Laurie Herviou

Fanny Izard

Ouissem Karmous-Gadacha

Claire Gourzones

Celine Bellanger

Eva Desmedt

Anqi Ma

Laure Vincent

Guillaume Cartron

Karin Vanderkerken

Jin Jian

Elke De Bruyne

Charlotte Grimaud

Eric Julien
email: eric.julien@inserm.fr

Jérôme Moreaux
email: jerome.moreaux@igh.cnrs.fr

Targeting the methyltransferase SETD8 impairs tumor cell survival and overcomes drug resistance independently of p53 status in multiple myeloma

SUMMARY

Multiple myeloma (MM) is a malignancy of plasma cells that largely remains incurable.

The search for new therapeutic targets is therefore essential. Here we show that a higher expression of the lysine methyltransferase SETD8, which is responsible for histone H4K20 mono-methylation, is an adverse prognosis factor associated with a poor outcome in two cohorts of newly diagnosed patients. Remarkably, primary malignant plasma cells are particularly addicted to SETD8 activity. Indeed, pharmacological inhibition of this enzyme by the chemical compound UNC0379 demonstrated a significantly higher toxicity in MM cells compared to normal cells from the bone marrow microenvironment. Moreover, RNA sequencing and functional studies revealed that SETD8 inhibition induces a mature non-proliferating plasma cell signature and an activation of the p53 canonical pathway, which together leads to an impairment of myeloma cell proliferation and survival. However, UNC0379 treatment triggers a deadly level of replicative stress in p53 deficient MM cells, indicating that the cytotoxicity associated with SETD8 inhibition is independent of the p53 status. Consistent with this, the combination of UNC0379 with the conventional cytotoxic agent melphalan strongly enhances DNA damage and overcomes drug resistance in myeloma cells. Thus, targeting SETD8 could be of therapeutic interest to improve MM treatment in highrisk patients independently of the p53 status.

INTRODUCTION

Multiple Myeloma (MM) is a cancer of terminally differentiated plasma cells characterized by bone destruction, renal failure, and anemia [START_REF] Palumbo | Multiple myeloma[END_REF] . It is the second most common hematological malignancy after non-Hodgkin lymphoma [START_REF] Siegel | Cancer statistics[END_REF] . Over the past 15 years, several advances in treatments have led to a significantly higher survival of intensively treated patients. This involves a large panel of therapeutic agents, including immunomodulatory drugs and proteasome inhibitors, in combination with autologous stem cell transplantation, alkylating agents (melphalan) and glucocorticoids [START_REF]Multiple myeloma: 2018 update on diagnosis, risk--stratification, and management[END_REF] .

Unfortunately, despite the recent progress in MM treatments, most patients will ultimately relapse and develop drug resistance. This cancer thus remains incurable for the majority of patients.

In addition to a wide panel of genetic mutations, recent studies have pinpointed that epigenetic alterations, including aberrant DNA and histone methylation, might be also important players in multiple myeloma development [START_REF] Smedt | The Epigenome in Multiple Myeloma: Impact on Tumor Cell Plasticity and Drug Response[END_REF] . These recent findings could illuminate new mechanisms central to the genesis of multiple myeloma and offer the possibility to reveal novel approaches and targets for effective therapeutic intervention.

For example, the inhibition of the histone H3K27 methyltransferase EZH2 has recently emerged as a potential strategy for the treatment of myeloma [START_REF] Herviou | PRC2 targeting is a therapeutic strategy for EZ score defined high--risk multiple myeloma patients and overcome resistance to IMiDs[END_REF] . Moreover, classic epigenetic modulating agents, such as histone decatylase inhibitors and DNA methyltransferase inhibitors, are already tested in as monotherapy or in combination with conventional anti-MM agents [START_REF] Bruyer | DNMTi/HDACi combined epigenetic targeted treatment induces reprogramming of myeloma cells in the direction of normal plasma cells[END_REF][START_REF] Sivaraj | Panobinostat for the management of multiple myeloma[END_REF] . However, the occurrence of important side effects and the appearance of resistance to these drugs increase the need to identify novel epigenetic targets in multiple myeloma and evaluate their pre-clinical perspective. SETD8 (also known as SET8, PR-Set7, KMT5A) has been identified as the epigenetic enzyme responsible for the mono-methylation of histone H4 at lysine 20 (H4K20me1) [START_REF] Beck | PR--Set7 and H4K20me1: at the crossroads of genome integrity, cell cycle, chromosome condensation, and transcription[END_REF] . SETD8 and H4K20me1 are naturally increased during mitosis and play a critical role in chromatin compaction, gene regulation and cell-cycle progression . In addition, SETD8 could induce the methylation of non-histone proteins, such as the replication factor PCNA and the tumor suppressor p53 [START_REF] Takawa | Histone lysine methyltransferase SETD8 promotes carcinogenesis by deregulating PCNA expression[END_REF][START_REF] Shi | Modulation of p53 function by SET8--mediated methylation at lysine 382[END_REF] . While SETD8-mediated methylation of p53 inhibits apoptosis [START_REF] Shi | Modulation of p53 function by SET8--mediated methylation at lysine 382[END_REF] , PCNA methylation by SETD8 might enhance the interaction with the Flap endonuclease FEN1 and promote cell proliferation [START_REF] Takawa | Histone lysine methyltransferase SETD8 promotes carcinogenesis by deregulating PCNA expression[END_REF] .

Consistent with this, the overexpression of SETD8 has been reported in many different solid tumors [START_REF] Huang | Monomethyltransferase SETD8 regulates breast cancer metabolism via stabilizing hypoxia--inducible factor 1α[END_REF][START_REF] Veo | Combined functional genomic and chemical screens identify SETD8 as a therapeutic target in MYC--driven medulloblastoma[END_REF][START_REF] Liao | Histone methyltransferase KMT5A gene modulates oncogenesis and lipid metabolism of papillary thyroid cancer in vitro[END_REF][START_REF] Hou | SET8 induces epithelial-mesenchymal transition and enhances prostate cancer cell metastasis by cooperating with ZEB1[END_REF] and pharmacological inhibition of SETD8 is sufficient to activate the p53 pro-apoptotic program in neuroblastoma cell lines [START_REF] Veschi | Epigenetic siRNA and Chemical Screens Identify SETD8 Inhibition as a Therapeutic Strategy for p53 Activation in High--Risk Neuroblastoma[END_REF] . This has suggested that this enzyme could be an attractive target to rescue p53 functions in cancers displaying a low incidence of p53 genetic alterations, as it is the case at early stages in multiple myeloma [START_REF] Teoh | p53 abnormalities and potential therapeutic targeting in multiple myeloma[END_REF] . However, the role of SETD8 and its incidence in the development of multiple myeloma or any hematological malignancies is not known.

Here, we provide evidence that malignant plasma cells are addicted to SETD8 expression, which is associated with a poor outcome independently of changes in the steady state level of histone H4K20me1. Although inducing p53 canonical pathway, we show that the pharmacological inhibition of SETD8 by the chemical compound UNC0379 also triggers cell-cycle defects and apoptosis in myeloma cells deficient for p53. Finally, the combination of UNC0379 with the cytotoxic agent melphalan strongly enhances DNA damage and overcomes drug resistance, suggesting that targeting SETD8 activity could be beneficial to improve multiple myeloma treatment in high-risk patients independently of their mutational status for p53.

RESULTS

SETD8 up-regulation in myeloma is associated with a poor outcome. In order to identify epigenetic factors potentially involved in Multiple Myeloma, we used public affymetrix microarrays gene expression data sets to identify which genes encoding histone-modifying enzymes are differentially expressed between normal bone marrow plasma cells (BMPCs, n=22), purified primary MM cells from newly diagnosed patients (MMCs, n = 345) and human myeloma cell lines (HMCLs, N=42) [START_REF] Teoh | p53 abnormalities and potential therapeutic targeting in multiple myeloma[END_REF] . As shown in Figure 1A, a significant higher levels of mRNAs encoding the histone H4K20 monomethyltransferase SETD8 was found in HMCLs compared to BMPCs and MMCS (Fig 1A). Furthermore, although we did not observe a statistical difference with BMPCs, SETD8 mRNA levels appeared heterogeneous in MMCs (Figure 1A) ranging from 65 to 63338 in affymetrix signal. This contrasted SETD8 mRNA levels was not restrained to a particular MM molecular sub-type (supplementary Figure S1). Consistent with these observations, immunoblot analysis with specific SETD8 antibody showed that HMCLs and some MMCs displayed higher SETD8 protein levels compared with non-cancerous plasma cells (PC) (Figure 1B). These higher SETD8 protein levels were independent to the natural cell-cycle fluctuation of the enzyme [START_REF] Brustel | Coupling mitosis to DNA replication: the emerging role of the histone H4--lysine 20 methyltransferase PR--Set7[END_REF] , as the levels of the mitotic marker histone H3-S10 phosphorylation were relatively similar in all tested samples (Figure 1B). SETD8 is known as the unique enzyme responsible for the mono-methylation of histone H4 at lysine 20 (H4K20me1) [START_REF] Beck | PR--Set7 and H4K20me1: at the crossroads of genome integrity, cell cycle, chromosome condensation, and transcription[END_REF] . Yet, the levels of H4K20me1 remained roughly unchanged in HMCLs and MMCs displaying higher SETD8 levels (Figure 1B), indicating that SETD8 up-regulation does not trigger an increase in the steady state level of histone H4K20me1 in multiple myeloma.

We next investigated the prognostic value of SETD8 up-regulation in two independent cohorts of previously untreated MM patients (UAMS-TT2 n=256 and UAMS-TT3 n=158 cohorts), using Maxstat R algorithm. High SETD8 mRNA levels were predictive of both shorter event free survival and overall survival in the two cohorts (Figure 1C). Consistent with these results, SETD8 mRNA levels were significantly increased in patients harboring Chr1q21 gain (Figure 1D) or presenting a high gene expression-based proliferation index (GPI) (Figure 1E), molecular features being associated with a poor outcome in MM patients. However, SETD8 expression did not correlate with MMC plasma cell labeling index (PCLI) in a cohort of 101 newly diagnosed patients (supplementary Figure S2), suggesting that SETD8 up-regulation is likely not a hallmark of MMC proliferation status. Gene set expression analysis (GSEA) of patients with high SETD8 expression highlighted a significant enrichment of genes involved in IRF4 targets, MYC-MAX targets, MAPK pathway and DNA repair (Supplementary Figure S3, P<0.001), suggesting that SETD8 up-regulation correlates with changes in signaling pathways involved in MM pathophysiology. Furthermore, SETD8 expression is significantly higher in MM cell of patients at relapse compared to newly diagnosed patients, underlining a potential role of SETD8 in drug resistance (Supplementary Figure S4). Altogether, these data reveal that SETD8 is overexpressed in myeloma and this up-regulation is associated with a poor outcome and deregulation of major signaling pathways in MM patients.

UNC0379-mediated SETD8 inhibition leads to cell-cycle defects and apoptosis in

MMCs. To determine the biological significance of SETD8 up-regulation in MM pathophysiology, the effects of the small-molecule SETD8 inhibitor UNC0379 were examined in eight different HMCLs representative of the disease. UNC0379 is a well-characterized substrate-competitive inhibitor selective for SETD8 [START_REF] Veo | Combined functional genomic and chemical screens identify SETD8 as a therapeutic target in MYC--driven medulloblastoma[END_REF][START_REF] Veschi | Epigenetic siRNA and Chemical Screens Identify SETD8 Inhibition as a Therapeutic Strategy for p53 Activation in High--Risk Neuroblastoma[END_REF][START_REF] Ma | Discovery of a selective, substrate--competitive inhibitor of the lysine methyltransferase SETD8[END_REF] . As shown in Figure 2A, UNC0379 treatment was sufficient to inhibit the growth of all HMCLs in a dose dependent manner with an average half maximal inhibitory concentration (IC 50 ) ranging from 1.25 to 6.3 µM (Figure 2A). To determine the molecular mechanisms of this HMCL growth inhibition, the effects of UNC0379 treatment on SETD8 activity, cell proliferation and survival were examined using immunoblot and flow cytometry assays in XG7 and XG25 MM cell lines, which displayed similar IC 50 values for UNC0379. As shown in Figure 2B, analysis of whole cell extracts after 24 hours of treatment showed a strong decrease in H4K20me1, but not of SETD8 and histone H4, thereby demonstrating the rapid and efficient inhibition of SETD8 activity (Figure 2B). In the following hours, this SETD8 inhibition was associated with cell-cycle defects, as shown by an accumulation in G1 phase and a decrease in DNA replication (S) phase 48 hours after treatment (Figure 2C). At later time points, these cell cycle defects was followed by the activation of apoptosis, as measured by the appearance of 33% and 26% of annexin-V positive XG7 and XG25 cells (Figure 2D).

To confirm that SETD8 is essential for growth and viability of malignant plasma cells, bone marrow (BM) from MM patient samples were cultured with recombinant interleukin 6 in presence or not of UNC0379. Five days after treatment, the percentage of myeloma and non-myeloma cells was then measured by flow cytometry after staining with anti-CD138 antibody that specifically recognizes plasma cells. As shown in Figure 2E, the median number of CD138 positive malignant plasma cells were decreased in a dose-dependent manner, with 50% and 63% of reduction with 2.5 µM and 5 µM of UNC0379 respectively (P = 0.001 and P < 0.0001; N=8), whereas non-tumoral BM cells were less sensitive with a decrease of 26% and 24% at these UNC0379 concentrations.

In addition, to support the feasibility of preclinical studies with SETD8 inhibitors, primary 5T33vv murine MM models [START_REF] Asosingh | In vivo induction of insulin--like growth factor--I receptor and CD44v6 confers homing and adhesion to murine multiple myeloma cells[END_REF] were treated with growing concentrations of UNC0379 for 24h hours before cell viability analysis. As observed with human primary MM cells (Figure 2E), UNC0379 treatment results in significant reduction of 5T33vv viability in a dose dependent manner (Supplementary Figure S5). We therefore conclude that malignant plasma cells are particularly addicted to SETD8 activity and that the pharmacological inhibition of this epigenetic enzyme is highly toxic, leading rapidly to cell growth inhibition and apoptosis.

SETD8 inhibition impairs MM cell proliferation together with activation of p53

target gene pathways. SETD8 has been involved in all nuclear processes that use DNA as a matrix, including a critical role in the regulation of gene expression [START_REF] Beck | PR--Set7 and H4K20me1: at the crossroads of genome integrity, cell cycle, chromosome condensation, and transcription[END_REF] . In order to gain insights into the mechanisms contributing to SETD8-mediated MM cell growth inhibition and death, we therefore performed transcriptome analysis in XG7 and XG25 HMCLs after SETD8 inhibition using RNA sequencing (RNAseq). To identify gene expression alterations caused by SETD8 inhibition in HMCLs, we isolated total RNAs 18 hours after UNC0379 treatment or 48 hours after shRNA-induced SETD8 silencing, when H4K20me1 decrease did not trigger DNA replication defects yet [START_REF] Tardat | PR--Set7--dependent lysine methylation ensures genome replication and stability through S phase[END_REF][START_REF] Jørgensen | The histone methyltransferase SET8 is required for S-phase progression[END_REF] . A common signature of 820 up-regulated genes and 360 down-regulated genes was found in UNC0379-treated and SETD8-depleted cell lines compared to the untreated and shRNA control cell lines (Fold change > 2; FDR ≤ 0.05) (supplementary figure S6 and Supplementary Table 1). Gene Set Enrichment Analysis (GSEA) identified, as the most down-regulated pathways, genes involved in cell-cycle, stem cells, proliferating plasmablasts and MM proliferating molecular subgroup together with genes repressed upon loss of the histone H3K27 methyltransferase EZH2 (Figures 3A and3B).

Conversely and consistent with the presence of a functional p53 in XG7 and XG25 cell lines, a significant positive enrichment was found for p53 target genes, including p21 and GADD45A genes, and genes overexpressed in mature BMPCs versus plasmablasts (Figures 3C and3D). A positive enrichment for genes normally downregulated by c-MYC, EZH2, DNA methylation or histone deacetylases (HDAC) was also observed (Figure 3C), which might suggest some impairments of chromatin silencing pathways upon SETD8 inhibition in MM cells. As shown in figure 3E, immunoblot analysis of UNC0379-treated XG7 HMCLs confirmed the increased levels of p53 and p21 proteins upon UNC0379 treatment. However, we did not observe a significant phosphorylation of the histone variant H2A.X (Figure 3E), suggesting p53 activation in XG7 MM cells treated with UNC0379 occurs in absence or low level of DNA damage.

Altogether, these results data indicate that the cytotoxic effects of SETD8 inhibition in p53-proficient HMCLs are associated with mature non-proliferating plasma cell transcriptional signature and activation of the p53 canonical pathway.

The cytotoxicity of UNC0379 treatment is not dependent on p53 in malignant plasma cells. Previous studies showed that UNC0379-induced cell death depends on the activation of p53 in neuroblastoma cancer models (NB), thereby rending p53deficient NB cells more resistant to SETD8 inhibition (Veschi et al. 2017). To determine whether the cytotoxic effects of the pharmacological inhibition of SEDT8 mediated by UNC0379 was also dependent on p53 activation in MM cells, we compared the UNC0379 response in p53 wild-type HMCLs (n=7) and p53-deficient HMCLs (n=5) [START_REF] Moreaux | A high--risk signature for patients with multiple myeloma established from the molecular classification of human myeloma cell lines[END_REF][START_REF] Vikova | Comprehensive characterization of the mutational landscape in multiple myeloma cell lines reveals potential drivers and pathways associated with tumor progression and drug resistance[END_REF] that displayed similar SETD8 expression levels (Figure 4A). Noted of, there was no significant correlation between SETD8 and P53 expression in HMCLs (Supplementary

Figure S7

). Although IC 50 values for p53-deficient HMCLs following UNC0379 treatment were more heterogeneous, we found no statistical difference with the group of p53 wild-type HMCLs (Figure 4B). We also observed no statistical difference in the IC 50 values of UNC0379 according to the expression levels p53 in HMCLs, whatever their p53 status (Supplementary Figure S8). Altogether, these results suggested that the absence of a functional p53 did not alter the sensitivity of malignant plasma cells to the pharmacological inhibition of SETD8 activity. To verify this hypothesis and gain insights into the mechanisms by which UNC0379 could impair the viability of malignant plasma cells independently of p53, we examined by immunoblot and flow cytometry analysis the cytotoxic effects of UNC0379 treatment on p53-proficient XG7 HMCL transduced with high-titer of lentivirus encoding either a p53 shRNA or an irrelevant control shRNA. Both cell lines showed similar IC 50 values for UNC0379 (3.7 µM in control shRNA and 4.8 µM in P53 shRNA expressing cells). Immunoblot analysis confirmed the efficient p53 depletion in p53 shRNA XG7 HMCL relative to control cells (Figure 4C). Consistent with results in Figure 3E, UNC0379 treatment led to an up-regulation of p53 without detectable DNA damage in shRNA control XG7 cells (Figure 4C). In contrast, higher levels of DNA damage and replicative stress were observed in UNC0379-treated XG7 cells depleted for p53, as evidenced by the increased levels of both phosphorylated histone variant H2A.X and checkpoint protein CHK1 (Figure 4C) and by an accumulation of cells in G2/M phase of the cell cycle (Figure 4D). This was followed by the appearance of a high percentage of apoptotic cells, similarly to the percentage detected in UNC0379-treated control shRNA XG7 cells displaying p53 activation (Figure 4E). Importantly, a similar DNA damage signature was observed in XG1 HMCL naturally harboring a mutated inactive p53 (Supplementary Figure S9). Thus, these results indicated that UNC0379-induced cytotoxicity in MM cells is independent on p53 status and that a high level of SETD8 likely protects MM cells from spontaneous intrinsic DNA damage and replicative stress.

Pharmacological inhibition of SETD8 synergizes with melphalan. The results

presented above indicate that the pharmacological inhibition of SETD8 could constitute a promising strategy to improve multiple myeloma treatment by increasing DNA damage and genomic instability. To further explore this possibility, we investigated whether SETD8 inhibition could enhance the cytotoxicity of melphalan and overcome resistance to this alkylating agent widely used in MM treatment. To this end, we first measured by FACS the levels of apoptotic cells in sensitive (MelphS) and melphalan-resistance (MelphR) XG7 MM cell lines treated with either 5 µM of melphalan, 3 µM of UNC0379 or a combination of the two compounds. Note of, the levels of SETD8 and TP53 expression levels were similar in both cell lines (Supplementary Figure S10). Whereas UNC0379 alone slightly increased the percentage of annexinV-positive MelphS and MelphR cells, the combination with Melphalan significantly enhanced this percentage in MelphR cells and, to a lesser extent, in MelphS cells (Figure 5A). Remarkably, the overcome resistance to melphalan upon UNC0379 treatment in MelpR cells was associated with an enhancement of DNA breaks, as observed by a higher level of phosphorylated histone variant H2AX and by an increase in the number of DNA damage-induced 53BP1 foci in these cells (Figures 5B and5C). However, although we observed an activation of the cell-cycle checkpoint p21 (Figure 5C), UNC0379 sensitized HMCLs to melphalan treatment was independently from the presence of p53 (Figure 5D). Altogether, these results indicate that a low dose of UNC0379 is sufficient to significantly increase the percentage of melphalan-induced MM cell death in a p53 dependent manner and to overcome resistance to this alkylating agent, thereby demonstrating the therapeutic interest to target SETD8-mediated lysine methylation in multiple myeloma whatever their p53 status.

DISCUSSION

This study unveils for the first time a role of the lysine methytransferase SETD8 in multiple myeloma (MM) patho-physiology and drug resistance. We have shown that elevated levels of SETD8 are associated with a poor prognosis in two large cohorts of newly diagnosed patients and correlates with the deregulation of regulatory nodes involved in multiple myeloma, including IRF4, MYC/MAX, MAPK and DNA repair pathways (Figure 1). Moreover, patients displaying higher SETD8 expression are associated with specific molecular features, such as increase copy of Chr1q21 or a high GPI index (Figure 1). Consistent with this, primary MM cells are particularly addicted to SETD8 activity and the recently developed small-molecule inhibitor of SETD8, UNC0379, demonstrated a significantly higher toxicity in MM cells compared to normal cells from the bone marrow microenvironment (Figure 2). From a mechanistic point of view, our RNA-seq results show that the genetic or pharmacological inhibition of SETD8 in MM cell lines results in the activation of a mature non-proliferating plasma cell signature and of the p53 canonical pathway (Figure 3). However, UNC0379-induced cytotoxicity does not necessarily require p53 activation as p53 wild-type and deficient MM cells display similar sensitivity to SETD8 inhibition (Figures 3 and4). Finally, in order to support future pre-clinical study, we have shown that a low dose of UNC0379 enhances melphalan-induced cell death and overcomes the resistance associated with this DNA-damaging conventional cytotoxic agent in both p53 wild-type and deficient MM cells (Figure 5). Altogether, these results provide evidence for SETD8 inhibition as a potential novel therapeutic strategy in multiple myeloma independently from the mutational p53 status of these tumors.

An up-regulation of SETD8 is not specific to multiple myeloma, as it has also been observed in different types of solid tumors [START_REF] Takawa | Histone lysine methyltransferase SETD8 promotes carcinogenesis by deregulating PCNA expression[END_REF] , such as papillary thyroid cancer [START_REF] Liao | Histone methyltransferase KMT5A gene modulates oncogenesis and lipid metabolism of papillary thyroid cancer in vitro[END_REF] , breast carcinoma [START_REF] Huang | Monomethyltransferase SETD8 regulates breast cancer metabolism via stabilizing hypoxia--inducible factor 1α[END_REF][START_REF] Yang | SET8 promotes epithelial--mesenchymal transition and confers TWIST dual transcriptional activities[END_REF] , and childhood tumors of the nervous system [START_REF] Veo | Combined functional genomic and chemical screens identify SETD8 as a therapeutic target in MYC--driven medulloblastoma[END_REF][START_REF] Veschi | Epigenetic siRNA and Chemical Screens Identify SETD8 Inhibition as a Therapeutic Strategy for p53 Activation in High--Risk Neuroblastoma[END_REF] . However, the mechanisms that contribute to elevated levels of SETD8 in cancer still remained unclear. In neuroblastoma, a higher-level of SETD8 could be due in part to DNA copynumber gains at chr12q24, the region that encompasses SETD8 encoding gene [START_REF] Yang | SET8 promotes epithelial--mesenchymal transition and confers TWIST dual transcriptional activities[END_REF] .

Another non-exclusive mechanism is related to the deregulation of oncogenic c-MYC pathway, since SETD8 encoding gene has been found as a transcriptional target of c-MYC [START_REF] Driskell | The histone methyltransferase Setd8 acts in concert with c--Myc and is required to maintain skin[END_REF] and functionally required to mediate MYC-induced cell growth [START_REF] Veo | Combined functional genomic and chemical screens identify SETD8 as a therapeutic target in MYC--driven medulloblastoma[END_REF] . It is widely established that c-MYC is a key regulator in MM with deregulations related to translocations, gains and amplification, mutations in RAS genes and MYC transcription or translation activation [START_REF] Jovanović | Targeting MYC in multiple myeloma[END_REF] . Interestingly, while chr12q24 gains are not present in myeloma, we identified here a significant enrichment of c-MYC/MAX target genes in MM patients characterized by high SETD8 expression, thereby supporting a potential role of this oncogenic pathway in SETD8 deregulation. Furthermore, SETD8 depletion or inhibition results in up-regulation of genes repressed upon c-MYC expression (Figure 3C) suggesting that SETD8 might also participate in deregulation of c-MYC functions in multiple myeloma.

An unexpected result of our study is that the up-regulation of SETD8 in malignant plasma cells was not associated with significant changes in the steady state level of the mono-methylation of histone H4K20 (H4K20me1), the main target of SETD8 [START_REF] Beck | PR--Set7 and H4K20me1: at the crossroads of genome integrity, cell cycle, chromosome condensation, and transcription[END_REF] . This result is independent from cell-cycle progression, since changes in the levels of SETD8 do not correlate with cell proliferation (figure 1B and supplementary figure S2). One hypothesis is that an overexpression of the H4K20me1-specific demethylase PHF8, observed in many cancers including hematopoietic malignancies [START_REF] Björkman | Systematic knockdown of epigenetic enzymes identifies a novel histone demethylase PHF8 overexpressed in prostate cancer with an impact on cell proliferation, migration and invasion[END_REF][START_REF] Fu | The histone demethylase PHF8 promotes adult acute lymphoblastic leukemia through interaction with the MEK/ERK signaling pathway[END_REF] , could attenuate SETD8 activity on histone H4K20 [START_REF] Liu | PHF8 mediates histone H4 lysine 20 demethylation events involved in cell cycle progression[END_REF] . Thus, although we cannot rule out that some local changes in H4K20me1 levels may occur at specific genetic loci, our results indicate that the global level of this epigenetic modification is not a valuable marker of SEDT8 activity and functions in multiple myeloma.

Recent studies have suggested that the role of SETD8 in cancer might involve the methylation of other substrates than histone H4. Thus, Takawa et al. proposed that SEDT8 can methylate the proliferating cell nuclear antigen PCNA and thus favor HeLa cell proliferation [START_REF] Takawa | Histone lysine methyltransferase SETD8 promotes carcinogenesis by deregulating PCNA expression[END_REF] ; but this result was never further confirmed in other cell types.

Additionally, SETD8 can induce the mono-methylation of the tumor suppressor p53 at lysine 382 (p53K382), which attenuates its pro-apoptotic and growth arrest functions [START_REF] Shi | Modulation of p53 function by SET8--mediated methylation at lysine 382[END_REF][START_REF] Veschi | Epigenetic siRNA and Chemical Screens Identify SETD8 Inhibition as a Therapeutic Strategy for p53 Activation in High--Risk Neuroblastoma[END_REF] . Hence, in neuroblastoma, inhibition of SETD8 by UNC0379 leads to cell death in a dependent p53 manner and p53K382 is important for this phenotype [START_REF] Veschi | Epigenetic siRNA and Chemical Screens Identify SETD8 Inhibition as a Therapeutic Strategy for p53 Activation in High--Risk Neuroblastoma[END_REF] . Our RNA-seq and functional studies in MM cells shows that the genetic or pharmacological inhibition of SETD8 leads to the activation of p53 pathway, which correlates with an increased in p53 and p21 protein levels, G1/S arrest followed by cell death. However, in contrast to neuroblastoma [START_REF] Veschi | Epigenetic siRNA and Chemical Screens Identify SETD8 Inhibition as a Therapeutic Strategy for p53 Activation in High--Risk Neuroblastoma[END_REF] , UNC0379-induced cytotoxicity in MM cells is not necessarily dependent on p53 activation and, despite several attempts, we were unable to detect p53K382me1 in MM cells. Few DNA breaks are generally sufficient to activate P53 functions [START_REF] Huang | Sensitivity and selectivity of the DNA damage sensor responsible for activating p53--dependent G1 arrest[END_REF][START_REF] Loewer | The p53 response in single cells is linearly correlated to the number of DNA breaks without a distinct threshold[END_REF] . Since the first impact of loss of SETD8 activity is excessive chromatin relaxation and progressive DNA damage after exit of mitosis [START_REF] Shoaib | Histone H4K20 methylation mediated chromatin compaction threshold ensures genome integrity by limiting DNA replication licensing[END_REF] , we propose that the activation of p53 we detect in MM cells upon SETD8 inhibition is mainly triggered by cellular stresses during G1 progression. This would also explain why UNC0379mediated SETD8 inhibition is very toxic in P53-deficient MM cells, where the absence of a functional p53-mediated G1 arrest allows damaged cells to pursue into S-phase and accumulate a deadly level of DNA breaks, likely caused by improper replication fork progression [START_REF] Tardat | PR--Set7--dependent lysine methylation ensures genome replication and stability through S phase[END_REF] . Altogether, our findings are consistent with a model in which UNC0379mediated cell death is triggered by p53 activation in p53-proficient MM cells and rather associated with high replicative stress in cancer cells deficient for p53, thereby rending multiple myeloma sensitive to SEDT8 inhibition whatever the mutational status of p53.

In spite of effective therapeutic protocols developed in MM, drug resistance remains a major concern. In this regard, we report here that high SETD8 expression is associated with a poor prognosis in patients treated by high-dose melphalan and autologous stem cell transplantation. SETD8 expression is also significantly upregulated in patients at relapse compared to newly diagnosed patients. In agreement with this, UNC0379 treatment potentiates the cytotoxicity of melphalan and overcomes melphalan drug resistance in MM cells, underlining the interest to target SETD8 to improve the treatment of MM. Melphalan is an alkylating cytotoxic agent used in MM patients treated by high dose chemotherapy and hematopoietic stem cell autograft and in non-transplantable patients, in combination with other molecules. The protective effect against melphalan provided by SETD8 expression is associated with the poor prognosis of MM patients characterized by elevated levels of SETD8.

Deletion of the short arm of chromosome 17 (del 17p) is associated with a poor outcome in MM independently of treatment regimen [START_REF] Munshi | Consensus recommendations for risk stratification in multiple myeloma: report of the International Myeloma Workshop Consensus Panel 2[END_REF][START_REF] Avet--Loiseau | Bortezomib plus dexamethasone induction improves outcome of patients with t(4;14) myeloma but not outcome of patients with del(17p)[END_REF][START_REF] Dimopoulos | Treatment of patients with relapsed/refractory multiple myeloma with lenalidomide and dexamethasone with or without bortezomib: prospective evaluation of the impact of cytogenetic abnormalities and of previous therapies[END_REF][START_REF] Drach | Presence of a p53 gene deletion in patients with multiple myeloma predicts for short survival after conventional--dose chemotherapy[END_REF][START_REF] Schilling | Impact of genetic abnormalities on survival after allogeneic hematopoietic stem cell transplantation in multiple myeloma[END_REF] . Interestingly, MM cell toxicity mediated by SETD8 inhibitor is mainly p53-independent. The frequency of events targeting p53 (del 17p, TP53 mutation or double hits) increases during the progression of MM and consecutive relapses underlining a selection of cells harboring TP53 abnormalities in association with resistance to treatment. TP53 bi-allelic events are also associated with a dramatic impact on MM patients' survival after relapse [START_REF] Weinhold | Clonal selection and double--hit events involving tumor suppressor genes underlie relapse in myeloma[END_REF] . Therapies inducing significant toxicity of p53 defective MM cells are needed. Our results demonstrate the therapeutic interest of SETD8 inhibitor to target p53 deficient MM cells by increasing replicative stress and DNA damages. Accordingly, combination of SETD8 inhibitor with melphalan could be of clinical interest, notably in newly diagnosed patients presenting del17p and/or SETD8 overexpression and eligible to high dose melphalan and ASCT. Thus, SETD8 inhibition appears of therapeutic interest to overcome drug resistance and improve the treatment of MM patients at relapse independently of the p53 status.

MATERIALS AND METHODS

Primary multiple myeloma cells

Bone marrow samples were collected after patients' written informed consent in accordance with the Declaration of Helsinki and institutional research board approval from Heidelberg and Montpellier University hospital. Bone marrow were collected from 206 patients treated with high dose Melphalan (HDM) and autologous stem cell transplantation (ASCT) and this cohort is termed "Heidelberg-Montpellier" (HM) cohort.

Patients' MMCs were purified using anti-CD138 MACS microbeads (Miltenyi Biotec, Bergisch Gladbach, Germany) and their gene expression profile (GEP) obtained using Affymetrix U133 plus 2.0 microarrays as described [START_REF] Hose | Induction of angiogenesis by normal and malignant plasma cells[END_REF][START_REF] Hose | Inhibition of aurora kinases for tailored risk--adapted treatment of multiple myeloma[END_REF] . The CEL files and MAS5 files are available in the ArrayExpress public database (E-MTAB-372). The structural chromosomal aberrations, as well as numerical aberrations were assayed by fluorescence in situ hybridization (iFISH). We also used publicly available Affymetrix GEP (Gene Expression Omnibus, accession number GSE2658) of a cohort of 345 purified MMC from previously untreated patients from the University of Arkansas for Medical Sciences (UAMS, Little Rock, AR), termed in the following UAMS-TT2 cohort.

These patients were treated with total therapy 2 including HDM and ASCT [START_REF] Barlogie | Total therapy 2 without thalidomide in comparison with total therapy 1: role of intensified induction and posttransplantation consolidation therapies[END_REF] . We also used Affymetrix data from total therapy 3 cohort (UAMS-TT3; n=158; E-TABM-1138) [START_REF] Pineda--Roman | VTD combination therapy with bortezomib-thalidomide--dexamethasone is highly effective in advanced and refractory multiple myeloma[END_REF] of 188 relapsed MM patients subsequently treated with bortezomib (GSE9782) from the study by Mulligan et al [START_REF] Mulligan | Gene expression profiling and correlation with outcome in clinical trials of the proteasome inhibitor bortezomib[END_REF] . The mouse 5T33MMvv cells originated spontaneously in aging C57BL/KaLwRij mice and have since been propagated in vivo by intravenous transfer of the diseased marrow in young syngeneic mice as described [START_REF] Asosingh | In vivo induction of insulin--like growth factor--I receptor and CD44v6 confers homing and adhesion to murine multiple myeloma cells[END_REF][START_REF] De Bruyne | Epigenetic silencing of the tetraspanin CD9 during disease progression in multiple myeloma cells and correlation with survival[END_REF] .

Treatment of primary MM cells

Bone marrow of patients presenting with previously untreated MM (n = 8) at the university hospital of Montpellier was obtained after patients' written informed consent in accordance with the Declaration of Helsinki and agreement of the Montpellier University Hospital Centre for Biological Resources (DC-2008-417). Mononuclear cells were treated with or without UNC-0379 (1µM, 2.5µM or 5µM) and MMC cytotoxicity were evaluated using anti-CD138-phycoerythrin monoclonal antibody (Immunotech, Marseille, France) as described [START_REF] Moreaux | Gene expression--based prediction of myeloma cell sensitivity to histone deacetylase inhibitors[END_REF] .

Human Myeloma Cell Lines (HMCLs)

XG human myeloma cell lines (HMCLs) were cultured in the presence of recombinant IL-6 as previously described [START_REF] Moreaux | A high--risk signature for patients with multiple myeloma established from the molecular classification of human myeloma cell lines[END_REF] . XG7 Melphalan-resistant cells were generated by successively treating the sensitive parental XG7 cells with 0.6µM of Melphalan for 3 months. JJN3 was kindly provided by Dr Van Riet (Brussels, Belgium), JIM3 by Dr MacLennan (Birmingham, UK) and MM1S by Dr S. Rosen (Chicago, USA). AMO-1, LP1, L363, U266, OPM2, and SKMM2 were purchased from DSMZ (Braunsweig, Germany) and RPMI8226 from ATTC (Rockville, MD, USA). HMCLs were authenticated according to their short tandem repeat profiling and their gene expression profiling using Affymetrix U133 plus 2.0 microarrays deposited in the ArrayExpress public database under accession numbers E-TABM-937 and E-TABM-1088 [START_REF] Moreaux | A high--risk signature for patients with multiple myeloma established from the molecular classification of human myeloma cell lines[END_REF] .

Establishment of shRNA expressing HMCLs

Control and p53 shRNA sequences were cloned in the pLenti4-EZ-mIR plasmid as previously described [START_REF] Viziteu | RECQ1 helicase is involved in replication stress survival and drug resistance in multiple myeloma[END_REF] . SETD8 and associated control shRNA sequences were cloned into a puromycin retroviral vector RNAi Ready pSiren as described [START_REF] Tardat | PR--Set7--dependent lysine methylation ensures genome replication and stability through S phase[END_REF] . Retroviral particles were produced in 293FT cells. Briefly, 293FT cell line was cultured in Dulbecco's modified Eagle's medium and supplemented with 10% defined fetal bovine serum, 500µg/ml geneticin, 4mM L-glutamine, and 1mM MEM sodium pyruvate. The day before transfection, cells were plated into a 10cm tissue culture plate to 90%-95% confluence. 9µg of ViraPower packaging mix (Invitrogen) and 9µg of lentiviral plasmids were cotransfected into 293FT cells using 36µl Lipofectamine 2000 reagent (Invitrogen). Fortyeight hours later, culture supernatants were collected, concentrated 100 fold by ultracentrifugation (20000 g, 4 hours) and viral titers determined. Corresponding HMCLs were transduced with virus and stable transduced cells were obtained by adding zeocin (10 µg/ml) for pLenti4-EZ-mIR and puromycin (2.5µg/ml) for pSIREN viral particles.

Growth assays and cell cycle analysis

Cells were cultured for 4 days in 96-well flat-bottom microtiter plates in RPMI 1640 medium, 10% FCS, and 2 ng/ml IL-6 (control medium) in the presence of UNC-0379.

Cell growth was evaluated by quantifying intracellular ATP amount with a Cell Titer Glo Luminescent Assay (Promega, Madison, WI) using a Centro LB 960 luminometer (Berthold Technologies, Bad Wildbad, Germany). For cell cycle analysis, cells were cultured in 24-well flat-bottomed microtiter plates at 10 5 cells per well in RPMI1640-10% FCS or X-VIVO 20 culture medium with or without IL-6 (3ng/mL). The cell cycle was assessed using DAPI staining (Sigma-Aldrich, Saint-Louis, MO, USA) and cells in the S phase using incubation with bromodeoxyuridine (BrdU) for 1 h and labeling with an anti-BrdU antibody (APC BrdU flow kit, BD Biosciences, San Jose, CA, USA) according to the manufacturer's instructions. Flow cytometry analysis was done on a Fortessa flow cytometer (BD, Mountain View, CA, USA).

Apoptosis assays

Cells were cultured in 24-well, flat-bottomed microtiter plates at 10 5 cells per well in RPMI1640-10% FCS or X-VIVO 20 culture medium with or without IL-6 (3ng/mL) and appropriate concentration of chemical drugs. After 4 days of culture, cells were washed twice in PBS and apoptosis was assayed with PE-conjugated Annexin V labeling (BD Biosciences) using a Fortessa flow cytometer (BD) following manufacturer protocols.

RNA sequencing

HMCLs were cultured for 16 hours with or without 5 µM of UNC-0379, or infected with shcontrol or shRNA SETD8 pSIREN vectors for 48h. RNA samples were collected as previously described. The RNA sequencing (RNA-seq) library preparation was done with 150ng of input RNA using the Illumina TruSeq Stranded mRNA Library Prep Kit.

Paired-end RNA-seq were performed with Illumina NextSeq sequencing instrument (Helixio, Clermont-Ferrand, France). RNA-seq read pairs were mapped to the reference human GRCh37 genome using the STAR aligner [START_REF] Dobin | STAR: ultrafast universal RNA--seq aligner[END_REF] . All statistical analyses were performed with the statistics software R (version 3.2.3; available from https://www.rproject.org) and R packages developed by BioConductor project (available from https://www.bioconductor.org/) [START_REF] Gentleman | Bioconductor: open software development for computational biology and bioinformatics[END_REF] . The expression level of each gene was summarized and normalized using DESeq2 R/Bioconductor package [START_REF] Love | Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2[END_REF] . Differential expression analysis was performed using DESeq2 pipeline. P values were adjusted to control the global FDR across all comparisons with the default option of the DESeq2 package.

Genes were considered differentially expressed if they had an adjusted p-value of 0.05 and a fold change of 1.5. Pathway enrichment analyses were performed using online the curated gene set collection on the Gene Set Enrichment Analysis software (http://software.broadinstitute.org/gsea/msigdb/index.jsp) [START_REF] Liberzon | Molecular signatures database (MSigDB) 3.0. Bioinforma[END_REF][START_REF] Subramanian | Gene set enrichment analysis: a knowledge-based approach for interpreting genome--wide expression profiles[END_REF] .

Gene expression profiling and statistical analyses

Gene expression data were normalized with the MAS5 algorithm and analyses processed with GenomicScape (http://www.genomicscape.com) [START_REF] Kassambara | GenomicScape: an easy--to--use web tool for gene expression data analysis. Application to investigate the molecular events in the differentiation of B cells into plasma cells[END_REF] the R.2.10.1 and bioconductor version 2.5 programs [START_REF] Gentleman | Bioconductor: open software development for computational biology and bioinformatics[END_REF] . Gene Set Expression Analysis (GSEA) was used to identify genes and pathways differentially expressed between populations. Univariate and multivariate analysis of genes prognostic for patients' survival was performed using the Cox proportional hazard model. Difference in overall survival between groups of patients was assayed with a log-rank test and survival curves plotted using the Kaplan-Meier method (Maxstat R package) [START_REF] Küffner | Crowdsourced analysis of clinical trial data to predict amyotrophic lateral sclerosis progression[END_REF] .

53BP1 Staining-immunofluorescence microscopy

After deposition on slides using a Cytospin centrifuge, cells were fixed with 4% PFA, permeabilized with 0.5% Triton in PBS and saturated with 5% bovine milk in PBS. The rabbit anti-53BP1 (Novus Biologicals -Littleton, CO, USA -NB100304) antibody was diluted 1/300 in 5% bovine milk in PBS, and deposited on cytospins for 60 minutes at room temperature. Slides were washed twice and anti-rabbit alexa 488-conjugated antibody (diluted 1/500 in 5% bovine milk in PBS) was added for 60 minutes at room temperature. Slides were washed and mounted with Vectashield and 1% DAPI. Images and fluorescence were captured with a ZEISS Axio Imager Z2 microscope (X63 objective) (Oberkochen, Germany), analyzed with Omero (omero.mri.cnrs.fr) server and ImageJ software.

Immunoblot analysis. Cells washed with phosphate-buffered saline (PBS) were lysed in SDS buffer and boiled at 94°C for 5 minutes. After measuring protein quantity by Bradford, equal amounts of protein were resolved by SDS-PAGE, transferred to a nitrocellulose membrane (Millipore) and probed with one of the following antibodies: mouse anti-Chk1 (1:1000, abcam), rabbit anti-p21 (1:500, Cell signaling), rabbit anti-p53 (1:1000, Cell Signaling), rabbit anti-SETD8 (1:1000, Cell Signaling), mouse anti-βactin (1:20000, Sigma), rabbit anti-H2A.X and anti-phospho-H2A.X-Ser139 (1:1000, Cell signaling), rabbit anti-H4-K20me1 (1:1000 Cell Signaling), and rabbit anti-Histone H4

(1:1000, Cell Signaling). Membranes were then incubated with the appropriate horseradish peroxidase (HRP)-conjugated secondary antibodies. The immunoreactive bands were detected by chemiluminescence (Pierce).

SETD8 expression (Affymetrix signal)

Supplementary Figure S1

Figure 1 .

 1 Figure 1. SETD8 expression is a prognosis value in MM. (A) SETD8 gene

Figure 2 .

 2 Figure 2. SETD8 inhibitor UNC0379 is highly toxic in malignant plasma cells. (A)

Figure 3 .

 3 Figure 3. Gene expression changes in HMCLs upon genetic or pharmacological

Figure 4 .

 4 Figure 4. UNC0379 toxicity is independent of P53. (A) Comparison of SETD8

Figure 5 .

 5 Figure 5. UNC-0379 treatment sensitizes HMCLs to Melphalan-induced DNA

Figure 1 (

 1 Figure 1 (Herviou et al.)

ACKNOWLEDGMENTS

This work was supported by grants from labex Epigenmed, SIRIC-Montpellier-Cancer ; Ligue Nationale Contre le Cancer (LNCC). Institutional Support was provided by the Institut National de la Santé et de la Recherche Médicale (INSERM) and by the Centre National de la Recherche Scientifique (CNRS). F.I. was supported by fellowships from LNCC and fondation pour la recherche médicale (FRM).

ImageJ software (mean number of cells counted: 300). Statistical significance between conditions was assessed using Student paired t-test (*: pvalue<0.05). (D) Apoptosis induction in XG7-shControl and XG7-shTP53 HMCLs after 96h of treatment with Melphalan (5µM), UNC-0379-treated (3µM) or the combination of the two drugs.

AnnexinV-PE staining was analyzed by flow cytometry.

Legends of supplementary Figures: Supplementary


Steady and Unsteady compressible Reduced-Order Models of a

Zero-Net Mass-Flux Synthetic Jet Actuator R. Messahel and Y. Bury and J. Bodart and N. Doué Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Université de Toulouse, 31055 TOULOUSE Cedex 4 In the framework of an optimization study of a Zero-Net-Mass-Flux fluidic, synthetic jet actuator, based on a multi-objective optimization formulation, the consideration of optimization parameters such as the actuator location and the outlet design implies a re-meshing procedure that adds complexity. It is still the case even if the actuator is modeled with simple boundary conditions at the jet orifice exit since, locally, the re-mesh is still required. This strongly impacts the global computational cost, in particular if the considered geometry is complex. In a previous study, we proposed an alternative method to model Zero-Net Mass Flux synthetic jet actuators through the implementation of volumetric reduced-order models (ROM) as additional source terms. The previous reduced-order model consisted in a simplified ROM model where a constant-in-space momentum quantity was imposed in the ROM formulation and the compressible effects were neglected. In this paper, we propose to extend the previous work in an attempt to apply this ROM strategy to higher Mach number flows, where compressibility effects at the outlet of the pulsed jets can no more be neglected, while improving the early interaction of the pulsed jet with the surrounding flow by considering the starting jet influence when the actuators are operated in a pulsed manner.

I. Nomenclature

II. Introduction

A. Context

The present study is carried in the framework of the European Clean Sky 2 Programme funded by the European commission under the project X-Pulse (cleansky 2 / LPA / X-Pulse GA 738172). It aims at developing innovative active flow control strategies, based on high frequency (few kilohertz) synthetic Zero-Net Mass-Flux (ZNMF) pulsed jets.

The focus of this study is to define an active multi-parametric flow control strategy of massively separated flows on complex geometries for high Reynolds number flows, of the order of a few millions, when the implementation of a large number of Zero-Net-Mass-Flux (ZNMF) synthetic jets is considered. This definition relies on the optimization of several operating parameters such as position, spatial distribution, jet momentum, frequency, orientation relative to the airflow, orifice design, etc. of the series of actuators.

The commonly used 'velocity inlet boundary conditions' and 'full synthetic jet actuator modeling' approaches require consequent and costly CAD and mesh refinement operations in the vicinity of the synthetic jet actuators. This strongly impacts the global computational cost of the numerical predictions, in particular if the considered geometry is complex, or when several synthetic jet actuators have to be implemented on the geometry and numerous flow control parameters have to be optimized. An alternative method is proposed to model ZNMF synthetic jet actuators through the implementation of volumetric reduced-order models of ZNMF synthetic jet actuators as additional source terms [START_REF] Messahel | Volumetric Reduced-Order Models of Zero-Net Mass-Flux Actuator[END_REF], in the form of body forces on given local control volumes corresponding to the actual locations of the actuators. This approach is promising as it allows to skip both CAD and re-meshing procedures unlike the commonly used 'velocity inlet boundaries' or 'full synthetic jet actuator modeling' approaches. Practically, it consists in directly plugging the volumetric source terms at appropriate locations, corresponding to the actual locations of the ZNMF pulsed-jet actuator outlets. As a consequence, a considerable computational time is to be saved during an optimization process.

B. Objectives

In the previous study [START_REF] Messahel | Volumetric Reduced-Order Models of Zero-Net Mass-Flux Actuator[END_REF], a simplified ROM model was considered where a constant-in-space momentum quantity was imposed in the ROM formulation and the compressible effects were neglected. The Mach number was expected to be small enough and the influence of both the pressure field and the energy on the definition of the volumetric source terms could thus be considered as negligible.

In an attempt to apply this ROM strategy to higher Mach number flows, while improving the early interaction of the pulsed jet with the surrounding flow, it is proposed to extend the previous work through

• the incorporation of compressible effects in the ROM formulation,

• the investigation of more realistic non-constant-in-space profiles in the ROM control volume to promote the vortex structure formation at ROM control volume located at the SJA slot exit, • the implementation and the validation of the completed ROM formulation for both steady and unsteady cases. Validations are conducted using both steady (RANS) and unsteady (URANS) 'Reynolds-averaged Navier-Stokes' turbulence modeling approaches with commercial code Star-CCM+.

Firstly, we consider the validation of the completed compressible formulation for steady cases on a canonical M jet = 0.8 steady blowing jet in a cross-flow at M in f = 0.23. Secondly, we consider the validation of the completed compressible formulation for unsteady cases based on the experimental investigation of an axisymmetric pulsed jet in quiescent air provided by Krishnan and Mohseni [START_REF] Krishnan | Axisymmetric Synthetic Jets: An Experimental and Theoretical Examination[END_REF].

III. Methodology

The whole source term implementation strategy for the reduced-order modeling of the actuator relies on the use of the sponge boundary conditions technique [START_REF] Israeli | Approximation of radiation boundary condition[END_REF][START_REF] Bodony | Analysis of sponge zone for computational fluid mechanics[END_REF][START_REF] Mani | On the reflectivity of sponge zones in compressible flow simulations[END_REF], such that the conservative flow variables are forced to converge to given reference solutions through the addition of artificial volumetric source terms in the compressible Navier-Stokes governing equations.

The two key-steps in the derivation of a robust volumetric ROM of ZNMF actuators are the following 1) the definition of the reference quantity to be set at the specified control volume in order to model the nonrepresented ZNMF actuator, 2) the definition of the source term formulation in the compressible Navier-Stokes governing equations. Here, we focus on the second key step. For the first one, the reference quantities to be imposed in the ROM formulation are obtained by extracting the solution quantities from previously ran simulations including the simulation of the full geometry of the synthetic jet actuator as it is operated following a pulsed way.

The RANS/URANS simulations are performed using the finite-volume code STAR-CCM+ with the coupled density-based solver on hexahedral mesh. A third-order MUSCL spatial scheme and implicit second-order temporal scheme are used for space discretization and time advancement, respectively. The k -ω SST-Menter turbulence model is used to model the unresolved scales.

A. Governing equations

For a given control volume V with differential surface area da, the Navier-Stokes (NS) equations are the following

∂ ∂t ∫ V WdV + ∮ ∇. [F -G] .da = ∫ V SdV, (1)
W =        ρ ρu ρE        Conservative variables , F =        ρu ρu u + pI ρvH        Inviscid fluxes , G =        0 T T.u + q        Viscous fluxes , S = 1 τ        ρ re f -ρ (ρu) re f -ρu (ρE) re f -ρE        Source terms , (2)
where ρ, u, p, H, E and T denote the fluid density, velocity, pressure, total enthalpy, total energy per unit mass, and viscous stress tensor, respectively.

S represents the considered "sponge zone" volumetric source terms formulation as described in [START_REF] Israeli | Approximation of radiation boundary condition[END_REF][START_REF] Bodony | Analysis of sponge zone for computational fluid mechanics[END_REF][START_REF] Mani | On the reflectivity of sponge zones in compressible flow simulations[END_REF], where ρ re f , (ρu) r e f , and (ρE) r e f are the quantities we want to impose at control volumes located at the SJA slot exit location. τ represents a characteristic time scale. The reference quantities ρ re f , (ρu) re f and (ρE) re f are provided by preliminary simulations that include the full SJA. The source term formulation in Eq. ( 2) forces the solution to the user-specified reference solution at each time step using the adequate characteristic time scale τ.

B. Implicit time integration and dual time-stepping

In order to improve the time accuracy of the unsteady governing equations Eq. ( 1), a preconditioning matrix is introduced with a dual time-stepping approach to solve the unsteady flows, with inner iterations in pseudo-time as follows

∂ ∂t ∫ V WdV + Γ ∂ ∂τ ∫ V QdV + ∮ ∇. [F -G] .da = ∫ V SdV, Q = [p, u, T] t , (3)
where Γ, τ and t denote the preconditioning matrix, the pseudo-time variable and the transposed vector exponent, respectively (see [START_REF] Weiss | Preconditioning applied to variable and constant density flows[END_REF]).

The additional second term introduces a local pseudo-time variation that is solved using the following second order implicit time marching approach such that it tends to 0 when τ → ∞. For the specific steady case, we only consider the time marching of the pseudo-time differential Γ ∂ ∂τ ∫ V QdV term neglecting the first physical-time differential term which mathematically reads ∂ ∂t ∫ V WdV → 0 in Eq. ( 1). The time marching procedure is the following

Q 0 = Q τ , (4) 2
∆τ ∆t

∆W ∆Q ∆Q = -α i ∆τ        R i-1 + 1 2 3W i-1 -4W t + W t-∆t + S const ant in ∆τ        , S = W re f -W 0 ∆τ , (5)
where

∆Q = Q i -Q 0 and R i-1 = f aces F(Q i-1 ) -G(Q i-1 )
, and the characteristic time scale in Eq. ( 5) is set to the local pseudo-time step ∆τ(x) defined by the CFL condition

∆τ(x) = min CF L.V(x) λ max (x) , σ∆x 2 ν(x) (6)
Here CF L, V(x), λ max (x), σ, ∆x and v(x) denote the dimensionless Courant number, the cell volume, the maximum eigenvalue of the system, the Von Neumann number, a characteristic cell length scale and the kinematic viscosity, respectively.

C. Numerical implementation

The following steps summarize the numerical procedure to implement volumetric source terms in order to model ZNMF actuators:

1) Definition of the control volume V r oms (x) where the volumetric ROMs is applied to model ZNMF actuators: in the present study, four to six layers of cells in the direction normal to the "effective" section of the SJA slot exit, i.e. without considering potential recirculation zones which may appear at the periphery of the outlet due to design effects (see Fig. 1). 2) Definition of the reference quantities in the source term formulation (Eq. ( 2) and Eq. ( 5)) over the control volume V r oms (x). 3) Application of the source terms to all cells within the control volume V roms (x). 4) Application of pressure outlet boundary conditions at V roms (x) boundary faces such that the velocity at the boundary face is extrapolated from the interior domain using reconstruction gradients. The free-stream Mach number is M ∞ = 0.23, the thickness of the boundary layer is δ = 2mm and the associated Reynolds number for ISA conditions is Re δ ≈ 10000. The steady blowing jet Mach number is set to M jet = 0.8 and the jet orifice exit diameter is d = 5mm.

The computational domain is composed of a computational box region of size (L x, L y, Lz) = (75d, 20d, 15d). The region contains ≈ 40million polyhedral cells. The domain is coarsened above 20d downstream the jet orifice. Velocity inlet BC, wall, pressure outlet and symmetry BCs are applied to both domain and jet inlets, bottom wall, outlet, top wall and the sides, respectively. A sketch of the configuration and an overview of the mesh in the refinement area are shown in Fig. 2.

Results

For a qualitative comparison of the flow features between the 'velocity inlet' and 'ROM' configurations, we show in Fig. 3, Fig. 4 and Fig. 5, Fig. 6,Fig. 7 the steady jet Q-criterion iso-surfaces and the contours of the vorticity in normal planes to the cross-flow stream-wise direction located at distances ranging from 4d to 12d for both "velocity inlet" (left) and "ROM" (right) modeling approaches after the convergence is reached, respectively. Good agreements are found in terms of flow topology : synthetic-jet initial development and stream-wise evolution under the influence of the outer flow. The synthetic jets and their induced vortices are well reproduced by the ROM approach in comparison with the velocity inlet approach.

For a quantitative comparison of the flow features between the 'velocity inlet' and 'ROM' configurations, we plot in Fig. 8 vertical profiles of the stream-wise velocity at the symmetric mid-plane for various x/d locations ranging from 4d to 8d for both 'velocity inlet' (left) and 'ROM' (right) modeling approaches after the convergence is reached, respectively. We can see that the results are also quantitatively in good agreements and thus, we can conclude that the 'ROM' approach can accurately model steady blowing jets in replacement of the 'velocity inlet'. The experimental setup consists in a canonical cylindrical axi-symmetric actuator that generates pulsed jets emanating from its circular orifice through the vibration of a membrane located at the base of the cylinder. A sketch of the setup and the SJA's parameters are shown in Fig. 9.

Considering the axial symmetry of the problem, we used the StarCCM+ two-dimensional axi-symmetric solver. The membrane motion is simulated by advanced StarCCM+ moving-mesh techniques. The membrane motion is defined as follows:

y(r) = 1 2 1 - r R 2 + 2 r 2 R 2 ln r R , (7)
where r and R = D/2 represent the distance to the symmetry axis and the membrane radius, respectively. The computational outer domain is composed of a box region of size (L x, L y) = (30d, 30d). The region contains ≈ 70, 000 hexahedral cells. An overview of the mesh is shown in Fig. 10. In the right side of Fig. 10, we highlight the control volume V r oms (x) corresponding to a layer of cells in the normal direction at the SJA slot exit where the data are extracted from 'SJA' modeling simulation and applied later to the 'ROM' modeling simulation at the same location.

The simulations are run for fifteen periods of oscillation of the membrane, i.e. 15 pulsations of the jet. The first ten periods are considered to evacuate the transient phenomena while the last five periods are considered to accumulate the data and compute the time averages. Pressure outlet boundary conditions are applied to the outer domain boundaries.

Results

Prior to both quantitative and qualitative analysis, we show in Fig. 11 the time history of density, momentum and energy volume average over the control volume V roms (x) domains in order to ensure that the extracted reference quantities over the control volume are well imposed through the ROM formulation. We clearly see that the data are well correlated between the SJA and ROM approaches except a slight over-estimation of the momentum in the longitudinal direction. The inefficient design of this benchmark actuator generates a re-circulation area in the side of the SJA outlet from the inside of the the tube to the outer zones with enhance of that can be seen as a pre-mixing of the emanating jet with the outer quiescent air. This pre-mixing is not present in the ROM case due to the absence of SJA the tube that is not modeled. The flow efficient section is reduced in the ROM case compared to the SJA case which results in a greater acceleration in the longitudinal direction for the ROM approach.

In Fig. 12 and Fig. 13, we show the contours of the radial momentum and vorticity for the 'SJA' model on the upper side and the 'ROM' on the lower side, respectively. From a qualitative point of view the flow features between the SJA and ROM configurations are in good agreement in terms of flow topology: synthetic-jet initial development and stream-wise evolution under the influence of the outer flow. The synthetic jets and their induced vortices are well reproduced and advected by the ROM approach in comparison with the SJA approach. However, as a direct consequence of the previous observation we can observe that the vortices are advected more rapidly using the 'ROM' approach. With regard to the analysis of average fields over time, Fig. 14 •10 -3

1.17

1.17

V. Conclusion

In this paper,we have presented an extension of the volumetric Reduced Order Models of ZNMF actuator in replacement of the more standard approaches based on the modeling of the full SJA cavity or the application of velocity inlet boundary conditions at the exit orifice of Zero-Net-Mass-Flux, Synthetic Jet Actuators.

The validation of the ROMs is performed on both steady and unsteady test cases and at both low and high Mach numbers. Each time, the ROM solution has been compared to one of the state-of-art used approaches, that is to say: velocity inlet boundary conditions or full SJA modeling.

Qualitatively, good agreement is found in terms of flow topology and synthetic jet development and further advection by the external flow and very accurate results were observed for the steady blowing jet case at high Mach number. However, an over-prediction of the longitudinal momentum of the emanating jet, resulting in a faster advection of the jet in the longitudinal direction can still be observed.

The proposed ROM approach proved to be relevant for optimized actuator geometries but still requires to be adapted when considering on-optimized actuators. Future works will be conducted in the analysis of the flow around the jet outlet, and of cross-flow jet interactions in order to define generic reference quantities according to the nature of the flow. It will allow us to avoid launching a first full SJA simulation to the reference quantities.

VI. Acknowledgment

.

  vector H = fluid's total enthalpy M = fluid's Mach number p = fluid's pressure Q = primitive variables vector R = Residual vector Re c = Reynolds number based on the chord length S = source terms vector t f = simulation final physical time T = fluid's temperature T = viscous stress tensor u = velocity vector U jet,max = peak velocity at the outlet of the SJA orifice V = control volume V r oms = ROM control volume W = conservative variables vector

Fig. 1

 1 Fig. 1 Highlight of the control volume V r oms (x), depicted as a pink thick line in the figure, corresponding to a layer of four cells in the normal direction at the SJA slot exit limited to the flow effective section

Fig. 2

 2 Fig. 2 Two dimensional sketch of the 3D numerical setup and mesh overview at the refinement area.

Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 yFig. 8

 345678 Fig. 3 Iso-surface of Q-criterion colored by the normalized velocity vector U/U ∞ and bottom wall colored by the wall shear stress: (left) velocity inlet BC setup, (right) ROM setup. Cross-planes located from 1d to 12d downstream the jet orifice exit with a 1d interval between two planes are displayed in grey.

1 Fig. 9

 19 Fig. 9 Schematic of the actuator model, in which the volume of fluid displaced by the diaphragm is ejected through the orifice in the form of a slug[2]

Fig. 11 Fig. 12 Fig. 13 Fig. 14

 11121314 Fig. 11 Time history of density, momentum and energy volume average over the control volume V roms (x) domains.

The authors are grateful to the European commission for funding this research project from H2020 Programme for the Clean Sky 2 Joint Technology Initiative under Grant Agreement: cleansky 2 / LPA / X-Pulse GA 738172. The authors would like to thank the continuous support and computational resources provided by Eos (CALMIP, Grant 2018-P17023) and Olympe (CALMIP, Grant 2019-P17023).