Anne-Laure Hemonnot-Girard

Audrey J Valverde

Jennifer Hua

Charlene Delaygue

Nathalie Linck

Tangui Maurice

François Rassendren

Helene Hirbec
email: helene.hirbec@igf.cnrs.fr

Analysis of CX3CR1 haplodeficiency in male and female APP swe /PSEN1 dE9 mice along Alzheimer disease progression

Keywords:

Microglia, the resident immune cells of the brain, have recently emerged as key players in Alzheimer Disease (AD) pathogenesis, but their roles in AD remain largely elusive and require further investigation. Microglia functions are readily altered when isolated from their brain environment, and microglia reporter mice thus represent valuable tools to study the contribution of these cells to neurodegenerative diseases such as AD. The CX3CR1 +/eGFP mice is one of the most popular microglia reporter mice, and has been used in numerous studies to investigate in vivo microglial functions, including in the context of AD research. However, until now, the impact of CX3CR1 haplodeficiency on the typical features of Alzheimer Disease has not been studied in depth.

To fill this gap, we generated APP swe /PSEN1 dE9 :CX3CR1 +/eGFP mice and analyzed these mice for Alzheimer's like pathology and neuroinflammation hallmarks. More specifically, using robust multifactorial statistical and multivariate analyses, we investigated the impact of CX3CR1 deficiency in both males and females, at three typical stages of the pathology progression: at early stage when Amyloid-β (Aβ) deposition just starts, at intermediate stage during Aβ accumulation phase and at more advanced stages when Aβ plaque number stabilizes. We found that CX3CR1 haplodeficiency had little impact on the progression of the pathology in the APP swe / PSEN1 dE9 model and demonstrated that the APP swe /PSEN1 dE9 :CX3CR1 +/eGFP line is a relevant and useful model to study the role of microglia in Alzheimer Disease. In addition, although Aβ plaques density is higher in females compared to age-matched males, we show that their glial reaction, inflammation status and memory deficits are not different.

Introduction

Alzheimer Disease (AD) is a progressive neurodegenerative disorder and the most common cause of dementia worldwide. It mainly affects the elderly, with a much higher prevalence among women [START_REF] Niu | Prevalence and incidence of Alzheimer's disease in Europe: A meta-analysis[END_REF]. The disease is characterized by different hallmarks including amyloid plaques, neurofibrillary tangles, neuroinflammation and, at advanced stages, brain atrophy [START_REF] Bedner | Astrocyte uncoupling as a cause of human temporal lobe epilepsy[END_REF]. Higher production and/or lower degradation of Amyloid-β (Aβ) fragments is thought to result in amyloid plaque formation, which represents one of the earliest and key events in AD pathogenesis. Transgenic mice harboring mutated human genes involved in the amyloid cascade provide valuable tools to study the disease progression [START_REF] Esquerda-Canals | Mouse models of Alzheimer's disease[END_REF]. Among these models, the APP swe /PSEN1 dE9 is one of the most popular as it recapitulates most of the important features of the disease [START_REF] Jankowsky | APP processing and amyloid deposition in mice haplo-insufficient for presenilin 1[END_REF]. It has been characterized at behavioral, histological and molecular levels in several studies (see https://www.alzforum.org/r esearch-models/appswepsen1de9-c57bl6), however none of them have evaluated the effect of sex on disease progression using these multiple approaches.

Long considered as a consequence of the pathology, reactive glia and associated neuroinflammation are now regarded as playing key roles in AD initiation and progression. Indeed, human genetic studies identified over 25 genetic loci that robustly associate with AD risk [START_REF] Hansen | Microglia in Alzheimer's disease[END_REF][START_REF] Verheijen | Understanding Alzheimer disease at the interface between genetics and transcriptomics[END_REF]. Among them, most genetic variants (Trem2, Ms4a genes, Picalm, etc.) code for proteins that are preferentially or exclusively expressed in microglia [START_REF] Bellenguez | Genetics of Alzheimer's disease: where we are, and where we are going[END_REF]. These findings strongly support a causal involvement of microglial cells in AD pathogenesis and generated a strong interest for studying these cells in AD [START_REF] Cuello | Early and late CNS inflammation in Alzheimer's disease: Two extremes of a continuum?[END_REF][START_REF] Fan | An early and late peak in microglial activation in Alzheimer's disease trajectory[END_REF][START_REF] Hampel | A path toward precision medicine for neuroinflammatory mechanisms in Alzheimer's disease[END_REF][START_REF] Nordengen | Glial activation and inflammation along the Alzheimer's disease continuum[END_REF]). Yet, the roles of microglia in AD initiation and progression are unclear and heavily debated, with conflicting reports regarding their detrimental or protective contribution to the disease (for review see [START_REF] Takatori | Genetic risk factors for Alzheimer disease: emerging roles of microglia in disease pathomechanisms[END_REF]. Microglia are very sensitive cells that rapidly change morphology and function in-vitro, prompting the development of microglial reporter mice to study microglia in their natural environment [START_REF] Gosselin | An environment-dependent transcriptional network specifies human microglia identity[END_REF].

CX3CR1 is a receptor for the chemokine Fractalkine/CX3CL1 whose expression is almost entirely restricted to myeloid cells. Heterozygous CX3CR1 +/eGFP mutant mice which harbor a green fluorescent protein (eGFP) in the cx3cr1 loci has become a valuable and widely used animal model to investigate microglial function [START_REF] Jung | Analysis of fractalkine receptor CX(3)CR1 function by targeted deletion and green fluorescent protein reporter gene insertion[END_REF]. In most studies CX3CR1 +/eGFP mice are used instead of WT and there are only few reports describing the impact of CX3CR1 haplodeficiency on the microglia functions or reactions [START_REF] Maggi | CX(3)CR1 deficiency alters hippocampal-dependent plasticity phenomena blunting the effects of enriched environment[END_REF][START_REF] Reshef | Microglia and their CX3CR1 signaling are involved in hippocampal-but not olfactory bulb-related memory and neurogenesis[END_REF][START_REF] Rogers | CX3CR1 deficiency leads to impairment of hippocampal cognitive function and synaptic plasticity[END_REF]. However, CX3CR1-Fractalkine interactions regulate microglia homeostatic functions and is involved in many brain functions, including hippocampal neurogenesis [START_REF] Reshef | Microglia and their CX3CR1 signaling are involved in hippocampal-but not olfactory bulb-related memory and neurogenesis[END_REF][START_REF] Sellner | Microglial CX3CR1 promotes adult neurogenesis by inhibiting Sirt 1/p65 signaling independent of CX3CL1[END_REF], synaptic maturation [START_REF] Arnoux | Fractalkine Signaling and microglia functions in the developing brain[END_REF], microglia chemotaxis [START_REF] Zhang | Role of fractalkine/CX3CR1 interaction in light-induced photoreceptor degeneration through regulating retinal microglial activation and migration[END_REF], or neuronal survival [START_REF] Zujovic | In vivo neutralization of endogenous brain fractalkine increases hippocampal TNFalpha and 8-isoprostane production induced by intracerebroventricular injection of LPS[END_REF]. CX3CR1 signaling in microglia also constitutes an important regulatory mechanism by which neuronally-derived CX3CL1 restrains microglia overactivation during various inflammatory conditions [START_REF] Wolf | Microglia, seen from the CX3CR1 angle[END_REF]. Conflicting consequences of CX3CR1 partial and complete deficiency on cognitive functions have been reported [START_REF] Maggi | CX(3)CR1 deficiency alters hippocampal-dependent plasticity phenomena blunting the effects of enriched environment[END_REF][START_REF] Reshef | Microglia and their CX3CR1 signaling are involved in hippocampal-but not olfactory bulb-related memory and neurogenesis[END_REF]. Unsurprisingly, CX3CR1 pathway is also altered in AD: fractalkine signaling is deficient in AD patient brains [START_REF] Cho | CX3CR1 protein signaling modulates microglial activation and protects against plaque-independent cognitive deficits in a mouse model of Alzheimer disease[END_REF] and the CX3CR1-V249I variant has been associated with a higher neurofibrillary pathology progression [START_REF] Lopez-Lopez | Association of the CX3CR1-V249I variant with neurofibrillary pathology progression in late-onset Alzheimer's disease[END_REF]. However, its exact role remains uncertain, as complete deletion of CX3CR1 has either neuroprotective or neurotoxic effects (for review [START_REF] Guedes | Roles of microglial and monocyte chemokines and their receptors in regulating Alzheimer's diseaseassociated amyloid-beta and tau pathologies[END_REF]. A few studies reported effects of CX3CR1 haplodeficiency on pathological features in AD mouse models but these studies were limited in terms of features and of co-factors evaluated [START_REF] Hickman | Heterozygous CX3CR1 deficiency in microglia restores neuronal beta-amyloid clearance pathways and slows progression of Alzheimer's like-disease in PS1-APP mice[END_REF][START_REF] Lee | CX3CR1 deficiency alters microglial activation and reduces beta-amyloid deposition in two Alzheimer's disease mouse models[END_REF][START_REF] Liu | CX3CR1 in microglia regulates brain amyloid deposition through selective protofibrillar amyloid-beta phagocytosis[END_REF].

By crossing the APP swe /PSEN1 dE9 (afterwards referred to as AD-C57) and CX3CR1 eGFP/eGFP lines, we generated the APP swe /PSEN1 dE9 : CX3CR1 +/eGFP line (afterwards referred to as AD-CX3) which represents a convenient model to study microglia during AD progression. Here, we validated this model by investigating in depth, whether CX3CR1 haplodeficiency has an impact on AD-like pathology progression. We analyzed the effects of this factor on cognitive behaviors, classic histological hallmarks of the disease (i.e. amyloid plaque burden, microgliosis and astrogliosis), as well as molecular changes (glial reaction and neuroinflammation). Impact of CX3CR1 partial deficiency may vary by stage of the disease or sex; the effects were thus evaluated in early, intermediate and advanced stages of the disease, in both males and females. Our findings confirmed that, compared to males, AD-C57 and AD-CX3 females display higher dense core plaques burden but we found that this is not associated with higher gliosis nor alteration of the neuroinflammation profile. Contrasting with the very recent study from [START_REF] Hickman | Heterozygous CX3CR1 deficiency in microglia restores neuronal beta-amyloid clearance pathways and slows progression of Alzheimer's like-disease in PS1-APP mice[END_REF], our findings indicate that CX3CR1 haplodeficiency has only limited impact on hallmarks of disease progression. Our analyses thus ascertain that APP swe /PSEN1 dE9 : CX3CR1 +/eGFP mice provide a relevant model to investigate the role of microglia in Alzheimer Disease initiation and progression.

Results

Sex but not CX3CR1 haplodeficiency affects learning performances in APP swe /PSEN1 dE9 mice

In AD-C57 mice, behavioral deficits emerge between 6 and 10 months of age and worsen with age [START_REF] Minkeviciene | Age-related decrease in stimulated glutamate release and vesicular glutamate transporters in APP/PS1 transgenic and wild-type mice[END_REF]. To measure the contribution of sex and CX3CR1 haplodeficiency in both AD and control (non-AD) mice on cognitive behavior, we assessed the visuospatial learning and memory in 12-months-old (mo) mice using the Morris water-maze test. Acquisition profiles were analyzed using a 4way linear mixed-effects model (LMM) with sex (Sex), CX3CR1haplodeficiency (CX3-hdf) and AD-status (AD) as between subjects' factors and training session (Session#) as within subjects repeatedmeasure factor. Regardless of the experimental group, all mice managed to learn the task (Session#: p < 0.001, LMM). Statistical analysis also revealed that after Session#, Sex was the factor that most affected the learning behavior (Sex: p < 0.05, LMM). Interestingly, sex seems to alter learning performances of controls but not AD mice (Figure-supp 2). Next analyses were thus performed separately on males and females using 3-way ANOVA (Fig. 1). In males, AD but not CX3-hdf has significant effects on the learning abilities with both AD-CX3 and AD-C57 mice showing learning deficits compared to their respective control littermates (Fig. 1C & 1E; AD: p < 0.01, LMM). There was also a significant contribution of the interaction between the 3 factors (i.e. Session#*CX3-hdf*AD: p < 0.01, LMM) indicating that learning deficits are not strictly identical in AD-C57 and AD-CX3 male mice. Indeed, in the two last training sessions AD-CX3 mice performed better than AD-C57 (Fig. 1G). In females, only the CX3-hdf slightly affected the learning skills (CX3-hdf: p < 0.05, LMM); post-hoc analysis further revealed that this effect is mainly due to slightly better performances of controls-CX3 mice compared to their C57 counterpart (Fig. 1B).

Retention was tested 48h after the last training session, by assessing mouse ability to remember the location of the hidden platform. Results were analyzed using a 3-way LM model with Sex, AD and CX3-hdf as fixed factors. As sex did not significantly contribute to the model (Sex: p = 0.683, 3-way LM-model), results from both males and females were consolidated and analyzed using a 2-way ANOVA (Fig. 2A). As expected, contrary to controls, both AD-C57 and AD-CX3 mice did not properly discriminate the training quadrant, and meandered randomly in the pool (Fig. 2A-B). Two-way ANOVA post hoc analyses revealed that AD-CX3 mice performed significantly worse than their respective controls. The same trend was observed for C57 mice but difference did not reach statistical significance. Overall statistical analysis revealed that CX3-hdf did not affect mice memory (CX3-hdf: p = 0.71, 2-way ANOVA).

Of note similar results for learning and memory were obtained in the Barnes Maze test, another visuo-spatial memory test (Figure -supp 3A-E). These results were not due to altered exploratory behavior in AD mice as, on the opposite, we observed slightly increased locomotor activity in AD mice compared to controls in the open-field test (Figure-supp 3F; AD: p < 0.05, 3-way ANOVA; no difference in post hoc tests).

Sex and CX3CR1 haplodeficiency affect amyloid plaque load in a stage-dependent manner

Alzheimer Disease is characterized by specific histological and immuno-histological hallmarks. The most prominent feature, and a key pathogenic event in AD, is the presence of Amyloid-β (Aβ) deposits. To determine if Sex, CX3-hdf or interaction between these two factors alter AD-like pathology progression in APP swe /PSEN1 dE9 mice, we assessed plaques burden in the cerebral cortex of 4-, 8-and 12-mo mice. Thiazine Red (TR) was used to quantify plaques area fractions (Fig. 3) and the plaques densities (Figure-supp 4) in all experimental groups. As expected, no significant TR staining was observed in control mice brains . In 4-mo AD-mice only very rare plaques were detected, but stage-dependent increase in the plaques area fraction and density was observed in all experimental groups (Fig. . Results from quantifications were analyzed separately in controls and AD mice. Three-way ANOVA confirmed the prominent importance of the Age factor for amyloid plaque load in AD-mice (Age: p < 0.001). Sex and Cx3-hdf did not affect the plaque load (p > 0.05 each), but there was a significant effect of the interaction between the three factors indicating that Sex and CX3-hdf affect plaque load differentially depending on the stage of the disease. In 4-mo mice, all AD mice presented the same plaque load. In contrast, 8-mo females displayed increased plaques load compared to males (Sex: p < 0.001; 2-way ANOVA on data in 8-mo mice), but, at this age, CX3-hdf factor did not alter this disease hallmark. Interestingly in these older mice, levels of soluble Aβ 1-40 and Aβ 1-42 was affected neither by sex nor CX3CR1 haplodeficiency (Figure-supp 4E) suggesting that higher plaques load in females is caused either by greater Aβ aggregation or increased Aβ production. In 12-mo mice, plaque load was affected by the interaction between Sex and CX3-hdf factors. It was increased in AD-CX3 male mice compared to their AD-C57 counterparts, while in females it was independent from CX3-hdf. Of note, we observed similar results for Sex or CX3-hdf effects in terms of disease progression over age, when measuring plaques densities (Figure-supp 4D).

Sex and CX3CR1 haplodeficiency have little impact on gliosis progression in APP swe /PSEN1 dE9 mice

Increased microgliosis and astrogliosis are other important hallmarks of AD. To determine if CX3CR1 haplodeficiency and sex had any effect on microgliosis, we investigated microglial reaction by measuring IBA1 positive area fraction in mice cerebral cortex. Results from quantifications were analyzed separately in controls and AD-mice using 3-way ANOVA. In control mice, IBA1 area fraction was similar in males and females, was independent of CX3-hdf and remains stable until the mice are aged 12 months (Fig. 4A-B). In AD mice, no significant microglia reaction was detected at the early stage (i.e., 4-mo animals). However, from 8 months, we observed stage-dependent increase of microgliosis, with the Age factor displaying very significant effects (Age: p < 0.001; 3-way ANOVA; Fig. 4C-D). On the opposite, neither Sex nor CX3-hdf significantly contributed to the observed variance. Statistical analysis revealed a significant but dim interaction between the Age and CX3-hdf factors (Age*CX3-hdf: p = 0.02; 3-way ANOVA; Fig. 4D), with slightly increased microgliosis in 12-mo APP/S1:CX3CR1 +/eGFP female mice compared to males.

In the cerebral cortex, homeostatic astrocytes express low levels of GFAP which remains almost undetectable by immunohistochemistry. Area fraction for this marker was used as a proxy to evaluate astrogliosis and to determine if age, sex or CX3CR1 haplodeficiency had any impact on astrocytes reaction. As for microgliosis, results from quantifications were analyzed separately in control and AD mice; 3-way ANOVA with Sex, CX3-hdf and Age as between subjects' factors were used. In control mice, GFAP immunoreactivity stayed globally stable across the ages. Statistical analysis revealed a dim effect of the interaction between the 3 factors (Age*Sex*CX3-hdf: p = 0.016; 3-way ANOVA) with slight decrease in GFAP positive fraction in 12-mo females C57BL6/J compared to males (Fig. 5B). However, the contribution of this interaction to the global variance was <10%. Compared to control mice, 4mo AD mice did not exhibit significant astrogliosis (Fig. 5D, analyses not shown). Increased astrogliosis was detected from intermediate stage (i.e., 8-mo mice) but stayed globally stable afterwards (Age: p < 0.001; 3-way ANOVA; Fig. 5D). Statistical analysis revealed that CX3-hdf had a significant (CX3-hdf: p = 0.018, 3-way ANOVA) but modest contribution (i.e., <5% of the global variance).

Sex and CX3CR1 haplodeficiency have little impact on the cortical neuroinflammation in APP swe /PSEN1 dE9 mice

Microgliosis and astrogliosis occur late in AD progression. However, recent studies support that microglia and possibly astroglia reactions can arise already in the early AD stages. To determine if sex or CX3CR1 haplodeficiency could impact on the transcriptome remodeling in the cerebral cortex of AD-mice, we measured genes expression for 20 genes known to be deregulated under neurodegenerative conditions and/or specifically in AD. The majority of these genes are microglia specific and/or deregulated in reactive microglia (Hexb,P2ry12,Ccl12,Ccl2,H2Aa,Cd68,Cd72,Cd86,Trem2,Tyrobp & Myd88). We also included few neuroinflammation associated genes (ApoE, Cxcl10, Il1b, Gfap & Tgfb), as well as genes involved in APP processing (Ctsd, Ide, Mme & Mmp9). Gene expression changes and effects of AD, Sex and CX3-hdf fixed factors were analyzed individually at the different stages of the pathology using 3-way ANOVA. Complete results of these analyses are presented in Fig. 6 and Table S3. In addition, to get a global picture of gene expression changes we also performed complementary multivariate analyses at the different stages of the pathology.

In 4-mo mice, only few of the tested genes were significantly dysregulated. The most relevant effects (i.e., p < 0.01 and contribution to global variance higher than 15%) were an increased expression of Cxcl10 in females but not males AD-mice and a decreased expression of Mme in controls CX3CR1 +/eGFP mice. Consistent with these results, neither Principal Component Analysis (PCA) nor Agglomerative Hierarchical Clustering (AHC) managed to cluster the samples according to any of the fixed factor (Fig. 7A-B). Linear Discriminant Analysis (LDA) is complementary approach to PCA which focuses on maximizing the separability among known groups. Although samples tended to separate according to Sex, LDA also failed to clearly segregate the samples. In LDA analyses, cross-validation is a necessary step to determine the performance of a given predictive model, generated on a learning dataset, on new datasets. Here, two-fold cross validation indicated low model's performance as only 25% of the samples were correctly classified. As a whole, qPCR results indicated that, at 4-mo, genes expression are not affected by neither pathology, sex nor CX3CR1 haplodeficiency.

In 8-mo mice, pathology had significant impact on the expression of 60% (12/20) of the genes tested (Table S3) while Sex and CX3-hdf had much lower impact. Indeed, the most relevant effects were a slight decreased expression of both Mme and Ide in CX3CR1 haplodeficient mice. Consistent with these results, both PCA and AHC clustered samples in two groups corresponding to controls and AD mice (Fig. 7C-D), but none of these two analyses further discriminated for Sex nor CX3hdf. PCA analysis revealed that leading genes for discriminating controls and AD samples are Tgfb, Ctsd, Trem2, Gfap, Cd68 and Tyrobp (Fig. 7E). At this age, LDA clearly segregated controls from AD samples on the first component and there was also a trend for discrimination according to CX3-hdf on the second component. However, with about 35% of the samples with correct classification two-fold cross validation indicated low performance for this model (data not shown).

As expected, in 12-mo mice, AD factor affected the expression of almost all the genes we tested (17/20; Table S3). In contrast, Sex and CX3-hdf had no or little significant impact on gene expression. Accordingly, PCA and AHC appropriately segregated AD-mice from controls (Fig. 7F-G), but did not distinguish further for Sex and CX3-hdf factors. PCA analysis indicated that leading genes for discriminating controls from AD samples are Cd68, Cd86, Cxcl10, Tyrobp, Gfap, Ctsd, Tgfb, Hexb and Ccl12 (Fig. 7H). Like PCA, LDA analysis segregated ADmice from controls on the first component. However, two-fold cross validation indicated that the model led to a poor correct classification of the samples (i.e 30%). Of note we observed that, both in PCA and LDA, males AD-C57 samples tended to segregate from male AD-CX3 on the second component (i.e. plain pink dots versus plain green dots in Fig. 7F). However, the variance explained by the second component only represented 12.6% of the total variance and no specific gene could be associated with this discrimination.

As a whole, our qPCR analysis revealed that in early stage of the disease AD-like pathology, sex and CX3CR1 haplodeficiency have little impact on microglia reaction, neuroinflammation and pathways known to be altered in Alzheimer Disease. At more advanced stages, AD-like pathology leads to increased microglial response and neuroinflammation, but sex and CX3CR1 haplodeficiency have only very limited impact on this pathology driven features.

Complex impact of CX3CR1 haplodeficiency, age and AD-like pathology on the expression of Aβ degrading enzymes in APP swe /PSEN1 dE9 mice

Brain Aβ levels are partly regulated by Aβ degrading enzymes, including Insulin Degrading Enzyme (IDE or Insulysin), Neprilysin (MME) and Metalloproteinase-9 (MMP9). Progression of AD has been associated with reduced expression of theses enzymes in microglia resulting in decreased Aβ degradation and increased accumulation of the Aβ peptide [START_REF] Hickman | Microglial dysfunction and defective beta-amyloid clearance pathways in aging Alzheimer's disease mice[END_REF][START_REF] Miller | Amyloid-beta peptide levels in brain are inversely correlated with insulysin activity levels in vivo[END_REF]. Recently, Hickman et al. [START_REF] Hickman | Heterozygous CX3CR1 deficiency in microglia restores neuronal beta-amyloid clearance pathways and slows progression of Alzheimer's like-disease in PS1-APP mice[END_REF] reported higher expression of Ide and Mmp9, but not Mme in the brains of APP swe /PSEN1 dE9 :CX3CR1 +/eGFP mice compared to that of APP swe /PSEN1 dE9 . We thus measured cortical RNA levels of the three enzymes and assessed the impact of the AD, Sex and CX3-hdf factors. In contrast to Hickman's study and regardless of the mice age, we did not measure any significant reduction in Ide and Mmp9 expression in the cortices of the AD-mice (Fig. 8A-F; Table S3). Our analysis also revealed that Sex did not impact significantly the expression levels of these two enzymes. However, in both 8-and 12-mo mice, we detected a decreased expression of Ide in CX3CR1 haplodeficient mice (Table S3; Fig. 8B-C).

Our results also indicated, in contrast to Hickman's results, a Sex and CX3-hdf independent decreased expression of Mme in 12-mo AD-mice (Table S3). Additionally, in 4-mo mice we measured higher Mme expression in controls CX3CR1 +/eGFP mice compared to either C57 controls and AD-CX3CR1 +/eGFP mice (Fig. 8G), while in 8-mo mice, CX3CR1 haplodeficiency led to AD independent Mme decreased expression. It should be noted that, although statistically significant, Mme's expression varies at max by 30%. As a whole, these results suggest complex and tight CX3CR1, age and pathology dependent (but Sex independent) control of the expression of Aβ degrading enzymes in the brains of AD-57 mice.

Discussion

Numerous reports highlighted the importance of neuroinflammation in AD pathophysiology [START_REF] Heneka | Innate immunity in Alzheimer's disease[END_REF], and recent GWAS and clinical imaging studies revealed its upstream role in the disease pathogenesis [START_REF] Hampel | A path toward precision medicine for neuroinflammatory mechanisms in Alzheimer's disease[END_REF]. Microglia are the main immune cells in the brain. They play a key role in the immune surveillance of the brain parenchyma and initiate the inflammatory response when brain homeostasis is impaired, as it is the case when protein aggregates are formed. In AD, microglia are involved in both Aβ pathogenesis and in Tau pathology spreading (van der Kant et al., 2020) and thus represent an interesting therapeutic target. CX3CR1 +/eGFP reporter mice provide useful tools to study microglia while preserving their in vivo physiological and pathophysiological functions. However, an important prerequisite to the use of this model is to demonstrate its relevance compared to the unaltered model. Here we provide a comprehensive study based on the assessment of multiple AD features (learning ability, histological hallmarks and neuroinflammation status), for both sexes AD is a progressive neurodegenerative disease that develops over years in humans and months in AD-mouse models. Recent data suggest that neuroinflammation, and microglia reaction in particular, occurs in two phases: an early phase, which initiates before cognitive deficits and is thought to have beneficial effects on the disease outcomes; and a second phase that contributes to increased neuroinflammation and neurotoxicity [START_REF] Cuello | Early and late CNS inflammation in Alzheimer's disease: Two extremes of a continuum?[END_REF][START_REF] Fan | An early and late peak in microglial activation in Alzheimer's disease trajectory[END_REF]. To our knowledge, our study is the first to present a thorough overview of the disease progression in APP swe /PSEN1 dE9 mice (1) over different histological and molecular AD hallmarks, (2) in both sexes and (3) across three stages of the pathology. As attested by the absence of significant microgliosis, astrogliosis and change in the gene expression of a large range of inflammation related genes, our results demonstrate that in AD early stages, when plaques barely form, brain inflammation status is overall not different from that of control mice. As AD mice get older, hallmarks of the disease worsen: plaques burden increases in an age-dependent manner as do microgliosis and astrogliosis. Accordingly, we show an age-dependent increase of pro-inflammatory profiles in AD mice. This increase corresponds to both greater number of deregulated genes and stronger gene deregulation.

Sex effect in AD is well documented: prevalence is twice as high among women and higher longevity is not the only explanation [START_REF] Hebert | Alzheimer disease in the United States (2010-2050) estimated using the 2010 census[END_REF][START_REF] Vina | Why women have more Alzheimer's disease than men: gender and mitochondrial toxicity of amyloid-beta peptide[END_REF]. However, most AD pre-clinical studies use either males or females, but rarely both. In APP swe / PSEN1 dE9 , influence of sexual dimorphism was investigated in a handful of studies but they were mainly limited to mice at advanced stage of the disease (i.e., 12-mo or higher) and mainly focused on Aβ load [START_REF] Gallagher | Impaired performance of female APP/PS1 mice in the Morris water maze is coupled with increased Abeta accumulation and microglial activation[END_REF][START_REF] Janus | Behavioral abnormalities in APPSwe/PS1dE9 mouse model of AD-like pathology: comparative analysis across multiple behavioral domains[END_REF][START_REF] Jiao | Sex dimorphism profile of Alzheimer's disease-type pathologies in an APP/PS1 mouse model[END_REF][START_REF] Wang | Gender differences in the amount and deposition of amyloidbeta in APPswe and PS1 double transgenic mice[END_REF][START_REF] Zhou | Sex differences in the white matter and myelinated fibers of APP/PS1 mice and the effects of running exercise on the sex differences of AD mice[END_REF]. In parallel, a growing number of studies highlights the impact of sexual dimorphism on microglia functions [START_REF] Bordeleau | Microglia along sex lines: From brain colonization, maturation and function, to implication in neurodevelopmental disorders[END_REF]. In agreement with previous studies [START_REF] Gallagher | Impaired performance of female APP/PS1 mice in the Morris water maze is coupled with increased Abeta accumulation and microglial activation[END_REF][START_REF] Jiao | Sex dimorphism profile of Alzheimer's disease-type pathologies in an APP/PS1 mouse model[END_REF][START_REF] Wang | Gender differences in the amount and deposition of amyloidbeta in APPswe and PS1 double transgenic mice[END_REF], we confirmed that compared to males, female APP swe /PSEN1 dE9 mice display greater plaques burden at both intermediate and advanced age but equal levels of soluble levels of Aβ 1-42 and Aβ 1-40 . However, in contrast to Jiao et al. [START_REF] Jiao | Sex dimorphism profile of Alzheimer's disease-type pathologies in an APP/PS1 mouse model[END_REF], we found that higher plaques burden was not associated with increased gliosis. The weak effect of sex on the brain inflammatory status was confirmed by our transcriptomic analysis of a substantial number of inflammation related genes. Indeed, sex only affected the gene expression of a few genes, namely Tyrobp in 8-and 12-mo; Cd86 in 8-mo and Cd16 in 12-mo mice, and even for these few genes, impact on the global variance was weak (i.e., <10%). Additionally, the different multivariate analyses of our qPCR data failed to segregate males from females. Together, our results on plaques burden, soluble Aβ and neuroinflammation suggest that brain inflammatory status better correlates with soluble rather than aggregated Aβ concentration. This is consistent with data from the literature suggesting that non fibrillar soluble Aβ oligomers are more noxious than plaques aggregated Aβ fibrils [START_REF] He | Self-assembly of Abeta-based peptide amphiphiles with double hydrophobic chains[END_REF]. Effects of sex on learning impairment in APP swe /PSEN1 dE9 mice have not been well documented and most studies either focused on one sex or males and females pooled in the same experimental groups [START_REF] Janus | Behavioral abnormalities in APPSwe/PS1dE9 mouse model of AD-like pathology: comparative analysis across multiple behavioral domains[END_REF]. The most relevant study showed small deficits for 8/9-mo females APP swe /PSEN1 dE9 in the Morris Water Maze reversal learning test [START_REF] Gallagher | Impaired performance of female APP/PS1 mice in the Morris water maze is coupled with increased Abeta accumulation and microglial activation[END_REF], but no deficit in the training phase. Here we show that although both male and female quickly learned the task, learning abilities vary between males and females, with females showing a slower learning curve. Yet, we reveal spatial learning impairment in male but not female 12-mo AD-C57 mice. As for memory processes, they were not different in male and female controls and were similarly impaired in AD-C57 mice of both sexes. Overall, our data confirm the impact of the sex on the plaque load, but the lack of correlation between higher cortical Aβ deposition and neuroinflammation or behavioral deficits suggest that plaques load should not be used as a single marker to assess AD progression. Importantly, our study highlights the need to study progression of AD-like pathology in males and Fig. 6. Variation in the expression of selected genes across AD-like pathology. Heatmap showing expression fold-changes of selected genes. Genes were chosen from previous studies because they are (1) microglia specific and/or deregulated in reactive microglia (Hexb,P2ry12,Ccl12,Ccl2,H2Aa,Cd68,Cd72,Cd86,Trem2,Tyrobp & Myd88) [START_REF] Hirbec | The microglial reaction signature revealed by RNAseq from individual mice[END_REF][START_REF] Keren-Shaul | A unique microglia type associated with restricting development of Alzheimer's disease[END_REF]; (2) We also included few neuroinflammation associated genes (ApoE, Cxcl10, Il1b, Gfap & Tgfb) [START_REF] Orre | Isolation of glia from Alzheimer's mice reveals inflammation and dysfunction[END_REF], as well as genes involved in APP processing (Ctsd, Ide, Mme & Mmp9) [START_REF] Hickman | Heterozygous CX3CR1 deficiency in microglia restores neuronal beta-amyloid clearance pathways and slows progression of Alzheimer's like-disease in PS1-APP mice[END_REF]. Statistical analyses: 3-way ANOVA FDR corrected post-hoc tests;*significant pvalue compared to respective control. Fig. 7. Gene expression changes in the mice cortical homogenates for a range of inflammation and AD-related gens: Changes in gene expression were measured by qPCR in whole cortex, -ΔCq were calculated. Multivariate analyses were performed on -ΔCq. Gene expression is not significantly altered by sex, CX3CR1 haplodeficiency nor pathology in the early stage (A-B). In intermediate (C-E) and advanced (F-H) stages of the disease AD mice segregate from controls, but sex and CX3CR1 haplodeficiency does foster further segregation. In PCA, correlation circles allow identifying the most relevant variables for the separation of the observations on the different component/axes. Indeed, length of the vector, and closeness to the circle and the axe allows identifying the most relevant genes. In the present study, they (E-H) highlight the leading genes for segregation of AD versus control mice. Complete statistical results are given in Table S3. Included in these analyses are: Microglia related genes (Hexb,P2ry12,Ccl12,Ccl2,H2Aa (except in 4mo),Cd68,Cd72,Cd86,Trem2,Tyrobp & Myd88), neuroinflammation associated genes (ApoE, Cxcl10, Il1b, Gfap & Tgfb), and APP processing related genes (Ctsd, Ide, Mme & Mmp9). females separately, using appropriate controls. The reason for higher plaque loads in female AD mice is currently unknown. Our qPCR analyses were limited to 20 genes and did not reveal any sex-difference in gene expression of Aβ degrading enzymes. Whether Aβ aggregation processes are increased in females, and whether microglia are involved in these processes remains to be explored. High-content approaches, such as RNA-seq, could be helpful in obtaining this information.

Our ultimate goal was to determine whether the APP swe /PSEN1 dE9 : CX3CR1 +/eGFP mouse line could represent a relevant AD mouse model. To this purpose, we analyzed the impact of CX3CR1 haplodeficiency on AD progression. In AD mouse models, deletion of CX3CR1 had contrasting effects in different models: it reduced Aβ deposition, enhanced microglial Aβ phagocytosis and altered the neuroinflammation milieu in the APPPS1, R1.40 and CRND8 models [START_REF] Lee | CX3CR1 deficiency alters microglial activation and reduces beta-amyloid deposition in two Alzheimer's disease mouse models[END_REF][START_REF] Liu | CX3CR1 in microglia regulates brain amyloid deposition through selective protofibrillar amyloid-beta phagocytosis[END_REF], whereas in the hAPPJ20 and in the hTau models, it worsened the pathology by either increasing cytokine production (hAPPJ20; [START_REF] Cho | CX3CR1 protein signaling modulates microglial activation and protects against plaque-independent cognitive deficits in a mouse model of Alzheimer disease[END_REF] or Tau phosphorylation and aggregation (hTau, [START_REF] Bhaskar | Tyrosine phosphorylation of tau accompanies disease progression in transgenic mouse models of tauopathy[END_REF], and by exacerbating the behavioral deficits. Several AD mouse models have been crossed with the CX3CR1 eGFP/eGFP line to investigate microglial functions in the context of AD [START_REF] Baik | Microglia contributes to plaque growth by cell death due to uptake of amyloid beta in the brain of Alzheimer's disease mouse model[END_REF][START_REF] Gyoneva | Altered motility of plaque-associated microglia in a model of Alzheimer's disease[END_REF][START_REF] Koenigsknecht-Talboo | Rapid microglial response around amyloid pathology after systemic anti-Abeta antibody administration in PDAPP mice[END_REF]. However, only very few of these studies investigated the impact of haplodeficiency on the AD-like pathology progression [START_REF] Hickman | Heterozygous CX3CR1 deficiency in microglia restores neuronal beta-amyloid clearance pathways and slows progression of Alzheimer's like-disease in PS1-APP mice[END_REF][START_REF] Lee | CX3CR1 deficiency alters microglial activation and reduces beta-amyloid deposition in two Alzheimer's disease mouse models[END_REF], and none explored its impact according to sex: Hickman's study focused on males, whereas in Lee's work the sex of the mice is not reported. At advanced disease stage, both studies described lower Aβ deposition in CX3CR1 haplodeficient mice, but results in terms of microgliosis, neuroinflammation and APP processing differs between the two studies. In agreement with Hickman et al. [START_REF] Hickman | Heterozygous CX3CR1 deficiency in microglia restores neuronal beta-amyloid clearance pathways and slows progression of Alzheimer's like-disease in PS1-APP mice[END_REF], our learning and memory test analyses revealed slightly improved performance in 12-mo haplodeficient AD males compared to the AD-C57, with escape latencies similar to that of WT and CX3CR1 +/ eGFP mice in the two last training session. However, careful examination of the learning kinetics showed impairment for AD-CX3 in males compared to the appropriate controls. In our study, the slightly better cognitive performances of male AD-CX3 compared to males AD-C57 were associated with increase rather than decrease in plaques load and plaques densities. We also did not find any change in the expression of Insulin Degrading Enzyme (Ide) and Metalloproteinase-9 (Mmp9) genes in whole homogenates in either the AD versus controls, or CX3CR1 +/+ versus CX3CR1 +/eGFP comparisons. Finally, we agree that CX3CR1 haplodeficiency does not affect microgliosis. The basis for the S3.

contradictory results between our study and that of Hickman is not clear as the AD mouse models are similar (i.e. APP swe /PSEN1 dE9 on C57BL6/J background). However, stages at which some of the analyses were performed (i.e. Ide, Mme, and Mmp9 expression) may partly explain some of the differences observed. In addition, microglia are very sensible to their environment, and change in microbiota for example has been shown affect microglial transcriptome [START_REF] Erny | Communicating systems in the body: how microbiota and microglia cooperate[END_REF][START_REF] Thion | Microbiome Influences prenatal and adult microglia in a sex-specific manner[END_REF]. Thus, it is possible that some difference in environmental parameters between the two labs could explain at least some of the observed discrepancies. Although individual gene expressions were modestly affected by CX3CR1 haplodeficiency in 12-mo male AD mice, multivariate analyses revealed a tendency towards segregation of males AD mice as a result of their CX3CR1 haplodeficiency. This suggested that, in older males, partial CX3CR1 deficiency may have a subtle impact on the pathology. Although it does not lead to higher plaques load, nor increased soluble Aβ concentration, astrogliosis or microgliosis, this interaction between sex and CX3CR1 haplodeficiency in 12-mo males AD mice correlates with higher expression of the hAPP swe and hPS1 dE9 transgenes in the males C57-AD mice. Importantly, in the younger mice of both sexes and in 12-mo females, our study demonstrates that CX3CR1 haplodeficiency do not significantly affect plaques load, neuroinflammation or APP processing in the APP swe /PSEN1 dE9 model.

In summary, our study provides a comprehensive overview of the effect of the loss of one copy of the Cx3cr1 gene on disease progression in the popular APP swe /PSEN1 dE9 mouse model in both males and females. It reveals that, under our experimental conditions, CX3CR1 haplodeficiency does not significantly affect the evolution of the main hallmarks of the disease at early and intermediate stage of the pathology. The same is true at later stages in females. Overall, it demonstrates that the APP swe /PSEN1 dE9 :CX3CR1 +/eGFP line is a relevant and useful model to study the role of microglia in Alzheimer Disease. In addition, our study provides useful comparison of the disease progression between males and females.

Methods

Animals

The APP swe /PSEN1 dE9 mice used in this study co-express two genetic mutations associated with familial AD: a humanized amyloid precursor protein carrying the swedish mutation (APP swe ) and a mutant exon-9deleted variant of the presinilin1(PS1 dE9 ). The APP and PSEN transgenes are integrated into a single locus and are expressed under the prion promotor [START_REF] Jankowsky | APP processing and amyloid deposition in mice haplo-insufficient for presenilin 1[END_REF][START_REF] Jankowsky | Co-expression of multiple transgenes in mouse CNS: a comparison of strategies[END_REF]. These mice, thereafter referred to as APP swe /PSEN1 dE9 , were purchased from the Jackson Laboratories and subsequently bred in the SPF animal facility of the Institute for Functional Genomic (IGF, Montpellier, France; Agreement from the Ministry of Agriculture N • D34-172-13) to a C57BL6/J background. CX3CR1 eGFP/eGFP mice were generous gift from Dan Littman [START_REF] Jung | Analysis of fractalkine receptor CX(3)CR1 function by targeted deletion and green fluorescent protein reporter gene insertion[END_REF] and are also maintained in the IGF facility under the C57BL6/J background.

To generate the genotypes used in this study, heterozygous APP swe / PSEN1 dE9 male mice were crossed either with females C57BL6/J (purchased at Janvier Laboratories, France) or females CX 3 CR 1 eGFP/eGFP , to obtain respectively APP swe /PSEN1 dE9 :CX3CR1 +/+ and APP swe / PSEN1 dE9 :CX3CR1 +/eGFP mice, and their respective control littermates (i.e. C57BL6/J and CX3CR1 +/eGFP ). For the sake of simplification, the different genotypes are referred to in the text and the figures as follows: C57/purple (C57BL6/J); CX3/Dark green (CX3CR1 +/eGFP ), C57-AD/ pink (APP swe /PSEN1 dE9 :CX3CR1 +/+ ) and CX3-AD/light green (APP swe /PSEN1 dE9 :CX3CR1 +/eGFP ). C57 & CX3 are referred to as controls, and C57-AD & CX3-AD as AD-mice. Mice were housed in a 12 h light-dark schedule with food and water ad libitum. All experiments followed European Union (Council directive 86/609EEC) and institutional guidelines for the care and use of laboratory animals. The animal experiment protocols used in this study were approved by the Comité d'Ethique pour l'Expérimentation Animale Languedoc Roussillon (CEEA-LR; APAFiS#5252). Experiments were performed in 4-, 8-and 12-months-old (mo) animals. Males and females were used in parallel experiments. The experimenters were blind to group assignment.

The stability of expression of the endogenous mApp and mPs1 genes and of the hAPP swe and hPS1 dE9 transgenes was tested for Age, Sex and CX3-haplodeficiency (Cx3cr1-hdf). Supplementary Fig. 1 shows that the expression of the endogenous App and Ps1 transcripts is not affected by any of the factors. In 12-mo animals, statistical analyses revealed significant but small effects for some factors and interactions (i.e. representing <10% of the global variance). These were considered to be biologically irrelevant. Transgene expression was not affected by any of the factors in 4-mo animals, but 8-mo CX3-AD mice show slightly higher expression of hAPP swe (Cx3-hdf: p < 0.01; 2-ways ANOVA; Fold Change (FC) = 1.25). On the contrary, in the oldest animals, expression of the transgenes was significantly higher in males, but not females, C57-AD mice (hAPP swe : p < 0.01 post-hoc multiple comparisons, FC = 1.81; hPs1 dE9 :, p < 0.01 post-hoc multiple comparisons, FC = 1.44). In CX3CR1 +/eGFP mice, the expression of GFP is under the control of the Cx3cr1 promotor. In both 8-and 12-mo CX3-AD mice, the expression of the Gfp transcript was increased compared to the controls but this effect is probably due to the microgliosis observed at these ages.

Behavioral studies: Morris Water Maze

The Morris Water Maze allows testing long-term spatial memory. The mice were tested in a 140 cm diameter 40 cm height circular maze containing water at 20 ± 1 • C, opacified with lime carbonate. The light was adjusted to a non-aversive intensity of 80 lx. Fixed visual cues are displayed on distant walls around the maze for mice orientation. The protocol consisted of 6 days of learning during which mice had to locate and climb on an immerged platform always placed in the same quadrant, referred to as the training quadrant. For each trial mice started facing the wall from a randomly determined quadrant and were allowed to swim for 90 s. If the mice didn't reach the platform within the 90 s, they were gently placed on it for 20 s. Each mouse was given three trials per day with an inter-trial interval of 10 min. The escape time was calculated as the median latency of the three trials. The training phase was followed by a single probe test ("Retention test") performed 48 h after the last learning session, in the course of which the platform was removed. For the probe test, each mouse was allowed to swim once for 60 s. The trajectories were analyzed using videotracking (ViewPoint, Lissieu, France) and the time spent in each quadrant calculated. Mice failing to reach the platform at least once during the training sessions, whatever the experimental group, were discarded from the calculations. 10 mice over 78 were discarded accordingly (attrition 13%). Behavioral experiments were performed on 12-mo animals only. At least 5 mice were analyzed in each experimental condition, the numbers of mice are given in Table S1.

Tissue collection, preparation and staining

After induction of deep anesthesia with 2 µg/g pentobarbital (Euthasol Vet, TVM), the mice were perfused intracardially with 15 ml of phosphate buffer saline (PBS). For gene expression studies, the cortex was dissected, immediately frozen, and stored at -80 • C until use. For histological studies, the brains were fixed with 4% paraformaldehyde (PFA, Sigma Aldrich, P6148) for 2 h at room temperature (RT) and then overnight at 4 • C in fresh 4% PFA. Fixed brains were stored at 4 • C in PBS containing 0.1% Sodium Azide until they were cut into 40 µm sections using a Vibratome (Microm Microtec, Brignais, France).

Thiazine Red Staining for Aβ plaques detection: Thiazine red (TR) is an analog of naphthol-based azo structures which binds β-pleated sheet structures. Like Thioflavin-S, it stains dense core plaques but with maximum emission at 580 nm [START_REF] Luna-Munoz | Thiazin red as a neuropathological tool for the rapid diagnosis of Alzheimer's disease in tissue imprints[END_REF]. Vibratome floating sections were briefly washed with PBS and incubated for 5 min at RT with 16 mg/L Thiazine Red (TR; Sigma Aldrich, S570435) in PBS. After a final rinsing session, sections were then mounted using Dako Fluorescent Mounting Medium (Dako, S3023) and stored at 4 • C until imaging.

Immunohistochemistry: Vibratome floating sections were incubated overnight at 4 • C with the appropriate primary antibodies: Rabbit-IBA1 (1:2000, Wako, MNK4428) or Rabbit-GFAP (1:500, Sigma Aldrich, G3893) diluted in 2% BSA, 0.1% Triton X-100, PBS Solution. Sections were then rinsed 3 times with PBS and incubated for 2 h at RT with Goat anti-Rabbit Cy3 secondary antibody (1:500, Jackson, 111-165-144). After a final rinsing session, sections were then mounted using Dako Fluorescent Mounting Medium (Dako, S3023) and stored at 4 • C until imaging.

Images acquisition, sampling and quantification

Slides were viewed using a classical epifluorescence microscope and images were acquired using an Imager Z1 microscope (Zeiss) equipped with an AxioCam MR R3 camera. Depending on the staining, 10X/ 0.3M27 Zeiss Plan-Neofluar (Thiazin-red) or 20X/0.50 M27 Zeiss Plan-Neofluar (IBA1 and GFAP staining) air objectives were used. The experimenters were blind to group assignment.

Amyloid plaque load quantification: For amyloid plaque detection, exposure time was maintained the same for all the acquisitions (ie: Cy3 30 ms). Images were acquired in mosaic mode at 10X magnification to visualize both cortical and hippocampal regions. Brain regions were delimited under CFP fluorescence, and the number of TzR positive deposits and the TzR positive area were quantified in the cortex and the hippocampus using a custom ImageJ macro. For the size of the particle, a threshold was set to skip particles smaller than 25 µm. The plaques were counted if they had a circularity between 0.2 and 1. 6 slices per animal were analyzed. At least 4 mice were analyzed in each experimental condition, the numbers of mice are given in Table S1.

Microglial and Astrocyte quantification: For analysis of IBA1 staining, for each field, 11 images (corresponding to 10 µm-thick optical sections) were acquired. For analysis of GFAP staining, for each field, 5 images (corresponding to 4 µm-thick optical sections) were acquired. In both cases, the exposure time was maintained constant (IBA1, 80 ms and GFAP, 30 ms). Stacked images were projected on the Z-axis and analyzed using a custom ImageJ macro to determine the percentage of immunopositive surface. For each animal, quantifications were performed in 4-5 randomly selected fields per section and 5 sections per animal. At least 4 mice were analyzed in each experimental condition, the numbers of mice are given in Table S1.

Gene expression studies

RNA from cortices were extracted using the Qiagen RNeasy Plus Mini kit (Qiagen, #74136) following manufacturer protocol. The quality of the total RNA was checked using the Agilent 2100 Bioanalyzer (Agilent). All RNAs had RNA Integrity Numbers (RINs) higher than 8.0. Reverse transcription of 500 ng total RNA were performed using the iScript kit (BioRad). Real-time PCR was performed in 384-well plates in a final volume of 10 µl using SYBR Green dye detection on the LightCycler480 system (Roche-Diagnostic). The primers pairs were designed using Primer 3 software. Lists of genes analyzed and primers sequences are given in Table S2. All analyzed genes showed detectable expression levels. Hptr1 was selected as normalizing gene and we verified at each run that it is indeed expressed at similar levels in all groups. The results were expressed as Cq and normalized to the Cq value of the Hptr1 (-ΔCq). At least 5 mice were analyzed in each experimental condition, the numbers of mice are given in Table S1.

Statistics

In the present study, we considered that only strong and medium effect sizes would be biologically relevant, i.e. only for strong and medium effect sizes, it would be possible to confer the factors or their interactions an impact on the characteristics of the disease. As a result, our experiments were designed to detect at least medium effect size of the different factors and/or their interactions. Thus, sample size was determined for an effect size of 0.4 and an expected power of 80%. Posthoc analyses revealed that for factors and interactions with p-values comprised between 0.05 and 0.1, the actual effect size were <0.3, thus validating our conclusions regarding the lack of effect of any factor/ interaction.

All data are presented as mean ± standard error of the mean (SEM). They were analyzed using General Linear Model procedures and were subjected to two-, three-or four-way ANOVA to determine significant main effects and interactions. Softwares used for statistical analysis were R (four-way ANOVA) or GraphPad Prism (8.4) (two-and three-way ANOVA). Post-hoc analyses for multiple comparisons were performed with Benjamini, Krieger & Yekutieli False Discovery Rate (FDR) corrections. In the Morris Water Maze probe test, time spent in the training quadrant was compared to the theoretical value of 25% using the Wilcoxon signed ranked test.

In gene expression studies, Principal Component Analysis (PCA), Agglomerative Hierarchical Clustering (AHC) and Linear Discriminant Analysis (LDA) multivariate analyses were performed using dedicated R packages. Missing data represented <10% of the datasets, for analyses they were imputed using the R missMDA package. P-values smaller than 0.05 were considered significant.

Supplementary procedures

Behavioral analyses

Open-field: Mice were tested in a white arena (50 × 50 cm 2 and 45 cm height). The light was adjusted to a non-aversive intensity of 80 lx. The test consists of a single 10 min trial in which the mouse freely explores the environment. Analysis of trajectories was performed using the Vid-eotrack® software (ViewPoint, Lissieu, France).

Barnes Maze: This test was used to assess spatial memory in a low stressful environment. The maze consists of a 120 cm elevated white flat circular platform (1 m of diameter) with 20 circular holes (50 mm of diameter) located equidistantly at the periphery of the platform. A hidden box located under one target hole allows the mice to escape from the platform. Fixed visual cues are displayed on distant walls around the maze for orientation. To motivate the mice finding the escape hole we used an aversive light stimulus of 370 lx and turned off the light as a reward. For each trial the mice were placed for 10 s in an opaque start box located in the center of the platform. To reduce mice stress, we performed a familiarization task 24 h prior to the first learning day. For the familiarization, after released from the start box, the mice were allowed to explore the maze once for 60 s and then gently placed in the hidden cage for 120 s with the reward. For the training trial, each mouse performed 4 trials per day with an inter trial interval of 15 min for 4 consecutive days. For each trial, after release from the start box, the mice were let to explore the maze for maximum 180 s. Trial was stopped when the mouse's four paws were in the target hole or when the maximum duration of the trial was reached. Mice that did not find the escape box within the 180 s were gently picked up and moved to the target hole, into the escape box. Mice were left in the escape box with the lights off for 60 s before being returned to their home cage. 72 h after the fourth training session we performed the retention test where the hidden cage was removed. We let the mice explore the maze once for 90 s and then returned to their home cage. The platform surface and holes were carefully cleaned with 20% ethanol solution and distilled water between each trial to remove any olfactory cues. All trials were recorded with an automated videotracking software (Ethovision® XT13, Noldus). Primary error (number of wrong pokes before poking the target hole), primary latency (time before poking the target hole), training latency (time before entering the hidden cage) and time spent in the target quadrant were measured.

Quantification of Aβ1-42 and Aβ1-40

ELISA were performed only in 8-mo mice. All the steps were performed in LoBind tubes to limit loss of amyloid peptides. Homogenization Buffer (HB) was 50 mM Tris-HCl (sigma, T2788), 1X Protease Inhibitor (ThermoFisher, A32961), 150 mM NaCl (Sigma, S5886), 1% Triton X-100 (Sigma, 066 K0089), pH 7.4. Cortex were weighted and the ratio tissue/ HB adjusted to 2.5 µg/ml. Samples were sonicated (7 pulses, 40% amplitude) in HB then centrifuged at 17,500 g, 4 • C for 20 min. Protein concentration in the supernatant (soluble fraction) was determined using BCA technique, and adjusted to 0.2 µg/µl using MSD Diluent 35. For Aβ species detection, the MSD multiplex Aβ 6E10 kit (MSD, K15200E) protocol was followed. Briefly, wells were incubated with Diluent 35 at RT for 1 h under agitation, then rinsed 3 times with 0.05% Tween-20 containing PBS (Washing Solution, WS). In each well, the Detection Solution (2% 6E10, 1% Aβ 1-40 blocker in Diluent 100) was added, followed by the samples. After 2 h incubation at RT under agitation, the wells were rinsed 3 times with the WS. Finally, 2X Read Buffer T was added and the plate was read on a MESO QuickPlex SQ 120 plate reader.

Fig. 1 .

 1 Fig. 1. In 12-mo mice, learning in the Morris Water Maze task is impacted by AD and to a much lesser extend by CX3CR1 haplodeficiency. Color code for the mouse genotypes are: C57BL6/J (C57; purple), APP/PS1:CX3CR1 +/+ (C57-AD; pink), CX3CR1 +/eGFP (CX3; dark green) and APP/PS1:CX3CR1 +/eGFP (CX3-AD; light green); plain and empty dots are for males and females respectively. Statistical analyses in males: 3-way ANOVA with AD, CX3-hdf as between subjects' factors and Session# as within subjects, repeated measures factor; Session#: p < 0.001; AD: p < 0.01; Statistical analyses in females: 3-way ANOVA with AD, CX3-hdf as between subjects' factors and Session# as within subjects, repeated measures factor factor; Session#: p < 0.001; CX3-hdf: p < 0.05. FDR corrected post-hoc tests; time point comparison: * p < 0.05, ** p < 0.01. Data are Mean ± SEM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .

 2 Fig. 2. 12-mo AD mice from both C57 and CX3 lines display memory deficit in the Morris Water Maze retention task. (A) Contrary to C57-AD (pink, n = 10) and CX3-AD (light green, n = 14), C57 (purple, n = 21) and CX3 (dark green, n = 23) control mice properly discriminate the learning quadrant. Data are Mean ± SEM. Statistical analyses for memory performance: Wilcoxon t-test: *** p < 0.001 compared to 25% theoretical value; Inter-group comparison: Two-way ANOVA with FDR corrected post-hoc tests: # p < 0.05. (B) Representative mice tracks during the retention task. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. Amyloid plaques load increase during AD progression: Sex and CX3CR1 haplodeficiency impact Aβ plaque load in an age/stage dependent manner. Representative Thiazine Red staining of 12-mo AD mice (A). Cortical and hippocampal contours are shown by grey and turquoise lines respectively, scale bar: 500 µm. Quantification of cortical Thiazine Red positive area (in % of total area) in AD mice (B) for both males (plain bars) and females (open bars) at the different ages. Data are Mean ± SEM. Statistical analyses: 3-way ANOVA with Age, Sex, CX3-hdf as between subjects' factors. AD-mice: Age: p < 0.001. FDR corrected post-hoc tests; compared to 4-mo: ** p < 0.01, *** p < 0.001; compared to 8-mo: # p < 0.5, ## p < 0.01, ### p < 0.001; CX3-hdf comparison: •• p < 0.01, •• • p < 0.001; sexes comparison: $$ p < 0.01. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .

 4 Fig. 4. Microgliosis increases during AD progression: sex and CX3CR1 haplodeficiency have little impact on the microgliosis in AD-mice. Representative IBA1 immunostaining in 12-mo control (A) and AD mice (C), scale bar: 50 µm. Quantification of cortical IBA1 fraction area in control (B) and AD-mice (D), for both males (plain bars) and females (open bars) at the different ages. Data are Mean ± SEM. Statistical analyses: 3-way ANOVA with Age, Sex, CX3-hdf as between subjects' factors. AD-mice: Age: p < 0.001. FDR corrected post-hoc tests; compared to 4-mo: ** p < 0.01, *** p < 0.001; compared to 8-mo: # p < 0.05, ### p < 0.001; sexes comparison: $ p < 0.05.

Fig. 5 .

 5 Fig. 5. Astrogliosis increases during AD progression: sex and CX3CR1 haplodeficiency have limited impact on the astrogliosis in AD-mice. Representative GFAP immunostaining in 12-mo control (A) and AD mice (C), scale bar: 50 µm. Quantification of cortical GFAP positive area (in % of total area) in control (B) and AD mice (D), for both males (plain bars) and females (open bars) at the different ages. Data are Mean ± SEM. Statistical analyses: 3-way ANOVA with Age, Sex, CX3-hdf as between subjects' factors. AD-mice: Age: p < 0.001; CX3-hdf: p < 0.05. FDR corrected post-hoc tests; compared to 4-month-old: ** p < 0.01, *** p < 0.001; sexes comparison: $ p < 0.05; CX3-hdf comparison: 0 p < 0.05.

Fig. 8 .

 8 Fig. 8. Ide, Mmp9 and Mme, APP degrading enzymes gene expression changes in mice cortical homogenates: Changes in gene expression were measured by qPCR in whole cortex and plotted as -ΔCq. Statistical analysis for each gene at every stage: 3-way ANOVA with AD, Sex, CX3-hdf as between subjects' factors. FDR corrected post-hoc tests; compared for AD status: # p < 0.05; CX3-hdf comparison: ** p < 0.01. Complete statistical results are given in TableS3.

Acknowledgements

We acknowledge Leportier M. and Dr Mesbah K. (RAM-iExplore plateform) for help with animal breeding; the imaging facility MRI (Dr Cau J.), member of the national infrastructure France-BioImaging infrastructure supported by the French National Research Agency (ANR-10-INBS-04, «Investments for the future») for help with immunohistochemistry quantification; Drs Tiers L. and Lehmann S. (Laboratory of Biochemistry -Clinical Proteomic (LBPC) for help with MSD quantification. Drs Pisa L., Pastore M. and Reynes C. (StatAbio plateform, BCM, Univ. Montpellier, CNRS, INSERM, Montpellier, France) for useful advice on statistical analyses.

Funding

This work was supported by funding from France Alzheimer (Grant AAP 2013 _ MicroMalzh). The PhD funding of J. Hua was supported by the Labex ICST (ANR 11-LABX-0015).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.bbi.2020.10.021.


est destinée au dépôt

A new experiment to assess the impact of groundwater table level variations on petroleum hydrocarbon pollutants remobilization (LNAPL) in the climate change context

Amélie Cavelan, Pierre Faure, Fabrice Golfier, Anne-Julie Tinet, Constantin

Oltean, Stéfan Colombano, Hossein Davarzani, Jacques Deparis, Catherine

Lorgeoux, Noële Enjelvin

To cite this version:

Amélie Cavelan, Pierre Faure, Fabrice Golfier, Anne-Julie Tinet, Constantin Oltean, et al

  ? o Gaseous surface emissions (flux, composition: O2, CO2, hydrocarbons) o The LNAPL saturation distribution in soil (48 electrical resistivity and permittivity in-situ sensors per lysimeter); o Other soil properties: 4 in-situ sensors for temperatures, pH, RedOx, soil water potential at different depths. o The concentration and composition of the dissolved LNAPL phase: sampling using suction cups and laboratory analysis (SPE, GC/MS, TPH, DOC, FTIR) Contaminated water samples analytical protocol improvements Lysimeters Time 2D tanks 1D centimetric columns Calibrations of tensiometers, electrical permittivity and resistivity data under controlled LNAPL/water/air saturations in the laboratory GC/MS apparatus Numerical simulation of LNAPLs transport and mobilization under fluctuating groundwater level from the pore scale to the lysimetric scale Gas collection chambers and µG

new experiment to assess the impact of groundwater table level variations on petroleum hydrocarbon pollutants remobilization (LNAPL) in the climate change context. Amélie Cavelan 1

  , Pierre Faure 1 , Fabrice Golfier 2 , Anne-Julie Tinet 2 , Constantin Oltéan 2 , Stéfan Colombano 3 , Hossein Davarzani 3 , Jacques Deparis 3 , Catherine Lorgeoux 2 , Noële Enjelvin 4 1 Université de Lorraine, CNRS, LIEC, Nancy, France; 2 Université de Lorraine, CNRS, GeoRessources, Nancy, France;

.. A new experiment to assess the impact of groundwater table level variations on petroleum hydrocarbon pollutants remobilization (LNAPL) in the climate change context. 1st OZCAR TERENO International conference: Advancing critical zone science, Oct 2021, Strasbourg, France. , 1st OZCAR TERENO international conference: Advancing critical zone science : abstract book, 37, pp.240-241, 2021. hal-A 3 BRGM, Orléans, France; 4 Université de Lorraine, INRAE, LSE, GISFI, Nancy, France amelie.

cavelan@univ-lorraine.fr OZCAR-TERENO First International Conference S9.P4 LIGHT-NON-AQUEOUS-PHASE-LIQUIDS (LNAPLs)? LNAPLs AND GROUNDWATER GROUNDWATER AND CLIMATE CHANGE HOW DO WE STUDY THESE PHENOMENA? IN THE LABORATORY

	Origin	Petroleum hydrocarbons (oil, gasoline, diesel fuel)
	State and density	Viscous liquids, density < 1 g/cm3
	Origin	Saturated/unsaturated hydrocarbons (mainly normal-alcanes) and BTEX
	Occurrence	~ 45% of contaminated soils and groundwater tables
	Residence time	> 10 years
	Solubility, Biodegradability and Volatility	Low to moderate, dependent on the LNAPL compounds
				Buried rain
				simulator
				LNAPLs	2 m
		«Extreme» water table fluctuations	Groundwater level control	1 m «Current» water table fluctuations and
		and precipitations		precipitations

Fig.

1

. Measured and projected evolutions of the global earth surface temperature, population growth, extreme events intensity and frequency, groundwater withdrawal and groundwater table level variations intensity from 1900 to 2100. After the data of the IPCC (

2021

), the European Environment Agency, and Wada (2016) https://doi.org/10.1007/s10712-015-9347-x.

Fig.2. LNAPL mobilization and release processes during groundwater table level (GWL) fluctuations: (i) initial, (ii) low (dry season), (iii) high water table level (wet season). VOC: volatil

organic carbon. SZ: saturated zone. USZ: unsaturated zone. PERSPECTIVES: o Consider the effect of biodegradation in the climate change context o Real-time contaminated sites monitoring (field scale). o Effect of increasing temperatures ? EXPECTED GOALS: o Improve monitoring techniques of contaminated sites o Improve the understanding of LNAPLs behavior under various climatic conditions o Help to adapt remediation methods in the climate change context CLIMATE CHANGE MAY: o Change precipitation and groundwater recharge patterns (Fig.1) o Increase groundwater use, decrease the average water table level. o Increase the amplitude of variations in the groundwater table level. o Favor the vertical spreading of the LNAPLs across the soil o Favor the short-term LNAPL release to the air and water o Increased long-term LNAPL natural attenuation rates

Fig. 3. Experimental setup used to simulate the effect of two scenarios (current and extreme/climate change) of precipitations and groundwater level variations on LNAPL contaminated sand.

In-situ sensors + scution cups

	Monitoring wells:
	Pure LNAPL sampling,
	thickness, depth monitoring
	USZ LNAPLs	USZ
	SZ	Sandy porous media
	Water table
	fluctuation zone	Water table	SZ
		fluctuation
		zone
	Scale


Lap Luat Nguyen

Anthony Fiche

Roland Gautier

Modulated Wideband Converter Compressed Sensing Spectrum Reconstruction in Multi-Level Power of Transmitters Signal Scenarios

This paper studies the impacts of transmitters power levels on spectrum reconstruction performances in order to monitor a wideband spectrum. A sub-Nyquist blind sampling scheme based on the Modulated Wideband Converter (MWC) has been considered to achieve this task. Reconstruction performances are evaluated in simulation in terms of correct reconstruction and false alarm rates by studying several multi-level power scenarios.

The study shows that the performance of reconstruction depends on the In-Band Signal-to-Noise ratio (IBSNR) of each transmitter. Based on these results, a threshold of In-Band Signal-to-Noise ratio to ensure the correct reconstruction is proposed.

I. INTRODUCTION

In context of cognitive radio, the limitation of frequency resources motivates the studies on frequency sharing [START_REF] Mitola | Cognitive radio architecture evolution[END_REF], [START_REF] Tabaković | A survey of cognitive radio systems[END_REF]. To not affect the primary (licensed) users, the secondary users must know whether the frequency band is vacant. A very common way to detect the present of power spectrum at licensed band is to apply an energy detector, since it is low complexity, however it is sensitive to noise level [START_REF] Tandra | SNR walls for signal detection[END_REF]. Another possible method is considered as spectrum sensing, which can detect multiple power level of primary users and secondary users [START_REF] Chen | Sensing and power allocation for cognitive radio with multiple primary transmit powers[END_REF], [START_REF] Gao | Sensing and recognition when primary user has multiple transmit power levels[END_REF]. A problem of spectrum sensing that needs to be taken in account is the sensed bandwidth. In some applications, the sensed bandwidth may go beyond several GHz. Consequently, the limited sampling rate and limited input bandwidth of a conventional Analog-to-Digital Converter (ADC) will be a constraint for spectrum sensing. In the literature, the sub-Nyquist sampling methods such as Random Modulator [START_REF] Laska | Theory and implementation of an analog-to-information converter using random demodulation[END_REF], [START_REF] Tropp | Beyond nyquist: Efficient sampling of sparse bandlimited signals[END_REF], Multicoset Sampling [START_REF] Venkataramani | Perfect reconstruction formulas and bounds on aliasing error in sub-Nyquist nonuniform sampling of multiband signals[END_REF], [START_REF] Mishali | Blind multiband signal reconstruction: Compressed sensing for analog signals[END_REF] or Modulated Wideband Converter (MWC) [START_REF] Mishali | From theory to practice: Sub-nyquist sampling of sparse wideband analog signals[END_REF]- [START_REF] Mishali | Xampling: Signal acquisition and processing in union of subspaces[END_REF] are seen as a premise to deploy spectrum sensing into practice. In [START_REF] Lexa | Compressive power spectral density estimation[END_REF], a multicoset based on Compressed Sensing (CS) [START_REF] Donoho | Compressed Sensing[END_REF], [START_REF] Candès | Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[END_REF] is proposed to estimate the power spectral density, at sub-Nyquist sampled wide sense-stationary. To the best of our knowledge, the MWC seems to be the most convenient scheme in terms of practical implementation, since it has been deployed by different prototypes and analog boards [START_REF] Mishali | Xampling: Analog to digital at sub-Nyquist rates[END_REF], [START_REF] Israeli | Hardware calibration of the modulated wideband converter[END_REF], [START_REF] Cohen | Analog to Digital Cognitive Radio: Sampling, Detection, and Hardware[END_REF].

In practice, primary users use multiband spectra with different parameters of interest, such as power, bandwidth or modulation. The MWC has potential of wideband spectrum sensing and multiband detection in real-time, which benefits on practical implementation than other schemes. As a result, it comes up with some practical applications in cognitive radio [START_REF] De | Sparse representation for blind spectrum sensing in cognitive radio: a compressed sensing approach[END_REF], [START_REF] Wael | Performance analysis of sub-nyquist sampling for wideband spectrum sensing in cognitive radio[END_REF], and fast spectrum sensing and receiver flexibility in spectrum sensing applications [START_REF] Song | A survey on spectrum sensing and learning technologies for 6g[END_REF] and meet the LTE specifications [START_REF] Adams | A practical implementation of the Modulated Wideband Converter Compressive Sensing receiver architecture[END_REF].

The MWC has proved its efficiency to monitor multiband spectra, such as Phase Shift Keying modulation scenario [START_REF] Israeli | Hardware calibration of the modulated wideband converter[END_REF] or rectangular shapes [START_REF] Mishali | From theory to practice: Sub-nyquist sampling of sparse wideband analog signals[END_REF] with different energy ratios. However, the authors do not focus on the detection sensibility of transmitter with low power level. For example, in cognitive radio, the low power signal detection could bring benefit. In case of frequency sharing, an idle band can be occupied by a secondary user with very weak signal strength, to without affects the primary user. A spectrum sensing system can verify the presence of the secondary user. The attempt to detect very low power level transmitter contributes to the study of fading for both primary and secondary users [START_REF] Sahai | Some fundamental limits on cognitive radio[END_REF], [START_REF] Develi | Spectrum sensing in cognitive radio networks: threshold optimization and analysis[END_REF]. To balance the fading in cognitive radio, the primary user can increase its performance if the channel information is known, especially the SNR. Consequently, the motivation of this paper is to study the impacts of amplitude level ratio between transmitters on spectrum reconstruction performances (correct reconstruction and false alarm rates) and propose a threshold based on our simulations which ensure high reconstruction performances.

This paper is organized as follows. Section II presents the background of the MWC. In Section III, several multi-level power scenarios are studied by comparing In-Band Signal-to-Noise Ratio of all transmitters (called global in-Band SNR and noticed IBSNR G ) and In-Band SNR of each transmitter taken separately (noticed IBSNR 1T ). Then, the evaluation of the simulation results based on the correct reconstruction rate and false alarm rate according to the proposed scenarios is presented.

II. MODULATED WIDEBAND CONVERTER

A. Physical scheme and operation description

The MWC physical scheme [START_REF] Mishali | Xampling: Signal acquisition and processing in union of subspaces[END_REF] is shown in Fig. 1. A wideband signal x(t) comprises multiband, but sparse and unknown carrier frequency. The signal x(t) is considered as an input of the MWC scheme. This scheme consists of M physical channels, each has one mixer, one lowpass filter and one ADC. The mixer with mixing sequence p i (t) is to shift all spectra of x(t) into baseband. The mixing sequence p i (t) can be any sequence in communications such as Gold [START_REF] Gold | Optimal binary sequences for spread spectrum multiplexing (corresp.)[END_REF], Kasami [START_REF] Kasami | Weight distribution formula for some class of cyclic codes[END_REF] or random sequences with the repetition frequency F p . The lowpass filter keeps the signal only in baseband bandwidth [-F s /2; F s /2], with cutoff frequency F c = F s /2. Then, the sampling rate of ADC will be chosen F s for convenience. The output of the mixer is

x i (t) = p i (t)x(t), (1)
and the output of lowpass filter y i (t) as

y i (t) = h(t) * x i (t), (2)
where h(t) the ideal lowpass filter transfer function. At last, the conversion output reads as

y i [n] = y i (nT s ), (3)
where T s the sampling period. For further development, consider that the Nyquist bandwidth is divided into L subbands, then the relationship between Nyquist frequency and mixing frequency is L = F N yq /F p . It means that each subband has F p bandwidth. The active subband l which comprises the input spectrum will be detected among L subbands ( L = 2L 0 + 1 and -L 0 ≤ l ≤ L 0 ) by the MWC scheme and Compressed Sensing technique [START_REF] Donoho | Compressed Sensing[END_REF], [START_REF] Candès | Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[END_REF]. The mixing sequences are generated by pseudo-random sequences. At the mixer, there will be one transmitter to be shifted in the baseband of each MWC physical channel. Thus, the more number of MWC physical channels there are, the more transmitters will be detected. In practice, the number of MWC physical channels cannot be high, due to the exponential increase cost of analog components such as mixer, lowpass filter and ADC. Consequently, a collapsing factor q is introduced to overcome this problem [START_REF] Mishali | Xampling: Signal acquisition and processing in union of subspaces[END_REF]. Instead of M physical channels, it can be considered as q × M collapsed channels. With M channels, the sampling rate is F s , thus with q × M channels, the sampling rate can be considered F p , by q = F s /F p . This assumption can help to extend virtually the number of MWC channels.

B. Number of active subbands estimation

In Fig. 1, before reconstruction, the number of active subbands s needs to be estimated. The output of the MWC y i [n] (1 ≤ i ≤ M ) has L sub-Nyquist samples, it can be formed to a M × N matrix y output, or qM × L matrix y if collapsing factor q is used.

The number of active subbands is estimated based on the singular values of matrix y ∈ P M ×L , or the autocorrelation matrix eigenvalues. The active subbands s is related to the variation of these values. Then, there are s non-zero eigenvalues. In the simulation of this paper, the number of active subbands s is estimated by two discriminant functions [START_REF] Radoi | A New Method for Estimating the Number of Harmonic Components in Noise with Application in High Resolution Radar[END_REF].

C. Spectrum reconstruction

The mixing sequences p i (t) is used to form a sensing matrix (P) il = p il [START_REF] Mishali | From theory to practice: Sub-nyquist sampling of sparse wideband analog signals[END_REF], where p il = F p Tp/2 -Tp/2 p i (t)e -j2πlFpt dt are the Fourier coefficients obtained from p i (t). The Fourier transform of the input signal (multi-subband) in the l th subband is denoted z l [n] with l ∈ [1, L]. Thus, the MWC system equation with a MWC output and a sensing matrix is y = Pz, with P ∈ C qM ×L [11] [START_REF] Mishali | Xampling: Signal acquisition and processing in union of subspaces[END_REF]. Fig. 2 shows an illustration of the system equation. In Compressed Sensing, a main condition needed to be respected is s ≤ M q -1, with s the number of active subbands or the non-zero elements in z. This condition is called sparsity because the matrix size of y (q × M ) has to be smaller than the size of input z (L elements) and there is a few number of s. The reconstruction step is to look for z from y. In our simulation, a greedy algorithm Orthogonal Matching Pursuit (OMP) [START_REF] Cai | Orthogonal Matching Pursuit for sparse signal recovery with noise[END_REF] is applied to reconstruct the input signal.

III. MULTIPLE POWER LEVELS SENSING AND

RECONSTRUCTION

For the rest of the paper, the MWC parameters are chosen as M = 4, L = 96, q = 7 and F N yq = 1 GHz. Each transmitter is a band-limited white noise and has the same bandwidth B = 2F p /3 = 7 MHz. The central frequency of each transmitter has been randomly generated between [ B 2 ;

F N yq 2 -B 2 ],
i.e. [3.5;496.5] MHz. To respect the sparsity condition, the maximum number of symmetric transmitter must be equal to N tmax = M q-1 4 = 6 (by assuming that each transmitter can locate astride two channels of the equivalent model).

The spectrum is contaminated by a wideband additive Gaussian noise at different SNR. The SNR is defined into two categories, a SNR in all active subbands (or so-called global SNR in-band noticed IBSNR G ) and a SNR in the whole Nyquist bandwidth noticed SNR Nyq . Then, the relationship between the two categories of SNR can be seen as

IBSNR G = SNR Nyq + 10 log F N yq 2 × N t × B = SNR Nyq + 10 log 3 × L 4 × N t (4)
with N t the number of transmitters and B = 2F p /3. The number of transmitters is fixed to 6. The low SNR Nyq will make the active subbands to be aliased by the noise. It leads to the overestimation due to the unexpected high power in active subbands and difficult to determine the number of active subbands s or number of transmitters N t . Another factor that needs to be taken into account is the SNR in each transmitter bandwidth (not global SNR), this factor impacts directly to the reconstructions and in the next section, corresponding to each global In-Band SNR value IBSNR G , the In-Band SNR in each transmitter bandwidth will be figured out.

Moreover, the correct reconstruction rate [START_REF] Nguyen | Digital compensation of lowpass filters imperfection in the Modulated Wideband Converter Compressed Sensing scheme for radio frequency monitoring[END_REF] (resp. false alarm rate) is estimated by

P c = %(Br B d ) %Br (resp. P f = %((B d \Br)∩ Br) 1-%Br
), where B r the real active subbands from input signal and B d the detected active subbands. It should be noted that for each simulation scenario, 2000 trials have been tested to compute the reconstruction and false alarm rates.

To study the impact of transmitter power levels, with this configuration of the MWC, four scenarios are considered. In the first scenario, all six transmitters have the same power level. The second scenario, assume that one pair of transmitters has greatest power, then the second pair of transmitters has 75% level of the first pair, and the third pair has 50% level of the first pair. Third scenario, we assume that the second pair has 50% level of the first pair, and the third pair has only 25% level of the first pair. In the last scenario, 6 transmitters have different power levels and reduce gradually Table I

A. Reconstruction performances in function of Global In-Band Signal to Noise Ratio for all scenarios

Firstly, the spectrum reconstruction will be tested at the same power level (scenario 1), then reduced the power levels of transmitters followed the scenarios in Table I, to obtain and compare the correct reconstruction and false alarm rates in function of IBSNR G . Fig. 3 shows the correct reconstruction rate and false alarm rate for 6 transmitters of all scenarios. When reducing the power level, the correct reconstruction rate is reduced too. In scenario 2, the P c in function of global SNR in-band is higher than the P c in scenario 3 and 4, due to the fact that the proportion of useful power in an active subband is higher. In scenario 3 and 4, the correct reconstruction rates and the false alarm rates are nearly the same, although the power levels in scenario 3 and 4 are different, the power proportion in all active subbands can be considered the same globally. It should be noted that from Fig. 3, the correct reconstruction rates start to decrease at 15 dB for scenario 1 and 2, and at 20 dB for scenario 3 and 4. Hence, these values can be considered as threshold values which ensure correct reconstruction. Due to the multiple thresholds for IBSNR G , it is hard to determine which transmitter cannot be reconstructed, in next subsection, we propose a relationship to find an In-Band Signalto-Noise Ratio for each transmitter. This relationship helps to determine an unique IBSNR threshold for each transmitter and each scenario which ensures high reconstruction performances. Moreover, to verify the threshold, the bandwidth B of each transmitter is reduced to B = F p /3 ≈ 3.47 MHz. The correct reconstruction and false alarm rates are shown in Fig 4 . It can be seen that the P c at this bandwidth also starts to decrease at 15 dB for scenario 1 and 2, and 20 dB for scenario 3 and 4. This result helps to conclude that the proposed threshold can be used to make sure the correct reconstruction in these scenarios with an acceptable bandwidth. Besides, an example of spectrum reconstruction of 6 identical power level transmitters is shown in Fig. 5 at IBSNR G = 20 dB. It can be seen that at this noise level, all the transmitters can be correctly reconstructed with their level and no false alarm.

B. Correct reconstruction performance in function of In-Band

Signal to Noise Ratio 1) Scenario 2: In this scenario, the correct reconstruction rate is shown in Fig. 6, in function of the exact IBSNR 1T . It can be observed that at the same global in-band SNR, the low power level transmitters have to deal with higher noise than the higher power level, then leads to a bad reconstruction. It can be seen that the pair which has the greatest power level ({P 1 , P 2 } = 1) can achieve high performance even at low IBSNR G . For the second pair ({P 3 , P 4 } = 0.75), the correct reconstruction rate is still high, more than 85% at 5 dB of IBSNR 1T . Otherwise, the lowest level pair ({P 5 , P 6 } = 0.5) has low performance when IBSNR 1T is low (typically less than 5 dB). It means that the reconstruction is not correct at this noise level. Overall, the correct reconstruction rate starts to decrease at IBSNR 1T = 15 dB, then this is a threshold proposed for this scenario to ensure the correct reconstruction for all transmitters. Fig. 7 shows the correct reconstruction rate for this scenario with a reduction of bandwidth (B = F p /3), it should be noted that P c starts to decrease at IBSNR 1T = 15 dB for all transmitters. This result verifies the proposed threshold for this scenario. An example of spectrum reconstruction of this scenario at IBSNR G = 20 dB is shown in Fig. 8. It can be seen that in this scenario and at this noise level, it is difficult to reconstruct the low power transmitters with their levels correctly. Moreover, it appears to be a false alarm and that makes confusion with low power transmitters.

Moreover, the spectrum reconstruction of this scenario at IBSNR G = 5 dB is shown in Fig. 9. It is clear that at this noise level, the reconstruction is not absolutely correct, and false alarm spectra appear along the Nyquist bandwidth. For the blind spectrum detection application, this noise level (IBSNR G = 5 dB) makes it difficult to determine the useful transmitters. 2) Scenario 3: In the third scenario, the power level of the second pair and third pair are continuously reduced ({P 3 , P 4 } = 0.5 and {P 5 , P 6 } = 0.25). This scenario is to test the reconstruction performance of the MWC in case of very low power transmitters. The reconstruction rate is presented in Fig. 10 in function of IBSNR 1T . It is clear to see that the reconstruction rate of the third pair ({P 5 , P 6 } = 0.25) has low performance in the presence of noise (less than 6 dB). Due to the power ratio of transmitters that is reduced in this scenario, the second pair can achieve higher performance than the previous scenario. Also, from Fig. 10, the reconstruction rate starts to decrease at IBSNR 1T = 15 dB. This is considered as a threshold to ensure the correct reconstruction for all transmitters in this scenario. An example of spectrum reconstruction for the third scenario is presented in Fig. 12 at IBSNR G = 20 dB. It can be seen that in this scenario and at this noise level, the first pair and the second pair can be reconstructed correctly with their frequency location and their power level. The lowest power level is always difficult to reconstruct because the ratio between the lowest level with the maximum level is always low. Moreover, at this noise level, all the transmitters can be detected correctly and there is no false alarm. 3) Scenario 4: This scenario is to study more levels, such as each transmitter has a different level to the others and is reduced gradually. The correct reconstruction rate and false alarm rate are shown in Fig. 13. It can be seen from this figure, the P c of the power level which is under 50% the maximum power (i.e. for P 4 = 0.4, P 5 = 0.3 and P 6 = 0.2) is low, even the global correct reconstruction rate, at low IBSNR G (5 and 10 dB). These values show that some transmitters have been lost at these power ratios and SNR levels. Moreover, from Fig. 3 the false alarm rate of this scenario is highest compared to the other scenarios. It means that the system cannot determine the frequency locations of the small power transmitters and then the wrong detection appears. Finally, a threshold proposed for this scenario is also at 15 dB.

The correct reconstruction rate with the reduction of band- width (B = F p /3) is shown in Fig. 14, this also verifies that the proposed threshold is IBSNR 1T = 15 dB to ensure the correct reconstruction.

Besides, an example of spectrum reconstruction is shown in Fig. 15 at IBSNR G = 20 dB. At this noise level, all the transmitters can be detected correctly. The lowest power level transmitter (P 6 = 0.2 in this example) at IBSNR G = 20 dB is equivalent IBSNR 1T = 10.2 dB at its subbands. Then, the reconstruction rate of this level is nearly 90% and the false alarm rate is low, less than 2% (in Fig. 13). Hence, the reconstruction of MWC is correct in the frequency locations at this noise level and no false alarm. The power level is impacted by noise, however, the monitoring system cannot reconstruct exactly the transmitter power level, mainly some near value and low levels (for example, P 5 = 0.3 and P 6 = 0.2).

Based on our simulations, the threshold for IBSNR 1T , with an acceptable bandwidth, to ensure the correct reconstruction can be concluded is 15 dB for all cases.

IV. CONCLUSION

This paper studies the impact of transmitters power levels on the reconstruction performance of the MWC system in terms of correct reconstruction and false alarms rates. It is clear that the noise power has a negative impact on the reconstruction performance, by adding false alarm and by introducing miss detection, especially for transmitters with low power levels. Based on our simulations, reconstruction performances depend on the In-Band Signal to Noise ratio (IBSNR) of each transmitter and a threshold value of IBSNR 1T = 15 dB has been proposed to ensure high reconstruction performances.

V. ACKNOWLEDGMENT

This research is supported by the IBNM (Brest Institute of Computer Science and Mathematics) CyberIoT Chair of Excellence at the University of Brest.

Fig. 1 :

 1 Fig. 1: The MWC scheme and processing stages.

Fig. 2 :

 2 Fig. 2: Illustration of the system equation.

Fig. 3 :

 3 Fig. 3: Correct reconstruction rate and false alarm rate for all scenarios in function of IBSNRG (with B = 2Fp/3).

Fig. 4 :

 4 Fig. 4: Correct reconstruction rate and false alarm rate for all scenarios in function of IBSNRG (with B = Fp/3).

Fig. 5 :

 5 Fig. 5: Example of spectrum reconstruction of 6 identical power level transmitters at IBSNRG = 20 dB (scenario 1). From scenario 2 to 4, we show the performance of reconstruction in function of the in-band Signal-to-Noise Ratio for each transmitter. It is determined by the ratio between signal levels which is linked to the in-band SNR of each transmitter taken separately. It is possible to compute the In-band Signalto-Noise Ratio for each transmitter IBSNR 1T by: IBSNR 1T = SNR 1T Nyq + 10 log F N yq 2 × B

Fig. 6 :

 6 Fig. 6: Correct reconstruction rate of 6 transmitters with different power levels in function of IBSNR1T (scenario 2, B = 2Fp/3).

Fig. 7 :

 7 Fig. 7: Correct reconstruction rate of 6 transmitters with different power levels in function of IBSNR1T (scenario 2, B = Fp/3).

Fig. 8 :

 8 Fig. 8: Spectrum reconstruction of 6 transmitters with different power levels in scenario 2 at IBSNRG = 20 dB.

Fig. 9 :

 9 Fig. 9: Spectrum reconstruction of 6 transmitters with different power levels in scenario 2 at IBSNRG = 5 dB.

Fig. 10 :

 10 Fig. 10: Correct reconstruction rate of 6 transmitters with different power levels in function of IBSNR1T (scenario 3, B = 2fp/3).

Fig. 11 :

 11 Fig. 11: Correct reconstruction rate of 6 transmitters with different power levels in function of IBSNR1T (scenario 3, B = Fp/3).

Fig. 12 : 2 Fig. 13 :

 12213 Fig. 12: Spectrum reconstruction of 6 transmitters with different power levels in scenario 3 at IBSNRG = 20 dB.

Fig. 14 :

 14 Fig. 14: Correct reconstruction rate of 6 transmitters with different power levels in function of IBSNR1T (scenario 4, B = Fp/3).

Fig. 15 :

 15 Fig. 15: Spectrum reconstruction of 6 transmitters with different power levels in scenario 4 at IBSNRG = 20 dB.

  summarizes these scenarios.

		P 1	P 2	P 3	P 4	P 5	P 6
	Scenario 1	1	1	1	1	1	1
	Scenario 2	1	1	0.75	0.75	0.5	0.5
	Scenario 3	1	1	0.5	0.5	0.25 0.25
	Scenario 4	1	0.8	0.6	0.4	0.3	0.2

TABLE I :

 I Simulation scenarios and transmitters power levels.