case of a genegal property of homogeneous functions, which allows their volume integration through the integration over the volume's surface, irrespective of the dimension of the considered space [START_REF] Lasserre | Integration and homogeneous functions[END_REF].

In this work, we show that, in three dimensional spaces, the specific properties of the integrands allow to transform the volume integrals, that express the polyhedral potential harmonic coefficients, into line integrals without the need of a recurrence relation for their numerical evaluation. Theses findings provide the basis for a new computation approach.

After presenting the adopted notations (section 2), we present a comprehensive ouline of the proposed method (section 3). Section 4 gives the analytical expressions of the involved integrals. These expressions are then tested through a numerical experiment on a simple body (section 5).

Notations

In the present work, we consider the general polyhedral source illustrated in figure 1.

The problem we are adressing was exposed previously by [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF]. The spherical harmonic decomposition of the gravitationnal potential V (r, θ, λ)

where G is the gravitational constant, M the total mass of the body and a the radius of a sphere centered at the origin which circumscribes the extended body. (r, θ , λ) are the spherical coordinates of the field point (radius, colati-tude and longitude, respectively, with respect to the coordinate origin O, according to figure 1) and P n,m are the Legendre polynomials (for m = 0) or associated Legendre functions (for m > 0) as defined by [START_REF] Heiskanen | Physical Geodesy[END_REF].

As stated before by [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF], the coefficients {(C n,m , S n,m )} n,m can be expressed as

C n,m S n,m = 2 -δ 0,m M a n (n -m)! (n + m)! ˚Q∈U h c n,m (Q) h s n,m (Q) du (Q) (2)
where du (Q) is the volume element of the total volume U at point Q, and where the function h c n,m and h s n,m are defined as h c n,m (r, θ, λ) = r n P n,m (cos θ) cos (mλ)

(3)

h s n,m (r, θ, λ) = r n P n,m (cos θ) sin (mλ) (4)
Let us note h n,m any of the h c n,m or h s n,m functions. [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF] showed that the integral of h n,m over the volume U could be expressed as a surface integral through the relation

˚U h n,m (Q) du (Q) = 1 n + 3 ‹ ∂U h n,m (P ) OP • dS (P ) = 1 n + 3 F ∈∂U ¨F h n,m r • ndS = 1 n + 3 F ∈∂U d F ¨F h n,m dS (5)
where P is a point of the surface ∂U, OP ≡ r is the vector from the origin O to the point P , n is the unitary vector normal to the surface ∂U, dS is the surface element at point P (see figure 1), F is a given planar face of the polyhedron, and d F is the algebric distance from the origin O to the plane bearing the planar face F: for any point P on the face F, d F = OP • n F , with n F , the oriented unit normal vector to the face. The problem of computing the coefficients is thus equivalent to the problem of computing on any plolyhedron face F the integral I n,m defined as

I n,m = ¨F h n,m dS (6)
In the following, we denote vectors with a boldface typesetting. The natural basis of the considered 3D space, associated to the cartesian coordinates (x, y, z), will be noted (e x , e y , e z ). For a given face F of the boundary of the polyhedron, the normal vector will be written n, or n F when several faces are involved. The edges of the face F will be noted {E} E∈∂F . For each edge E, the leading unit oriented vector will be written u E .

We will use the ∇ operator to denote the gradient of a scalar field f (∇f ) or the divergence of a vector field F (∇ • F). We will use the subscript 2 (for instance ∇ 2 f ) to indicate when the ∇ operator applies in a 2 dimension space.

Outline of our approach

The purpose of this section is to give a comprehensive explanation of the proposed method. A mathematical formulation is briefly presented in section 4.

The proposed approach makes use of the following relation that allows to express h n,m as a derivative oh h n+1,m (see demonstration in the appendix, section A.1).

∇h n+1,m • e z = ∂h n+1,m ∂z = (n + m + 1) h n,m (7)
Figure 2: Decomposition of the unit vector e z into two parts: e ⊥ , perpendicular to the face, and e , parallel to the face.

Expressed that way, the integral is first decomposed into two parts, one using the derivative along the normal to the face, and the second one using the derivative along a vector parallel to the face. These two parts are shown to be easily expressed as sums of line integrals.

Decomposition

F being a planar face of normal unitary vector n, the vector e z can be decomposed on the whole integration domain as

e z = e ⊥ + e (8)
where e ⊥ is othogonal to the plane bearing the face F, and e is parallel to this plane (figure 2). Theses two components of e z are thus defined by relation 8 and by

e ⊥ n (9) e ⊥ n (10)
We thus decompose the surface integration into two parts I n⊥ and I n defined as

I n = 1 n + m + 1 I n⊥ + I n (11)
I n⊥ = ¨F ∇h n+1,m .e ⊥ dS (12)
I n = ¨F ∇h n+1,m .e dS (13)

Parallel part

The reduction of the dimension of the integral for the parallel part is straightforward. Let (u, v) be an orthonormal frame of the face F, associated to the cartesian coordinates (u, v), chosen so as

e = e u (14)
The I n integral can be written as

I n = e ¨F ∂h n+1,m ∂u dudv (15)
Noting that in the 2D space defined by the plane of the face F, the derivative ∂hn+1,m ∂u can be expressed as a divergence

∂h n+1,m ∂u = ∇ 2 • (h n+1,m u) (16)
the integral can be expressed as a flow through the boundary of the face, that is through its edges.

We give the expression of this sum of line integrals along the edges of F in section 4.

Orthogonal part

The expression of the orthogonal part comes from specific properties of function h n+1,m . I n⊥ can be expressed as the flow of ∇h n+1,m through the face F

I n⊥ = (e ⊥ .n) ¨F ∇h n+1,m • dS (17)
Let {E} E∈∂F be the set of the edges of F. For each edge E, let us consider the triangular face (O, E) defined by the origin O of the frame and the edge itself, as shown in figure 3. Let us consider the polyhedron V F defined by the set of faces F, {(O, E)} E∈∂F .

Since h n+1,m is harmonic it will hold

‹ ∂V F ∇h n+1,m • dS = 0 (18)
where dS denote the vector elementary surface normal to the surface, and ∂V F is the whole surface of the volume V F associated to face F

∂V F ≡ F, {(O, E)} E∈∂F (19) As a consequence ¨F ∇h n+1,m • dS = - E∈∂F ¨(0,E) ∇h n+1,m • dS = - E∈∂F ¨(0,E) ∇h n+1,m • n (0,E) dS (20)
Figure 3: Volume V F associated to face F

where n (0,E) is the outgoing normal vector of the face (0, E) (figure 3) and dS ≡ dSn (0,E) .

Let us consider ∇h n+1,m • n as a function defined in the plane of the face (O, E), expressed in cartesian coordinates as

∇h n+1,m • n (0,E) ≡ f (u, v) (21)
f (u, v) is an homogeneous function of degree n which verifies the Euler identity

n f (u, v) = u ∂f ∂u + v ∂f ∂v (22)
and thus the following relation for any point P in face (0, E)

(n + 2) f (P ) = ∇ 2 (f (P ) OP) (23)
As a consequence, each integral of the sum of the right member of equation 20 can be expression as the flow of (f (P ) OP) through the boundary of the face (O, E), that is as a sum of line integrals. An simpler expression of this sum of line integrals is proposed in section 4 by expressing ∇h n+1,m as the rotational of a vector field.

Analytical formulation

Vectors e ⊥ and e can be expressed as

e ⊥ = (e z • n) n (24) e = (n × e z ) × n (25)

Parrallel part

Relation 25 leads to

I n = ¨F ∇h n+1,m • ((n × e z ) × n) dS = ¨F (∇h n+1,m × (n × e z )) • ndS (26)
Since the vector n × e z is constant over the face F, we can write

∇h n+1,m × (n × e z ) = ∇ × (h n+1,m (n × e z )) (27)
By applying of the Kelvin-Stokes theorem, we have

I n = ˛∂F (h n+1,m (n × e z )) • dL = E∈∂F ˆE h n+1,m (n × e z ) • u E dL = E∈∂F [n, e z , u E ] ˆE h n+1,m dL (28)
where dL ≡ dLu E is the elementary length vector along edge E and [n, e z , u E ] is the triple product between these three vectors, defined as the determinant of the matrix composed by their corresponding components.

Orthogonal part

The proposed expression of the orthogonal part results from the following property of ∇h n,m (see Appendix, section A.2)

(n + 1) ∇h n,m = ∇ × (∇ × (h n,m r)) (29)
where r ≡ OP denotes the vector from the origin to any point P of the face. As a consequence, denoting elementary surface and line elements as in the previous sections and using relation 24, we can write

I n⊥ = (e z .n) n + 2 ¨F ∇ × (∇ × (h n+1,m r)) • dS (30)
and, in application of the Kelvin-Stokes theorem

I n⊥ = (e z • n) n + 2 ˛∂F (∇ × (h n+1,m r)) • dL = (e z • n) n + 2 E∈∂F ˆE (∇h n+1,m × r) • u E dL = (e z • n) n + 2 E∈∂F ˆE ∇h n+1,m • (r × u E ) dL (31)
Let O E be the nearest point from the origin O of the line bearing the edge E (figure 3), d E the distance from the origin O to this line and v E the unit vector of direction

--→ OO E d E ≡ --→ OO E (32) v E ≡ 1 d E --→ OO E if d E > 0 - → 0 if d E = 0 (33)
The cross product (r × u E ) is constant along the edge and can be expressed as

v E × u E = d E (v E × u E )
Thus the orthogonal part can be expressed as a weighted sum of line integrals of the derivative of h n+1 along the constant (but edge dependant) direction

v E × u E I n⊥ = (e z • n) n + 2 E∈∂F d E ˆE ∇h n+1,m • (v E × u E ) dL (34)
5 Numerical implementation

A prototype software implementing the method based on the relations given in section 4 was written in the interpreted language Python (van Rossum and Drake, 2011).

Coordinates (x, y, z) where normalized by the reference radius a: (x , y , z ) ≡ (x/a, y/a, z/a). Legendre functions were normalized with the usual normalisation factor following Heiskanen and Moritz (1967, p. 31)

N n,m = (2 -δ 0,m ) (2n + 1) (n -m)! (n + m)! (35)
All the used relations were adapted to the computation of the cormalized coefficients

C n,m S n,m = C n,m /N n,m S n,m /N n,m (36)
through the integration of

h n,m (x , y , z ) = N n,m a n h n,m (x, y, z) (37)
Line integrals were computed thought the decimation of edges of the test body into 2 k segments, the computation of h n,m and its derivatives at the 2 k + 1 end points of the semgents, and the use of Romberg's integration method [START_REF] Romberg | Vereinfachte numerische integration[END_REF] as implemented in the scipy.integrate package of Python (function romb()). The exponent k was chosen as a function of the maximum computed spherical harmonic degree n max , the lenght l of the considered edge and

l 2 k ≤ 1 2 π n max d (38)
In this formula, πd/n max gives an raw approximate value of the resolution of the spherical harmonic model on the considered edge. The factor 1/2 aims at dividing the edge beyond this resolution.

Test body and reference values.

We chose as test body a cube of size 1000 meters, centered on the point (1500, 1500, 1500), and rotated by 13 degres around the diagonal passing through the origin (figure 4). The cube was located away from the center of the frame and rotated to avoid symetries that would cause many spherical harmonic coefficients to vanish. The density of the cube was arbitrarily set to 2.67 g cm -3 .

The computed spherical harmonic series were compared to the value of the potential and of the gravity on a single point P located at the furthest corner from the origin (see figure 4). The distance OP was chosen as the reference radius a for the computation of the spherical harmonic coefficients. The point P was chosen at a corner in order to test a region of the space where high spatial frequencies are important.

The potential and gravitationnal attraction of the cube at point P was derived from the exact formulas for the prism [START_REF] Nagy | The gravitational potential and its derivatives for the prism[END_REF], by expressing the limit of the expression given by Nagy et al. when the computation point reaches the corner P . The obtained reference values are

V cube (t) = Gρ 3 log 1 + √ 3 √ 2 - π 4 t 2 (39)
g cube (t) = Gρ π 6 + 2 log √ 2 1 + √ 2 1 + √ 3 √ 3 t ( 40
)
where t si the size of the cube, G the gravitationnal constant, and ρ the volumic mass of the cube. For our given example, we had V cube = 2.120624 10 -1 m 2 s -2 and g cube = 2.991996 10 -4 ms -2 .

Results.

The coefficient for our test cube were computed up to degree and order 360.

The strategy adopted for splitting the edges of the cube led to 129 computation points per edge. The overall computation of the spherical harmonic coefficients took one hour and a half on a computer with 8 Gbytes of RAM and a quad-core 2.5 GHz Intel Core i7 processor.

We controlled the accuracy of the integrals on the vertical edges, for which an analytical solution is available through relation 7.

Figure 5 shows the base 10 logarithm of the relative error of the integrals on vertical edges. The relative error is computed as the difference between the numerical value of the integrals and its reference value obtained from its analytical formula, divided by this reference value. The errors grow steadily up to nearly 100% at degree 360. We note that the adopted numerical integration strategy looks sufficient up to degree 100 to 150, but should be improved to properly handle computations at dergee and order 360 or more. Nevertheless, we considered it as sufficient to test the behavious of the method up to that degree.

Table 1 shows some of the computed coefficients. The values of C 1,0 , C 1,1 and S 1,1 are coherent with the position of the center of mass of the cube at the 10 -14 level of relative accuracy.

The convegence of the spherical harmonic series toward the total values at test point P (figure 4), given by the equations 39 and 40, is shown on the figure 6, for the potential and for the gravitationnal attraction. Figure 6: Base 10 log of the diffence between the total reference value and the value computed from the expansion of the spherical harmonic serie up to a given degree as a function of the degree; grey line: potential; black line: gravitationnal attraction.

show any artifact. Of course, the relative error of the serie developed up to degree and order 360 is better for the potential value (< 10 -4 ) that for the acceleration (> 10 -2 ), since the derivation enhances high frequencies.

Concluding remarks

We presented here a new method for computing the spherical harmonic coefficients of a general polyhedron of constant density and tested it on a simple cubic shape. We gave original analytical expressions of theses coefficients as sums of line integrals. This finding voids the necessity for either handling complex and unstable recurrent computations as in [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF] or splitting the body and rotating its parts as in [START_REF] Chen | Evaluation of the spherical harmonic coefficients for the external potential of a polyhedral body with linearly varying density[END_REF]. The complexity of the proposed method ranges between the algorithm by [START_REF] Werner | Spherical harmonic coefficients for the potential of a constant-density polyhedron[END_REF], the computation burden of which varies like n 4 to get all the coefficients at degree and order n, and the one by [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF] or [START_REF] Chen | Evaluation of the spherical harmonic coefficients for the external potential of a polyhedral body with linearly varying density[END_REF] the computation buden of which varies like n 2 . In our case, the number of points computed to sample the edges of the body is of course a function of the aimed resolution, and thus of the wished maximum degree. This make the method in the order of complexity of n 3 . The processing time mentionned in the section 5 was given as an indication that the computation is possible. It has though no significant meaning. First, our prototype computation was handled though an interpreted langage. And secondly, the method can of course be highly parallelized.

The tests presented in section 5show that our method allows to compute the spherical harmonic coefficients of a simple body at least up to degree and order 360 with a better stability than previous methods. The method proposed by [START_REF] Tsoulis | Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron[END_REF] failed to provide accurate coefficients beyond degree 60. It was though assessed on a much more complex body. The tests presented by [START_REF] Chen | Evaluation of the spherical harmonic coefficients for the external potential of a polyhedral body with linearly varying density[END_REF] on a prism with variable density did not allow to assess the behaviour of their method up to the same degree as here. Chen et al. chose the computation point at a distance of 1.1078 a, a being the reference radius, which minimize the effect of very high frequencies due to the factor (1/1.1078)

n . It yields a convergence to the reference value as soon as degree 150 for the potential, 240 for the acceleration and 290 for the second derivatives, which prevents from assessing the quality of higher coefficients. Besides, the convergence cuves shown in their work appear very noisy compared to the one we observe with our method.

This good behaviour of the convergence curves (figure 6) lets us expect a good accuracy of the coefficients. Besides, the methods can still be improved, since our tests show also that the currently adopted line integration strategy presents some limits at high degrees.

Further works will focus on deeper numerical experiments in order to assess the accuracy of the computed coefficients, as well as to study the behaviour of the method on more realistic bodies.

Figure 1 :

 1 Figure 1: A polyhedron and its associated coordinate frames

Figure 4 :

 4 Figure 4: Test body

Figure 5 :

 5 Figure 5: log 10 of the relative error of the h n,m line integrals on the vertical edges of the cube ; grey line: for h c n,m ; black line: for grey line : for h s n,m

  where P n,m is the first derivative of the polynomial P n,m : P n,m (x) = d dx P n,m (x). Using the relationx 2 -1 d dx P n,m (x) = nxP n,m (x) -(n + m) P n-1,m (x) of h n,m as a rotationnalStarting from the identity∇ × (∇ × F) = ∇ (∇.F) -F (47) we have ∇ × (∇ × (h n,m r)) = ∇ (∇. (h n,m r)) -∆ (h n,m r)(48)From the homogeneity of h n,m , we get, through the Euler relation∇. (h n,m r) = (n + 3) h n,m(49)and thus ∇ (∇. (h n,m r)) = (n + 3) ∇h n,m

Table 1 :

 1 The evolution of the values toward the full potential and attraction is steady and does not seem to Spherical harmonic coefficients of the test cube (sample)

	n	m	C n,m	S n,m
	1	0	2.50000000000e -01	0.0
	1	1	2.50000000000e -01	2.50000000000e -01
	2	0	-6.28013820649e -15	0.0
	2	1	1.45236875483e -01	1.45236875483e -01
	2	2	3.86367158115e -14	1.45236875483e -01
	...	...	...	...
	180	0	-1.01265250801e -08	0.0
	180	2	-7.23646197302e -12	1.48621884351e -08
	...	...	...	...
	360	1	-2.52287113787e -09 -2.51541751845e -09
	360 360 -5.51466428191e -41	5.14086641792e -40

Acknowledgements This study was partly supported by IdEx Université de Paris ANR-18-IDEX-0001. This is IPGP contribution number 4055.

Appendix

A.1 Derivative of h n,m along the z axis

The relation expressed by equation 7 is obtained in polar coordinates as follows (the calculus is identical with a sin (mλ) dependency to the longitude)

The second term of the relation 48 can be written in cartesian coordinates

Since h n,m is harmonic, h n,m = 0 and we get ∇ × (∇ × (h n,m r)) = (n + 1) ∇h n,m (52)