Dioxygen Binding in the Active Site of Histone Demethylase JMJD2A and the Role of the Protein Environment

JMJD2A catalyses the demethylation of di‐ and trimethylated lysine residues in histone tails and is a target for the development of new anticancer medicines. Mechanistic details of demethylation are yet to be elucidated and are important for the understanding of epigenetic processes. We have evaluated the initial step of histone demethylation by JMJD2A and demonstrate the dramatic effect of the protein environment upon oxygen binding using quantum mechanics/molecular mechanics (QM/MM) calculations. The changes in electronic structure have been studied for possible spin states and different conformations of O₂, using a combination of quantum and classical simulations. O₂ binding to this histone demethylase is computed to occur preferentially as an end‐on superoxo radical bound to a high‐spin ferric centre, yielding an overall quintet ground state. The favourability of binding is strongly influenced by the surrounding protein: we have quantified this effect using an energy decomposition scheme into electrostatic and dispersion contributions. His182 and the methylated lysine assist while Glu184 and the oxoglutarate cofactor are deleterious for O₂ binding. Charge separation in the superoxo‐intermediate benefits from the electrostatic stabilization provided by the surrounding residues, stabilizing the binding process significantly. This work demonstrates the importance of the extended protein environment in oxygen binding, and the role of energy decomposition in understanding the physical origin of binding/recognition.     

A Mononuclear Uranium(IV) Single‐Molecule Magnet with an Azobenzene Radical Ligand

A tetravalent uranium compound with a radical azobenzene ligand, namely, [{(SiMe₂NPh)₃‐tacn}U^IV(η²‐N₂Ph₂^.)] ( 2 ), was obtained by one‐electron reduction of azobenzene by the trivalent uranium compound [U^III{(SiMe₂NPh)₃‐tacn}] ( 1 ). Compound 2 was characterized by single‐crystal X‐ray diffraction and ¹H NMR, IR, and UV/Vis/NIR spectroscopy. The magnetic properties of 2 and precursor 1 were studied by static magnetization and ac susceptibility measurements, which for the former revealed single‐molecule magnet behaviour for the first time in a mononuclear U^IV compound, whereas trivalent uranium compound 1 does not exhibit slow relaxation of the magnetization at low temperatures. A first approximation to the magnetic behaviour of these compounds was attempted by combining an effective electrostatic model with a phenomenological approach using the full single‐ion Hamiltonian.     

Complete Caps in with Both N and q Odd

In this work, an inductive method to construct complete caps in affine spaces is provided. Using this tool, for odd and q odd, complete caps smaller than all already known ones are obtained.     

Convergence of a non-failable mean-field particle system

The existing literature contains many examples of mean-field particle systems converging to the distribution of a Markov process conditioned to not hit a given set. In many situations, these mean-field particle systems are failable, meaning that they are not well defined after a given random time. Our first aim is to introduce an original mean-field particle system, which is always well defined and whose large number particle limit is, in all generality, the distribution of a process conditioned to not hit a given set. Under natural conditions on the underlying process, we also prove that the convergence holds uniformly in time as the number of particles goes to infinity. As an illustration, we show that our assumptions are satisfied in the case of a piece-wise deterministic Markov process.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

An axiomatic duality framework for the theta body and related convex corners

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the corresponding antiblocking duality relations. Our framework describes several semidefinite and polyhedral relaxations of the stable set polytope of a graph as generalized theta bodies. As a by-product of our approach, we introduce the notion of “Schur Lifting” of cones which is dual to PSD Lifting (more commonly used in SDP relaxations of combinatorial optimization problems) in our axiomatic generalization. We also generalize the notion of complements of graphs to diagonally scaling-invariant polyhedral cones. Finally, we provide a weighted generalization of the copositive formulation of the fractional chromatic number by Dukanovic and Rendl from 2010.     

Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids

A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.     

A thermodynamic approach with internal variables using Lagrange formalism. Part II. Continuous symmetries in the case of the time–temperature equivalence

In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium.     

Rheological studies of the gelation of aqueous solutions of acrylamide-acrylic acid copolymers in the presence of chromium chloride

The gelation kinetics of aqueous solutions of acrylamideacrylic acid copolymers in the presence of chromium ions was studied with different rheometers. The gel time is found to vary with the principle of the apparatus because of a low shear dependence of the elongation of the macromolecules. The variations of the gel time with the experimental conditions of the gel preparation were investigated and we conclude that the gelation is governed by the oligornerization kinetics of the chromium ions which are instantaneously, complexated by the carboxylate groups of the polymer. The variation laws of the gel time and of the elastic modulus with chromium and polymer concentrations, temperature and ionic strength are in qualitative agreement with the structure of the temporary network of the semi-dilute solutions of these copolymers.