Anna Benini

On the Existence of Elementary Abelian Cycle Systems

We present some necessary and/or sufficient conditions for the existence of an elementary abelian cycle system of the complete graph. We propose a construction for some classes of perfect elementary abelian cycle systems. Finally we consider elementary abelian k-cycle systems of the complete multipartite graph.

Characterization and expression analysis of mcoln1.1 and mcoln1.2, the putative zebrafish co-orthologs of the gene responsible for human mucolipidosis type IV

Mucolipidosis type IV (MLIV) is an autosomal recessive lysosomal storage disorder caused by mutations in the MCOLN1 gene coding for mucolipin-1 (TRPML1). TRPML1 belongs to a transient receptor potential channels (TRP) subfamily, which in mammals includes two other members: mucolipin-2 (TRPML2) and mucolipin-3 (TRPML3). Bioinformatic analysis of the Danio rerio (zebrafish) genome and trascriptome revealed the presence of five different genes related to human mucolipins: mcoln1.1, mcoln1.2, mcoln2, mcoln3.1 and mcoln3.2. We focused our efforts on the characterization of the two putative zebrafish MCOLN1 co-orthologs. Transient-expression experiments in human HeLa cells demonstrated that fish Mcoln1.1 and Mcoln1.2, similarly to TRPML1, localize to late endosomal/lysosomal compartments. Real-Time PCR (RT-PCR) experiments showed that both genes are maternally expressed and transcribed at different levels during embryogenesis. RT-PCR analysis in different zebrafish tissues displayed ubiquitary expression for mcoln1.1 and a more tissue-specific pattern for mcoln1.2. Spatial and temporal expression studies using whole-mount in situ hybridization confirmed that both genes are maternally expressed and ubiquitously transcribed during gastrulation and early somitogenesis. Notably, in the next developmental stages they are more expressed in neural regions and in retina layers, tissues affected in MLIV. Interestingly, mcoln1.1 is detected, from 10 somite-stage until to 36 hpf, in the yolk syncytial layer (YSL) and in the intermediate cell mass (ICM), the earliest site of hematopoiesis. Overall, the redundancy of mucolipins together with their expression profile support the biological relevance of this class of proteins in zebrafish. The data herein presented indicate that Danio rerio could be a suitable vertebrate model for the study of some aspects of MLIV pathogenesis.

Characterization and expression pattern analysis of the facilitative glucose transporter 10 gene (slc2a10) in Danio rerio

The SLC2A10 gene located on chromosome 20q13.1 encodes the facilitative glucose transporter 10 (GLUT10), a class III member of the SLC2A facilitative glucose transporter family. Mutations in the human SLC2A10 gene cause arterial tortuosity syndrome (ATS), a rare autosomal recessive connective tissue disorder. In this work, we report the characterization of the slc2a10 ortholog gene in zebrafish (Danio rerio) and its expression pattern during embryonic development and in adult tissues. The slc2a10 gene consists of 5 exons, spanning 8 kb and mapping to a region on chromosome 11 that exhibits conserved synteny with human chromosome 20. The gene encodes Glut10, a 513 amino acid protein that maintains the 12 transmembrane domain structure typical of the GLUTs family, and shares the specific functional motifs involved in sugar transport with the vertebrate GLUT10. RT-PCR analysis showed that two specific splice variants, both including the 5’-UTR region, were expressed during embryogenesis and in different adult zebrafish tissues and organs. In situ hybridization analyses demonstrated a maternal origin of the total slc2a10 mRNA and its ubiquitous distribution until the early somitogenesis stage. In later embryonic stages, slc2a10 mRNA was detected in the otic vesicles, hatching gland cells, pectoral fin, posterior tectum and swim bladder. Overall, these results suggest a wide role of slc2a10 during zebrafish development.

slc7a6os Gene Plays a Critical Role in Defined Areas of the Developing CNS in Zebrafish

The aim of this study is to shed light on the functional role of slc7a6os, a gene highly conserved in vertebrates. The Danio rerio slc7a6os gene encodes a protein of 326 amino acids with 46% identity to human SLC7A6OS and 14% to Saccharomyces cerevisiae polypeptide Iwr1. Yeast Iwr1 specifically binds RNA pol II, interacts with the basal transcription machinery and regulates the transcription of specific genes. In this study we investigated for the first time the biological role of SLC7A6OS in vertebrates. Zebrafish slc7a6os is a maternal gene that is expressed throughout development, with a prevalent localization in the developing central nervous system (CNS). The gene is also expressed, although at different levels, in various tissues of the adult fish. To determine the functional role of slc7a6os during zebrafish development, we knocked-down the gene by injecting a splice-blocking morpholino. At 24 hpf morphants show morphological defects in the CNS, particularly the interface between hindbrain and midbrain is not well-defined. At 28 hpf the morpholino injected embryos present an altered somite morphology and appear partially or completely immotile. At this stage the midbrain, hindbrain and cerebellum are compromised and not well defined compared with control embryos. The observed alterations persist at later developmental stages. Consistently, the expression pattern of two markers specifically expressed in the developing CNS, pax2a and neurod, is significantly altered in morphants. The co-injection of embryos with synthetic slc7a6os mRNA, rescues the morphant phenotype and restores the wild type expression pattern of pax2a and neurod. Our data suggest that slc7a6os might play a critical role in defined areas of the developing CNS in vertebrates, probably by regulating the expression of key genes.

Codes and combinatorial structures from circular planar nearrings

Nearrings are generalized rings in which addition is not in general abelian and only one distributive law holds. Some interesting combinatorial structures, as tactical configurations and balanced incomplete block designs (BIBDs) naturally arise when considering the class of planar and circular nearrings. In [12] the authors define the concept of disk and prove that in the case of field-generated planar circular nearrings it yields a BIBD, called disk-design. In this paper we present a method for the construction of an association scheme which makes the disk-design, in some interesting cases, an union of partially incomplete block designs (PBIBDs). Such designs can be used in the construction of some classes of codes for which we are able to calculate the parameters and to prove that in some cases they are also cyclic.

α-Labelings of a Class of Generalized Petersen Graphs

Abstract An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → {0, 1, 2, . . . , e} such that {|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . . , e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class of decompositions of complete graphs into copies of PSn,3.

Decompositions of graphs via generalized graceful labelings

Abstract In [Pasotti, A., On d-graceful labelings, to appear on Ars Combin] a d-divisible α-labeling is defined as a generalization of the classical one of Rosa (see [Rosa, A., On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349–355]) and, similarly to the classical case, it is proved that there exists a link between d-divisible α-labelings of a graph Γ and cyclic Γ-decompositions. In [Benini, A., and Pasotti, A., Decompositions of complete multipartite graphs via generalized graceful labelings, submitted. ( arXiv:1210.4370 )] we have dealt with the existence of d-divisible α-labelings of caterpillars and certain classes of cycles and hairy cycles and the resulting possible decompositions.

Partially balanced incomplete block designs from weakly divisible nearrings

In [[6] Riv. Mat. Univ. Parma 11 (2) (1970) 79-96] Ferrero demonstrates a connection between a restricted class of planar nearrings and balanced incomplete block designs. In this paper, bearing in mind the links between planar nearrings and weakly divisible nearrings (wd-nearrings), first we show the construction of a family of partially balanced incomplete block designs from a special class of wd-nearrings; consequently, we are able to give some formulas for calculating the design parameters.

New designs from circular nearrings

Let \({(N, \Phi)}\) be a finite circular Ferrero pair. We define the disk with center b and radius \({a, \mathcal{D}(a;b)}\), as