Ikuhiro Okamoto

Catherine Patrat

Dominique Thepot Thépot

Nathalie Peynot

Patricia Fauque

Nathalie Daniel

Patricia Diabangouaya

Jean-Philippe Wolf

Jean Paul Renard

Véronique Duranthon

Eutherian mammals use diverse strategies to initiate X-chromosome inactivation during development

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

Eutherian mammals use diverse strategies to initiate X-chromosome inactivation during development

Ikuhiro Okamoto1 *, Catherine Patrat 1,2 *, Dominique The ´pot [START_REF] Huynh | Inheritance of a pre-inactivated paternal chromosome in early mouse embryos[END_REF] , Nathalie Peynot3 , Patricia Fauque [START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Mak | Reactivation of the paternal X chromosome in early mouse embryos[END_REF] , Nathalie Daniel 3 , Patricia Diabangouaya 1 , Jean-Philippe Wolf [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] , Jean-Paul Renard [START_REF] Huynh | Inheritance of a pre-inactivated paternal chromosome in early mouse embryos[END_REF] , Ve ´ronique Duranthon [START_REF] Huynh | Inheritance of a pre-inactivated paternal chromosome in early mouse embryos[END_REF] & Edith Heard 1 X-chromosome inactivation (XCI) in female mammals allows dosage compensation for X-linked gene products between the sexes [START_REF] Lyon | Gene action in the X-chromosome of the mouse (Mus musculus L.)[END_REF] . The developmental regulation of this process has been extensively investigated in mice, where the X chromosome of paternal origin (Xp) is silenced during early embryogenesis owing to imprinted expression of the regulatory RNA, Xist (X-inactive specific transcript). Paternal XCI is reversed in the inner cell mass of the blastocyst and random XCI subsequently occurs in epiblast cells. Here we show that other eutherian mammals have very different strategies for initiating XCI. In rabbits and humans, the Xist homologue is not subject to imprinting and XCI begins later than in mice. Furthermore, Xist is upregulated on both X chromosomes in a high proportion of rabbit and human embryo cells, even in the inner cell mass. In rabbits, this triggers XCI on both X chromosomes in some cells. In humans, chromosome-wide XCI has not initiated even by the blastocyst stage, despite the upregulation of XIST. The choice of which X chromosome will finally become inactive thus occurs downstream of Xist upregulation in both rabbits and humans, unlike in mice. Our study demonstrates the remarkable diversity in XCI regulation and highlights differences between mammals in their requirement for dosage compensation during early embryogenesis.

Most eutherian mammals display random XCI in their soma [START_REF] Lyon | Gene action in the X-chromosome of the mouse (Mus musculus L.)[END_REF] , whereas marsupials show imprinted, paternal XCI [START_REF] Sharman | Late DNA replication in the paternally derived X-chromosome of female kangaroos[END_REF] . In mice, however, XCI is also imprinted initially, with silencing of Xp from the 4-8-cell stage [START_REF] Huynh | Inheritance of a pre-inactivated paternal chromosome in early mouse embryos[END_REF][START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Mak | Reactivation of the paternal X chromosome in early mouse embryos[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] . Xp remains inactive in the trophectoderm [START_REF] Takagi | Preferential inactivation of the paternally derived X-chromosome in the extraembryonic membranes of the mouse[END_REF] but is reactivated in the inner cell mass [START_REF] Mak | Reactivation of the paternal X chromosome in early mouse embryos[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] (ICM) with subsequent random XCI in epiblast cells. Initiation of XCI is controlled by the non-coding Xist transcript [START_REF] Penny | Requirement for Xist in X chromosome inactivation[END_REF][START_REF] Marahrens | Xist-deficient mice are defective in dosage compensation but not spermatogenesis[END_REF] , which coats the chromosome in cis and triggers gene silencing. During murine pre-implantation development, Xist is maternally repressed and paternally expressed, consistent with its role in regulating imprinted XCI [START_REF] Huynh | Inheritance of a pre-inactivated paternal chromosome in early mouse embryos[END_REF][START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF][START_REF] Marahrens | Xist-deficient mice are defective in dosage compensation but not spermatogenesis[END_REF]10 . By the epiblast stage, the imprint is lost or ignored, Xp has been reactivated and Xist can be upregulated randomly, from either Xp or the maternally derived X chromosome, Xm. This second, random wave of XCI involves downregulation of pluripotency factors, activation of Xist by means of X-linked competence factors and precise, random monoallelic regulation of Xist, possibly through antisense transcription, homologous pairing and other events (for a review, see ref . 11). Mice are the only eutherian for which XCI has been analysed in detail during early embryogenesis. The fact that marsupials also show XCI and yet have no gene homologous to Xist (refs 12, 13 and references therein) suggests that multiple strategies for initiating XCI must exist. To explore XCI during early embryogenesis in other eutherian mammals, we analysed human (primate) and rabbit (lagomorph) embryos, the latter being closely related to rodents [START_REF] Hajjoubi | Ruminants genome no longer contains Whey Acidic Protein gene but only a pseudogene[END_REF] .

First we examined rabbit embryos in vivo, from the 4-cell stage to the blastocyst stage, using Xist RNA fluorescence in situ hybridization (FISH; Fig. 1 and Supplementary Fig. 1). Sex chromosome constitution was determined after RNA FISH, by DNA FISH using X-and Y-chromosome probes. Punctate Xist RNA signals could be detected from both X chromosomes in females and from the single X chromosome in males, from the 8-cell stage (Fig. 1b,d), which corresponds to major embryonic genome activation (EGA) in rabbits [START_REF] Manes | The participation of the embryonic genome during early cleavage in the rabbit[END_REF][START_REF] Christians | Sequential acquisition of transcriptional control during early embryonic development in the rabbit[END_REF] . This contrasts with mice, where maternal Xist is never expressed [START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF][START_REF] Navarro | An embryonic story: analysis of the gene regulative network controlling Xist expression in mouse embryonic stem cells[END_REF] between major EGA (the 2-cell stage [START_REF] Flach | The transition from maternal to embryonic control in the 2-cell mouse embryo[END_REF] ) and the blastocyst stage. Xist RNA accumulation was first detected in female, but not male, embryos at the morula stage (62 hours post-coitum (h.p.c.); about 60-70 cells). However, the percentage of female blastomeres showing Xist expression was low at this stage (Fig. 1c,d). By the early blastocyst stage (96 h.p.c.; Fig. 2a), over 90% of trophectoderm cells had at least one Xist RNA domain (Fig. 2a,c). Surprisingly, a substantial proportion of blastomeres (26%) showed Xist RNA domains on both X chromosomes (Fig. 2a,c). The detection of double Xist RNA domains in rabbit blastocysts contrasts with mouse, where such a situation is not usually seen in vivo [START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Mak | Reactivation of the paternal X chromosome in early mouse embryos[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] except in polyploid trophectoderm cells or in a low percentage (,4%) of in vitro differentiating female embryonic stem cells [START_REF] Monkhorst | X inactivation counting and choice is a stochastic process: evidence for involvement of an X-linked activator[END_REF] . This unusual pattern is transient, however, as it is no longer observed in trophectoderm cells of 120 h.p.c. blastocysts (Fig. 2b), where a single Xist RNA domain is seen, as in XX somatic cells (Supplementary Fig. 2). In male rabbit embryos, Xist RNA domains were rarely detected (Fig. 2c). Instead, Xist was progressively silenced after the 8-cell stage (Fig. 2b,c). Thus, Xist upregulation is sensitive to XX status in rabbits, as in mice during random XCI, but Xist monoallelic regulation differs between the two animals.

During mouse development, X-linked gene silencing follows Xist RNA accumulation [START_REF] Huynh | Inheritance of a pre-inactivated paternal chromosome in early mouse embryos[END_REF][START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Mak | Reactivation of the paternal X chromosome in early mouse embryos[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] . However, the timing of XCI in other mammals is less clear. We investigated expression of two X-linked genes using RNA FISH in rabbit embryos: Hprt1 (also known as Hprt), which is X-inactivated in somatic cells, and Jarid1c (Kdm5c), which escapes XCI (Supplementary Fig. 2b). Expression of both genes was biallelic in female embryos from the 4-16-cell stage (Fig. 1). Thus, X-linked genes are active from both Xp and Xm at EGA, as in mice [START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted X-chromosome inactivation in mice[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] .

Hprt1 silencing on the Xist-RNA-coated chromosome was first detectable at the 96-h.p.c. blastocyst stage and was complete in trophectoderm cells by the 120-h.p.c. stage (Fig. 2d), whereas Jarid1c still showed biallelic expression indicating escape from XCI, as in somatic cells. Importantly, the onset of Hprt1 silencing coincided with the time window (96 h.p.c.) when both X chromosomes were sometimes found to be Xist RNA coated (Fig. 2a). Indeed, by comparing the proportion of cells showing no Hprt1 primary transcript signal and two Xist RNA domains with those showing a single Xist RNA domain (46%, n 5 192 versus 12%, n 5 250), we conclude that Hprt1 silencing has initiated on both X chromosomes in cells with two Xist RNA domains at the 96h.p.c. stage (Fig. 2e). This situation was found to be rapidly reversed 24 h later (at the 120-h.p.c. stage), as only one X chromosome showed Xist RNA coating and Hprt1 silencing; the other expressed Hprt1 in almost all blastomeres (Fig. 2b).

We also analysed histone H3 lysine 27 trimethylation (H3K27me3) enrichment, which marks the onset of XCI in mice [START_REF] Plath | Role of histone H3 lysine 27 methylation in X inactivation[END_REF][START_REF] Silva | Establishment of histone h3 methylation on the inactive X chromosome requires transient recruitment of Eed-Enx1 polycomb group complexes[END_REF] and is present on the inactive X chromosome in rabbit somatic cells (Supplementary Fig. 2c). In 96-h.p.c. blastocysts, where two Xist-RNA-coated X chromosomes could be detected (25%, n 5 325), both of them showed H3K27me3 enrichment (Supplementary Fig. 3). At the 120-h.p.c. stage, where only one Xist RNA domain is detectable, two spots of H3K27me3 staining per nucleus could still sometimes be observed (8%, n 5 285), one overlapping with Xist RNA and the other presumably corresponding to the second X chromosome (Supplementary Fig. 3).

Taken together, these results suggest that XCI initiates on both X chromosomes in a significant proportion of blastomeres in early rabbit blastocysts, but the situation is somehow resolved. As no differences in cell death rates could be detected between female and male 120-h.p.c. embryos (Supplementary Fig. 4), we conclude that cells initiating XCI on both X chromosomes do not necessarily die. They either reverse XCI on one X chromosome or proliferate more slowly and become out-competed by cells with one inactive X chromosome, which is a distinct possibility given the massive cell proliferation occurring between 96 h.p.c. (,100 cells) and 120 h.p.c. (.1,000 cells; Fig. 2f).

We also analysed the ICMs of rabbit blastocysts for XCI status. In mice, inactive Xp is progressively reactivated in pre-epiblast ICM cells [START_REF] Mak | Reactivation of the paternal X chromosome in early mouse embryos[END_REF][START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] positive for Oct4 (Pou5f1) and Nanog [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] . Rabbit ICM cells were isolated from blastocysts by immunosurgery or manual dissection. In early blastocysts (96 h.p.c.), most putative ICM cells were negative for Xist RNA accumulation (Supplementary Fig. 5a,c), in contrast to trophectoderm cells, where Xist RNA coating of one or both X chromosomes was present in most cells (Fig. 2a). One day later (120 h.p.c.), however, the majority of putative (strongly Oct4-positive) epiblast cells displayed Xist RNA coating on one or both X chromosomes, as well as the onset of Hprt1 gene silencing and H3K27me3 enrichment (Supplementary Fig. 5).

Thus, in rabbits, two waves of XCI with similar characteristics seem to occur, one in the trophectoderm and the second in the ICM. During both waves, the two X chromosomes seem to be affected initially in some cells, implying that there is no imprinting, unlike in the mouse. However, we could not analyse parent-specific X-linked gene expression owing to lack of polymorphisms in our rabbit colonies. Instead, we investigated rabbit parthenogenotes (two maternal genomes) for their XCI patterns. We found Xist and Hprt1 expression patterns similar to those of wild-type female embryos (Supplementary Fig. 6), indicating that imprinting may not have a major role in rabbit XCI, but we cannot formally exclude that there is some parent-of-origin bias. In summary, we show that although rabbits and mice are phylogenetically close, they have taken very different evolutionary trajectories with respect to Xist regulation and the onset of XCI.

In human embryos, XIST expression is detected from the 4-8-cell stage and XCI has been proposed to follow kinetics similar to those in mouse [START_REF] Van Den Berg | X chromosome inactivation is initiated in human preimplantation embryos[END_REF] , although it does not seem to be imprinted in extra-embryonic tissues [START_REF] Migeon | X-chromosome inactivation: theme and variations[END_REF][START_REF] Moreira De Mello | Random X inactivation and extensive mosaicism in human placenta revealed by analysis of allele-specific gene expression along the X chromosome[END_REF] . To investigate this further, we examined in vitro conceived pre-implantation human embryos (Fig. 3; Methods and Supplementary Information). Human blastocysts showed either a single or double XIST RNA accumulation (67% cells, n 5 13 embryos and 85% cells, n 5 15 embryos, respectively; Fig. 3a), corresponding to male and female embryos, confirmed by X/Y DNA FISH (Fig. 3a). Similar XIST patterns were detected in morulae and blastocysts (days 5 and 6), whether derived by IVF (in vitro fertilization) or ICSI (intracytoplasmic sperm injection), and whatever their history (discarded or frozenthawed embryos).

To assess XCI status, X-linked genes (ATRX, FGD1 and HUWE1) were analysed by RNA FISH. In human somatic cells, these genes are silent on the inactive X chromosome (Supplementary Fig. 7). In female blastocysts, the majority of blastomeres showed two primary transcript foci for X-linked genes (ATRX and FGD1, Fig. 3a, e; HUWE1, data not shown), indicating that both X chromosomes are active. Furthermore, although small foci of H3K27me3 enrichment could be detected throughout the nucleus, no specific enrichment on the XIST-coated chromosomes was found (Fig. 3b). We also analysed a few even later human blastocysts (cultured to day 7). Male, day-7 blastocysts showed either no (66%, n 5 271 cells, n 5 2 embryos) or just a small punctate XIST RNA signal (Supplementary Fig. 8), suggesting that XIST expression was downregulated by this stage. A heterochromatic Y body [START_REF] Barlow | The Y chromosome in human spermatozoa[END_REF] was also visible in these embryos. In the one female embryo obtained at day 7, the majority of cells still showed biallelic FGD1 expression (83%, n 5 30 cells) and biallelic XIST RNA signals, with no sign of a heterochromatic Barr body (Supplementary Fig. 8).

A previous study reported that XCI can be detected in early human embryos [START_REF] Van Den Berg | X chromosome inactivation is initiated in human preimplantation embryos[END_REF] . The discrepancy with our study may be due to differences in immunofluorescence/FISH techniques resulting in less efficient detection of biallelic RNA signals, for example, and/or to different culture conditions (see Supplementary Information for discussion). There is also some debate concerning XCI status in human embryonic stem cells. A recent study [START_REF] Lenger | Derivation of pre-X inactivation human embryonic stem cells under physiological oxygen concentrations[END_REF] reported that human embryonic stem cells cultured in 5% oxygen retain pre-XCI cells, whereas in atmospheric oxygen XIST upregulation and an inactive X chromosome are often found. However, this may be specific to the tissue culture conditions of human embryonic stem cells. We therefore analysed the ICM in both male and female human embryos. Putative ICM cells (strongly OCT4 positive) showed similar XIST RNA patterns to surrounding trophectoderm cells and no sign of an inactive X chromosome (n 5 4 embryos; Fig. 3b). We conclude that in human pre-implantation embryos, under our conditions, XIST RNA upregulation occurs on all X chromosomes regardless of parental origin or sex but does not seem to result in chromosome-wide XCI even in late blastocysts. Although we cannot rule out that in vitro culture and atmospheric oxygen might have an impact on XCI, in our conditions the X seems to be in a pre-XCI state in human ICM cells, in agreement with ref. 25.

In conclusion, our findings reveal substantial diversity in the timing and regulation of XCI initiation between mammals (Supplementary Fig. 9a). First, Xist expression is not imprinted in early rabbit and human embryos, unlike in mice. The maternal Xist imprint found in mice may therefore be a recent event, which we have proposed [START_REF] Okamoto | Evidence for de novo imprinted X-chromosome inactivation independent of meiotic inactivation in mice[END_REF] evolved to avoid premature maternal XCI given the early onset of EGA and Xist expression. Indeed, in mouse XpXp androgenotes, which lack an imprinted maternal Xm, Xist is upregulated biallelically initially, as in rabbits and humans [START_REF] Okamoto | X-chromosome inactivation in XX androgenetic mouse embryos surviving implantation[END_REF] . However, rabbits and humans have later EGA and may not require Xist imprinting for early XCI control. Second, the choice of which X chromosome to inactivate seems to occur downstream of Xist upregulation in rabbits and humans, unlike in mice, where Xist is tightly monoallelically regulated during random XCI (Supplementary Fig. 9b). One difference could be that antisense transcription (Tsix), which is critical for random, monoallelic Xist expression in mice [START_REF] Lee | Regulation of X-chromosome counting by Tsix and Xite sequences[END_REF] , is poorly conserved and may even be lacking in other mammals [START_REF] Chang | Identification of regulatory elements flanking human XIST reveals species differences[END_REF] .

Another difference between human and rabbit or mouse embryos is that XIST upregulation occurs in males and females, suggesting that XIST activators are not XX-specific, at least initially (Supplementary Fig. 9a). However, XIST upregulation is dissociated from the immediate onset of chromosome-wide XCI, possibly as a result of incomplete XIST RNA cis-coating. Indeed, XIST RNA signals were quite diffuse in human embryos (Fig. 3) in comparison with somatic cells (Supplementary Fig. 7). Importantly, the lack of chromosome-wide XCI in the trophectoderm of human blastocysts implies that dosage compensation may not be critical at this stage. Finally, we also reveal differences between mammals in XCI status in the ICM. In humans the two X chromosomes seem to be active in the ICM (even though XIST is expressed), whereas in rabbits the two X chromosomes are initially active and then become inactive. This is the reverse situation to mice, where Xp is initially inactive and then becomes reactivated in the ICM [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] . These differences may explain the diverse XCI patterns reported in embryonic stem cells of non-murine mammals and point to differences in Xist control via pluripotency factors [START_REF] Navarro | Molecular coupling of Xist regulation and pluripotency[END_REF] . The diversity of XCI initiation strategies we have uncovered here probably reflects the fact that developmental processes are constantly changing during evolution and that the regulation of processes such as XCI have to display substantial plasticity to accommodate these changes.

METHODS SUMMARY

Human and rabbit embryos were manipulated under strict ethical guidelines and analysed using published protocols for immunostaining, RNA and DNA FISH [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF][START_REF] Okamoto | Evidence for de novo imprinted X-chromosome inactivation independent of meiotic inactivation in mice[END_REF] . Human embryos obtained following IVF or ICSI were cultured in 5% CO 2 and atmospheric O 2 , fixed and used for immunofluorescence or RNA FISH, as previously described [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] . Rabbit embryos were obtained from New Zealand White rabbit females mated with males. In vivo rabbit embryos were recovered from oviducts or uterus flushed with PBS at appropriate times post-coitum. The mucin coat and zona pellucida were removed before fixation for immunofluorescence/FISH [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF] Rabbit ICMs (96 h.p.c.) were isolated by immunosurgery; embryonic discs (120 h.p.c.) were dissected out with tungsten needles. Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.

METHODS

Recovery of pre-implantation rabbit embryos. Experiments were performed in accordance with the International Guiding Principles for Biomedical Research involving animals, as promulgated by the Society for the Study of Reproduction and with the European Convention on Animal Experimentation. Researchers involved in direct work with the animals possessed an animal experimentation licence delivered by the French veterinary services. New Zealand White rabbit females (INRA line 1077) were superovulated and mated with normal males. Superovulation was performed by five subcutaneous injections of pFSH (Stimufol, Merial Lyon) for three days before mating: two 5-mg injections on day 1 at 12-h intervals, two 10-mg injections on day 2 at 12-h intervals and one 5-mg injection on day 3, followed 12 h later by an intravenous injection of 30 IU human chorionic gonadotrophin (Chorulon, Intervet) at mating time. In vivo, four-cell, eight-cell, sixteen-cell and morula-stage embryos were recovered from oviducts and uterus flushed with PBS at 30, 38, 46, 62-72 h.p.c., respectively.

Uterus flushing was at 96 and 120 h.p.c. for the recovery of early and late blastocysts, respectively. Mucin coat was removed by incubation of the embryos in a pre-warmed pronase solution (0.5% Protease, Sigma) at 37 uC for 1 to 6 min depending on its thickness and on the stage of the embryo. Embryos were then immediately rinsed twice in M199 HEPES with 10% FCS. In the second wash, the zona pellucida was removed by mechanical pipetting. For immunofluorescence and RNA FISH, embryonic discs were dissected out from the late (120-h.p.c.) blastocysts with tungsten needles. ICM isolation from early (96-h.p.c.) rabbit blastocyst. Mucin coat and zona pellucida were removed by pronase treatment of blastocysts. ICMs were then isolated by immunosurgery. Briefly, embryos were incubated in anti-rabbit goat serum (Sigma R-5131) for one hour at 37 uC. They were then rinsed twice in PBS and incubated in guinea pig complement (Sigma S-1639) for one to two minutes. Blastocysts were then rinsed in PBS and vacuolated trophectoderm cells were mechanically removed by pipetting with a small adjusted pipette (70-90-mm diameter). Parthenogenetic activation of rabbit embryos. In vitro activation was performed on morphologically normal, fresh MII oocytes (14 h.p.c.), as previously described [START_REF] Chesne | Cloned rabbits produced by nuclear transfer from adult somatic cells[END_REF][START_REF] Challah-Jacques | Production of cloned rabbits by somatic nuclear transfer[END_REF] for nuclear transfer experiments. Briefly, oocytes were washed three times in the TCM199, HEPES plus 10% FCS and placed in a mannitol solution containing 0.3 M mannitol, 100 mM MgCl 2 and 100 mM CaCl 2 in sterile, filtered water. After 30 s in the mannitol solution, oocytes were 'electroactivated' with a succession of three d.c. pulses of 3.2 kV cm 21 for 20 ms each, using a BTX stimulator (Biotechnologies & Experimental Research). Then oocytes were incubated for 1 h in TCM199 plus 10% FCS at 38.5 uC and 5% CO 2 in a humidified atmosphere. Then they received, in the mannitol solution, a second set of three d.c. pulses and were incubated for 1 h in TCM199 plus 10% FCS supplemented with 2 mM 6-DMAP (kinase inhibitor) and 5 mg ml 21 cycloheximid (protein synthesis inhibitor) to finalize activation. Lastly, they were washed three times in the TCM199 plus 10% FCS to remove all traces of chemical agents, and were rinsed for 30 min in TCM199 plus 10% FCS at 38.5 uC and 5% CO 2 . They were then incubated in microdrops of B2 plus 2.5% FCS under mineral oil at 38.5 uC and 5% CO 2 .

Recovery of human pre-implantation embryos. All attempts using assisted reproductive techniques were performed at Cochin-Saint Vincent Hospital (Paris, France). Ovarian stimulation, oocyte retrieval, sperm processing and IVF and/or ICSI were performed as previously described [START_REF] Fauque | Cumulative results including obstetrical and neonatal outcome of fresh and frozen-thawed cycles in elective single versus double fresh embryo transfers[END_REF] . The choice of ICSI or conventional IVF as fertilization method was dependent on semen-sample characteristics and couple's history. Briefly, oocytes retrieval was performed under vaginal ultrasound guidance, 36 h after administration of human chorionic gonadotrophin. Motile spermatozoa were selected through a two-step 90-45% density gradient (Puresperm, JCD) or after sperm washing with FertiCult medium (JCD).

On the day of oocyte retrieval, sperm-inseminated or -microinjected oocytes were cultured in 30 ml culture medium (IVF or ISM1, Origio) under oil, at 37 uC, 5% CO 2 and humidified atmosphere. Fertilization was assessed 18 h after insemination or injection and normal fertilization was defined as the presence of two distinct pronuclei and a second polar body. Embryo quality was evaluated on day 2 or day 3 according to the number of blastomeres, the degree of fragmentation and the presence or not of multinuclear blastomeres. Embryos were either transferred or cryopreserved on day 2 or day 3, depending on the embryo quality evaluation. Embryos that were neither transferred nor cryopreserved, given poor embryo morphology, were discarded. Collection of human embryos. Research on human embryos was authorized by the French Biomedicine Agency (RE07-011R). In the present study, only diploid embryos that were either discarded or cryopreserved were used. In both cases, written consent was obtained from the couples allowing these discarded or cryopreserved embryos to be used for the research. Embryos (after thawing (Embryo Thawing Pack, Origio), for day-2-3 cryopreserved embryos) were placed in 30 ml of fresh, equilibrated sequential culture medium (ISM1 culture medium from day 2 to day 3 and ISM2 from day 3, Medicult) at 37 uC, 5% CO 2 , under oil and humidified atmosphere, for further culture. Blastocysts were obtained at day 5 or day 6 post-insemination or -injection and classified according to Gardner's classification [START_REF] Gardner | Towards Reproductive Certainty: Infertility and Genetics Beyond[END_REF] , taking into account the global morphology and ICM and trophectoderm aspect from mid blastocyst. Rabbit probes. All rabbit bacterial artificial chromosomes (BACs) were isolated from a rabbit library maintained at the UR1313, Unite ´de Ge ´ne ´tique Animale et Biologie Inte ´grative, Institut National de la Recherche ´Agronomique (INRA). Hprt1 and Jarid1c BACs had been previously published [START_REF] Hayes | Establishment of R-banded rabbit karyotype nomenclature by FISH localization of 23 chromosome-specific genes on both G-and R-banded chromosomes[END_REF][START_REF] Chantry-Darmon | 133 new gene localization on the rabbit cytogenetic map[END_REF] . Xist-containing BACs (573D5, 614B8 and 717B2) were isolated by a PCR-based screening protocol (C. Rogel-Gaillard, unpublished results). BACs were verified for their location and single-copy nature by DNA FISH on metaphase spreads. For Xist RNA FISH, shorter probes were derived from the BACs. First, the human XIST gene sequence was compared with discontinuous megaBLAST to rabbit whole-genome shotgun sequences from the Trace Archives of the NCBI site to identify homologous rabbit Xist sequences. Second, these genomic sequences were extracted and then assembled in six large sequences using the CAP3 assembly program [START_REF] Huang | CAP3: A DNA sequence assembly program[END_REF] . These six large sequences encompass the promoter and beginning of exon 1 (4,090 base pairs (bp)), the middle of exon 1 (6,255 bp), the end of exon 1 and part of intron 1 (3,250 bp), from the end of intron 4 to more than 3 kb into exon 6 (5,792 bp), the middle of exon 6 (1,300 bp) and the end of exon 6 (2,067 bp), respectively. Finally, primers were designed to amplify large parts of the rabbit Xist gene from the BACs.

For RNA FISH, a mixture of these three probes obtained from long-range PCR products (Roche) were amplified using the 8F/17R, 16F/3R and 6F/6R primers pairs, respectively (8F, 59-TATAGGAATGCTGACCACTGA-39; 17R, 59-GTTTT TTCAGTCAAGGGAGAC-39; 16F, 59-TCATGCTCCTGAATCTTCTTG-39; 3R, 59-GCCGCACAAGGAAGAAAAAAG-39; 6F, 59-TGTGTATTTCTCTTTGTCT TT-39; 6R, 59-GTTCTCAAAGCAGTACATTTTTATTTTACAGTACACAAC 39).

The three PCR products encompass sequences from the middle of exon 1 to the end of intron 1 (,8 kb), the beginning of intron 1 to the beginning of exon 6 (,10 kb), and all of exon 6 (,7.3 kb) (Supplementary Fig. 1). Human probes. BAC probes (Supplementary Table 2) were used following verification of their location and single-copy nature by DNA FISH on female human metaphases. Two DNA probes detecting XIST RNA were used: (i) a 10-kb fragment corresponding to XIST exon 1 (gift from C. Brown, Department of Medical Genetics, University of British Columbia) and (ii) a VI.34 Flp-In T-Rex XIST CDNA DH10B construct [START_REF] Chow | Inducible XIST-dependent X-chromosome inactivation in human somatic cells is reversible[END_REF] (gift from C. Brown).

Immunofluorescence, RNA FISH and DNA FISH. Immunofluorescence and RNA FISH were carried out as described previously [START_REF] Okamoto | Epigenetic dynamics of imprinted X inactivation during early mouse development[END_REF][START_REF] Okamoto | Evidence for de novo imprinted X-chromosome inactivation independent of meiotic inactivation in mice[END_REF] . DNA FISH was performed following RNA FISH. The coverslips carrying the embryos were then recovered in 32 SSC and incubated in RNase A (100 mg ml 21 ) in 32 SSC at 37 uC for 1 h, before a brief rinse in 32 SSC, dehydration through an ethanol series and air drying. The coverslips were treated with 0.03% pepsin in 0.01 N HCl for 10-30 min at 37 uC to enhance the penetration of probes. After washing in PBS, they were dehydrated through an ethanol series. The DNA was then denatured in 70% formamide, 32 SSC (pH 7.4) for 10 min at 80 uC and dehydrated again through an ice-cold ethanol series. Hybridization and revelation of the chromosome paint probes were performed according to manufacturer's instructions (Cambio). Cover slips were counterstained with DAPI (1 mg ml 21 ), mounted and viewed under the fluorescence microscope. TUNEL assay and sexing of rabbit embryos. In vivo developed blastocysts were recovered at 120 h.p.c. They were dissected into two halves. One half of each embryo was used for sexing by nested PCR against the Sry gene. Briefly, frozen hemi-embryos were lysed in 10 ml of TE buffer containing 0.01 mg ml [START_REF] Van Den Berg | X chromosome inactivation is initiated in human preimplantation embryos[END_REF] proteinase K and incubated in this buffer for 2 h at 56 uC. Proteinase K was then inactivated by heating at 94 uC for 10 min. PCR was then directly performed in a 50-ml final volume using Takara Taq DNA polymerase (Lonza) for 30 cycles using external primers (Sry F2 59-gttcggagcactgtacagcg-39 and Sry R2 59-gcgttcatgggtcgcttgac-39).

A quantity (3 ml) of the first PCR reaction was then re-amplified in a 50-ml PCR reaction for 35 cycles using the internal primers (Sry F1 59-tgcttacacaccagccaaaca-39 and Sry R1 59-ttcctggccgctcactttac-39) (PCR cycles: 94 uC for 3 min, then 94 uC for 30 s, 58 uC for 30 s and 72 uC for 1 min). PCR products (20 ml) were analysed by electrophoresis on a 2% agarose gel. The other half of each embryo was underwent TUNEL assay using the DeadEnd Fluorometric TUNEL System (Promega). Briefly, hemi-embryos were fixed in paraformaldehyde (4%) overnight at 4 uC. After rinsing in PBS containing 0.2% BSA, they were incubated in 10 mg ml [START_REF] Van Den Berg | X chromosome inactivation is initiated in human preimplantation embryos[END_REF] Proteinase K for 2 min. After rinsing, they were fixed again in 4% paraformaldehyde and 0.2% glutaraldehyde for 15 min at room temperature (22 uC). They were then rinsed twice in PBS containing 0.2% BSA. Positive control embryos were treated by RQ1 RNase-free DNase for 10 min as recommended by the manufacturer. TUNEL reaction was then performed on all the embryos as recommended by the manufacturer. The embryos were then incubated for 10 min at room temperature in

Figure 1 |

 1 Figure 1 | Xist and Hprt1 expression in early pre-implantation rabbit embryos. Examples of embryos after RNA FISH for Xist RNA (green) and X-linked Hprt1 primary transcripts (red). An intact male or female embryo and several representative nuclei are shown. a, Representative 4-cell embryos: XX (nuclei 1 and 2) and XY (nuclei 3 and 4) blastomeres. DAPI, 49,6-diamidino-2phenylindole; PB, polar body. b, Representative 8-cell embryos: XX (nuclei 1 and 2) and XY (nuclei 3 and 4) blastomeres. c, Representative XX (nuclei 1-4) and XY (nuclei 5-6) morula-stage embryos. d, Percentage of cells showing different Xist expression patterns in the 4-cell to morula stages. The low percentage of Xist RNA detection in morulae is not a technical issue, as Hprt1 primary transcript signals could be efficiently detected at this stage in most male and female blastomeres.

Figure 2 |

 2 Figure 2 | Xist and Hprt1 expression in early-(96-h.p.c.) and late-stage (120-h.p.c.) rabbit blastocysts. Examples of embryos (Giemsa-stained) analysed by RNA FISH to detect Xist (green) and Hprt1 (red), followed by DNA FISH using X-chromosome (red) and Y-chromosome (green) probes. Intact male and female embryos, together with representative nuclei, are shown. a, Individual XX and XY early (96-h.p.c.) blastocysts: representative XX (nuclei 1-4) and XY (nuclei 5-8) cells. b, Late XX and XY blastocysts: representative XX (nuclei 1 and 2) and XY (nuclei 3 and 4) blastomeres. c, Percentage of cells showing different Xist expression patterns in rabbit embryos at early and late blastocyst stages. d, Average percentage of blastomeres showing primary transcripts for Hprt1 or Jarid1c in female and male embryos from the 4-cell stage to the blastocyst stage (n $ 10, each stage). TE, trophectoderm. e, Summary of X-linked gene expression patterns in blastomeres with double Xist RNA domains in early female blastocysts. f, Phase contrast images of living early (day-4, 96-h.p.c.) and late (day-5, 120-h.p.c.) rabbit blastocysts. ED, embryonic disc.

Male

Figure 3 |

 3 Figure 3 | XIST RNA, X-linked gene expression and H3K27me3 profiles in human blastocysts. a, Examples of individual female and male human embryos (Giemsa) analysed by RNA FISH for XIST RNA (green) and primary transcription from the X-linked ATRX gene (red), followed by DNA FISH for the X chromosome (red) and Y centromere (green). Representative XX (nuclei 1 and 2) and XY blastomeres (nuclei 3 and 4) are shown. Zones of intense green signal outside nuclei are background. b, Examples of individual female and male human embryos (Giemsa) analysed by immunolabelling with antibodies against H3K27me3 (red) and OCT4 (white), combined with XIST RNA FISH (green). For each sex, an intact embryo (Giemsa, immunofluorescence/RNA FISH) together with several enlarged nuclei are shown: representative XX (nuclei 1 and 2) and XY blastomeres (nuclei 3 and 4). c, Phase contrast images of an expanding blastocyst (left) and a fully expanded blastocyst (right). d, Percentage of cells showing different XIST expression patterns in morula-to blastocyst-stage embryos. e, Percentage of female and male blastocyst cells showing different X-linked gene expression patterns in blastomeres with XIST RNA domains.

Mammalian Developmental Epigenetics Group, Institut Curie, CNRS UMR 3215, INSERM U934, Paris 75248, France.

Universite ´Paris Diderot -Assistance Publique Ho ˆpitaux de Paris -Service de Biologie de la Reproduction, Ho ˆpital Bichat-Claude Bernard, 75018 Paris, France.

INRA UMR 1198 Biologie du De ´veloppement et de la Reproduction, F-78352 Jouy en Josas Cedex, France.

Laboratoire de Biologie de la reproduction CECOS, CHU de Dijon, Universite ´de Bourgogne, 21079 Dijon, France.

Epigenetic Decisions and Reproduction in mammals, Institut Curie, CNRS UMR 3215, INSERM U934, 75248 Paris, France.

Unite ´Inserm 1016, Universite ´Paris Descartes -Assistance Publique Ho ˆpitaux de Paris -Service de Biologie de la Reproduction, Ho ˆpital Cochin,

Paris, France. *These authors contributed equally to this work.

Acknowledgements We thank members of the Heard lab for advice and discussions, V. Colot for comments on the manuscript, and P. Jouannet and Ho ˆpital Cochin's IVF unit for support and advice on human embryo experiments. We are indebted to the Unite ´Commune d'Expe ´rimentation Animale in charge of the rabbit colonies, C. Archilla for technical help in sexing rabbit embryos, C. Rogel-Gaillard for providing rabbit bacterial artificial chromosomes before publication, and the UMR3215 PICT-IBiSA imaging facility. Funding is from the FRM (Equipe FRM), the ANR and the ERC (E.H.); the Agence de Biomedecine (C.P. and P.F.); and the INRA PHASE department (ACI 2007) (V.D. and J.-P.R.).


Alexis Bottero
email: bottero@lma.cnrs-mrs.fr

Paul Cristini

Dimitri Komatitsch

Quentin Brissaud

Broadband transmission losses and time dispersion maps from full-wave time-domain numerical simulations in ocean acoustics

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

Broadband transmission losses and time dispersion maps from time-domain numerical simulations in ocean acoustics

Introduction

In underwater acoustics, several numerical methods are available in the literature for the solution of acoustic wave propagation problems in complex marine environments. Most of them solve the Helmholtz equation, thus providing a frequency-domain solution. This is the traditional way that wave propagation problems in the ocean are handled, and results from these simulations are presented as transmission loss (TL) curves or transmission loss maps.

The reason for this choice is the high variability of the ocean, which generates strong signal fluctuations and makes the analysis of time signals difficult. When time-domain solutions are sought, they are often obtained after Fourier transform of the results of several frequencydomain simulations but, in some situations, it may be more convenient to generate the results directly in the time domain. Recently, a time-domain spectral-element method [START_REF] Komatitsch | Introduction to the spectral-element method for 3-D seismic wave propagation[END_REF] has been shown to efficiently solve full-wave propagation problems in ocean acoustics [START_REF] Bottero | An axisymmetric timedomain spectral-element method for full-wave simulations: Application to ocean acoustics[END_REF][START_REF] Cristini | Some illustrative examples of the use of a spectralelement method in ocean acoustics[END_REF]. Beyond its capability of handling complex geometries and rheologies accurately, as any finite-element technique, the time-domain spectral-element method runs efficiently on very large computers, thus providing a drastic reduction of the duration of numerical simulations, which is one of its attractive properties. Nevertheless, this property is partly lost if, instead of the time-domain wave equation, it is the Helmholtz equation that is solved in the framework of a spectralelement method. Consequently, the choice of solving the time-domain wave equation is mandatory to take advantage of the possibility of running such numerical simulations on large supercomputers. The reason for this situation is the behavior of linear system solvers used for the inversion of the mass matrix when solving in the frequency domain. They typically exhibit decreasing performance when increasing the number of cores and have difficulties scaling when more than a thousand processor cores or so are used. This is a significant limitation because such a number of cores is not that high in terms of current standards, and even less so in the future. Consequently, when solving wave propagation problems requiring a high number of processor cores, the question of the generation of frequency-domain results from time-domain numerical simulations arises, since the underwater acoustics community is used to analyzing results in the frequency domain. A simple way of addressing this question consists in storing all time signals for all receiver positions and then performing a Fourier transform to convert them to the frequency domain. However, this solution is realistic from a technical point of view only if the number of receivers is small to moderate because of the amount of storage (in memory or to disk) that this operation requires when the number of recording points and/or the number of time steps computed are large to very large. In practice, this limits the generation of frequency-domain results from time-domain simulations to the creation of a small number of transmission loss curves, which implies that producing 2D transmission loss maps will require an amount of storage too large to be handled. The objective of this letter is thus to present an efficient way of creating transmission loss maps from time-domain full-wave numerical simulations that avoids the storage of individual time signals. Since the source time signal can be arbitrary chosen, the transmission loss maps can be evaluated for quasi-monochromatic signals as well as for signals with a wider bandwidth, leading to the possibility of analyzing the influence of bandwidth on the distribution of acoustic energy inside the domain. In addition, time dispersion maps can also be calculated on the fly during the simulation, providing an insight into the structure of the received time signals. All these quantities are obtained at a negligible additional numerical cost.

The letter is organized as follows: Sec. 2 is devoted to the definition of the different physical quantities that we want to study, and to how one can compute them efficiently in a time-domain numerical simulation. Then, in Sec.3, we provide and discuss some examples of the evaluation of these quantities within the framework of a time-domain spectral-element method. Wave propagation over a fluid and then over an elastic upslope wedge is considered for several source bandwidths. We finally draw some conclusions in Sec.4.

Generalization of the calculation of transmission losses and evaluation of signal time spreading

In this section, we define the different physical quantities that we want to study and show how they can be calculated on-the-fly in a time-domain full-wave numerical simulation. These quantities will allow for the evaluation of the transmission losses and of the time structure of signals at all the discrete points of the spatial domain under study. Let us note u x (x, t) and u z (x, t) the horizontal and vertical displacement field, respectively, and P (x, t) the pressure field at time t and position x = (x, z). u(x, t) = ux (x, t) 2 + uz (x, t) 2 is the norm of the particle velocity field. The instantaneous energy per unit volume field in the fluid is given by ( (Jensen et al., 2011) pp.11-12):

E(x, t) = 1 2 ρ u2 (x, t) + 1 2 P 2 (x, t) ρ(x)c 2 (x) , (1)
where ρ = 1000 kg.m -3 is the density of water and c(x) is the distribution of sound velocity.

Likewise, in a linear isotropic solid medium the instantaneous energy field reads [START_REF] Achenbach | Wave Propagation in Elastic Solids[END_REF]:

E(x, t) = 1 2 ρ(x) u2 (x, t) + 1 2 i,j ij (x, t)σ ij (x, t). (2)
where (x, t) and σ(x, t) are the second-order strain and stress tensor fields, respectively. Let T f refer to the duration that is considered, then the integrated energy field reads:

E(x) = T f 0 E(x, t) dt. ( 3
)
This physical parameter represents the amount of energy received at a given position inside the model at time T f . It is similar to the radiated seismic energy introduced by [START_REF] Boatwright | Teleseismic estimates of the energy radiated by shallow earthquakes[END_REF] and evaluated from body waves measurements, or to the T-Phase Energy Flux (TPEF) proposed by [START_REF] Okal | T waves from the 1998 Papua New Guinea earthquake and its aftershocks: Timing the tsunamigenic slump[END_REF] to characterize the energy generated by an earthquake source in the form of a T-wave. Then, knowing the energy E 0 of the emitting source, it is possible to evaluate the transmission losses for time T f as:

T L(x) = -10 log E(x) E 0 (4)
Energy is determined by an integral in time, but with the value that we get we have no knowledge on how this energy is distributed within the time interval that we are considering.

For a given energy value, time spreading can be very different depending on the propagation path followed by the signal. It is therefore very useful to get such a piece of information. In order to calculate it, we first define the maximum energy field by:

M (x) = max t<T f E(x, t).
(5)

This field gives the maximum of the instantaneous energy for each point and provides a way of defining an "effective" time dispersion for a signal as:

T (x) = 2 E(x) M (x) . ( 6
)
This quantity is homogeneous to a duration. It represents the duration of the triangle-shaped signal that has the same energy and maximum amplitude as those that we have calculated. It is therefore a measure of the time spreading of the signal. Time-domain full-wave numerical simulations provide access to these physical parameters at each time step δt and thus allow for the computation of transmission losses and time dispersion maps on-the-fly during the run at a negligible additional computational cost. In practice, at iteration i + 1 and position

x, one can evaluate:

E i+1 (x) = E i (x) + E(x, t i+1 )δt (7) M i+1 (x) = max [M i (x), E(x, t i+1 )] (8) T i+1 (x) = 2 E i+1 (x) M i+1 (x) (9)
Time domain full-wave numerical methods can thus also provide an at-a-glance view of how the acoustic energy emitted by a source is distributed inside a complex heterogeneous model.

In the following sections, we will show examples of the maps that can be obtained based on the calculation of these physical quantities.

Application to wave propagation in a 2D upslope wedge

In order to validate our approach and to present new results, we choose to investigate the classical two-dimensional (2D) wedge benchmark problem, whose characteristics can be found in Section 6.9.2 of [START_REF] Jensen | Computational Ocean Acoustics[END_REF]. This configuration illustrates several wave propagation phenomena such as mode conversion and mode cutoff due to a varying water column depth.

In the context of an attenuating fluid bottom, transmission loss maps for a monochromatic source have already been published and can thus be used for comparison. In addition, with our approach, the transmission loss concept can be extended to broadband source signals and to elastic media. This is an interesting feature that enables us to determine the energy spreading in the whole computational domain. As a consequence these new maps may help to understand the physical mechanisms that lead to the distribution of acoustic energy inside a given configuration. For the sake of illustration, let us first generate a transmission loss map from a full-wave time-domain numerical simulation for exactly the same configuration as in [START_REF] Jensen | Computational Ocean Acoustics[END_REF]. These previous results were obtained with a split-step implementation of the Thomson-Chapman parabolic equation using a Greene wide-angle source to initialize the solution. It is worth noting that the results that will be generated using our approach will be obtained based on a time-domain full-wave numerical simulation that makes no approximation. As a consequence, comparing our results with those obtained with a parabolic equation will also lead to a comparison of the two numerical methods. Then, in a second step, we will consider the influence of the bandwidth of the emitted signal for both a fluid and an elastic bottom. For this purpose, we define a source time function signal by:

s(t) =            A 2 (1 -cos (∆πt) sin (2πf 0 t)) if 0 < t < 2 ∆ 0 else ( 10
)
where A is the maximum amplitude of the source, f 0 is the dominant frequency of the source signal, and ∆ is its bandwidth. This type of time sequence will allow us to control the bandwidth of the emitted signal by changing the value of parameter ∆. Quasi-monochromatic signals that will provide results close to frequency-domain calculations as well as narrowband or broadband signals can be generated. We will thus be able to study the influence of the bandwidth on the spreading of acoustic energy inside the computational domain. In addition to a fluid viscoacoustic bottom, we will also consider a solid viscoelastic bottom by adding a shear velocity of c s = 600 m.s -1 and a shear attenuation coefficient α S = 0.5 dB.λ -1 S to the sediment characteristics. In the spectral-element method, viscoacoustic or viscoelastic effects are represented based upon three generalized Zener standard linear solids placed in parallel, with different relaxation times for each, to mimic a constant Q quality factor over the frequency band under study in the simulation [START_REF] Komatitsch | Introduction to the spectral-element method for 3-D seismic wave propagation[END_REF]. In order to avoid spurious reflections from the sides of the computational domain, for all configurations the domain is extended up to a range of 20 km and down to a depth of 1 km and equipped with perfectly matched absorbing layers (PMLs, [START_REF] Xie | A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms[END_REF]).

The first results are shown in Fig. 1, which provides the comparison between a monochromatic TL map (Fig. 1(a)) taken from [START_REF] Jensen | Computational Ocean Acoustics[END_REF] and a quasi- The quasi-monochromatic signal was generated using a bandwidth ∆ = 0.5 Hz. We performed several simulations with signals having smaller bandwidth but did not notice any changes in the TL map. We thus consider this value of the bandwidth as a good approximation of a monochromatic signal for this configuration. Note that this is a fluid answer to the question raised by the author of [START_REF] Buckingham | EUR-OP)[END_REF] on the accuracy of TL maps obtained using the parabolic equation for an upslope fluid wedge. Based on the results

that we obtain, it can be considered that the accuracy is very good.

Since our numerical method works in the time domain, we can also consider signals with different bandwidths in order to evaluate how this parameter may influence the spreading of energy inside the computational domain. A smoothing of the interference structure is observed in the water column mainly from the beginning of the wedge to its end. The reason for this situation lies in the fact that for each frequency there is a different modal structure, with different grazing angles and therefore different cutoff depths varying continuously with frequency. This smoothing is also observed in the sediment. The complex structure that was observed below the source also disappears. (c) TL map, in dB, for an elastic bottom using a quasi-monochromatic source (f 0 = 25 Hz, ∆ = 0.5 Hz).

(d) TL map, in dB, for an elastic bottom using a broadband source (f 0 = 25 Hz, ∆ = 8.0 Hz).

the presence of shear waves is strong and dominant. The associated narrow beams are almost vertical because of the low velocity of shear waves in this configuration. Below the sloping interface, it can be seen that the beams exhibit an interference structure due to the leaking, in this case, of both the shear waves and the propagating modes. This structure is also seen in the near field but, in this case, it is generated by the leaking of evanescent modes. Similar results were presented in [START_REF] Abawi | Propagation in an elastic wedge using the virtual source technique[END_REF] (top figure of their Figure 1). It can also be noted that the leaking of the first mode is strongly affected by the presence of shear waves, as it does not penetrate deep into the sediment. There is much less energy in the water column at the end of the wedge than in the fluid-only configuration. A large amount of energy is captured by the shear waves of the bottom. The structure of the sound field in the sediment suggests that if another interface is considered, i.e. if we consider an elastic layer over a semi-infinite half-space, the presence of shear waves is critical and may generate complex effects because of the potential interaction between these beams and this interface.

As in the pure fluid case, increasing the bandwidth (Figure 2 (d)) leads to a smoothing of the energy levels mainly in the area of the slope.

As mentioned in the previous section, another type of information can be extracted from time-domain simulations. This piece of information is related to the spreading of energy with time at a receiver location. Indeed, for a given energy level, the time structure of the received signal can be very different and provide additional information on the propagation process that led to this received signal. This is particularly useful e.g. for T-waves analysis because the time structure of a received signal is different depending on the source mechanism that led to the generation of this signal. In order to illustrate the kind of information that is provided by this type of map, we performed a full-wave time domain numerical simulation for a fluid bottom and a broadband signal (f 0 = 25 Hz, ∆ = 25.0 Hz).

Conclusions

We have presented an efficient procedure to compute transmission losses and time dispersion maps from time-domain full-wave numerical simulations. This procedure allowed us to extend the notion of transmission losses to non-monochromatic signals and to elastic media. Some results using this procedure were obtained for a 2D wedge configuration in ocean acoustics. In the case of a simulation in the frequency domain and for a fluid bottom, these results were compared with results previously obtained using a parabolic equation, showing that both methods give similar results and that the main structures of the sound field are correctly captured by the parabolic equation. Discrepancies between the two approaches were found in regions where the parabolic approximation is known to fail. As a result, our approach can provide reference solutions for more complex configurations because the numerical simulations that are performed are realized without any such approximation and are able to handle complex geometries accurately. In future work we expect to present results

  Fig. 1. (Color online) (a) Original TL map, in dB, from reference (Jensen et al., 2011) page 514. (b) TL

  only configuration. The two TL maps are very similar. Mode cutoff of the three modes, which exist in the flat part of the model, are recovered almost identically in both cases. The main differences are observed for short ranges. This is not surprising since the parabolic equation, which is used to generate the results of Fig1(a), has angular limitations. Moreover, a source with a limited aperture was used, contrary to our simulation, which implements a point source. Therefore the discrepancies between the two TL maps are attributed to the known inaccuracy of PE codes for steep angles. Nevertheless, interference structures in the water column are very close, except at the end of the wedge where again the grazing angles are steepened because of the varying depth and thus cannot be handled correctly through numerical modeling based on the parabolic equation. This comparison may be seen as a first

  Figure 2 (b) represents the TL map for a signal with a bandwidth ∆ = 8.0 Hz.

(

  Fig. 2.

  Fig. 3. (Color online) Figure illustrating the use of time dispersion maps. The geometry is the same as

Figure 3

 3 Figure 3 (a) represents the TL map, and Figure 3 (b) represents the time dispersion

Acknowledgments

We are grateful to Jean-Pierre Vilotte, Oleg A. Godin and Raphaël F. Garcia for fruitful discussion. The Ph.D. grant of Alexis Bottero was awarded by ENS Cachan, France. This work was granted access to the French HPC resources of TGCC under allocation #gen7165 and of CINES under allocation #A0020407165, both made by GENCI, and of the Aix-Marseille Supercomputing Mesocenter under allocations #b025. We gratefully acknowledge the support of NVIDIA Corporation with the donation of hardware for this research through their Hardware Grant Request program.

Our SPECFEM open source spectral-element software package used in this study is freely available at geodynamics.org; it contains all the tools needed to reproduce the simulations presented in this letter.