Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

Aberrant Regulation of mRNA m6A Modification in Cancer Development

N6-methyladenosine (m6A) is the most prevalent internal modification of eukaryotic messenger RNAs (mRNAs). The m6A modification in RNA can be catalyzed by methyltransferases, or removed by demethylases, which are termed m6A writers and erasers, respectively. Selective recognition and binding by distinct m6A reader proteins lead mRNA to divergent destinies. m6A has been reported to influence almost every stage of mRNA metabolism and to regulate multiple biological processes. Accumulating evidence strongly supports the correlation between aberrant cellular m6A level and cancer. We summarize here that deregulation of m6A modification, resulting from aberrant expression or function of m6A writers, erasers, readers or some other protein factors, is associated with carcinogenesis and cancer progression. Understanding the regulation and functional mechanism of mRNA m6A modification in cancer development may help in developing novel and efficient strategies for the diagnosis, prognosis and treatment of human cancers

Reprogramming of H3K27me3 Is Critical for Acquisition of Pluripotency from Cultured <em>Arabidopsis</em> Tissues

<div><p>In plants, multiple detached tissues are capable of forming a pluripotent cell mass, termed callus, when cultured on media containing appropriate plant hormones. Recent studies demonstrated that callus resembles the root-tip meristem, even if it is derived from aerial organs. This finding improves our understanding of the regeneration process of plant cells; however, the molecular mechanism that guides cells of different tissue types to form a callus still remains elusive. Here, we show that genome-wide reprogramming of histone H3 lysine 27 trimethylation (H3K27me3) is a critical step in the leaf-to-callus transition. The Polycomb Repressive Complex 2 (PRC2) is known to function in establishing H3K27me3. By analyzing callus formation of mutants corresponding to different histone modification pathways, we found that leaf blades and/or cotyledons of the PRC2 mutants <em>curly leaf swinger</em> (<em>clf swn</em>) and <em>embryonic flower2</em> (<em>emf2</em>) were defective in callus formation. We identified the H3K27me3-covered loci in leaves and calli by a ChIP–chip assay, and we found that in the callus H3K27me3 levels decreased first at certain auxin-pathway genes. The levels were then increased at specific leaf genes but decreased at a number of root-regulatory genes. Changes in H3K27me3 levels were negatively correlated with expression levels of the corresponding genes. One possible role of PRC2-mediated H3K27me3 in the leaf-to-callus transition might relate to elimination of leaf features by silencing leaf-regulatory genes, as most leaf-preferentially expressed regulatory genes could not be silenced in the leaf explants of <em>clf swn</em>. In contrast to the leaf explants, the root explants of both <em>clf swn</em> and <em>emf2</em> formed calli normally, possibly because the root-to-callus transition bypasses the leaf gene silencing process. Furthermore, our data show that PRC2-mediated H3K27me3 and H3K27 demethylation act in parallel in the reprogramming of H3K27me3 during the leaf-to-callus transition, suggesting a general mechanism for cell fate transition in plants.</p> </div

Delineation of a human Mendelian disorder of the DNA demethylation machinery: TET3 deficiency

Germline pathogenic variants in chromatin-modifying enzymes are a common cause of pediatric developmental disorders. These enzymes catalyze reactions that regulate epigenetic inheritance via histone post-translational modifications and DNA methylation. Cytosine methylation (5-methylcytosine [5mC]) of DNA is the quintessential epigenetic mark, yet no human Mendelian disorder of DNA demethylation has yet been delineated. Here, we describe in detail a Mendelian disorder caused by the disruption of DNA demethylation. TET3 is a methylcytosine dioxygenase that initiates DNA demethylation during early zygote formation, embryogenesis, and neuronal differentiation and is intolerant to haploinsufficiency in mice and humans. We identify and characterize 11 cases of human TET3 deficiency in eight families with the common phenotypic features of intellectual disability and/or global developmental delay; hypotonia; autistic traits; movement disorders; growth abnormalities; and facial dysmorphism. Mono-allelic frameshift and nonsense variants in TET3 occur throughout the coding region. Mono-allelic and bi-allelic missense variants localize to conserved residues; all but one such variant occur within the catalytic domain, and most display hypomorphic function in an assay of catalytic activity. TET3 deficiency and other Mendelian disorders of the epigenetic machinery show substantial phenotypic overlap, including features of intellectual disability and abnormal growth, underscoring shared disease mechanism

ChIP–chip analysis to identify genes with changes in the H3K27me3 levels between leaf and callus.

<p>(A) Leaf explants (left) and calli (right) were used for the ChIP-chip experiment. For preparation of experimental materials, leaf explants that were just cut from leaves of 20-day-old wild-type Col-0 seedlings and calli that were on the margins of leaf explants cultured on CIM for 20 days were harvested for nuclei extraction. (B) A comparison of H3K27me3 covered loci taken from three independent genome-wide analyses (seedlings from Zhang et al. <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002911#pgen.1002911-Zhang1" target="_blank">[13]</a>, and leaves and calli in this work). (C) Classifications by annotated functions of the identified H3K27me3-covered genes with either decreased (left) or increased (right) levels. (D) Expression profiles of the genes identified by the ChIP-chip experiment with the decreased (left) or increased (right) H3K27me3 levels. The original expression data were downloaded from the online program Genevestigator <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002911#pgen.1002911-Hruz1" target="_blank">[30]</a>.</p

PcG is required for silencing leaf-regulatory genes during the leaf-to-callus transition.

<p>(A–F) Expression level changes of <i>GH3.2</i> (A), <i>IAA2</i> (B), <i>SAW1</i> (C), <i>SAW2</i> (D), <i>WOX5</i> (E), and <i>SHR</i> (F) in leaf explants of <i>clf-50 swn-1</i> from time 0 to 8 DAC, revealed by qRT-PCR analyses. Bars show s.e.</p

H3K27me3 hypomethylations occur at several root-regulatory genes.

<p>(A) qRT-PCR analyses show increased expression levels of root-regulatory genes <i>WOX5</i> and <i>SHR</i>. (B) ChIP analysis of <i>WOX5</i> and <i>SHR</i>. Bars show s.e. (C–G) GUS staining of the <i>WOX5_pro:GUS</i> transgenic line in the root (C) and leaf explants cultured for 2 to 8 days on CIM (D–G). (H–M) GUS staining of the <i>SHR_pro:GUS</i> transgenic line in the root (H), and in leaf explants at time 0 to 8 DAC (I–M). (N) ChIP-chip results in calli showed the reduced H3K27me3 levels at <i>WOX5, SHR, LOB33</i> and <i>AGL21</i>. Bars = 100 µm in (C, H) and 2 mm in (D–G, I–M).</p