Tropical Quadrics Through Three Points

We tropicalize the rational map that takes triples of points in the projective plane to the plane of quadrics passing through these points. The image of its tropicalization is contained in the tropicalization of its image. We identify these objects inside the tropical Grassmannian of planes in projective 5-space, and we explore a small tropical Hilbert scheme.Comment: 9 pages, 3 figure

Moduli of Tropical Plane Curves

We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves. For fixed genus $g$, our moduli space is a stacky fan whose cones are indexed by regular unimodular triangulations of Newton polygons with $g$ interior lattice points. It has dimension $2g+1$ unless $g \leq 3$ or $g = 7$. We compute these spaces explicitly for $g \leq 5$.Comment: 31 pages, 25 figure

Epigenetic Telomere Protection by Drosophila DNA Damage Response Pathways

Analysis of terminal deletion chromosomes indicates that a sequence-independent mechanism regulates protection of Drosophila telomeres. Mutations in Drosophila DNA damage response genes such as atm/tefu, mre11, or rad50 disrupt telomere protection and localization of the telomere-associated proteins HP1 and HOAP, suggesting that recognition of chromosome ends contributes to telomere protection. However, the partial telomere protection phenotype of these mutations limits the ability to test if they act in the epigenetic telomere protection mechanism. We examined the roles of the Drosophila atm and atr-atrip DNA damage response pathways and the nbs homolog in DNA damage responses and telomere protection. As in other organisms, the atm and atr-atrip pathways act in parallel to promote telomere protection. Cells lacking both pathways exhibit severe defects in telomere protection and fail to localize the protection protein HOAP to telomeres. Drosophila nbs is required for both atm- and atr-dependent DNA damage responses and acts in these pathways during DNA repair. The telomere fusion phenotype of nbs is consistent with defects in each of these activities. Cells defective in both the atm and atr pathways were used to examine if DNA damage response pathways regulate telomere protection without affecting telomere specific sequences. In these cells, chromosome fusion sites retain telomere-specific sequences, demonstrating that loss of these sequences is not responsible for loss of protection. Furthermore, terminally deleted chromosomes also fuse in these cells, directly implicating DNA damage response pathways in the epigenetic protection of telomeres. We propose that recognition of chromosome ends and recruitment of HP1 and HOAP by DNA damage response proteins is essential for the epigenetic protection of Drosophila telomeres. Given the conserved roles of DNA damage response proteins in telomere function, related mechanisms may act at the telomeres of other organisms

Mutations in FRMD7, a newly identified member of the FERM family, cause X-linked idiopathic congenital nystagmus.

Idiopathic congenital nystagmus is characterized by involuntary, periodic, predominantly horizontal oscillations of both eyes. We identified 22 mutations in FRMD7 in 26 families with X-linked idiopathic congenital nystagmus. Screening of 42 singleton cases of idiopathic congenital nystagmus (28 male, 14 females) yielded three mutations (7%). We found restricted expression of FRMD7 in human embryonic brain and developing neural retina, suggesting a specific role in the control of eye movement and gaze stability

Loss of Free Fatty Acid Receptor 2 leads to impaired islet mass and beta cell survival

The regulation of pancreatic β cell mass is a critical factor to help maintain normoglycemia during insulin resistance. Nutrient-sensing G protein-coupled receptors (GPCR) contribute to aspects of β cell function, including regulation of β cell mass. Nutrients such as free fatty acids (FFAs) contribute to precise regulation of β cell mass by signaling through cognate GPCRs, and considerable evidence suggests that circulating FFAs promote β cell expansion by direct and indirect mechanisms. Free Fatty Acid Receptor 2 (FFA2) is a β cell-expressed GPCR that is activated by short chain fatty acids, particularly acetate. Recent studies of FFA2 suggest that it may act as a regulator of β cell function. Here, we set out to explore what role FFA2 may play in regulation of β cell mass. Interestingly, Ffar2(-/-) mice exhibit diminished β cell mass at birth and throughout adulthood, and increased β cell death at adolescent time points, suggesting a role for FFA2 in establishment and maintenance of β cell mass. Additionally, activation of FFA2 with Gαq/11-biased agonists substantially increased β cell proliferation in in vitro and ex vivo proliferation assays. Collectively, these data suggest that FFA2 may be a novel therapeutic target to stimulate β cell growth and proliferation

Formation of Chimeric Genes by Copy-Number Variation as a Mutational Mechanism in Schizophrenia

Chimeric genes can be caused by structural genomic rearrangements that fuse together portions of two different genes to create a novel gene. We hypothesize that brain-expressed chimeras may contribute to schizophrenia. Individuals with schizophrenia and control individuals were screened genome wide for copy-number variants (CNVs) that disrupted two genes on the same DNA strand. Candidate events were filtered for predicted brain expression and for frequency < 0.001 in an independent series of 20,000 controls. Four of 124 affected individuals and zero of 290 control individuals harbored such events (p = 0.002); a 47 kb duplication disrupted MATK and ZFR2, a 58 kb duplication disrupted PLEKHD1 and SLC39A9, a 121 kb duplication disrupted DNAJA2 and NETO2, and a 150 kb deletion disrupted MAP3K3 and DDX42. Each fusion produced a stable protein when exogenously expressed in cultured cells. We examined whether these chimeras differed from their parent genes in localization, regulation, or function. Subcellular localizations of DNAJA2-NETO2 and MAP3K3-DDX42 differed from their parent genes. On the basis of the expression profile of the MATK promoter, MATK-ZFR2 is likely to be far more highly expressed in the brain during development than the ZFR2 parent gene. MATK-ZFR2 includes a ZFR2-derived isoform that we demonstrate localizes preferentially to neuronal dendritic branch sites. These results suggest that the formation of chimeric genes is a mechanism by which CNVs contribute to schizophrenia and that, by interfering with parent gene function, chimeras may disrupt critical brain processes, including neurogenesis, neuronal differentiation, and dendritic arborization

Mutations in FRMD7, a newly identified member of the FERM family, cause X-linked idiopathic congenital nystagmus

Idiopathic congenital nystagmus (ICN) is characterised by involuntary, periodic, predominantly horizontal, oscillations of both eyes. We identified 22 mutations in FRMD7 in 26 families with X-linked idiopathic congenital nystagmus. Screening of 42 ICN singleton cases (28 male, 14 females) yielded three mutations (7%). We found restricted expression of FRMD7 in human embryonic brain and developing neural retina suggesting a specific role in the control of eye movement and gaze stability