Bioorthogonal Chemical Reporters for Selective In Situ Probing of Mycomembrane Components in Mycobacteria

The global pathogen Mycobacterium tuberculosis and other species in the suborder Corynebacterineae possess a distinctive outer membrane called the mycomembrane (MM). The MM is composed of mycolic acids, which are either covalently linked to an underlying arabinogalactan layer or incorporated into trehalose glycolipids that associate with the MM non‐covalently. These structures are generated through a process called mycolylation, which is central to mycobacterial physiology and pathogenesis and is an important target for tuberculosis drug development. Current approaches to investigating mycolylation rely on arduous analytical methods that occur outside the context of a whole cell. Herein, we describe mycobacteria‐specific chemical reporters that can selectively probe either covalent arabinogalactan mycolates or non‐covalent trehalose mycolates in live mycobacteria. These probes, in conjunction with bioorthogonal chemistry, enable selective in situ detection of the major MM components.     

Discovery of a Highly Selective Glycogen Synthase Kinase‐3 Inhibitor (PF‐04802367) That Modulates Tau Phosphorylation in the Brain: Translation for PET Neuroimaging

Glycogen synthase kinase‐3 (GSK‐3) regulates multiple cellular processes in diabetes, oncology, and neurology. N‐(3‐(1H‐1,2,4‐triazol‐1‐yl)propyl)‐5‐(3‐chloro‐4‐methoxyphenyl)oxazole‐4‐carboxamide (PF‐04802367 or PF‐367) has been identified as a highly potent inhibitor, which is among the most selective antagonists of GSK‐3 to date. Its efficacy was demonstrated in modulation of tau phosphorylation in vitro and in vivo. Whereas the kinetics of PF‐367 binding in brain tissues are too fast for an effective therapeutic agent, the pharmacokinetic profile of PF‐367 is ideal for discovery of radiopharmaceuticals for GSK‐3 in the central nervous system. A ¹¹C‐isotopologue of PF‐367 was synthesized and preliminary PET imaging studies in non‐human primates confirmed that we have overcome the two major obstacles for imaging GSK‐3, namely, reasonable brain permeability and displaceable binding.     

Mechanistic Characterisation of Two Sesquiterpene Cyclases from the Plant Pathogenic Fungus Fusarium fujikuroi

Two sesquiterpene cyclases from Fusarium fujikuroi were expressed in Escherichia coli and purified. The first enzyme was inactive because of a critical mutation, but activity was restored by sequence correction through site‐directed mutagenesis. The mutated enzyme and two naturally functional homologues from other fusaria converted farnesyl diphosphate into guaia‐6,10(14)‐diene. The second enzyme produced eremophilene. The absolute configuration of guaia‐6,10(14)‐diene was elucidated by enantioselective synthesis, while that of eremophilene was evident from the sign of its optical rotation and is opposite to that in plants but the same as in Sorangium cellulosum. The mechanisms of both terpene cyclases were studied with various ¹³C‐ and ²H‐labelled FPP isotopomers.     

To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England

ABSTRACT

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics (EDSM) analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In this article we address the issue of how students over this period have been expected to engage with the specialised discourse of school mathematics. We explain our analytic methods and present some outcomes of the analysis. We identify changes in engagement with algebraic manipulation, proving, relating mathematics to non-mathematical contexts and making connections between specialised mathematical objects. These changes are discussed in the light of public and policy domain debates about ‘standards’ of examinations.     

On the Elliptic Genera of Manifolds of Spin(7) Holonomy

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The \({\mathcal{N} = 1}\) superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a c = 12 realization of the symmetry group \({\mathcal{S}W(3/2,2)}\). In this paper, we compute the characters of this supergroup and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. We find suggestive relations to various sporadic groups, which are made more precise in a companion paper.     

Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions

Heat kernel perturbation theory is a tool for constructing explicit approximation formulas for the solutions of linear parabolic equations. We review the crux of this perturbative formalism and then apply it to differential equations which govern the transition densities of several local volatility processes. In particular, we compute all the heat kernel coefficients for the CEV and quadratic local volatility models; in the later case, we are able to use these to construct an exact explicit formula for the processes’ transition density. We then derive low order approximation formulas for the cubic local volatility model, an affine-affine short rate model, and a generalized mean reverting CEV model. We finally demonstrate that the approximation formulas are accurate in certain model parameter regimes via comparison to Monte Carlo simulations.     

Ferrous Iron Binding Key to Mms6 Magnetite Biomineralisation: A Mechanistic Study to Understand Magnetite Formation Using pH Titration and NMR Spectroscopy

Formation of magnetite nanocrystals by magnetotactic bacteria is controlled by specific proteins which regulate the particles’ nucleation and growth. One such protein is Mms6. This small, amphiphilic protein can self‐assemble and bind ferric ions to aid in magnetite formation. To understand the role of Mms6 during in vitro iron oxide precipitation we have performed in situ pH titrations. We find Mms6 has little effect during ferric salt precipitation, but exerts greatest influence during the incorporation of ferrous ions and conversion of this salt to mixed‐valence iron minerals, suggesting Mms6 has a hitherto unrecorded ferrous iron interacting property which promotes the formation of magnetite in ferrous‐rich solutions. We show ferrous binding to the DEEVE motif within the C‐terminal region of Mms6 by NMR spectroscopy, and model these binding events using molecular simulations. We conclude that Mms6 functions as a magnetite nucleating protein under conditions where ferrous ions predominate.     

Arithmetic differential equations on $$GL_n$$, II: arithmetic Lie–Cartan theory

Motivated by the search of a concept of linearity in the theory of arithmetic differential equations (Buium in Arithmetic differential equations. Math. surveys and monographs, vol 118. American Mathematical Society, Providence, 2005), we introduce here an arithmetic analogue of Lie algebras, of Chern connections, and of Maurer–Cartan connections. Our arithmetic analogues of Chern connections are certain remarkable lifts of Frobenius on the p-adic completion of \(GL_n\) which are uniquely determined by certain compatibilities with the “outer” involutions defined by symmetric (respectively, antisymmetric) matrices. The Christoffel symbols of our arithmetic Chern connections will involve a matrix analogue of the Legendre symbol. The analogues of Maurer–Cartan connections can then be viewed as families of “linear” flows attached to each of our Chern connections. We will also investigate the compatibility of lifts of Frobenius with the inner automorphisms of \(GL_n\); in particular, we will prove the existence and uniqueness of certain arithmetic analogues of “isospectral flows” on the space of matrices.     

Arithmetic differential equations on $$GL_n$$, III Galois groups

Differential equations have arithmetic analogues (Buium in Arithmetic differential equations, Mathematical Surveys and Monographs, vol 118. American Mathematical Society, Providence 2005) in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations, and the present paper is concerned with the “linear” ones. The equations themselves were introduced in a previous paper (Buium and Dupuy, in Arithmetic differential equations on \(GL_{n}\), II: arithmetic Lie–Cartan theory, arXiv:1308.0744). In the present paper we deal with the solutions of these equations as well as with the Galois groups attached to the solutions.