Maud Borensztein

Laurène Syx

Katia Ancelin

Patricia Diabangouaya

Christel Picard

Tao Liu

Jun-Bin Liang

Ivaylo Vassilev

Rafael Galupa

Nicolas Servant

Picard

Emmanuel Barillot

Azim Surani

Chong-Jian Chen

Edith Heard

Xist-dependent imprinted X inactivation and the early developmental consequences of its failure

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

dynamics of X-linked genes depends both on strain and parent-of-origin, as well as on 29 location along the X chromosome. This study demonstrates that dosage compensation 30 failure has an impact as early as the blastocyst stage and reveals the genetic and 31 epigenetic basis for orchestrating the transcriptional silencing of the X chromosome 32 during early embryogenesis.

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In early mouse embryos, XCI has been shown to be dynamic and its requirements, both in cis 35 at the level of the X-inactivation center (Xic) and in trans, have been debated [START_REF] Galupa | X-chromosome inactivation: New insights into cis and trans 272 regulation[END_REF] . Imprinted XCI 36 has been proposed to initiate de novo [START_REF] Okamoto | Evidence for de novo imprinted X-chromosome inactivation 263 independent of meiotic inactivation in mice[END_REF][START_REF] Brockdorff | Dosage compensation in Mammals[END_REF] following the onset of zygotic genome activation 37 (ZGA) and Xist expression. One study proposed that Xp inactivation is initially Xist-38 independent and that Xist may only be required for early maintenance of silencing [START_REF] Kalantry | Evidence 269 of Xist RNA-independent initiation of mouse imprinted X-chromosome inactivation[END_REF] , while 39 another reported a lack of Xp gene silencing in the absence of Xist [START_REF] Namekawa | Two-step 274 imprinted X inactivation: repeat versus genic silencing in the mouse[END_REF] . These studies were all pipeline and expression thresholds were valid. The one gene (out of the 13) for which slightly 92 earlier Xp silencing was found by scRNAseq compared to previous reports was Atrx. We 93 confirmed that Atrx is inactivated on the Xp in most cells by the morula stage using RNA 94 FISH with a gene-specific probe (Supplementary Figure 3a). We also confirmed its 95 previously reported Xp reactivation in the blastocyst [START_REF] Patrat | Dynamic changes in paternal X-chromosome activity during imprinted[END_REF] (Supplementary Figure 2).

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We established an in vivo chromosome-wide map of X-linked gene activity between 97 the 4-cell and blastocyst stages. Of the 580 X-linked genes expressed in our scRNAseq, we 98 focused on the 164 (BC cross) and 134 (CB cross) most highly expressed and informative 99 genes (RPRT>4 and expressed in at least 25% of the cells of each stage and cross with a 100 minimum of 2), for which we could establish allelic expression profiles with confidence 101 (Supplementary Figure 3b and Figure 2 for the 125 common genes between BC and CB 102 crosses, see Online Methods for allelic expression threshold details). A striking switch from 103 biallelic (grey, pale pink or pale blue) expression at the 4-cell stage, to monoallelic, maternal 104 (red) expression at the blastocyst stage can be observed for most X-linked genes. Several 105 genes underwent only partial or no XCI (escapees) and will be discussed later. As expected,

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Xist expression was exclusively of paternal origin throughout (Figure 2 and Supplementary 107 Figure 3b). Another gene showing only paternal expression was Fthl17f, part of the ferritin, 108 heavy polypeptide-like 17 family (also known as Gm5635), which has previously been 109 reported to be exclusively paternally expressed and imprinted 12 . By the blastocyst stage 110 Fthl17f expression was no longer detectable, presumably due to XCI (Figure 2 and 111 Supplementary Figure 3b).

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We categorized genes into different groups with respect to their timing of XCI for 113 each cross (early ≤ 16-cell; intermediate ≤32-cell; late = blastocyst; Figure 3a, SI Table 2 and Pnma5, Figure 2 and Supplementary Figure 3b). By the blastocyst stage, Xp reached a very 116 similar state of inactivation in both BC and CB crosses (respectively 83.5% and 84.3% of the 117 164 and 134 X-linked informative and expressed genes are either silenced or maternally 118 biased at the blastocyst stage, Figures 2, 3a and 3b). However, when comparing gene 119 expression in embryos derived from BC and CB crosses (125 common genes), marked 120 differences were seen between crosses, with only 71.2% (89 of 125 genes) of X-linked genes 121 falling into the same or a similar category between BC and CB crosses (eg early/mid or 122 late/biased). The degree of consistency in silencing kinetics between crosses was evaluated if 123 no more than one developmental stage separated the same gene between BC and CB crosses 124 (Supplementary Table 2 and Online Methods for classification details). Furthermore, several 125 genes show strain-specific escape, some of which have previously been described 13 or 126 reported to escape in a tissue-specific fashion at later stages of development or in somatic 127 tissues (eg Ddx3x, Idh3g) [13][14][15] . Several genes remain biallelically expressed, even at the 128 blastocyst stage and tend to show escape independent of strain (Figure 3b and Supplementary 129 Table 3). Many of these also show escape in somatic tissues 16 (eg Eif2s3x, Kdm5c, Utp14a).

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We then assessed whether gene-silencing kinetics was correlated with genomic 131 position along the X chromosome. We first focused on the 71.2% (n=89 genes) of genes with 132 correlated kinetics between crosses and the strain-specific genes (n=48). Although early and 133 intermediate silenced genes do tend to lie closer to the Xic compared to late silenced genes 134 (Figure 3c), gene silencing does not appear to occur as a simple linear gradient from the Xic 135 according to our allele-specific expression heatmap, with presence of escapees close to the 136 Xic (Figure 2). Rather, we noted several regions across the X chromosome, containing early-137 silenced genes, (eg Pnma5, Kif4, Magt1) from which silencing appeared to "spread" locally 138 (Figure 2). A recent study in ES cells showed that Xist RNA initially binds to specific 139 genomic regions (Xist "entry" sites) along the X chromosome, dependent on 3D proximity to the Xist locus 17 . This binding has been hypothesized to silence genes locally and to then 141 spread along the rest of the X chromosome by Engreitz et al 17 . We found that X-linked genes 142 lying within (8 and 11 genes respectively in 32-cell and blastocysts), or close to (20 and 23 143 respectively in 32-cell and blastocysts) these regions showed the earliest silencing and 144 strongest maternal imbalance (p=0.02 and p=0.03, KW, respectively in 32-cell and 145 blastocysts, Figure 3d). Thus, we show that Xist RNA "entry" sites as defined in ESCs 17 could 146 correspond to XCI initiation sites in vivo, during imprinted XCI.

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These findings suggest that Xist RNA plays a key early role in triggering gene 148 silencing during imprinted XCI. This contrasts with a previous report suggesting that 149 initiation of imprinted XCI could be is Xist-independent [START_REF] Kalantry | Evidence 269 of Xist RNA-independent initiation of mouse imprinted X-chromosome inactivation[END_REF] . Indeed, although Xist pat∆ females 150 die around E10.5, with major growth delay 18 , mutant and wt females appear morphologically 151 indistinguishable during pre-implantation development (data not shown). To evaluate whether 152 XCI is established in the absence of Xist expression, as previously reported [START_REF] Kalantry | Evidence 269 of Xist RNA-independent initiation of mouse imprinted X-chromosome inactivation[END_REF] , we examined X-153 linked gene expression profiles in single cells of pre-implantation female embryos carrying a 154 paternal Xist deletion (Xist pat∆ ) 18, [START_REF] Moreover | aberrant over-expression of Prdm14, Esrrb and Tcl1 was observed in Xist -References 260[END_REF] . Xist is normally expressed exclusively from the Xp in pre-155 implantation embryos 2 (Figure 2). Transcriptomes of single blastomeres from hybrid F1 156 embryos (Cast females crossed with Xist mat∆ B6 males) were compared to CB wt embryos 157 between the 8-cell stage (when XCI normally initiates for some genes) to the blastocyst stage.

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We found similar X:A expression ratios between female mutants and controls up to the 32-159 cell stage (Figure 4a). However at the blastocyst stage, X:A ratios remained much higher in 160 mutants compared to wt embryos where this ratio normally decreases due to XCI (p=1.77*10 - 161 4 , KW). This demonstrates that Xp silencing is not initiated in Xist pat∆ female blastocysts.

162

Bioinformatics analysis on the Xist-mutant single cell transcriptomes was used to produce an 163 allele-specific expression heatmap (see Online Methods) and, as expected, given the absence 164 of apparent dosage compensation in the mutants, we found that X-linked genes remained significantly biallelically expressed in Xist pat∆ embryos (Figure 4b). Only 1.6% genes (2 out of 166 122 genes: Rgn and Tktl1) showed maternal monoallelic expression in Xist pat∆ mutant 167 blastocysts, compared to 84.3% in CB controls. One of these, Tktl1, has been hypothesized to 168 be imprinted 20 . Moreover, Fthl17f, a well-known imprinted gene was aberrantly expressed in 169 Xist pat∆ blastocysts, suggesting a lack of Xp silencing.

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We thus found no evidence for Xist-independent XCI (Supplementary Figure 5a), even 171 for the X-linked genes previously proposed to be silenced independently of Xist 5 (11 out of 14 assayed, only Rnf12, Abcb7 and Atrx were found to be Xist-dependent in the Kalantry et al 173 study). Three of the genes assayed by Kalantry et al (Abcb7, Fmr1 and Pgk1) showed a slight 174 maternal bias at the 16-cell or 32-cell stages in the Xist pat∆ cells (left column, Supplementary Figure 5a). However this is probably due to variability in their parental-origin expression, also 176 observed in CB controls (Abcb7 and Fmr1, Supplementary Figures 3 and5a) or low parental-177 origin information (Pgk1, data not shown) rather than to Xp silencing. Instead, our data is in agreement with the Namekawa et al study [START_REF] Namekawa | Two-step 274 imprinted X inactivation: repeat versus genic silencing in the mouse[END_REF] where Xist-dependent Xp silencing was proposed 4). Expression profiles of single blastomeres of controls and mutants 188 were still found to cluster according to developmental stage by PCA (data not shown). genes (FDR<0.05) was found in Xist pat∆ embryos compared to wt (Supplementary Figure 5b).

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By the blastocyst stage, when paternal XCI is normally complete in wt females, 30% of the 192 total up-regulated genes in Xist pat∆ embryos were found to be X-linked, corroborating an XCI We explored the degree to which transcriptomes were perturbed in the Xist mutant 198 embryos using Ingenuity Pathway Analysis software. We found that many aberrantly down-199 regulated genes in Xist pat∆ female blastocysts were associated with extra-embryonic tissue 200 pathways, embryonic growth and cell viability (Figure 4c and Supplementary Table 5). Key Correspondence and requests for material should be addressed to E.H. (edith.heard@curie.fr). 368 1).

(c) Dosage compensation during preimplantation development. Level ratio of X chromosome

Oo_Cast_10 Oo_Cast_11 Oo_Cast_12 Oo_B6_4 Oo_B6_18 Oo_B6_20 Oo_B6_21 64C_BC_9 64C_BC_11 32C_BC_27 32C_BC_20 32C_BC_21 32C_BC_33 32C_BC_35 32C_BC_31 32C_BC_30 32C_BC_36 32C_BC_28 32C_BC_29 32C_CB_72 32C_CB_6E 32C_CB_57 32C_CB_6C 32C_CB_2G 32C_CB_2C 32C_CB_2E 32C_CB_2A 32C_CB_2B 32C_CB_2F 32C_CB_6B 32C_BC_19 64C_BC_64 32C_CB_73 32C_CB_80 32C_CB_58 32C_CB_84 64C_CB_52 64C_CB_58 64C_CB_56 64C_CB_54 64C_CB_49 64C_CB_60 64C_BC_35 64C_BC_75 64C_BC_19 64C_BC_40 64C_BC_36 64C_BC_26 64C_BC_21 64C_BC_24 64C_BC_23 64C_CB_50 64C_CB_51 16C_BC_71 16C_BC_68 16C_BC_64 16C_BC_65 16C_BC_59 16C_BC_61 16C_BC_57 16C_BC_62 16C_CB_46 16C_CB_47 16C_CB_49 8C_BC_51 8C_BC_48 8C_BC_46 8C_BC_49 8C_BC_33 8C_BC_31 8C_BC_32 8C_BC_42 8C_BC_40 8C_BC_38 8C_BC_39 8C_BC_45 8C_BC_41 8C_BC_43 8C_BC_44 16C_CB_37 16C_BC_3 16C_BC_5 16C_BC_19 8C_CB_17 8C_CB_20 8C_CB_19 8C_CB_21 8C_CB_23 2C_CB_4 2C_CB_6 2C_CB_2 2C_BC_11 2C_BC_9 2C_BC_10 8C_BC_5 8C_BC_1 8C_BC_9 8C_BC_2 8C_BC_4 8C_BC_8 8C_BC_14 8C_BC_3 8C_BC_11 4C_CB_32 4C_CB_29 4C_CB_33 4C_BC_2 4C_BC_3 4C_BC_5 4C_BC_50A 4C_BC_51A 4C_BC_50C 4C_BC_51C
496 497 Oo_B6_4 Oo_B6_18 Oo_B6_20 Oo_B6_21 Oo_Cast_10 Oo_Cast_11 Oo_Cast_12 2C_BC_9 2C_BC_10 2C_CB_6 2C_BC_11 2C_CB_2 2C_CB_4 4C_BC_2 4C_BC_3 4C_BC_5 4C_BC_50A 4C_BC_51A 4C_CB_29 4C_CB_32 4C_CB_33 4C_BC_50C 4C_BC_51C 8C_BC_1 8C_BC_2 8C_BC_3 8C_BC_4 8C_BC_5 8C_BC_8 8C_BC_9 8C_BC_11 8C_BC_31 8C_BC_32 8C_BC_33 8C_BC_38 8C_BC_39 8C_BC_40 8C_BC_41 8C_BC_42 8C_BC_43 8C_BC_44 8C_BC_45 8C_CB_17 8C_CB_19 8C_CB_20 8C_CB_21 8C_BC_14 8C_BC_46 8C_BC_48 8C_BC_49 8C_BC_51 8C_CB_23 16C_BC_57 16C_BC_59 16C_BC_61 16C_BC_62 16C_BC_64 16C_BC_65 16C_BC_68 16C_BC_71 16C_CB_46 16C_CB_47 16C_CB_49 16C_BC_3 16C_BC_5 16C_BC_19 16C_CB_37 32C_BC_19 32C_BC_20 32C_BC_21 32C_BC_27 32C_BC_28 32C_CB_2A 32C_CB_2B 32C_CB_2C 32C_CB_2E 32C_CB_2F 32C_CB_2G 32C_CB_6B 32C_CB_6C 32C_CB_6E 32C_BC_29 32C_BC_30 32C_BC_31 32C_BC_33 32C_BC_35 32C_BC_36 32C_CB_57 32C_CB_58 32C_CB_72 32C_CB_73 32C_CB_80 32C_CB_84 64C_BC_19 64C_BC_35 64C_BC_36 64C_BC_40 64C_BC_64 64C_BC_75 64C_CB_49 64C_CB_50 64C_CB_51 64C_CB_52 64C_CB_54 64C_CB_56 64C_BC_9 64C_BC_11 64C_BC_21 64C_BC_23 64C_BC_24 64C_BC_26 64C_CB_58 64C_CB_60
Supplementary Figure 5 -Borensztein et al

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  to occur based on nascent RNA-FISH on 2-cell to blastocyst stage embryos, although their 180 study was only based on 8 genes, 4 of which were in common with ref 5. The discrepancies 181 between these previous studies were likely due to technical differences. The scRNAseq 182 analysis we provide here represents chromosome-wide evidence for Xist-dependent gene 183 silencing during pre-implantation embryogenesis. 184 The transcriptome of Xist pat∆ embryos also provides us with a unique opportunity to 185 explore the molecular defects that occur in the absence of paternal XCI. A genome-wide 186 differentially expressed (DE) gene analysis was performed in wt and Xist pat∆ embryos 187 (Supplementary Table

193

  defect in the absence of Xist. DE genes included Tsix (the antisense transcript to Xist) which is 194 normally not expressed from the Xp at the 32-64 cell stage 21 (Figures4b and dand 195 Supplementary Figure5b). The absence of Xist on the paternal X thus releases paternal Tsix 196 repression in cis (without affecting the maternally imprinted Xist/Tsix alleles).

  197

  201extra-embryonic development genes that were aberrantly down-regulated included Tead4 202 (trophectoderm) 22 , Sox17 23 (primitive endoderm PrE and ExE), Bmp4 24 (trophectoderm TE 203 and PrE), Arid3a 25 (TE specification) and Socs3 26 (placental development) (Figure 4d). To 204 confirm the aberrant decrease of Sox17-positive cells in the PrE in Xist pat∆ females, we 205 performed immunofluorescence on late blastocysts (Supplementary Figure 6a, c, e and g). In 206 Xist pat∆ females, fewer cells express Sox17 compared to their male littermates and the 207 intensity of fluorescence of Sox17 is slightly decreased (Supplementary Figure 6g), which 208 corroborates the decrease in mRNA expression that we observe by scRNAseq. 209 Importantly, in addition to aberrant down regulation or repression of extra-embryonic 210 genes, we also found abnormal overexpression of several pluripotency genes including 211 Prdm14, Esrrb and Tcl1 in Xist pat∆ embryos. This suggested an inappropriate activation or 212 lack of repression of such factors in the absence of XCI (Figure 4d). This is relevant to our 213 recent findings showing that the presence of two active X chromosomes delays exit from 214 pluripotency in ESCs, by preventing down-regulation of key genes, such as Prdm14 or gene (10 log fold change) in Xist pat∆ female blastocysts was the imprinted Rhox5 gene, also 218 known as Pem-1. Rhox5 is a member of the reproductive X-linked Hox (Rhox) cluster, and is 219 expressed exclusively in the male germ line and in female (but not male) pre-implantation 220 embryos (Xp only) 27 . Following implantation, its expression switches to the maternal allele 221 and becomes restricted to extra-embryonic tissues 27 . The human RHOXF1 gene that is 222 hypothesized to be related to the murine Rhox5 28 shows similar sex-specific and lineage-223 specific expression in human pre-implantation embryos 29 . Importantly, previous in vitro 224 studies demonstrated that over-expression of Rhox5 can block differentiation of ESCs by 225 preventing exit from pluripotency 30,31 . We validated Rhox5 up-regulation at the protein level 226 using immunofluorescence and found that Xist pat∆ female blastocysts show significantly 227 higher Rhox5 staining, particularly in the polar trophectoderm and inner cell mass region of 228 the embryo, compared to wt blastocysts (Supplementary Figure 6b, d, f and g). Quantification 229 of Rhox5 immunofluorescence showed a significant increase in Rhox5 protein levels 230 (p=0.0171, Kolmogorov-Smirnov KS test, Supplementary Figure 6h) and in the number of 231 cells stained by Rhox5 antibody (Supplementary Figure6f). This correlates well with our 232 scRNAseq data.233We conclude that even by the early blastocyst stage, the lack of initiation of Xp 234 inactivation in Xist pat∆ embryos leads to inappropriate down-regulation of several key genes 235 involved in extra-embryonic development, overexpression of several pluripotency genes and 236 massive overexpression of Rhox5. Together some or all of these defects must ultimately result 237 in compromised extra-embryonic development and redirection towards what appears to be a 238 more pluripotent state, or at least a state from which further differentiation is 239 perturbed. Importantly, aberrant induction of maternal Xist and Xm inactivation in extra-embryonic tissues of blastocysts carrying a maternal Tsix deletion demonstrates that the 241 presence of two active X chromosomes at the blastocyst stage can still be rescued in some 242 females, and suggests that the major defect associated with a lack of paternal XCI is initially 243 in the extra-embryonic lineage 32 . 244 In conclusion, we have demonstrated here the key role that Xist RNA plays in 245 initiating imprinted XCI. Our scRNAseq has enabled us to identify the molecular defects in 246 developmental pathways that emerge from this absence of dosage compensation and result in 247 lethality a few days later. We also reveal the influence of chromosomal location, as well as 248 genetic background and parent-of-origin on XCI kinetics. Our finding that Xist's predicted 249 initial binding sites on the X chromosome correspond to the earliest regions silenced, between 250 the 8-16 cell stage, with evidence for local spreading in cis at the 32-blastocyst stage will 251 enable exploration of the local features that underlie the spread of silencing along the X 252 chromosome in an in vivo context. Our study demonstrates the critical requirement for 253 accurate X-chromosome gene dosage during early embryo development and uncovers some 254 of the key pathways and factors that are affected in the absence of XCI. Future dissection of 255 these pathways and their relationship to X-linked gene dosage should provide a better 256 understanding of the important role that small changes in RNA and protein levels can play, 257 not only development but also in disease. X-chromosome inactivation in mice. Proc. Natl. Acad. Sci. U. S. A. 106, 5198-203 285 (2009).286 12. Kobayashi, S. et al. The X-linked imprinted gene family Fthl17 shows predominantly 287 female expression following the two-cell stage in mouse embryos. Nucleic Acids Res. 288 38, 3672-3681 (2010).

289 13 .

 13 Calabrese, J. M. et al. Site-Specific Silencing of Regulatory Elements as a Mechanism 290 of X Inactivation. Cell 151, 951-963 (2012).

291 14 .

 14 Berletch, J. B. et al. Escape from X Inactivation Varies in Mouse Tissues. PLOS Genet. 292 11, e1005079 (2015).

  293 15. Marks, H. et al. Dynamics of gene silencing during X inactivation using allele-specific 294 RNA-seq. Genome Biol. 16, 149 (2015).

295 16 .

 16 Balaton, B. P. & Brown, C. J. Escape Artists of the X Chromosome. Trends Genet. 32, 296 348-359 (2016).

297 17 .

 17 Engreitz, J. M. et al. The Xist lncRNA exploits three-dimensional genome architecture 298 to spread across the X chromosome. Science 341, 1237973 (2013).

299 18 .

 18 Marahrens, Y., Panning, B., Dausman, J., Strauss, W. & Jaenisch, R. Xist-deficient 300 mice are defective in dosage compensation but not spermatogenesis. Genes Dev. 11, 301 156-166 (1997).

302 19 .

 19 Schulz, E. G. et al. The two active X chromosomes in female ESCs block exit from the 303 pluripotent state by modulating the ESC signaling network. Cell Stem Cell 14, 203-216 304 (2014).

305 20 .

 20 Nesbitt, A. M. Genomic imprinting of the X-linked gene transketolase-like 1 in mouse 306 and human. ProQuest Diss. Theses A&I. 884624661, (2010).

  307 21. Lee, J. T., Davidow, L. S. & Warshawsky, D. Tsix, a gene antisense to Xist at the X-308 inactivation centre. Nat. Genet. 21, 400-4 (1999). 22. Nishioka, N. et al. Tead4 is required for specification of trophectoderm in pre-310 implantation mouse embryos. Mech. Dev. 125, 270-283 (2008).311 23. Niakan, K. K. et al. Sox17 promotes differentiation in mouse embryonic stem cells by 312 directly regulating extraembryonic gene expression and indirectly antagonizing self-313 renewal. Genes Dev. 24, 312-326 (2010).

314 24 .

 24 Graham, S. J. L. et al. BMP signalling regulates the pre-implantation development of 315 extra-embryonic cell lineages in the mouse embryo. Nat. Commun. 5, 5667 (2014).

316 25 .

 25 Rhee, C. et al. Arid3a is essential to execution of the first cell fate decision via direct 317 embryonic and extraembryonic transcriptional regulation. Genes Dev. 28, 2219-2232 318 (2014).

  319 26. Takahashi, Y. et al. SOCS3: An essential regulator of LIF receptor signaling in 320 trophoblast giant cell differentiation. EMBO J. 22, 372-384 (2003).

321 27 .

 27 Kobayashi, S. et al. Comparison of gene expression in male and female mouse 322 blastocysts revealed imprinting of the X-linked gene, Rhox5/Pem, at preimplantation 323 stages. Curr. Biol. 16, 166-172 (2006).

324 28 .

 28 Li, Q., O'Malley, M. E., Bartlett, D. L. & Guo, Z. S. Homeobox gene Rhox5 is 325 regulated by epigenetic mechanisms in cancer and stem cells and promotes cancer 326 growth. Mol Cancer 10, 63 (2011).

327 29 .

 29 Petropoulos, S. et al. Single-Cell RNA-Seq Reveals Lineage and X Chromosome 328 Dynamics in Human Preimplantation Embryos. Cell 165, 1012-1026 (2016).

329 30 .

 30 Fan, Y., Melhem, M. F. & Chaillet, J. R. Forced expression of the homeobox-330 containing gene Pem blocks differentiation of embryonic stem cells. Dev Biol 210, 331 481-96. (1999).

332 31 .

 31 Cinelli, P. et al. Expression profiling in transgenic FVB/N embryonic stem cells 333 overexpressing STAT3. BMC Dev. Biol. 8, 57 (2008). 32. Sado, T., Wang, Z., Sasaki, H. & Li, E. Regulation of imprinted X-chromosome 335 inactivation in mice by Tsix. Development 128, 1275-1286 (2001). bioinformatics analysis. L.S. built the computational pipeline for scRNAseq and analyzed the data with M.B. M.B. and E.H. wrote the paper. 363 www.nature.com/reprints. The authors declare no competing financial interests.

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Figure 1 :

 1 Figure 1: Single cell RNA sequencing of early hybrid embryos and dosage compensation

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  expression is measured over autosomal one (XX:AA or X:AA) between 2-cell stage to 383 blastocyst embryos, by Dunn's test (Kruskal-Wallis), p<0.001 to **. 384 (d) Allele-specific gene ratios from autosomes (plain red or yellow) and from X 385 chromosomes (dash red or yellow) in female single blastomeres (2-cell to blastocyst) from 386 BC and CB crosses. Allele-specific proportion represents the number of reads mapped on 387 paternal genome divided by the total number of paternal and maternal reads mapped for each 388 gene. 389 e) Example of expression dynamics of three X-linked genes with their classification as "early 390 inactivated", "intermediate inactivated" or "escapee" as described in Patrat et al, 2009 11 (see 391 also Supplementary Figure 2). Percentage of parental origin transcripts is represented between 392 oocytes and blastocyst.

Figure 1 -

 1 Figure 1-Borensztein et al

Figure 2 :Figure 2 -Figure 3 :aFigure 3 -

 2233 Figure 2: Kinetics of silencing of X-linked genes over the entire X chromosome during

Figure 4 :

 4 Figure 4: Paternal knockout of Xist impaired XCI, dosage compensation and

  RNA FISH using probes recognizing Xist (signal in green) and Atrx (signal in red) 483 nascent RNAs on a 16C female embryo. DAPI is in blue. Right pictures are enhanced pictures 484 of two individual blastomeres. Percentage of nuclei showing pinpoints of nascent transcripts (b) Heatmaps are representing the mean of allele-specific expression of X-linked genes 491 between Oocytes to blastocyst in CB and BC crosses. Strictly maternally expressed genes 492 (allelic ratio ≤0.15) are represented in red and strictly paternally expressed genes (allelic ratio 493 ≥0.85) in blue. Color gradients are used in between and genes have been ordered by genomic 494 position. Oocytes and 2C data have been included to Figure 2 heatmaps as well as strain-495 specific genes.

6 -

 6 Borensztein et al Mouse crosses and collection of embryos 564 All experimental designs and procedures were in agreement with the guidelines from French 565 legislation and institutional policies. 566 All BC and CB embryos were respectively derived from natural meetings between C57BL/6J 567 (B6) females crossed with CAST/EiJ (Cast) males or by the reciprocal cross. The Xist pat∆ 568 mutant embryos (Xist +/-) have been obtained by mating between Cast females and Xist -/Y 569 males (mixed background: B6D2F1: C57BL/6J and DBA/2J, 129S1/SvlmJ and BALB/cJ). 570 Embryos have been harvested at 2-cell, 4-cell, 8-cell, 16-cell, 32-cell and blastocyst 571 (approximately 60 to 64-cell) stages, respectively at E1.5, E2.0, E2.25, E2.75, E3.25 and 572 E3.5. B6 and Cast pure oocytes have been collected at E0.5 after matings of females with 573 vasectomized males (Figure 1a). The collected embryos were only included in the analysis if 574 they showed a normal morphology and the right number of blastomeres in relation with their 575 developmental stage. 576 577 RNA Fluorescent In Situ Hybridization 578 RNA FISH on preimplantation embryos was performed as previously described 3 using the 579 intron-spanning Fosmid probe WI1-2039P10 (BacPac Consortium at Children's Hospital 580 Oakland Research Institute) for Atrx and the intron-spanning plasmid probe p510 for Xist. 581 Images were acquired using a wide-field Deltavision core microscope (Applied Precision -582 GE Healthcase) with a 60× objective (1,42 oil PL APO N) and 0.2 µm Z-sections. Images 583 were analyzed using ImageJ software (Fiji, NIH).

b Total differentially expressed genes in Xist pat∆ CB females a Kinetics of XCI of candidate genes in Xist pat∆ and wt CB females

			Maternal Xist pat∆ allele Maternal wt allele	Paternal Xist pat∆ allele Paternal wt allele	Xist pat∆ females wt CB females
	0 4 8 50% (RPRT, log2) Expression 75% 100% Parental origin 0% 25%	8C 16C 32C Abcb7 Biallelic Monoallelic 8C 16C 32C Blasto Blasto 100% 0 4 8 50% 75% 25% Monoallelic 0%	8C 16C 32C Blasto Atp7a 50% 0 4 8 75% 100% 25% 8C 16C 32C Blasto 0%	8C 16C 32C Blasto Atrx 50% 0 4 8 75% 100% 25% 8C 16C 32C Blasto 0%	8C 16C 32C Blasto Ddx3x 8C 16C 32C Blasto
	0 4 8 50% (RPRT, log2) Expression 75% 100% Parental origin 0% 25%	8C 16C 32C Blasto Fmr1 Biallelic Monoallelic 100% 0 4 8 50% 75% 8C 16C 32C Blasto 25% Monoallelic 0%		8C 16C 32C Blasto G6pdX 50% 0 4 8 75% 100% 25% 8C 16C 32C Blasto 0%	8C 16C 32C Blasto Kdm5c (Smcx) 50% 0 4 8 75% 100% 25% 8C 16C 32C Blasto 0%	8C 16C 32C Blasto Pdha1 8C 16C 32C Blasto
	0 4 8 50% (RPRT, log2) Expression 75% 100% Parental origin 0% 25%	8C 16C 32C Blasto Pgk1 Biallelic Monoallelic 100% 0 4 8 50% 75% 8C 16C 32C Blasto 25% Monoallelic 0%		8C 16C 32C Blasto Rnf12 50% 0 4 8 75% 100% 25% 8C 16C 32C Blasto 0%	8C 16C 32C Blasto Uba1 (Ube1x) 50% 0 4 8 75% 100% 25% 8C 16C 32C Blasto 0%	8C 16C 32C Blasto Zfx 8C 16C 32C Blasto
	Developmental stages	% Total Upregulated Total Downregulated n % n DE genes from the X chromosome	% DE genes from the autosomes n % n Total Upregulated Total Downregulated
		8-cell	5.0%	27	1.9%	14	95.0%	514	98.1%	541
		16-cell	11.6%	15	1.0%	1	88.4%	114	99.0%	129
		32-cell	4.7%	29	2.3%	12	95.3%	591	97.7%	620
		Blastocyst	29.6%	16	3.6%	2	70.4	38	96.4%	54

Annoroad Gene Technology Co., Ltd, Beijing, China

/-female ESCs induced to differentiate[START_REF] Moreover | aberrant over-expression of Prdm14, Esrrb and Tcl1 was observed in Xist -References 260[END_REF] . Intriguingly, the most significantly up-regulated

Acknowledgements We thank S. Bao and N. Grabole for experimental help in single

feedbacks and critical input. This work was funded by a fellowship of Région Ile-de-France 349 (DIM STEMPOLE) to M.B., the Paris Alliance of Cancer Research Institutes (PACRI-ANR) 350 to LS and ERC Advanced Investigator award (ERC-2010-AdG -No. 250367), EU FP7 grants 351 SYBOSS (EU 7th Framework G.A. no. 242129) and MODHEP (EU 7th Framework G.A. no. 352 259743), La Ligue, Fondation de France, Labex DEEP (ANR-11-LBX-0044) part of the 353 IDEX Idex PSL (ANR-10-IDEX-0001-02 PSL) and ABS4NGS (ANR-11-BINF-0001) to E.H 354 and France Genomique National infrastructure (ANR-10-INBS-09) to EH, NS, EB.

Hccs Msl3 Rab9 Ofd1 Gemin8 Fancb Zrsr2 Syap1 Txlng Pdha1 Map7d2 Eif1ax Mbtps2 Sms Prdx4 Acot9 Sat1 Kdm5c Smc1a Hsd17b10 Huwe1 Phf8 Tsr2 Gnl3l Apex2 Amot Alg13 Acsl4 Psmd10 Prps1 Trap1a Gla Hmgn5 Brwd3 Magt1 Atrx Pbdc1 Abcb7 Rlim Xist Cited1 Ercc6l Ogt Nono Zmym3 Kif4 Pdzd11 Igbp1 Eda Yipf6 Las1l Apoo Eif2s3x Zfx Pcyt1b Pola1 Tab3 Vbp1 Mpp1 Dkc1 G6pdx Ikbkg Fam3a Ubl4a Lage3 Fam50a Taz Tktl1 Hcfc1 Renbp Naa10 Idh3g Bcap31 Slc6a8 Pnma5 Hmgb3 1110012L19Rik Ids Rbmx Htatsf1 Mmgt1 Mospd1 Hprt Rbmx2 Slc25a14 Elf4 Utp14a Ocrl Xiap Cul4b Lamp2 Nkap Pgrmc1 Uxt Araf Cdk16 Uba1 Ndufb11 Rgn Jade3 Kdm6a Ddx3x Usp9x Med14 Atp6ap2 Fthl17f Ftsj1 Porcn Ebp Tbc1d25 Rbm3 Wdr13 Suv39h1 Gata1 Hdac6 Timm17b Pqbp1 Slc35a2 Pim2 Otud5 Tfe3 Praf2 Wdr45 Gpkow Plp2

Supplementary Figure 2), giving us confidence that our scRNAseq data, bioinformatics Online Methods). Even by the 8-cell stage, XCI is complete for a few genes (eg Rnf12, Supplementary Information is linked to the online version of the paper at 338 www.nature.com/nature.

339

Author Information ScRNAseq data are deposited in Gene Expression Omnibus under 365 accession number GSE80810. Reprints and permissions information is available at ratio at blastocyst), "biased" (Bias: maternally biased in blastocyst, 0.15<allelic ratio ≤0.3) 413 and "escapee" (Esc., not silenced). The allelic ratio of each gene represents the number of 414 reads mapped on the paternal genome divided by the total number of paternal and maternal 415 reads mapped and is represented at 4-cell, 16-cell, 32-cell and blastocyst stages from single 416 female blastomeres. Further information is provided in Supplementary Table 2 and Online 417 Methods. n= 137 X-linked genes (89 with consistent silencing kinetics between BC and CB 418 crosses and 48 BC or CB-specific). Each dot represents a single gene. The upper section represents data from BC embryos; lower 421 section is the data from CB embryos (reverse cross). Xist is represented by a red dot. Green 422 dots represent genes that escape from early XCI in both strains; orange dots represent genes 423 that are strain-specific escapees. Some genes with biallelic ratios are represented by black 424 dots and correspond to genes that previously underwent Xp silencing, prior to the blastocyst 425 stage, but then became re-expressed. Further information on escapees is found in 426 Supplementary Table 3. n= 125 common X-linked genes.

Xist pat∆ CB females (with a paternally inherited knock-out allele) (right panel). Kinetics of XCI in wt females

Supplementary Figure 5 Immunofluorescence was essentially carried out as described previously 34 with an additional 588 step of blocking in 3% FCS before the primary antibody incubation. Immunofluoroscence of 589 embryos either from mutant or control male progeny have been always performed in parallel 3b and Supplementary Table 3).

749

Existence of a consistency in silencing kinetics between crosses was evaluated if no more 750 than one developmental stage separated the same gene between BC and CB crosses. If the 751 consistent genes belonged to two different classes, a class for all (BC+CB) has been attributed 752 thanks to their parental ratio mean of (BC mean + CB mean) in Figure 3a and3d.

753 754

Dosage compensation, X:A expression ratio 755

We measured the global X:A expression ratio in females (XX :AA ratio) and males (X :AA 756 ratio) as the level of expression of X-linked genes divided by the global level of expression of 757 the autosomal genes. Only genes with an expression value RPRT >4 were used for subsequent 758 analysis (Figures 1d and4a). Adjustment of the number of expressed genes between X and 759 autosomes has been published to be critical for X:A expression ratio measurement 41 . We then 760 added a bootstrapping step and randomly selected, for each sample, an autosomal gene set 761 with the same number of expressed genes compared to the X to estimate the global X:A ratio.


W Knafo

S Araki

G Lapertot

D Aoki

G Knebel

D Braithwaite

Squeezing out field-induced reentrant hidden-order in URu 2 Si 2

The mystery of the hidden-order phase in the correlated-electron paramagnet URu 2 Si 2 is still resisting after decades of experimental and theoretical efforts. To solve the problem, one strategy is to search for clues in the subtle competition between this state and neighboring magnetically-ordered states. It is now well-established that longrange magnetic order can be stabilized in this metal under pressure (antiferromagnetism) or magnetic field applied along the easy magnetic axis c (spindensity wave). However, the full boundaries of the hidden-order phase in the pressuremagnetic field plane have not been determined so far. Here, we present a systematic investigation of URu 2 Si 2 under combined high pressures and intense magnetic fields.

The boundaries of the hidden-order, antiferromagnetic and spin-density-wave phases are mapped out, indicating a rich and complex three-dimensional phase diagram. We show that the field-induced spin-density-wave and hidden-order phases disappear in favor of antiferromagnetism at high pressure. Interestingly, a large number of phase boundaries are controlled by the field-and pressure-dependences of a single parameter. These results constitute new constraints for theories aiming to model the electronic correlations and the ordered phases in URu 2 Si 2 .

Intense research on correlated-electrons quantum materials is focused on the competition between ordered and disordered electronic states, their tuning via quantum phase transitions and their possible relationship with unconventional superconductivity [START_REF] Armitage | Progress and perspectives on electrondoped cuprates[END_REF], [START_REF] Johnston | The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides[END_REF], [START_REF] Flouquet | On the heavy-fermion road[END_REF], [START_REF] Von Löhneysen | Fermi-liquid instabilities at magnetic quantum phase transitions[END_REF], [START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF], [START_REF] Pfleiderer | Superconducting phases of f -electron compounds[END_REF]. Amongst these systems, URu 2 Si 2 occupies a very special place, due to the unique richness of its quantum electronic properties and the challenge to understand them [START_REF] Mydosh | Colloquium: Hidden order, superconductivity, and magnetism: The unsolved case of URu 2 Si 2[END_REF]. After now more than 30 years and hundreds of experimental and theoretical papers, discussions and controversies are still going on about the nature of the so-called 'hiddenorder' (HO) phase, which is established below the temperature T 0 = 17.5 K. Efforts have been devoted to elucidate its order parameter, but none was successful to determine it unambiguously so far. The transition at T 0 is associated with strong physical responses, such as a large jump in the heat capacity [START_REF] Palstra | Superconducting and Magnetic Transitions in the Heavy-Fermion System URu 2 Si 2[END_REF], an enhancement and a sudden gapping of intersite magnetic fluctuations [START_REF] Broholm | Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2[END_REF], [START_REF] Bourdarot | Neutron scattering studies on URu 2 Si 2[END_REF], a boost of the carrier mobility and a modification of the Fermi surface [START_REF] Ler | Electrical transport in URu 2 Si 2[END_REF], [START_REF] Bel | Thermoelectricity of URu 2 Si 2 : Giant Nernst effect in the hidden-order state[END_REF], [START_REF] Kasahara | Exotic superconducting properties in the electron-hole-compensated heavy-fermion "semimetal" URu 2 Si 2[END_REF], [START_REF] Santander-Syro | Fermi-surface instability at the 'hidden-order' transition of URu 2 Si 2[END_REF], and the opening of an electronic gap [START_REF] Schmidt | Imaging the Fano lattice to 'hidden order' transition in URu 2 Si 2[END_REF], [START_REF] Aynajian | Visualizing the formation of the Kondo lattice and the hidden order in URu 2 Si 2[END_REF]. While a small antiferromagnetic (AF) moment was observed below T 0 by neutron diffraction [START_REF] Broholm | Magnetic excitations and ordering in the heavy-electron superconductor URu 2 Si 2[END_REF], ambientpressure antiferromagnetism is now accepted to be an extrinsic property induced by crystal defects and distortions [START_REF] Niklowitz | Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism in URu 2 Si 2 Observed by Larmor Diffraction[END_REF]. From Fermi surface studies under pressure, it has been proposed that the HO has the same periodicity of wavevector k 0 = (0 0 1) than the AF phase stabilized under pressure [START_REF] Hassinger | Similarity of the Fermi Surface in the Hidden Order State and in the Antiferromagnetic State of URu 2 Si 2[END_REF]. The symmetry of the HO has also been considered: following torque [START_REF] Okazaki | Rotational Symmetry Breaking in the Hidden-Order Phase of URu 2 Si 2[END_REF] and diffraction [START_REF] Tonegawa | Direct observation of lattice symmetry breaking at the hiddenorder transition in URu 2 Si 2[END_REF] experiments, a nematic behavior in the HO phase has been proposed. However, this picture faces now a series of contradictory diffraction [START_REF] Choi | Pressure-induced rotational symmetry breaking in URu 2 Si 2[END_REF], [START_REF] Tabata | X-Ray Backscattering Study of Crystal Lattice Distortion in Hidden Order of URu 2 Si 2[END_REF], NMR [START_REF] Kambe | Odd-parity electronic multipolar ordering in URu 2 Si 2 : Conclusions from Si and Ru NMR measurements[END_REF], and thermodynamic [START_REF] Wang | Electronic nematicity in URu 2 Si 2 revisited[END_REF] experiments and the question of the symmetry remains open. Beyond experiments, many theories were proposed to describe the HO within different approaches: localized, itinerant, or dual (localized/itinerant) f-electrons, multipolar order, nematicity, spin liquid, 'hastatic' order, etc. [START_REF] Fujimoto | Spin Nematic State as a Candidate of the Hidden Order Phase of URu 2 Si 2[END_REF], [START_REF] Haule | Complex Landau-Ginzburg theory of the hidden order in URu 2 Si 2[END_REF], [START_REF] Thomas | Three-dimensional modulated spin liquid model applied to URu 2 Si 2[END_REF], [29], [START_REF] Ikeda | Emergent rank-5 nematic order in URu 2 Si 2[END_REF]. A difficulty is to evidence experimentally, in a direct and unambiguous manner, the order parameters proposed by these models.

To reveal the physics of the hidden order, an alternative route is to study how it can be destabilized by tuning external parameters [START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF]. In the HO state, gapped low-energy magnetic fluctuations peaked at the wavevectors k 0 and k 1 = (0.6 0 0) [START_REF] Broholm | Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2[END_REF], [START_REF] Bourdarot | Neutron scattering studies on URu 2 Si 2[END_REF] can be seen as precursors of long-range magnetic ordering with the same wavevectors and indicate nearby quantum phase transitions. In heavy-fermion paramagnets, such intersite magnetic fluctuations often indicate the proximity of a magnetically-ordered phase. For instance, in the textbook CeRu 2 Si 2 case quantum magnetic fluctuations with wavevector k 1 = (0.31 0 0) can be transformed into long-range magnetic order with the same wavevector by La-doping [START_REF] Knafo | Antiferromagnetic criticality at a heavy-fermion quantum phase transition[END_REF].

As well as doping, pressure and magnetic field are ideal tools to tune the electronic interactions. In URu 2 Si 2 , hydrostatic pressure [START_REF] Hassinger | Temperature-pressure phase diagram of URu 2 Si 2 from resistivity measurements and ac calorimetry: Hidden order and Fermi-surface nesting[END_REF], [START_REF] Bourdarot | Hidden order in URu 2 Si 2[END_REF], [START_REF] Amitsuka | Pressure-temperature phase diagram of the heavy-electron superconductor URu 2 Si 2[END_REF] (but also uniaxial strain [START_REF] Bourdarot | Magnetic properties of URu 2 Si 2 under uniaxial stress by neutron scattering[END_REF], and doping with Rh or Fe [START_REF] Yokoyama | Neutron Scattering Study on Competition between Hidden Order and Antiferromagnetism in U(Ru 1-x Rh x ) 2 Si 2 (x ≤0.05)[END_REF], [START_REF] Das | Chemical pressure tuning of URu 2 Si 2 via isoelectronic substitution of Ru with Fe[END_REF]) leads to a phase transition from the HO phase towards an AF state, with the wavevector k 0 and the moments aligned along the c-axis of the tetragonal crystal. At ambient pressure, under a magnetic field from 35 to 39 T applied along c, the hidden order is replaced by a spin-density wave (SDW), where the magnetic moments are ordered with the wavevector k 1 and aligned along c [START_REF] Knafo | Field-induced spindensity wave beyond hidden order in URu 2 Si 2[END_REF], [START_REF] Knafo | URu 2 Si 2 under intense magnetic fields: from hidden order to spin-density wave[END_REF]. Remarkably, experiments under combined magnetic field and pressure, in the limited ranges 16 T / 2 GPa [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], and 45 T / 1 GPa [START_REF] Jo | Field-Induced Fermi Surface Reconstruction and Adiabatic Continuity between Antiferromagnetism and the Hidden-Order State in URu 2 Si 2[END_REF], showed that a magnetic field applied to the pressure-induced AF phase induces a return into the HO phase [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], and that the SDW phase shrinks and moves to higher fields under pressure [START_REF] Jo | Field-Induced Fermi Surface Reconstruction and Adiabatic Continuity between Antiferromagnetism and the Hidden-Order State in URu 2 Si 2[END_REF]. The relative stability of these different types of order is clearly complex, and a full description of how URu 2 Si 2 evolves under combined pressure and magnetic field is needed.

Here, we benefited from the recent development of a specifically designed anvil-type cell for pulsed magnetic fields [START_REF] Braithwaite | Pressure cell for transport measurements under high pressure and low temperature in pulsed magnetic fields[END_REF], [START_REF] Settai | Development of Bridgman-Type Pressure Cell for Pulsed High Magnetic Field, Review of High Pressure Science and Technology / Koatsuryoku No[END_REF] to extract the three-dimensional (3D) magnetic field -pressure -temperature phase diagram of URu 2 Si 2 . Its magnetoresistivity was measured in magnetic fields up to 60 T combined with pressures up to 4 GPa. We find a rich and complex phase diagram indicating a subtle competition between the electronic interactions. The main features are the disappearance of the field-induced SDW phase and a squeezing out of the HO phase under high pressure. We emphasize that many of the boundaries of the 3D phase diagram are controlled by the field-and pressure-dependences of a single parameter characterizing the electronic correlations.

Results

Zero-field phase diagram

Before tackling the question of the high-field properties of URu 2 Si 2 under pressure, we recall in Figure 1(a) its zero-field (p,T) phase diagram (from data in Refs. [START_REF] Hassinger | Temperature-pressure phase diagram of URu 2 Si 2 from resistivity measurements and ac calorimetry: Hidden order and Fermi-surface nesting[END_REF], [START_REF] Pfleiderer | Pressure dependence of the magnetization of URu 2 Si 2[END_REF] and data shown in Figure S1, Supplementary Materials). The hidden-order and superconducting (SC) phases develop at ambient pressure below the temperatures T 0 = 17.5 K and T SC = 1.5 K, respectively. Superconductivity is suppressed at the critical pressure p c = 0.5 GPa, where a transition from the hidden order to long-range antiferromagnetism, delimited by the Néel temperature T N , is observed. The upper temperature scale T χ max > T N ,T 0 , at which a broad maximum in the magnetic susceptibility χ for H || c is observed, indicates a crossover to a correlated paramagnetic (CPM) regime characterized by strong magnetic correlations. For p > p c , T 0 slowly increases while T N rises steeply under pressure, and a sequence AF → HO → CPM can be induced by increasing temperature. T 0 and T N merge at the critical point (p* = 1.3 GPa, T* = 18 K), which separates the HO, AF, and CPM phases in the (p,T) phase diagram. For p > p*, the hidden order has vanished and a direct sequence AF → CPM can be induced by increasing temperature. The fact that T 0 , T N , and T χ max all increase under pressure indicates that their associated energy scales are continuously enhanced.

Ambient-pressure high-field phase diagram

At ambient pressure a magnetic field leads to the destruction of the hidden order. The HO phase is replaced by a SDW phase preceding a polarized paramagnetic (PPM) regime, whose boundary can be defined through a crossover at the onset of a large magnetization M > 1.4 µ B /U (see Ref. [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF]). The ambient pressure high-field phase diagram of URu 2 Si 2 is shown in Figures 1(c) and 4(a). The SDW phase is delimited by sharp step-like increases at µ 0 H 1 = 35 T and µ 0 H 3 = 39 T (in rising fields) in the magnetization, which are the signatures of firstorder metamagnetic transitions [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF]. Inside the SDW phase, another first-order transition at µ 0 H 2 = 37 T (in rising fields) is presumably related with a subtle change in the magnetic structure [START_REF] Knafo | Field-induced spindensity wave beyond hidden order in URu 2 Si 2[END_REF]. These boundaries are also visible in the resistivity ρ and its field-derivative ∂ρ/∂H [see Figures 2 and3(a)]. At higher temperatures, a broad maximum in the resistivity is ascribed to the metamagnetic field H m [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF], [START_REF] Kim | Magnetic Field-Induced Quantum Critical Point and Competing Order Parameters in URu 2 Si 2[END_REF]. The field H m and the temperature T χ max , at which the magnetic susceptibility also presents a broad maximum, delimit a CPM regime [START_REF] Knafo | Field-induced spindensity wave beyond hidden order in URu 2 Si 2[END_REF] similar to that of other heavy-fermion paramagnets (see review in Ref. [START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF]). The boundary of the CPM regime is not visible from ∂M/∂H versus H plots at temperatures T < T χ max , where a broad maximum at H ∂M/∂H max > H m delimits the high-field polarized regime.

When the temperature is lowered, H∂ M/∂H max and H m converge before the SDW phase develops [START_REF] Sugiyama | Metamagnetic Transition in a Heavy Fermion Superconductor URu 2 Si 2[END_REF]. Interestingly, the suppression of the 'high-temperature' correlated paramagnetism precedes that of the hidden order, indicating that the CPM regime is a precursor of the HO phase [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF].

High-field phase boundaries under pressure

We describe here the low-temperature properties of URu 2 Si 2 under combined pressure and magnetic field H || c. Figures 1(b-c) show the two-dimensional (2D) lowtemperature (p,H) and the 3D (p,H,T) phase diagrams built here, from a large set of resistivity data presented in Figures 2 and3(a), completed by data from Refs.

[32], [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], [START_REF] Pfleiderer | Pressure dependence of the magnetization of URu 2 Si 2[END_REF], [START_REF] Aoki | Field re-entrant hidden-order phase under pressure in URu 2 Si 2[END_REF]. In particular, we detail how a magnetic field leads to the destabilization of the HO, SDW and AF ground states in favor of the PPM regime.

SDW phase boundaries:

The upper boundary H 3 of the SDW phase is visible under pressures up to 1 GPa. However, no signature of H 1 can be found in our high-pressure data, possibly due to a stronger signal at the HO phase boundary H 0 . No trace of H 1 , H 2 or H 3 is seen for p ≥ 2 GPa, indicating that pressure rapidly suppresses the field-induced SDW phase.

HO phase boundary: Under pressures p = 0.6 and 1 GPa, the field-destabilization of the HO phase precedes the SDW phase, and no sharp anomaly identifies H 0 which we have placed at a kink in ∂ρ/∂H. For 2 ≤ p < 2.9 GPa, the transition at H 0 directly occurs between the HO and the PPM phases and the shape of the resistivity curve has changed. H 0 again is defined at a kink in ∂ρ/∂H. As summarized in Figure 1(b), at low temperature H 0 increases almost linearly with p, reaching 47 T at p = 2.9 GPa.

AF phase boundary: At the highest pressures p = 3.6 and 3.9 GPa of this study, a sharp step-like anomaly in ∂ρ/∂H indicates a transition of different nature than at the lower pressures. Knowing that antiferromagnetism is stabilized under pressure, we assign this anomaly to the AF boundary. The AF critical field (defined at the mid of the step in ∂ρ/∂H) equals µ 0 H c = 48 T at p = 3.6 and 3.9 GPa. A difficulty comes from the non-observation in our resistivity data of the AF→HO transition at H c in the pressure range p c ≤ p < 3.6 GPa.

This transition at H c was observed by neutron diffraction and dilatometry on stoichiometric URu 2 Si 2 under pressure [START_REF] Bourdarot | Hidden order in URu 2 Si 2[END_REF], [START_REF] Amitsuka | Pressure-temperature phase diagram of the heavy-electron superconductor URu 2 Si 2[END_REF], [START_REF] Aoki | Field re-entrant hidden-order phase under pressure in URu 2 Si 2[END_REF] and in the electrical resistivity of Fe-doped samples, for which a small orbital contribution, related to a high number of impurities, probably allowed the observation of an anomaly [START_REF] Ran | Phase diagram of URu 2-x Fe x Si 2 in high magnetic fields[END_REF]. Interestingly, the extrapolation of the low-

High-temperature effects

Figure 3 presents our resistivity data measured as function of magnetic field for a large collection of temperatures and pressures. Figure 4 shows isobar (H,T) phase diagrams constructed from our resistivity data at pressures p from 1 bar to 3.9 GPa (with complementary data from Refs. [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], [START_REF] Aoki | Field re-entrant hidden-order phase under pressure in URu 2 Si 2[END_REF]). The main features are described below. Both HO and AF critical fields H 0 and H c decrease with increasing temperature and vanish at the temperatures T 0 and T N , respectively. At all pressures, a broad maximum in ρ(H) observed at high temperatures is identified as the signature of the pseudo-metamagnetic field H m . H m corresponds to a crossover between the low-field CPM regime and a high-field paramagnetic state. For p ≤ 1 GPa, when the temperature is decreased H m ends on top of the lowtemperature SDW dome, and the strong anomalies in ρ at H 1 , H 2 , and H 3 mask that at H m .

The extrapolated low-temperature pseudo-metamagnetic field µ 0 H m (T→0) = 36.5 T lies within the SDW dome. For 2.1 ≤ p ≤ 2.9 GPa, when T is reduced, H m ends on top of the H 0 line, and the anomaly at H 0 hides that at H m too. In this pressure range, we find an extrapolated value µ 0 H m (T→0) ≈ H 0 . For p ≥ 3.6 GPa, H m is clearly decoupled from H c , but we lose again its trace at low temperatures, due to the high-field tail of the anomaly at H c .

Interestingly, µ 0 H m (T→0) increases almost linearly under pressure, from 36.5 T at ambient pressure to 51.5 T at p = 3.9 GPa. We further find that the CPM regime, restricted to nonzero temperatures for p < p**, extends down to the lowest temperatures in a narrow field window H c < H < H m (T→0) for p > p** [see Figure 1(b)]. This decoupling of H c and H m indicates the nearby quantum antiferromagnetic instability, as already observed in heavyfermion antiferromagnets [START_REF] Knafo | Threedimensional critical phase diagram of the Ising antiferromagnet CeRh 2 Si 2 under intense magnetic field and pressure[END_REF], [START_REF] Aoki | Decoupling between fieldinstabilities of antiferromagnetism and pseudo-metamagnetism in Rh-doped CeRu 2 Si 2 Kondo lattice[END_REF].

Orbital contribution to the resistivity

URu 2 Si 2 being a compensated metal, its low-temperature high-field resistivity (in high-quality single crystals, as those investigated here) is controlled by the cyclotron motion of the carriers. For an isotropic Fermi surface, such orbital contribution to the resistivity is expected to diverge as H 2 in the high-field limit ω c τ ≫ 1, where ω c is the cyclotron frequency and τ is the relaxation time. Deviations from this behavior are observed in URu 2 Si 2 under a magnetic field H || c. At ambient pressure, the destruction of the hidden order at high temperature or in a high magnetic field is accompanied by a reduction of the carrier mobility and the orbital contribution to ρ(H) vanishes [START_REF] Knafo | URu 2 Si 2 under intense magnetic fields: from hidden order to spin-density wave[END_REF], [START_REF] Jo | Field-Induced Fermi Surface Reconstruction and Adiabatic Continuity between Antiferromagnetism and the Hidden-Order State in URu 2 Si 2[END_REF], [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF], [START_REF] Scheerer | Fermi surface in the hidden-order state of URu 2 Si 2 under intense pulsed magnetic fields up to 81[END_REF]. Fermi surface reconstructions inside the HO phase [START_REF] Shishido | Possible Phase Transition Deep Inside the Hidden Order Phase of Ultraclean URu 2 Si 2[END_REF], [START_REF] Altarawneh | Sequential Spin Polarization of the Fermi Surface Pockets in URu 2 Si 2 and Its Implications for the Hidden Order[END_REF], [START_REF] Harrison | Magnetic field-tuned localization of the 5f-electrons in URu 2 Si 2[END_REF], [START_REF] Aoki | High-Field Fermi Surface Properties in the Low-Carrier Heavy-Fermion Compound URu 2 Si 2[END_REF], [START_REF] Pourret | Fermi Surface Reconstruction inside the Hidden Order Phase of URu 2 Si 2 Probed by Thermoelectric Measurements[END_REF] make this orbital contribution continuously suppressed over a field-range of width ≃ 5 T, leading to a broad and pronounced maximum of ρ at H ρ max,LT < H 0 .

Figure 2 shows that the maximum in ρ is progressively weakened under pressures p ≤ 3.6 GPa, and then almost suppressed at p = 3.9 GPa. At p = 3.9 GPa, the maximum in ρ is replaced by a broad plateau in ρ. This change of behavior is emphasized in a plot of ∂ρ/∂H versus H, where a minimum at H ∂ρ/∂H min for p ≤ 3.6 GPa is replaced a continuous decrease of ∂ρ/∂H at p = 3.9 GPa. The fact that the maximum at H ρ max,LT survives at p = 3.6 GPa, where the field-induced hidden order is squeezed out, indicates that a strong orbital contribution, and possible associated Fermi surface reconstructions, are present in the AF phase. However, we cannot fully exclude an alternative picture where this maximum would be a signature of the HO phase, indicating then a possible coexistence of the AF and HO phases under combined fields and pressures.

Discussion

Importance of a single parameter δ

A striking feature of the 3D phase diagram of URu 2 Si 2 is the high number of competing electronic states: two magnetically-ordered phases (antiferromagnetism and spindensity wave) and two magnetic regimes (correlated and polarized paramagnetisms), in addition to the HO and SC phases. Beyond this apparent complexity, we observe simple general trends: the fall of the main energy scales under magnetic field and their increase under pressure. As shown in Figure 5 The quasi-proportionality between these different energy scales is confirmed by the plot of their ratios presented in Figure 6. Figure 6(a) shows that the ratio T χ max / T 0 is almost invariant under magnetic field and pressure. This plot indicates that the variations of the higher temperature scale T χ max drive those of T 0 , and thus that the fall or stabilization of the CPM regime drives that of the HO phase. As shown in Figure 6(a), the ratio R CPM = T χ max / (µ 0 H m ) of the CPM regime boundaries is also invariant under pressure. Its value is close to the almost universal ratio R CPM = T χ max / (µ 0 H m ) ≃ 1 K/T observed for a large number of heavy-fermion paramagnets and indicates a conventional behavior [START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF]. Similarly to R CPM introduced for the CPM regime, we define the characteristic ratio R HO = T 0 / (µ 0 H 0 ) for the HO phase. Figure 6(c) shows that R HO is constant under pressure, confirming that T 0 and H 0 increase in a proportional manner. For p > p*, the proportionality of T N with T χ max , H 0 , and Similar conclusion was found for a large number of heavy-fermion antiferromagnets [START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF], [START_REF] Knafo | Threedimensional critical phase diagram of the Ising antiferromagnet CeRh 2 Si 2 under intense magnetic field and pressure[END_REF].

H
At ambient pressure, the temperature-dependent Grüneisen parameters reported in Ref. [START_REF] Flouquet | Trends in Heavy Fermion Matter[END_REF] also indicate that the parameter δ is not sufficient to describe all properties of URu 2 Si 2 .

However, a surprise here is to find that the HO boundaries T 0 and H 0 , but also the AF Néel temperature T N for p > p*, are proportional to T χ max and H m , and that their pressure-and magnetic-field-variations are driven by those of the same parameter δ. This, together with the fact that T N for p > p* is a high-pressure prolongation of T 0 (see Figure 1), indicates that the antiferromagnetic and hidden orders have some common magnetic nature. Indeed, longrange order in the AF phase and gapped excitations in the HO phase have been observed with the same magnetic wavevector k 0 [START_REF] Bourdarot | Hidden order in URu 2 Si 2[END_REF], [START_REF] Amitsuka | Pressure-temperature phase diagram of the heavy-electron superconductor URu 2 Si 2[END_REF], [START_REF] Villaume | Signature of hidden order in heavy fermion superconductor URu 2 Si 2 : Resonance at the wave vector Q 0 =(1,0,0)[END_REF]. An interplay between the magnetic and Fermi surface properties was also emphasized by the similar Fermi surfaces observed in the two states, for which a simple tetragonal symmetry has been proposed [START_REF] Hassinger | Similarity of the Fermi Surface in the Hidden Order State and in the Antiferromagnetic State of URu 2 Si 2[END_REF], [START_REF] Bareille | Momentum-resolved hidden-order gap reveals symmetry breaking and origin of entropy loss in URu2Si2[END_REF].

New constraints for a microscopic description

Two models proposed a description of the field-induced reentrance of the hidden order in URu 2 Si 2 under pressure: i) a phenomenological Landau-Ginzburg theory based on LDA+DMFT calculation, where the hidden order was identified as a hexadecapole with periodicity k 0 , [START_REF] Haule | Complex Landau-Ginzburg theory of the hidden order in URu 2 Si 2[END_REF], and a spin-liquid model based on correlations with wavevector k 0 [START_REF] Thomas | Three-dimensional modulated spin liquid model applied to URu 2 Si 2[END_REF].

A question is whether these models, as well as other propositions for the HO phase [START_REF] Fujimoto | Spin Nematic State as a Candidate of the Hidden Order Phase of URu 2 Si 2[END_REF], [29], [START_REF] Ikeda | Emergent rank-5 nematic order in URu 2 Si 2[END_REF], could be adjusted to describe the full 3D phase diagram of URu 2 Si 2 . Although the purpose of discriminating the different existing theories is beyond the scope of this paper, the phase diagram reported here imposes new constraints. We detail below these constraints.

The with increased doping and a field-induced reentrance of the hidden order [START_REF] Das | Chemical pressure tuning of URu 2 Si 2 via isoelectronic substitution of Ru with Fe[END_REF], [START_REF] Ran | Phase diagram of URu 2-x Fe x Si 2 in high magnetic fields[END_REF], [START_REF] Ran | Phase diagram and thermal expansion measurements on the system URu 2-x Fe x Si 2[END_REF]. A theory aiming to describe the hidden order in URu 2 Si 2 would need to reproduce the various features in its 3D phase diagram, i.e., the way the HO phase competes with other ordered (AF, SDW) phases or paramagnetic (CPM, PPM) regimes.

Although URu 2 Si 2 has a rich and complex 3D electronic phase diagram, we have seen that many of its boundaries (T χ max , T 0 , H m , H 0 , and T N for p > p*) vary proportionally and are controlled by the pressure-or magnetic-field variation of a unique parameter δ. We have discussed that, within a Fermi liquid description of the CPM regime, the effective mass m*, possibly controlled by magnetic fluctuations with wavevector k 1 [START_REF] Broholm | Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2[END_REF], [START_REF] Bourdarot | Neutron scattering studies on URu 2 Si 2[END_REF], could be a realization of δ. However, the magnetic fluctuations are strongly modified in the HO phase, and a single parameter is not sufficient to describe the gapped excitations reported at the two wavevectors k 0 and k 1 [START_REF] Bourdarot | Neutron scattering studies on URu 2 Si 2[END_REF], [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], [START_REF] Villaume | Signature of hidden order in heavy fermion superconductor URu 2 Si 2 : Resonance at the wave vector Q 0 =(1,0,0)[END_REF]. The relative roles played by the correlations with the wavevector k 1 in the CPM regime, as well as the sharp and inelastic fluctuations with the wavevectors k 0 and k 1 in the HO phase, might be clarified. How do they contribute to the mass enhancement? How these correlations evolve and drive the phase boundaries under pressure and magnetic field?

For such purpose, a description of the Fermi surface and its evolution under combined pressures and magnetic fields is important. From Shubnikov-de-Haas experiments, a cascade of Fermi surface reconstructions under magnetic field was reported [START_REF] Knafo | URu 2 Si 2 under intense magnetic fields: from hidden order to spin-density wave[END_REF], [START_REF] Jo | Field-Induced Fermi Surface Reconstruction and Adiabatic Continuity between Antiferromagnetism and the Hidden-Order State in URu 2 Si 2[END_REF], [START_REF] Scheerer | Fermi surface in the hidden-order state of URu 2 Si 2 under intense pulsed magnetic fields up to 81[END_REF], [START_REF] Shishido | Possible Phase Transition Deep Inside the Hidden Order Phase of Ultraclean URu 2 Si 2[END_REF], [START_REF] Altarawneh | Sequential Spin Polarization of the Fermi Surface Pockets in URu 2 Si 2 and Its Implications for the Hidden Order[END_REF], [START_REF] Harrison | Magnetic field-tuned localization of the 5f-electrons in URu 2 Si 2[END_REF], while no Fermi-surface reconstruction was observed under pressure at low field [START_REF] Hassinger | Similarity of the Fermi Surface in the Hidden Order State and in the Antiferromagnetic State of URu 2 Si 2[END_REF]. Fermi-surface-driven changes of RKKY magnetic exchange interactions J ex (k) may lead to the appearance of long-range magnetic order, either antiferromagnetism with wavevector k 0 or spin-density wave with wavevector k 1 , under pressure and magnetic field, respectively. Within this picture, pressure-enhanced exchange J ex (k 0 ) would result in antiferromagnetic order with wavevector k 0 , while magnetic-fieldenhanced exchange J ex (k 1 ) would lead to a spin-density wave with wavevector k 1 . These magnetic orders could be accompanied by Fermi surface nestings with their respective wavevectors k 0 and k 1 . The gapped magnetic excitations with the wavevectors k 0 and k 1 reported at ambient pressure and zero-field [START_REF] Broholm | Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2[END_REF], [START_REF] Bourdarot | Neutron scattering studies on URu 2 Si 2[END_REF] could be related to inelastic nestings with the same wavevectors of the electronic band. To our knowledge, the origin of the RKKY interactions J ex (k 0 ) and J ex (k 1 ) was not modeled so far. Understanding how these exchange parameters and the related magnetic excitations evolve under pressure and magnetic field would allow identifying the parameter δ and describing the 3D phase diagram reported here.

This could constitute a decisive step in the search for a consensus about the nature of the hidden order.

Methods

URu 2 Si 2 single crystals measured here were grown by the Czochralski technique in a tetra-arc furnace. Their electrical resistivity (contacts along a) of samples #A and #B has been measured under magnetic fields up to 58 T applied along c combined with pressures up to 3.9 GPa and temperatures down to 1.5 K. The residual resistivity ratio RRR = ρ x,x (300 K)/ ρ x,x (2 K), defined at zero field by the ratio of the resistivities at 300 K and 2 K, i.e., just above the superconducting temperature, was equal to ≃ 110 for both samples #A and #B, indicating their high quality. Resistivity was measured using the four-contact technique, with an excitation current of 10 mA at a frequency of ≃ 50-70 kHz. A Bridgman-type pressure cell specially designed for the pulsed fields has been used. To avoid significant heating by eddy currents, ceramic anvils and a pyrophilit gasket were used in the cell, whose body is made of MP35N. The data presented here correspond to the rise of the field pulses, where maximal heating is estimated, for 58-T pulses, to be less that 0.1 K at temperatures T ≤ 4.2 K, close to 1-1.5 K at temperatures from 5 K to 20 K, and negligible at higher temperatures. For lowerfield pulses, the heating effects are reduced. We note that, in addition to heating effects by eddy-current generated in the body of the cell, small deviations from an isothermal limit due to magnetocaloric cooling effect cannot be excluded. Magnetocaloric effects can be observed in large samples of several-mm dimensions under pulsed magnetic fields, for which an adiabatic limit allows the sample temperature to change. Here, thin samples of thickness of typically 50 µm were measured and long-duration pulse-fields (rise of 55 ms, total duration > 300 ms) were used, which constitute favorable conditions for a quasi-isothermal limit.

Pressure was estimated by measuring the resistance of a lead gage simultaneously to the resistance of the URu 2 Si 2 sample. More information about the pressure cell setup can be found in two technical papers [START_REF] Braithwaite | Pressure cell for transport measurements under high pressure and low temperature in pulsed magnetic fields[END_REF], [START_REF] Settai | Development of Bridgman-Type Pressure Cell for Pulsed High Magnetic Field, Review of High Pressure Science and Technology / Koatsuryoku No[END_REF]. Complementary resistivity measurements have been made on a third sample (sample #C, RRR = 60) under pressures up to 4 GPa in steady fields up to 14 T using a Physical Properties Measurements System from Quantum Design. [32], [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], [START_REF] Pfleiderer | Pressure dependence of the magnetization of URu 2 Si 2[END_REF], [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF], [START_REF] Aoki | Field re-entrant hidden-order phase under pressure in URu 2 Si 2[END_REF] (data points from these works and their references are indicated in the Figure ) were used to construct these phase diagrams. 1GPa, (c) 2.1 GPa, (d) 2.9 GPa, (e) 3.6 GPa, and (f) 3.9 GPa.. PM, CPM, and PPM are the high-temperature, the low-temperature correlated, and the high-field polarized paramagnetic regimes, respectively, HO and SC the hidden-order and superconducting phases, respectively, AF the antiferromagnetic state, and SDW the spin-density wave state. In addition to data from this work, data from Refs. [START_REF] Hassinger | Temperature-pressure phase diagram of URu 2 Si 2 from resistivity measurements and ac calorimetry: Hidden order and Fermi-surface nesting[END_REF], [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF], [START_REF] Pfleiderer | Pressure dependence of the magnetization of URu 2 Si 2[END_REF], [START_REF] Aoki | Field re-entrant hidden-order phase under pressure in URu 2 Si 2[END_REF] were used to construct these phase diagrams. vanished. We note that, due to higher noise, this low-temperature decoupling of H 0 and H 1 was not observed in our previous resistivity studies [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF], [START_REF] Scheerer | Fermi surface in the hidden-order state of URu 2 Si 2 under intense pulsed magnetic fields up to 81[END_REF]. Figure S3 (c) shows that the SDW phase is a well-defined dome separated from the hidden-order phase, in agreement with a proposition made in Ref. [START_REF] Mydosh | High magnetic field behavior of strongly correlated uranium-based compounds[END_REF]. At temperatures T ≥ 10 K, the anomaly at H 0 turns into a minimum in ∂ρ/∂H, which is observed up to the temperature T 0 = 17.5 K, above which the hidden-order phase is destroyed.

At p = 1 GPa, the HO and AF boundaries are decoupled and anomalies in ∂ρ/∂H at T ≤ 17 K are observed at H 0 : by continuity with the ambient pressure data, we identify H 0 at a kink in ∂ρ/∂H at low-temperatures, which is replaced by a sharp minimum in ∂ρ/∂H at higher temperatures. At p = 3.6 and 3.9 GPa, the ground state is AF, there is no HO phase at zero-field, and anomalies in ∂ρ/∂H at T ≤ 21 and 24 K, respectively, are associated with H c :

we identify H c at the mid-step in ∂ρ/∂H at low-temperatures, which is replaced by a sharp minimum in ∂ρ/∂H at higher temperatures. At the intermediate pressures p = 2.1 and 2.9

GPa, a field-induced decoupling of the HO boundary H 0 and the AF boundary H c is expected from previous experiments [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF]. However, at temperatures T ≥ 10 K both transitions at H 0 and H c induce a sharp and negative peak in ∂ρ/∂H and we cannot distinguish them (for this reason the characteristic fields of these anomalies are denoted by H 0,c in Figure S2). As shown in Figure S3, anomalies are observed H 0 , H 2 and H 3 , but not at H 1 , in the resistivity of sample #B at p = 0.6 GPa. A signature of the upper boundary H 3 of the SDW phase is observed at p = 1 GPa, and no indication for a spin-density wave phase is found for p ≥ 2.1

GPa. Since we could not observe the antiferromagnetism-to-HO boundary H c under pressures p < p x , H c data from Ref. [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF] were used to construct the phase diagrams. As well, to offer a complete phase diagram, the superconducting boundary from Ref. [START_REF] Aoki | Field re-entrant hidden-order phase under pressure in URu 2 Si 2[END_REF] was added to Figure S3(c).

At the onset of the high-field PPM phase, the HO and AF critical fields H 0 and H c were identified in our low-temperature resistivity data. However, we could not observe the low-temperature AF→HO boundary H c nor differentiate the H 0 and H c lines at high temperature and the H c versus T lines plotted in Figures 4(b-d) were taken from Ref. [START_REF] Aoki | Field Reentrance of the Hidden Order State of URu 2 Si 2 under Pressure[END_REF] (thermal expansion).

Figures S2(b,d) highlight that the appearance of a step in ∂ρ/∂(µ 0 H) at H c almost coincides with the disappearance of the broad anomalies at H ρ max,LT and H∂ ρ/∂H min , a coexistence of all these anomalies being observed at p = 3.6 GPa. The crossover field H ρ max,LT increases with p, and the associated maximal value of ρ decreases and is observed up to p = 3.6 GPa, before being replaced by a broad plateau at p = 3.9 GPa. This is accompanied by the disappearance of a broad minimum in ∂ρ/∂(µ 0 H) at the field H ∂ρ/∂H min , where the slope in ρ(H) is minimal.

Figure S7 shows that the field scales H 0 , H m (T→0), H ρ max,LT and H∂ ρ/∂H min increase in a similar linear manner under pressure, suggesting their close relationship.

Figure S8 shows low-temperature ρ versus H data at ambient pressure from different samples: sample #A studied here, samples #1 and #2 from Refs. [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF], [START_REF] Scheerer | Fermi surface in the hidden-order state of URu 2 Si 2 under intense pulsed magnetic fields up to 81[END_REF], sample #R from

Ref. [START_REF] Ran | Phase diagram of URu 2-x Fe x Si 2 in high magnetic fields[END_REF] and sample #L from Ref. [START_REF] Levallois | On the destruction of the hidden order in URu 2 Si 2 by a strong magnetic field[END_REF]. While the resistivity is almost sample-independent in fields H > H 1 , a strong sample-dependence in fields H < H 1 is attributed to strong orbital contribution to the resistivity inside the HO phase, due to a large carrier mobility. A fall of ρ observed for all samples in fields µ 0 H > µ 0 H ρ max,LT = 29 T is attributed to a Fermi surface reconstruction inside the HO phase. A kink is observed at a lower field of ≃ 25 T in sample #1 at T = 100 mK (and at ≃ 24 T at T = 1.4 K), ≃ 28 T in sample #2 at T = 100 mK (but not at T = 1.4 K) [START_REF] Scheerer | Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu 2 Si 2[END_REF], [START_REF] Scheerer | Fermi surface in the hidden-order state of URu 2 Si 2 under intense pulsed magnetic fields up to 81[END_REF], ≃ 25 T in sample #R at T = 380 mK [START_REF] Ran | Phase diagram of URu 2-x Fe x Si 2 in high magnetic fields[END_REF], but neither in sample #A measured here at 1.5 K nor in sample #L [START_REF] Levallois | On the destruction of the hidden order in URu 2 Si 2 by a strong magnetic field[END_REF]. Such kink was initially reported by Shishido et al. and was interpreted as the signature of a Fermi surface reconstruction [START_REF] Shishido | Possible Phase Transition Deep Inside the Hidden Order Phase of Ultraclean URu 2 Si 2[END_REF]. The large enhancement of the high-field resistivity is induced by an orbital motion of the conduction electron, and is directly related to the sample quality. Indeed, large residual-resistivity-ratio sample generally have a higher crystal quality and a higher orbital contribution to the resistivity. The reasons why different -or no -kinks are observed in the different samples are not understood yet. They could result from different electrical contact directions.

Alternatively, these kinks could result from the quenching of the non-intrinsic AF moment reported at ambient pressure [START_REF] Broholm | Magnetic excitations and ordering in the heavy-electron superconductor URu 2 Si 2[END_REF], [START_REF] Niklowitz | Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism in URu 2 Si 2 Observed by Larmor Diffraction[END_REF], due to internal sample distortions and inhomogeneities. Further high-pressure and high-field studies on different samples of different qualities are needed to understand the kink observed in some samples at ambient pressure, but also to determine a criterion at the AF→HO boundary H c for pressures p > p c .

  pressure H c line (from [48]) ends at a critical point (p** ≃ 3.25 GPa, µ 0 H** ≃ 48 T) where the low-pressure H 0 line transforms into the high-pressure H c line. The low-temperature (p,H) phase diagram shown in Figure 1 (b) indicates that the field-induced HO phase has vanished beyond the critical point, i.e., under pressures p > p**.

  (a), a plot of the magnetic-field-variation of T χ max and T 0 normalized by their zero-field values at ambient pressure shows that both quantities decrease and are almost proportional under magnetic field. Similarly, Figure5(b) presents a plot of the pressure variation of normalized values of T χ max , T 0 , T N (for p > p*), H 0 , and H m , which indicates that they all increase and are quasi-proportional under pressure.

  m is shown i) by the constant value of T χ max / T N , which reaches a value ≃ 3.5 similar to that of T χ max / T 0 for p < p* [Figure6(b)], and ii) by the constant values of T N / (µ 0 H 0 ) and T N / (µ 0 H m ) for p > p* and p > p**, respectively, both reaching the same value ≃ 0.5 K/T thanR HO = T 0 / (µ 0 H 0 ) for p < p* [Figure 6(c)].Their proportionality indicate that the pressure and magnetic field-variations of T χ max , T 0 , T N (for p > p*), H 0 , and H m are controlled by those of a unique parameter, which we label δ. We discuss below what this parameter δ could be. In most of heavy-fermion paramagnets, the magnetic susceptibility χ (in a field applied along the easy magnetic axis) nearly saturates at temperatures smaller below T χ max and a Fermi liquid description is made within a first approximation. A naïve picture is to identify T χ max as the Fermi liquid temperature T F ∝ 1/m* of the heavy-fermion regime with an effective mass m*. In such description, one parameter is controlling a large set of low temperature properties, as the heat capacity C p and the magnetic susceptibility which verify C p /T ∝ χ ∝ m*. From the relationship R CPM = T χ max / (µ 0 H m ) ≃ 1 K/T evidenced for a large set of heavy-fermion paramagnets[START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF], it comes out that m* ∝ 1 / T χ max ∝ 1 / H m . In addition, T χ max and H m are almost proportional to the quasielastic line width Γ of intersite magnetic fluctuations in several heavy-fermion paramagnets, including URu 2 Si 2[START_REF] Aoki | Heavy fermions in a high magnetic field[END_REF]. Thereafter, the effective mass m* in URu 2 Si 2 may be controlled by the magnetic fluctuations with wavevector k 1 which develop in the CPM regime[START_REF] Broholm | Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2[END_REF],[START_REF] Bourdarot | Neutron scattering studies on URu 2 Si 2[END_REF]. Within this Fermi-liquid picture, the parameter δ driving the proportionality between the multiple phase boundaries in URu 2 Si 2 could be the effective mass m*. Of course, beyond this simple approach a more subtle description and several parameters are needed to describe all properties of the phase diagram.All boundaries of the 3D phase diagram of URu 2 Si 2 are not fully controlled by the parameter δ. A single energy scale is not sufficient to explain why the hidden order is replaced by antiferromagnetism under pressure, and the situation concerning the AF phase for p < p* is complex. As shown in Figure6(b), the strong variation of T χ max / T N for p < p* shows that T χ max and T N are not proportional. Figure 6(d) further indicates that the ratio R AF ≃ T N / (µ 0 H c ) characteristic of the AF boundaries varies strongly under pressure. It decreases with p for p < p*, passes thought a minimum, and finally slightly increases for p ≳ p*. This implies that several parameters are needed to relate the pressure-variations of T N and H c .

Figure 1 .

 1 Figure 1. Electronic phase diagram of URu 2 Si 2 under pressure and magnetic field H || c. (a) Temperature -pressure phase diagram at zero field, (b) magnetic field -pressure phase diagram in the limit T → 0, (c) temperature -pressure -magnetic field phase diagram. PM, CPM, and PPM are the high-temperature, the low-temperature correlated, and the high-field polarized paramagnetic regimes, respectively, HO and SC the hidden-order and superconducting phases, respectively, AF the antiferromagnetic state, and SDW the spindensity wave state. In addition to data from this work, data from Refs.

Figure 2 .

 2 Figure 2. Low-temperature resistivity ρ and its derivative ∂ρ/∂H of URu 2 Si 2 versus magnetic field H || c at different pressures. (a) ρ versus H and (b) ∂ρ/∂H versus H at different pressures p from 1 bar to 3.9 GPa, at T = 2.2 K.

Figure 3 .

 3 Figure 3. Resistivity ρ of URu 2 Si 2 versus magnetic field H || c at different temperatures and pressures. ρ versus H at temperatures T from 2.2 to 65 K, at the pressures p = (a) 1 bar, (b) 1GPa, (c) 2.1 GPa, (d) 2.9 GPa, (e) 3.6 GPa, and (f) 3.9 GPa. The insets present hightemperatures data while the main graphs present low-temperature data.

Figure 4 .

 4 Figure 4. Magnetic field-temperature phase diagrams of URu 2 Si 2 under pressure and magnetic field H || c. Magnetic phase diagrams obtained at the pressures p = (a) 1 bar, (b)

Figure 5 .

 5 Figure 5. Field-and pressure-variations of normalized characteristic temperatures and magnetic fields. (a) Plot of normalized values of T χ max and T 0 versus H, (b) plot of normalized values of T χ max , T 0 , T N , H 0 , and H m versus p.

Figure 6 .

 6 Figure 6. Field-and pressure-variations of characteristic temperature and magneticfield ratios. Plots of (a) T χ max / T 0 versus H and p, (b) T χ max / T N versus p, (c) R CPM = T χ max / (µ 0 H m ), R HO = T 0 / (µ 0 H 0 ), T N / (µ 0 H 0 ), and T N / (µ 0 H m ) versus p, (d) R AF ≃ T N / (µ 0 H c ) versus p. T χ max is the temperature at which the magnetic susceptibility is maximal. H m is the metamagnetic field. T 0 and H 0 are the boundaries of the hidden-order phase. T N and H c are the boundaries of the antiferromagnetic phase.

Figure

  Figure S1 shows ρ and ∂ρ/∂T versus T data on sample #C at zero field and different pressures up to 4 GPa. The critical temperatures T 0 and T N are extracted for p < p* and p > p*, respectively, at a sharp minimum of ∂ρ/∂T.

Figures

  Figures S2, S3(a,b,d,e), S4(a,b,d,e), S5(a,b,d,e), and S6(a,b) present ρ and ∂ρ/∂Hversus H data measured for two samples (samples #A and #B) for a large set of pressures p from 1 bar to 3.9 GPa and temperatures T from 2.2 K to 65 K. These data were used to extract the phase diagrams shown in FiguresS3(c,f), S4(c,f), S5(c,f), and S6(c).We note that, for sample #A, the measurements at ambient pressure were done using different electric contacts than the measurements under pressure. Below we describe how the different boundaries have been extracted.

Figure S5 .

 S5 Figure S5. Resistivity ρ and its derivative ∂ρ/∂H versus magnetic field, and the resulting temperature-magnetic field phase diagrams of URu 2 Si 2 (sample #A) at the pressures p = 3.6 and 3.9 GPa, in a magnetic field H || c.

Figure S6 .

 S6 Figure S6. Resistivity ρ, its derivative ∂ρ/∂H versus magnetic field, and the resulting temperature-magnetic field phase diagrams of URu 2 Si 2 (sample #B) at p = 0.6 GPa, in a magnetic field H || c.

  main results of our work are the observed suppressions of the field-induced SDW state under moderate pressure and of the field-induced HO state under high pressure. A critical point at (p** ≃ 3.25 GPa, µ 0 H** ≃ 48 T) can be defined at the crossing of the H 0 line observed for p < p** and the decoupled H c and H m lines observed for p > p**. This point (p**,H**) lies just on the linear extrapolation of the low pressure H c transition and separates four states: the AF and HO phases and the CPM and PPM regimes. Recent studies on Fedoped URu 2 Si 2 reported a similar phase diagram, with a strengthening of antiferromagnetism

Acknowledgments

We acknowledge Jacques Flouquet for discussions and critical reading of the paper, and Sébastien Burdin for discussions. The work at the LNCMI was supported by the 'Programme Investissements d' Avenir' under the project NEXTREME / NEXT (program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT). We acknowledge the Propulse Program, the Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers from JSPS (R2705), and the KAKENHI program (JP15H05882, JP15H05884, JP15K21732, JP19H00646,JP15H05745).

SUPPLEMENTARY MATERIALS

Squeezing out field-induced reentrant hidden-order in URu 2 Si 2 W. Knafo 1 , S. Araki 2 , G. Lapertot 3 , D. Aoki 3,4 , G. Knebel 3 , D. Braithwaite