Molecular Diffusion Measurement in Lipid Bilayers over Wide Concentration Ranges: A Comparative Study

Molecular diffusion in biological membranes is a determining factor in cell signaling and cell function. In the past few decades, three main fluorescence spectroscopy techniques have emerged that are capable of measuring molecular diffusion in artificial and biological membranes at very different concentration ranges and spatial resolutions. The widely used methods of fluorescence recovery after photobleaching (FRAP) and single‐particle tracking (SPT) can determine absolute diffusion coefficients at high (>100 μm^?2) and very low surface concentrations (single‐molecule level), respectively. Fluorescence correlation spectroscopy (FCS), on the other hand, is well‐suited for the intermediate concentration range of about 0.1–100 μm^?2. However, FCS in general requires calibration with a standard dye of known diffusion coefficient, and yields only relative measurements with respect to the calibration. A variant of FCS, z‐scan FCS, is calibration‐free for membrane measurements, but requires several experiments at different well‐controlled focusing positions. A recently established FCS method, electron‐multiplying charge‐coupled‐device‐based total internal reflection FCS (TIR‐FCS), referred to here as imaging TIR‐FCS (ITIR–FCS), is also independent of calibration standards, but to our knowledge no direct comparison between these different methods has been made. Herein, we seek to establish a comparison between FRAP, SPT, FCS, and ITIR–FCS by measuring the lateral diffusion coefficients in two model systems, namely, supported lipid bilayers and giant unilamellar vesicles.     

Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients

For any positive integers $n\ge 3$, $r\ge 1$ we present formulae for the number of irreducible polynomials of degree n over the finite field ${\mathbb{F}}_{2^r}$ where the coefficients of $x^{n-1}$, $x^{n-2}$ and $x^{n-3}$ are zero. Our proofs involve counting the number of points on certain algebraic curves over finite fields, a technique which arose from Fourier-analysing the known formulae for the ${\mathbb{F}}_2$ base field cases, reverse-engineering an economical new proof and then extending it. This approach gives rise to fibre products of supersingular curves and makes explicit why the formulae have period 24 in n.     

GM1 Ganglioside Inhibits β‐Amyloid Oligomerization Induced by Sphingomyelin

β‐Amyloid (Aβ) oligomers are neurotoxic and implicated in Alzheimer's disease. Neuronal plasma membranes may mediate formation of Aβ oligomers in vivo. Membrane components sphingomyelin and GM₁ have been shown to promote aggregation of Aβ; however, these studies were performed under extreme, non‐physiological conditions. We demonstrate that physiological levels of GM₁, organized in nanodomains do not seed oligomerization of Aβ₄₀ monomers. We show that sphingomyelin triggers oligomerization of Aβ₄₀ and that GM₁ is counteractive thus preventing oligomerization. We propose a molecular explanation that is supported by all‐atom molecular dynamics simulations. The preventive role of GM₁ in the oligomerization of Aβ₄₀ suggests that decreasing levels of GM₁ in the brain, for example, due to aging, could reduce protection against Aβ oligomerization and contribute to the onset of Alzheimer's disease.     

Mechanism and Kinetics of Heterogeneous Reactions of Unsaturated Organic Acids on α‐Al2O3 and CaCO3

Heterogeneous reactions have a vital role in the atmosphere due to their significant effects on the evolution of atmospheric aerosols, which in turn contribute to air pollution. However, the mechanism and kinetics of these processes involving unsaturated organic acids, important types of volatile organic compounds, are still unclear. In this work, the heterogeneous uptake of two representative atmospheric unsaturated organic acids (acrylic acid and methacrylic acid) on mineral aerosols including α‐Al₂O₃ and CaCO₃ are investigated using a Knudsen cell reactor and an in situ diffuse reflectance infrared Fourier transform spectrometry (DRIFTS) reactor. The corresponding reaction pathways are proposed from the DRIFTS analysis. In addition, the initial uptake coefficients of unsaturated organic acids and their heterogeneous fate are obtained for the first time. Our results suggest that heterogeneous reactions on α‐Al₂O₃ and CaCO₃ can be important sinks for acrylic acid and methacrylic acid, as well as possible contributors to the organic coating found on atmospheric aerosols, especially in high‐pollution events.     

NMR Diffusion Measurements as a Simple Method to Examine Solvent–Solvent and Solvent–Solute Interactions in Mixtures of the Ionic Liquid [Bmim][N(SO2CF3)2] and Acetonitrile

The self‐diffusion coefficients of each component in mixtures of 1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide ([Bmim][N(SO₂CF₃)₂]) and acetonitrile were determined. The results suggest that the hydrodynamic boundary conditions change from “stick” to “slip” as the solvent composition transitions from “ionic liquid dissolved in acetonitrile” (χ_IL<0.4) to “acetonitrile dissolved in ionic liquid” (χ_IL>0.4). At higher χ_IL, the acetonitrile species are affected by “cage” and “jump” events, as the acetonitrile molecules reside nearer to the charged centre on the ions than in the “non‐polar” regions. The self‐diffusion coefficients of hexan‐1‐amine, dipropylamine, 1‐hexanol and dipropylether in mixtures of [Bmim][N(SO₂CF₃)₂] and acetonitrile were determined. In general, the nitrogen‐containing solutes were found to diffuse slower than the oxygen‐containing solutes; this indicates that there are greater ionic liquid–N interactions than ionic liquid–O interactions. This work demonstrates that the self‐diffusion coefficients of species can provide valuable information about solvent–solvent and solvent–solute interactions in mixtures containing an ionic liquid.     

The twist-bend nematic phase: translational self-diffusion and biaxiality studied by 1H nuclear magnetic resonance diffusometry

ABSTRACT

Recently, there has been a surge of interest in mesogens exhibiting the twist-bend nematic (N_TB) phase that is shown to be chiral even though formed by effectively achiral molecules. Although it now seems to be clear that the N_TB phase in the bulk is formed by degenerate domains having opposite handedness, the presence of a supramolecular heliconical structure proposed in the Dozov model has been contradicted by the Hoffmann et al. model in which the heliconical arrangement is replaced by a polar nematic phase. The evidence in support of this is that the quadrupolar splitting tensor measured in various experiments is uniaxial and not biaxial as expected for the twist-bend nematic structure. In this debate, among other evidence, the molecular translational diffusion, and its magnitude with respect to that in the nematic phase above the N_TB phase, has also been invoked to eliminate or to confirm one model or the other. We attempt to resolve this issue by reporting the first measurements of the translational self-diffusion coefficients in the nematic and twist-bend nematic phases formed 1″,7″-bis-4-(4′-cyanobiphenyl-4′-yl) heptane (CB7CB). Such measurements certainly appear to resolve the differences between the two models in favour of that for the classic twist-bend nematic phase.     

A solution for the local plane strain problems using elliptic integrals of Cauchy type

We consider a parallel fiber‐reinforced periodic elastic composite that present an imperfect contact of spring type between the fiber and the matrix. We use the elliptic integral of Cauchy type for solving the plane strain local problems that arise from the asymptotic homogenization method. Several general conditions are assumed, which include that the fibers are disposed of arbitrary manner in the local cell, that all fibers present contact perfect with different constants of imperfection, and that their cross section is a smooth closed arbitrary curve. We find that there are infinity solutions for these problems, and we find relations between these solutions and effective coefficients of the composite. Finally, we obtain analytic formulae for the circular fiber case and show some numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Computation methods for combinatorial sums and Euler‐type numbers related to new families of numbers

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order. We can show that these numbers are related to the well‐known numbers and polynomials such as the Stirling numbers of the second kind and the central factorial numbers, the array polynomials, the rook numbers and polynomials, the Bernstein basis functions and others. In order to derive our new identities and relations for these numbers, we use a technique including the generating functions and functional equations. Finally, we give not only a computational algorithm for these numbers but also some numerical values of these numbers and the Euler numbers of negative order with tables. We also give some combinatorial interpretations of our new numbers. Copyright © 2016 John Wiley & Sons, Ltd.