Crystalline protein domains and lipid bilayer vesicle shape transformations

Cellular membranes can take on a variety of shapes to assist biological processes including endocytosis. Membrane-associated protein domains provide a possible mechanism for determining membrane curvature. We study the effect of tethered streptavidin protein crystals on the curvature of giant unilamellar vesicles (GUVs) using confocal, fluorescence, and differential interference contrast microscopy. Above a critical protein concentration, streptavidin domains align and percolate as they form, deforming GUVs into prolate spheroidal shapes in a size-dependent fashion. We propose a mechanism for this shape transformation based on domain growth and jamming. Osmotic deflation of streptavidin-coated GUVs reveals that the relatively rigid streptavidin protein domains resist membrane bending. Moreover, in contrast to highly curved protein domains that facilitate membrane budding, the relatively flat streptavidin domains prevent membrane budding under high osmotic stress. Thus, crystalline streptavidin domains are shown to have a stabilizing effect on lipid membranes. Our study gives insight into the mechanism for protein-mediated stabilization of cellular membranes.     

A Characterization of Nilpotent Leibniz Algebras

W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper, using the definition of a Leibniz-derivation from Moens (2010), we show that a similar result for non-Lie Leibniz algebras is not true. Namely, we give an example of non-nilpotent Leibniz algebra that admits an invertible Leibniz-derivation. In order to extend the results of the paper by Moens (2010) for Leibniz algebras, we introduce a definition of a Leibniz-derivation of Leibniz algebras that agrees with Leibniz-derivation of the Lie algebra case. Further, we prove that a Leibniz algebra is nilpotent if and only if it admits an invertible Leibniz-derivation of Definition 3.4. Moreover, the result that a solvable radical of a Lie algebra is invariant with respect to a Leibniz-derivation was extended to the case of Leibniz algebras.     

A reliable approach to the solution of Navier–Stokes equations

In this paper we will demonstrate an affective approach of solving Navier–Stokes equations by using a very reliable transformation method known as the Cole–Hopf transformation, which reduces the problem from nonlinear into a linear differential equation which, in turn, can be solved effectively.     

Corrigendum to “Maximal linear groups induced on the Frattini quotient of a p-group” [J. Pure Appl. Algebra 222 (10) (2018) 2931–2951]

We give a correction to Fig. 1 and supporting text published in the paper: ‘Maximal linear groups induced on the Frattini quotient of a p-group’, J. Pure Appl. Algebra 222 (10) (2018) 2931–2951.     

Large Cliques in -Free Graphs

Dedicated to the memory of Paul Erdős A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs. Received October 25, 1999 RID="*" ID="*" Supported by OTKA grant T029074. RID="**" ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.     

Carbazolylmethylphosphonate compounds – Synthesis,coordination and fluorescence in solution and cells

The compounds diethyl-N-carbazolylmethylphosphonate 1 and diethyl-2-oxymethylphosphonate carbazole 2 have been synthesised and characterized by a range of techniques including NMR, absorption and emission spectroscopy, infrared, and mass spectroscopy. Compound 1 forms a 2:1 complex 3 with calcium nitrate and the single crystal X-ray diffraction structure of 3 is described. Titrations of 1 with Zn²⁺ and Ca²⁺ in ethanol reveal that the intrinsic fluorescence is only slightly perturbed in the presence of these metal ions in micromolar ethanol solutions. Compounds 1 and 2 are readily taken up and visualized in L929 fibrosarcoma and DRG (Dorsal root ganglia) cell lines.