Regulation of phyllotaxis

Plant architecture is characterized by a high degree of regularity. Leaves, flowers and floral organs are arranged in regular patterns, a phenomenon referred to as phyllotaxis. Regular phyllotaxis is found in virtually all higher plants, from mosses, over ferns, to gymnosperms and angiosperms. Due to its remarkable precision, its beauty and its accessibility, phyllotaxis has for centuries been the object of admiration and scientific examination. There have been numerous hypotheses to explain the nature of the mechanistic principle behind phyllotaxis, however, not all of them have been amenable to experimental examination. This is due mainly to the delicacy and small size of the shoot apical meristem, where plant organs are formed and the phyllotactic patterns are laid down. Recently, the combination of genetics, molecular tools and micromanipulation has resulted in the identification of auxin as a central player in organ formation and positioning. This paper discusses some aspects of phyllotactic patterns found in nature and summarizes our current understanding of the regulatory mechanism behind phyllotaxis.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

A role for tuned levels of nucleosome remodeler subunit ACF1 during Drosophila oogenesis

The Chromatin Accessibility Complex (CHRAC) consists of the ATPase ISWI, the large ACF1 subunit and a pair of small histone-like proteins, CHRAC-14/16. CHRAC is a prototypical nucleosome sliding factor that mobilizes nucleosomes to improve the regularity and integrity of the chromatin fiber. This may facilitate the formation of repressive chromatin. Expression of the signature subunit ACF1 is restricted during embryonic development, but remains high in primordial germ cells. Therefore, we explored roles for ACF1 during Drosophila oogenesis. ACF1 is expressed in somatic and germline cells, with notable enrichment in germline stem cells and oocytes. The asymmetrical localization of ACF1 to these cells depends on the transport of the Acf1 mRNA by the Bicaudal-D/Egalitarian complex. Loss of ACF1 function in the novel Acf1(7) allele leads to defective egg chambers and their elimination through apoptosis. In addition, we find a variety of unusual 16-cell cyst packaging phenotypes in the previously known Acf1(1) allele, with a striking prevalence of egg chambers with two functional oocytes at opposite poles. Surprisingly, we found that the Acf1(1) deletion - despite disruption of the Acf1 reading frame - expresses low levels of a PHD-bromodomain module from the C-terminus of ACF1 that becomes enriched in oocytes. Expression of this module from the Acf1 genomic locus leads to packaging defects in the absence of functional ACF1, suggesting competitive interactions with unknown target molecules. Remarkably, a two-fold overexpression of CHRAC (ACF1 and CHRAC-16) leads to increased apoptosis and packaging defects. Evidently, finely tuned CHRAC levels are required for proper oogenesis.