From isolated subgroups to generic permutation representations

Let $G$ be a countable group, $\operatorname{Sub}(G)$ the (compact, metric) space of all subgroups of $G$ with the Chabauty topology and $\operatorname{Is}(G) \subset \operatorname{Sub}(G)$ the collection of isolated points. We denote by $X!$ the (Polish) group of all permutations of a countable set $X$. Then the following properties are equivalent: (i) $\operatorname{Is}(G)$ is dense in $\operatorname{Sub}(G)$, (ii) $G$ admits a "generic permutation representation". Namely there exists some $\tau^* \in \operatorname{Hom}(G,X!)$ such that the collection of permutation representations $\{\phi \in \operatorname{Hom}(G,X!) \ | \ \phi {\text{is permutation isomorphic to}} \tau^*\}$ is co-meager in $\operatorname{Hom}(G,X!)$. We call groups satisfying these properties solitary. Examples of solitary groups include finitely generated LERF groups and groups with countably many subgroups.Comment: 21 page

The evolution of metabolic networks of E. coli

<p>Abstract</p> <p>Background</p> <p>Despite the availability of numerous complete genome sequences from <it>E. coli </it>strains, published genome-scale metabolic models exist only for two commensal <it>E. coli </it>strains. These models have proven useful for many applications, such as engineering strains for desired product formation, and we sought to explore how constructing and evaluating additional metabolic models for <it>E. coli </it>strains could enhance these efforts.</p> <p>Results</p> <p>We used the genomic information from 16 <it>E. coli </it>strains to generate an <it>E. coli </it>pangenome metabolic network by evaluating their collective 76,990 ORFs. Each of these ORFs was assigned to one of 17,647 ortholog groups including ORFs associated with reactions in the most recent metabolic model for <it>E. coli </it>K-12. For orthologous groups that contain an ORF already represented in the MG1655 model, the gene to protein to reaction associations represented in this model could then be easily propagated to other <it>E. coli </it>strain models. All remaining orthologous groups were evaluated to see if new metabolic reactions could be added to generate a pangenome-scale metabolic model (iEco1712_pan). The pangenome model included reactions from a metabolic model update for <it>E. coli </it>K-12 MG1655 (iEco1339_MG1655) and enabled development of five additional strain-specific genome-scale metabolic models. These additional models include a second K-12 strain (iEco1335_W3110) and four pathogenic strains (two enterohemorrhagic <it>E. coli </it>O157:H7 and two uropathogens). When compared to the <it>E. coli </it>K-12 models, the metabolic models for the enterohemorrhagic (iEco1344_EDL933 and iEco1345_Sakai) and uropathogenic strains (iEco1288_CFT073 and iEco1301_UTI89) contained numerous lineage-specific gene and reaction differences. All six <it>E. coli </it>models were evaluated by comparing model predictions to carbon source utilization measurements under aerobic and anaerobic conditions, and to batch growth profiles in minimal media with 0.2% (w/v) glucose. An ancestral genome-scale metabolic model based on conserved ortholog groups in all 16 <it>E. coli </it>genomes was also constructed, reflecting the conserved ancestral core of <it>E. coli </it>metabolism (iEco1053_core). Comparative analysis of all six strain-specific <it>E. coli </it>models revealed that some of the pathogenic <it>E. coli </it>strains possess reactions in their metabolic networks enabling higher biomass yields on glucose. Finally the lineage-specific metabolic traits were compared to the ancestral core model predictions to derive new insight into the evolution of metabolism within this species.</p> <p>Conclusion</p> <p>Our findings demonstrate that a pangenome-scale metabolic model can be used to rapidly construct additional <it>E. coli </it>strain-specific models, and that quantitative models of different strains of <it>E. coli </it>can accurately predict strain-specific phenotypes. Such pangenome and strain-specific models can be further used to engineer metabolic phenotypes of interest, such as designing new industrial <it>E. coli </it>strains.</p

Evolution of the metabolic and regulatory networks associated with oxygen availability in two phytopathogenic enterobacteria

<p>Abstract</p> <p>Background</p> <p><it>Dickeya dadantii </it>and <it>Pectobacterium atrosepticum </it>are phytopathogenic enterobacteria capable of facultative anaerobic growth in a wide range of O₂concentrations found in plant and natural environments. The transcriptional response to O₂remains under-explored for these and other phytopathogenic enterobacteria although it has been well characterized for animal-associated genera including <it>Escherichia coli </it>and <it>Salmonella enterica</it>. Knowledge of the extent of conservation of the transcriptional response across orthologous genes in more distantly related species is useful to identify rates and patterns of regulon evolution. Evolutionary events such as loss and acquisition of genes by lateral transfer events along each evolutionary branch results in lineage-specific genes, some of which may have been subsequently incorporated into the O₂-responsive stimulon. Here we present a comparison of transcriptional profiles measured using densely tiled oligonucleotide arrays for two phytopathogens, <it>Dickeya dadantii </it>3937 and <it>Pectobacterium atrosepticum </it>SCRI1043, grown to mid-log phase in MOPS minimal medium (0.1% glucose) with and without O₂.</p> <p>Results</p> <p>More than 7% of the genes of each phytopathogen are differentially expressed with greater than 3-fold changes under anaerobic conditions. In addition to anaerobic metabolism genes, the O₂responsive stimulon includes a variety of virulence and pathogenicity-genes. Few of these genes overlap with orthologous genes in the anaerobic stimulon of <it>E. coli</it>. We define these as the conserved core, in which the transcriptional pattern as well as genetic architecture are well preserved. This conserved core includes previously described anaerobic metabolic pathways such as fermentation. Other components of the anaerobic stimulon show variation in genetic content, genome architecture and regulation. Notably formate metabolism, nitrate/nitrite metabolism, and fermentative butanediol production, differ between <it>E. coli </it>and the phytopathogens. Surprisingly, the overlap of the anaerobic stimulon between the phytopathogens is also relatively small considering that they are closely related, occupy similar niches and employ similar strategies to cause disease. There are cases of interesting divergences in the pattern of transcription of genes between <it>Dickeya </it>and <it>Pectobacterium </it>for virulence-associated subsystems including the type VI secretion system (T6SS), suggesting that fine-tuning of the stimulon impacts interaction with plants or competing microbes.</p> <p>Conclusions</p> <p>The small number of genes (an even smaller number if we consider operons) comprising the conserved core transcriptional response to O₂limitation demonstrates the extent of regulatory divergence prevalent in the Enterobacteriaceae. Our orthology-driven comparative transcriptomics approach indicates that the adaptive response in the eneterobacteria is a result of interaction of core (regulators) and lineage-specific (structural and regulatory) genes. Our subsystems based approach reveals that similar phenotypic outcomes are sometimes achieved by each organism using different genes and regulatory strategies.</p

Using Comparative Genomics for Inquiry-Based Learning to Dissect Virulence of Escherichia coli O157:H7 and Yersinia pestis

Genomics and bioinformatics are topics of increasing interest in undergraduate biological science curricula. Many existing exercises focus on gene annotation and analysis of a single genome. In this paper, we present two educational modules designed to enable students to learn and apply fundamental concepts in comparative genomics using examples related to bacterial pathogenesis. Students first examine alignments of genomes of Escherichia coli O157:H7 strains isolated from three food-poisoning outbreaks using the multiple-genome alignment tool Mauve. Students investigate conservation of virulence factors using the Mauve viewer and by browsing annotations available at the A Systematic Annotation Package for Community Analysis of Genomes database. In the second module, students use an alignment of five Yersinia pestis genomes to analyze single-nucleotide polymorphisms of three genes to classify strains into biovar groups. Students are then given sequences of bacterial DNA amplified from the teeth of corpses from the first and second pandemics of the bubonic plague and asked to classify these new samples. Learning-assessment results reveal student improvement in self-efficacy and content knowledge, as well as students’ ability to use BLAST to identify genomic islands and conduct analyses of virulence factors from E. coli O157:H7 or Y. pestis. Each of these educational modules offers educators new ready-to-implement resources for integrating comparative genomic topics into their curricula

Enteropathogen Resource Integration Center (ERIC): bioinformatics support for research on biodefense-relevant enterobacteria

ERIC, the Enteropathogen Resource Integration Center (www.ericbrc.org), is a new web portal serving as a rich source of information about enterobacteria on the NIAID established list of Select Agents related to biodefense—diarrheagenic Escherichia coli, Shigella spp., Salmonella spp., Yersinia enterocolitica and Yersinia pestis. More than 30 genomes have been completely sequenced, many more exist in draft form and additional projects are underway. These organisms are increasingly the focus of studies using high-throughput experimental technologies and computational approaches. This wealth of data provides unprecedented opportunities for understanding the workings of basic biological systems and discovery of novel targets for development of vaccines, diagnostics and therapeutics. ERIC brings information together from disparate sources and supports data comparison across different organisms, analysis of varying data types and visualization of analyses in human and computer-readable formats

Carbapenemase-producing Enterobacteriaceae in Europe:assessment by national experts from 38 countries, May 2015

In 2012, the European Centre for Disease Prevention and Control (ECDC) launched the 'European survey of carbapenemase-producing Enterobacteriaceae (EuSCAPE)' project to gain insights into the occurrence and epidemiology of carbapenemase-producing Enterobacteriaceae (CPE), to increase the awareness of the spread of CPE, and to build and enhance the laboratory capacity for diagnosis and surveillance of CPE in Europe. Data collected through a post-EuSCAPE feedback questionnaire in May 2015 documented improvement compared with 2013 in capacity and ability to detect CPE and identify the different carbapenemases genes in the 38 participating countries, thus contributing to their awareness of and knowledge about the spread of CPE. Over the last two years, the epidemiological situation of CPE worsened, in particular with the rapid spread of carbapenem-hydrolysing oxacillinase-48 (OXA-48)-and New Delhi metallo-betalactamase (NDM)-producing Enterobacteriaceae. In 2015, 13/38 countries reported inter-regional spread of or an endemic situation for CPE, compared with 6/38 in 2013. Only three countries replied that they had not identified one single case of CPE. The ongoing spread of CPE represents an increasing threat to patient safety in European hospitals, and a majority of countries reacted by establishing national CPE surveillances systems and issuing guidance on control measures for health professionals. However, 14 countries still lacked specific national guidelines for prevention and control of CPE in mid-2015

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

Novae Ejecta as Colliding Shells

Following on our initial absorption-line analysis of fifteen novae spectra we present additional evidence for the existence of two distinct components of novae ejecta having different origins. As argued in Paper I one component is the rapidly expanding gas ejected from the outer layers of the white dwarf by the outburst. The second component is pre-existing outer, more slowly expanding circumbinary gas that represents ejecta from the secondary star or accretion disk. We present measurements of the emission-line widths that show them to be significantly narrower than the broad P Cygni profiles that immediately precede them. The emission profiles of novae in the nebular phase are distinctly rectangular, i.e., strongly suggestive of emission from a relatively thin, roughly spherical shell. We thus interpret novae spectral evolution in terms of the collision between the two components of ejecta, which converts the early absorption spectrum to an emission-line spectrum within weeks of the outburst. The narrow emission widths require the outer circumbinary gas to be much more massive than the white dwarf ejecta, thereby slowing the latter's expansion upon collision. The presence of a large reservoir of circumbinary gas at the time of outburst is suggestive that novae outbursts may sometime be triggered by collapse of gas onto the white dwarf, as occurs for dwarf novae, rather than steady mass transfer through the inner Lagrangian point.Comment: 12 pages, 3 figures; Revised manuscript; Accepted for publication in Astrophysics & Space Scienc

Innovation in assessment: building student confidence in preparation for unfamiliar assessment methods

Innovative assessment methods in which students are active participants promote deeper learning. A group debate and a webfolio were implemented as methods of assessment in the 2015 undergraduate midwifery curriculum, with the assessment tools being evaluated by students. Thematic analysis of the evaluations showed students enjoyed undertaking innovative methods of assessment, they developed confidence and engaged meaningfully with the content to be assessed. Students also commented they developed multiple skills required for future professional practice as a midwife. Thorough preparation of students to undertake an innovative method of assessment however is vital in fostering student confidence