Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations

We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is bounded by the best-approximation error times a constant that tends to one as the mesh is refined and/or the polynomial degree is increased. Moreover, under the same conditions on the mesh and/or the polynomial degree, we establish discrete inf-sup stability with a constant that corresponds to the continuous constant up to a factor of two at most. Our proofs apply under minimal regularity assumptions on the exact solution, so that general domains, material coefficients, and right-hand sides are allowed

Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization

We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound on the solution operator, with both valid for sufficiently-large frequency and for a class of coefficients that satisfy certain monotonicity conditions in one spatial direction, and are only assumed to be bounded (i.e., $L^\infty$) in the other spatial directions. This class of coefficients therefore includes coefficients modelling transmission by penetrable obstacles with a (potentially large) number of layers (in 2-d) or fibres (in 3-d). Importantly, the frequency-explicit bound holds uniformly for all coefficients in this class; this uniformity allows us to consider highly-oscillatory coefficients and study the limiting behaviour when the period of oscillations goes to zero. In particular, we bound the $H^1$ error committed by the first-order bulk correction to the homogenized transmission problem, with this bound explicit in both the period of oscillations of the coefficients and the frequency of the Helmholtz equation; to our knowledge, this is the first homogenization result for the Helmholtz equation that is explicit in these two quantities and valid without the assumption that the frequency is small

Finite Element Simulations of Logging-While-Drilling and Extra-Deep Azimuthal Resistivity Measurements using Non-Fitting Grids

We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting grids when the geometry is complex. On the other side, fitting grids have been historically preferred because they offer additional accuracy for a fixed problem size in the general case. In this work, we analyse the use of non-fitting grids to simulate the response of logging instruments that are based on magnetic field resistivity measurements using 2.5D Maxwell’s equations. We provide various examples demonstrating that, for these applications, if the finite element matrix coefficients are properly integrated, the accuracy loss due to the use of non-fitting grids is negligible compared to the case where fitting grids are employed

Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media

We consider the time-harmonic Maxwell equations posed in $\mathbb{R}^3$. We prove a priori bounds on the solution for $L^\infty$ coefficients $\epsilon$ and $\mu$ satisfying certain monotonicity properties, with these bounds valid for arbitrarily-large frequency, and explicit in the frequency and properties of $\epsilon$ and $\mu$. The class of coefficients covered includes (i) certain $\epsilon$ and $\mu$ for which well-posedness of the time-harmonic Maxwell equations had not previously been proved, and (ii) scattering by a penetrable $C^0$ star-shaped obstacle where $\epsilon$ and $\mu$ are smaller inside the obstacle than outside. In this latter setting, the bounds are uniform across all such obstacles, and the first sharp frequency-explicit bounds for this problem at high-frequency

Oligomeric Status and Nucleotide Binding Properties of the Plastid ATP/ADP Transporter 1: Toward a Molecular Understanding of the Transport Mechanism

Background: Chloroplast ATP/ADP transporters are essential to energy homeostasis in plant cells. However, their molecular mechanism remains poorly understood, primarily due to the difficulty of producing and purifying functional recombinant forms of these transporters. Methodology/Principal Findings: In this work, we describe an expression and purification protocol providing good yields and efficient solubilization of NTT1 protein from Arabidopsis thaliana. By biochemical and biophysical analyses, we identified the best detergent for solubilization and purification of functional proteins, LAPAO. Purified NTT1 was found to accumulate as two independent pools of well folded, stable monomers and dimers. ATP and ADP binding properties were determined, and Pi, a co-substrate of ADP, was confirmed to be essential for nucleotide steady-state transport. Nucleotide binding studies and analysis of NTT1 mutants lead us to suggest the existence of two distinct and probably inter-dependent binding sites. Finally, fusion and deletion experiments demonstrated that the C-terminus of NTT1 is not essential for multimerization, but probably plays a regulatory role, controlling the nucleotide exchange rate. Conclusions/Significance: Taken together, these data provide a comprehensive molecular characterization of a chloroplas

Heterologous Expression of Membrane Proteins: Choosing the Appropriate Host

International audienceBACKGROUND: Membrane proteins are the targets of 50% of drugs, although they only represent 1% of total cellular proteins. The first major bottleneck on the route to their functional and structural characterisation is their overexpression; and simply choosing the right system can involve many months of trial and error. This work is intended as a guide to where to start when faced with heterologous expression of a membrane protein. METHODOLOGY/PRINCIPAL FINDINGS: The expression of 20 membrane proteins, both peripheral and integral, in three prokaryotic (E. coli, L. lactis, R. sphaeroides) and three eukaryotic (A. thaliana, N. benthamiana, Sf9 insect cells) hosts was tested. The proteins tested were of various origins (bacteria, plants and mammals), functions (transporters, receptors, enzymes) and topologies (between 0 and 13 transmembrane segments). The Gateway system was used to clone all 20 genes into appropriate vectors for the hosts to be tested. Culture conditions were optimised for each host, and specific strategies were tested, such as the use of Mistic fusions in E. coli. 17 of the 20 proteins were produced at adequate yields for functional and, in some cases, structural studies. We have formulated general recommendations to assist with choosing an appropriate system based on our observations of protein behaviour in the different hosts. CONCLUSIONS/SIGNIFICANCE: Most of the methods presented here can be quite easily implemented in other laboratories. The results highlight certain factors that should be considered when selecting an expression host. The decision aide provided should help both newcomers and old-hands to select the best system for their favourite membrane protein

Minimal information for studies of extracellular vesicles 2018 (MISEV2018):a position statement of the International Society for Extracellular Vesicles and update of the MISEV2014 guidelines

The last decade has seen a sharp increase in the number of scientific publications describing physiological and pathological functions of extracellular vesicles (EVs), a collective term covering various subtypes of cell-released, membranous structures, called exosomes, microvesicles, microparticles, ectosomes, oncosomes, apoptotic bodies, and many other names. However, specific issues arise when working with these entities, whose size and amount often make them difficult to obtain as relatively pure preparations, and to characterize properly. The International Society for Extracellular Vesicles (ISEV) proposed Minimal Information for Studies of Extracellular Vesicles (“MISEV”) guidelines for the field in 2014. We now update these “MISEV2014” guidelines based on evolution of the collective knowledge in the last four years. An important point to consider is that ascribing a specific function to EVs in general, or to subtypes of EVs, requires reporting of specific information beyond mere description of function in a crude, potentially contaminated, and heterogeneous preparation. For example, claims that exosomes are endowed with exquisite and specific activities remain difficult to support experimentally, given our still limited knowledge of their specific molecular machineries of biogenesis and release, as compared with other biophysically similar EVs. The MISEV2018 guidelines include tables and outlines of suggested protocols and steps to follow to document specific EV-associated functional activities. Finally, a checklist is provided with summaries of key points

A single active catalytic site is sufficient to promote transport in P-glycoprotein

P-glycoprotein (Pgp) is an ABC transporter responsible for the ATP-dependent efflux of chemotherapeutic compounds from multidrug resistant cancer cells. Better understanding of the molecular mechanism of Pgp-mediated transport could promote rational drug design to circumvent multidrug resistance. By measuring drug binding affinity and reactivity to a conformation-sensitive antibody we show here that nucleotide binding drives Pgp from a high to a low substrate-affinity state and this switch coincides with the flip from the inward- to the outward-facing conformation. Furthermore, the outward-facing conformation survives ATP hydrolysis: the post-hydrolytic complex is stabilized by vanadate, and the slow recovery from this state requires two functional catalytic sites. The catalytically inactive double Walker A mutant is stabilized in a high substrate affinity inward-open conformation, but mutants with one intact catalytic center preserve their ability to hydrolyze ATP and to promote drug transport, suggesting that the two catalytic sites are randomly recruited for ATP hydrolysis