Mariana Ramos-Brossier

Caterina Montani

Nicolas Lebrun

Laura Gritti

Christelle Martin

Christine Seminatore-Nole

Aurelie Toussaint

Sarah Moreno

Karine Poirier

Olivier Dorseuil

Jamel Chelly

Anna Hackett

Jozef Gecz

Eric Bieth

Anne Faudet

Delphine Heron

R Frank Kooy

Bart Loeys

Yann Humeau

Carlo Sala

Pierre Billuart
email: pierre.billuart@inserm.fr

Novel IL1RAPL1 mutations associated with intellectual disability impair synaptogenesis AUTHORS

Mutations in interleukin-1 receptor accessory protein like 1 (IL1RAPL1) gene have been associated with non-syndromic intellectual disability and autism spectrum disorder. This protein interacts with synaptic partners like PSD-95 and PTPδ, regulating the formation and function of excitatory synapses. The aim of this work is to characterize the synaptic consequences of three IL1RAPL1 mutations, two novel causing the deletion of exon 6 (Δex6) and one point mutation (C31R), identified in patients with intellectual disability. Using immunofluorescence and electrophysiological recordings we examined the effects of IL1RAPL1 mutants over-expression on synapse formation and function in cultured rodent hippocampal neurons. Δex6 but not C31R mutation leads to IL1RAPL1 protein instability and mislocalization within dendrites. Analysis of different markers of excitatory synapses and sEPSC recording revealed that both mutants fail to induce pre-and post-synaptic differentiation, contrary to WT IL1RAPL1 protein. Cell aggregation and immunoprecipitation assays in HEK293 cells showed a reduction of the interaction between IL1RAPL1 mutants and PTPδ that could explain the observed synaptogenic defect in neurons.

However, these mutants do not affect all cellular signaling since their over-expression still activates JNK pathway. We conclude that both mutations described in this study lead to a partial loss of function of the IL1RAPL1 protein through different mechanisms. Our work highlights the important function of the transsynaptic PTPδ/ IL1RAPL1 interaction in synaptogenesis and as such, in intellectual disability in the patients.

INTRODUCTION

Intellectual disability (ID) is defined as an overall intelligence quotient (IQ) lower than 70 and limitations in adaptive behavior, with an onset before the age of 18. ID affects around 3% of the population, and Xlinked ID (XLID) is responsible for 10% of severe ID cases. To date, 116 of XLID genes have been identified. Mutations in one of these genes, interleukin-1 receptor accessory protein-like 1 (IL1RAPL1), are associated with cognitive impairment ranging from non-syndromic ID to autism spectrum disorder (ASD). Until now, described mutations include exon deletions and nonsense mutations that result in the absence of protein, in most of the cases [START_REF] Carrié | A new member of the IL-1 receptor family highly expressed in hippocampus and involved in X-linked mental retardation[END_REF][START_REF] Kozak | Mapping of a gene for non-specific X linked mental retardation : evidence for linkage to chromosomal region Xp21.1-Xp22.3[END_REF][START_REF] Tabolacci | A Truncating Mutation in the IL1RAPL1 Gene Is Responsible for X-linked Mental Retardation in the MRX21 Family[END_REF][START_REF] Nawara | Novel mutation of IL1RAPL1 gene in a nonspecific X-linked mental retardation (MRX) family[END_REF][START_REF] Piton | Mutations in the calcium-related gene IL1RAPL1 are associated with autism[END_REF][START_REF] Behnecke | Intragenic deletions of IL1RAPL1: Report of two cases and review of the literature[END_REF][START_REF] Whibley | Fine-scale survey of X chromosome copy number variants and indels underlying intellectual disability[END_REF][START_REF] Franek | Deletion of the immunoglobulin domain of IL1RAPL1 results in nonsyndromic X-linked intellectual disability associated with behavioral problems and mild dysmorphism[END_REF][START_REF] Mikhail | Clinically relevant single gene or intragenic deletions encompassing critical neurodevelopmental genes in patients with developmental delay, mental retardation, and/or autism spectrum disorders[END_REF][START_REF] Youngs | IL1RAPL1 gene deletion as a cause of X-linked intellectual disability and dysmorphic features[END_REF][START_REF] Barone | Intragenic ILRAPL1 deletion in a male patient with intellectual disability, mild dysmorphic signs, deafness, and behavioral problems[END_REF][START_REF] Cacciagli | Intragenic rearrangements in X-linked intellectual deficiency: Results of a-CGH in a series of 54 patients and identification of TRPC5 and KLHL15 as potential XLID genes[END_REF][START_REF] Tucker | Single exon-resolution targeted chromosomal microarray analysis of known and candidate intellectual disability genes[END_REF][START_REF] Redin | Efficient strategy for the molecular diagnosis of intellectual disability using targeted high-throughput sequencing[END_REF].

IL1RAPL1 is a member of interleukin 1 receptor family, and shares 52% of homology with the IL-1 receptor accessory protein (IL1RAcP) [START_REF] Carrié | A new member of the IL-1 receptor family highly expressed in hippocampus and involved in X-linked mental retardation[END_REF]. It contains 3 extracellular Immunoglobulin (Ig) -like domains, a single transmembrane domain, an intracellular Toll/IL-1R (TIR) domain and a C-terminal tail of 150 amino acids, that is not shared with other family members. IL1RAPL1 is expressed in the brain, and is located on excitatory synapses with an enrichment at the postsynaptic compartment [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF].

The importance of IL1RAPL1 in brain function was demonstrated by studies of Il1rapl1 knockout mouse model [START_REF] Gambino | IL1RAPL1 controls inhibitory networks during cerebellar development in mice[END_REF]. These mice show impaired associative learning and synaptic defects, including decrease in dendritic spines and synaptic plasticity in different brain regions [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Houbaert | Target-specific vulnerability of excitatory synapses leads to deficits in associative memory in a model of intellectual disorder[END_REF].

Growing body of evidence underlines the importance of IL1RAPL1 on synapse physiology. Several IL1RAPL1-interacting proteins necessary for IL1RAPL1-induced pre-and post-synaptic differentiation have been identified. IL1RAPL1 interacts through its C-terminal domain with the calcium sensor NCS-1, regulating the activity of N-type voltage-gated calcium channel (VGCC) in PC12 cells [START_REF] Bahi | IL1 receptor accessory protein like, a protein involved in X-linked mental retardation, interacts with Neuronal Calcium Sensor-1 and regulates exocytosis[END_REF][START_REF] Gambino | IL1-receptor accessory protein-like 1 (IL1RAPL1), a protein involved in cognitive functions, regulates N-type Ca 2+ -channel and neurite elongation[END_REF]. In neurons, IL1RAPL1 interacts with PSD-95, a major scaffolding protein of excitatory synapses, and modulates its synaptic localization by regulating JNK activity and PSD-95 phosphorylation [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF].

Interaction with RhoGAP2 and Mcf2l, two regulators of Rho GTPases activity, is required for IL1RAPL1 to induce dendritic spine formation and function [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF]21). Hayashi et al., identified other proteins interacting with the intracellular domain of IL1RAPL1, like PKCε, PLCβ1 and Rasal1 (21). Trans-synaptic interaction with the protein tyrosine phosphatase PTPδ through the extracellular domain of IL1RAPL1 was also shown to be essential for synaptogenesis [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF][START_REF] Yoshida | IL-1 receptor accessory protein-like 1 associated with mental retardation and autism mediates synapse formation by trans-synaptic interaction with protein tyrosine phosphatase δ[END_REF].

We identified two novel IL1RAPL1 mutations, an in frame deletion of exon 6 (Δex6), in two unrelated patients with ID. Unlike the majority of previously reported IL1RAPL1 mutations, which primarily lead to loss of IL1RAPL1 protein, this deletion and one point mutation in exon 3 (c.91T>C; p.(Cys31Arg)) [START_REF] Tarpey | A systematic, large-scale resequencing screen of X-chromosome coding exons in mental retardation[END_REF], are compatible with IL1RAPL1 protein synthesis, but are predicted to affect the function of its extracellular domain. As part of this work we explore the impact of these mutations on synapse formation and function and how this can explain the intellectual disability of the patients.

RESULTS

Clinical characterization of patients and identification of two novel mutations on IL1RAPL1

P72 Family. The pedigree of family P72 is shown in Figure 1A. Patient II-2 (male, 30 years) presents moderate ID, autistic-like behaviour, is extraverted, aggressive, and has language and motor delay. He has large hands, big ears, long face and synophrys. Patient II-3 (male, 43 years) presents mild ID and has no major behavioural problems. He also has autistic-like behaviour and language and motor delay. He has facial dysmorphism, big ears and round face. Neurological examination was normal. The only clinical feature of III-2 (female, 10 years) is ID, needing special care.

During a search for mutations in IL1RAPL1 gene in male patients with XLID, we found a deletion of exon 6 in genomic DNA from patient II-2. This deletion was also found in the affected brother II-3. Physical mapping of the deletion by CGH array and long range PCR allowed us to characterize its size (7744 base pairs (bp)) and define the DNA breakpoints between intron 5 and 6 of IL1RAPL1 (g.29684073_29691812del; c.1212_1286del; hg19/LOVD3 IL1RAPL1_000009). Using oligonucleotides flanking the deletion breakpoints, we studied by real-time PCR the segregation of the deletion in P72 family. As shown in Figure 1B, the deletion is present in II-2, II-3 and III-2 but not in II-1 and II-4 DNA isolated from blood; the low level of amplification in obligate carrier I-2 suggests somatic mosaicism. The in frame deletion of IL1RAPL1 exon 6 is predicted to lead to a protein lacking 25 amino acids in the extracellular domain, between immunoglobulin domain (Ig) 2 and 3 (p.(Ala235_Leu259del); Fig. 1G).

In order to elucidate if III-2's phenotype is due to a skewed X chromosome inactivation we evaluated her X-inactivation pattern using the AR, FMR1 or FMR2 loci in her fibroblasts. Unfortunately none of these markers was informative and given that IL1RAPL1 expression in fibroblasts and blood cells is very low, we assessed the X-inactivation skewing by testing the expression of one SNP (single-nucleotide polymorphism) in the 3'UTR of APOO, a gene located on the X chromosome at < 5 kb from IL1RAPL1, in fibroblasts from III-2. Using this SNP (rs8680) we were able to differentiate her parent's contribution, and we found the expression of both alleles in III-2 cDNA suggesting random X-inactivation in her fibroblasts (Suppl. Fig. 1).

BMC Family. The proband II-1 (male, 27 months old) was born after an uneventful pregnancy as the second child of non-consanguineous parents (Fig. 1C). He had some delay of motor development, sitting at 9 months and walking at 25 months. At the age of 27 months he only speaks three words and formal developmental testing confirmed delay. He was advised to start in special education. Family history is significant for learning difficulties in the mother; she attended special education. The proband has one sister with learning difficulties. Physical examination reveals height of 84 cm (below third percentile), weight 12.7 kg (25 th percentile) and head circumference 48.4 cm (25 th percentile). He has mild facial dysmorphism with a prominent forehead. He has generalized joint hyperlaxity, normal male genitalia and skin significant eczema. Brain MRI was normal.

Microarray analysis revealed a deletion of ~200 kb with the proximal breakpoint in intron 5 and the distal breakpoint in intron 6 of IL1RAPL1 (g.29517322_29746541del; c.703+99897_778+59920del; hg19/ LOVD3 IL1RAPL1_000008) predicted to result in a deletion of the entire exon 6 (Fig. 1D). Additionally, a duplication on chromosome 19q13.41 of unknown clinical significance was observed (g.52860055_52996104dup; c.-41492_*76112dup; hg19, LOVD3 ZNF528_000001). The parents and sister of the proband were also tested and both the deletion and duplication are inherited from the mother, and present in the sister. Similarly to the above-described deletion of exon 6, this one is predicted to lead to the same IL1RAPL1 mutant protein lacking 25 amino acids in the extracellular domain, between immunoglobulin domain (Ig) 2 and 3 (p.(Ala235_Leu259del); Fig. 1G).

A28 Family. The pedigree of family A28 is shown in Figure 1E. II-1 (male, now deceased) had moderate ID (IQ assessed as 36-51), gynaecomastia, obesity, small testes, normal height (169 cm) and head circumference (54.5 cm), sexual deviant behavior (treated with an anti-androgen medication and necessitating living in care). II-2 (male, 57 years) presents mild ID, obesity, significant behavioral issues, normal head circumference, normal facial features, gynaecomastia, normal hands and feet. The female obligate carrier I-2 is phenotypically normal, with normal height (153 cm) and head circumference (54.2 cm). She appeared to have low average intelligence.

A missense substitution in IL1RAPL1 exon 3 (c.91T>C) (LOVD3 IL1RAPL1_000003) leading to an amino acid change p.(Cys31Arg) (C31R) was initially reported by Tarpey et al. in II-2 patient ( 23), but no clinical information about the family nor further characterisation of this variant (ie. if deleterious to IL1RAPL1 function or not) was studied. We first confirmed the segregation of this variant in the A28 family (Fig. 1F) and subsequently investigated its functional consequences. This point mutation is located in the extracellular domain of IL1RAPL1 protein before the first Ig domain (Fig. 1G). We assessed the pathogenicity of this variant by in silico analysis using the following software: Mutation taster [START_REF] Schwarz | MutationTaster evaluates disease-causing potential of sequence alterations[END_REF], SIFT [START_REF] Ng | Predicting deleterious amino acid substitutions[END_REF] and PolyPhen 2 [START_REF] Adzhubei | A method and server for predicting damaging missense mutations[END_REF]. Mutation taster analysis predicted that this missense variant is a disease-causing mutation. PolyPhen analysis, which predicts possible impact of an amino acid substitution on the structure and function of a human protein using straightforward physical and comparative considerations, of the missense mutation also considered it to be "probably damaging" (score 1.0). Finally, SIFT analysis predicted also the substitution at position 31 from Cys to Arg to affect protein function with a score of 0.00 (damaging). Alamut splicing predictions (Interactive Biosoftware) suggested no significant impact of this substitution on donor and acceptor splice sites.

Finally, a point mutation in IL1RAPL1 exon 11 (c.1927A>G) leading to an amino acid change p.(Ile643Val) (I643V), was found in a male with ID, but was not observed in his affected brother potentially ruling out this variant as the genetic cause of the disease in this XLID family. This IL1RAPL1 variant was reported before by Piton et al., [START_REF] Piton | Mutations in the calcium-related gene IL1RAPL1 are associated with autism[END_REF] and is unlikely to be pathogenic since in silico analysis considered it to be tolerated by the protein. In our study, we use this variant as a control, as this single amino acid change is located in the intracellular domain (Fig. 1G), contrary to Δex6 and C31R mutations.

In this and previous studies [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF] we used as controls two IL1RAPL1 mutant proteins, ΔC and ΔN, lacking a large part of intra or extra cellular domains, respectively (Fig. 1G and Table 1).

ΔC mutant corresponds to a nonsense IL1RAPL1 mutation in exon 11 (c.1377C>A) observed in a patient with non syndromic ID [START_REF] Carrié | A new member of the IL-1 receptor family highly expressed in hippocampus and involved in X-linked mental retardation[END_REF]. The construct used in our study lacks the half of the TIR and the complete Cterminal domains (p.(Tyr459X)).

ΔN mutant protein lacks the first two Ig-like domains, and corresponds to the deletion of exons 1 to 6 of IL1RAPL1 (c.1_778del) (Fig. 1G and Table 1). Deletions of these exons were found in different patients with ID, but they probably lead to the absence of IL1RAPL1 expression [START_REF] Nawara | Novel mutation of IL1RAPL1 gene in a nonspecific X-linked mental retardation (MRX) family[END_REF][START_REF] Behnecke | Intragenic deletions of IL1RAPL1: Report of two cases and review of the literature[END_REF][START_REF] Whibley | Fine-scale survey of X chromosome copy number variants and indels underlying intellectual disability[END_REF][START_REF] Franek | Deletion of the immunoglobulin domain of IL1RAPL1 results in nonsyndromic X-linked intellectual disability associated with behavioral problems and mild dysmorphism[END_REF][START_REF] Mikhail | Clinically relevant single gene or intragenic deletions encompassing critical neurodevelopmental genes in patients with developmental delay, mental retardation, and/or autism spectrum disorders[END_REF].

IL1RAPL1 protein expression and localization is affected by mutations in its extracellular domain

In order to evaluate the effect of IL1RAPL1 mutations on protein stability, HEK293 cells were co transfected with GFP and vectors bearing HA-tagged WT or mutant IL1RAPL1. Protein expression of mutants is significantly decreased (~75% for Δex6 (108 KDa) and ~60% for C31R (115 KDa), compared to the WT (115 KDa) protein) 24 hours after transfection as revealed by immunoblot (Suppl. Fig. 2). The decrease in protein is not due to lower transfection efficiency (evaluated by GFP signal) suggesting that both mutations lead to decreased stability of the IL1RAPL1 protein in these cells. Protein expression of an IL1RAPL1 mutant lacking the half of the TIR and the complete C-terminal domains (ΔC, 62 KDa) is decreased to similar levels than Δex6 and C31R. Next, we studied the stability of the mutants in mouse hippocampal neurons. Whereas IL1RAPL1 protein expression in Δex6 transfected neurons is severely abolished to the background level, C31R mutant protein has similar expression level to WT protein (Fig. 2A and2B). I643V variant is more abundant compared to WT protein, but there are probably no consequences since this excess of protein does not affect other analyzed parameters (see below). All IL1RAPL1 variants including Δex6 are correctly targeted to the membrane of neurons as measured by the ratio of surface HA per total HA signal, compared to WT IL1RAPL1 protein (Fig. 2C and2D). As WT IL1RAPL1 protein is present in the dendrites and enriched at the postsynaptic site in the dendritic spines [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF], we analyzed the subcellular localization of the variants by measuring the coefficient of variation of HA-IL1RAPL1 signal along dendrites (CV, see material and methods) and also the distribution of IL1RAPL1 signal in spines versus dendrites. Both C31R and I643V mutant proteins are distributed in dendritic shafts and are also enriched in spines similarly to WT (Fig. 2E and2F). In contrast and despite its low abundance, Δex6 mutant is predominantly observed forming discrete puncta within dendritic shafts. Coefficient of variation analysis of Δex6 IL1RAPL1 signal along the dendritic shaft clearly shows more variations than WT and other mutated proteins (*** p <0.001 compared to WT protein, n=14 neurons (not shown)). In addition, Δex6 mutant shows a decrease of IL1RAPL1 signal in dendritic spines of neurons compared to WT transfected neurons (Fig. 2F).

In conclusion, deletion of the region between Ig2 and Ig3 domains in Δex6 mutant is responsible for its instability and mislocalization in dendrite and spines. In contrast, these parameters are not altered by C31R mutation.

Impact of IL1RAPL1 mutations on excitatory synapse formation

Knocking-down or overexpressing IL1RAPL1 decreases or increases excitatory synapse formation, respectively [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF][START_REF] Yoshida | IL-1 receptor accessory protein-like 1 associated with mental retardation and autism mediates synapse formation by trans-synaptic interaction with protein tyrosine phosphatase δ[END_REF][START_REF] Yoshida | Zebrafish orthologue of mental retardation protein IL1RAPL1 regulates presynaptic differentiation[END_REF]. In order to evaluate the impact of the three newly described mutants on this IL1RAPL1-dependent synaptogenic phenotype, we co-transfected cultured hippocampal neurons with GFP and HA-tagged IL1RAPL1 constructs and their effect on pre-and post-synapse formation was evaluated using specific markers.

WT and I643V IL1RAPL1 transfected neurons at DIV18 present a large increase of the pre-synaptic marker synaptophysin that is not observed in neurons overexpressing Δex6 or C31R mutant (Suppl. Fig. 3). As synaptophysin labels both excitatory and inhibitory pre-synapses, we stained transfected neurons with more specific markers using anti-VGLUT1 and anti-VGAT antibodies to label excitatory or inhibitory pre-synapses, respectively. We observed that IL1RAPL1 increases the excitatory pre-synaptic marker, an effect that is not observed after Δex6 or C31R mutant over-expression (Fig. 3A and3B).

Staining for the inhibitory pre-synaptic marker VGAT is not affected after WT or mutants expression confirming the specific function of IL1RAPL1 in excitatory synapses (Suppl. Fig. 4A).

Over-expression of both WT and I643V IL1RAPL1 induces an increase of the excitatory post-synaptic marker PSD-95 (Fig. 3C and 3D, ~100 and ~150% respectively, no statistical differences between them) together with an increase in the number of dendritic protrusions (Fig. 3E, ~20% in both cases), compared to control neurons. In agreement with these data and as previously reported, WT and I643V IL1RAPL1 over-expression increase the frequency (~300% in both cases), but not the amplitude of spontaneous excitatory post-synaptic currents (sEPSC) (Fig. 3F and3G). In contrast, none of the post-synaptic effects are observed in neurons overexpressing Δex6 or C31R mutants (Fig. 3C-E) suggesting that these mutants lose their synaptogenic properties. According to immunocytochemistry data, neither WT nor mutant protein altered the frequency and amplitude of spontaneous inhibitory post-synaptic currents (sIPSC, Suppl. Fig. 4B).

Worth noting, ΔC mutant lacking part of intracellular domain is able to increase synaptophysin (Suppl. Fig. 3) and VGLUT1 staining, but not to increase PSD-95 staining (n=16 neurons per group from 2 independent experiments) or the number of dendritic spines [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF]. On the other hand, a mutant lacking part of the extracellular domain (ΔN in Fig. 1G) is also unable to increase pre-and post-synaptic differentiation (Suppl. Fig. 3). These observations support the fact that pre-synaptic differentiation is dependent on IL1RAPL1 extracellular domain, while both extra and intracellular domains are important for post-synaptic differentiation [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF][START_REF] Yoshida | IL-1 receptor accessory protein-like 1 associated with mental retardation and autism mediates synapse formation by trans-synaptic interaction with protein tyrosine phosphatase δ[END_REF]. This suggests that extracellular domain of IL1RAPL1 is damaged in C31R mutant, and that this could account for its synaptogenic deficit. In the case of Δex6 mutant, this deficit is probably due to the decrease in protein stability and mislocalization within dendrites as shown above.

Mechanism of synaptic deficits induced by IL1RAPL1 mutants

The synaptogenic activity of IL1RAPL1 is dependent on its interaction with a specific isoform of the tyrosine phosphatase PTPδ [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF][START_REF] Yoshida | IL-1 receptor accessory protein-like 1 associated with mental retardation and autism mediates synapse formation by trans-synaptic interaction with protein tyrosine phosphatase δ[END_REF][START_REF] Pulido | The LAR/PTP delta/PTP sigma subfamily of transmembrane protein-tyrosine-phosphatases: multiple human LAR, PTP delta, and PTP sigma isoforms are expressed in a tissue-specific manner and associate with the LAR-interacting protein LIP.1[END_REF]. This protein interacts with IL1RAPL1 extracellular domain, and was shown to be specific as other members of the protein family, like LAR and PTPσ, are able neither to interact with nor to induce IL1RAPL1-dependent synaptogenesis.

As C31R mutant lack synaptogenic activity, presumably because of changes in its extracellular domain structure, we hypothesized that this mutation perturbed the trans-synaptic interaction with PTPδ. In order to test this hypothesis, a group of HEK293 cells overexpressing either GFP or HA-IL1RAPL1 proteins and another group expressing Myc-PTPδ ectodomain were subjected to a cluster assay as previously described [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF]. After counting the number of red/green clusters (yellow in merge image in Fig. 4A), this assay revealed some but not significant interaction between C31R IL1RAPL1 mutant and PTPδ, compared to control cells and ΔN mutant that lacks the 2 first Ig-like domains (Fig. 4A). Similarly, the small amount of the Δex6 mutant expressed shows a severe reduction of clustering. However compared to WT IL1RAPL1, both mutants show significant decrease of clustering efficiency, suggesting that the mutants reduce somehow the interaction with PTPδ (~40% for both mutants). This deficit could contribute to the inability of C31R mutant to induce the formation of excitatory synapses.

To support this conclusion, we performed in vitro interaction tests by immunoprecipitating IL1RAPL1 from protein lysates containing both IL1RAPL1 and Myc-PTPδ proteins, and we evaluated by immunoblotting the presence of Myc-PTPδ ectodomain in the immunoprecipitate. Whereas WT or I643V efficiently interact with PTPδ, we observed a strong reduction of Myc staining after immunoprecipitation of both Δex6 and C31R mutants (Fig. 4B). However, decrease of Δex6 protein expression is likely to be also responsible for this observation (Suppl. Fig. 2 and Fig. 4B, input 10% and immunoprecipitated IL1RAPL proteins).

Taken together, cell aggregation and immunoprecipitation assays lead us to conclude that C31R mutation decreases the interaction of IL1RAPL1 with PTPδ.

Mutants regulate other IL1RAPL1-dependent signaling

Besides PTPδ, IL1RAPL1 interacts with NCS-1, PSD-95, RhoGAP2, Mcf2l, PKCε and PLCβ1 [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Bahi | IL1 receptor accessory protein like, a protein involved in X-linked mental retardation, interacts with Neuronal Calcium Sensor-1 and regulates exocytosis[END_REF][START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF]21). These proteins interact with the intracellular domain of IL1RAPL1, suggesting that signaling independent from the extracellular domain could still be induced in neurons expressing IL1RAPL1 mutants with intact intracellular domains.

Even if there is no evidence for direct interaction with c-jun N-terminal kinase (JNK), the role of IL1RAPL1 on the regulation of activity of this kinase has been reported [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Khan | Crystal structure of the Toll/interleukin-1 receptor domain of human IL-1RAPL[END_REF][START_REF] Pavlowsky | Neuronal JNK pathway activation by IL-1 is mediated through IL1RAPL1 , a protein required for development of cognitive functions[END_REF]. Over-expression of IL1RAcP and IL1RAPL1 was shown to increase JNK basal activity in HEK293 cells [START_REF] Khan | Crystal structure of the Toll/interleukin-1 receptor domain of human IL-1RAPL[END_REF][START_REF] Brint | Characterization of signaling pathways activated by the interleukin 1 (IL-1) receptor homologue T1/ST2. A role for Jun N-terminal kinase in IL-4 induction[END_REF]. In order to evaluate the capacity of the mutants to activate JNK, we assessed by immunoblotting the basal activity of this kinase in HEK293 cells overexpressing different IL1RAPL1 constructs.

We show that over-expression of IL1RAPL1 mutants in HEK293 cells increases the basal JNK phosphorylation, to levels comparable to the WT protein (Fig. 4C). Even if only p56 JNK isoform was quantified, phosphorylation of p46 isoform appears also to be increased after IL1RAPL1 over-expression. This result suggests that Δex6 and C31R mutants do not lose all signaling capacity, independently from synaptogenesis, and that even low expression of the IL1RAPL1 Δex6 mutant is able to induce this signaling.

DISCUSSION

There are hundreds of genes in which mutations are known to cause intellectual disability or ASD or both.

Since its discovery as a gene implicated in ID, several mutations of IL1RAPL1 were found in patients with different severity of ID. As shown in Table 1, the majority of the described mutations include large deletions. It is of particular interest that they mostly involve the first exons coding for extracellular domain of IL1RAPL1 protein. Some authors suggest that because of the incidence of genomic rearrangements, such as pericentromeric inversions, this region must be particularly prone to recombination [START_REF] Tabolacci | A Truncating Mutation in the IL1RAPL1 Gene Is Responsible for X-linked Mental Retardation in the MRX21 Family[END_REF][START_REF] Leprêtre | Dissection of an inverted X(p21.3q27.1) chromosome associated with mental retardation[END_REF].

Moreover, the majority of mutations likely results in the absence of the IL1RAPL1 protein, or is predicted to lead to truncated proteins. Until now only one frame shift mutation leading to a shorter IL1RAPL1 protein has been characterized functionally [START_REF] Piton | Mutations in the calcium-related gene IL1RAPL1 are associated with autism[END_REF]. The impact of mutations described so far on IL1RAPL1 protein production and function, when available, is summarized in Table 1.

Here we report two novel mutations of IL1RAPL1 related to non-syndromic ID and we characterize their functional consequences. Both mutations result in an in frame deletion of exon 6, leading to a 25 amino acids loss in the extracellular domain of IL1RAPL1. These mutations were identified in two unrelated families (P72 and BMC) and have different DNA breakpoints. In both cases, the deletion co-segregates with the ID phenotype in an X-linked recessive manner. Besides exon 6 deletion, patient II-1 in family BMC presents also a duplication on chromosome 19 that includes ZNF528 gene. Missense mutations of this gene were previously identified in two patients with mild ID [START_REF] Schuurs-Hoeijmakers | Identification of pathogenic gene variants in small families with intellectually disabled siblings by exome sequencing[END_REF]. Due to the fact that Δex6 mutation was also found in members of the P72 family presenting ID, we propose the deletion in IL1RAPL1 as the major cause of ID in these 2 families, but we cannot rule out that the severity of cognitive impairment could be modulated by deletions or duplications in other genes, such as ZNF528.

We also characterized the functional consequences of a unique missense variant C31R previously reported, but not further investigated [START_REF] Tarpey | A systematic, large-scale resequencing screen of X-chromosome coding exons in mental retardation[END_REF]. This variant was predicted to be damaging to IL1RAPL1 protein, which can be due to the importance of this region for protein folding. To our knowledge, this is the only pathogenic IL1RAPL1 missense variant described so far.

Several studies on XLID genes, including IL1RAPL1, raise the question of the role of X chromosome inactivation on female phenotype [START_REF] Tabolacci | A Truncating Mutation in the IL1RAPL1 Gene Is Responsible for X-linked Mental Retardation in the MRX21 Family[END_REF][START_REF] Nawara | Novel mutation of IL1RAPL1 gene in a nonspecific X-linked mental retardation (MRX) family[END_REF][START_REF] Behnecke | Intragenic deletions of IL1RAPL1: Report of two cases and review of the literature[END_REF][START_REF] Franek | Deletion of the immunoglobulin domain of IL1RAPL1 results in nonsyndromic X-linked intellectual disability associated with behavioral problems and mild dysmorphism[END_REF]. In the present study, IL1RAPL1 mutations were found in healthy as well as in affected females from the three families (Fig. 1). Females I-2 and II-2 (BMC family), and I-2 (A28 family) have some learning problems or low average intelligence. But unlike III-2 from P72 family, they do not have ID. We speculate that, even if not observed in fibroblasts, the X chromosome inactivation pattern may be skewed in III-2's brain or in particular subsets of neurons, resulting in a predominant expression of the mutant allele [START_REF] Wu | Cellular resolution maps of X chromosome inactivation: implications for neural development, function, and disease[END_REF].

Together with Δex6, the C31R mutation allowed us to address the impact of relatively milder mutations, in comparison to large deletions or nonsense mutations, on IL1RAPL1 protein stability, localization and synaptic function. IL1RAPL1 is located at both pre-and post-synaptic compartments of excitatory synapses, but is enriched in the post-synaptic membrane [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF], and it's over-expression is known to increase the formation of this type of synapses on hippocampal neurons [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF]21). We showed that Δex6 mutation lead to decreased protein stability in neurons, mislocalization within dendrites and decreased presence in spines, even if mutant protein is correctly targeted to the membrane. In the other hand, C31R mutation does not affect IL1RAPL1 stability in neurons nor localization on dendritic spines and shafts. Our experiments clearly show that Δex6 and C31R were not able to increase excitatory synapse number, after evaluation of either pre-or post-synaptic markers. In the case of Δex6 mutant, the lack of synaptogenic effect can be explained by the severe decrease in IL1RAPL1 protein expression and its miss localization, as shown in Figure 2A-B and2E-F. However C31R mutant protein, whose expression is similar to WT, also fails to increase synaptic formation. This impairment was also observed in ΔN, which lack the majority of the IL1RAPL1 extracellular domain (Suppl. Fig. 3 and Table 1). As previously shown [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF], ΔC mutant with intact extracellular domain is able to increase the pre-synaptic marker synaptophysin establishing that this domain is essential for pre-synaptic differentiation (Suppl. Fig. 3). We then hypothesized that C31R mutation affects this domain and the binding to interacting partners. PTPδ is the only partner known to interact with IL1RAPL1 extracellular domain and this interaction was shown to be essential for IL1RAPL1-mediated synaptogenesis [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF][START_REF] Yoshida | IL-1 receptor accessory protein-like 1 associated with mental retardation and autism mediates synapse formation by trans-synaptic interaction with protein tyrosine phosphatase δ[END_REF]. In order to dissect the molecular mechanism underlying the synaptic deficits observed in neurons transfected with C31R, we evaluated mutant's capacity to interact with PTPδ. The cell aggregation and immunoprecipitation assays shown in Figure 4 allowed us to conclude that the decrease of interaction with this tyrosine phosphatase participates to the inability of C31R IL1RAPL1 mutant to increase the number of excitatory synapses.

Despite reduced expression (Δex6) and perturbed synaptogenesis (C31R), we hypothesized that some of the signaling could be preserved in cells transfected with Δex6 and C31R mutants. Indeed, we observed that both mutant proteins were able to induce JNKs basal activation. The capacity of IL1RAPL1 to regulate JNK activity was previously shown [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Khan | Crystal structure of the Toll/interleukin-1 receptor domain of human IL-1RAPL[END_REF][START_REF] Pavlowsky | Neuronal JNK pathway activation by IL-1 is mediated through IL1RAPL1 , a protein required for development of cognitive functions[END_REF], even if the mechanism is still unclear. PSD-95 phosphorylation by JNK has been shown to regulate PSD-95 at the excitatory synapses and we proposed that the reduction of excitatory synapses in Il1rapl1 knockout neurons was secondary to reduced JNK activity [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF][START_REF] Kim | Synaptic Accumulation of PSD-95 and Synaptic Function Regulated by Phosphorylation of Serine-295 of PSD-95[END_REF]. Our results suggest that Δex6 and C31R mutations decrease IL1RAPL1 synaptogenic activity while maintaining other signaling, like JNK activation, uncoupling the two events. Alternatively, JNKs belong to the MAPK family, and in neurons they are involved in diverse roles including cell death, radial migration, neurite formation, metabolism regulation, and behavioral control. JNK signaling has an impact on synaptic plasticity, as a regulator of AMPA receptors trafficking [START_REF] Zhu | Rap2-JNK removes synaptic AMPA receptors during depotentiation[END_REF][START_REF] Thomas | Rapid and bi-directional regulation of AMPA receptor phosphorylation and trafficking by JNK[END_REF]. The functional role of JNK, in particular in response to IL1β stimulation, is still under investigation [START_REF] Pavlowsky | Neuronal JNK pathway activation by IL-1 is mediated through IL1RAPL1 , a protein required for development of cognitive functions[END_REF].

Finally, the I643V variant was reported in ID patients as well as in controls. This, together with in silico prediction suggests that this variant is not deleterious for IL1RAPL1 function. In this study we evaluated the potential functional consequences of this amino acid change within the intracellular domain of IL1RAPL1 with the aim to assess if it may act as a susceptibly variant to ID. We observed that I643V protein was significantly increased in transfected neurons, but the increase of excitatory synapse number was comparable to WT IL1RAPL1. These observations support the hypothesis that the functional interactions, but not the quantity of IL1RAPL1 protein is important for synapse formation. This functional characterization strongly suggests I643V to be a neutral IL1RAPL1 variant.

In conclusion, the cognitive deficits observed in patients carrying Δex6 mutations can be explained by the decrease of IL1RAPL1 protein stability in neurons, together with the fact that residual produced protein is mislocalized. In the other hand, deficits observed in patients with C31R mutation are caused by a decrease of the capacity to interact with PTPδ, and thus to increase synaptogenesis. In addition, these mutations allowed us to rule out the functional involvement of JNK in the PTPδ induced synaptogenic activity of IL1RAPL1.

MATERIALS AND METHODS

Genetic analysis

DNA was extracted from peripheral blood or skin fibroblasts using standard methods after parental and patients' consent was obtained.

The following intronic primers were used to investigate the exon 6 deletion in P72 family: (TGGGATTAGCTGCCTCCCTCT and ACTGACTTCTATGCCATTTTTCTGT). X-chromosome inactivation studies were performed using the AR, FMR1 and FMR2-specific HpaII/PCR assay, to assess X-inactivation pattern.

SNP array analysis on BMC family members was performed using a HumanCytoSNP-12v2.1 beadchip following standard protocols as provided by the manufacturer on an iScan system (Illumina, San Diego, CA). CNV analysis was performed using CNV-WebStore [START_REF] Vandeweyer | CNV-WebStore: online CNV analysis, storage and interpretation[END_REF]. Familial relationships were validated by comparing the SNP patterns of the patient with those of the parents.

Identification of c.91T>C (C31R) mutation II-2 member of family A28 is described elsewhere [START_REF] Tarpey | A systematic, large-scale resequencing screen of X-chromosome coding exons in mental retardation[END_REF].

Segregation studies were performed by PCR and Sanger sequencing.

Newly identified variants were submitted to Leiden Open Variation Database 3.0 (LOVD 3.0) [START_REF] Fokkema | LOVD v.2.0: the next generation in gene variant databases[END_REF] (IL1RAPL1_000008 and IL1RAPL1_000009).

cDNA constructs

HA-tagged human IL1RAPL1 described before (15) was modified using QuikChange II XL Site-Directed Mutagenesis Kit (Agilent Technologies) to generate Δex6, C31R, I643V and ΔIg123 constructs. Myctagged PTPδ, ΔC, ΔN were described elsewhere [START_REF] Valnegri | The X-linked intellectual disability protein IL1RAPL1 regulates excitatory synapse formation by binding PTPδ and RhoGAP2[END_REF].

Antibodies

The following primary antibodies were used: rabbit anti-IL1RAPL1 (K10,( 15)), goat anti-IL1RAPL1

(R&D), mouse anti-GFP (Roche and Abcam), rabbit anti-VGlut1 (Synaptic Systems), rabbit anti-VGAT (Synaptic Systems), rabbit anti-HA-tag (Santa Cruz Biotechnology), mouse anti-HA-tag (Roche), mouse anti-c-Myc (Santa Cruz Biotechnology), mouse anti-PSD-95 (Affinity Bioreagents), rabbit antisynaptophysin (Cell Signaling), rabbit anti-P-Thr183/Tyr185 JNK (Cell Signaling), mouse anti-JNK (Cell Signaling), mouse anti-GAPDH (Ambion). All fluorophore conjugated secondary antibodies were purchased from Jackson ImmunoResearch Labs.

HEK293 cells culture, transfection and immunoblotting

HEK293 cells were grown in Dulbecco's modified Eagle's medium supplemented with 10% fetal bovine serum and penicillin/streptomycin (all Invitrogen). Cells were seeded at 60-70% of confluence and transfected with the different constructs using Lipofectamine 2000 (Life Technologies). 24h after transfection, cells were lysed and an equal amount of protein was submitted to SDS-PAGE and transferred to nitrocellulose membrane. Membranes were incubated over night with HA tag, GFP, GAPDH or P-JNK antibodies. Total JNK was evaluated after stripping P-JNK signal. After incubation with HRP-conjugated secondary antibodies (Dako), Super Signal West Femto and ECL substrate (Pierce) were used for revelation. Acquisition was performed with LAS-4000 (General Electric) and quantification of band software (Molecular Devices). Recordings were performed under blind conditions. Typically, time periods of 120 seconds were used for analysis of synaptic events occurring at both membrane potentials.

Cell aggregation and immunoprecipitation assays

Two groups of HEK293 cells grown in 12-well plates were transfected, one with HA-IL1RAPL1 WT or mutants, and the other with Myc-PTPδ ectodomain. Cells transfected with GFP were used as negative control. After 12 h, cells were detached and counted for the cell aggregation assay, or lysated with 50 mM TRIS-HCl, 200 mM NaCl, 1 mM EDTA, 1% NP40, 1% Triton X-100 and protease inhibitors (RIPA buffer), for the immunoprecipitation assay.

For the cell aggregation assay, cell suspension was transferred to microtubes and gently centrifuged (800 g, 5 minutes, RT) to eliminate PBS-EDTA. The pellets were resuspended in aggregation medium (AM) containing HBSS 1x, MgCl 2 1mM, and CaCl 2 2mM. The two groups of transfected cells were mixed together and rotated at room temperature for 30 min to allow cells to aggregate. Cell mixtures (4 x 10 6 cells) were added to 1 ml AM on poly-L-Lys coated coverslips in multiwall (12 well) plate and let attach for some minutes at 37°C with 5% CO 2 . Once attached, cells were fixed and stained. Image analysis was performed under blind conditions, and aggregation coefficient was calculated by the number of green + red clusters (yellow in merge images) divided by the number of total transfected (green + red) cells and expressed as percent.

For the immunoprecipitation assay, protein A Sepharose beads (GE Healthcare) were washed in RIPA buffer. Anti-IL1RAPL1 antibody (K10, [START_REF] Pavlowsky | A postsynaptic signaling pathway that may account for the cognitive defect due to IL1RAPL1 mutation[END_REF]) was added to the beads at 5μg/ml in RIPA buffer and incubated for 1 h. Lysates from the two groups of transfected cells in RIPA buffer were mixed in a in a volume proportion of 1 (for IL1RAPL1) to 1.5 (for Myc-PTPδ) and incubated overnight at 4° C with the beads/IL1RAPL1 antibody. The beads were washed 3 times with RIPA buffer and elution was performed in sample buffer for SDS-PAGE (5 min at 100°C), and loaded to 10% SDS-PAGE. Protein detection was performed as described in immunoblotting section.

LEGENDS TO FIGURES

8 (

 8 TGAAAGTGAAAAATATTTGGGAAA, and CACAATGTAACGAGAGCAGCA. Confirmation of the deletion was obtained by qPCR (LightCycler LC480, Roche) targeting exon ACATCAGATTCGGATTCATC and GCGTGTCGACGTCCATT) was used as a reference. CGH array (NimbleGen's, Roche) and long range PCR (TGTGAGTGAGTGTGCATATGTGTGTATAGGTG and CGTGGGGACTAGACCAGGAGTTG) was used to map exon 6 deletion in P72 family members.Germinal mosaicism of the deletion was explored by qPCR (TGCTTGACAGAATTTTCCAAGGAGCA and GTTACCACTTTCATTTACCTTGGGATGA) were COL6A5 expression was used as a reference (ACCACTGGCAGCTTCTGGCAA and CGCCCCTGGACATCCTGCAA). The following primers were

  Whole-cell patch-clamp recordings were made from GFP or IL1RAPL1 transfected mouse hippocampal neurons at 18-21 DIV. Non transfected cells from the same coverslip were also recorded as controls. Patch electrodes, fabricated from thick borosilicate glass, were pulled and fire polished to a final resistance of 2-4 M and filled with internal solution containing (in mM): 125 CsMeSO 3 , 2 MgCl 2 , 1 CaCl 2 , 4 Na 2 ATP, 10 EGTA, 10 HEPES, 0.4 NaATP, and 5 QX314. Cultured neurons were superfused with an oxygenated external solution containing (in mM): 130 NaCl, 2.5 KCl, 2.2 CaCl 2 , 1.5 MgCl 2 , 10 HEPES, and 10 D-Glucose. Neurons were voltage clamped at -70 mV to record EPSCs and at 0V to record IPSCs. All of the experiments were performed at room temperature. Inward synaptic currents at -70 mV and outward currents at 0 mV were automatically detected by an automatic template based routine using pClamp 10.4

Figure 1 .

 1 Figure 1. Identification of two novel mutations on IL1RAPL1 associated with intellectual disability.

Figure 2 .

 2 Figure 2. Protein expression and localization of Δex6 and C31R IL1RAPL1 mutants. (A) Protein

Figure 3 .

 3 Figure 3. Consequences of IL1RAPL1 mutations on excitatory synapse formation. (A) Rat

Table 1 .

 1 TABLES Reported mutations on IL1RAPL1 gene in ID patients, and their consequences for protein function.

	Reference	Mutation / exons	Protein	Functional consequences
	(1)	deletion exon 3-5	Probably not produced
	(1)	nonsense exon 11	Y459X predicted to lead to a protein lacking part of the TIR domain and the entire C-ter domain	ΔC (15, 20)  Does not increase dendritic spines number nor changes their
				length and width
	(2, 3)	nonsense exon 11	W487X predicted to produce a protein lacking half of the TIR domain and the entire C-ter domain	 Increases the number of active pre-synaptic compartments  Fails to target RhoGAP2 to synapses
	(4)	deletion exons 3-6*	Probably not produced
			I367SX6 predicted to produce a protein	I367SX6 (5)
	(5)	nonsense exon 9	lacking part of the trans membrane domain as well as the entire C-ter	 Not targeted to the membrane  Rescues neurite number and length phenotype after Il1rapl1
			domain	knock down
			Frame shift A28EfxX15 predicted to
	(5)	deletion exon 3-7	produce a short protein containing only 8 amino acids in addition to the
			signal peptide
			I643V variant produces a full length	I643V (Current report)
	(5) and current	missense	protein	 Induce dendritic spines formation and increase functional
	report	exon 11	In silico analysis predicts it to be	excitatory synapses
			tolerated by the protein	 Interacts with PTPδ and induces basal JNK activation
			The resulting protein should lack the
	(6)	deletion exon 3-5	first two Ig-like domains, but it is possible that synthesis stops after
			deletion
	(6)	deletion exon 2	Probably not produced
	(7)	deletion exons 3-5	Probably not produced
	(8)	deletion exons 1-5	Probably not produced
				ΔN (20)
	(8)	deletion exons 3-6*	In frame deletion (p.28_259del) predicted to produce a shorter protein devoid of the two first Ig-like domains	 Does not increase dendritic spine density, nor changes spine length and width  Fails to increase functional excitatory synapses  Lacks interaction with PTPδ and fails to target RhoGAP2 to
				synapses
	(9)	deletion exons 2-6	Probably not produced
	(10)	deletion exons 3-11	Probably not produced

* Modified from original article, in accordance with hg38 assembly.

We thank Cherif Beldjord for X chromosome inactivation and segregation studies; Thierry Bienvenu for mutation analyzes and in silico prediction of genetic variant pathogenicity; Cellular imaging facility of Institut Cochin for image analysis advice.

AKNOWLEDGMENTS

This work was supported by the European Union's FP7 large scale integrated network Gencodys (http://www.gencodys.eu/, HEALTH-241995); by the French Research Agency (ANR-2010-BLANC-1434-03); by the European Union's EraNet program (ANR 2010-Neuro-001-01); by Institut national de la santé et de la recherche médicale (INSERM); by Ecole des Neurosciences de Paris (to M. R-B); by Comitato Telethon Fondazione Onlus (grant no. GGP13187 and GGP11095 (to C. S.)); Fondazione CARIPLO project number 2012-0593; Italian Institute of Technology; Seed Grant; Ministry of Health in the frame of ERA-NET NEURON; PNR-CNR Aging Program 2012-2014 and Foundation Jérôme Lejeune (to C. S.).

intensity was done with ImageJ software (Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA, http://imagej.nih.gov/ij/, 1997-2014.). IL1RAPL1 abundance was evaluated in lysates from cells co transfected with IL1RAPL1 constructs and GFP (control of transfection efficiency), by dividing HA intensity signal by GAPDH signal (protein loading control). JNK phosphorylation was measured by calculating the ratio between P-JNK (P-p54) and total JNK (p54). Statistical analysis was performed by one way analysis of variance (ANOVA) followed by Tukey's post-hoc test for multiple comparisons.

Cell culture and transfection of primary rat and mouse hippocampal neurons

Low-density rat hippocampal neuronal cultures were prepared from embryonic day (E) 18-19 hippocampi as previously described with minor modifications [START_REF] Sala | Regulation of dendritic spine morphology and synaptic function by Shank and Homer[END_REF][START_REF] Verpelli | Synaptic activity controls dendritic spine morphology by modulating eEF2-dependent BDNF synthesis[END_REF] and were grown in 12-well Petri dishes (Primo).

Cultured mouse hippocampal neurons were prepared from E16.5 embryos, grown in 10 mm glass coverslips and maintained in Neurobasal B27-supplemented medium (Life Technologies). Neurons were transfected using Lipofectamine 2000 on Days In Vitro 11 (DIV11) and experiments were performed at DIV14-18. Experimental procedures on animals were approved by the local ethical committee.

Neuron surface staining

At DIV 14-15, live hippocampal neurons were labeled for 10 min at 37°C with anti-HA-tag rabbit antibody (10 μg/ml). After washing, neurons were fixed with paraformaldehyde (PFA) 4% plus 4% sucrose and incubated with anti-HA-tag mouse antibody in GDB (30 mM phosphate buffer, pH 7.4, 0.2% gelatin, 0.5% Triton X-100, 0.8 M NaCl (all Sigma-Aldrich)) for 3 h at room temperature. Cells were washed in 20 mM phosphate buffer containing 0.5 M NaCl and incubated with FITC-and Cy3conjugated secondary antibodies.

Immunocytochemistry and image analysis

Cells were fixed in 4% PFA plus 4% sucrose at room temperature for 20 minutes, or 100% methanol at -20° for 10 min. Primary (1:100-1:800) and secondary (1:200) antibodies were applied in GDB buffer or in PBS (pH 7.4) containing 3% BSA and 0.2% Tween 20.

Confocal images were obtained using a Zeiss 510 confocal microscope (Carl Zeiss, a gift from Fondazione Monzino) or a Leica DMI6000 Spinning disk microscope. Quantification of synaptic protein staining was performed using MetaMorph (Molecular Devices, Downingtown, PA), and ImageJ software and NeuronJ plugin [START_REF] Meijering | Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images[END_REF]. Labeled, transfected cells were chosen randomly for quantification from six coverslips from 3 independent experiments for each condition and image analysis was performed under blind condition.

Coefficient of variation of IL1RAPL1 staining was calculated by dividing the standard deviation of HA signal by mean pixel intensity within dendrites [START_REF] Lyles | Synapse formation and mRNA localization in cultured Aplysia neurons[END_REF] .The dendritic spine number was measured as described previously [START_REF] Verpelli | Synaptic activity controls dendritic spine morphology by modulating eEF2-dependent BDNF synthesis[END_REF][START_REF] Piccoli | Proteomic Analysis of Activity-Dependent Synaptic Plasticity in Hippocampal Neurons research articles[END_REF] with minor modifications. For each neuron we measured the number of protrusions present in all the dendrites along their entire length. Then we calculated mean and SEM (Standard Error of the Mean) for the neurons transfected with the same construct.

Quantification of protein surface staining was performed using MetaMorph (Molecular Devices, Downingtown, PA), and ImageJ software. The ratio of integrated intensity of surface rabbit anti-HA signal per total mouse anti-HA signal was measured for each neuron. Then we calculated the mean and SEM for the neurons transfected with the same construct.

HA-IL1RAPL1 in spines and dendritic shafts was quantified using IMARIS 7.2 software and Filament Tracer wizard (Bitplane). Integrated density of HA signal was normalized by GFP integrated density in each compartment. The ratio of HA/GFP in spines and in dendritic shafts was assessed for each neuron and mean + SEM was reported for neurons transfected with the same IL1RAPL1 construct.

Statistical analysis was performed by one way analysis of variance (ANOVA) followed by Tukey's posthoc test.

Electrophysiological recording on mouse hippocampal cultured neurons CONFLICT OF INTEREST STATEMENT

None declared. transfected neurons per condition and 32 non transfected neurons (nt) * p< 0.01, compared to control neurons).


A Fuhrmanek

Y R P Sortais

P Grangier

A Browaeys

Measurement of the atom number distribution in an optical tweezer using single photon counting

Keywords: numbers: 37, 10, -x, 05, 40, Jc

We demonstrate in this paper a method to reconstruct the atom number distribution of a cloud containing a few tens of cold atoms. The atoms are first loaded from a magneto-optical trap into a microscopic optical dipole trap and then released in a resonant light probe where they undergo a Brownian motion and scatter photons. We count the number of photon events detected on an image intensifier. Using the response of our detection system to a single atom as a calibration, we extract the atom number distribution when the trap is loaded with more than one atom. The atom number distribution is found to be compatible with a Poisson distribution.

I. INTRODUCTION

The last few years have seen a growing interest in the study of mesoscopic systems consisting of typically a few tens of interacting particles. The properties of these systems usually cannot be described by a mean-field approach and are already too complicated to be calculated from the behavior of each individual interacting particle. Dense clouds of ultra-cold atoms provide an ideal test bed to study these mesoscopic systems. The interactions are well-understood at the two-body level and, experimentally, one benefits from the host of tools developed over the years to investigate ultra-cold atomic clouds (see e.g. [1]). Various implementations have already been realized such as arrays of optical tweezers [2] or of magnetic traps [3], double-well potential geometries [4] and optical lattices (e.g. [5,6]).

Beyond their intrinsic interest, a possible application of dense clouds of ultra-cold atoms is the production of atomic states for which the fluctuations of the number of atoms are reduced with respect to the Poissonian case. These clouds could for example be useful for atomic interferometry below the standard quantum limit [7]. Recent demonstrations have been achieved using Bose-Einstein condensates with a few thousand atoms ( [8,9]). The clouds could also be used as a source delivering a given number of atoms, as was already demonstrated in the single atom case in an optical tweezer [10] or in a onedimensional optical lattice [11]. For larger numbers of atoms, experiments showing the reduction of the atomnumber fluctuations have been reported in Bose-Einstein condensates in an optical trap [12], in optical lattices [13], or in arrays of magnetic micro-traps [14]. For all these applications the knowledge of the distribution of the number of atoms, and not only the average number of atoms, is essential.

The number of atoms in a cold atomic cloud can be * corresponding author: yvan.sortais@institutoptique.fr measured by usual optical techniques, such as laser induced fluorescence or absorption. Nevertheless, special care must be taken when the number of interacting particles involved is small. For instance, when using fluorescence imaging the small number of atoms combined with the low collection efficiency makes it hard to collect more than a few photons per realization of the experiment, therefore preventing the reliable extraction of the number of atoms in single shot. To circumvent this problem, a method was recently demonstrated [15] where freely propagating atoms fall through a sheet of resonant light leading to the detection of many photons per atom.

In this paper we present a method to measure the distribution of the number of atoms trapped in a microscopic optical dipole trap in a regime where the number of atoms is a few tens. The method relies on singlephoton counting. The principle is as follows: we release the cloud of cold atoms from the dipole trap and let them expand in a resonant light probe. The atoms diffuse in the probe in a Brownian motion and emit photons. Some of the photons are collected by an imaging system and impinge on an image intensifier where we count them. By repeating the experiment several times and recording the counting results, we reconstruct the distribution of the number of detected photons. Our experimental setup can work either with exactly one atom, or with a cloud of up to a few tens of atoms. In this way we perform a calibration of the number of detected photon events when a single atom is trapped, and use this calibration to determine the atom number distribution.

The paper is organized as follows. In Sect. II we describe briefly the setup. Section III describes the loading of our microscopic dipole trap in the single-atom regime and in the many-atom regime. In section IV we describe the experimental sequence and in Sect. V we present the image analysis used to count the number of photon events. Sect. VI deals with the calibration of our detection system using a single atom. Section VII explains how we extract the atom number distribution in the multiatom regime. In Sect. VIII we compare the mean number of atoms extracted by this counting method to the result obtained by direct integration of the laser induced fluorescence, and find good agreement between the two methods.

II. EXPERIMENTAL SETUP

Our experimental setup has been described in details elsewhere [16][17][18] and consists essentially in a microscopic optical dipole trap, in which we trap up to a few tens of 87 Rb atoms (see details in Section III). The trap is produced by a laser beam at 850 nm that is focused by an aspheric lens with a numerical aperture N.A. = 0.5. The resulting spot has a Gaussian profile with a waist w = 1.1 µm. A power of 9 mW yields a trap depth of 2 mK. The dipole trap is loaded from a cold atomic cloud held in a magneto-optical trap produced around the focal point of the aspheric lens. The magneto-optical trap captures atoms from a Zeeman decelerated atomic beam coming from an oven.

We use the same aspheric lens to collect the fluorescence light at 780 nm. A dichroic beam-splitter separates the fluorescence light from the dipole trap light. A fraction of the fluorescence light is sent to a fiber-coupled avalanche photodiode operating in a single photon counting mode. The remaining fluorescence is directed onto an image intensifier, followed by a low-noise CCD camera. We have measured a detection efficiency η ≃ 3 × 10 -3 , which takes into account the solid angle of the aspheric lens (7%), the transmission of the optics (40%), and the measured quantum efficiency of the intensifier photocathode (10%). Here, we note that using an image intensifier is crucial for the experiment presented in this paper because it enables our imaging system to detect single photon events. In the absence of the intensifier, single photon events have an amplitude lower than the noise of the CCD camera alone (6e -/pixel). The intensifier amplifies a single photon event to an average amplitude of 920e -/pixel, well above this noise level.

In order to characterize the atomic cloud, we use a probe consisting in two counter-propagating laser beams in a σ + -σ -configuration. This probe is tuned to the (5 2 S 1/2 , F = 2) to (5 2 P 3/2 , F ′ = 3) transition and is sent together with a repumping light tuned to the (5 2 S 1/2 , F = 1) to (5 2 P 3/2 , F ′ = 2) transition. The probe light is focused down to a waist of 0.9 mm and has a saturation parameter I/I sat ≈ 2.7 for each beam.

III. LOADING OF THE DIPOLE TRAP

The experiment can operate either in a regime where only one atom is present in the dipole trap or in a regime where up to ∼ 10 atoms are trapped. The transition between the two regimes is governed by the atomic density in the magneto-optical trap, which is controlled by the flux of the atomic beam. The average number of atoms N in the dipole trap is set by two competing processes: the loading from the magneto-optical trap, and the twobody losses due to collisions assisted by the near-resonant light of the cooling and trapping lasers [19]. When the loading rate of the dipole trap is lower than the lightassisted collision rate, only one atom can be present at a time in the trap: if a second atom enters the trap a lightassisted collision takes place and both atoms are lost. On the contrary, when the loading rate of the dipole trap overcomes the inelastic loss rate, the average number of atoms is larger than one [19,20]. For the experiments presented below we find that, after a fixed loading time ( < ∼ 1 s typically), the mean number of atoms in our microscopic trap increases linearly with the trap depth and reaches N = 9 for a trap depth of ∼ 20 mK. We measure the temperature of the trapped atom(s) using either a release-and-recapture method [17] or a time-of-flight method [18]. We find a temperature around 150 µK in the single atom case and around 1 mK in the multi-atom regime.

In the single-atom regime, the presence of an atom in the trap is revealed by a step in the fluorescence signal collected on the APD [16]. This step is used to trigger an imaging sequence where the number of fluorescing atoms is exactly 1: this way there are no fluctuations in the atom number from shot to shot (variance ∆N 2 = 0). In the multi-atom regime, the situation is different as we observe no such steps on the APD signal: firstly because when the atomic density increases, the time spent on average by each atom in the trap decreases below the time bin resolution of the APD counter due to an increasing inelastic loss rate, and secondly because the height of the steps itself decreases due to light-induced dipole-dipole interactions that shift and broaden the atomic line [21]. One thus cannot rely on fluorescence steps to perform an in situ measurement of the number of trapped atoms. Instead, the technique presented in this paper goes around this problem by converting the multi-atom signal into a sum of single atom events, spatially separated on a CCD camera. In this second regime, the absence of fluorescence steps on the APD signal also makes it impossible to trigger the imaging sequence after a given number of atoms is loaded in the trap. We thus trigger the imaging sequence after a fixed loading duration. Due to the random nature of the two-body losses during the loading this procedure leads to fluctuations in the number of trapped atoms from shot to shot (∆N 2 = 0) [19].

IV. EXPERIMENTAL PROCEDURE AND FLUORESCENCE IMAGES

Once the trap is loaded, either with exactly one atom, or with N atoms, we switch off the cooling and repumping lasers and wait an additional 30 ms before switching off the dipole trap. This waiting period allows enough time for the atoms of the magneto-optical trap to leave the observation region, otherwise they would strongly contribute to the signal observed with the intensifier. We then switch off the dipole trap (in ∼ 200 ns) and, after a time of flight of the atoms of 1 µs in free space, we turn on the resonant probe, while gating the intensifier for a given period of time ∆t (in the 10 -60 µsec range). Finally, we read out the CCD camera, which lasts ∼ 500 ms, while launching the next loading sequence.

During the 1 µs time of flight in free space, the atoms start separating from each other. Then they walk randomly in the retro-reflected light probe and scatter photons at a rate ∼ Γ/2 ≃ 2 × 10 7 s -1 (Γ is the line-width of the atomic transition). Some of the scattered photons are collected on the image intensifier and impinge on the CCD at different positions due to the random walk of the atom in the probe light [22]. The total number n of detected events is proportional to the number of atoms N on average. The images shown in Fig. 1(a) and (b) were obtained after a single realization of the experimental sequence. Figure 1(a) corresponds to the time of flight of a single atom moving randomly in the probe light. Figure 1(b) corresponds to the time of flight of about 8 initially trapped atoms. In both cases, the detected photons correspond in a large extent to photons being scattered by the atom and detected by the intensifier and, in a smaller extent, to photons due to spurious laser light or self-induced charges generated inside the intensifier (see more details below). This fact led us to adjust the size of the region of interest to the measured temperature of the atom(s): for a time of flight of duration ∆t, we chose a square with a side dimension ∼ 4σ v ∆t, where σ v = k B T /M , T being the temperature of the atoms, M their mass, and k B the Boltzman constant. This choice leads to a negligible probability of missing an atomic event, while reducing the number of background events, which are uniformly distributed on the CCD.

V. PROCEDURE FOR ANALYZING THE IMAGES

In order to count the number of events detected on the CCD camera, one has to decide what one calls an event.

In order to do so, we first characterize the noise of the CCD camera, which is essentially due to the readout of the CCD chip. We find a root-mean-square (rms) noise σ CCD = 6e -/pixel. We then apply the following procedure. We search for the pixel with the largest amplitude of the signal. If the signal amplitude on this pixel is larger than 6σ CCD , we call it a peak and exclude from the image a zone of 13 × 13 pixels around it, the rms size of an individual event being 1.3 × 1.3 pixels (set by the intensifier resolution and corresponding to 0.6 × 0.6 µm 2 in the plane of the atoms) [23]. We then repeat this procedure by searching for the pixel with the next largest amplitude until no peak with an amplitude larger than 6σ CCD is found.

have independently measured the amplitude distribution of single-photon events recorded by the intensifier followed by the CCD camera. Using this distribution, we have found that less than 4% of the events have a peak amplitude smaller than 6σ CCD . Our procedure for counting the events therefore does not underestimate their number by more than 4%.

VI. CALIBRATION USING A SINGLE ATOM

The first step of the calibration of the imaging system as a counting device was to measure the histogram of the number of background events in one image when no atom is trapped in the dipole trap. The background events have three different origins: the largest contribution comes from light scattering by the atoms of the atomic beam that cross the region of observation (60%); the second largest contribution comes from self-induced events generated by the gated intensifier when the high voltage is switched on and off (33% of the counts); finally, a smaller contribution comes from scattering of the probe beams on the surfaces inside the vacuum chamber (7%). The histogram of the total number of background events is shown in Fig. 2, which results from the analysis of 200 images of the background. The probe pulse duration was ∆t = 30 µs. The data are well fitted by a Poisson distribution with average nbg = 0.7.

In a second step, we repeated the same experiment with exactly one atom trapped in the dipole trap. In particular, the probe duration was the same as above (∆t = 30 µs). As the detection efficiency is small and corresponds to a random collection of photons, we also expect a Poisson distribution for the number of detected photons emitted by the atom. In this case, the distribution of detected events, including the background events, is a Poisson distribution with a mean value: nsingle = nat + nbg .

(1) The experimental distribution is shown in Fig. 2, together with a fit by a Poisson distribution. We obtain a good agreement for nsingle = 2.5. This yields an average number of detected photons, emitted by one atom, of nat = 1.8. Finally, we tested the linearity of our counting system with the duration of the probe pulse. The results are shown in Fig. 3, where we plot the average number of detected events due to scattering by a single atom, nat , obtained after subtraction of the average number of background events. We first performed the experiment with a single atom with a temperature T ∼ 150 µK and observed a linear dependency of nat with the duration of the probe illumination. A linear fit to the data yields a photon detection rate, for one atom released from the trap, of R d = 57200 ± 3100 s -1 (the error bar is from the fit). Knowing the detection efficiency of the imaging system (∼ 3 × 10 -3 ), we deduce a scattering rate of 1.9 × 10 7 s -1 , in agreement with the value calculated for the parameters of our probe.

In order to further test the linearity of our counting system, we also performed the same measurement for an atom adiabatically cooled down to 16 µK [17]. In this case, the detected events tend to accumulate on a smaller area on the I-CCD, due to the smaller velocity of the atom (the time of flight of the atom is maintained constant and equal to 1 µs with respect to the previous case at T ∼ 150 µK). In spite of the increase in the surface density of detected events, we were still able to discriminate between individual events and found the same FIG. 3: (Color Online) Average number of detected photons after scattering by a single atom with temperature 16 µK (blue circles) or 150 µK (red diamonds), versus the duration of the atom illumination by the probe light. Linear fits to the data (dashed lines) yield a photon detection rate R d = 57200 ± 3100 s -1 for 16 µK and R d = 61800 ± 2400 s -1 for 150 µK. linear dependency as above, with a photon detection rate of 61800 ± 2400 s -1 .

To conclude, we detect on average nat = 1.1 photons scattered by a single atom for a probe duration ∆t = 20 µs. This value will serve as a calibration in the experiments described below, where the average number of atoms is the unknown.

VII. ATOM NUMBER DISTRIBUTION IN THE MULTI-ATOM REGIME

We now operate in the regime where more than one atom are loaded in the dipole trap. We repeat the same experimental procedure and extract the histogram of the number of detected events for a probe duration ∆t = 20 µs. Figure 4 shows the histogram of the background events as well as the probability distribution of the total number of detected events (including the background events) when about 6.3 atoms are loaded in the dipole trap on average. The background gives an average number of events nbg = 2.1, larger than in Sect. VI, as we needed to increase the flux of the atomic beam in order to load more than one atom in the trap.

To fit the distribution of events in the multi-atom regime, we consider the distribution of the number of atoms N in the dipole trap, P (N, N ), with N the mean atom number. The probability to detect n photon events is then given by the composed law [19]:

p(n) = ∞ N =0 P (N, N ) × Π(n, N × nat + nbg ) (2)
with Π(n, α) the Poisson distribution of mean α. Even in the case when P (N, N ) is a Poisson law, the distribution p(n) is not Poissonian. Nevertheless, for any distribution P (N, N ), the mean value of this composed law is given by: nmulti = N × nat + nbg .

A direct calculation of the mean of the data shown in We now discuss the Poissonian assumption mentioned above for the atom number distribution P (N, N ). We extract from the data the variance of the number of detected events, ∆n 2 multi = n 2 multi -n2 multi . This variance is related to the variance of the number of atoms ∆N 2 by the following expression, calculated using the probability p(n) of equation ( 2), and valid for any distribution P (N, N ):

∆n 2 multi = n2 at × ∆N 2 + nmulti . (4)
Taking again nat = 1.1, we find for the data of Fig. 4 a ratio of ∆N 2 / N = 0.86 ± 0.13 (the error bar is statistical). This value is compatible with P (N, N ) being a Poisson distribution. We repeat this measurement for various average numbers of atoms ranging from N = 2 to N = 9 and find that ∆N 2 / N is equal to 0.76 in average with a rms dispersion of 0.13. This 1 σ uncertainty does not clearly indicate a sub-Poissonian behavior as ∆N 2 / N does not deviate from 1 by more than 2 σ.

VIII. COMPARISON WITH FLUORESCENCE INTEGRATION

We have checked that the average number of atoms extracted by the counting method described so far is consistent with the number of atoms extracted by a second method based on fluorescence integration. This second method consists in illuminating the cloud of freely propagating atoms by a 2 µs probe pulse, and accumulating the fluorescence detected on the CCD over many realizations of the experiment. In each time-of-flight experiment, we let the atoms fly during 1 µs before we illuminate them with the probe pulse. As explained in [18], after typically several hundreds repetitions of the experiment, the image shows a nearly gaussian distribution, reconstructed from many individual detected events. We perform this experiment in the multi-atom regime and then in the singleatom regime. We use the latter to extract the number of atoms in the multi-atom regime, by calculating the ratio of the integrated fluorescence values obtained in the two regimes.

This fluorescence integration based method was implemented in two trap configurations that we now describe. As already explained, a significant fraction of the background events come from photons being scattered when the atomic beam interacts with the probe light. To min-imize this effect, we decreased the flux of the beam by reducing the temperature of the oven. This is at the expense of the loading rate of the dipole trap: in this first configuration, we could not load more than ∼ 10 atoms in the microscopic dipole trap. In order to calibrate our detection scheme with a larger number of atoms, we implemented a dipole trap with a larger waist w = 4 µm. In this second configuration, the atomic density is smaller and the light-assisted collisions limit the number of atoms to a larger value than in the microscopic dipole trap [20], typically 30. The results of the experiment are shown in Fig. 5 where we plot the average number of atoms obtained from the counting method versus the average number of atoms obtained by fluorescence integration. The numbers of atoms obtained by the two methods are compatible : a linear fit to the data yields a slope of 1.08 which is compatible with 1, as the statistical uncertainty on the slope is 0.05 and we evaluate the bias uncertainties attached to each method to 4% for the counting method, and 11% for the integrated-fluorescence based method.

IX. CONCLUSION

We have demonstrated in this paper a method to reconstruct the distribution of the number of atoms trapped in an optical dipole trap. This method gives access to the distribution of the number of atoms for clouds containing up to a few tens of ultra-cold atoms. It is based on the detection, at the single photon level, of fluorescence events scattered by the atoms when they undergo a random walk in the resonant probe light. So far, we have investigated a regime where the distribution of the number of atoms does not clearly depart from a Poisson law. Our technique is in principle applicable to any distribution and could therefore be useful to investigate blockade effects leading to sub-Poissonian distributions of the number of trapped atoms.

FIG. 1 :

 1 FIG. 1: (Color Online) Figure (a) is an image taken for a 40µsillumination period of a single atom. The region of interest has a size of 50 µm×50 µm in the plane of the atoms, corresponding to a measured temperature of 150 µK (see text). In figure (b), about 8 atoms were released from the trap and illuminated with a 20 µs probe pulse. The image size is 100 µm×100 µm in the plane of the atoms, corresponding to a temperature of 1 mK.

  Duration of the probe pulse (µs)

FIG. 4 :

 4 FIG.4: (Color Online) Probability distribution of the number of detected events when the dipole trap is filled with 6.3 atoms on average (blue circles). The data are well-fitted by a composed law that includes a Poisson law for the number of atoms in the trap. The data in red diamonds correspond to the background events only (n bg = 2.1) fitted by a Poisson law. The duration of the probe is set to 20 µs so that the average number of detected photons scattered per atom is nat = 1.1.

Fig. 4

 4 yields nmulti = 9. Taking into account that the probe duration has been chosen to detect nat = 1.1 events per atom and that nbg = 2.1, equation (3) yields an average number of atoms N = 6.3. Taking a Poisson distribution for P (N, N ), a fit of the data by the composed law (2) leads to the same result. The result of the fit is shown inFig 4.

FIG. 5 :

 5 FIG.5:(Color Online) Comparison of the results for the average number of atoms N by two methods : direct counting of single fluorescence events (vertical axis) versus fluorescence integration (horizontal axis). Both methods give comparable results, as indicated by the linear fit to the data (dashed line) with a slope of ∼ 1 (see text). The experiments were performed in two configurations: with a microscopic dipole trap (red diamonds, w = 1 µm) or with a larger dipole trap (blue dots, waist w = 4 µm).

  Red diamonds : background events (no atom present in the trap). Blue circles : total number of detected events (including background events) when the dipole trap is filled with exactly one atom. In both cases, the probability p to measure a given number a counts in one image is deduced by analyzing 200 images. The error bar on each data point is calculated by p(1 -p)/200, which we tested by repeatability measurements. A Poisson distribution fits the data very well in both cases (dotted lines).

		0.5
		0.4
	Probability	0.3 0.2
		0.1
		0.0
		0	2	4	6	8	10
				Number of counts
	FIG. 2: (Color Online) Probability distribution of the num-
	ber of detected events in one image. The probe duration is
	30 µs.

Acknowledgments

We thank A.M. Lance and C. Tuchendler for their contribution at an early stage of the experiment. We acknowledge support from IARPA, the European Union through the Integrated Project AQUTE and the ERC starting grant ARENA, the Institut Francilien des Atomes Froids (IFRAF) and from the PPF 'Information quantique' and 'Manipulation d'atomes froids par des lasers de puissance'. A. Fuhrmanek acknowledges partial support from the DAAD Doktorandenstipendium.