Elisa Marti

Angeles Rabadan

Jordi Cayuso

Gwenvael Le Dreau

Catarina Cruz

Mercedes Barci

Sebastian Pons

James Briscoe

Angeles Rabadán

Gwenvael Le Dréau

Mercedes Barzi

Elisa Martí

Jagged2 Controls the generation of Motor Neuron and Oligodendrocyte progenitors in the ventral Spinal Cord

Keywords: Sonic hedgehog, Notch, Jagged2, Olig2, Hes5, spinal cord, motor neurons, oligodendrocytes, neurogenesis, gliogenesis, chick, mouse

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

INTRODUCTION

In many developing tissues, most notably the central nervous system, the identity of a cell is linked to the time at which it is generated. However the mechanisms that underpin the temporal specification of cell fate are poorly understood. A well defined example of this problem is the sequential generation of motor neurons (MNs) and oligodendrocytes (OLPs) in the developing spinal cord. These two cell types arise from a common domain of progenitors, termed the motor neuron progenitor (pMN) domain, which is located in the ventral neural tube. Initially, the pMN domain produces somatic MNs that send axonal trajectories out of the CNS to innervate peripheral targets.

Subsequently progenitors in the same region produce oligodendrocytes, the myelinating cells of the CNS, which disperse throughout the grey matter of the spinal cord. The pMN domain is specified by the instructive activity of the secreted protein Sonic hedgehog (Shh), which, signalling through the canonical Gli pathway, provides positional identity to neural progenitors by directing a transcription network in responding cells (reviewed in 1). Amongst the members of this network is the basic-Helix-Loop-Helix (bHLH) transcription factor Olig2, which is expressed in the pMN domain and provides a molecular identifier for the pMN domain [START_REF] Lu | Sonic hedgehog-regulated oligodendrocyte lineage genes encoding bHLH proteins in the mammalian central nervous system[END_REF][START_REF] Zhou | Identification of a novel family of oligodendrocyte lineage-specific basic helix-loop-helix transcription factors[END_REF].

Early studies showed that Shh is both necessary and sufficient for the generation of spinal MNs [START_REF] Martí | Requirement of 19K form of Sonic hedgehog for induction of distinct ventral cell types in CNS explants[END_REF][START_REF] Roelink | Floor plate and motor neuron induction by different concentrations of the amino-terminal cleavage product of sonic hedgehog autoproteolysis[END_REF][START_REF] Chiang | Cyclopia and defective axial patterning in mice lacking Sonic hedgehog gene function[END_REF]. Subsequently Shh was shown to be required for OLPs to emerge at the appropriate developmental stages [START_REF] Soula | Distinct sites of origin of oligodendrocytes and somatic motorneuons in the chick spinal cord: oligodendrocytes arise from Nkx2.2-expressing progenitors by a Shh-dependent mechanism[END_REF]8). This indicated a dual role for Shh in both MN and OLP generation. Consistent with this, Shh induces the expression of Olig2 and a related gene, Olig1, in the pMN domain. MNs and OLPs are depleted or eliminated in the spinal cord of mice and zebrafish lacking Olig2 (9,10,11,12). In addition Olig2 promotes the expression of the neurogenic bHLH factor Ngn2 that contributes to the terminal differentiation of MNs (13,14). These data led to a model in which MNs and OLPs derive from a common progenitor that expresses Olig2, which switches from MN to OLP generation at a defined developmental time point. However, the factors regulating the temporal switch from MN to OLP and maintaining the population of progenitors undifferentiated to ensure that the appropriate numbers of each cell type are generated, remain elusive.

The Notch pathway has a well recognized role in maintaining the balance between progenitor self renewal and differentiation (reviewed in 15). Ligands of the Notch pathway (Dll1, Jag1) are expressed in distinct patterns along the DV axis in the developing spinal cord (16,[START_REF] Lindsell | Expression patterns of Jagged, Delta1, Notch1, Notch2, and Notch3 genes identify ligand-receptor pairs that may function in neural development[END_REF][START_REF] Myat | A chick homologue of Serrate and its relationship with Notch and Delta homologues during central neurogenesis[END_REF][START_REF] Marklund | Domain-specific control of neurogenesis achieved through patterned regulation of Notch ligand expression[END_REF]. Notch signalling is a cell-cell communication system and activation of Notch signalling results from the interaction between the Notch receptor and its ligands, Delta and Jagged, expressed by adjacent cells. The ligand receptor interaction induces a proteolytic cleavage of the Notch protein and nuclear translocation of its intracellular domain (Notch ICD), which interacts with the DNA-binding protein CSL (RBP-Jk) to activate Notch downstream genes, such as the Hes transcription factors (15). These proteins have been demonstrated to mediate their functions, at least in part, by repressing the neurogenic bHLH factor Ngn2 that contributes to the terminal differentiation of MNs (13, 14), and by inhibiting the maturation of OLPs, at least in the optic nerve [START_REF] Wang | Notch receptor activation inhibits oligodendrocyte differentiation[END_REF]. Thus a plausible model might entail Notch activity preserving undifferentiated progenitors in the pMN during the period of MN generation so that sufficient are available when oligogenesis supervenes. Supporting this view, in the zebrafish embryo, Notch signalling is required during embryogenesis to maintain radial glia and permit oligodendrocyte development [START_REF] Park | Delta-Notch signalling regulates oligodendrocyte specification[END_REF]. However, whether Notch signalling plays a direct role in determining the timing, and the switch, from neurogenesis to gliogenesis is unknown.

Here we show that in the chick and the mouse embryo, the expression of the Notch ligand Jagged2 is restricted to the pMN domain during the period of motor neuron generation, and that this pattern of expression depends on Shh activity. In vivo experiments demonstrate that loss of Jagged2 resulted in the accelerated differentiation of MNs and the premature generation of OLPs. Conversely, gain of function experiments demonstrate that Jagged2 activity prevents the differentiation of pMNs, at least in part by lowering the levels of Olig2 protein, thus preserving Olig2+ progenitors for later oligodendrogenesis. In search for the Notch-dependent effector regulating this cell fate switch we found that Hes5, a Notch target and direct repressor of OLP specific genes, is regulated and mediates the activity of Jagged2. Together the data provide new insight into the genetic network responsible for the timely generation of spinal motor neurons and oligedendrocyte progenitors..

RESULTS

Shh signaling directs expression of Jagged2 to the pMN domain

An in vivo transcriptome analysis of neural progenitors responding to different levels of Shh activity in a cell autonomous manner (see methods) [START_REF] Cruz | Foxj1 regulates floor plate cilia architecture and modifies the response of cells to sonic hedgehog signalling[END_REF], focussed our attention on the Notch pathway, and the possibility that Notch signalling plays a role in patterning the neural tube. In response to activators of the Shh pathway expression of the Notchligand Serrate2/Jagged2 appeared up-regulated (Figure1A).

To examine the spatiotemporal distribution of Jagged2 in the developing spinal cord, we mapped its expression in relation to proteins defining different dorsoventral (DV) domains using immunohistochemistry and in situ hybridization at different developmental stages. The onset of expression occurred after neural tube closure in scattered cells (data not shown). From HH15 to HH18 Jagged2 was expressed within the motor neuron progenitor domain (pMN) (Figure 1B,C). At these stages Jagged2 was co-expressed with the MN progenitor protein Olig2 in a salt-and-pepper pattern (Figure 1F,G) and was excluded from the differentiated MNs. Additionally, Jagged2 was expressed in a subset of dorsal progenitors (Figure 1C,D). Expression of Jagged2 in the pMN was transient, however was maintained in the transition zone by HH23/24 (Figure 1D,H) and was extinguished by HH30 (Figure 1E,I). However, dorsal expression of Jagged2 is maintained at HH30, together with lower expression levels in some subpopulations of differentiated MNs. Interestingly, the down-regulation of Jagged2 expression in the pMN domain correlates with the time OLP generation supervenes (Figure 1E,J).

We tested whether the ventral expression of Jagged2 depends on Shh activity. Analysis of the Shh-/-embryos showed the lack of Jagged2 expression in the ventral hindbrain and spinal cord (Supplementary Figure1). Additionally, inhibition of Shh signalling by a dominant negative version of Gli3 (Gli3 R , 23) resulted in the loss of Jagged2 expression from pMN (Supplementary Figure 1). Conversely, constitutive activation of the Shh pathway, using Gli3 Act , resulted in a dorsal expansion of Jagged2 (Supplementary Figure1). Together these results indicate that Shh signalling is required and sufficient for the ventral expression of Jagged2.

Experimental evidence supports a model in which the specific distribution of Notch ligands, along the DV axis of the neural tube, endows distinct progenitor domains with the ability to influence the pace of cell differentiation in a domain-and cell type-specific manner [START_REF] Marklund | Domain-specific control of neurogenesis achieved through patterned regulation of Notch ligand expression[END_REF][START_REF] Barrio | A regulatory network involving Foxn4, Mash1 and delta-like 4/Notch1 generates V2a and V2b spinal interneurons from a common progenitor pool[END_REF][START_REF] Ferreira-Rocha | Dll1 and Dll4 function sequentially in the retina and pV2 domian of the spinal cord to regulate neurogenesis and creat cell diversity[END_REF]. This prompted us to ask whether Jagged2 activity influenced the generation of either MNs and/or OLPs from the pMN domain. To test the function of Jagged2 in the pMN domain, we first generated short-hairpin RNA (shRNA) to knockdown endogenous Jagged2. Analysis by qPCR of target RNA in transfected neural cells indicated that the shJagged2 (LOF-JAG2) reduces RNA levels to ~50% of normal without reducing the closely related ligand Jagged1 (Supplementary Figure 2). Additionally, knock-down of Jagged2 did not affect the relative distribution of proliferating progenitors and differentiated neurons in the spinal cord, neither changed the identity of progenitors along the DV axis (Supplementary Figure 2 and data not shown) similar to the results recently reported for Jagged1 [START_REF] Marklund | Domain-specific control of neurogenesis achieved through patterned regulation of Notch ligand expression[END_REF]. Thus this analysis indicated that shJagged2 did not affect the anatomical integrity of the neural tube, prompting us to analyse domain specific cell fate identities.

Jagged2 activity regulates the timely generation of MNs

In the spinal cord MNs are generated from the pMN domain in a narrow time-window (stage HH15 to stage HH23/24; 26). To test the role of Jagged2 in MN generation, brachial regions of embryos were electroporated at HH14, before the onset of MN generation, and assayed with the early MN marker MNR2/HB9 (14). Quantification of MNs and their spatial distribution was performed relative to the ventricular lumen (Figure 2A). MNR2+ cells positioned adjacent to the VZ correspond to newly generated MNs (MNR2+ cells in the Transition Zone, TZ), whereas those positioned towards the basal/pial surface correspond to terminally differentiated MNs (MNR2+ cells in the Marginal Zone, MZ). Knock-down of Jagged2 (LOF-JAG2) markedly changed the distribution of MNR2+ cells: more cells were positioned adjacent to the VZ and less terminally differentiated MNs were present. By contrast, forced expression of Jagged2 (GOF-JAG2) reduced the total number of MNR2+ cells at both locations (Figure 2B). This suggested that Jagged2 activity might regulate the tempo of MN generation and prompted us to analyse MN differentiation.

To unequivocally identify the birth date of MNs, we administered a single dose of BrdU at HH20 (24h-PE, the time at which ~50% should be post-mitotic; 26) and harvested the embryos at HH23/24 (48h-PE). Double immunohistochemistry for BrdU and the definitive MN marker Islet1 allowed us to identify MNs (Islet1+/BrdU-) that had exited the cell cycle and initiated differentiation prior to HH20 (Figure 2C,D). Embryos that were electroporated at HH14 (before the onset of MN generation) with the control vector contained 43±0,015% of Islet1+/BrdU-cells, confirming that ~50% of MNs were generated prior to HH20 (Figure 2E,F). By contrast, in embryos in which Jagged2 activity was depleted from HH14, the percentage of Islet1+/BrdU-MNs increased significantly to 61±0,017% (~2 fold increase) Furthermore, the total number of Islet1+ cells appeared reduced, 48h-PE of LOF-JAG2 (Figure 2E,F). This suggests that loss of Jagged2 activity promotes the premature differentiation of MNs.

Conversely, gain-of-function experiments with Jagged2 (GOF-JAG2) resulted in the significant decrease in MN differentiation and the percentage of Islet1+/BrdUdecreased to 33±0,02% (~1.5 fold decrease) (Figure 2E,F). Importantly, these experiments indicated that the ability of Jagged2 to activate Notch is limited to pMN progenitors, since differentiation of other neuronal identities was largely unaffected (Supplementary Figure 3). This is in concordance to the recently reported roles for Dll1 and Jagged1 [START_REF] Marklund | Domain-specific control of neurogenesis achieved through patterned regulation of Notch ligand expression[END_REF][START_REF] Ferreira-Rocha | Dll1 and Dll4 function sequentially in the retina and pV2 domian of the spinal cord to regulate neurogenesis and creat cell diversity[END_REF].

Jagged2 activity inhibits the differentiation of Olig2+ progenitors.

Intriguingly both LOF-and GOF-in vivo experiments resulted in a reduction of the final numbers of differentiated MNs. To better understand this result, we took advantage of the data generated by the determination of the percentages of born motor neurons (Figure 2F), to model the behaviour of the pMN domain for three cell divisions (~48 hours). We took the simplifying assumption that normally 50% of divisions were asymmetric. We next examined the effect of the changes in the rate of neurogenesis measured in the LOF-and the GOF-experiments. Plotting the ratios of predicted differentiated MNs in each experimental condition showed the initial increase in MN in the absence of Jagged2, while at the end of the 48h period, the final MN number decreased in both conditions. These profiles were similar to those obtained empirically (Figure 3A). Moreover, the model predicted specific changes in progenitor numbers, prompting us to experimentally test this prediction.

Olig2 is a basic-Helix-Loop-Helix (bHLH) transcription factor expressed in the pMN domain that provides a molecular identifier for the pMN domain and is a key component of the genetic network operating for the generation of MNs [START_REF] Lu | Sonic hedgehog-regulated oligodendrocyte lineage genes encoding bHLH proteins in the mammalian central nervous system[END_REF][START_REF] Zhou | Identification of a novel family of oligodendrocyte lineage-specific basic helix-loop-helix transcription factors[END_REF]14).

Consistent with the prediction of the model, the forced expression of Jagged2 (GOF-JAG2) resulted in an increase in Olig2+ progenitor cells within the VZ (Figure 3B).

Conversely, reduced Jagged2 activity (LOF-JAG2) caused a gradual loss of Olig2+ cells from the VZ (Figure 3B). Noticeably, these experimental data match the changes in progenitor numbers predicted by our model. All together these data suggests that Jagged2 controls MN differentiation through the regulation of Olig2+ cells.

We observed that forced expression of Jagged2 laterally inhibit Olig2+ cells that are retained as progenitors within the VZ (Figure 3C). Furthermore, it also came to our attention the fact that Olig2+ cells, retained in the VZ by the activity of Jagged2, appeared to express lower levels of Olig2 protein, when compared to the control contralateral Olig2+ progenitors (Figure 3C). To further assess this observation, we next quantified total protein levels by WB in neural tube extracts that were electroporated with either Olig2 alone or together with Jagged2. Co-electroporation of Jagged2 caused a ~50% reduction on both Olig2 protein bands (Figure 4A). This observation suggested a mechanism by which Jagged2 reduced Olig2 protein to a level below the threshold require to generate MNs, thus resulting in the lateral inhibition of MN differentiation, Indeed, over-expression of Olig2 alone was sufficient to promote MN generation as shown by the ectopic MNR2+ cells (Figure 4C) (14). However, exposure to Jagged2 inhibits the MN differentiation activity of Olig2+ (Figure 4C). Altogether, our data suggest a model in which Jagged2 function in the pMN domain to inhibit laterally the Olig2-expressing progenitor from becoming MNs. Olig2-expressing progenitors that do not contact with Jagged2, were primed to enter the differentiation pathway to generate MNs. Lateral contact to Jagged2, prevents MN differentiation, at least in part, by reducing the Olig2 protein levels.

Jagged2 activity is necessary to prevent premature OLP generation

Once neurogenesis of MNs is terminated, progenitors in the pMN domain switch to the generation of oligodendrocyte progenitors (OLPs). We therefore analysed the effect of Jagged2 depletion on the oligodendrogenesis. Strikingly, after knock-down of Jagged2 function at HH14, Olig2 expressing cells were observed migrating away from the pMN (mean 19,14± 1,99 cells/section, n=20) (Figure 5A,B). This contrasted with control embryos in which Olig2 was robustly expressed in the pMN domain and no migratory Olig2+ cells were detectable. Furthermore Olig2+ migratory cells were significantly reduced when the human-Jagged2 (GOF-JAG2) was co-electroporated, supporting the specificity of the phenotype (rescue experiments: mean 9± 2,27 cells/section, n=15) (Figure 5C,H). In both mouse and chick spinal cord, Olig2 expressing cells that migrate away from the VZ have been characterized as OLPs (2,3,9,10), but these are not normally generated until HH30 [START_REF] Soula | Distinct sites of origin of oligodendrocytes and somatic motorneuons in the chick spinal cord: oligodendrocytes arise from Nkx2.2-expressing progenitors by a Shh-dependent mechanism[END_REF], after the period of MN generation. In order to characterize the molecular nature of these migratory Olig2+ cells we co-immunostained with the OLP specific marker O4 [START_REF] Soula | Distinct sites of origin of oligodendrocytes and somatic motorneuons in the chick spinal cord: oligodendrocytes arise from Nkx2.2-expressing progenitors by a Shh-dependent mechanism[END_REF]. This revealed that most of the migratory Olig2+ cells co-expressed O4 (Figure 5G), consistent with these cells being OLPs. Furthermore, the SoxE proteins have a prominent role in OLP generation. Sox9 is required for OLP specification and is expressed transiently in early migrating OLP.

Sox8 and Sox10 are also expressed in early migrating OLPs and Sox10 activates myelin genes as part of the terminal differentiation program of oligodendrocytes [START_REF] Stolt | Transcription factors Sox8 and Sox10 perform non-equivalent roles during oligodendrocyte development despite functional redundancy[END_REF][START_REF] Finzsch | Sox9 and Sox10 influence survival and migration of oligodendrocyte precursors in the spinal cord by regulating PDGF receptor alpha expression[END_REF].

Consistent with migratory cells being OLPs, knock down of Jagged2 resulted in the premature migration of Sox9+ cells (mean 28,57±5,73 cells/section, n=16) and the concomitant reduction of Sox9+ cells from the pMN. Again in a Jagged2-LOF background, the number of Sox9+ migratory cells was significantly reduced when NT was co-electroporated with the human Jagged2 cDNA (GOF_JAG2) that was resistant to the short hairpin (rescue experiments; mean 7,2±2,1 migratory cells/section) further supporting the specificity of this phenotype (Figure 5D-F,H). Furthermore, premature migratory OLPs expressed expressed Sox8 (not shown), Sox10 and the myelin specific gene PLPDM20 (Figure 5I-N). Knock-down of Jagged2 additionally increased levels of platelet derived growth factor receptor alpha (PDGFRa) and PLP expression, as assessed by real-time PCR (Figure 5O), as well as the activity of the Myelin Basic Reporter as assessed by Luciferase activity (Figure 5P). Altogether, these data indicate that knockdown of Jagged2 activity results in the precocious generation of OLPs from the pMN domain.

Converse gain-of-function experiments allowed the maintenance of high levels of Jagged2 expression at the time of OLP generation, when Jagged2 expression is normally extinguished from pMN. This resulted in the loss of migratory OLP identified by double immunohistochemistry for Olig2+/Nkx2.2+ and Olig2+/O4+ , at the stage at which migratory OLPs were abundant in the control contralateral side (Figure 6A-E) [START_REF] Soula | Distinct sites of origin of oligodendrocytes and somatic motorneuons in the chick spinal cord: oligodendrocytes arise from Nkx2.2-expressing progenitors by a Shh-dependent mechanism[END_REF][START_REF] Sun | Olig bHLH proteins interact with homeodomain proteins to regulate cell fate acquisition in progenitors of the ventral neural tube[END_REF][START_REF] Zhou | The bHLH transcription factor Olig2 promotes oligodendrocyte differentiation in collaboration with Nkx2.2[END_REF]. This result is consistent with the finding that JAG2 has a negative role on Olig2 expression. Together these data supports the idea that MNs and OLPs are sequentially generated from a single progenitor and that Jagged2 activity ensures progenitors do not switch from neurogenesis to gliogenesis prematurely.

Jagged2 controls OLP generation through the regulation of Hes5 expression

How might Jagged2 prevent precocious OLP generation? Members of the Hes family of bHLH transcription factors are the best characterized Notch targets that function as effectors of the cell fate decisions mediated by Notch signalling. In the chick spinal cord Hes5 is the only member expressed in the pMN domain (Figure 7A,B) (31) and its expression is reduced from these progenitors as they switch from MN to OLP generation (Figure 7C). Moreover, mice lacking Hes5 generate excess oligodendrocytes [START_REF] Liu | A molecular insight of Hes5-dependent inhibition of myelin gene expression: old partners and new players[END_REF]. These data raised the possibility that Hes5 is the transcriptional effector that regulates the timing of OLP generation.

We first tested whether Jagged2 regulates Hes5 expression in the pMN. Reduction of Jagged2 function caused the loss of Hes5 expression (Figure 7D,F). Moreover, even though Hes5 is broadly expressed, the loss of Hes5 expression was restricted to the pMN. Conversely, gain-of-function experiments showed that forced expression of Jagged2 resulted in the maintenance of high levels of Hes5 in the pMN domain (Figure 7F).

We next asked whether Hes5 activity could rescue the premature generation of OLP observed in the absence of Jagged2. Indeed, in embryos in which Jagged2 was depleted by shRNA, the forced expression of Hes5 significantly reduced the premature migration of Olig2+/Sox9+ cells, caused by depletion of Jagged2 activity (Olig2+ from 19,14± 1,99 to 3,62±0,53 cells/section; Sox9+ from 28,57±5,73 to 7,09±1,28 cells/section, Figure 7G-K). Consequently, Olig2 and Sox9 expressing cells were maintained in the VZ of the pMN domain (Figure 7G,H). This supports the conclusion that Hes5 acts downstream of Jagged2 to control the premature generation of OLPs.

DISCUSSION

In this study we provide evidence that the generation of MN and OLP in the ventral spinal cord depends on the activity of the Notch-ligand Jagged2. The activity of Jagged2 appears to prevent the neighbouring Olig2-expressing progenitor from entering the differentiation pathway. In pMN progenitors in which the Notch pathway is activated by Jagged2 MN differentiation program is prevented, at least in part, by reducing the Olig2 protein levels. This preserves a pool of progenitors and, at the same time, maintains high levels of Hes5 expression that in turn directly inhibit the oligodendrocyte generation during the neurogenic phase.

In the absence of Jagged2 however, pMN progenitors enter the differentiation program to generate first MNs and next, when Hes5 levels are sufficiently reduced, to generate oligodendrocytes. Together the data support a model in which MN and OLP arise sequentially from a common progenitor population residing in the pMN. Jagged2 controls the timing of the switch from MN to OLP production by suppressing OLP generation during the neurogenic phase.

During the process of writing these results, two independent studies show posttranscriptional modifications of Olig2 that changed the activity of Olig2 and thus the outcome of the Olig2+ progenitors in the pMN. On the one hand, Li and cols (33) find a phosphorylation site in the bHLH domain of Olig2 that favours the homodimerization capability of Olig2, and thus its transcriptional activity. Mice carrying a mutant version of Olig2 (Olig2S147A) show the loss of progenitors at the pMN domain and the loss of differentiated MNs, a phenotype that is highly comparable to the over-expression of Jagged2. This suggested that changes in the MN-differentiation capacity of Olig2 that we reported in the presence of Jagged2, might be the result of a similar posttrancriptional modification. On the other hand, Sun and cols [START_REF] Sun | Phosphorylation state of olig2 regulates proliferation of neural progenitors[END_REF] The generation of both MNs and OLPs requires Shh signalling. Olig2 expression depends on Shh and is required for the generation of both MNs and OLPs suggesting an explanation for the requirement for Shh in pMN derivatives. Here we provide evidence that, in addition to Olig2, the regulation of Jagged2 expression by Shh signalling also contributes to the generation of both MNs and OLPs. Shh activity is required and sufficient for the restricted expression of Jagged2 to the pMN domain. Moreover, the involvement of Jagged2 in regulating the timing of the transition from MN to OLP production links the process of spatial patterning, which positions the pMN domain in the ventral neural tube, with temporal patterning that determines when each cell type is generated. Whether Jagged2 expression is directly or indirectly regulated by Shh signalling, remains to be determined. Furthermore, the timely loss of Jagged2 expression from the pMN domain appears as an important pre-requisite for OLP formation. Molecular mechanism operating directly to pause Jagged2 expression might include transcriptional repression and/or epigenetic silencing, among many others, and understanding these mechanisms remains as an important unresolved question.

Whether the Notch pathway is required simply to maintain pools of undifferentiated progenitor cells, or whether it plays instructive roles in promoting specific cell fates has been the subject of debate. Our data indicate that Notch signalling, activated by Jagged2, maintains pMN progenitors in an undifferentiated state but also provides an instructive signal that blocks the fate switch from MN to OLP. This suggests a dual role for Notch signalling and is consistent with other studies of glial development. The Notch effector Hes1 promotes Muller and radial glia identities [START_REF] Kondo | Basic helix-loop-helix proteins and the timing of oligodendrocyte differentiation[END_REF], while Hes5 directly regulates expression of myelin genes [START_REF] Liu | A molecular insight of Hes5-dependent inhibition of myelin gene expression: old partners and new players[END_REF]. Moreover, Notch signalling has been implicated in the diversification of neuronal identities in the neural tube [START_REF] Barrio | A regulatory network involving Foxn4, Mash1 and delta-like 4/Notch1 generates V2a and V2b spinal interneurons from a common progenitor pool[END_REF][START_REF] Rocha | Dll1 and Dll4 function sequentially in the retina and pV2 domain of the spinal cord to regulate neurogenesis and create cell diversity[END_REF]. The observation that Notch-ligands are expressed in discrete domains along the DV axis of the CNS is in line with the idea that Notch-ligands play specific roles in the cell fate decisions of progenitors. Thus our data support the idea that Notch ligands can serve both to prevent the untimely differentiation of neural progenitors and to generate diversity within a population of progenitors [START_REF] Park | Delta-Notch signalling regulates oligodendrocyte specification[END_REF][START_REF] Barrio | A regulatory network involving Foxn4, Mash1 and delta-like 4/Notch1 generates V2a and V2b spinal interneurons from a common progenitor pool[END_REF][START_REF] Rocha | Dll1 and Dll4 function sequentially in the retina and pV2 domain of the spinal cord to regulate neurogenesis and create cell diversity[END_REF][START_REF] Yeo | Jagged-mediated Notch signalling maintains proliferating neural progenitors and regulates cell diversity in the ventral spinal cord[END_REF].

Our results suggest a model in which, early in the developing spinal cord, a common neuro-glioblast progenitor is present in the pMN domain and this has the capacity to generate MN and OLP [START_REF] Li | Phosphorylation Regulates OLIG2 Cofactor Choice and the Motor Neuron-Oligodendrocyte Fate Switch[END_REF][START_REF] Sun | Phosphorylation state of olig2 regulates proliferation of neural progenitors[END_REF]. During MN generation, Hes5 induced by Jagged2 prevents premature OLP differentiation and, at the same time, maintains a proportion of these progenitors in an undifferentiated state. The switch to OLP generation depends on the downregulation of Jagged2 expression which facilitates the differentiation of the remaining progenitors and disinhibits OLP generation. When Jagged2 activity is artificially depleted in vivo, the precocious generation of OLP is accompanied by a reduction in MN generation. This argues against a model in which separate OLP and MN precursors are present in the pMN and suggests that in the absence of Notch activity the progenitors of MN adopt a gliogenic identity. Nevertheless, our results cannot formally rule out the presence of separate lineage-restricted neuroblasts and glioblasts within the pMN that are derived from a single common precursor [START_REF] Wu | Motoneurons and oligodendrocytes are sequentially generated from neural stem cells but do not appear to share common lineage-restricted progenitors in vivo[END_REF]. In this case, Jagged2 activity would act on these populations separately to inhibit differentiation and OLP generation. High resolution analysis of the behaviour of individual pMN progenitors will be necessary to conclusively test this possibility.

Notwithstanding this question, the data presented here demonstrate a novel role for Jagged2 and Notch signaling in the temporal control of cell type identity in the vertebrate CNS.

MATERIALS AND METHODS

Fluorescence Associated Cell Sorting (FACS) and Microarray analysis

Plasmid DNA encoding either GFP alone, a deleted form of mouse Patched lacking the second large extra cellular loop (mPtc1Δ loop2 ) or an activated version of Gli3 (Gli3 Act aa1402-4743) were inserted into pCAGGS-ires-EGFP vector as reported [START_REF] Cayuso | The Sonic hedgehog pathway independently controls the patterning, proliferation and survival of neuroepithelial cells by regulating Gli activity[END_REF], for in ovo electroporation into HH11-12 stage embryos. Neural tubes were dissected out 14 or 36 hours later, and single cell suspension was obtained by 10-15 minutes incubation on Tripsin-EDTA (SIGMA). GFP fluorescence was determined by flow cytometry using a MoFlo flow cytometer (DakoCytomation, Fort Collins, Colorado, USA). The resulting cell population, consisting of ~90% of GFP+ cells, was used for total RNA extraction.

GeneChip Chicken Genome Arrays (Affymetrix) containing 32,773 chicken transcripts were used for the hybridization of the samples. Unpaired analysis of the data, based on the comparison between the average values of the logRed and logGreen intensities, was performed using SOLAR System v2.0 (Alma Bioinformatics S.L.). Results were filtered using unpaired t-tests using thresholds of ≥1.5 fold change and p-value ≤0.05 [START_REF] Cruz | Foxj1 regulates floor plate cilia architecture and modifies the response of cells to sonic hedgehog signalling[END_REF]

Mouse and Chick embryos

Mice homozygous for the Shh null allele were as published [START_REF] Chiang | Cyclopia and defective axial patterning in mice lacking Sonic hedgehog gene function[END_REF]. Eggs from White-Leghorn chickens were staged according to Hamburger and Hamilton (HH) [START_REF] Hamburger | A series of normal stages in the development of chick embryo[END_REF]. For chick embryos electroporation, plasmid DNA was injected into the lumen of neural tubes and electroporation carried out using and Intracel Dual Pulse (TSS10) electroporator.

For BromodeoxyUridine (BrdU) labelling, 5μg/μl BrdU was injected into the neural tubes at the indicated times prior fixation. Transfected embryos were allowed to develop to the indicated stages, then dissected, and processed for immunohistochemistry, in situ hybridisation, or FACS sorting and qPCR analysis.

Immunohistochemistry and in situ hybridization

For immunohistochemistry, embryos were fixed 2-4 hours at 4ºC in 4% PF in PB. For BrdU detection, sections were incubated in 2N HCl for 30 minutes followed by 0.1M For in situ hybridisation, embryos were fixed overnight at 4ºC in 4% PF in PB, rinsed and processed for whole mount RNA in situ hybridization following standard procedures using probes for chick Jagged2, Hes5, Sox8, Sox9, Sox10 and PLPDM20 (from the chicken EST project, UK-HGMP RC). Mouse Jagged2 probe was used (JL de la Pompa). Hybridized embryos were developed either with NBT/BCIP, or with FAST-RED Chromogen (Roche) for Fluorescent in situs, rinsed in PBT and vibratome sectioned and photographed on a Leica DMR microscope, or a Leica SP5 confocal.

DNA Constructs

A deleted form of mouse Patched (mPtc1Δ loop2 ), deleted forms of human Gli3 (Gli3 Rep aa1-768 and Gli3 Act aa1402-4743), human full-coding sequences for Jagged2 and Hes5 were cloned into pCAGGS-ires-GFP for in vivo gain-of-function (GOF) experiments.

The full-length mouse Olig2 cDNA into pCDNA3.1 was also used (14).

For in vivo loss-of-function (LOF) experiments, short RNA hairpin-based expression vectors for RNA interference were generated using the pSUPER RNAi system TM (OligoEngine Inc.) A pair of custom oligonucleotides that contained a unique 19-nt sequence derived from the chicken Jagged2 mRNAs were designed using the RNAi Design Tool (www.oligoengine.com). Forward and reverse 64-nt oligos (Sigma) were used for annealing and cloning into the pSUPER vector (Supplementary Figure 1A), according to the manufacturer's guidelines. Control short hairpin RNA was generated for a human HDAC sequence, cloned into the pSUPER vector and electroporated at same developmental stages for each experiment. (A) Western blots from NT total lysates were immunobloted with anti-Olig2, anti-Myc and anti-RFP antibodies. Embryos co-EP at HH14 with Jagged2-Myc, Olig2 and pCAGGS-ires-RFP, were dissected 12h-PE. Note that Olig2 protein is distributed within two separate bands that were both shifted but maintained in the presence of CIAP, showing that both forms are phosphoproteins. These two bands might reflect alternate translation initiation sites [START_REF] Lu | Sonic hedgehog-regulated oligodendrocyte lineage genes encoding bHLH proteins in the mammalian central nervous system[END_REF]. Anti-Myc reveals the presence or absence of Jagged2-Anti-RFP, as EP control. (B) Quantitative analysis of upper and lower Olig2 bands, in the presence or the absence of Jagged2, normalized to RFP levels.

RT-Quantitative

Olig2 protein levels are significantly reduced in NT co-transfected with Jagged2.

(C) The Olig2 capacity to differentiate MNs is prevented by Jagged2 activity. Embryos EP at HH14 with the indicated DNAs were analysed 12h-PE for the MN progenitor marker Olig2 (red) and the MN definitive marker MNR2 (green). GFP is shown in blue. EP of Olig2 is sufficient for the generation of ectopic MNR2+ MNs. Quantification of ratio of MNR2+ cells in EP vs control non-EP side revealed a ratio of 0,85±0,07 in control EP embryos, while in Olig2-EP increased to 2,02±0,03. EP of Jag2 prevents the generation of MNR2+ cells to 0,58±0,02, while co-EP of Olig2 and Jag2 also reduced the appearance of MNR2+ cells to 0,51±0,05 in the normal ventral domain, but also prevented the generation of ectopic dorsal MNs (D) Summary model of Jagged2 activity in the pMN domain, Jagged2 activity splits Olig2+ve progenitors into two different identities.

  find a triple serine phosphorylation motif at the N-terminal part of the Olig2 protein, which are required for the Olig2 mediated proliferation of neural progenitors however are dispensable for the Olig2-mediated specification of OLPs. Altogether these data indicate a pivotal role played by post-transcriptional modifications of Olig2 in the outcome of the pMN progenitors, and our data indicate that Jagged2 might be among the upstream signals regulating these modifications.

  Na 2 B 4 O 7 pH8.5 rinses further PBT rinses and anti-BrdU incubation. Immunostainings were performed following standard procedures on either vibratome or cryostat sections. Antibodies against the following proteins were used; green fluorescence protein (GFP) (Molecular Probes), caspase3 (BD), a unique beta-Tubulin (Tuj-1, MEDPASS S.a.r.l.), phospho-Histone 3 (p-H3, Upstate Biochemicals), Olig2 (Zhou et al., 2001), Pax2 (Zymed), Sox9 (M. Wegner), O4 (C. Soula). Monoclonal antibodies to BrdU, MNR2, Nkx2.2, Islet1 and Islet2 were obtained from the Developmental Studies Hybridoma Bank (DSHB). Alexa488-and Alexa555-conjugated anti-mouse or anti-rabbit antibodies (Molecular Probes) were used. After single or double staining, sections were mounted, photographed using a Leica SP5 Confocal microscope, and processed with Adobe Photoshop CS3.

  Real-Time-PCR EGFP-containing plasmid DNAs were electroporated and neural tubes dissected out 24-48 hours later. Single cell suspension was obtained by 10-15 minutes incubation on Tripsin-EDTA (SIGMA). GFP expressing cells were FACS sorted and the resulting cell population was used for total RNA extraction. PCR reactions were carried out by triplicate using fixed amounts of template DNA. Oligonucleotides were obtained from QIAGEN, (QuantiTec Primer Assays) for use in real-time RT-PCR with SYBR green detection. References for QuantiTect Primer Assay were as follows: GgJagged1 QT00598003, GgJagged2 QT01512749, GgPDGFRalpha QT00598969, GgPLP QT00598955. A standard curve was made for each amplicon by plotting the number of cycles at which the fluorescence crossed the threshold (crossing values) against increasing amounts of DNA template. All experimental values were normalized to those obtained for GAPDH. Western Blot HH Stage 14 embryos were electroporated with a Myc-Tagged-Jagged2, a V5-Tagged-Olig2, and pCAGGS-ires-RFP for transfection control. Neural tubes dissected 12h-PE were collected in PBS and directly lysed in 1X SDS loading buffer (10% glycerol, 2%SDS, 100mM DTT and 60 mM Tris-HCl pH 6.8) and the DNA disrupted by sonication. Selected samples were treated with Calf Intestin Alkaline Phosphatase 8.-Oh S, Huang X and Chiang C Specific requirements of sonic hedgehog signalling during oligodendrocyte development. Dev Dyn. 2005; 234: 489-496 9.-Lu QR, Sun T, Zhu Z, Ma N, Garcia M, Stiles CD and Rowitch DH. Common developmental requirement for Olig function indicates a motor neuron/oligodendrocyte connection. Cell 2002; 109: 75-86 10.-Zhou Q and Anderson D. The bHLH transcription factors OLIG1 and OLIG2 couple neuronal and glial subtype specification. Cell 2002;109: 61-73. 11.-Takebayashi H, Nabeshima Y, Yoshida S, Chisaka O, Ikenaka K and Nabeshima Y. The basic-helix-loop-helix factor Olig2 is essential for the development of motor neuron and oligodendrocyte lineages. Curr Biol. 2002; 12: 1157-1163 12.-Park HC, Mehta A, Richardson JS and Appel B. Olig2 is required for zebrafish primary motor neuron and oligodendrocyte development Dev Biol. 2003; 248: 356-368. 13.-Mizuguchi R, Sugimori M, Takebayashi H, Kosako H, Nagao M, Yoshida S, Nabeshima Y, Shimamura K and Nakafuku M Combinatorial roles of olig2 and neurogenin2 in the coordinated induction of pan-neuronal and subtype-specific properties of motoneurons. Neuron 2001; 31:757-771. 14.-Novitch BG, Chen AI and Jessell TM Coordinate regulation of motor neuron subtype identity and pan-neuronal properties by the bHLH repressor Olig2. Neuron 2001; 31:773-789 15.-Louvi A and Artavanis-Tsakonas S. Notch signalling in vertebrate neural development. Nat Rev Neurosci. 2006; 7:93-102. 16.-Henrique D, Adam J, Myat A, Chitnis A, Lewis J and Ish-Horowicz D. Expression of a Delta homologue in prospective neurons in the chick. Nature 1995; 375:787-790 Quantitative data showing the proportion of born MNs, plots corresponds to the ratio of EP vs non-EP side in each experimental condition (control: black dots, GOF-Jag2: red dots, LOF-Jag2: green dots). Time is represented as hours of incubation and HH stages. First dot corresponds to the EP time, second to the BrdU-/Islet1+ cells (MNs born at the time of the BrdU pulse), third dot represents the total Islet1+ cells (MNs terminally differentiated 48h-PE). Bars correspond to the standard error (SEM).

FIGURE 3 .

 3 FIGURE 3.-Over-expression of Jagged2 retain Olig2+ cells in a progenitor stage (A) Model representing the fate of pMN progenitors along three cell cycles, in control situation in which 50% divisions are asymmetric, giving rise to one MN (green) and one progenitor cell (red). Percentages of asymmetric divisions are adapted from data provided by BrdU incorporation experiments in the presence or the absence of Jagged2. Drawing shows the resulting proportion of neurons (N) and progenitors (P). Plots represent the ratio of theoretical MNs generated in each condition, dots correspond to each cell cycle. Plots represents the ratio of theoretical progenitors that remain in each condition, dots correspond to each cell cycle. (B) Quantitative data showing the ratio of Olig2+ cells, plots corresponds to the ratio of EP vs non-EP side in each experimental condition (control: black dots, GOF-Jag2: red dots, LOF-Jag2: green dots). Time is represented as hours of incubation and HH stages. Dots correspond to 12h-, 24h-, 48h-and 72h-PE. Bars correspond to the standard error (SEM). (C) Sample sections, EP with indicated DNAs, and immunostained with Olig2 (red). EP sides are shown to the right, GFP (green) show transfected cells.

FIGURE 4 .

 4 FIGURE 4.-Jagged2 reduced Olig2 protein levels and inhibits the Olig2 capacity to differentiate MNs

FIGURE 5 .

 5 FIGURE 5.-Depletion of Jagged2 activity at the time of MN generation results in premature OLP generation. (A-H) Embryos electroporated at HH14 with the indicated DNAs were analysed 48h-PE with OLP markers. EP side is shown to the right, GFP (green) show transfected cells (A,B) Olig2 is expressed at pMN in control NT, while GOF-JAG2 EP shows migratory Olig2+ cells. (C) Co-EP with human Jagged2 (GOF-JAG2) restores Olig2+ cells to pMN. (D,E) Sox9 is expressed throughout the VZ in control NT, while LOF-JAG2 electroporated NT shows depletion of Sox9+ cells at pMN and migratory Sox9+ cells. (F) Co-EP with GOF-JAG2 restores Sox9 expression in pMN. (G) Olig2+ migratory cells (red) co-expressed the OLP marker O4 (green). (H) Quantitative analysis of Olig2+ and Sox9+ migratory cells, 48h-PE after electroporation of the indicated DNAs. Numbers are shown as migratory marker expressing cell in each experimental condition. Bars correspond to the standard error (SEM). (I-N) 72h-PE of LOF-JAG2, Sox9 is extinguished from the VZ, and premature expression of the OLP markers Sox10 and PLPDM 20 are detected by in situ hybridization. In control electroporated spinal cords Sox10 and PLPDM20 are only expressed in the ventral roots. (O) Premature OLP generation as revealed by the Real-Time PCR detection of a significant increase in the expression of PDGF Receptor alfa and in the myelin specific gene PLP, 48h-PE of LOF-JAG2 (P) Premature OLP generation as revealed by the increased activity of the MBP-Luc reporter 24h-PE of LOF-JAG2.

FIGURE 6 :

 6 FIGURE 6:Persistent over-expression of Jagged2 inhibits OLP generation.

(CIAP) for 30 minutes, normalized by total protein content, separated by SDS-PAGE gel electrophoresis and transferred to nitrocellulose membranes; blocked with 8% non fat dry milk in TTBS (137mM NaCl; 0.05 Tween 20 and 20 mM Tris-HCl pH 7.4) and probed with in house produced monoclonal anti-Myc antibody (9E10) and polyclonal mouse anti-RFP or rabbit polyclonal anti-Olig2 [START_REF] Zhou | The bHLH transcription factor Olig2 promotes oligodendrocyte differentiation in collaboration with Nkx2.2[END_REF]. The blots were developed using anti-rabbit or anti-mouse coupled to IRDye800CW or IRDye680LT and scanned with the Odyssey Infrared Imaging System (LI-COR Biosciences).

Luciferase-reporter Assay

A transcriptional activity assay of Jagged2 activity on the Myelin Basic Protein (MBP) reporter was performed in vivo. Chick embryos were electroporated with indicated DNAs or empty pCAGGS-GFP vector as control; together with a firefly-luciferase reporter construct containing the MBP-reporter (M. Wegner) and a renilla-luciferase reporter construct (Promega) for normalization. Embryos were harvested after 24 hours incubation in ovo and GFP-positive neural tubes were dissected and homogenized with a douncer in Passive Lysis Buffer on ice. Firefly-and renilla-luciferase activities were measured by the Dual Luciferase Reporter Assay System (Promega).

Quantifications and statistical analysis

Cell countings were made on 10-20 different sections of at least 4 different embryos after each experimental condition, from confocal images. Quantitative data were expressed as mean±s.e.m.

AKNOWLEDGEMENTS

The authors thank Susana Usieto and Mónica Pons for invaluable research assistance. and in Jag2 were 0,92±0,03. Dorsal Islet1+ cells (dI3) were 1,02±0,05 and in Jag2 were 0,85±0,06. MNR2+ cells were 0,99±0,06 and in Jag2 were 0,52±0,03. Ventral Islet1+ cells (MNs) were 0,99±0,04 and in Jag2 were 0,43±0,03. Bars correspond to the standard error (SEM).


N F De Barros
email: nuno.barros@tu-dresden.de

K Zuber
email: zuber@physik.tu-dresden.de

Solar neutrino-electron scattering as background limitation for double beta decay

The background on double beta decay searches due to elastic electron scattering of solar neutrinos of all double beta emitters with Q-value larger than 2 MeV is calculated, taking into account survival probability and flux uncertainties of solar neutrinos. This work determines the background level to be 1 -2 × 10 -7 counts keV -1 kg -1 yr -1 , depending on the precise Q-value of the double beta emitter. It is also shown that the background level increases dramatically if going to lower Q-values. Furthermore, studies are done for various detector systems under consideration for next generation experiments. It was found that experiments based on loaded liquid scintillator have to expect a higher background. Within the given nuclear matrix element uncertainties any approach exploring the normal hierarchy has to face this irreducible background, which is a limitation on the minimal achievable background for purely calorimetric approaches. Large scale liquid scintillator experiments might encounter this problem already while exploring the inverted hierarchy. Potential caveats by using more sophisticated experimental setups are also discussed.

Introduction

In the last decade the field of non-accelerator particle physics and particle astrophysics has made major progress and is now considered to be a reliable research area complementary to high energy accelerator physics.

A special subset is the field of low background physics, searching for extremely rare events normally hidden in an overwhelming large background. Best examples for this scenario are dark matter searches and neutrino physics. As part of this, it is one of the big achievements of the last decade that the observation of neutrino oscillations have shown the existence of a non-vanishing rest mass of the neutrinos. It is known that the problem of missing solar neutrinos can be explained by matter effects which is confirmed by the KamLAND reactor experiment [START_REF] Eguchi | First results from KamLAND: Evidence for reactor anti-neutrino disappearance[END_REF][START_REF] Araki | Measurement of neutrino oscillation with KamLAND: Evidence of spectral distortion[END_REF][START_REF]Constraints on 13 from a three-flavor oscillation analysis of reactor antineutrinos at kamland[END_REF]. Additionally, also the atmospheric neutrino anomaly observed in water Čerenkov detectors like Super-Kamiokande has been confirmed by long baseline accelerator experiments [START_REF] Fukuda | Evidence for oscillation of atmospheric neutrinos[END_REF][START_REF] Adamson | First observations of separated atmospheric nu(mu) and anti-nu(mu) events in the MINOS detector[END_REF]. All evidences can be converted into quantities of the PMNS mixing matrix elements linking weak and mass eigenstates given by ∆m 2 12 , sin 2 2θ 12 , ∆m 2 13 and sin 2 2θ 13 . However, neutrino oscillations do not fix the absolute neutrino mass scale, thus leaving two possible scenarios open: almost degenerate neutrinos, a valid scenario if the neutrino mass is larger than about 100 meV, or a hierarchical structure if the mass is smaller. The latter can be split in a normal (m 1 < m 2 < m 3 ) or inverted (m 3 < m 1 < m 2 ) hierarchy, depending on the sign of the atmospheric splitting. In addition to beta decay end-point measurements, the process of neutrino-less double beta decay is used to explore the absolute mass scale. The double beta decay process, changing Z by two units while leaving the atomic number A constant can occur in two ways (Z, A) → (Z + 2, A) + 2e -+ 2ν e (2νββ -decay) [START_REF] Eguchi | First results from KamLAND: Evidence for reactor anti-neutrino disappearance[END_REF] and (Z, A) → (Z + 2, A) + 2e -(0νββ -decay).

(

) 2
The latter is of enormous importance for neutrino physics. This total lepton number violating process is not allowed in the Standard Model and requires that neutrinos and antineutrinos are identical. Furthermore, a non-vanishing rest mass is required to account for helicity matching. The signal of this decay is a peak at the Q-value of the nuclear transition in the sum energy spectrum of the two emitted electrons. For more details see [START_REF] Schechter | Neutrinoless double-β decay in su(2)×u(1) theories[END_REF][START_REF] Avignone | Next generation double-beta decay experiments: Metrics for their evaluation[END_REF][START_REF] Steven | Double-beta decay[END_REF]. The physics quantity deduced is called effective Majorana mass and is given by

m ν = U 2 e1 m 1 + U 2 e2 m 2 e iα + U 2 e3 m 3 e iβ . (3)
Here U e1 = cos θ 12 cos θ 13 , U e2 = sin θ 12 cos θ 13 and U 2 e3 = 1-U 2 e1 -U 2 e2 . The current knowledge of these mixing angles is given in table [START_REF] Eguchi | First results from KamLAND: Evidence for reactor anti-neutrino disappearance[END_REF].

The life-time of 0νββ -decay is inversely proportional to the effective mass squared. where G 0ν is the phase space factor, including coupling constants, and M 0ν is the nuclear matrix element of the decay.

T 0ν 1/2 -1 = m ν 2 m 2 e G 0ν M 0ν 2 , (4)
Current and future experiments are aiming to improve their sensitivity into the inverted hierarchy range, which requires already hundreds of kilogram of isotopes and more and more stringent requirements on background. However, if being forced to go to ever smaller neutrino masses, and hence longer half-lives, new background components might become important, which were not considered before. Especially dangerous are those which are irreducible. One potential irreducible source for experiments which will be encountered are solar neutrino interactions. Evidently, the major irreducible background is 2νββ -decay which is not discussed here. In this paper we explore the background due to elastic neutrino-electron scattering caused by these neutrinos. For that we use all eleven double beta emitters with a Q-value larger than 2 MeV. One can also define a limit to the half-life sensitivity of an experiment, based on it's backgrounds level [START_REF] Avignone | Next generation double-beta decay experiments: Metrics for their evaluation[END_REF]. The number of background events can be expressed as

B = bMt∆E ( 5
)
where b is the background index in counts keV -1 kg -1 yr -1 , M is the mass of the detector in kg, t is the experiment running time in years and ∆E is the energy resolution at the peak position of the double beta decay Q ββ . This expression is merely an approximation assuming that the background level is approximately constant in the energy resolution window ∆E. As we are only considering the effect of solar neutrino background, this approximation remains valid.

The discovery potential for a 0νββ -decay experiment is usually defined as [START_REF] Avignone | Next generation double-beta decay experiments: Metrics for their evaluation[END_REF]]

N ββ = n σ N ββ + B ( 6
)
where n σ is the confidence level in units of σ, N ββ is the number of 0νββ -decay events and B is the number of background events. Considering a one-to-one signal to background ratio N ββ ≈ B, eq. 6 becomes

N ββ = n σ √ 2B. (7)
Furthermore, the number of 0νββ -decay events can also be expressed as a function of the decay rate λ ββ :

N ββ = N 0 λ ββ t = M × 10 3 × a × N A W ln 2 T 0ν 1/2 × t × ( 8
)
where M is the detector total mass in kg, N A is the Avogadro number, is the detection efficiency, a and W are the isotopic abundance and the atomic weight of the 0νββ -decay isotope, respectively. Combining eq. 6 and 8 one can obtain an expression for the limit on the 0νββ -decay half-life:

T 0ν 1/2 (n σ ) = N A × 10 3 ln 2 √ 2n σ a × W M × t b × ∆E (9)

Background estimate

The differential neutrino-electron scattering

ν + e → ν + e ( 10
)
cross section is given by [START_REF] Hooft | Predictions for neutrino -electron cross-sections in Weinberg's model of weak interactions[END_REF]

dσ dT = 2G 2 F m e π g 2 L + g 2 R 1 - T E ν 2 -g L g R m e T E ν (11)
with T as the kinetic energy of the recoiling electron, G F the Fermi constant, g L = ± 1 2 + sin 2 θ W , g R = sin 2 θ W and the Weinberg angle given by sin 2 θ W = 0.23116(13) [START_REF] Nakamura | Review of particle physics[END_REF]. The sign convention for g L is + for ν e and -for other active neutrinos. Thus the cross section is about a factor 6 higher for electron neutrinos. For the analysis, radiative corrections were taken into account [START_REF] Bahcall | Solar neutrinos: Radiative corrections in neutrino-electron scattering experiments[END_REF].

To obtain the expected electron recoil spectrum the cross section has to be folded with the corresponding solar neutrino fluxes. As all Q-values of the double beta emitters of interest are above 2 MeV only the 8 B and hep-neutrinos have to be considered. The latter is much smaller and can be neglected, nevertheless it is taken into account for the following analysis. To determine the actual neutrino flux and composition for a specific isotope the survival probability P ee ≡ P ee (θ 12 , θ 13 , ∆m 2 21 , ∆m 2 31 ) at the specific peak energy has to be taken into account.

The survival probability depends on these parameters in a complex way. Figure 1 shows the survival probability of solar neutrinos as a function of neutrino energy. In the figure, the effect of the 3σ uncertainties on each individual parameter is also shown. It is important to notice that by varying θ 12 inside its 3σ uncertainty effectively causes a "rotation" in the survival probability. While the θ 12 + 3σ results in a smaller P ee at lower energies and a larger one at higher energies with respect to the best fit curve, this behaviour is converted when changing to θ 12 -3σ.

The effect of ∆m 2 21 is small and only appears at intermediate energies (4-10 MeV), being barely noticeable in low and high energies.

In principle, in order to accurately propagate the uncertainties in the oscillation parameters, the correlation between the parameters should be taken into account. However, a more conservative approach was taken by ignoring this correlation and obtaining the maximum variation on the survival probability caused by the parameter uncertainties. Through this method, the upper and lower limit on the survival Electron neutrino survival probability of [START_REF] Steven | Double-beta decay[END_REF]B neutrinos as a function of E ν and the effect of varying the individual oscillation parameters. The black filled line represents the current best fit point [START_REF] Schwetz | Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters[END_REF] and the dashed lines represent the conservative 3σ variation ignoring correlation between the oscillation parameters.

θ 13 = 0 θ 13 (95%C.L.) ∆m 2
21 -3σ ∆m 2 21 + 3σ probability were obtained, which are represented as dashed black lines in figure 1.

The most stable values of P ee are around 3-4 MeV.

In order to obtain the solar neutrino induced background, the survival probability must be folded with the [START_REF] Steven | Double-beta decay[END_REF]B and hep fluxes. As in this paper we are only considering the 0νββ -decay decay candidates with a Q ββ above 2 MeV, only these fluxes contribute to the background. For the [START_REF] Steven | Double-beta decay[END_REF]B flux the measured spectrum from SNO was used [START_REF] Aharmim | Low Energy Threshold Analysis of the Phase I and Phase II Data Sets of the Sudbury Neutrino Observatory[END_REF]:

Φ SNO [8]B = 5.140 +0.107 -0.158 (stat.) +0.132 -0.117 (syst.)×10 6 cm -2 s -1 = 5.140 +0.170 -0.197 ×10 6 cm -2 s -1 (12)
and for the negligible hep flux the solar model flux of [START_REF] Serenelli | New solar composition: The problem with solar models revisited[END_REF] is used

Φ hep = (7.91 ± 1.19) × 10 3 cm -2 s -1 ( 13
)
The total resulting recoil spectrum for a single electron in the region of interest is shown in figure 2. As mentioned, in double beta experiments only isotopes with a Q ββ larger than 2 MeV are used , resulting in a total of 11 candidates. They are compiled in table 2.

Taking the natural abundance of the involved elements into account, the number of background events can be estimate and is shown in figure 3. The numerical background levels are quoted in table 3. All values are within 1.3 -2.0 ×10 -7 counts/keV/kg/yr where the highest(lowest) central value is for [76]Ge ([150]Nd). Basically three parameters determine the background level: the atomic number, i.e. the number of electrons per atom, the atomic mass, i.e. the number of atoms per kg, and the Q-value, as the number of ν e changes as a function of neutrino energy due to flux and P ee . Scaling all isotopes to a level of 90% enrichment does not change the results dramatically, except in the case of [48]Ca, which, due to its low natural abundance and small atomic mass, enriching the double beta emitter up to 90% causes a 10% decrease in the background levels. The common enrichment factor was chosen arbitrarily and can easily be adjusted to any value.

It should be noted that in these calculations only the solar neutrino induced elastic scattering backgrounds on electrons were considered. Furthermore, the background levels describe the number of recoils on a detector constructed purely from atoms which contain one of the considered 0νββ -decay candidates. In fact, only a few of these candidates are planned to be studied in pure form, being most of them mixed into compounds, to facilitate the construction of a detector. Nonetheless, it is interesting to notice that there is a clear dependence on Q ββ . Best fit (SSM+P ν e →ν e ) Uncertainty (3σ MSW+1σ SSM )

Further studies

Several other features can be studied. In this section some particular cases will be discussed.

Low energy double beta emitters

Besides the 0νββ -decay candidates already discussed, another 24 double beta emitters with Q-values below 2 MeV exist, which are normally not considered for double beta searches because the neutrino-less decay rate scales with Q 5 .

However, several experiments have some of these in their detectors. Examples would be COBRA ( 114 Cd), CUORE ( 128 Te), EXO, KamLAND-Zen ( 134 Xe) and SNO+ ( 146,148 Nd). To investigate how the background due to neutrino electron scattering changes over different energy ranges, the background of 114 Cd, with a Q-value of 534 keV, is explored as a test bench. The total recoil spectrum, considering all solar neutrino fluxes, including CNO, for the full energy range is shown in figure 4.

Evidently the number of recoils increase strongly in the low energy regime as more prominent solar flux contributions will have to be considered. Thus, 114 Cd would be effected by all solar neutrino flux components except the pp-flux. It turns out that at this energy the background would be already three orders of magnitude larger, resulting in a background rate of b = 2.09 +0. 26 -0.16 × 10 -4 counts . keV -1 kg -1 yr -1 .

Experimental Considerations

A second important consideration is closer to the experimental approaches, namely thinking about the compounds used. Most of the double beta emitters under consideration are not used as the only element in the detector, but rather in molecular compounds or dissolved. This will change the number of electrons and atoms/kg significantly and consequently the expected background. We explore this effect for a series of compounds currently under consideration for use in 0νββ -decay experiments: CaF 2 (CANDLES [START_REF] Yoshida | CANDLES project for double beta decay of Ca-48[END_REF]), CdTe (COBRA [START_REF] Zuber | COBRA: Double beta decay searches using CdTe detectors[END_REF]), TeO 2 (CUORE [START_REF] Arnaboldi | CUORE: A cryogenic underground observatory for rare events[END_REF]), ZnSe (LUCIFER [20]), CaMoO 4 [START_REF] Belogurov | CaMoO-4 scintillation crystal for the search of Mo-100 double beta decay[END_REF] and liquid scintillators (LS) with a dissolved isotope like Xe (KamLAND-zen [START_REF] Terashima | R&D for possible future improvements of KamLAND[END_REF]) or Nd (SNO+ [START_REF] Chen | The SNO+ Experiment[END_REF]). For comparison we also show the background levels from table 3 which are currently being used "in pure form": Xe (EXO [START_REF] Danilov | Detection of very small neutrino masses in double-beta decay using laser tagging[END_REF],XMASS [START_REF] Sekiya | Xmass. 06 2010[END_REF]) and Ge (GERDA [START_REF] Abt | A new Ge-76 double beta decay experiment at LNGS[END_REF],MAJORANA [START_REF] Aalseth | The Majorana neutrinoless double-beta decay experiment[END_REF]).

The results are shown in figure 5 and the numerical values are quoted in table 4. Like before, the study was performed both using natural abundances and 90% double beta emitter enrichment. In this case the difference in background levels due to the different abundances is not so pronounced, which is clearly understood by the reduced contribution of the double beta emitter to the total molecular mass and electron density. Again, the exception in this case is observed for CaF 2 , which is due to the low mass of both molecular components.

It should be noted that the units of the background level quoted in both figure 5 and table 4 are counts/keV/kg(compound)/yr. Thus, it should be kept in mind that in order to compare the sensitivity one has also to keep in mind the mass of 0νββ -decay isotope present per kg of detector.

For comparison we also incorporate the results obtained from two pure compound examples: Ge and Xe. The backgrounds are in units of (counts.keV -1 .kg -1 .yr -1 ). However, it is important to remark that the mass normalisation is the total detector mass. Thus, although these results give a good idea of the solar neutrino induced background levels for these compounds, it should be kept in mind that a compound based experiment will require considerably more detector mass to have the same sensitivity as a "pure isotope" experiment. This is particularly relevant for liquid scintillator experiments (LS), whose typical detector masses are in the order of tens or hundreds of tons, while the mass of 0νββ -decay isotope in these experiments is on the order of tens or hundreds of kg.

The results show a steady increase when compared with the pure isotope calculations. This is not surprising, as the other atomic components of the compounds are usually lighter than the double beta emitter, increasing the density of electrons per kg. This is further confirmed by the results from CdT e. Tellurium, being heavier than Cd, causes a reduction of the number of electrons per kg (of detector) which translates into a lower background level than the one quoted for single Cd in table 3.

From these results it is clear that the specific detector model used in a given experiment can intrinsically limit the achievable precision 0νββ -decay . For instance, all the previous considerations describe experiments that do not have a way to directly discriminate between single a two electron events. Such a discrimination would at least partially remove the solar neutrino background and therefore improve over the achievable neutrino mass. There are under investigation several experiments that potentially could tag and therefore remove the solar neutrino background, each employing different technologies. The COBRA experiment [START_REF] Schwenke | Exploration of pixelated detectors for double beta decay searches within the cobra experiment[END_REF] has a plan to construct the detector in several pixels (sub-detectors) which would potentially allow to reconstruct the vertex of the detected events and therefore discriminate between single and double electron events. The NEXT [START_REF] Álvarez | The next-100 experiment for neutrinoless double beta decay searches[END_REF] experiment employs a similar approach consisting in a a High Pressure TPC. This will permit to reconstruct the tracks of each event providing a clear differentiation between 0νββ -decay and solar neutrino events. Finally the SuperNEMO experiment [START_REF] Arnold | Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO[END_REF], by using a detector where the double-beta isotope is deposited in foils also permits to independently detect each emitted electron and therefore reduce the solar neutrino background. Finally, the EXO [START_REF] Flatt | A linear rfq ion trap for the enriched xenon observatory[END_REF] experiment plans to deploy a laser system to tag the daughter Barium ion resulting from the 0νββ -decay . The employment of such a technology would permit to identify only double-beta decays therefore strongly suppressing any other type of event.

T 1/2 constraints

Finally, the question arises at what kind of half-life sensitivity or neutrino mass one has to start worrying about this background.

Fixing a measuring time of 10 years, an enrichment of 90%, assuming 100 % detection efficiency and assuming the background discussed in this paper as the only contribution, one can explore the half-life sensitivity as a function of the two parameters ∆E and M, by using eq. 9.

Restricting the region to 3-300 keV for energy resolution (from Ge to massively loaded scintillators) and an active mass region of 10 kg to 1t, contour plots for the halflife can be made as shown in figure 6, assuming a detector composed solely of the pure double-beta decay element. Figure 7 shows a detail of the sensitivity for Ge and Xe, two istotopes for which there exist already experiments using them without bounding to any other element. It should be noted that in figure 7 the range in the energy resolution for a Ge detector was zoomed to the region 0 to 10 keV, as it is unlikely to build a Ge based detector with worse resolution.

However, these results do not translate directly into the reality, as most of these elements are planned to be used in compounds, either by bounding them with other elements, or dissolving them into some secondary compound.

In order to better reflect the reality of present and near future experiments, this study was also performed for the compounds discussed in subsection 3.2. The results are shown in figure 8.

It is clearly visible that the sensitivities are considerably different due to the nature of the compounds. In figure 9 one can see a more detailed contour map of the half-life bound for two Xe based experiments. One can see straight away that for the same total detector mass and resolution there is a difference in the half-life limit of about one order of magnitude. It should also be noted that some sensitivity is necessary when reading these figures, as the active mass does not reflect the limitations in building a detector with a large active mass. However, the amount of active mass considered is achievable with most detectors considered. Furthermore, it should also be taken under consideration the achievable resolution with the particular detection techniques. For instance, liquid scintillators have worse energy resolution which also affects the limit on

T 1/2 .
Using the half-life limits shown in figure 6 and figure 8, and choosing sensitive values for the detector mass and energy resolution, one can establish a limit on the effective neutrino mass that can be achieved by the experiments using these compounds before worrying about solar neutrino background. Using eq. 4, the limit on the effective neutrino mass will be:

m ν = G T 0ν 1/2 |M 0ν | 2 , with G = m 2 e G 0ν (14)
It should be noticed though that from this point on the results are strongly dominated by the choice of nuclear matrix elements. There are several calculations available, but most only cover a select range of double beta emitters. In this work 5. Phase space terms and nuclear matrix elements for the double beta decays discussed in this work. The phase space term G 0ν already includes the electron mass squared and has units of yr [START_REF] Boehm | Physics of Massive Neutrinos[END_REF]. The nuclear matrix element M 0ν is dimensionless [START_REF] Barea | Neutrinoless double-beta decay in the microscopic interacting boson model[END_REF][START_REF] Menendez | Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay[END_REF] we used the matrix elements calculated using the microscopic interacting boson model (IBM-2) [START_REF] Barea | Neutrinoless double-beta decay in the microscopic interacting boson model[END_REF]33], except for [48]Ca, in which case we used the value obtained by the interacting shell model (ISM) [START_REF] Menendez | Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay[END_REF][START_REF] Caurier | The Shell Model as Unified View of Nuclear Structure[END_REF]. This was done because from IBM-2 there was a full set of calculations available for ten of the isotopes used in this study.

The phase space term used in this work was taken from [START_REF] Boehm | Physics of Massive Neutrinos[END_REF]. Table 5 summarises the values used for 0νββ -decay candidate.

In table 6 are the 3σ limits obtained for the T 1/2 and m ν for some selected values, also shown in the table, of active mass and resolution, considering the detector compositions discussed in the previous sections. In these calculations it was always assumed an enrichment of 90% of 0νββ -decay isotope.

From the results shown in the table, it is clearly noticeable that the solar neutrino background affect each experiment differently. While in some cases this background would only be an issue when probing the normal hierarchy region, for a few of the considered experiments this background can limit the sensitivity to the inverted hierarchy region. Here, the liquid scintillator experiments stand out as being the most affected by this background.

Several considerations should be taken into account while interpreting these results: the resolution of the detectors will strongly affect the number of background events in the analysis window. The energy resolution values were collected, where possible, from experimental publications. Some values were taken from [START_REF] Gomez-Cadenas | Sense and sensitivity of double beta decay experiments[END_REF]. Additionally, as stated before, the nuclear matrix elements vary considerably from model to model. Our choice for using the IBM-2 model was based on the consistency of the calculation, as this model is the only one to have calculations for all isotopes discussed here, except [48]Ca. Any other choice of nuclear matrix elements will very likely change the achievable effective neutrino mass m ν , but not T 1/2 .

Summary and conclusions

We have determined the elastic neutrino-electron scattering background due to solar neutrinos for all double beta isotopes with Q> 2 MeV. Within the current knowledge of mixing angles all values are within the range 1-2 ×10 -7 counts/keV/kg/yr . The results show a strong dependence of the solar neutrino induced background on the Q-value of the double-beta emitter, where the electron neutrino survival probability determines the flavour content of the solar neutrino flux, which has a direct relation with the interaction cross sections. Furthermore, the electron density of the material used was also shown to have a strong influence in the background level, which is dominated by the atomic mass and number of the isotopes present.

It was also verified that values change significantly if actual detector systems are used. In general, it was observed that the detector systems led to a higher electron density in the detector, significantly increasing the total solar neutrino induced background. From table 6 it was observed that this issue becomes relevant even for the inverted hierarchy regime, in the case of some experiments. In particular, the liquid scintillator based experiments are particularly affected, as these compounds have a large electron density and a considerably worse energy resolution. In these cases it was observed that the neutrino mass sensitivity is almost one order of magnitude worse.

The only way to circumvent this bound are detector systems being able to distinguish between one and two electron events, i.e. these are typically tracking detectors or to detect the daughter ion produced in double beta decay in addition to the electrons.

Figure 1 .

 1 Figure 1.Electron neutrino survival probability of[START_REF] Steven | Double-beta decay[END_REF]B neutrinos as a function of E ν and the effect of varying the individual oscillation parameters. The black filled line represents the current best fit point[START_REF] Schwetz | Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters[END_REF] and the dashed lines represent the conservative 3σ variation ignoring correlation between the oscillation parameters.

Figure 2 .Figure 3 .

 23 Figure 2. Recoil energy spectrum of a single elastic scattering electron induced by a solar neutrino in the region of interest for this paper. The 3σ uncertainty band is also shown.

Figure 4 .

 4 Figure 4. Total recoil energy spectrum of elastic scattering electrons induced by solar neutrinos. A dramatic increase in the recoil spectrum occurs at low energies where the much more intense fluxes pp, [7]Be and pep dominate.

Figure 5 .

 5 Figure 5. Expected background level for a selection of compounds used in 0νββ -decay . For comparison, the backgrounds from Ge and Xe, which are used in pure form, are also shown. Both natural abundances and 90% enrichment are considered.

Figure 6 .

 6 Figure 6. 3σ bounds on T 1/2 for the considered double beta emitters as a function of active mass and energy resolution.

Figure 7 .

 7 Figure 7. Detail of T 1/2 3σ bounds for Ge and Xe as a function of active isotope mass and energy resolution.

Figure 8 .

 8 Figure 8. 3σ bounds of T 1/2 for the considered double beta emitters as a function of detector mass M and energy resolution ∆E.

Figure 9 .

 9 Figure 9. Detail of T 1/2 3σ bounds for liquid Xe and Xe loaded liquid scintillator as a function of detector mass M and energy resolution ∆E.

Table 1 .

 1 Neutrino mixing parameters: best-fit values as well as 1σ and 3σ ranges[START_REF] Schwetz | Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters[END_REF]. Normal hierarchy was assumed.

	Parameter	Best-fit +1σ -1σ	3σ
	sin 2 θ 12	0.316 ± 0.016	0.27 -0.37
	sin 2 θ 13	0.017 +0.007 -0.009	≤ 0.040
	∆m 2 21 10 -5 eV 2	7.64 +0.19 -0.18	7.12 -8.23
	∆m 2 31 10 -3 eV 2	2.45 ± 0.09	2.18 -2.73

Table 2 .

 2 Q-value for the ground state to ground state transition which is calculated using isotope masses from[START_REF] Wapstra | The 2003 atomic mass evaluation: (i). evaluation of input data, adjustment procedures[END_REF][START_REF] Audi | The 2003 atomic mass evaluation: (ii). tables, graphs and references[END_REF]. Values in brackets are from Penning trap measurements and the natural abundance is quoted in percent.

	Isotope	Q-value (keV )	n a t . a b u n d . ( % )
	48 Ca	4273.7	0.187
	76 Ge	2039.1 (2039.04)	7.8
	82 Se	2995.5	9.2
	96 Zr	3347.7	2.8
	100 Mo	3035.0 (3034.40)	9.6
	110 Pd	2004.0	11.8
	116 Cd	2809.1	7.6
	124 Sn	2287.7	5.6
	130 Te	2530.3 (2527.01)	34.5
	136 Xe	2461.9 (2457.83)	8.9
	150 Nd	3367.3 (3371.38)	5.6

Table 3 .

 3 Estimated

	48 Ca	1.60 +0.20 -0.21	1.36 +0.17 -0.18
	76 Ge	1.90 +0.21 -0.23	1.83 +0.20 -0.22
	82 Se	1.67 +0.19 -0.21	1.62 +0.19 -0.20
	96 Zr	1.62 +0.19 -0.21	1.55 +0.18 -0.20
	100 Mo	1.69 +0.19 -0.21	1.63 +0.19 -0.21
	110 P d	1.87 +0.21 -0.23	1.82 +0.20 -0.22
	116 Cd	1.70 +0.19 -0.21	1.65 +0.19 -0.21
	124 Sn	1.77 +0.20 -0.22	1.71 +0.19 -0.21
	130 T e	1.72 +0.19 -0.21	1.70 +0.19 -0.21
	136 Xe	1.70 +0.19 -0.21	1.65 +0.19 -0.20
	150 Nd	1.54 +0.18 -0.20	1.49 +0.17 -0.19

background for each 0νββ -decay candidate depicted in figure

3

.Units are in in (counts.keV -1 .kg -1 .yr -1 ). 0νββ -decay candidate Background (Natural ab.) (10 -7 ) Background (90% enrichment)

Table 4 .

 4 Estimate background for each 0νββ -decay candidate depicted in figure3.Units in(10 -7 counts.keV -1 .kg -1 .yr -1 ).

	Compound	Relevant Nuclide	Background (Natural) (10 -7 )	Background (90% enrichment)
	LS-Xe	136 Xe	2.34 +0.26 -0.29	2.34 +0.26 -0.29
	LS-Nd	150 Nd	2.07 +0.24 -0.26	2.07 +0.24 -0.26
	CaF 2	48 Ca	1.56 +0.19 -0.21	1.43 +0.18 -0.19
	CaM oO 4	100 Mo	1.82 +0.21 -0.23	1.75 +0.20 -0.22
	CdTe	116 Cd	1.66 +0.19 -0.21	1.63 +0.19 -0.20
	ZnSe	82 Se	1.72 +0.20 -0.22	1.69 +0.19 -0.21
	T eO 2	130 T e	1.80 +0.20 -0.22	1.78 +0.20 -0.22
	Pure Ge	76 Ge	1.90 +0.21 -0.23	1.83 +0.20 -0.22
	Pure Xe	136 Xe	1.70 +0.19 -0.21	1.65 +0.19 -0.20

Table 6 .

 6 Estimate 3σ bounds on T 1/2 and m ν for a selection of 0νββ -decay experiments over assuming 10 years of operation.

	Compound 0νββ -decay isotope Mass of isotope (kg) ∆E (keV) T 1/2 (yr)	m ν (meV)
	LS-Xe	[136]Xe	500	230	1.08 × 10 27 21.31
	LS-Nd	[150]Nd	1000	220	2.77 × 10 26 28.93
	CaF 2	[48]Ca	100	145	9.64 × 10 27 22.42
	CaM oO 4	[100]Mo	100	150	3.81 × 10 27 10.37
	CdTe	[116]Cd	100	53	5.67 × 10 28 10.97
	ZnSe	[82]Se	100	5.0	2.65 × 10 28 4.24
	T eO 2	[130]Te	100 500	5.0 5.0	2.05 × 10 28 4.18 4.58 × 10 28 2.79
	Ge	[76]Ge	100	3.5	4.63 × 10 28 5.44
	Xe	[136]Xe	100 500	80 80	5.69 × 10 27 9.29 1.27 × 10 28 6.22

Acknowledgments

We thank F. Iacchello for providing us with all relevant matrix elements. This work is supported by the Bundesministerium für Bildung und Forschung (BMBF grant 05A08OD1).