Potential analytical applications of lysenin channels for detection of multivalent ions

Transmembrane protein transporters possessing binding sites for ions, toxins, pharmaceutical drugs, and other molecules constitute excellent candidates for developing sensitive and selective biosensing devices. Their attractiveness for analytical purposes is enhanced by the intrinsic amplification capabilities shown when the binding event leads to major changes in the transportation of ions or molecules other than the analyte itself. The large-scale implementation of such transmembrane proteins in biosensing devices is limited by the difficulties encountered in inserting functional transporters into artificial bilayer lipid membranes and by the limitations in understanding and exploiting the changes induced by the interaction with the analyte for sensing purposes. Here, we show that lysenin, a pore-forming toxin extracted from earthworm Eisenia foetida, which inserts stable and large conductance channels into artificial bilayer lipid membranes, functions as a multivalent ion-sensing device. The analytical response consists of concentration and ionic-species-dependent macroscopic conductance inhibition most probably linked to a ligand-induced gating mechanism. Multivalent ion removal by chelation or precipitation restores, in most cases, the initial conductance and demonstrates reversibility. Changes in lipid bilayer membrane compositions leading to the absence of voltage-induced gating do not affect the analytical response to multivalent ions. Microscopic current analysis performed on individual lysenin channels in the presence of Cu²⁺ revealed complex open–closed transitions characterized by unstable intermediate sub-conducting states. Lysenin channels provide an analytical tool with a built-in sensing mechanism for inorganic and organic multivalent ions, and the excellent stability in an artificial environment recommend lysenin as a potential candidate for single-molecule detection and analysis.     

Topological groups and covering dimension

We consider a natural way of extending the Lebesgue covering dimension to various classes of infinite dimensional topological groups. The dimension function that we introduce extends Lebesgue covering dimension, has the hereditary property, and has a product theory that is more similar to the product theory for the finite dimensional case.     

Microstructural characterization of next generation nuclear graphites

This article reports the microstructural characteristics of various petroleum and pitch based nuclear graphites (IG-110, NBG-18, and PCEA) that are of interest to the next generation nuclear plant program. Bright-field transmission electron microscopy imaging was used to identify and understand the different features constituting the microstructure of nuclear graphite such as the filler particles, microcracks, binder phase, rosette-shaped quinoline insoluble (QI) particles, chaotic structures, and turbostratic graphite phase. The dimensions of microcracks were found to vary from a few nanometers to tens of microns. Furthermore, the microcracks were found to be filled with amorphous carbon of unknown origin. The pitch coke based graphite (NBG-18) was found to contain higher concentration of binder phase constituting QI particles as well as chaotic structures. The turbostratic graphite, present in all of the grades, was identified through their elliptical diffraction patterns. The difference in the microstructure has been analyzed in view of their processing conditions.     

Branching of t-periodic solutions for a certain class of ordinary differential equations *

Sufficient conditions are given for the existence of periodic solutions of the weakly forced ODE X¹ = f(x) + F(t, x, λ) where x λ R², λ is a small parameter in a Banach space and F is T-periodic in its first variable. Some illustrative examples are provided     

A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

The current paper establishes the computational efficiency and accuracy of the RBF-FD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as Gibbs phenomena, sharp gradients, and complex vortical dynamics with rapid energy transfer from large to small scales over short time periods. The computations were possible as well as very competitive due to the implementation of hyperviscosity on large RBF stencil sizes (corresponding roughly to 6th to 9th order methods) with up to O(10⁵) nodes on the sphere. The RBF-FD method scaled as O(N) per time step, where N is the total number of nodes on the sphere. In Appendix A, guidelines are given on how to chose parameters when using RBF-FD to solve hyperbolic PDEs.     

Dopant Spin States and Magnetic Interactions in Transition Metal (Fe3+)-Doped Semiconductor Nanoparticles: An EMR and Magnetometric Study

In this work, electron magnetic resonance (EMR) spectroscopy and magnetometry studies were employed to investigate the origin of the observed room-temperature ferromagnetism in chemically synthesized Sn_1?x Fe _x O₂ powders. EMR data clearly established the presence of two different types of signals due to the incorporated Fe ions: paramagnetic spectra due to isolated Fe³⁺ ions and broad ferromagnetic resonance (FMR) spectra due to magnetically coupled Fe³⁺ dopant ions. EMR data analysis and simulation suggested the presence of high-spin (S = 5/2) Fe³⁺ ions incorporated into the SnO₂ host lattice both at substitutional and at interstitial sites. The FMR signal intensity and the saturation magnetization M _s of the ferromagnetic component increased with increasing Fe concentration. For Sn_0.953Fe_0.047O₂ samples, well-defined EMR spectra revealing FMRs were observed only for samples prepared in the 350–600°C range, whereas for samples prepared at higher annealing temperatures up to 900°C, the FMRs and saturation magnetization were vanished due to diffusion and eventual expulsion of the Fe ions from the nanoparticles, in agreement with data obtained from Raman and X-ray photoelectron spectroscopy.     

A Bijective Approach to the Area of Generalized Motzkin Paths

For fixed positive integer k, let E_n denote the set of lattice paths using the steps (1, 1), (1, − 1), and (k, 0) and running from (0, 0) to (n, 0) while remaining strictly above the x-axis elsewhere. We first prove bijectively that the total area of the regions bounded by the paths of E_n and the x-axis satisfies a four-term recurrence depending only on k. We then give both a bijective and a generating function argument proving that the total area under the paths of E_n equals the total number of lattice points on the x-axis hit by the unrestricted paths running from (0, 0) to (n − 2, 0) and using the same step set as above.