Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Improving Short DNA Sequence Alignment with Parallel Computing

Variations in different types of genomes have been found to be responsible for a large degree of physical diversity such as appearance and susceptibility to disease. Identification of genomic variations is difficult and can be facilitated through computational analysis of DNA sequences. Newly available technologies are able to sequence billions of DNA base pairs relatively quickly. These sequences can be used to identify variations within their specific genome but must be mapped to a reference sequence first. In order to align these sequences to a reference sequence, we require mapping algorithms that make use of approximate string matching and string indexing methods. To date, few mapping algorithms have been tailored to handle the massive amounts of output generated by newly available sequencing technologies. In otrder to handle this large amount of data, we modified the popular mapping software BWA to run in parallel using OpenMPI. Parallel BWA matches the efficiency of multithreaded BWA functions while providing efficient parallelism for BWA functions that do not currently support multithreading. Parallel BWA shows significant wall time speedup in comparison to multithreaded BWA on high-performance computing clusters, and will thus facilitate the analysis of genome sequencing data.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Rational O(2)–Equivariant Spectra

The category of rational O(2)-equivariant cohomology theories has an algebraic model A(O(2)), as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational O(2)-equivariant spectra and the derived category of the abelian model DA(O(2)). In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.

SOME PROPERTIES OF THE MULTIPLICITY SEQUENCE FOR ARBITRARY IDEALS

In this work we prove that the Achilles-Manaresi multiplicity sequence, like the classical Hilbert-Samuel multiplicity, is additive with respect to the exact sequence of modules. We also prove the associativity formula for his mulitplicity sequence. As a consequence, we give new proofs for two results already known. First, the Achilles-Manaresi multiplicity sequence is an invariant up to reduction, a result first proved by Ciuperca. Second, I subset of J is a reduction of (J,M) if and only if c(0)(I(p), M(p)) = c(0)(J(p), M(p)) for all p is an element of Spec(A), a result first proved by Flenner and Manaresi.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

EVOLUTION OF FLORAL MORPHOLOGY AND POLLINATION SYSTEM IN BIGNONIEAE (BIGNONIACEAE)

The radiation of angiosperms is associated with shifts among pollination modes that are thought to have driven the diversification of floral forms. However, the exact sequence of evolutionary events that led to such great diversity in floral traits is unknown for most plant groups. Here, we characterize the patterns of evolution of individual floral traits and overall floral morphologies in the tribe Bignonieae (Bignoniaceae). We identified 12 discrete traits that are associated with seven floral types previously described for the group and used a penalized likelihood tree of the tribe to reconstruct the ancestral states of those traits at all nodes of the phylogeny of Bignonieae. In addition, evolutionary correlations among traits were conducted using a maximum likelihood approach to test whether the evolution of individual floral traits followed the correlated patterns of evolution expected under the ""pollination syndrome"" concept. The ancestral Bignonieae flower presented an Anemopaegma-type morphology, which was followed by several parallel shifts in floral morphologies. Those shifts occurred through intermediate stages resulting in mixed floral morphologies as well as directly from the Anemopaegma-type morphology to other floral types. Positive and negative evolutionary correlations among traits fit patterns expected under the pollination syndrome perspective, suggesting that interactions between Bignonieae flowers and pollinators likely played important roles in the diversification of the group as a whole.

E2F1 mediates DNA damage and apoptosis through HCF-1 and the MLL family of histone methyltransferases.

E2F1 is a key positive regulator of human cell proliferation and its activity is altered in essentially all human cancers. Deregulation of E2F1 leads to oncogenic DNA damage and anti-oncogenic apoptosis. The molecular mechanisms by which E2F1 mediates these two processes are poorly understood but are important for understanding cancer progression. During the G1-to-S phase transition, E2F1 associates through a short DHQY sequence with the cell-cycle regulator HCF-1 together with the mixed-lineage leukaemia (MLL) family of histone H3 lysine 4 (H3K4) methyltransferases. We show here that the DHQY HCF-1-binding sequence permits E2F1 to stimulate both DNA damage and apoptosis, and that HCF-1 and the MLL family of H3K4 methyltransferases have important functions in these processes. Thus, HCF-1 has a broader role in E2F1 function than appreciated earlier. Indeed, sequence changes in the E2F1 HCF-1-binding site can modulate both up and down the ability of E2F1 to induce apoptosis indicating that HCF-1 association with E2F1 is a regulator of E2F1-induced apoptosis.

Biochemical characterization of recombinant human telomerase

Résumé Les télomères sont les structures ADN-protéines des extrémités des chromosomes des eucaryotes. L'ADN télomérique est constitué de courtes séquences répétitives. L'intégrité des télomères est essentielle pour protéger les extrémités des chromosomes contre les systèmes de dégradations et pour les distinguer des cassures de l'ADN double brin. Parce que la machinerie de la réplication de l'ADN n'est pas capable de répliquer l'extrémité des chromosomes, les télomères raccourcissent au fur et à mesure des cycles de réplication. Dès que les télomères atteignent une longueur critique, leur structure protectrice est perdue. Cela induit un signal de dommage de l'ADN et l'arrêt du cycle cellulaire. Pour contrebalancer le raccourcissement des télomères, les cellules qui s'auto régénèrent, dont les cellules de la moelle osseuse, les lymphocytes activés et 80-90% des cellules cancéreuses, expriment la télomérase. C'est une ribonucléoprotéine qui a la capacité de synthétiser des séquences télomériques par transcription inverse d'une courte séquence contenue dans sa propre sous-unité ARN avec laquelle elle est associée. La télomérase humaine est une enzyme processive au niveau de l'addition des nucléotides et aussi des répétitions télomériques. La télomérase de levure et la télomérase humaine sont toutes deux dimériques et il a été montré que la télomérase humaine recombinante contient deux ARN qui coopèrent pour fonctionner ainsi que deux sous-unités catalytiques. Cependant, il n'a pas encore été montré quel est le rôle de la dimérisation dans l'activité de la télomérase. Afin d'élucider ce rôle, nous avons exprimé, reconstitué et purifié la télomérase humaine dimérique recombinante. Et pour étudier l'effet d'ARN mutants sur l'activité de la télomérase, nous avons développé une méthode pour reconstituer et enrichir en hétérodimères de télomérase. Les hétérodimères contiennent une sous-unité ARN sauvage et une sous-unité ARN mutée au niveau de la séquence de la matrice. Sur l'ARN muté nous avons introduit une étiquette aptamer ARN-S1 puis nous avons purifié la télomérase via l'etiquette Si. Nous avons montré que la dimérisation est essentielle pour l'activité de la télomérase. Nos données indiquent que chaque télomérase du dimère allonge leur substrat, l'ADN télomérique, indépendamment l'une de l'autre à chaque cycle d'élongation mais que l'addition itérative de répétitions télomériques nécessite une coopération entre les deux télomérases du dimère. Nous proposons donc un modèle dans lequel les deux télomérases du dimères se lient et allongent deux substrats télomères et que pendant l'élongation processive les deux enzymes subissent un changement de conformation de manière coordonnée, ce changement va permettre le repositionnement des substrats pour d'autres cycles d'additions de répétitions télomériques. Dyskeratosis congenita est une maladie mortelle due majoritairement au disfonctionnement de la moelle osseuse. Dans la forme autosomale de la maladie, l'ARN de la télomérase contient des mutations. En utilisant notre système de reconstitution, nous avons montré que ces ARN mutés, qui ont perdu leur activité enzymatique dans le cas d'un homodimère de mutants, sont dominant négatifs quand ils sont présents dans les hétérodimères sauvage/mutant. Cet effet trans-dominant négatif pourrait contribuer à la progression de la maladie. Abstract Telomeres are protein-DNA structures at the ends of linear eukaryotic chromosomes. The telomeric DNA consists of tandemly repeated sequences. Telomeric integrity is essential to protect chromosomal ends from nucleolytic degradation and to prevent their recognition as DNA double strand breaks. Due to the inability of the conventional DNA replication machinery to replicate terminal DNA stretches, telomeres shorten with continuous rounds of DNA replication. As soon as telomeres reach a critical length, their protective structure is lost and the deprotected telomeres will induce a DNA damage response leading to cell cycle arrest. To counteract telomere shortening, self-renewing cells, including bone marrow cells, activated lymphocytes and 80-90% of cancer cells express the cellular reverse transcriptase telomerase, which has the capacity to synthesize telomeric repeats by reverse transcription of a short template sequence encoded by its stably associated RNA subunit. Human telomerase is a processive enzyme for nucleotide as well as repeat addition. Both yeast and human telomerase are dimeric enzymes and recombinant human telomerase has been shown to contain two functionally cooperating RNAs and most probably also two protein subunits. However, it has remained unclear how dimerization may contribute to telomerase activity. To study the role of dimerization, we expressed, reconstituted and purified recombinant human telomerase. We also developed a new method to reconstitute and enrich for telomerase heterodimers containing wild-type (wt) and mutant telomerase RNA subunits. To this end we introduced an S1-RNA-aptamer tag into telomerase RNA and purified telomerase reconstituted with a mixture of untagged and tagged RNA via the S1-tag. Using this experimental system, we introduced template mutations in the tagged RNA subunit and examined the effect of mutant RNAs on wt telomerase activity in wt/mutant heterodimers. We obtained evidence that dimerization is essential for telomerase activity. Our data indicate that the two subunits elongate telomere substrates independently of each other during single rounds of elongation, but that iterative addition of telomeric repeats requires cooperation between the two subunits. We suggest a model, in which dimeric telomerases bind and elongate two telomere substrates and that the two subunits undergo coordinated conformational changes during processive elongation that enable repositioning the substrates for subsequent rounds of repeat addition. Dyskeratosis congenita is a multisystemic disease with bone marrow failure as the major cause of death. The autosomal form of this disease was found to harbor mutations in the telomerase RNA. Using our reconstitution system, we tested whether mutant dyskeratosis telomerase RNAs behaved in a dominant negative manner. We observed that dyskeratosis telomerase RNA mutants, which lacked enzymatic activity were dominant negative, when present in wt/ mutant heterodimers. The transdominant negative effect of these mutants may contribute to disease progression.

Identification of novel expressed sequences, up-regulated in the leucocytes of chronic fatigue syndrome patients

BACKGROUND: Chronic fatigue syndrome (CFS) is an increasing medical phenomenon of unknown aetiology leading to high levels of chronic morbidity. Of the many hypotheses that purport to explain this disease, immune system activation, as a central feature, has remained prominent but unsubstantiated. Supporting this, a number of important cytokines have previously been shown to be over-expressed in disease subjects. The diagnosis of CFS is highly problematic since no biological markers specific to this disease have been identified. The discovery of genes relating to this condition is an important goal in seeking to correctly categorize and understand this complex syndrome. OBJECTIVE: The aim of this study was to screen for changes in gene expression in the lymphocytes of CFS patients. METHODS: 'Differential Display' is a method for comparing mRNA populations for the induction or suppression of genes. In this technique, mRNA populations from control and test subjects can be 'displayed' by gel electrophoresis and screened for differing banding patterns. These differences are indicative of altered gene expression between samples, and the genes that correspond to these bands can be cloned and identified. Differential display has been used to compare expression levels between four control subjects and seven CFS patients. RESULTS: Twelve short expressed sequence tags have been identified that were over-expressed in lymphocytes from CFS patients. Two of these correspond to cathepsin C and MAIL1 - genes known to be upregulated in activated lymphocytes. The expression level of seven of the differentially displayed sequences have been verified by quantifying relative level of these transcripts using TAQman quantitative PCR. CONCLUSION: Taken as a whole, the identification of novel gene tags up-regulated in CFS patients adds weight to the idea that CFS is a disease characterized by subtle changes in the immune system.

Postlarval stages and growth patterns of the spider crab Pyromaia tuberculata (Brachyura, Majidae) from laboratory-reared material

The spider crab Pyromaia tuberculata was introduced into southeastern Brazil; ovigerous material was collected and reared in the laboratory. Morphologic changes and growth patterns of post-larval development are reported. Results show that within-stage size variation is lowest in mature stages, especially in the case of females in which there is an apparent size threshold for the last juvenile stages to undergo the puberty molt. A prepuberty molt taking place at the fourth crab stage is indicated by analyzing the allometric growth of the abdomen in females. In contrast, the same procedure using the allometric growth of chelae failed in detecting both the prepuberty and puberty molts in males. Conversely to females, which develop a complex brood chamber at the puberty molt, the enlargement of chelae was not consistent in all postpuberty males. The short instar sequence of this species, in no case exceeding nine stages, is marked by conspicuous morphologic alterations achieved at each molt. Almost all stages can be identified by examining diagnostic features of rostrum, abdomen, sternum, and pleopods.

Remarks on immersions in the metastable dimension range

In this work we present a generalization of an exact sequence of normal bordism groups given in a paper by H. A. Salomonsen (Math. Scand. 32 (1973), 87-111). This is applied to prove that if h : M-n --> Xn+k, 5 less than or equal to n < 2k, is a continuous map between two manifolds and g : M-n --> BO is the classifying map of the stable normal bundle of h such that (h, g)(*) : H-i (M, Z(2)) --> H-i (X x BO, Z(2)) is an isomorphism for i < n - k and an epimorphism for i = n - k, then h bordant to an immersion implies that h is homotopic to an immersion. The second remark complements the result of C. Biasi, D. L. Goncalves and A. K. M. Libardi (Topology Applic. 116 (2001), 293-303) and it concerns conditions for which there exist immersions in the metastable dimension range. Some applications and examples for the main results are also given.