Attracting Sets Of Nonlinear Difference Equations With Time-Varying Delays

In this paper, a class of nonlinear difference equations with time-varying delays is considered. Based on a generalized discrete Halanay inequality, some sufficient conditions for the attracting set and the global asymptotic stability of the nonlinear difference equations with time-varying delays are obtained

Robust stability and boundedness of uncertain conformable fractional-order delay systems under input saturation

In this article, a class of uncertain conformable fractional-order delay systems under input saturation is considered. By establishing the Lyapunov boundedness theorem for conformable fractional-order delay systems, some sufficient conditions for robust stability and boundedness of the systems are obtained. Examples are given to illustrate the obtained theory

Arabidopsis COMPASS-Like Complexes Mediate Histone H3 Lysine-4 Trimethylation to Control Floral Transition and Plant Development

Histone H3 lysine-4 (H3K4) methylation is associated with transcribed genes in eukaryotes. In Drosophila and mammals, both di- and tri-methylation of H3K4 are associated with gene activation. In contrast to animals, in Arabidopsis H3K4 trimethylation, but not mono- or di-methylation of H3K4, has been implicated in transcriptional activation. H3K4 methylation is catalyzed by the H3K4 methyltransferase complexes known as COMPASS or COMPASS-like in yeast and mammals. Here, we report that Arabidopsis homologs of the COMPASS and COMPASS-like complex core components known as Ash2, RbBP5, and WDR5 in humans form a nuclear subcomplex during vegetative and reproductive development, which can associate with multiple putative H3K4 methyltransferases. Loss of function of ARABIDOPSIS Ash2 RELATIVE (ASH2R) causes a great decrease in genome-wide H3K4 trimethylation, but not in di- or mono-methylation. Knockdown of ASH2R or the RbBP5 homolog suppresses the expression of a crucial Arabidopsis floral repressor, FLOWERING LOCUS C (FLC), and FLC homologs resulting in accelerated floral transition. ASH2R binds to the chromatin of FLC and FLC homologs in vivo and is required for H3K4 trimethylation, but not for H3K4 dimethylation in these loci; overexpression of ASH2R causes elevated H3K4 trimethylation, but not H3K4 dimethylation, in its target genes FLC and FLC homologs, resulting in activation of these gene expression and consequent late flowering. These results strongly suggest that H3K4 trimethylation in FLC and its homologs can activate their expression, providing concrete evidence that H3K4 trimethylation accumulation can activate eukaryotic gene expression. Furthermore, our findings suggest that there are multiple COMPASS-like complexes in Arabidopsis and that these complexes deposit trimethyl but not di- or mono-methyl H3K4 in target genes to promote their expression, providing a molecular explanation for the observed coupling of H3K4 trimethylation (but not H3K4 dimethylation) with active gene expression in Arabidopsis

Repression of FLOWERING LOCUS C and FLOWERING LOCUS T by the Arabidopsis Polycomb Repressive Complex 2 Components

Polycomb group (PcG) proteins are evolutionarily conserved in animals and plants, and play critical roles in the regulation of developmental gene expression. Here we show that the Arabidopsis Polycomb repressive complex 2 (PRC2) subunits CURLY LEAF (CLF), EMBRYONIC FLOWER 2 (EMF2) and FERTILIZATION INDEPENDENT ENDOSPERM (FIE) repress the expression of FLOWERING LOCUS C (FLC), a central repressor of the floral transition in Arabidopsis and FLC relatives. In addition, CLF directly interacts with and mediates the deposition of repressive histone H3 lysine 27 trimethylation (H3K27me3) into FLC and FLC relatives, which suppresses active histone H3 lysine 4 trimethylation (H3K4me3) in these loci. Furthermore, we show that during vegetative development CLF and FIE strongly repress the expression of FLOWERING LOCUS T (FT), a key flowering-time integrator, and that CLF also directly interacts with and mediates the deposition of H3K27me3 into FT chromatin. Our results suggest that PRC2-like complexes containing CLF, EMF2 and FIE, directly interact with and deposit into FT, FLC and FLC relatives repressive trimethyl H3K27 leading to the suppression of active H3K4me3 in these loci, and thus repress the expression of these flowering genes. Given the central roles of FLC and FT in flowering-time regulation in Arabidopsis, these findings suggest that the CLF-containing PRC2-like complexes play a significant role in control of flowering in Arabidopsis

Arabidopsis Homologs of Retinoblastoma-Associated Protein 46/48 Associate with a Histone Deacetylase to Act Redundantly in Chromatin Silencing

RNA molecules such as small-interfering RNAs (siRNAs) and antisense RNAs (asRNAs) trigger chromatin silencing of target loci. In the model plant Arabidopsis, RNA–triggered chromatin silencing involves repressive histone modifications such as histone deacetylation, histone H3 lysine-9 methylation, and H3 lysine-27 monomethylation. Here, we report that two Arabidopsis homologs of the human histone-binding proteins Retinoblastoma-Associated Protein 46/48 (RbAp46/48), known as MSI4 (or FVE) and MSI5, function in partial redundancy in chromatin silencing of various loci targeted by siRNAs or asRNAs. We show that MSI5 acts in partial redundancy with FVE to silence FLOWERING LOCUS C (FLC), which is a crucial floral repressor subject to asRNA–mediated silencing, FLC homologs, and other loci including transposable and repetitive elements which are targets of siRNA–directed DNA Methylation (RdDM). Both FVE and MSI5 associate with HISTONE DEACETYLASE 6 (HDA6) to form complexes and directly interact with the target loci, leading to histone deacetylation and transcriptional silencing. In addition, these two genes function in de novo CHH (H = A, T, or C) methylation and maintenance of symmetric cytosine methylation (mainly CHG methylation) at endogenous RdDM target loci, and they are also required for establishment of cytosine methylation in the previously unmethylated sequences directed by the RdDM pathway. This reveals an important functional divergence of the plant RbAp46/48 relatives from animal counterparts

Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay Integrodifferential Equations

<p/> <p>The exponential stability of singularly perturbed impulsive delay integrodifferential equations (SPIDIDEs) is concerned. By establishing an impulsive delay integrodifferential inequality (IDIDI), some sufficient conditions ensuring the exponentially stable of any solution of SPIDIDEs for sufficiently small <inline-formula> <graphic file="1029-242X-2009-369185-i1.gif"/></inline-formula> are obtained. A numerical example shows the effectiveness of our theoretical results.</p

Establishment of the Winter-Annual Growth Habit via FRIGIDA-Mediated Histone Methylation at FLOWERING LOCUS C in Arabidopsis[C][W]

In Arabidopsis thaliana, flowering-time variation exists among accessions, and the winter-annual (late-flowering without vernalization) versus rapid-cycling (early flowering) growth habit is typically determined by allelic variation at FRIGIDA (FRI) and FLOWERING LOCUS C (FLC). FRI upregulates the expression of FLC, a central floral repressor, to levels that inhibit flowering, resulting in the winter-annual habit. Here, we show that FRI promotes histone H3 lysine-4 trimethylation (H3K4me3) in FLC to upregulate its expression. We identified an Arabidopsis homolog of the human WDR5, namely, WDR5a, which is a conserved core component of the human H3K4 methyltransferase complexes called COMPASS-like. We found that recombinant WDR5a binds H3K4-methylated peptides and that WDR5a also directly interacts with an H3K4 methyltransferase, ARABIDOPSIS TRITHORAX1. FRI mediates WDR5a enrichment at the FLC locus, leading to increased H3K4me3 and FLC upregulation. WDR5a enrichment is not required for elevated H3K4me3 in FLC upon loss of function of an FLC repressor, suggesting that two distinct mechanisms underlie elevated H3K4me3 in FLC. Our findings suggest that FRI is involved in the enrichment of a WDR5a-containing COMPASS-like complex at FLC chromatin that methylates H3K4, leading to FLC upregulation and thus the establishment of the winter-annual growth habit