Generalizing the rotation interval to vertex maps on graphs

Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the rotation elements associated to periodic points in a given edge of the graph. Most of the results show that the existence of two periodic points with certain rotation elements will imply an infinite family of other periodic points with related rotation elements. These results for periodic points can be considered as generalizations of the rotation interval for degree one maps of the circle

Immobilisation of electroactive macrocyclic complexes within titania films

The 4-carboxyphenyl-appended macrocyclic ligand trans-6,13-dimethyl-6-((4-carboxybenzyl)amino)-1,4,8,11-tetraazacyclotetradecane-6-amine (HL10) has been synthesised and complexed with Co-III. The mononuclear complexes [Co(HL10)(CN)](2+) and [CoL10(OH)](+) have been prepared and the crystal structures of their perchlorate salts are presented, where the ligand is bound in a pentadentate mode in each case while the 4-carboxybenzyl-substituted pendent amine remains free from the metal. The cyano-bridged dinuclear complex [CoL10-mu-NC-Fe(CN)(5)](2-) was also prepared and chemisorbed on titania-coated ITO conducting glass. The adsorbed complex is electrochemically active and cyclic voltammetry of the modified ITO working electrode in both water and MeCN solution was undertaken with simultaneous optical spectroscopy. This experiment demonstrates that reversible electrochemical oxidation of the Fe-II centre is coupled with rapid changes in the optical absorbance of the film

Geometric isomers of chloro(6-methyl-1,4,8,11-tetraazacyclotetradecane-6-amine)cobalt(III) tetrachlorozincate(II)

The crystal structures of a pair of cis and trans isomers of the macrocyclic chloropentaamine title complex, as their tetrachlorozincate(II) salts, [CoCl(C11H27N5)][ZnCl4], are reported. The two distinct isomeric forms lead to significant variations in the Co-N bond lengths and, furthermore, hydrogen bonding between the complex ions is influenced by the folded (cis) or planar (trans) conformations of the coordinated ligand

The response of the ionosphere to the injection of chemically reactive vapors

As a gas released in the ionosphere expands, it is rapidly cooled. When the vapor becomes sufficiently tenuous, it is reheated by collisions with the ambient atmosphere and its flow is then governed by diffusive expansion. As the injected gas becomes well mixed with the plasma, a hole is created by chemical processes. In the case of diatomic hydrogen release, depression of the electron concentrations is governed by the charge exchange reaction between oxygen ions and hydrogen, producing positive hydroxyl ions. Hydroxyl ions rapidly react with the electron gas to produce excited oxygen and hydrogen atoms. Enhanced airglow emissions result from the transition of the excited atoms to lower energy states. The electron temperature in the depleted region rises sharply causing a thermal expansion of the plasma and a further reduction in the local plasma concentration

Tuning the metal-to-metal charge transfer energy of cyano-bridged dinuclear complexes

The metal-to-metal charge transfer (MMCT) transitions of a series of Class II mixed valence dinuclear complexes bearing cyano bridging ligands may be varied systematically by variations to either the hexacyanometallate(II) donor or Co-III acceptor moieties. Specifically, the new dinuclear species trans-[(LCoNCFe)-Co-14S(CN)(5)](-) (L-14S = 6-methyl-1,11-diaza-4,8-dithia- cyclotetradecane-6-amine) and trans-[(LCoNCRu)-Co-14(CN)(5)]-(L-14 = 6-methyl-1,4,8,11-tetraazacyclotetradecane-6-amine) have been prepared and their spectroscopic and electrochemical properties are compared with the relative trans-[(LCoNCFe)-Co-14(CN)(5)](-). The crystal structures of Na{trans-[(LCoNCFe)-Co-14S(CN)(5)]}.51/2H(2)O.1/2EtOH, Na{trans-[(LCoNCRu)-Co-14(CN)(5)]}.3H(2)O and Na{trans-[(LCoNCRu)-Co-14(CN)(5)]}.8H(2)O are also reported. The ensuing changes to the MMCT energy have been examined within the framework of Hush theory, and it was found that the free energy change between the redox isomers was the dominant effect in altering the energy of the MMCT transition

trans-Cyano(6-methyl-1,4,8,11-tetraazacyclotetradecan-6-amine)cobalt(III) bis(perchlorate) hydrate and trans-hydroxo(6-methyl-1,4,8,11-tetraazacyclotetradecan-6-amine)cobalt(III) bis(perchlorate)

The crystal structures of a pair of closely related macrocyclic cyano- and hydroxopentaaminecobalt(III) complexes, as their perchlorate salts, are reported. Although the two complexes, [Co(CN)(C11H27N5)](ClO4)2.H2O and [Co(OH)(C11H27N5)](ClO4)(2), exhibit similar conformations, significant differences in the Co-N bond lengths arise from the influence of the sixth ligand (cyano as opposed to hydroxo). The ensuing hydrogen-bonding patterns are also distinctly different. Disorder in the perchlorate anions was clearly resolved and this was rationalized on the basis of distinct hydrogen-bonding motifs involving the anion O atoms and the N-H and O-H donors

Sneutrino as Lightest Supersymmetric Particle in B3 mSUGRA Models and Signals at the LHC

We consider B3 mSUGRA models where we have one lepton number violating LQD operator at the GUT scale. This can alter the supersymmetric mass spectrum leading to a sneutrino as the lightest supersymmetric particle in a large region of parameter space. We take into account the restrictions from neutrino masses, the muon anomalous magnetic moment, b -> s gamma and other precision measurements. We furthermore investigate existing restrictions from direct searches at LEP, the Tevatron and the CERN p\bar p collider. We then give examples for characteristic signatures at the LHC.Comment: 22 pages, 11 figure

Primordial soup or vinaigrette: did the RNA world evolve at acidic pH?

<p>Abstract</p> <p>Background</p> <p>The RNA world concept has wide, though certainly not unanimous, support within the origin-of-life scientific community. One view is that life may have emerged as early as the Hadean Eon 4.3-3.8 billion years ago with an atmosphere of high CO₂producing an acidic ocean of the order of pH 3.5-6. Compatible with this scenario is the intriguing proposal that life arose within alkaline (pH 9-11) deep-sea hydrothermal vents like those of the 'Lost City', with the interface with the acidic ocean creating a proton gradient sufficient to drive the first metabolism. However, RNA is most stable at pH 4-5 and is unstable at alkaline pH, raising the possibility that RNA may have first arisen in the acidic ocean itself (possibly near an acidic hydrothermal vent), acidic volcanic lake or comet pond. As the Hadean Eon progressed, the ocean pH is inferred to have gradually risen to near neutral as atmospheric CO₂levels decreased.</p> <p>Presentation of the hypothesis</p> <p>We propose that RNA is well suited for a world evolving at acidic pH. This is supported by the enhanced stability at acidic pH of not only the RNA phosphodiester bond but also of the aminoacyl-(t)RNA and peptide bonds. Examples of <it>in vitro</it>-selected ribozymes with activities at acid pH have recently been documented. The subsequent transition to a DNA genome could have been partly driven by the gradual rise in ocean pH, since DNA has greater stability than RNA at alkaline pH, but not at acidic pH.</p> <p>Testing the hypothesis</p> <p>We have proposed mechanisms for two key RNA world activities that are compatible with an acidic milieu: <it>(i) </it>non-enzymatic RNA replication of a hemi-protonated cytosine-rich oligonucleotide, and <it>(ii) </it>specific aminoacylation of tRNA/hairpins through triple helix interactions between the helical aminoacyl stem and a single-stranded aminoacylating ribozyme.</p> <p>Implications of the hypothesis</p> <p>Our hypothesis casts doubt on the hypothesis that RNA evolved in the vicinity of alkaline hydrothermal vents. The ability of RNA to form protonated base pairs and triples at acidic pH suggests that standard base pairing may not have been a dominant requirement of the early RNA world.</p> <p>Reviewers</p> <p>This article was reviewed by Eugene Koonin, Anthony Poole and Charles Carter (nominated by David Ardell).</p

Evidence from glycine transfer RNA of a frozen accident at the dawn of the genetic code

<p>Abstract</p> <p>Background</p> <p>Transfer RNA (tRNA) is the means by which the cell translates DNA sequence into protein according to the rules of the genetic code. A credible proposition is that tRNA was formed from the duplication of an RNA hairpin half the length of the contemporary tRNA molecule, with the point at which the hairpins were joined marked by the canonical intron insertion position found today within tRNA genes. If these hairpins possessed a 3'-CCA terminus with different combinations of stem nucleotides (the ancestral operational RNA code), specific aminoacylation and perhaps participation in some form of noncoded protein synthesis might have occurred. However, the identity of the first tRNA and the initial steps in the origin of the genetic code remain elusive.</p> <p>Results</p> <p>Here we show evidence that glycine tRNA was the first tRNA, as revealed by a vestigial imprint in the anticodon loop sequences of contemporary descendents. This provides a plausible mechanism for the missing first step in the origin of the genetic code. In 448 of 466 glycine tRNA gene sequences from bacteria, archaea and eukaryote cytoplasm analyzed, CCA occurs immediately upstream of the canonical intron insertion position, suggesting the first anticodon (NCC for glycine) has been captured from the 3'-terminal CCA of one of the interacting hairpins as a result of an ancestral ligation.</p> <p>Conclusion</p> <p>That this imprint (including the second and third nucleotides of the glycine tRNA anticodon) has been retained through billions of years of evolution suggests Crick's 'frozen accident' hypothesis has validity for at least this very first step at the dawn of the genetic code.</p> <p>Reviewers</p> <p>This article was reviewed by Dr Eugene V. Koonin, Dr Rob Knight and Dr David H Ardell.</p

The transition from noncoded to coded protein synthesis: did coding mRNAs arise from stability-enhancing binding partners to tRNA?

<p>Abstract</p> <p>Background</p> <p>Understanding the origin of protein synthesis has been notoriously difficult. We have taken as a starting premise Wolf and Koonin's view that "evolution of the translation system is envisaged to occur in a compartmentalized ensemble of replicating, co-selected RNA segments, i.e., in an RNA world containing ribozymes with versatile activities".</p> <p>Presentation of the hypothesis</p> <p>We propose that coded protein synthesis arose from a noncoded process in an RNA world as a natural consequence of the accumulation of a range of early tRNAs and their serendipitous RNA binding partners. We propose that, initially, RNA molecules with 3' CCA termini that could be aminoacylated by ribozymes, together with an ancestral peptidyl transferase ribozyme, produced small peptides with random or repetitive sequences. Our concept is that the first tRNA arose in this context from the ligation of two RNA hairpins and could be similarly aminoacylated at its 3' end to become a substrate for peptidyl transfer catalyzed by the ancestral ribozyme. Within this RNA world we hypothesize that proto-mRNAs appeared first simply as serendipitous binding partners, forming complementary base pair interactions with the anticodon loops of tRNA pairs. Initially this may have enhanced stability of the paired tRNA molecules so they were held together in close proximity, better positioning the 3' CCA termini for peptidyl transfer and enhancing the rate of peptide synthesis. If there were a selective advantage for the ensemble through the peptide products synthesized, it would provide a natural pathway for the evolution of a coding system with the expansion of a cohort of different tRNAs and their binding partners. The whole process could have occurred quite unremarkably for such a profound acquisition.</p> <p>Testing the hypothesis</p> <p>It should be possible to test the different parts of our model using the isolated contemporary 50S ribosomal subunit initially, and then with RNAs transcribed <it>in vitro </it>together with a minimal set of ribosomal proteins that are required today to support protein synthesis.</p> <p>Implications of the hypothesis</p> <p>This model proposes that genetic coding arose <it>de novo </it>from complementary base pair interactions between tRNAs and single-stranded RNAs present in the immediate environment.</p> <p>Reviewers</p> <p>This article was reviewed by Eugene Koonin, Rob Knight and Berthold Kastner (nominated by Laura Landweber).</p