Several examples of neigbourly polyhedra in co-dimension 4

In the article, a series of neigbourly polyhedra is constructed. They have $N=2d+4$ vertices and are embedded in $\mathbb R^{2d}$. Their (affine) Gale diagrams in $\mathbb R^2$ have $d+3$ black points that form a convex polygon. These Gale diagams can be enumerated using 3-trees (trees with some additional structure). Given $d$ and $m$, each of the constructed polyhedra in $\mathbb R^{2d}$ has a fixed number of faces of dimension $m$ that contain a vertex $A$. (This number depends on $d$ and $m$ does not depend on the polyhedron and the vertex $A$).Comment: In russian, 25 pages, 16 figure

Construction and Analysis of Projected Deformed Products

We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products such that specified faces (e.g. all the k-faces) are ``strictly preserved'' under projection. Thus, starting from an arbitrary neighborly simplicial (d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose projection to the last dcoordinates yields a neighborly cubical d-polytope. As an extension of thecubical case, we construct matrix representations of deformed products of(even) polygons (DPPs), which have a projection to d-space that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both cases the combinatorial structure of the images under projection is completely determined by the neighborly polytope Q: Our analysis provides explicit combinatorial descriptions. This yields a multitude of combinatorially different neighborly cubical polytopes and DPPs. As a special case, we obtain simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler (2000) as well as of the ``projected deformed products of polygons'' that were announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets arbitrarily close to 9.Comment: 20 pages, 5 figure

Jasmonic acid and salicylic acid play minor roles in stomatal regulation by CO2, abscisic acid, darkness, vapor pressure deficit, and ozone

Jasmonic acid (JA) and salicylic acid (SA) regulate stomatal closure, preventing pathogen invasion into plants. However, to what extent abscisic acid (ABA), SA and JA interact, and what the roles of SA and JA are in stomatal responses to environmental cues, remains unclear. Here, by using intact plant gas-exchange measurements in JA and SA single and double mutants, we show that stomatal responsiveness to CO2, light intensity, ABA, high vapor pressure deficit and ozone either did not or, for some stimuli only, very slightly depended upon JA and SA biosynthesis and signaling mutants, including dde2, sid2, coi1, jai1, myc2 and npr1 alleles. Although the stomata in the mutants studied clearly responded to ABA, CO2, light and ozone, ABA-triggered stomatal closure in npr1-1 was slightly accelerated compared with the wild type. Stomatal reopening after ozone pulses was quicker in the coi1-16 mutant than in the wild type. In intact Arabidopsis plants, spraying with methyl-JA led to only a modest reduction in stomatal conductance 80 min after treatment, whereas ABA and CO2 induced pronounced stomatal closure within minutes. We could not document a reduction of stomatal conductance after spraying with SA. Coronatine-induced stomatal opening was initiated slowly after 1.5-2.0 h, and reached a maximum by 3 h after spraying intact plants. Our results suggest that ABA, CO2 and light are major regulators of rapid guard cell signaling, whereas JA and SA could play only minor roles in the whole-plant stomatal response to environmental cues in Arabidopsis and Solanum lycopersicum (tomato).Peer reviewe

Totally Splittable Polytopes

A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a complete classification of the totally splittable polytopes.Comment: 15 pages, 7 figures; v2: major revision: corrections of some minor errors and some addition

Re-evaluating microglia expression profiles using RiboTag and cell isolation strategies

Transcriptome profiling is widely used to infer functional states of specific cell types, as well as their responses to stimuli, to define contributions to physiology and pathophysiology. Focusing on microglia, the brain’s macrophages, we report here a side-by-side comparison of classical cell-sorting-based transcriptome sequencing and the ‘RiboTag’ method, which avoids cell retrieval from tissue context and yields translatome sequencing information. Conventional whole-cell microglial transcriptomes were found to be significantly tainted by artifacts introduced by tissue dissociation, cargo contamination and transcripts sequestered from ribosomes. Conversely, our data highlight the added value of RiboTag profiling for assessing the lineage accuracy of Cre recombinase expression in transgenic mice. Collectively, this study indicates method-based biases, reveals observer effects and establishes RiboTag-based translatome profiling as a valuable complement to standard sorting-based profiling strategies

Electrotonic Signals along Intracellular Membranes May Interconnect Dendritic Spines and Nucleus

Synapses on dendritic spines of pyramidal neurons show a remarkable ability to induce phosphorylation of transcription factors at the nuclear level with a short latency, incompatible with a diffusion process from the dendritic spines to the nucleus. To account for these findings, we formulated a novel extension of the classical cable theory by considering the fact that the endoplasmic reticulum (ER) is an effective charge separator, forming an intrinsic compartment that extends from the spine to the nuclear membrane. We use realistic parameters to show that an electrotonic signal may be transmitted along the ER from the dendritic spines to the nucleus. We found that this type of signal transduction can additionally account for the remarkable ability of the cell nucleus to differentiate between depolarizing synaptic signals that originate from the dendritic spines and back-propagating action potentials. This study considers a novel computational role for dendritic spines, and sheds new light on how spines and ER may jointly create an additional level of processing within the single neuron

Sequences Sufficient for Programming Imprinted Germline DNA Methylation Defined

Epigenetic marks are fundamental to normal development, but little is known about signals that dictate their placement. Insights have been provided by studies of imprinted loci in mammals, where monoallelic expression is epigenetically controlled. Imprinted expression is regulated by DNA methylation programmed during gametogenesis in a sex-specific manner and maintained after fertilization. At Rasgrf1 in mouse, paternal-specific DNA methylation on a differential methylation domain (DMD) requires downstream tandem repeats. The DMD and repeats constitute a binary switch regulating paternal-specific expression. Here, we define sequences sufficient for imprinted methylation using two transgenic mouse lines: One carries the entire Rasgrf1 cluster (RC); the second carries only the DMD and repeats (DR) from Rasgrf1. The RC transgene recapitulated all aspects of imprinting seen at the endogenous locus. DR underwent proper DNA methylation establishment in sperm and erasure in oocytes, indicating the DMD and repeats are sufficient to program imprinted DNA methylation in germlines. Both transgenes produce a DMD-spanning pit-RNA, previously shown to be necessary for imprinted DNA methylation at the endogenous locus. We show that when pit-RNA expression is controlled by the repeats, it regulates DNA methylation in cis only and not in trans. Interestingly, pedigree history dictated whether established DR methylation patterns were maintained after fertilization. When DR was paternally transmitted followed by maternal transmission, the unmethylated state that was properly established in the female germlines could not be maintained. This provides a model for transgenerational epigenetic inheritance in mice

Analysis of Imprinted Gene Expression in Normal Fertilized and Uniparental Preimplantation Porcine Embryos

In the present study quantitative real-time PCR was used to determine the expression status of eight imprinted genes (GRB10, H19, IGF2R, XIST, IGF2, NNAT, PEG1 and PEG10) during preimplantation development, in normal fertilized and uniparental porcine embryos. The results demonstrated that, in all observed embryo samples, a non imprinted gene expression pattern up to the 16-cell stage of development was common for most genes. This was true for all classes of embryo, regardless of parental-origins and the direction of imprint. However, several differentially expressed genes (H19, IGF2, XIST and PEG10) were detected amongst the classes at the blastocyst stage of development. Most interestingly and despite the fact that maternally and paternally expressed genes should not be expressed in androgenones and parthenogenones, respectively, both uniparental embryos expressed these genes when tested for in this study. In order to account for this phenomenon, we compared the expression patterns of eight imprinted genes along with the methylation status of the IGF2/H19 DMR3 in haploid and diploid parthenogenetic embryos. Our findings revealed that IGF2, NNAT and PEG10 were silenced in haploid but not diploid parthenogenetic blastocysts and differential methylation of the IGF2/H19 DMR3 was consistently observed between haploid and diploid parthenogenetic blastocysts. These results appear to suggest that there exists a process to adjust the expression status of imprinted genes in diploid parthenogenetic embryos and that this phenomenon may be associated with altered methylation at an imprinting control region. In addition we believe that imprinted expression occurs in at least four genes, namely H19, IGF2, XIST and PEG10 in porcine blastocyst stage embryos

Dicer Deficiency Differentially Impacts Microglia of the Developing and Adult Brain

Microglia seed the embryonic neuro-epithelium, expand and actively sculpt neuronal circuits in the developing central nervous system, but eventually adopt relative quiescence and ramified morphology in the adult. Here, we probed the impact of post-transcriptional control by microRNAs (miRNAs) on microglial performance during development and adulthood by generating mice lacking microglial Dicer expression at these distinct stages. Conditional Dicer ablation in adult microglia revealed that miRNAs were required to limit microglial responses to challenge. After peripheral endotoxin exposure, Dicer-deficient microglia expressed more pro-inflammatory cytokines than wild-type microglia and thereby compromised hippocampal neuronal functions. In contrast, prenatal Dicer ablation resulted in spontaneous microglia activation and revealed a role for Dicer in DNA repair and preservation of genome integrity. Accordingly, Dicer deficiency rendered otherwise radio-resistant microglia sensitive to gamma irradiation. Collectively, the differential impact of the Dicer ablation on microglia of the developing and adult brain highlights the changes these cells undergo with time