The Density of States and the Spectral Shift Density of Random Schroedinger Operators

In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.Comment: 1 figur

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Unconventional Transcriptional Response to Environmental Enrichment in a Mouse Model of Rett Syndrome

Background: Rett syndrome (RTT) is an X-linked postnatal neurodevelopmental disorder caused by mutations in the gene encoding methyl-CpG binding protein 2 (MeCP2) and one of the leading causes of mental retardation in females. RTT is characterized by psychomotor retardation, purposeless hand movements, autistic-like behavior and abnormal gait. We studied the effects of environmental enrichment (EE) on the phenotypic manifestations of a RTT mouse model that lacks MeCP2 (Mecp2 2/y). Principal Findings: We found that EE delayed and attenuated some neurological alterations presented by Mecp2 2/y mice and prevented the development of motor discoordination and anxiety-related abnormalities. To define the molecular correlate of this beneficial effect of EE, we analyzed the expression of several synaptic marker genes whose expression is increased by EE in several mouse models. Conclusions/Significance: We found that EE induced downregulation of several synaptic markers, suggesting that th

Cell-Autonomous Alterations in Dendritic Arbor Morphology and Connectivity Induced by Overexpression of MeCP2 in Xenopus Central Neurons In Vivo

Methyl CpG binding protein-2 (MeCP2) is an essential epigenetic regulator in human brain development. Mutations in the MeCP2 gene have been linked to Rett syndrome, a severe X-linked progressive neurodevelopmental disorder, and one of the most common causes of mental retardation in females. MeCP2 duplication and triplication have also been found to affect brain development, indicating that both loss of function and gain in MeCP2 dosage lead to similar neurological phenotypes. Here, we used the Xenopus laevis visual system as an in vivo model to examine the consequence of increased MeCP2 expression during the morphological maturation of individual central neurons in an otherwise intact brain. Single-cell overexpression of wild-type human MeCP2 was combined with time-lapse confocal microscopy imaging to study dynamic mechanisms by which MeCP2 influences tectal neuron dendritic arborization. Analysis of neurons co-expressing DsRed2 demonstrates that MeCP2 overexpression specifically interfered with dendritic elaboration, decreasing the rates of branch addition and elimination over a 48 hour observation period. Moreover, dynamic analysis of neurons co-expressing wt-hMeCP2 and PSD95-GFP revealed that even though neurons expressing wt-hMeCP2 possessed significantly fewer dendrites and simpler morphologies than control neurons at the same developmental stage, postsynaptic site density in wt-hMeCP2-expressing neurons was similar to controls and increased at a rate higher than controls. Together, our in vivo studies support an early, cell-autonomous role for MeCP2 during the morphological differentiation of neurons and indicate that perturbations in MeCP2 gene dosage result in deficits in dendritic arborization that can be compensated, at least in part, by synaptic connectivity changes

The Role of MeCP2 in Brain Development and Neurodevelopmental Disorders

Methyl CpG binding protein-2 (MeCP2) is an essential epigenetic regulator in human brain development. Rett syndrome, the primary disorder caused by mutations in the X-linked MECP2 gene, is characterized by a period of cognitive decline and development of hand stereotypies and seizures following an apparently normal early infancy. In addition, MECP2 mutations and duplications are observed in a spectrum of neurodevelopmental disorders, including severe neonatal encephalopathy, X-linked mental retardation, and autism, implicating MeCP2 as an essential regulator of postnatal brain development. In this review, we compare the mutation types and inheritance patterns of the human disorders associated with MECP2. In addition, we summarize the current understanding of MeCP2 as a central epigenetic regulator of activity-dependent synaptic maturation. As MeCP2 occupies a central role in the pathogenesis of multiple neurodevelopmental disorders, continued investigation into MeCP2 function and regulatory pathways may show promise for developing broad-spectrum therapies

Synaptic Maturation at Cortical Projections to the Lateral Amygdala in a Mouse Model of Rett Syndrome

Rett syndrome (RTT) is a neuro-developmental disorder caused by loss of function of Mecp2 - methyl-CpG-binding protein 2 - an epigenetic factor controlling DNA transcription. In mice, removal of Mecp2 in the forebrain recapitulates most of behavioral deficits found in global Mecp2 deficient mice, including amygdala-related hyper-anxiety and lack of social interaction, pointing a role of Mecp2 in emotional learning. Yet very little is known about the establishment and maintenance of synaptic function in the adult amygdala and the role of Mecp2 in these processes. Here, we performed a longitudinal examination of synaptic properties at excitatory projections to principal cells of the lateral nucleus of the amygdala (LA) in Mecp2 mutant mice and their wild-type littermates. We first show that during animal life, Cortico-LA projections switch from a tonic to a phasic mode, whereas Thalamo-LA synapses are phasic at all ages. In parallel, we observed a specific elimination of Cortico-LA synapses and a decrease in their ability of generating presynaptic long term potentiation. In absence of Mecp2, both synaptic maturation and synaptic elimination were exaggerated albeit still specific to cortical projections. Surprisingly, associative LTP was unaffected at Mecp2 deficient synapses suggesting that synaptic maintenance rather than activity-dependent synaptic learning may be causal in RTT physiopathology. Finally, because the timing of synaptic evolution was preserved, we propose that some of the developmental effects of Mecp2 may be exerted within an endogenous program and restricted to synapses which maturate during animal life

Expression Profiling of Autism Candidate Genes during Human Brain Development Implicates Central Immune Signaling Pathways

The Autism Spectrum Disorders (ASD) represent a clinically heterogeneous set of conditions with strong hereditary components. Despite substantial efforts to uncover the genetic basis of ASD, the genomic etiology appears complex and a clear understanding of the molecular mechanisms underlying Autism remains elusive. We hypothesized that focusing gene interaction networks on ASD-implicated genes that are highly expressed in the developing brain may reveal core mechanisms that are otherwise obscured by the genomic heterogeneity of the disorder. Here we report an in silico study of the gene expression profile from ASD-implicated genes in the unaffected developing human brain. By implementing a biologically relevant approach, we identified a subset of highly expressed ASD-candidate genes from which interactome networks were derived. Strikingly, immune signaling through NFκB, Tnf, and Jnk was central to ASD networks at multiple levels of our analysis, and cell-type specific expression suggested glia—in addition to neurons—deserve consideration. This work provides integrated genomic evidence that ASD-implicated genes may converge on central cytokine signaling pathways

Co-Localization of the Oncogenic Transcription Factor MYCN and the DNA Methyl Binding Protein MeCP2 at Genomic Sites in Neuroblastoma

MYCN is a transcription factor that is expressed during the development of the neural crest and its dysregulation plays a major role in the pathogenesis of pediatric cancers such as neuroblastoma, medulloblastoma and rhabdomyosarcoma. MeCP2 is a CpG methyl binding protein which has been associated with a number of cancers and developmental disorders, particularly Rett syndrome.Using an integrative global genomics approach involving chromatin immunoprecipitation applied to microarrays, we have determined that MYCN and MeCP2 co-localize to gene promoter regions, as well as inter/intragenic sites, within the neuroblastoma genome (MYCN amplified Kelly cells) at high frequency (70.2% of MYCN sites were also positive for MeCP2). Intriguingly, the frequency of co-localization was significantly less at promoter regions exhibiting substantial hypermethylation (8.7%), as determined by methylated DNA immunoprecipitation (MeDIP) applied to the same microarrays. Co-immunoprecipitation of MYCN using an anti-MeCP2 antibody indicated that a MYCN/MeCP2 interaction occurs at protein level. mRNA expression profiling revealed that the median expression of genes with promoters bound by MYCN was significantly higher than for genes bound by MeCP2, and that genes bound by both proteins had intermediate expression. Pathway analysis was carried out for genes bound by MYCN, MeCP2 or MYCN/MeCP2, revealing higher order functions.Our results indicate that MYCN and MeCP2 protein interact and co-localize to similar genomic sites at very high frequency, and that the patterns of binding of these proteins can be associated with significant differences in transcriptional activity. Although it is not yet known if this interaction contributes to neuroblastoma disease pathogenesis, it is intriguing that the interaction occurs at the promoter regions of several genes important for the development of neuroblastoma, including ALK, AURKA and BDNF

Partial Loss of Ataxin-1 Function Contributes to Transcriptional Dysregulation in Spinocerebellar Ataxia Type 1 Pathogenesis

Spinocerebellar ataxia type 1 (SCA1) is a dominantly inherited neurodegenerative disease caused by expansion of a CAG repeat that encodes a polyglutamine tract in ATAXIN1 (ATXN1). Molecular and genetic data indicate that SCA1 is mainly caused by a gain-of-function mechanism. However, deletion of wild-type ATXN1 enhances SCA1 pathogenesis, whereas increased levels of an evolutionarily conserved paralog of ATXN1, Ataxin 1-Like, ameliorate it. These data suggest that a partial loss of ATXN1 function contributes to SCA1. To address this possibility, we set out to determine if the SCA1 disease model (Atxn1154Q/+ mice) and the loss of Atxn1 function model (Atxn1−/− mice) share molecular changes that could potentially contribute to SCA1 pathogenesis. To identify transcriptional changes that might result from loss of function of ATXN1 in SCA1, we performed gene expression microarray studies on cerebellar RNA from Atxn1−/− and Atxn1154Q/+ cerebella and uncovered shared gene expression changes. We further show that mild overexpression of Ataxin-1-Like rescues several of the molecular and behavioral defects in Atxn1−/− mice. These results support a model in which Ataxin 1-Like overexpression represses SCA1 pathogenesis by compensating for a partial loss of function of Atxn1. Altogether, these data provide evidence that partial loss of Atxn1 function contributes to SCA1 pathogenesis and raise the possibility that loss-of-function mechanisms contribute to other dominantly inherited neurodegenerative diseases

Ex Vivo Treatment with a Novel Synthetic Aminoglycoside NB54 in Primary Fibroblasts from Rett Syndrome Patients Suppresses MECP2 Nonsense Mutations

BACKGROUND: Nonsense mutations in the X-linked methyl CpG-binding protein 2 (MECP2) comprise a significant proportion of causative MECP2 mutations in Rett syndrome (RTT). Naturally occurring aminoglycosides, such as gentamicin, have been shown to enable partial suppression of nonsense mutations related to several human genetic disorders, however, their clinical applicability has been compromised by parallel findings of severe toxic effects. Recently developed synthetic NB aminoglycosides have demonstrated significantly improved effects compared to gentamicin evident in substantially higher suppression and reduced acute toxicity in vitro. RESULTS: We performed comparative study of suppression effects of the novel NB54 and gentamicin on three MECP2 nonsense mutations (R294X, R270X and R168X) common in RTT, using ex vivo treatment of primary fibroblasts from RTT patients harboring these mutations and testing for the C-terminal containing full-length MeCP2. We observed that NB54 induces dose-dependent suppression of MECP2 nonsense mutations more efficiently than gentamicin, which was evident at concentrations as low as 50 µg/ml. NB54 read-through activity was mutation specific, with maximal full-length MeCP2 recovery in R168X (38%), R270X (27%) and R294X (18%). In addition, the recovered MeCP2 was translocated to the cell nucleus and moreover led to parallel increase in one of the most important MeCP2 downstream effectors, the brain derived neurotrophic factor (BDNF). CONCLUSION: Our findings suggest that NB54 may induce restoration of the potentially functional MeCP2 in primary RTT fibroblasts and encourage further studies of NB54 and other rationally designed aminoglycoside derivatives as potential therapeutic agents for nonsense MECP2 mutations in RTT