Rafael Alcala

Ali Awada

Anne-Laurence Boutillier

Dr Karine Merienne

Epigenetic mechanisms underlying enhancer modulation of neuronal identity and activity and neurodegeneration

Keywords: Epigenetic regulations, super enhancer, neuronal identity, neuronal activity, Huntington's disease, Alzheimer disease

Neurodegenerative diseases, including Huntington's disease (HD) and Alzheimer disease (AD), are progressive conditions characterized by selective loss of neuronal regions and/or subpopulations, in disease-dependent manner. Neuronal loss is preceded by a long period of neuronal dysfunction, during which glial cells also undergo major changes, resulting in particular in neuroinflammation.

Those dramatic changes affecting both neurons and glial cells associate with epigenetic and transcriptional dysregulations, characterized by defined cell type-specific signatures. Notably, increasing studies support the view that altered regulation of transcriptional enhancers, which are distal regulatory regions of the genome capable of modulating the activity of promoters through chromatin looping, play critical role in transcriptional dysregulation in HD and AD. We review current knowledge on enhancers in HD and AD, and highlight challenging issues to better decipher the epigenetic code of neurodegenerative diseases.

Neuronal-specific enhancers: neuronal identity vs neuronal activity

. Epigenetic mechanisms also comprise regulation of 3D chromatin architecture, including chromatin loops modulating promoter-enhancer interactions and higher-order chromatin

organization, such as topologically associated domains (TADs) [START_REF] De Laat | Topology of mammalian developmental enhancers and their regulatory landscapes[END_REF][START_REF] Rowley | Organizational principles of 3D genome architecture[END_REF]. Histone acetylation, through the action of a family of histone acetyltransferases (HAT), plays a key role in chromatin relaxation. Histone acetylation at promoters and enhancers, corresponding to distal regulatory regions, is a prerequisite to target gene activation. Particularly, acetylation at lysine K27 of histone H3 (H3K27ac) by the HAT CBP/P300 is a mark of active enhancers [START_REF] Tie | Trithorax monomethylates histone H3K4 and interacts directly with CBP to promote H3K27 acetylation and antagonize Polycomb silencing[END_REF]. Mechanistically, transcriptional complexes comprising HAT, RNA polymerase II (RNAPII) and various transcriptional regulators, including transcription factors and proteins promoting chromatin loop formation such as CTCF and cohesin, are recruited at H3K27ac-enriched regions to facilitate enhancer-promoter interactions [START_REF] Rowley | Organizational principles of 3D genome architecture[END_REF] .

Super-enhancers and cellular identity. During cellular differentiation, H3K27ac signal undergoes massive changes and get particularly enriched at genes defining specific cellular identities [START_REF] Whyte | Master transcription factors and mediator establish super-enhancers at key cell identity genes[END_REF]. Lineage-determining transcription factors, expressed in developmental-and cell typedependent manners, provide specificity to the mechanism, driving the targeting of H3K27ac at selective genes in time and space controlled manners. Thus, H3K27ac is strongly cell type-dependent, and H3K27ac cellular profile at transcriptional enhancers reflects specific cellular identity. Cellular identity enhancers, regulating genes that specify cell type identity and function, are controlled by super enhancers, which are broad enhancers composed of multiple clusters of active enhancers [START_REF] Heinz | The selection and function of cell typespecific enhancers[END_REF] (Figure 1). Super-enhancers, which generally encompass their target genes, are more highly enriched in H3K27ac when compared to classical enhancers [START_REF] Heinz | The selection and function of cell typespecific enhancers[END_REF].

Chromatin architecture at super enhancers displays extensive chromatin looping, enabling multiple promoter/enhancer interactions, thereby insuring elevated and sustained expression of cellular identity genes, a feature essential to cellular identity acquisition and maintenance [START_REF] Nord | Neurobiological functions of transcriptional enhancers[END_REF][START_REF] Yap | Activity-Regulated Transcription: Bridging the Gap between Neural Activity and Behavior[END_REF].

Neuronal activity-regulated enhancers. Enhancers also display highly dynamic regulation since they respond to cellular stimulation, thereby integrating environmental signals and triggering adaptive genomic response. Dynamic regulation of enhancers is especially critical to neuronal function. In response to environmental stimuli, it drives transcriptional reprogramming promoting synaptic plasticity and adaptive behavior, including learning and memory [START_REF] Campbell | How the epigenome integrates information and reshapes the synapse[END_REF][START_REF] Gräff | Histone acetylation: molecular mnemonics on the chromatin[END_REF][START_REF] Kim | Widespread transcription at neuronal activity-regulated enhancers[END_REF][START_REF] Lopez-Atalaya | Can changes in histone acetylation contribute to memory formation?[END_REF][START_REF] Yap | Activity-Regulated Transcription: Bridging the Gap between Neural Activity and Behavior[END_REF]. In response to stimulation, signaling cascades (e.g. cAMP-and Ras/MAPK-dependent pathways) are activated in neuronal tissue, which leads to the recruitment and/or activation of transcription factors and HAT (e.g. CREB and CBP) to enhancers and promoters of early response genes (ERGs), notably the transcription factor Fos. This first, rapid response leads to increased H3K27ac, enhancer RNA transcription, strengthening of enhancer/promoter interaction and up-regulation of ERGs, thereby inducing a second regulatory wave, leading to activation of cell type-specific late response genes (LRGs). In brain tissue, LRGs are effector genes promoting synaptic plasticity. In response to neuronal stimulation, H3K27ac is increased at LRGs enhancers (Figure 2). LRGs are induced in time and cell type-specific controlled manners thanks to the cooperation between AP-1 proteins, especially FOS, cell type-specific pioneer transcription factors and factors regulating nucleosome eviction [START_REF] Vierbuchen | AP-1 Transcription Factors and the BAF Complex Mediate Signal-Dependent Enhancer Selection[END_REF]. It is noteworthy that, in contrast to activity-regulated enhancers, cellular identity enhancers did not show increased H3K27ac in response to cellular stimulation [START_REF] Vierbuchen | AP-1 Transcription Factors and the BAF Complex Mediate Signal-Dependent Enhancer Selection[END_REF].

Thus, neuronal enhancers (and H3K27ac regulation) are critical for the acquisition and maintenance of stable neuronal identity, but also for the dynamic regulation of neuronal activity.

While genome wide association studies (GWAS) provide increasing evidence that cell type-specific enhancers, especially super enhancers, are hotspots for risk variants modulating susceptibility to neurological diseases, fewer epigenomic studies have addressed the role of enhancers in brain diseases [START_REF] Heinz | The selection and function of cell typespecific enhancers[END_REF][START_REF] Nord | Neurobiological functions of transcriptional enhancers[END_REF][START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. However, the advent of genome-wide scale approaches to investigate brain epigenome has made possible the identification of defined epigenetic signatures in neurological diseases, including neurodegenerative diseases such as HD and AD. Whereas genetic mouse models of these diseases have led to pioneered and critical exploratory studies, increasing data are currently being produced using human brain samples. Here we focus on epigenomic data generated using brain tissues from HD and AD mouse models, as well as post-mortem brain samples from patients. Remarkably, the data indicate that, in both HD and AD brains, neuronal-and glial-specific enhancers show distinct epigenetic signatures, which might stimulate the development of common innovative therapeutic strategies.

Epigenetic dysregulation and enhancer regulation in HD

Etiology and neuropathology of HD. HD is a progressive neurodegenerative disease, usually characterized by adult onset, though rare juvenile forms of the disease also exist that display severer clinical presentation and faster progression when compared to the adult form. The disease is caused by an unstable CAG triplet repeat expansion in the first exon of the HTT gene, which results in the production of mutated protein with toxic polyglutamine (polyQ) expansion, highly prone to aggregation. The number of CAG repeats at HTT is polymorphic in the normal population and does not exceed 36-39 CAGs. Above this threshold, the CAG repeat is pathogenic, and since longer repeats are more toxic, there is an inverse correlation between the number of repeats and age of disease onset [START_REF] Bates | Huntington disease[END_REF]. Moreover, the HD mutation is unstable in the germline and in somatic tissues, which results in increasing numbers of CAG repeats in successive generations and in somatic tissues with age [START_REF] Castel | Repeat instability as the basis for human diseases and as a potential target for therapy[END_REF]. GWAS showed that genetic modifiers in HD predominantly target DNA repair genes implicated in CAG repeat instability (Genetic Modifiers of Huntington's Disease (GeM-HD) Consortium, 2019Consortium, , 2015;;[START_REF] Jones | DNA repair in the trinucleotide repeat disorders[END_REF]. Despite ubiquitous expression of the HTT gene, polyQ-HTT is predominantly toxic to specific neurons of the striatum, e.g. medium spiny neurons (MSNs). However, as disease progresses, additional brain regions are affected, including cortical regions. Microglia and astrocytes also contribute to the pathogenic process through astrogliosis and inflammatory response, as observed in several neurodegenerative diseases. Neurodegeneration results from a long period of brain cell dysfunction, characterized by multiple cellular defects, resulting from both gain-and loss-of function mechanisms [START_REF] Bates | Huntington disease[END_REF][START_REF] Saudou | The Biology of Huntingtin[END_REF]. Particulalry, the HD mutation induces large-scale transcriptional and epigenetic dysregulation in HD brain [START_REF] Francelle | Contribution of Neuroepigenetics to Huntington's Disease[END_REF].

HD transcriptomic signatures.

A numbers of transcriptomic studies were performed using brain tissues of HD mice and post-mortem brain tissues [START_REF] Francelle | Contribution of Neuroepigenetics to Huntington's Disease[END_REF][START_REF] Hodges | Regional and cellular gene expression changes in human Huntington's disease brain[END_REF][START_REF] Kuhn | Mutant huntingtin's effects on striatal gene expression in mice recapitulate changes observed in human Huntington's disease brain and do not differ with mutant huntingtin length or wild-type huntingtin dosage[END_REF][START_REF] Labadorf | Evidence of Extensive Alternative Splicing in Post Mortem Human Brain HTT Transcription by mRNA Sequencing[END_REF][START_REF] Luthi-Carter | Decreased expression of striatal signaling genes in a mouse model of Huntington's disease[END_REF][START_REF] Seredenina | What have we learned from gene expression profiles in Huntington's disease?[END_REF]. Specifically, comprehensive transcriptomic profiling using HD knockin mice expressing mutated Htt with different CAG repeat lengths indicated that transcriptional dysregulation in HD is CAG length-, age-and tissue-dependent, being most extensive in the striatum, and thus correlated with disease progression [START_REF] Langfelder | Integrated genomics and proteomics define huntingtin CAG length-dependent networks in mice[END_REF]. Dysregulated genes in HD striatal tissue display characteristic signature that is conserved across mouse models, including knockin and transgenic mice, and also in post mortem brain tissues from HD patients [START_REF] Achour | Neuronal identity genes regulated by super-enhancers are preferentially down-regulated in the striatum of Huntington's disease mice[END_REF][START_REF] Kuhn | Mutant huntingtin's effects on striatal gene expression in mice recapitulate changes observed in human Huntington's disease brain and do not differ with mutant huntingtin length or wild-type huntingtin dosage[END_REF][START_REF] Langfelder | Integrated genomics and proteomics define huntingtin CAG length-dependent networks in mice[END_REF][START_REF] Luthi-Carter | Decreased expression of striatal signaling genes in a mouse model of Huntington's disease[END_REF][START_REF] Vashishtha | Targeting H3K4 trimethylation in Huntington disease[END_REF]. Specifically, down-regulated genes in HD striatum are enriched in neuronal function genes, particularly in genes that specify striatal identity [START_REF] Achour | Neuronal identity genes regulated by super-enhancers are preferentially down-regulated in the striatum of Huntington's disease mice[END_REF][START_REF] Hervás-Corpión | Early alteration of epigenetic-related transcription in Huntington's disease mouse models[END_REF][START_REF] Langfelder | Integrated genomics and proteomics define huntingtin CAG length-dependent networks in mice[END_REF][START_REF] Vashishtha | Targeting H3K4 trimethylation in Huntington disease[END_REF].

These genes include typical markers of mature MSNs, including dopamine D1 receptor (D1R), dopamine D2 receptor (D2R), RGS9, DARPP32… [START_REF] Francelle | Contribution of Neuroepigenetics to Huntington's Disease[END_REF]. Data analyses indicate that gene down-regulation in HD striatal tissue is not just the consequence of neuronal death [START_REF] Kuhn | Mutant huntingtin's effects on striatal gene expression in mice recapitulate changes observed in human Huntington's disease brain and do not differ with mutant huntingtin length or wild-type huntingtin dosage[END_REF]. Furthermore, mouse data generated at different time points, including presymptomatic age, suggest gene down-regulation in HD is an early process [START_REF] Langfelder | Integrated genomics and proteomics define huntingtin CAG length-dependent networks in mice[END_REF]. In contrast, upregulated genes in HD brain tissue are enriched in immune and developmental genes, and thus display distinct functional signature [START_REF] Achour | Neuronal identity genes regulated by super-enhancers are preferentially down-regulated in the striatum of Huntington's disease mice[END_REF][START_REF] Kuhn | Mutant huntingtin's effects on striatal gene expression in mice recapitulate changes observed in human Huntington's disease brain and do not differ with mutant huntingtin length or wild-type huntingtin dosage[END_REF][START_REF] Labadorf | Evidence of Extensive Alternative Splicing in Post Mortem Human Brain HTT Transcription by mRNA Sequencing[END_REF][START_REF] Langfelder | Integrated genomics and proteomics define huntingtin CAG length-dependent networks in mice[END_REF]. HD epigenomic signatures. Several epigenomic studies have been generated using brain tissues of HD mice and HD patients [START_REF] Achour | Neuronal identity genes regulated by super-enhancers are preferentially down-regulated in the striatum of Huntington's disease mice[END_REF][START_REF] Bai | Epigenetic dysregulation of hairy and enhancer of split 4 (HES4) is associated with striatal degeneration in postmortem Huntington brains[END_REF][START_REF] Dong | The Role of H3K4me3 in Transcriptional Regulation Is Altered in Huntington's Disease[END_REF][START_REF] Horvath | Huntington's disease accelerates epigenetic aging of human brain and disrupts DNA methylation levels[END_REF][START_REF] Mcfarland | Genome-wide histone acetylation is altered in a transgenic mouse model of Huntington's disease[END_REF][START_REF] Merienne | Cell-Type-Specific Gene Expression Profiling in Adult Mouse Brain Reveals Normal and Disease-State Signatures[END_REF][START_REF] Ng | Extensive changes in DNA methylation are associated with expression of mutant huntingtin[END_REF][START_REF] Valor | Genomic landscape of transcriptional and epigenetic dysregulation in early onset polyglutamine disease[END_REF][START_REF] Vashishtha | Targeting H3K4 trimethylation in Huntington disease[END_REF]. Histone acetylation, including H3K27ac, H3K9,14ac, H4K12ac and H2Aac, was a major focus in those studies. ChIP-seq analyses indicated that changes in H3K9,14ac and H4K12ac were limited in the hippocampus and cerebellum of the HD transgenic mouse N171-82Q, and did not particularly correlated with transcriptional changes [START_REF] Valor | Genomic landscape of transcriptional and epigenetic dysregulation in early onset polyglutamine disease[END_REF]. In contrast, extensive changes in H3K27ac were observed in the striatum of HD R6/1 transgenic mice, which correlated with RNAPII and transcriptional changes [START_REF] Achour | Neuronal identity genes regulated by super-enhancers are preferentially down-regulated in the striatum of Huntington's disease mice[END_REF][START_REF] Gras | Altered enhancer transcription underlies Huntington's disease striatal transcriptional signature[END_REF]. Similar results were found analyzing H3K27ac ChIPseq data generated using post mortem striatal tissue of HD patients at early symptomatic stage [START_REF] Merienne | Cell-Type-Specific Gene Expression Profiling in Adult Mouse Brain Reveals Normal and Disease-State Signatures[END_REF]. Although the bulk of striatal tissue was used in these studies, integrated analysis with cell type-specific transcriptomic striatal database allowed specifying the contribution of neurons and glial cells to H3K27ac changes: H3K27ac was depleted at neuronal super enhancers in HD vs controls, while it was increased at glial-specific enhancers (Figure 3). Moreover, those cell type-specific H3K27ac changes positively correlated with cell type-specific transcriptional changes, indicating that the HD mutation leads to opposite transcriptional and epigenetic reprogramming in neurons and glial cells [START_REF] Merienne | Cell-Type-Specific Gene Expression Profiling in Adult Mouse Brain Reveals Normal and Disease-State Signatures[END_REF]. Whether maintenance or acquisition of striatal cell identity is compromised in HD is an intriguing possibility that could underlie the mechanism.

HD promoter features were also investigated targeting H3K4me3, a mark enriched at active promoters [START_REF] Bai | Epigenetic dysregulation of hairy and enhancer of split 4 (HES4) is associated with striatal degeneration in postmortem Huntington brains[END_REF][START_REF] Dong | The Role of H3K4me3 in Transcriptional Regulation Is Altered in Huntington's Disease[END_REF][START_REF] Guiretti | Specific promoter deacetylation of histone H3 is conserved across mouse models of Huntington's disease in the absence of bulk changes[END_REF][START_REF] Vashishtha | Targeting H3K4 trimethylation in Huntington disease[END_REF]. ChIP-seq data generated using the striatum and cortex of HD R6/2 transgenic mice indicated that H3K4me3 was widely depleted at neuronal identity gene promoters, which displayed broad H3K4me3 profile, while genes showing increased H3K4me3 showed developmental signature [START_REF] Vashishtha | Targeting H3K4 trimethylation in Huntington disease[END_REF].

H3K4me3 was also investigated using post mortem prefrontal cortex from HD patients, a region however showing mild neuropathological involvement in HD [START_REF] Bai | Epigenetic dysregulation of hairy and enhancer of split 4 (HES4) is associated with striatal degeneration in postmortem Huntington brains[END_REF][START_REF] Dong | The Role of H3K4me3 in Transcriptional Regulation Is Altered in Huntington's Disease[END_REF].

These studies specifically analysed cortical neurons after nuclei sorting using fluorescently activated nuclei sorting (FANS), and identified hundreds of regions differentially enriched in H3K4me3 in HD vs control samples, which were preferentially depleted in H3K4me3. Although the connection between increased H3K4me3 and transcription in HD brain remains elusive, depleted H3K4me3 in HD vs control samples correlated with reduced transcription [START_REF] Dong | The Role of H3K4me3 in Transcriptional Regulation Is Altered in Huntington's Disease[END_REF].

Collectively, H3K4me3 and H3K27ac epigenomic data indicate that the HD mutation induces loss of activity of neuronal-specific enhancers and promoters implicated in the control of neuronal identity genes. Whether the HD mutation also affects activity-driven epigenetic regulation of neuronal-specific genes implicated in neuronal plasticity is yet unknown, since none of epigenomic studies above described were performed using behavioral paradigm challenging the brain.

Abnormal epigenetic aging vs development.

On the one hand, HD is an age-related disease that is progressive in nature and generally characterized by adult onset, which might suggest that epigenetic aging is altered in HD. This question was addressed assessing the epigenetic clock, which compares biological and chronological clocks through analysis of hundreds of defined DNA methylation sites [START_REF] Horvath | DNA methylation age of human tissues and cell types[END_REF]. Analysis of frontal lobe, parietal lobe and cingulate gyrus of HD patients revealed significant acceleration of epigenetic age [START_REF] Horvath | Huntington's disease accelerates epigenetic aging of human brain and disrupts DNA methylation levels[END_REF]. Moreover, a negative correlation was observed between CAG repeat length in HTT and the epigenetic age.

Although epigenetic age was not accelerated in striatal tissue of HD patients, likely due to neuronal loss, these data suggest that accelerated aging contributes to dysregulation of HD epigenome [START_REF] Horvath | Huntington's disease accelerates epigenetic aging of human brain and disrupts DNA methylation levels[END_REF]. Whether enhancers and/or promoters would be more particularly targeted by such a mechanism is an intriguing hypothesis.

On the other hand, increasing evidences indicate that HD comprises a neurodevelopmental component, likely due to partial loss of physiological neurodevelopmental function of normal HTT [START_REF] Barnat | Huntingtin-Mediated Multipolar-Bipolar Transition of Newborn Cortical Neurons Is Critical for Their Postnatal Neuronal Morphology[END_REF][START_REF] Mehler | Loss-of-Huntingtin in Medial and Lateral Ganglionic Lineages Differentially Disrupts Regional Interneuron and Projection Neuron Subtypes and Promotes Huntington's Disease-Associated Behavioral, Cellular, and Pathological Hallmarks[END_REF][START_REF] Molero | Selective expression of mutant huntingtin during development recapitulates characteristic features of Huntington's disease[END_REF][START_REF] Molero | Impairment of developmental stem cell-mediated striatal neurogenesis and pluripotency genes in a knock-in model of Huntington's disease[END_REF]. More specifically, several studies using human and mouse stem cells differentiated into neurons, including striatal-like cells, show that mutated HTT leads to defects in neuronal specification and maturation [START_REF] Conforti | Faulty neuronal determination and cell polarization are reverted by modulating HD early phenotypes[END_REF]HD iPSC Consortium, 2017;[START_REF] Molero | Impairment of developmental stem cell-mediated striatal neurogenesis and pluripotency genes in a knock-in model of Huntington's disease[END_REF][START_REF] Ring | Genomic Analysis Reveals Disruption of Striatal Neuronal Development and Therapeutic Targets in Human Huntington's Disease Neural Stem Cells[END_REF][START_REF] Ruzo | Chromosomal instability during neurogenesis in Huntington's disease[END_REF][START_REF] Smith-Geater | Aberrant Development Corrected in Adult-Onset Huntington's Disease iPSC-Derived Neuronal Cultures via WNT Signaling Modulation[END_REF].

Using induced pluripotent stem cells (iPSC) differentiated in MSN-like neurons showed delayed differentiation in the HD background, which correlated with altered epigenetic and transcriptional reprogramming (HD iPSC Consortium, 2017;[START_REF] Smith-Geater | Aberrant Development Corrected in Adult-Onset Huntington's Disease iPSC-Derived Neuronal Cultures via WNT Signaling Modulation[END_REF]. Specifically, persistent expression of developmental genes, including OCT4, was observed during striatal neuron differentiation of HD iPSCs, together with abnormal H3K27ac and H3K4me3 profiles, which reflected more immature neuronal state than in controls (HD iPSC Consortium, 2017;[START_REF] Smith-Geater | Aberrant Development Corrected in Adult-Onset Huntington's Disease iPSC-Derived Neuronal Cultures via WNT Signaling Modulation[END_REF]. Thus, abnormal epigenetic regulation during neurodevelopment might compromise proper acquisition of cellular identity of HD terminally differentiated neurons. It is possible, however, that HD-mediated epigenetic alterations during development render neurons more vulnerable to environemental stressors, which may be compensated during early life, but not at later stage, due to cellular aging. Thus, HD epigenetic neurodevelopmental and aging-related components may be related.

Dysregulation of epigenetic regulators by mutated HTT.

A number of studies have provided evidence for dysregulation of specific chromatin regulators in HD, which may contribute to disruption of HD epigenetic landscape. It was found in early studies that the HAT CBP is recruited in polyQ-HTT aggregates in HD neurons [START_REF] Nucifora | Interference by huntingtin and atrophin-1 with cbp-mediated transcription leading to cellular toxicity[END_REF][START_REF] Seredenina | What have we learned from gene expression profiles in Huntington's disease?[END_REF][START_REF] Steffan | Histone deacetylase inhibitors arrest polyglutamine-dependent neurodegeneration in Drosophila[END_REF]. Since H3K27ac is a bona-fide target of CBP [START_REF] Tie | Trithorax monomethylates histone H3K4 and interacts directly with CBP to promote H3K27 acetylation and antagonize Polycomb silencing[END_REF], titration of CBP by HD neuronal aggregates could lead to neuronal-specific depletion of H3K27ac. Noticeably however, mutant HTT aggregate formation is a rather late event with respect to HD pathogenesis. Thus, sequestration of CBP in polyQ-HTT aggregates is unlikely to explain epigenetic dysregulation during neuronal differentiation. Nonetheless, a numbers of studies indicate that targeting histone acetylation in HD is beneficial, at least in animal models [START_REF] Butler | Histone deacetylase inhibitors as therapeutics for polyglutamine disorders[END_REF][START_REF] Francelle | Contribution of Neuroepigenetics to Huntington's Disease[END_REF]. Specifically, several histone deacetylase inhibitors (HDACi) have been used to treat HD mice and drosophila models, which led to partial recovery of HD-like phenotypes [START_REF] Ferrante | Histone deacetylase inhibition by sodium butyrate chemotherapy ameliorates the neurodegenerative phenotype in Huntington's disease mice[END_REF][START_REF] Gardian | Neuroprotective effects of phenylbutyrate in the N171-82Q transgenic mouse model of Huntington's disease[END_REF][START_REF] Hockly | Suberoylanilide hydroxamic acid, a histone deacetylase inhibitor, ameliorates motor deficits in a mouse model of Huntington's disease[END_REF][START_REF] Jia | The Effects of Pharmacological Inhibition of Histone Deacetylase 3 (HDAC3) in Huntington's Disease Mice[END_REF][START_REF] Naia | Histone Deacetylase Inhibitors Protect Against Pyruvate Dehydrogenase Dysfunction in Huntington's Disease[END_REF][START_REF] Siebzehnrübl | Early postnatal behavioral, cellular, and molecular changes in models of Huntington disease are reversible by HDAC inhibition[END_REF][START_REF] Steffan | Histone deacetylase inhibitors arrest polyglutamine-dependent neurodegeneration in Drosophila[END_REF][START_REF] Suelves | A selective inhibitor of histone deacetylase 3 prevents cognitive deficits and suppresses striatal CAG repeat expansions in Huntington's disease mice[END_REF][START_REF] Thomas | The HDAC inhibitor 4b ameliorates the disease phenotype and transcriptional abnormalities in Huntington's disease transgenic mice[END_REF]. Interestingly enough, the HDACi LBH589 improved HD neuronal differentiation [START_REF] Siebzehnrubl | Histone deacetylase inhibitors increase neuronal differentiation in adult forebrain precursor cells[END_REF][START_REF] Siebzehnrübl | Early postnatal behavioral, cellular, and molecular changes in models of Huntington disease are reversible by HDAC inhibition[END_REF]. However, since no epigenomic data have been generated on HDACi treated animals, it is unclear whether histone acetylation is restored at neuronal super enhancers upon treatment. Moreover, the few transcriptomic data do not support complete rescue of neuronal identity gene transcription, and rather suggest that HDACi modulate metabolic genes [START_REF] Naia | Histone Deacetylase Inhibitors Protect Against Pyruvate Dehydrogenase Dysfunction in Huntington's Disease[END_REF]). Yet, in mature neurons, histone acetylation is critical to activity-driven transcription, i.e. to the dynamic regulation of plasticity genes in response to neural stimulation. Thus, it would be interesting to test whether compounds that target histone acetylation affect activity-driven genes in the context of HD.

Additional pieces of evidence indicate that protein complexes and/or enzymes facilitating repressive chromatin are activated by the HD mutation, which could impair the balance between euchromatin and heterochromatin. For example, the activity of polycomb repressive complex 2 (PRC2) was enhanced by mutant HTT, and during neuronal differentiation, HTT was required for proper regulation of H3K27me3, a PRC2 target, enriched in facultative heterochromatin [START_REF] Biagioli | Htt CAG repeat expansion confers pleiotropic gains of mutant huntingtin function in chromatin regulation[END_REF][START_REF] Seong | Huntingtin facilitates polycomb repressive complex 2[END_REF][START_REF] Song | Systematic genetic interaction studies identify histone demethylase Utx as potential target for ameliorating Huntington's disease[END_REF]. However, the effect of mutant HTT on H3K27me3 in mature neurons remains elusive. Other studies showed that the histone H3K9 methylase ESET/SETDB1 was increased in the striatum of HD transgenic mice, a feature correlating with dysregulation of H3K9me3, a marker of constitutive heterochromatin [START_REF] Lee | Remodeling of heterochromatin structure slows neuropathological progression and prolongs survival in an animal model of Huntington's disease[END_REF][START_REF] Ryu | ESET/SETDB1 gene expression and histone H3 (K9) trimethylation in Huntington's disease[END_REF]. Underlying mechanism might involve impaired interaction between mutant HTT and ATF7IP-ESET/SETDB1 complex [START_REF] Irmak | Mechanism suppressing H3K9 trimethylation in pluripotent stem cells and its demise by polyQ-expanded huntingtin mutations[END_REF]. Finally, using a genetic screen in a drosophila model system indicated that HTT physiological function includes chromatin re-organization through regulation of H3 methylation at heterochromatin-euchromatin boundaries [START_REF] Dietz | The Drosophila Huntington's disease gene ortholog dhtt influences chromatin regulation during development[END_REF]. While these studies support the notion that HTT is an epigenetic regulator contributing to reprogramming of facultative and/or constitutive heterochromatin during neurodevelopment, the direct effect of mutant HTT on repressive histone marks in mature neurons and their impact on transcriptional regulation remains unclear.

Epigenetic dysregulation and enhancer regulation in AD

Etiology and neuropathology of AD. AD is an aging-related neurodegenerative disease characterized by the accumulation of amyloid beta peptides (Aβ) and neurofibrillary tangles, which are composed of abnormally phosphorylated Tau protein. AD leads to progressive synaptic and neuronal loss, most particularly in the prefrontal cortex and hippocampus, thereby resulting in memory decline [START_REF] Serrano-Pozo | Neuropathological alterations in Alzheimer disease[END_REF]. Neuroinflammatory response is also a major hallmark of AD. A minority of cases, usually characterized by early onset (i.e. <65 years), is caused by mutations in genes implicated in Aβ processing, including APP and presinilins. However, the vast majority of cases is sporadic (>95%) and late onset, and results from more complex etiology implicating both environmental and genetic risk factors. While aging is the strongest environmental risk factor, GWAS studies revealed several genetic risk variants, including variants associated with APOE and BIN1 [START_REF] Bellenguez | Genetics of Alzheimer's disease: where we are, and where we are going[END_REF][START_REF] Jansen | Genome-wide meta-analysis identifies new loci and functional pathways influencing Alzheimer's disease risk[END_REF].

Brain enhancers, hotspots for AD-risk variants.

Consistent with AD pathogenesis, genes associated to AD-risk variants are enriched in 4 major functions, including Aβ formation, tau, lipid metabolism and immune response [START_REF] Jansen | Genome-wide meta-analysis identifies new loci and functional pathways influencing Alzheimer's disease risk[END_REF]. Thus, it is believed that risk variants play causal role, modulating transcription of associated genes [START_REF] Grubman | A single-cell atlas of entorhinal cortex from individuals with Alzheimer's disease reveals cell-type-specific gene expression regulation[END_REF][START_REF] Jansen | Genome-wide meta-analysis identifies new loci and functional pathways influencing Alzheimer's disease risk[END_REF][START_REF] Klein | The epigenome in Alzheimer's disease: current state and approaches for a new path to gene discovery and understanding disease mechanism[END_REF][START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. However, the interpretation of risk variants remains elusive in many instances, since they are often located in non-coding regions of the genome that may be distant to the gene(s) they modulate [START_REF] Maurano | Systematic localization of common disease-associated variation in regulatory DNA[END_REF][START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. Analysis of GWAS catalog database showed that nearly 30% of non-coding AD SNPs are located in enhancers, with 95% of the AD SNPs located in enhancers co-localizing with their expressed quantitative trait locus (eQTL) genes in TADs [START_REF] Kikuchi | Enhancer variants associated with Alzheimer's disease affect gene expression via chromatin looping[END_REF]. Epigenome-wide studies using post mortem brain tissues of AD patients further point to a critical role for enhancers in AD-risk variants, since differential DNA methylation patterns between AD and control individuals were enriched at enhancers (De Jager et al., 2014;[START_REF] Li | Epigenetic dysregulation of enhancers in neurons is associated with Alzheimer's disease pathology and cognitive symptoms[END_REF][START_REF] Lunnon | Methylomic profiling implicates cortical deregulation of ANK1 in Alzheimer's disease[END_REF]. The role of enhancers and DNA methylation in mediating the effect of risk factors in AD was further supported by a study showing that the AD-risk associated haplotype at PM20D1 locus leads to altered enhancer-promoter interaction in a CTCFdependent manner (Sanchez-Mut et al., 2018) (Figure 4).

The heterogeneity of cerebral tissues represents another limitation to the interpretation of risk variants, especially since increasing evidence indicates that functional consequences of risk variants are cell type-specific [START_REF] Yeh | TREM2, Microglia, and Neurodegenerative Diseases[END_REF][START_REF] Tansey | Genetic risk for Alzheimer's disease is concentrated in specific macrophage and microglial transcriptional networks[END_REF][START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. Network analysis of bulk AD brain transcriptome indicated gain of microglial gene connectivity and loss of neuronal connectivity [START_REF] Zhang | Integrated systems approach identifies genetic nodes and networks in late-onset Alzheimer's disease[END_REF]. Moreover, studies using single-nucleus/cell RNA sequencing on AD and control cortices provided additional insights, showing that APOE is upregulated in an AD-specific microglial subpopulation, while repressed in AD oligodendrocyte progenitor cells and astrocyte subpopulations [START_REF] Grubman | A single-cell atlas of entorhinal cortex from individuals with Alzheimer's disease reveals cell-type-specific gene expression regulation[END_REF][START_REF] Mathys | Author Correction: Single-cell transcriptomic analysis of Alzheimer's disease[END_REF]. To interpret the effects of AD risk variants in cell type-specific manner, Nott et al. performed cell typespecific epigenomic analysis using human resected cortical brain tissues and found that microgliaspecific enhancers were more particularly enriched in AD risk variants [START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. Using proximity ligation assisted ChIP-seq (PLAC-seq) to establish cell type-specific enhancer-promoter interactome maps and CRISPR/Cas9 technology, they further showed that risk variant rs6733839, the second highest AD-risk variant, is located in microglia enhancer controlling microglia-specific transcription of BIN1 [START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. Thus, increasing evidence indicates that brain-specific enhancers, most particularly microglial-specific enhancers, are hotspots for genetic and/or epigenetic variations in AD, thereby contributing to AD pathogenesis in cell type-specific manner (De Jager et al., 2014;[START_REF] Jansen | Genome-wide meta-analysis identifies new loci and functional pathways influencing Alzheimer's disease risk[END_REF][START_REF] Kikuchi | Enhancer variants associated with Alzheimer's disease affect gene expression via chromatin looping[END_REF][START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF].

Genome-wide scale enhancer dysregulation in AD.

Several studies indicate disruption of transcriptional enhancers in AD brain tissue, correlating with transcriptional alterations [START_REF] Benito | HDAC inhibitor-dependent transcriptome and memory reinstatement in cognitive decline models[END_REF][START_REF] Chatterjee | Reinstating plasticity and memory in a tauopathy mouse model with an acetyltransferase activator[END_REF][START_REF] Gjoneska | Conserved epigenomic signals in mice and humans reveal immune basis of Alzheimer's disease[END_REF][START_REF] Klein | The epigenome in Alzheimer's disease: current state and approaches for a new path to gene discovery and understanding disease mechanism[END_REF][START_REF] Li | Epigenetic dysregulation of enhancers in neurons is associated with Alzheimer's disease pathology and cognitive symptoms[END_REF][START_REF] Marzi | A histone acetylome-wide association study of Alzheimer's disease identifies disease-associated H3K27ac differences in the entorhinal cortex[END_REF]. First evidence came from studies using AD mouse models [START_REF] Benito | HDAC inhibitor-dependent transcriptome and memory reinstatement in cognitive decline models[END_REF][START_REF] Gjoneska | Conserved epigenomic signals in mice and humans reveal immune basis of Alzheimer's disease[END_REF]. Transcriptomic and epigenomic profiling using the hippocampus of CK-p25 mouse model, showing amyloid and tau pathologies, revealed coordinated downregulation of synaptic plasticity genes and associated enhancers and promoters and, in contrast, upregulation of immune response genes and regulatory regions [START_REF] Gjoneska | Conserved epigenomic signals in mice and humans reveal immune basis of Alzheimer's disease[END_REF]. H3K27ac and H3K4me3 were reduced at neuronal-specific enhancers and promoters, respectively, which correlated with down-regulation of their target genes, whereas the direction of epigenetic and transcriptional changes at glial-specific regulatory regions/genes was opposite [START_REF] Gjoneska | Conserved epigenomic signals in mice and humans reveal immune basis of Alzheimer's disease[END_REF]. Consistently, decreased and increased-level regulatory regions were enriched in distinct DNA motifs, recognized by neuronal-and glial-specific transcriptional regulators, respectively [START_REF] Gjoneska | Conserved epigenomic signals in mice and humans reveal immune basis of Alzheimer's disease[END_REF]. H3K27ac profiling of AD post-mortem entorhinal cortex samples supported mouse data, showing that enhancer dysregulation is a major hallmark of AD brain [START_REF] Marzi | A histone acetylome-wide association study of Alzheimer's disease identifies disease-associated H3K27ac differences in the entorhinal cortex[END_REF]. Comparing samples of AD patients vs control individuals, thousands of genes were identified that associated with hyper-or hypo-acetylated peaks, and the direction of change in acetylation positively correlated with transcriptional changes [START_REF] Marzi | A histone acetylome-wide association study of Alzheimer's disease identifies disease-associated H3K27ac differences in the entorhinal cortex[END_REF]. Gene ontology analysis further indicated that genes nearby increased H3K27ac in AD samples were enriched in metabolic/glial functions, while neuronal processes associated with regions depleted in H3K27ac [START_REF] Marzi | A histone acetylome-wide association study of Alzheimer's disease identifies disease-associated H3K27ac differences in the entorhinal cortex[END_REF]. This suggests that AD, similar to HD, leads to opposite H3K27ac changes at neuronal-and glial-specific enhancers. Although super enhancers and identity genes have not been specifically investigated in AD studies, one cannot exclude that comparable genome-wide scale reprogramming of neuronal and glial cell identity operates in AD and HD brains.

Comprehensive fine-mapping of DNA methylation further suggests a crucial role for enhancer dysregulation in AD neuronal pathogenesis, since thousands of differentially methylated enhancers were identified in neurons isolated from prefrontal cortex of AD patients vs control individuals [START_REF] Li | Epigenetic dysregulation of enhancers in neurons is associated with Alzheimer's disease pathology and cognitive symptoms[END_REF]. Surprisingly however, most of these regions were hypomethylated non-CpG sites (e.g. CpH sites), a result that correlated with increased transcriptional activity of closest genes [START_REF] Li | Epigenetic dysregulation of enhancers in neurons is associated with Alzheimer's disease pathology and cognitive symptoms[END_REF].

The role of these non-canonical methylation sites in AD is yet to be uncovered. Finally, changes in additional histone modifications, particularly histone acetylation, including H3K9ac, H3K14ac, H4K5ac, H4K12ac, H4K16ac and H2Bac were also observed in brain tissues of AD mouse models and/or post mortem AD brain cells. While it is not clear whether those acetylation changes were enriched in specific regulatory regions, these results indicate a degree of complexity of AD epigenetic signature [START_REF] Benito | HDAC inhibitor-dependent transcriptome and memory reinstatement in cognitive decline models[END_REF][START_REF] Chatterjee | Reinstating plasticity and memory in a tauopathy mouse model with an acetyltransferase activator[END_REF][START_REF] Gräff | An epigenetic blockade of cognitive functions in the neurodegenerating brain[END_REF][START_REF] Klein | Epigenome-wide study uncovers large-scale changes in histone acetylation driven by tau pathology in aging and Alzheimer's human brains[END_REF][START_REF] Nativio | Publisher Correction: Dysregulation of the epigenetic landscape of normal aging in Alzheimer's disease[END_REF]. Collectively, those epigenomic data show that AD leads to significant cell type-specific epigenetic dysregulation of brain enhancers. While histone acetylation remains a major focus in AD epigenomic studies, H3K4me3 was found dysregulated in AD mice, indicating that epigenetic regulation of promoters might also be impaired in AD [START_REF] Gjoneska | Conserved epigenomic signals in mice and humans reveal immune basis of Alzheimer's disease[END_REF][START_REF] Kerimoglu | KMT2A and KMT2B Mediate Memory Function by Affecting Distinct Genomic Regions[END_REF].

Epigenetic control of activity-regulated genes in AD.

The dynamic epigenetic control of gene program regulating neuronal plasticity is critical to memory formation and maintenance, and histone acetylation plays a central role in this mechanism [START_REF] Yap | Activity-Regulated Transcription: Bridging the Gap between Neural Activity and Behavior[END_REF]. Several studies suggest that altered regulation of histone acetylation contributes to memory decline in AD (Fischer, 2014a).

Early study revealed that histone deacetylase 2 (HDAC2) was increased at neural plasticity genes, both in brain tissues of AD mice and in post-mortem brains from AD patients [START_REF] Gräff | An epigenetic blockade of cognitive functions in the neurodegenerating brain[END_REF].

Consequently, AD mice were treated with HDAC inhibitors (HDACi), which generally improved memory function and, when tested, also ameliorated synaptic plasticity [START_REF] Fischer | Targeting histone-modifications in Alzheimer's disease. What is the evidence that this is a promising therapeutic avenue?[END_REF][START_REF] Gräff | An epigenetic blockade of cognitive functions in the neurodegenerating brain[END_REF]. Interestingly enough, memory function and synaptic plasticity were restored in tauopathic mice treated with an activator of the HAT CBP/P300, the compound CSP-TTK21 [START_REF] Chatterjee | Reinstating plasticity and memory in a tauopathy mouse model with an acetyltransferase activator[END_REF][START_REF] Chatterjee | A novel activator of CBP/p300 acetyltransferases promotes neurogenesis and extends memory duration in adult mice[END_REF]. Epigenomic and transcriptomic analyses using the dorsal hippocampus of tauopathic mice further showed that functional amelioration associated with transcriptional rescue of activityregulated genes and increased H2B acetylation at CBP-regulated enhancers, while H3K27Ac remained unchanged [START_REF] Chatterjee | Reinstating plasticity and memory in a tauopathy mouse model with an acetyltransferase activator[END_REF]. In addition, CBP levels were decreased in the hippocampus of tauopathic mice as well as in postmortem prefrontal cortices of AD patients [START_REF] Bartolotti | Diminished CRE-Induced Plasticity is Linked to Memory Deficits in Familial Alzheimer's Disease Mice[END_REF][START_REF] Schueller | Dysregulation of histone acetylation pathways in hippocampus and frontal cortex of Alzheimer's disease patients[END_REF], suggesting a role for CBP in dysregulation of these genes [START_REF] Chatterjee | Reinstating plasticity and memory in a tauopathy mouse model with an acetyltransferase activator[END_REF], an hypothesis supported by an earlier study showing that gene transfer delivery of CBP in the hippocampus of AD mice improves memory processes [START_REF] Caccamo | CBP gene transfer increases BDNF levels and ameliorates learning and memory deficits in a mouse model of Alzheimer's disease[END_REF].

Epigenetic aging in AD.

Altered epigenetic aging may be another mechanism driving epigenetic defects in the AD brain. Whether epigenetic aging is accelerated and/or dysregulated was recently addressed through epigenomic studies using post mortem brain tissues of AD patients [START_REF] Li | Epigenetic dysregulation of enhancers in neurons is associated with Alzheimer's disease pathology and cognitive symptoms[END_REF][START_REF] Nativio | Publisher Correction: Dysregulation of the epigenetic landscape of normal aging in Alzheimer's disease[END_REF]. Investigating H4K16ac, a promoter mark linked to DNA damage repair and increased in senescent cells [START_REF] Dang | Histone H4 lysine 16 acetylation regulates cellular lifespan[END_REF][START_REF] Kozak | Inactivation of the Sas2 histone acetyltransferase delays senescence driven by telomere dysfunction[END_REF], Nativio et al. identified 3 types of changes in the lateral lobe of AD patients: disease-specific changes were observed in AD patients vs age-matched individuals, age-dysregulated changes were observed in aged vs young individuals but not in AD vs young individuals, and age-regulated changes were observed in both aged control and AD individuals [START_REF] Nativio | Publisher Correction: Dysregulation of the epigenetic landscape of normal aging in Alzheimer's disease[END_REF]. Interestingly, disease-specific changes affected genes enriched in neuronal functions, while age-dysregulated changes implicated immunity and stress response genes, reflecting glial responses. Age-dysregulated changes were predominantly characterized by agedependent increase in H4K16ac in control individuals, but age-dependent H4K16ac depletion in AD individuals, suggesting AD leads to dysregulated aging and is not simply accelerated aging [START_REF] Nativio | Publisher Correction: Dysregulation of the epigenetic landscape of normal aging in Alzheimer's disease[END_REF]. However, cell type-specific epigenomic analysis focusing on H4K12ac indicated agingrelated acceleration of decreased H4K12ac in hippocampal neurons of AD mice modeling amyloid pathology, and the mechanism correlated with down-regulation of target genes, which were enriched in neuronal plasticity genes [START_REF] Benito | HDAC inhibitor-dependent transcriptome and memory reinstatement in cognitive decline models[END_REF]. Also, using the epigenetic clock, Li et al. found that neurons of advanced AD cases show significant acceleration of epigenetic aging [START_REF] Li | Epigenetic dysregulation of enhancers in neurons is associated with Alzheimer's disease pathology and cognitive symptoms[END_REF]. Thus, current studies provide rather complex picture of the interplay between AD and epigenetic aging. Undoubtedly, investigating the impact of aging on additional epigenetic marks, including H3K27ac, and at cell type-specific resolution should help refine the conclusions and specify the role of epigenetic aging in AD. It is noteworthy that H3K27ac was found to be a key predictor of age-related transcriptional changes in various mammalian tissues [START_REF] Benayoun | Remodeling of epigenome and transcriptome landscapes with aging in mice reveals widespread induction of inflammatory responses[END_REF]. Finally, recent evidence suggests that tau-related alteration induce widespread reorganization of chromatin architecture and TADs, which could contribute to aging-related mechanisms [START_REF] Klein | Epigenome-wide study uncovers large-scale changes in histone acetylation driven by tau pathology in aging and Alzheimer's human brains[END_REF].

Remarkably, neurons appear to be more specifically affected by the mechanism [START_REF] Klein | Epigenome-wide study uncovers large-scale changes in histone acetylation driven by tau pathology in aging and Alzheimer's human brains[END_REF].

Altered maintenance and regulation of heterochromatin due to pathologically phosphorylated tau would be the driving force, through impairment of nuclear lamina organization [START_REF] Chang | Cdk5 is a major regulator of p38 cascade: relevance to neurotoxicity in Alzheimer's disease[END_REF][START_REF] Klein | Epigenome-wide study uncovers large-scale changes in histone acetylation driven by tau pathology in aging and Alzheimer's human brains[END_REF][START_REF] Mansuroglu | Loss of Tau protein affects the structure, transcription and repair of neuronal pericentromeric heterochromatin[END_REF].

Several mechanisms might contribute to large-scale dysregulation of epigenetic landscape in AD. Yet, is is unclear whether enhancer dysregulation is a primary defect driving other epigenetic changes or is secondary to earlier mechanisms.

Conclusions and perspectives

Epigenomic and transcriptomic data generated on animal models and tissues from HD and AD patients revealed epigenetic changes in affected brain tissues, for both diseases. Remarkably, despite different etiologies between HD and AD, current data indicate that HD and AD pathogeneses associate with large-scale dysregulation of enhancers and promoters, which positively correlates with transcriptional alterations. Although additional studies are required to specify temporal dynamics, spatial chromatin re-organization and cell type-specificity of changes at HD/AD enhancers and promoters, a picture emerges from current data. Neuronal-and glial-specific regulatory regions and their associated genes show lower and increased activities, respectively, in disease vs control brains, which might contribute to loss of neuronal function and inflammatory responses, two major pathological hallmarks. Microglial enhancers appear more specifically dysregulated in AD, whereas HD data indicate that neuronal super enhancers are particularly vulnerable, suggesting loss of neuronal identity in HD brain. Yet, the role for super enhancers in AD remains unclear. However, the regulation of activity-driven regulatory regions and their associated genes is impaired in AD, supporting the notion that dynamic regulation of neuronal activity is more specifically altered in AD.

Intriguing studies suggest that epigenetic alterations in HD/AD might interplay with epigenetic aging, which may be accelerated and/or dysregulated. Moreover, HD studies using ESCs or iPSCs suggest early epigenetic dysregulation originating from abnormal neurodevelopmental process.

In fact, a unifying mechanism that would underlie epigenetic defects in HD or AD remains to be uncovered, despite studies indicating that the regulation of specific chromatin regulators -that may be common to both diseases, e.g. CBP-is impaired in HD and/or AD. Understanding the mechanism(s) driving epigenetic dysregulation is a current challenge, with potentially major therapeutic implications.

Major limitations to take up the challenge include the brain complexity and the difficulty to address causal relationships between epigenetic changes and functional consequences. However, the current development of innovative deep sequencing methods, together with new genome editing tools and behavioral paradigms allowing to characterize and manipulate epigenomic and transcriptomic signatures of particular neural cell populations in specific activation states and at single cell resolution will undoubtedly overcome these issues [START_REF] Grubman | A single-cell atlas of entorhinal cortex from individuals with Alzheimer's disease reveals cell-type-specific gene expression regulation[END_REF][START_REF] Liu | Editing the Epigenome to Tackle Brain Disorders[END_REF]. Also, advanced methods (e.g. Hi-C) to establish 3D maps of enhancer-promoter interactions in vivo at genome-wide and cell type-specific levels will be critical to decipher causal roles of enhancers in neurodegenerative diseases [START_REF] Nott | Brain cell type-specific enhancer-promoter interactome maps and disease-risk association[END_REF]. Finally, the generation of multi-omic atlas and databases using diseased brains together with the development of bioinformatics methods will also be essential to provide comprehensive picture and build accurate models with predictive or instructive values [START_REF] Jager | A multi-omic atlas of the human frontal cortex for aging and Alzheimer's disease research[END_REF]Gosselin Science 2017). Yet, brain tissue availability from individuals at early disease stages, including pre-symptomatic and prodromal stages, represents a limitation to assess early temporal dynamics of epigenetic and transcriptional changes. In this context, mouse models will remain instrumental. Scheme representing the dynamics of chromatin changes at activity-driven genes, including early and late response genes (ERG and LRG, respectively), in response to neural stimulation. In top panels, from the left to the right, the pictures illustrate physiological neuronal state, starting with basal condition (left), followed by early state of neuronal activation (middle) and ending with late stage of neuronal activation (right), leading to neuronal plasticity. At the molecular level (bottom panels), the induction of ERGs is a crucial event initiating neuronal transcriptional cascade leading to the induction of LRGs implicated in synaptic plasticity. In basal condition (bottom, left panel), ERG promoters already display transcriptionally active features, including the binding of transcription factors (TFs) such as CREB and SRF/ELK1, RNAPII and chromatin loop formation components such as CTCF and cohesin, but also the histone lysine deacetylase 2 (HDAC2), which negatively regulates their expression. Upon neuronal activation, chromatin re-arrangement allow for a proper enhancerpromoter interaction and the histone acetyltransferase CBP is recruited, increasing the levels of H3K27ac (green circles). Altogether, these chromatin changes lead to the transition of RNAPII from a paused state to a transcriptional elongating state, ensuring the induction of ERGs. At late stages of neuronal activation (bottom right), the coordinated activity of ERGs and cell-type specific factors (CTSF) orchestrate the chromatin remodelling of late response gene (LRGs) promoters, triggering their expression and contributing to the final transcriptional wave enriched in synaptic plasticity genes.

Figure 1 .

 1 Figure 1. Regulation of brain cell-identity through super-enhancers. a, schematic representations of super-enhancer-regulated gene (top), conventional enhancer-regulated gene (middle) and repressed gene (bottom). Super-enhancers consist of dense clusters of enhancers and are highly enriched in H3K27ac (green circle), RNAPII and transcription factors (TF), including the mediator and cell typespecific TFs. Super-enhancers regulate genes that define cell-type specific identity and function. In contrast, conventional enhancers display more discrete features. Finally, repressed genes are enriched in histone modifications associated with compact chromatin state (red circles), such as H3K9me3 and/or H3K27me3, leading to the inability to recruit transcription factor and form RNAPII complexes. b, schematic representation of cell type-specific epigenetic signature of striatal super enhancers. The striatum comprises different cell types, including neurons (purple) and glial cells (green), expressing cellular identity genes regulated by super-enhancers. Identity genes may be neuronal-specific or glial-specific (e.g. neuronal SE, glial SE). The picture is even more complex since different subpopulations of neurons and glial cells are present in the mammalian striatum, expressing each specific subsets of cellular identity genes, controlled by specific super enhancers (for example D1 and D2 MSNs as compared to calretinin (Calb2) expressing interneurons, astrocytes expressing S100b, oligodendrocytes expressing the myelin basic protein (Mbp) or microglia expressing Cx3cr1).

Figure 2 .

 2 Figure 2. Neuronal activity modulation of chromatin loops in early and late response genes.

Figure 3 .

 3 Figure3. Cell type-specific dysregulation of super-enhancers in HD. Scheme illustrating epigenetic signatures in HD striatum. Super-enhancers regulating neuronal identity genes (purple) and glial identity genes (green) are differentially impaired in HD. In control striatum (top panels), both neuronal and glial super-enhancer regulated genes are highly enriched in H3K27ac (green circles), leading to extensive promoter-enhancer interactions and high transcriptional rates. In HD striatum (bottom panels), neuronal super-enhancers (bottom left panel) are depleted in H3K27ac, correlating with down-regulation of neuronal identity genes. In contrast, glial super-enhancers in HD (bottom right panel) show increased H3K27ac, associated with increased transcription.

Figure 4 .

 4 Figure 4. Disruption of promoter-enhancer chromatin loop at AD risk variant. On the left, an illustration of how Genome Wide Association Studies (GWAS), based on the comparison of Single Nucleotide Polymorphisms (SNPs, horizontal stripes) enriched in thousands of individuals corresponding to a healthy reference group (CTRL, grey) or presenting Alzheimer's disease (AD, red) can identify disease-associated risk variants (yellow horizontal stripes). On the right, a scheme

Acknowledgements

This work was supported by the Agence Nationale de la Recherche (ANR-2017-CE12-0027), the Centre National de la Recherche Scientifique (CNRS) and the University of Strasbourg. R.A.V. was supported by post-doctoral IDEX fellowship from University of Strasbourg. A.A. was recipient of doctoral fellowships from the Association Huntington France (AHF).


Olivier Bodart
email: olivier.bodart@univ-st-etienne.fr

Valérie Cayol
email: v.cayol@opgc.fr

Farshid Dabaghi
email: farshid.dabaghi@univ-st-etienne.fr

Jonas Koko
email: jonas.koko@uca.fr

Oliver Bodart

Oliver Bodart

Fictitious domain method for an inverse problem in volcanoes

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

General framework and problem setting

Problems in volcanology often involve elasticity models in presence of cracks (see e.g. [START_REF] Cayol | Magma sources involved in the 2002 Nyiragongo eruption, as inferred from an insar analysis[END_REF]). Most of the time the force exerted on the crack is unknown, and the position and shape of the crack are also frequently unknown or partially known (see e.g. [START_REF] Fukushima | Finding realistic dike models from interferometric synthetic aperture radar data: The february 2000 eruption at piton de la fournaise[END_REF]). Most of the time the model is approximated via boundary element methods.These methods are quite convenient to take into account the crack since the problem is then reformulated into an external problem where the crack is the only object to be meshed. However these methods do not allow to take the heterogeneity and/or the anisotropy of the medium into account. Another drawback is that, when it comes to identifying the shape and/or location of the crack, the variation of the latter implies a remeshing and assembling of all the matrices of the problem.

Using a domain decomposition technique then appears as the natural solution to these problems. In [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF], a first step was made with the development of a direct solver implementing a domain decomposition method. The present work represents a step further with the use of such a solver, which has been improved since the publication of [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF], to solve inverse problems in the field of earth sciences. To our knowledge, this is the first work using these kind of techniques in this field of application. The next step of our project will be the shape optimization problem to identify the shape and location of the crack.

Let Around the crack, Ω is split into Ω -and Ω + . The deformation field of the solid is supposed to satisfy the following elastostatic system:

Ω
               Find u ∈ H 1 (Ω \ Γ C ) such that : -div σ(u) = f in Ω \ Γ C , u = 0 in Γ D , σ(u) • n = 0 on Γ N , σ(u) • n ± = pn ± on Γ C . ( 1
)
where n is the outward unit normal to its boundaries. Typically in such a situation, Γ N is the ground surface and free to move. Practically, the displacement field can be observed on Γ N , whereas the pressure p exerted on the crack is unknown most of the time.

Consider the following function defined on L 2 (Γ C ):

J(p) := 1 2 ΓN (u -u d )C -1 (u -u d ) T dΓ N + α 2 p 2 L 2 (ΓC) , (2)
where u d ∈ L 2 (Γ N ) is the measured displacement field and u is the solution of (1) associated with p. Moreover, the matrix C is the covariance operator of the measurements uncertainties, and is assumed to be positive definite (see e.g. [START_REF] Tarantola | Inverse Problem Theory and Methods for Model Parameter Estimation[END_REF]), and finally α > 0 is a regularization parameter. The aim of this work is to study the following problem, of optimal control type:

min p∈L 2 (ΓC) J(p). (3)
The paper is organized as follows : the next section will be devoted to the presentation of the domain decomposition method and its discretization. Section 3 gives the optimality conditions for the problem (3) and establishes their discrete version. A special focus will be made on the adaptation of the problem to a domain decomposition formulation. Finally we present a relevant numerical test in section 4 and discuss the next steps of our project.

Domain decomposition : the direct solver

To solve the direct problem (1), we use a domain decomposition method. More precisely, following [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF], the domain Ω is split into two subdomains such that each point of the domain lies on one side of the crack or on the crack. Moreover, the global unknown solution u is decoupled in two sub-solutions for each side of the crack. For this purpose, we are using an artificial extension of the considered crack Γ C (e.g. Γ 0 in Figure 1). Therefore, instead of the crack

Γ + D Ω - Ω + Γ + N Γ - D Γ - D Γ 0 Γ + D Γ - N Γ 0 n + Γ C n -
Fig. 1 Splitting the volcanic cracked domain problem (1), we have to solve two Neumann-type boundary problems such that for each problem we impose a pressure on Γ C , which is more convenient from both theoretical and numerical points of view. More precisely we solve the following system:

                       Find u ∈ H 1 (Ω) such that : -div σ(u ± ) = f ± in Ω ± , u ± = 0 on Γ D ∩ ∂Ω ± , (σ(u) • n) ± = 0 on Γ N ∩ ∂Ω ± , (σ(u) • n) ± = pn ± on Γ C , u = 0 on Γ 0 , σ(u) • n + = 0 on Γ 0 , (4)
where u + = u |Ω + and u -= u |Ω -, and v denotes the jump of v across Γ 0 . The two last conditions in (4) enforce the continuity of displacement and stress across Γ 0 . Notice that the boundary conditions on Γ 0 ensure the construction of a global displacement field in H 1 (Ω \ Γ C ) solving the original problem (1). Let us define the following Hilbert spaces

V ± = {v ∈ H 1 (Ω ± ) | v = 0 on Γ D ∩ ∂Ω ± }, W = (H 1 2 (Γ 0 )).
and their dual spaces V ± and W , endowed with their usual norms. Prescribing the continuity of displacement across the Γ 0 via a Lagrangian formulation, the mixed weak formulation of Problem (4) reads as follows:

     Find u ± ∈ V ± and λ ∈ W such that : a(u ± , v ± ) ± b(λ, v ± ) = l ± (v ± ) ∀v ± ∈ V ± , b(µ, u ) = 0 ∀µ ∈ W , (5)
with a(u ± , v ± ) =

Ω ± σ(u ± ) : ε(v ± ) dΩ ±
bilinear, symmetric, coercive and

l ± (v ± ) = Ω ± f • v ± dΩ ± + ΓC (pn) ± • v ± dΓ C
linear and continuous. Moreover, b is defined as the duality pairing between W and W : b(λ, v ± ) = λ, v ± W ,W . Therefore, it is straightforward to prove the existence and uniqueness of a solution to Problem [START_REF] Tarantola | Inverse Problem Theory and Methods for Model Parameter Estimation[END_REF] (see e.g. [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF] ans references within).

Denoting then f ± and p the approximations of f and p in V ± and W h , setting p n = pn + = -pn -and

K =   A + 0 B + T 0 A --B -T B + -B - 0   , X =   u + u - λ   , F =   F + F - 0   =   M + Ω • f + M - Ω • f - 0   +   +M + c • p n -M - c • p n 0   := L Ω .f + L c .p,
the discretized form of system (5) has the linear algebraic formulation

KX = F. ( 6
)
The system (6) can be solved by a Uzawa Conjugate gradient/domain decomposition method [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF]. The method can be classically stabilized and the convergence of the numerical scheme can be proved as h → 0 .

In what follows, we will focus on the adaptation of a crack inverse problem to this domain decomposition formulation and its application to a realistic problem.

The crack inverse Problem

First, we have the following result.

Proposition 1 For any α > 0, the problem (3) admits a unique solution p * in L 2 (Γ C ).

Proof The proof is classical: applying the same method as in [START_REF] Louis | Optimal Control of Systems Governed by Partial Differential Equations[END_REF], one easily shows that J is strictly convex and coercive on L 2 (Γ C ).

The objective function J being strictly convex, first order optimality conditions can be computed to implement an suitable optimization method (in our case the conjugate gradient). Let us introduce the adjoint system

     -div σ(φ) = 0 in Ω, φ = 0 on Γ D , σ(φ) • n = C -1 (u -u d ) on Γ N , (7)
where u is a solution of system [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF]. Is is easy to prove that this adjoint system admits a unique solution φ ∈ H 1 (Ω). We have the following Proposition 2 Let p * be the solution of problem (3) and (u * , φ * ) be the associated solutions of (1) and (7). Then, the following optimality condition holds:

αp * + (φ * • n ± ) = 0. ( 8
)
This result can be proved using a classical sensitivity analysis technique. The important point here is that it gives a way to compute the gradient of the line search algorithm is necessary, which consequently reduces the computational cost.

Numerical experiments

Aiming at practical applications, we applied the technique to a realistic volcano, the Piton de la Fournaise, Île de la Réunion, France. The mesh was built from a digital elevation model (DEM), provided by the french institute IGN (Institut Géographique National, French National Geographic Institute).

Both the boundary and volume mesh for the whole domain were generated by Gmsh software (Figure 2, left). The crack geometry is assumed to be quadrangular and intersecting the surface. It is constructed following [START_REF] Fukushima | Finding realistic dike models from interferometric synthetic aperture radar data: The february 2000 eruption at piton de la fournaise[END_REF] (see Figure 2, left). The crack mesh does not match the volume mesh. Moreover, it can be easily extended in order to split the domain. We assume that the crack is submitted to an initial pressure p 0 . The inverse problem will consist in determining the unknown pressure from the surface displacements (Figure 2, right). The convergence curves in Figure 3, highlight the efficiency of adapted optimization algorithm. The conjugate gradient minimization performs efficiently, even for fine meshes.

Conclusion

We have studied a conjugate gradient type method for an interface pressure inverse problem using a Uzawa conjugate gradient domain decomposition method (from [START_REF] Bodart | XFEM-based fictitious domain method for linear elasticity model with crack[END_REF]) as inner solver. considering the constrained minimization problem (1)-( 2) and using sensitivity and adjoint systems techniques.

  be a bounded open set in R d , d = 2, 3 with smooth boundary ∂Ω := Γ D ∪ Γ N where Γ D and Γ N are of nonzero measure and Γ D ∩ Γ N = ∅. We assume that Ω is occupied by an elastic solid and we denote by u the displacement field of the solid and the density of external forces by f ∈ L 2 (Ω). The Cauchy stress σ(u) and strain ε(u) are given by σ(u) = λ Trε(u) I R d + 2µε(u) and ε(u) = 1 2 (∇u + ∇u T ), where (λ, µ) are the Lamé coefficients, I R d denotes the identity tensor, and Tr(•) represents the matrix trace. Consider a crack Γ C ⊂ Ω represented by a line (d = 2) or a surface (d = 3) parametrized by an injective mapping.

Fig. 2

 2 Fig. 2 Triangular surface mesh [2] representing the crack (left), amplitude of the displacement of a realistic volcano (right).

Fig. 3

 3 Fig.3Decay of the norm of gradient (left), the error of displacement on the ground in each iteration (right) and number of iteration to the converged p after each refinement of the mesh (center)

function J: for a given p ∈ L 2 (Γ C ), compute (u, φ) which solve (1) and (7). Then, the Gâteaux derivative of J is given in L 2 (Γ C ) by

For a given pressure p ∈ L 2 (Γ C ), the computation of the gradient J (p) then requires to solve two systems. Since we transformed our direct problem into system (4), we now need to adapt the inverse problem to this formulation. The cost function J defined by (2) then rewrites into

Notice that the observed data u d can be interpolated on two sub-domains Ω ± to obtain u ± d corresponding to u ± . In view of (6), denoting R the reduction matrix R : X → U and

the discrete cost function is defined as

where X is the solution of (6), M N and M F are the mass matrices on Γ N and Γ C , respectively. This finite dimensional problem then boils down to finding the saddle point of the following Lagrangian

Computing the KKT conditions for this problem allows to compute the gradient of J d : for a given vector p, let X be the solution of (6) and Φ be the solution of the adjoint problem

Then, we have

The system (12) and the gradient (13) are the discrete counterparts of ( 7) and ( 9). As (6), the adjoint system (12) is solved by a Uzawa conjugate gradient/domain decomposition method.

Computational aspects: the problem studied here is actually of quadratic type. Hence it is natural to use a suitable minimization technique, namely a conjugate gradient algorithm. It is important to notice that, using the underlying quadratic form, one can determine the optimal step size. Therefore no