Genomic characterisation of an endometrial pathogenic <i>Escherichia coli</i> strain reveals the acquisition of genetic elements associated with extra-intestinal pathogenicity

&lt;b&gt;Background&lt;/b&gt;&lt;p&gt;&lt;/p&gt; Strains of &lt;i&gt;Escherichia coli&lt;/i&gt; cause a wide variety of intestinal and extra-intestinal diseases in both humans and animals, and are also often found in healthy individuals or the environment. Broadly, a strong phylogenetic relationship exists that distinguishes most &lt;i&gt;E. Coli&lt;/i&gt; causing intestinal disease from those that cause extra-intestinal disease, however, isolates within a recently described subclass of Extra-Intestinal Pathogenic &lt;i&gt;E. Coli&lt;/i&gt; (ExPEC), termed endometrial pathogenic &lt;i&gt;E. Coli&lt;/i&gt;, tend to be phylogenetically distant from the vast majority of characterised ExPECs, and more closely related to human intestinal pathogens. In this work, we investigate the genetic basis for ExPEC infection in the prototypic endometrial pathogenic &lt;i&gt;E. Coli&lt;/i&gt; strain MS499.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Results&lt;/b&gt;&lt;p&gt;&lt;/p&gt; By investigating the genome of MS499 in comparison with a range of other E. coli sequences, we have discovered that this bacterium has acquired substantial lengths of DNA which encode factors more usually associated with ExPECs and less frequently found in the phylogroup relatives of MS499. Many of these acquired factors, including several iron acquisition systems and a virulence plasmid similar to that found in several ExPECs such as APEC O1 and the neonatal meningitis &lt;i&gt;E. Coli&lt;/i&gt; S88, play characterised roles in a variety of typical ExPEC infections and appear to have been acquired recently by the evolutionary lineage leading to MS499.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Conclusions&lt;/b&gt;&lt;p&gt;&lt;/p&gt; Taking advantage of the phylogenetic relationship we describe between MS499 and several other closely related &lt;i&gt;E. Coli&lt;/i&gt; isolates from across the globe, we propose a step-wise evolution of a novel clade of sequence type 453 ExPECs within phylogroup B1, involving the recruitment of ExPEC virulence factors into the genome of an ancestrally non-extraintestinal &lt;i&gt;E. Coli&lt;/i&gt;, which has repurposed this lineage with the capacity to cause extraintestinal disease. These data reveal the genetic components which may be involved in this phenotype switching, and argue that horizontal gene exchange may be a key factor in the emergence of novel lineages of ExPECs.&lt;p&gt;&lt;/p&gt

DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

Toxic Mixtures in Time—The Sequence Makes the Poison

“The dose makes the poison”. This principle assumes that once a chemical is cleared out of the organism (toxicokinetic recovery), it no longer has any effect. However, it overlooks the other process of re-establishing homeostasis, toxicodynamic recovery, which can be fast or slow depending on the chemical. Therefore, when organisms are exposed to two toxicants in sequence, the toxicity can differ if their order is reversed. We test this hypothesis with the freshwater crustacean Gammarus pulex and four toxicants that act on different targets (diazinon, propiconazole, 4,6-dinitro-o-cresol, 4-nitrobenzyl chloride). We found clearly different toxicity when the exposure order of two toxicants was reversed, while maintaining the same dose. Slow toxicodynamic recovery caused carry-over toxicity in subsequent exposures, thereby resulting in a sequence effect–but only when toxicodynamic recovery was slow relative to the interval between exposures. This suggests that carry-over toxicity is a useful proxy for organism fitness and that risk assessment methods should be revised as they currently could underestimate risk. We provide the first evidence that carry-over toxicity occurs among chemicals acting on different targets and when exposure is several days apart. It is therefore not only the dose that makes the poison but also the exposure sequence

Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach

We present a quantum cluster solver for spin-$S$ Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and nonabelian SU(2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice and a calculation of local observables is demonstrated. A symmetry based truncation procedure is suggested and verified numerically.Comment: willm appear in J. Phys.

Notes about the Caratheodory number

In this paper we give sufficient conditions for a compactum in $\mathbb R^n$ to have Carath\'{e}odory number less than $n+1$, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath\'{e}odory theorem and give a Tverberg type theorem for families of convex compacta

Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

Quantum Dynamics of Lorentzian Spacetime Foam

A simple spacetime wormhole, which evolves classically from zero throat radius to a maximum value and recontracts, can be regarded as one possible mode of fluctuation in the microscopic ``spacetime foam'' first suggested by Wheeler. The dynamics of a particularly simple version of such a wormhole can be reduced to that of a single quantity, its throat radius; this wormhole thus provides a ``minisuperspace model'' for a structure in Lorentzian-signature foam. The classical equation of motion for the wormhole throat is obtained from the Einstein field equations and a suitable equation of state for the matter at the throat. Analysis of the quantum behavior of the hole then proceeds from an action corresponding to that equation of motion. The action obtained simply by calculating the scalar curvature of the hole spacetime yields a model with features like those of the relativistic free particle. In particular the Hamiltonian is nonlocal, and for the wormhole cannot even be given as a differential operator in closed form. Nonetheless the general solution of the Schr\"odinger equation for wormhole wave functions, i.e., the wave-function propagator, can be expressed as a path integral. Too complicated to perform exactly, this can yet be evaluated via a WKB approximation. The result indicates that the wormhole, classically stable, is quantum-mechanically unstable: A Feynman-Kac decomposition of the WKB propagator yields no spectrum of bound states. Though an initially localized wormhole wave function may oscillate for many classical expansion/recontraction periods, it must eventually leak to large radius values. The possibility of such a mode unstable against growth, combined withComment: 37 pages, 93-