On invariant 2x2 \beta-ensembles of random matrices

We introduce and solve exactly a family of invariant 2x2 random matrices, depending on one parameter \eta, and we show that rotational invariance and real Dyson index \beta are not incompatible properties. The probability density for the entries contains a weight function and a multiple trace-trace interaction term, which corresponds to the representation of the Vandermonde-squared coupling on the basis of power sums. As a result, the effective Dyson index \beta_{eff} of the ensemble can take any real value in an interval. Two weight functions (Gaussian and non-Gaussian) are explored in detail and the connections with \beta-ensembles of Dumitriu-Edelman and the so-called Poisson-Wigner crossover for the level spacing are respectively highlighted. A curious spectral twinning between ensembles of different symmetry classes is unveiled. The proposed technical tool more generically allows for designing actual matrix models which i) are rotationally invariant; ii) have a real Dyson index \beta_{eff}; iii) have a pre-assigned confining potential or alternatively level-spacing profile. The analytical results have been checked through numerical simulations with an excellent agreement. Eventually, we discuss possible generalizations and further directions of research.Comment: Minor modifications. Published versio

Transcription and histone methylation changes correlate with imprint acquisition in male germ cells

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PRMT5-mediated histone H4 arginine-3 symmetrical dimethylation marks chromatin at G + C-rich regions of the mouse genome

Symmetrical dimethylation on arginine-3 of histone H4 (H4R3me2s) has been reported to occur at several repressed genes, but its specific regulation and genomic distribution remained unclear. Here, we show that the type-II protein arginine methyltransferase PRMT5 controls H4R3me2s in mouse embryonic fibroblasts (MEFs). In these differentiated cells, we find that the genome-wide pattern of H4R3me2s is highly similar to that in embryonic stem cells. In both the cell types, H4R3me2s peaks are detected predominantly at G + C-rich regions. Promoters are consistently marked by H4R3me2s, independently of transcriptional activity. Remarkably, H4R3me2s is mono-allelic at imprinting control regions (ICRs), at which it marks the same parental allele as H3K9me3, H4K20me3 and DNA methylation. These repressive chromatin modifications are regulated independently, however, since PRMT5-depletion in MEFs resulted in loss of H4R3me2s, without affecting H3K9me3, H4K20me3 or DNA methylation. Conversely, depletion of ESET (KMT1E) or SUV420H1/H2 (KMT5B/C) affected H3K9me3 and H4K20me3, respectively, without altering H4R3me2s at ICRs. Combined, our data indicate that PRMT5-mediated H4R3me2s uniquely marks the mammalian genome, mostly at G + C-rich regions, and independently from transcriptional activity or chromatin repression. Furthermore, comparative bioinformatics analyses suggest a putative role of PRMT5-mediated H4R3me2s in chromatin configuration in the nucleus

Imprinting control regions (ICRs) are marked by mono-allelic bivalent chromatin when transcriptionally inactive

International audienceParental allele-specific expression of imprinted genes is mediated by imprinting control regions (ICRs) that are constitutively marked by DNA methy-lation imprints on the maternal or paternal allele. Mono-allelic DNA methylation is strictly required for the process of imprinting and has to be faithfully maintained during the entire lifespan. While the regulation of DNA methylation itself is well understood, the mechanisms whereby the opposite allele remains unmethylated are unclear. Here, we show that in the mouse, at maternally methylated ICRs, the paternal allele, which is constitutively associated with H3K4me2/3, is marked by default by H3K27me3 when these ICRs are transcriptionally inactive, leading to the formation of a bivalent chromatin signature. Our data suggest that at ICRs, chromatin bivalency has a protective role by ensuring that DNA on the paternal allele remains unmethylated and protected against spurious and unscheduled gene expression. Moreover , they provide the proof of concept that, beside pluripotent cells, chromatin bivalency is the default state of transcriptionally inactive CpG island promoters , regardless of the developmental stage, thereby contributing to protect cell identity

In Vitro Corticogenesis from Embryonic Stem Cells Recapitulates the In Vivo Epigenetic Control of Imprinted Gene Expression

International audienceIn vitro corticogenesis from embryonic stem cells (ESCs) is an attractive model of cortical development and a promising tool for corticaltherapy. It is unknown to which extent epigenetic mechanisms crucial for cortex development and function, such as parental genomicimprinting, are recapitulated by in vitro corticogenesis. Here, using genome-wide transcriptomic and methylation analyses on hybridmouse tissues and cells, wefind a high concordance of imprinting status between invivo and ESC-derived cortices. Notably, in vitrocorticogenesis strictly reproduced the in vivo parent-of-origin-dependent expression of 41 imprinted genes (IGs), including Mest and Cdkn1c known to control corticogenesis. Parent-of-origin-dependent DNA methylation was also conserved at 14 of 18 imprinted differentially methylated regions. The least concordant imprinted locus was Gpr1-Zdbf2, where the aberrant bi-allelic expression of Zdbf2 and Adam23 was concomitant with a gain of methylation on the maternal allele in vitro. Combined, our data argue for a broad conservation of the epigenetic mechanisms at imprinted loci in cortical cells derived from ESCs. We propose that in vitro corticogenesis helps to define the still poorly understood mechanisms that regulate imprinting in the brain and the roles of IGs in cortical developmen