Universal properties of harmonic functions on trees

We consider an infinite locally finite tree T equipped with nearest neighbor transition coefficients, giving rise to a space of harmonic functions. We show that, except for trivial cases, the generic harmonic function on T has dense range in C. By looking at forward-only transition coefficients, we show that the generic harmonic function induces a boundary martingale that approximates in probability all measurable functions on the boundary of T. We also study algebraic genericity, spaceability and frequent universality of these phenomena. © 2016 Elsevier Inc

Frequently dense harmonic functions and universal martingales on trees

On a large class of infinite trees T, we prove the existence of harmonic functions h, with respect to suitable transient transition operators P, that satisfy the following universal property: h is the Poisson transform of a martingale on the end-point boundary Ω of T (equipped with the harmonic measure induced by P) such that, for every measurable function f on Ω, it contains a subsequence converging to f in measure. Moreover, the martingale visits every open set of measurable functions with positive lower density. © 2021 American Mathematical Societ

Crystal, magnetic and dielectric studies of the 2D antiferromagnet: β-NaMnO2

In this paper we present our recent studies on the crystal, magnetic and dielectric properties of the β-NaMnO2. Experimental results of neutron powder and electron diffraction combined with measurements of the dielectric permittivity suggest that the β-NaMnO2 is an excellent candidate for studying the coupling between the magnetic and electric degrees of freedom. Neutron powder diffraction data reveal the existence of a commensurate and an incommensurate magnetic structure at 200 K and below 100 K, respectively. Dielectric anomalies which appear at the temperature regions where the two magnetic structures emerge, indicate the appearance of magnetodielectric coupling. © 2014 SPIE

Genetically encoded self-assembling iron oxide nanoparticles as a possible platform for cancer-cell tracking.

The study of growth and possible metastasis in animal models of tumors would benefit from reliable cell labels for noninvasive whole-organism imaging techniques such as magnetic resonance imaging. Genetically encoded cell-tracking reporters have the advantage that they are contrast-selective for viable cells with intact protein expression machinery. Besides, these reporters do not suffer from dilution during cell division. Encapsulins, which are bacterial protein nanocompartments, can serve as genetically controlled labels for multimodal detection of cells. Such nanocompartments can host various guest molecules inside their lumen. These include, for example, fluorescent proteins or enzymes with ferroxidase activity leading to biomineralization of iron oxide inside the encapsulin nanoshell. The aim of this work was to implement heterologous expression of encapsulin systems from Quasibacillus thermotolerans using the fluorescent reporter protein mScarlet-I and ferroxidase IMEF in the human hepatocellular carcinoma cell line HepG2. The successful expression of self-assembled encapsulin nanocompartments with functional cargo proteins was confirmed by fluorescence microscopy and transmission electron microscopy. Also, coexpression of encapsulin nanoshells, ferroxidase cargo, and iron transporter led to an increase in T2-weighted contrast in magnetic resonance imaging of HepG2 cells. The results demonstrate that the encapsulin cargo system from Q. thermotolerans may be suitable for multimodal imaging of cancer cells and could contribute to further in vitro and in vivo studies

Encapsulins-bacterial protein nanocompartments: Structure, properties, and application.

Recently, a new class of prokaryotic compartments, collectively called encapsulins or protein nanocompartments, has been discovered. The shell proteins of these structures self-organize to form icosahedral compartments with a diameter of 25-42 nm, while one or more cargo proteins with various functions can be encapsulated in the nanocompartment. Non-native cargo proteins can be loaded into nanocompartments and the surface of the shells can be further functionalized, which allows for developing targeted drug delivery systems or using encapsulins as contrast agents for magnetic resonance imaging. Since the genes encoding encapsulins can be integrated into the cell genome, encapsulins are attractive for investigation in various scientific fields, including biomedicine and nanotechnology

Encapsulin based self‐assembling iron‐containing protein nanoparticles for stem cells mri visualization.

Over the past decade, cell therapy has found many applications in the treatment of different diseases. Some of the cells already used in clinical practice include stem cells and CAR‐T cells. Compared with traditional drugs, living cells are much more complicated systems that must be strictly controlled to avoid undesirable migration, differentiation, or proliferation. One of the approaches used to prevent such side effects involves monitoring cell distribution in the human body by any noninvasive technique, such as magnetic resonance imaging (MRI). Long‐term tracking of stem cells with artificial magnetic labels, such as magnetic nanoparticles, is quite problematic because such labels can affect the metabolic process and cell viability. Additionally, the concentration of exogenous labels will decrease during cell division, leading to a corresponding decrease in signal intensity. In the current work, we present a new type of genetically encoded label based on encapsulin from Myxococcus xanthus bacteria, stably expressed in human mesenchymal stem cells (MSCs) and coexpressed with ferroxidase as a cargo protein for nanoparticles’ synthesis inside encapsulin shells. mZip14 protein was expressed for the enhancement of iron transport into the cell. Together, these three proteins led to the synthesis of iron‐containing nanoparticles in mesenchymal stem cells—without affecting cell viability—and increased contrast properties of MSCs in MRI

Di[Aqua(1-Oxyethylidenediphosphonato(1-))]copper(II) Dihydrate: Crystal Structure

X-ray crystal structure of di[aqua(1-oxyethylidenediphosphonato(1-))]copper(II) dihydrate Cu[CH3C(OH)(P2O6H3) · H2O]2 · 2H2O is determined. These crystals are monoclinic (space group C2/c) at 24°C, a = 15.021(6) Å, b = 11,364(5) Å, c = 12.583(7) Å, β = 118.67(4)○, Z = 4, and V = 1885(2) Å3. Copper atoms form a complex whose geometry is a distorted octahedron with two bidentate-chelating ligands [CH3C(OH)(P2O6H3)]- in the equatorial plane (Cu-O bond lengths are 1.953(2) and 1.976(2) Å) and two apical water molecules (Cu-O bond lengths are 2.469 Å). The ligand in the equatorial plane forms a six-member chelate ring having a sofa conformation, in which one carbon atom deviates by 0.821 Å from the plane of other coplanar atoms. Because of the strong hydrogen bond P-O⋯H-O-P (2.506 Å long) between the neighboring coordination groups, the P-O double bond is elongated to 1.511 (2) Å and the ordinary bond P-OH is shortened to 1.537(2) Å