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  1. Abstract

    Trans-chromosomal interactions resulting in changes in DNA methylation during hybridization have been observed in several plant species. However, little is known about the causes or consequences of these interactions. Here, we compared DNA methylomes of F1 hybrids that are mutant for a small RNA biogenesis gene, Mop1 (Mediator of paramutation1), with that of their parents, wild-type siblings, and backcrossed progeny in maize (Zea mays). Our data show that hybridization triggers global changes in both trans-chromosomal methylation (TCM) and trans-chromosomal demethylation (TCdM), most of which involved changes in CHH methylation. In more than 60% of these TCM differentially methylated regions (DMRs) in which small RNAs are available, no significant changes in the quantity of small RNAs were observed. Methylation at the CHH TCM DMRs was largely lost in the mop1 mutant, although the effects of this mutant varied depending on the location of these DMRs. Interestingly, an increase in CHH at TCM DMRs was associated with enhanced expression of a subset of highly expressed genes and suppressed expression of a small number of lowly expressed genes. Examination of the methylation levels in backcrossed plants demonstrates that both TCM and TCdM can be maintained in the subsequent generation, but that TCdM is more stable than TCM. Surprisingly, although increased CHH methylation in most TCM DMRs in F1 plants required Mop1, initiation of a new epigenetic state of these DMRs did not require a functional copy of this gene, suggesting that initiation of these changes is independent of RNA-directed DNA methylation.

     
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    Free, publicly-accessible full text available December 18, 2024
  2. Plant genomes are littered with transposable elements (TEs). Because TEs are potentially highly mutagenic, host organisms have evolved a set of defense mechanisms to recognize and epigenetically silence them. Although the maintenance of TE silencing is well studied, our understanding of the initiation of TE silencing is limited, but it clearly involves small RNAs and DNA methylation. Once TEs are silent, the silent state can be maintained to subsequent generations. However, under some circumstances, such inheritance is unstable, leading to the escape of TEs to the silencing machinery, resulting in the transcriptional activation of TEs. Epigenetic control of TEs has been found to be closely linked to many other epigenetic phenomena, such as genomic imprinting, and is known to contribute to regulation of genes, especially those near TEs. Here we review and discuss the current models of TE silencing, its unstable inheritance after hybridization, and the effects of epigenetic regulation of TEs on genomic imprinting. 
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    Free, publicly-accessible full text available October 1, 2024
  3. Abstract

    We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group$\Gamma <{\operatorname{\mathrm{Isom}}}^+(\mathbb H^{n+1})$, each full rank cusp corresponds to a cohomology class in$H^{n}(\Gamma , V)$, whereVis either the trivial coefficient or the adjoint representation. Moreover, by computing the intertwining operator, we show that different cusps give rise to linearly independent classes.

     
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  4. Abstract

    We show convergence of small eigenvalues for geometrically finite hyperbolicn-manifolds under strong limits. For a class of convergent convex sets in a strongly convergent sequence of Kleinian groups, we use the spectral gap of the limit manifold and the exponentially mixing property of the geodesic flow along the strongly convergent sequence to find asymptotically uniform counting formulas for the number of orthogeodesics between the convex sets. In particular, this provides asymptotically uniform counting formulas (with respect to length) for orthogeodesics between converging Margulis tubes, geodesic loops based at converging basepoints, and primitive closed geodesics.

     
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  5. Abstract We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex, detection results for the Whitehead link and Borromean rings, and a structural property of the $d$-invariants of surgeries on certain algebraically split links. 
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  7. Meiotic recombination is a fundamental process that generates genetic diversity and ensures the accurate segregation of homologous chromosomes. While a great deal is known about genetic factors that regulate recombination, relatively little is known about epigenetic factors, such as DNA methylation. In maize, we examined the effects on meiotic recombination of a mutation in a component of the RNA-directed DNA methylation pathway,Mop1(Mediator of paramutation1), as well as a mutation in a component of thetrans-acting small interference RNA biogenesis pathway,Lbl1(Leafbladeless1). MOP1 is of particular interest with respect to recombination because it is responsible for methylation of transposable elements that are immediately adjacent to transcriptionally active genes. In themop1mutant, we found that meiotic recombination is uniformly decreased in pericentromeric regions but is generally increased in gene rich chromosomal arms. This observation was further confirmed by cytogenetic analysis showing that although overall crossover numbers are unchanged, they occur more frequently in chromosomal arms inmop1mutants. Using whole genome bisulfite sequencing, our data show that crossover redistribution is driven by loss of CHH (where H = A, T, or C) methylation within regions near genes. In contrast to what we observed inmop1mutants, no significant changes were observed in the frequency of meiotic recombination inlbl1mutants. Our data demonstrate that CHH methylation has a significant impact on the overall recombination landscape in maize despite its low frequency relative to CG and CHG methylation.

     
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