Coincidence isometries of a shifted square lattice

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating functions for the number of coincidence site lattices and coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool

A molecular overlayer with the Fibonacci square grid structure

Quasicrystals differ from conventional crystals and amorphous materials in that they possess long-range order without periodicity. They exhibit orders of rotational symmetry which are forbidden in periodic crystals, such as five-, ten-, and twelve-fold, and their structures can be described with complex aperiodic tilings such as Penrose tilings and Stampfli-Gaehler tilings. Previous theoretical work explored the structure and properties of a hypothetical four-fold symmetric quasicrystal-the so-called Fibonacci square grid. Here, we show an experimental realisation of the Fibonacci square grid structure in a molecular overlayer. Scanning tunnelling microscopy reveals that fullerenes (C ) deposited on the two-fold surface of an icosahedral Al-Pd-Mn quasicrystal selectively adsorb atop Mn atoms, forming a Fibonacci square grid. The site-specific adsorption behaviour offers the potential to generate relatively simple quasicrystalline overlayer structures with tunable physical properties and demonstrates the use of molecules as a surface chemical probe to identify atomic species on similar metallic alloy surfaces

Highly Precise and Developmentally Programmed Genome Assembly in Paramecium Requires Ligase IV–Dependent End Joining

During the sexual cycle of the ciliate Paramecium, assembly of the somatic genome includes the precise excision of tens of thousands of short, non-coding germline sequences (Internal Eliminated Sequences or IESs), each one flanked by two TA dinucleotides. It has been reported previously that these genome rearrangements are initiated by the introduction of developmentally programmed DNA double-strand breaks (DSBs), which depend on the domesticated transposase PiggyMac. These DSBs all exhibit a characteristic geometry, with 4-base 5′ overhangs centered on the conserved TA, and may readily align and undergo ligation with minimal processing. However, the molecular steps and actors involved in the final and precise assembly of somatic genes have remained unknown. We demonstrate here that Ligase IV and Xrcc4p, core components of the non-homologous end-joining pathway (NHEJ), are required both for the repair of IES excision sites and for the circularization of excised IESs. The transcription of LIG4 and XRCC4 is induced early during the sexual cycle and a Lig4p-GFP fusion protein accumulates in the developing somatic nucleus by the time IES excision takes place. RNAi–mediated silencing of either gene results in the persistence of free broken DNA ends, apparently protected against extensive resection. At the nucleotide level, controlled removal of the 5′-terminal nucleotide occurs normally in LIG4-silenced cells, while nucleotide addition to the 3′ ends of the breaks is blocked, together with the final joining step, indicative of a coupling between NHEJ polymerase and ligase activities. Taken together, our data indicate that IES excision is a “cut-and-close” mechanism, which involves the introduction of initiating double-strand cleavages at both ends of each IES, followed by DSB repair via highly precise end joining. This work broadens our current view on how the cellular NHEJ pathway has cooperated with domesticated transposases for the emergence of new mechanisms involved in genome dynamics

Gene expression in a paleopolyploid: a transcriptome resource for the ciliate Paramecium tetraurelia

International audienceBACKGROUND: The genome of Paramecium tetraurelia, a unicellular model that belongs to the ciliate phylum, has been shaped by at least 3 successive whole genome duplications (WGD). These dramatic events, which have also been documented in plants, animals and fungi, are resolved over evolutionary time by the loss of one duplicate for the majority of genes. Thanks to a low rate of large scale genome rearrangement in Paramecium, an unprecedented large number of gene duplicates of different ages have been identified, making this organism an outstanding model to investigate the evolutionary consequences of polyploidization. The most recent WGD, with 51% of pre-duplication genes still in 2 copies, provides a snapshot of a phase of rapid gene loss that is not accessible in more ancient polyploids such as yeast. RESULTS: We designed a custom oligonucleotide microarray platform for P. tetraurelia genome-wide expression profiling and used the platform to measure gene expression during 1) the sexual cycle of autogamy, 2) growth of new cilia in response to deciliation and 3) biogenesis of secretory granules after massive exocytosis. Genes that are differentially expressed during these time course experiments have expression patterns consistent with a very low rate of subfunctionalization (partition of ancestral functions between duplicated genes) in particular since the most recent polyploidization event. CONCLUSIONS: A public transcriptome resource is now available for Paramecium tetraurelia. The resource has been integrated into the ParameciumDB model organism database, providing searchable access to the data. The microarray platform, freely available through NimbleGen Systems, provides a robust, cost-effective approach for genome-wide expression profiling in P. tetraurelia. The expression data support previous studies showing that at short evolutionary times after a whole genome duplication, gene dosage balance constraints and not functional change are the major determinants of gene retention

Acquisition of genome-wide copy number alterations in monozygotic twins with acute lymphoblastic leukemia

Chimaeric fusion genes are highly prevalent in childhood acute lymphoblastic leukaemia (ALL) and are mostly pre-natal, early genetic events in the evolutionary trajectory of this cancer. ETV6-RUNX1-positive ALL also has multiple (~six per case) copy number alterations (CNA) as revealed by genome-wide SNP arrays. Recurrent CNA are probably 'driver' events contributing critically to clonal diversification and selection but, at diagnosis, their developmental timing is 'buried' in the leukaemia's covert natural history. This conundrum can be resolved with twin pairs. We identified and compared CNA in five pairs of monozygotic twins with concordant ETV6-RUNX1-positive ALL and one pair discordant for ETV6-RUNX1 positive ALL. We compared, within each pair, CNA classified as potential 'driver' or 'passenger' mutations based upon recurrency and, where known, gene function. An average of 5.1 (range 3-11) CNAs (excluding immunoglobulin/T-cell receptor alterations) were identified per case. All 'driver' CNA (total 32) were distinct within each of the five twin pairs with concordant ALL. 'Driver' CNA in another twin with ALL were all absent in the shared ETV6-RUNX1-positive pre-leukaemic clone of her healthy co-twin. These data place all 'driver' CNA secondary to the pre-natal gene fusion event and most probably post-natal in the sequential, molecular pathogenesis of ALL

Mentoring in Pediatric Oncology

A formal Mentorship Program within the Children's Oncology Group (COG) was established to pair young investigators (mentees) with established COG members (mentors). Despite the American Academy of Pediatrics policy statement promoting mentorship programs, there are no publications describing and evaluating national mentorship programs in pediatric subspecialties. In this study, a series of internal program evaluations were performed using surveys of both mentors and mentees. Responses were deidentified and analyzed to determine the utility of the program by both participant satisfaction and self-reported academic productivity. Results indicated that mentees were generally satisfied with the program. Mentor-mentee pairs that met at least quarterly demonstrated greater academic productivity than pairings that met less frequently. This formal mentorship program appeared to have subjective and objective utility for the development of academic pediatric subspecialists