Some constructions, related to noncommutative tori; Fredholm modules and the Beilinson-Bloch regulator

A noncommutative 2-torus is one of the main toy models of noncommutative geometry, and a noncommutative n-torus is a straightforward generalization of it. In 1980, Pimsner and Voiculescu in [17] described a 6-term exact sequence, which allows for the computation of the K-theory of noncommutative tori. It follows that both even and odd K-groups of n-dimensional noncommutative tori are free abelian groups on 2^n-1 generators. In 1981, the Powers-Rieffel projector was described [19], which, together with the class of identity, generates the even K-theory of noncommutative 2-tori. In 1984, Elliott [10] computed trace and Chern character on these K-groups. According to Rieffel [20], the odd K-theory of a noncommutative n-torus coincides with the group of connected components of the elements of the algebra. In particular, generators of K-theory can be chosen to be invertible elements of the algebra. In Chapter 1, we derive an explicit formula for the First nontrivial generator of the odd K-theory of noncommutative tori. This gives the full set of generators for the odd K-theory of noncommutative 3-tori and 4-tori.

In Chapter 2, we apply the graded-commutative framework of differential geometry to the polynomial subalgebra of the noncommutative torus algebra. We use the framework of differential geometry described in [27], [14], [25], [26]. In order to apply this framework to noncommutative torus, the notion of the graded-commutative algebra has to be generalized: the "signs" should be allowed to take values in U(1), rather than just {-1,1}. Such generalization is well-known (see, e.g., [8] in the context of linear algebra). We reformulate relevant results of [27], [14], [25], [26] using this extended notion of sign. We show how this framework can be used to construct differential operators, differential forms, and jet spaces on noncommutative tori. Then, we compare the constructed differential forms to the ones, obtained from the spectral triple of the noncommutative torus. Sections 2.1-2.3 recall the basic notions from [27], [14], [25], [26], with the required change of the notion of "sign". In Section 2.4, we apply these notions to the polynomial subalgebra of the noncommutative torus algebra. This polynomial subalgebra is similar to a free graded-commutative algebra. We show that, when restricted to the polynomial subalgebra, Connes construction of differential forms gives the same answer as the one obtained from the graded-commutative differential geometry. One may try to extend these notions to the smooth noncommutative torus algebra, but this was not done in this work.

A reconstruction of the Beilinson-Bloch regulator (for curves) via Fredholm modules was given by Eugene Ha in [12]. However, the proof in [12] contains a critical gap; in Chapter 3, we close this gap. More specifically, we do this by obtaining some technical results, and by proving Property 4 of Section 3.7 (see Theorem 3.9.4), which implies that such reformulation is, indeed, possible. The main motivation for this reformulation is the longer-term goal of finding possible analogs of the second K-group (in the context of algebraic geometry and K-theory of rings) and of the regulators for noncommutative spaces. This work should be seen as a necessary preliminary step for that purpose.

For the convenience of the reader, we also give a short description of the results from [12], as well as some background material on central extensions and Connes-Karoubi character.

Spawning behavior and larval development in Mopalia lignosa and Mopalia muscosa (Mollusca: Polyplacophora) in central California

Spawning behavior and external features of the larval development were studied in the chitons Mopalia muscosa and M. lignosa during the months of April-June, 1974, at Pacific Grove, California. ... The sequence of events in the development of the two species in the same, though some differences in timing exist.

Mitochondrial control region sequence variation within the argali wild sheep (Ovis ammon): evolution and conservation relevance

The phylogenetic relationship of several subspecies of Ovis ammon were analyzed by comparing DNA sequences within the entire mitochondrial D-loop region. Five putative subspecies of ammon (dalai-lamae, darwini, hodgsoni, sairensis and adamerzi) were sampled from four provinces in China [Xinjiang, Qinghai, Gansu and Xizang (Tibet)] and two (servertzovi and nigrimontana) from Uzbekistan. The argalis sampled represent most of the currently recognized putative Subspecies of argali. Analysis of mtDNA sequences revealed high variability within ammon (7.7%), ranging from 2.4 to 11.5%. MaxiMUM-Parsimony tree indicated that nigrimontana from Uzbekistan diverged First, followed by severtzovi from Uzbekistan. The dispersal of argalis into China gave rise to three clades, suggesting that the argali originated in Western Asia and then dispersed throughout the central Asian highlands on a southeastward course. Among the Chinese argalis, mtDNA analysis places dalailamae genetically closer to hodgsoni than to darwini. Severtzovi and.. nigrimontana are two separate subspecies and genetically distinct from the Chinese argali.

The first non-mammalian CXCR3 in a teleost fish: Gene and expression in blood cells and central nervous system in the grass carp (Ctenopharyngodon idella)

A novel fish chemokine receptor gene, chemokine (C-X-C motif) receptor 3 (CXCR3)-like was isolated from the grass carp Ctenopharyngodon idella , with its full-length genomic sequence. The cDNA of grass carp CXCR3-like (gcCXCR3-like) consists of 1261 bp with a 49bp 5'-UTR and a 189 bp 3'-UTR. An open reading frame of 1023 bp encodes a 341-amino acid peptide, with seven transmembrane helices. The deduced amino acid sequence showed the same sequence identities (37.8%) with its counterparts in goat and human. The gcCXCR3-like gene consists of two exons, with one intervening intron, spaced over approximately 2 kb of genomic sequence. Phylogenetic analyses clearly demonstrated that the gcCXCR3-like resembles the CXCR3s of other vertebrates. Real-time PCR analysis showed that gcCXCR3-like was expressed in all tested organs except heart and the expression level of gcCXCR3-like was highest in brain. Flow cytometric analyses showed the positive rate of labelled leukocytes from the healthy grass carp was 17.3%, and the labelled leukocytes were divided into three types by cell sorting. Immunohistochemical localization revealed that gcCXCR3-like expressed in whole brain regions including cerebel, diencephalon, medulla oblongata, optic lobe, and rhinencephalon, and that the labelled leukocytes are actually populations of monocyte and/or phagocyte, lymphocyte and the granulocyte. It is considered that fish CXCR expression and their function may need to be investigated in both nervous and immune systems. (c) 2006 Elsevier Ltd. All rights reserved.

Sequence variations in the mitochondrial DNA control region and their implications for the phylogeny of the Cypriniformes

The mitochondrial DNA control region of six cobitids and two catostomids was sequenced and compared with sequences of other cypriniforms to study their sequence variations. The extended termination associated sequence (ETAS) domain, central domain, and conserved sequence block (CSB) domain were partitioned and the ETAS sequence, CSB-D, CSB-E, ECSB-F, CSB1, CSB2, and CSB3 were identified. It is suggested that the "hairpin" TACAT-ATGTA is the key sequence of ETAS and GACATA is the symbol of CSB1. Phylogenetic analysis based on the CSB domain showed that all cyprinids evolved as one monophyletic group, while the non-cyprinid Cypriniformes could be another monophyly that is in accordance with the hypothesis proposed by Siebert. Further analysis of the phylogeny of the Cobitoidei was also conducted and it is tentatively suggested that their relationships are Catostomidae + (Gyrinocheilidae + (Botiinae + (Homalopteridae + (Cobitinae + Nemacheilinae)))).

Effect of DNA flanking sequence on charge transport in short DNA duplexes

Several factors can influence charge transport (CT)-mediated DNA, such as sequence, distance, base stacking, base pair mismatch, conformation, tether length, etc. However, the DNA context effect or how flanking sequences influence redox active drugs in the DNA CT reaction and later in DNA enzymatic repair and synthesis is still not well understood. The set of seven DNA molecules in this study have been characterized well for the study of flanking sequence effects. These DNA duplexes are formed from self-complementary strands and contain the common central four-base sequence 5'-A-G-C-T-3', flanked on both sides by either (AT)(n) or (AA)(n) (n = 2, 3, or 4) or AA(AT)(2). UV-vis, fluorescence, UV melting, circular dichroism, and cyclic voltammetry experiments were used to study the flanking sequence effect on CT-mediated DNA by using daunomycin or adriamycin cross-linked with these seven DNA molecules. Our results showed that charge transport was related to the flanking sequence, DNA melting free energy, and ionic strength. For (AA)(n) or (AT)(n) species of the same length, (AA)(n) series were more stable and more efficient CT was observed through the (AA)(n) series. The same trend was observed for (AA)(n) and (AT)(n) series at different ionic strengths, further supporting the idea that flanking sequence can result in different base stacking and modulate charge transport through these seven DNA molecules.

Homology Induction: the use of machine learning to improve sequence similarity searches

Karwath, A. King, R. Homology induction: the use of machine learning to improve sequence similarity searches. BMC Bioinformatics. 23rd April 2002. 3:11 Additional File Describes the title organims species declaration in one string [http://www.biomedcentral.com/content/supplementary/1471- 2105-3-11-S1.doc] Sponsorship: Andreas Karwath and Ross D. King were supported by the EPSRC grant GR/L62849.

Sequence and Structure Based Protein Folding Studies With Implications

As the expression of the genetic blueprint, proteins are at the heart of all biological systems. The ever increasing set of available protein structures has taught us that diversity is the hallmark of their architecture, a fundamental characteristic that enables them to perform the vast array of functionality upon which all of life depends. This diversity, however, is central to one of the most challenging problems in molecular biology: how does a folding polypeptide chain navigate its way through all of the myriad of possible conformations to find its own particular biologically active form? With few overarching structural principles to draw upon that can be applied to all protein architecture, the search for a solution to the protein folding problem has yet to produce an algorithm that can explain and duplicate this fundamental biological process. In this thesis, we take a two-pronged approach for investigating the protein folding process. Our initial statistical studies of the distributions of hydrophobic and hydrophilic residues within α-helices and β-sheets suggest (i) that hydrophobicity plays a critical role in helix and sheet formation; and (ii) that the nucleation of these motifs may result in largely unidirectional growth. Most tellingly, from an examination of the amino acids found in the smallest β-sheets, we do not find any evidence of a β-nucleating code in the primary protein sequence. Complementing these statistical analyses, we have analyzed the structural environments of several ever-widening aspects of protein topology. Our examination of the gaps between strands in the smallest β-sheets reveals a common organizational principle underlying β-formation involving strands separated by large sequential gaps: with very few exceptions, these large gaps fold into single, compact structural modules, bringing the β-strands that are otherwise far apart in the sequence close together in space. We conclude, therefore, that β-nucleation in the smallest sheets results from the co-location of two strands that are either local in sequence, or local in space following prior folding events. A second study of larger β-sheets both corroborates and extends these findings: virtually all large sequential gaps between pairs of β-strands organize themselves into an hierarchical arrangement, creating a bread-crumb model of go-and-come-back structural organization that ultimately juxtaposes two strands of a parental β-structure that are far apart in the sequence in close spatial proximity. In a final study, we have formalized this go-and-come-back notion into the concept of anti-parallel double-strandedness (DS), and measure this property across protein architecture in general. With over 90% of all residues in a large, non-redundant set of protein structures classified as DS, we conclude that DS is a unifying structural principle that underpins all globular proteins. We postulate, moreover, that this one simple principle, anti-parallel double-strandedness, unites protein structure, protein folding and protein evolution.

Novel dermaseptin, adenoregulin and caerin homologs from the Central American red-eyed leaf frog, Agalychnis callidryas, revealed by functional peptidomics of defensive skin secretion

By integrating systematic peptidome and transcriptome studies of the defensive skin secretion of the Central American red-eyed leaf frog, Agalychnis callidryas, we have identified novel members of three previously described antimicrobial peptide families, a 27-mer dermaseptin-related peptide (designated DRP-AC4), a 33-mer adenoregulin-related peptide (designated ARP-AC1) and most unusually, a 27-mer caerin-related peptide (designated CRP-AC1). While dermaseptin and adenoregulin were originally isolated from phyllomedusine leaf frogs, the caerins, until now. had only been described in Australian frogs of the genus, Litoria. Both the dermaseptin and adenoregulin were C-terminally amidated and lacked the C-terminal tripeptide of the biosynthetic precursor sequence. In contrast, the caerin-related peptide, unlike the majority of Litoria analogs. was not C-terminally amidated. The present data emphasize the need for structural characterization of mature peptides to ensure that unexpected precursor cleavages and/or post-translational modifications do not produce mature peptides that differ in structure to those predicted from cloned biosynthetic precursor cDNA. Additionally, systematic study of the secretory peptidome can produce unexpected results such as the CRP described here that may have phylogenetic implications. It is thus of the utmost importance in the functional evaluation of novel peptides that the primary structure of the mature peptide is unequivocally established - something that is often facilitated by cloning biosynthetic precursor cDNAs but obviously not reliable using such data alone. (C) 2008 Elsevier Masson SAS. All rights reserved.

Patterns of variation at a mitochondrial sequence-tagged-site locus provides new insights into the postglacial history of European Pinus sylvestris populations

Due to their maternal mode of inheritance, mitochondrial markers can be regarded as almost 'ideal' tools in evolutionary studies of conifer populations. In the present study, polymorphism was analysed at one mitochondrial intron (nad 1, exon B/C) in 23 native European Pinus sylvestris populations. In a preliminary screening for variation using a polymerase chain reaction-restriction fragment length polymorphism approach, two length variants were identified. By fully sequencing the 2.5 kb region, the observed length polymorphism was found to result from the insertion of a 31 bp sequence, with no other mutations observed within the intron. A set of primers was designed flanking the observed mutation, which identified a novel sequence-tagged-site mitochondrial marker for P. sylvestris. Analysis of 747 trees from the 23 populations using these primers revealed the occurrence of two distinct haplotypes in Europe. Within the Iberian Peninsula, the two haplotypes exhibited extensive population differentiation (Phi(ST) = 0.59; P less than or equal to 0.001) and a marked geographical structuring. In the populations of central and northern Europe, one haplotype largely predominated, with the second being found in only one individual of one population.

Late Holocene climate change in central Sweden inferred from lacustrine stable isotope data

Stable isotopes (delta O-18 and delta C-13) of lacustrine carbonates (Chara spp. algae and Pisidium spp. molluscs) from a lake sedimentary sequence in central Sweden were analysed to infer changes in lake hydrology and climate during the late Holocene. Results from analysis of lake water isotopes (delta O-18 and delta H-2) show that Lake Blektjarnen water isotope composition is responsive to the balance between evaporation and input water (E/l ratio). A high E/l ratio results from a dry and probably warmer climate, decreasing the relative importance of precipitation input. Under such conditions evaporation and atmospheric equilibration probably enrich lake water in O-18 and C-13, respectively, which is reflected in the isotopic composition of the carbonates in the lake. From the relatively positive Chara delta O-18 values we infer that conditions were dry and warm between 4400 and 4000 cal. a BP, whereas more negative values indicate that conditions were wetter and probably cooler between 4000 and 3000 cal. a BP. A drier climate is inferred from more positive values between 2500 and 1000 cal. a BP. However, a successive depletion after ca. 1750 cal. a BP, also detected in several other delta O-18 records (carbonate and diatom), suggest increasingly wetter conditions in Scandinavia after that time, which is probably related to increased strength of the zonal flow.

Complete Genome Sequence of Propionibacterium acnes Type IB Strain 6609

Propionibacterium acnes is an anaerobic Gram-positive bacterium that forms part of the normal human cutaneous microbiota and is thought to play a central role in acne vulgaris, a chronic inflammatory disease of the pilosebaceous unit (I. Kurokawa et al., Exp. Dermatol. 18:821-832, 2009). Here we present the whole genome sequence of P. acnes type IB strain 6609, which was recovered from a skin sample from a woman with no recorded acne history and is thus considered a nonpathogenic strain (I. Nagy, Microbes Infect. 8:2195-2205, 2006).

Sequence-Specific and Strand-Specific Cleavage In Oligodeoxyribonucleotides and DNA Containing 3'-Thiothymidine

Oligonucleotides containing a 3'-thiothymidine residue (T3's) at the cleavage site for the EcoRV restriction endonuclease (between the central T and A residues of the sequence GATATC) have been prepared on an automated DNA synthesizer using 5'-O-monomethoxytritylthymidine 3'-S-(2-cyanoethyl N,N-di-isopropylphosphorothioamidite). The self-complementary sequence GACGAT3'sATCGTC was completely resistant to cleavage by EcoRV, while the heteroduplex composed of 5'-TCTGAT3'sATCCTC and 5'-GAGGATATCAGA (duplex 4) was cleaved only in the unmodified strand (5'-GAGGATATCAGA). In contrast, strands containing a 3'-S-phosphorothiolate linkage could be chemically cleaved specifically at this site with Ag+. A T3's residue has also been incorporated in the (-) strand of double-stranded closed circular (RF IV) M13mp18 DNA at the cleavage site of a unique EcoRV recognition sequence by using 5'-pCGAGCTCGAT3'sATCGTAAT as a primer for polymerization on the template (+) strand of M13mp18 DNA. On treatment of this substrate with EcoRV, only one strand was cleaved to produce the RF II or nicked DNA. Taken in conjunction with the cleavage studies on the oligonucleotides, this result demonstrates that the 3'-S-phosphorothiolate linkage is resistant to scission by EcoRV. Additionally, the phosphorothiolate-containing strand of the M13mp18 DNA could be cleaved specifically at the point of modification using iodine in aqueous pyridine. The combination of enzymatic and chemical techniques provides, for the first time, a demonstrated method for the sequence-specific cleavage of either the (+) or (-) strand.