Cyclotomic Gaudin models: construction and Bethe ansatz

This is a pre-copyedited author produced PDF of an article accepted for publication in Communications in Mathematical Physics, Benoit, V and Young, C, 'Cyclotomic Gaudin models: construction and Bethe ansatz', Commun. Math. Phys. (2016) 343:971, first published on line March 24, 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2601-3 © Springer-Verlag Berlin Heidelberg 2016To any simple Lie algebra $\mathfrak g$ and automorphism $\sigma:\mathfrak g\to \mathfrak g$ we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of $U(\mathfrak g)^{\otimes N}$ generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case $\sigma = \text{id}$. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.Peer reviewe

Quantum character varieties and braided module categories

We compute quantum character varieties of arbitrary closed surfaces with boundaries and marked points. These are categorical invariants $\int_S\mathcal A$ of a surface $S$, determined by the choice of a braided tensor category $\mathcal A$, and computed via factorization homology. We identify the algebraic data governing marked points and boundary components with the notion of a {\em braided module category} for $\mathcal A$, and we describe braided module categories with a generator in terms of certain explicit algebra homomorphisms called {\em quantum moment maps}. We then show that the quantum character variety of a decorated surface is obtained from that of the corresponding punctured surface as a quantum Hamiltonian reduction. Characters of braided $\mathcal A$-modules are objects of the torus category $\int_{T^2}\mathcal A$. We initiate a theory of character sheaves for quantum groups by identifying the torus integral of $\mathcal A=\operatorname{Rep_q} G$ with the category $\mathcal D_q(G/G)-\operatorname{mod}$ of equivariant quantum $\mathcal D$-modules. When $G=GL_n$, we relate the mirabolic version of this category to the representations of the spherical double affine Hecke algebra (DAHA) $\mathbb{SH}_{q,t}$.Comment: 33 pages, 5 figures. Final version, to appear in Sel. Math. New Se

Emergence and Modular Evolution of a Novel Motility Machinery in Bacteria

Bacteria glide across solid surfaces by mechanisms that have remained largely mysterious despite decades of research. In the deltaproteobacterium Myxococcus xanthus, this locomotion allows the formation stress-resistant fruiting bodies where sporulation takes place. However, despite the large number of genes identified as important for gliding, no specific machinery has been identified so far, hampering in-depth investigations. Based on the premise that components of the gliding machinery must have co-evolved and encode both envelope-spanning proteins and a molecular motor, we re-annotated known gliding motility genes and examined their taxonomic distribution, genomic localization, and phylogeny. We successfully delineated three functionally related genetic clusters, which we proved experimentally carry genes encoding the basal gliding machinery in M. xanthus, using genetic and localization techniques. For the first time, this study identifies structural gliding motility genes in the Myxobacteria and opens new perspectives to study the motility mechanism. Furthermore, phylogenomics provide insight into how this machinery emerged from an ancestral conserved core of genes of unknown function that evolved to gliding by the recruitment of functional modules in Myxococcales. Surprisingly, this motility machinery appears to be highly related to a sporulation system, underscoring unsuspected common mechanisms in these apparently distinct morphogenic phenomena

Nitrous oxide as a function of oxygen and archaeal gene abundance in the North Pacific

Natural Environment Research Council (NERC) (NE/E01559X/1)

Emergency vaccination of rabies under limited resources – combating or containing?

BACKGROUND: Rabies is the most important viral zoonosis from a global perspective. Worldwide efforts to combat the disease by oral vaccination of reservoirs have managed to eradicate wildlife rabies in large areas of central Europe and North-America. Thus, repeated vaccination has been discontinued recently on a geographical scale. However, as rabies has not yet been eradicated globally, a serious risk of re-introduction remains. What is the best spatial design for an emergency vaccination program – particularly if resources are limited? Either, we treat a circular area around the detected case and run the risk of infected hosts leaving the limited control area, because a sufficient immunisation level has not yet been built up. Or, initially concentrate the SAME resources in order to establish a protective ring which is more distant from the infected local area, and which then holds out against the challenge of the approaching epidemic. METHODS: We developed a simulation model to contrast the two strategies for emergency vaccination. The spatial-explicit model is based on fox group home-ranges, which facilitates the simulation of rabies spread to larger areas relevant to management. We used individual-based fox groups to follow up the effects of vaccination in a detailed manner. Thus, regionally – bait distribution orientates itself to standard schemes of oral immunisation programs and locally – baits are assigned to individual foxes. RESULTS: Surprisingly, putting the controlled area ring-like around the outbreak does not outperform the circular area of the same size centred on the outbreak. Only during the very first baitings, does the ring area result in fewer breakouts. But then as rabies is eliminated within the circle area, the respective ring area fails, due to the non-controlled inner part. We attempt to take advantage of the initially fewer breakouts beyond the ring when applying a mixed strategy. Therefore, after a certain number of baitings, the area under control was increased for both strategies towards the same larger circular area. The circle-circle strategy still outperforms the ring-circle strategy and analysis of the spatial-temporal disease spread reveals why: improving control efficacy by means of a mixed strategy is impossible in the field, due to the build-up time of population immunity. CONCLUSION: For practical emergency management of a new outbreak of rabies, the ring-like application of oral vaccination is not a favourable strategy at all. Even if initial resources are substantially low and there is a serious risk of rabies cases outside the limited control area, our results suggest circular application instead of ring vaccination

A Step Forward in Molecular Diagnostics of Lyssaviruses – Results of a Ring Trial among European Laboratories

Rabies is a lethal and notifiable zoonotic disease for which diagnostics have to meet the highest standards. In recent years, an evolution was especially seen in molecular diagnostics with a wide variety of different detection methods published. Therefore, a first international ring trial specifically designed on the use of reverse transcription polymerase chain reaction (RT-PCR) for detection of lyssavirus genomic RNA was organized. The trial focussed on assessment and comparison of the performance of conventional and real-time assays. In total, 16 European laboratories participated. All participants were asked to investigate a panel of defined lyssavirus RNAs, consisting of Rabies virus (RABV) and European bat lyssavirus 1 and 2 (EBLV-1 and -2) RNA samples, with systems available in their laboratory. The ring trial allowed the important conclusion that conventional RT-PCR assays were really robust assays tested with a high concordance between different laboratories and assays. The real-time RT-PCR system by Wakeley et al. (2005) in combination with an intercalating dye, and the combined version by Hoffmann and co-workers (2010) showed good sensitivity for the detection of all RABV samples included in this test panel. Furthermore, all used EBLV-specific assays, real-time RT-PCRs as well as conventional RT-PCR systems, were shown to be suitable for a reliable detection of EBLVs. It has to be mentioned that differences were seen in the performance between both the individual RT-PCR systems and the laboratories. Laboratories which used more than one molecular assay for testing the sample panel always concluded a correct sample result. Due to the markedly high genetic diversity of lyssaviruses, the application of different assays in diagnostics is needed to achieve a maximum of diagnostic accuracy. To improve the knowledge about the diagnostic performance proficiency testing at an international level is recommended before using lyssavirus molecular diagnostics e.g. for confirmatory testing

The Elusive Third Subunit IIa of the Bacterial B-Type Oxidases: The Enzyme from the Hyperthermophile Aquifex aeolicus

The reduction of molecular oxygen to water is catalyzed by complicated membrane-bound metallo-enzymes containing variable numbers of subunits, called cytochrome c oxidases or quinol oxidases. We previously described the cytochrome c oxidase II from the hyperthermophilic bacterium Aquifex aeolicus as a ba3-type two-subunit (subunits I and II) enzyme and showed that it is included in a supercomplex involved in the sulfide-oxygen respiration pathway. It belongs to the B-family of the heme-copper oxidases, enzymes that are far less studied than the ones from family A. Here, we describe the presence in this enzyme of an additional transmembrane helix “subunit IIa”, which is composed of 41 amino acid residues with a measured molecular mass of 5105 Da. Moreover, we show that subunit II, as expected, is in fact longer than the originally annotated protein (from the genome) and contains a transmembrane domain. Using Aquifex aeolicus genomic sequence analyses, N-terminal sequencing, peptide mass fingerprinting and mass spectrometry analysis on entire subunits, we conclude that the B-type enzyme from this bacterium is a three-subunit complex. It is composed of subunit I (encoded by coxA2) of 59000 Da, subunit II (encoded by coxB2) of 16700 Da and subunit IIa which contain 12, 1 and 1 transmembrane helices respectively. A structural model indicates that the structural organization of the complex strongly resembles that of the ba3 cytochrome c oxidase from the bacterium Thermus thermophilus, the IIa helical subunit being structurally the lacking N-terminal transmembrane helix of subunit II present in the A-type oxidases. Analysis of the genomic context of genes encoding oxidases indicates that this third subunit is present in many of the bacterial oxidases from B-family, enzymes that have been described as two-subunit complexes

A Novel Replication-Competent Vaccinia Vector MVTT Is Superior to MVA for Inducing High Levels of Neutralizing Antibody via Mucosal Vaccination

Mucosal vaccination offers great advantage for inducing protective immune response to prevent viral transmission and dissemination. Here, we report our findings of a head-to-head comparison of two viral vectors modified vaccinia Ankara (MVA) and a novel replication-competent modified vaccinia Tian Tan (MVTT) for inducing neutralizing antibodies (Nabs) via intramuscular and mucosal vaccinations in mice. MVTT is an attenuated variant of the wild-type VTT, which was historically used as a smallpox vaccine for millions of Chinese people. The spike glycoprotein (S) of SARS-CoV was used as the test antigen after the S gene was constructed in the identical genomic location of two vectors to generate vaccine candidates MVTT-S and MVA-S. Using identical doses, MVTT-S induced lower levels (∼2-3-fold) of anti- SARS-CoV neutralizing antibodies (Nabs) than MVA-S through intramuscular inoculation. MVTT-S, however, was capable of inducing consistently 20-to-100-fold higher levels of Nabs than MVA-S when inoculated via either intranasal or intraoral routes. These levels of MVTT-S-induced Nab responses were substantially (∼10-fold) higher than that induced via the intramuscular route in the same experiments. Moreover, pre-exposure to the wild-type VTT via intranasal or intraoral route impaired the Nab response via the same routes of MVTT-S vaccination probably due to the pre-existing anti-VTT Nab response. The efficacy of intranasal or intraoral vaccination, however, was still 20-to-50-fold better than intramuscular inoculation despite the subcutaneous pre-exposure to wild-type VTT. Our data have implications for people who maintain low levels of anti-VTT Nabs after historical smallpox vaccination. MVTT is therefore an attractive live viral vector for mucosal vaccination

Changes in the distribution of red foxes (Vulpes vulpes) in urban areas in Great Britain: findings and limitations of a media-driven nationwide survey

Urbanization is one of the major forms of habitat alteration occurring at the present time. Although this is typically deleterious to biodiversity, some species flourish within these human-modified landscapes, potentially leading to negative and/or positive interactions between people and wildlife. Hence, up-to-date assessment of urban wildlife populations is important for developing appropriate management strategies. Surveying urban wildlife is limited by land partition and private ownership, rendering many common survey techniques difficult. Garnering public involvement is one solution, but this method is constrained by the inherent biases of non-standardised survey effort associated with voluntary participation. We used a television-led media approach to solicit national participation in an online sightings survey to investigate changes in the distribution of urban foxes in Great Britain and to explore relationships between urban features and fox occurrence and sightings density. Our results show that media-based approaches can generate a large national database on the current distribution of a recognisable species. Fox distribution in England and Wales has changed markedly within the last 25 years, with sightings submitted from 91% of urban areas previously predicted to support few or no foxes. Data were highly skewed with 90% of urban areas having <30 fox sightings per 1000 people km-2. The extent of total urban area was the only variable with a significant impact on both fox occurrence and sightings density in urban areas; longitude and percentage of public green urban space were respectively, significantly positively and negatively associated with sightings density only. Latitude, and distance to nearest neighbouring conurbation had no impact on either occurrence or sightings density. Given the limitations associated with this method, further investigations are needed to determine the association between sightings density and actual fox density, and variability of fox density within and between urban areas in Britain

Eliminating Rabies in Estonia

The compulsory vaccination of pets, the recommended vaccination of farm animals in grazing areas and the extermination of stray animals did not succeed in eliminating rabies in Estonia because the virus was maintained in two main wildlife reservoirs, foxes and raccoon dogs. These two species became a priority target therefore in order to control rabies. Supported by the European Community, successive oral vaccination (OV) campaigns were conducted twice a year using Rabigen® SAG2 baits, beginning in autumn 2005 in North Estonia. They were then extended to the whole territory from spring 2006. Following the vaccination campaigns, the incidence of rabies cases dramatically decreased, with 266 cases in 2005, 114 in 2006, four in 2007 and three in 2008. Since March 2008, no rabies cases have been detected in Estonia other than three cases reported in summer 2009 and one case in January 2011, all in areas close to the South-Eastern border with Russia. The bait uptake was satisfactory, with tetracycline positivity rates ranging from 85% to 93% in foxes and from 82% to 88% in raccoon dogs. Immunisation rates evaluated by ELISA ranged from 34% to 55% in foxes and from 38% to 55% in raccoon dogs. The rabies situation in Estonia was compared to that of the other two Baltic States, Latvia and Lithuania. Despite regular OV campaigns conducted throughout their territory since 2006, and an improvement in the epidemiological situation, rabies has still not been eradicated in these countries. An analysis of the number of baits distributed and the funding allocated by the European Commission showed that the strategy for rabies control is more cost-effective in Estonia than in Latvia and Lithuania