Some open problems related to creative telescoping

Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research. This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.     

New insights on the external features of egg capsules and embryo development in the squid Loligo vulgaris

The embryonic development of the squid Loligo vulgaris was observed from 183 egg masses collected from special devices deployed throughout Cabrera National Park (Baleares Islands, western Mediterranean Sea). Sequence alignment analysis of the cytochrome oxidase I gene revealed that all embryos belonged to L. vulgaris. In total, 549 egg capsules were examined. Viable egg capsules (n = 420) were classified into one of five maturation stages according to the primary external features. The length of the viable egg capsules varied between 40 and 170 mm, and increased with embryonic development. The non-viable capsules (n = 129) were categorized into four groups: I (Ginger root), non-viable II and III, and empty egg capsule (IV). The percentage of non-viable capsules (i.e. grades I, II and III) was 92.25%. Empty capsules accounted for 7.75% of the total non-viable egg capsules. Embryonic development was classified into a second scale of eight stages. Egg capsule stage and embryonic stage were significantly related (n = 420; p < 0.001), facilitating the determination of the embryo developmental phase based on the outward appearance of the egg capsules. The embryo development stage based on the external features of the egg capsules might constitute an innovative tool for in situ embryological data collection. This new method is neither time consuming nor invasive, and could be helpful in fishing cruises, for scuba diving visual census in natural habitats and for laboratory culture. Slight variability in the developmental embryonic stages within egg capsules from the same egg mass was identified. The origin of this asynchrony is discussed. Chronological appearance of organs was similar to that of the six loliginid species previously examined. However, some developmental changes in the timing or rate of events (heterochronies) were observed: Hoyle’s organ was formed earlier in L. vulgaris and the appearance of ventral chromatophores was slightly delayed (2 days) compared with the other species considered.     

Coral reef tanaidacean assemblages along the SW and SE Gulf of Mexico: biodiversity,geographic distribution and community structure

The biodiversity, geographic distribution, and community parameters of the benthic tanaidaceans associated with three coral reefs along the SW and SE Gulf of Mexico were analysed. A total of 15,525 specimens were grouped in 36 species. The highest value of abundance was found in the PNSAV with 6382 tanaidaceans. The PNSAV presented 30 species, the ANPT-L 16 species, and the SABS 17 species. The species with the widest distribution were Pseudonototanais sp., Condrochelia dubia, Leptochelia forresti, Synapseudes sp., Haplopolemius propinquus, Alloleptochelia longimana, and Paradoxapseudes bermudeus. In the Veracruz System Reef, the highest abundance was recorded for Condrochelia dubia and Pseudonototanais sp. The highest value of diversity was obtained in the SABS (3.08 bits/ind in the reef Bajo Diez), and the lowest value was found in the PNSAV (0.07 bits/ind in the reef Isla de Enmedio). The highest value of abundance was found in coral rubble and macroalgae. A significant relationship between depth and specific richness was found in the three reef systems. Using cluster analysis, three groups were found in each system, mainly related to the proximity to the coast and to urban areas. This is one of the first studies to show the specific substrate and attributes of three communities of tanaidaceans along the SE–SW coast of the Gulf of Mexico.     

Mutations in the RNA exosome component gene EXOSC3 cause pontocerebellar hypoplasia and spinal motor neuron degeneration

RNA exosomes are multi-subunit complexes conserved throughout evolution and are emerging as the major cellular machinery for processing, surveillance and turnover of a diverse spectrum of coding and noncoding RNA substrates essential for viability. By exome sequencing, we discovered recessive mutations in EXOSC3 (encoding exosome component 3) in four siblings with infantile spinal motor neuron disease, cerebellar atrophy, progressive microcephaly and profound global developmental delay, consistent with pontocerebellar hypoplasia type 1 (PCH1; MIM 607596). We identified mutations in EXOSC3 in an additional 8 of 12 families with PCH1. Morpholino knockdown of exosc3 in zebrafish embryos caused embryonic maldevelopment, resulting in small brain size and poor motility, reminiscent of human clinical features, and these defects were largely rescued by co-injection with wild-type but not mutant exosc3 mRNA. These findings represent the first example of an RNA exosome core component gene that is responsible for a human disease and further implicate dysregulation of RNA processing in cerebellar and spinal motor neuron maldevelopment and degeneration.     

Different roles of the human Orc6 protein in the replication initiation process

In eukaryotes, binding of the six-subunit origin recognition complex (ORC) to DNA provides an interactive platform for the sequential assembly of pre-replicative complexes. This process licenses replication origins competent for the subsequent initiation step. Here, we analyze the contribution of human Orc6, the smallest subunit of ORC, to DNA binding and pre-replicative complex formation. We show that Orc6 not only interacts with Orc1–Orc5 but also with the initiation factor Cdc6. Biochemical and imaging experiments reveal that this interaction is required for licensing DNA replication competent. Furthermore, we demonstrate that Orc6 contributes to the interaction of ORC with the chaperone protein HMGA1a (high mobility group protein A1a). Binding of human ORC to replication origins is not specified at the level of DNA sequence and the functional organization of origins is poorly understood. We have identified HMGA1a as one factor that might direct ORC to AT-rich heterochromatic regions. The systematic analysis of the interaction between ORC and HMGA1a revealed that Orc6 interacts with the acidic C-terminus of HMGA1a and also with its AT-hooks. Both domains support autonomous replication if targeted to DNA templates. As such, Orc6 functions at different stages of the replication initiation process. Orc6 can interact with ORC chaperone proteins such as HMGA1a to facilitate chromatin binding of ORC and is also an essential factor for pre-RC formation.     

A transition zone complex regulates mammalian ciliogenesis and ciliary membrane composition

Mutations affecting ciliary components cause ciliopathies. As described here, we investigated Tectonic1 (Tctn1), a regulator of mouse Hedgehog signaling, and found that it is essential for ciliogenesis in some, but not all, tissues. Cell types that do not require Tctn1 for ciliogenesis require it to localize select membrane-associated proteins to the cilium, including Arl13b, AC3, Smoothened and Pkd2. Tctn1 forms a complex with multiple ciliopathy proteins associated with Meckel and Joubert syndromes, including Mks1, Tmem216, Tmem67, Cep290, B9d1, Tctn2 and Cc2d2a. Components of this complex co-localize at the transition zone, a region between the basal body and ciliary axoneme. Like Tctn1, loss of Tctn2, Tmem67 or Cc2d2a causes tissue-specific defects in ciliogenesis and ciliary membrane composition. Consistent with a shared function for complex components, we identified a mutation in TCTN1 that causes Joubert syndrome. Thus, a transition zone complex of Meckel and Joubert syndrome proteins regulates ciliary assembly and trafficking, suggesting that transition zone dysfunction is the cause of these ciliopathies.