Note on vertex degrees of planar graphs

In this note the second moment of the vertex degree sequence of planar graphs is considered. We prove that

• 1 If G is an outerplanar graph of order n ? 3 then

• 2 If G is a planar graph of order n ? 4 then

where d₁,…,d_n is the vertex degree sequence of G. We exhibit all graphs for which these upper bounds are attained.     

Addition of elemental selenium to phosphonate carbanions- - a key step in the synthesis of vinylphosphonates. A new synthetic approach to 1,4-dicarbonyl systems.

A convenient synthesis of vinylphosphonates which involves addition of elemental selenium to phosphonate carbanions followed by alkylation and selenoxide elimination is described. A general approach to 1,4-dicarbonyl systems based on diethyl α-methylthiovinylphosphonate is also reported.     

The Selection of the Optimal Impregnation Conditions of Vegetable Matrices with Iodine

This study aimed to determine the use of selected vegetables (pumpkin, cauliflower, broccoli, carrot) as carriers of potassium iodide (KI) and potassium iodate (KIO₃) by determining changes in iodine content under various conditions of impregnation as the degree of hydration, impregnated sample temperature, and impregnation time. The influence of these conditions on iodine contents in vegetables after their fortification and storage (21 °C/230 days) was analyzed. The results showed that all selected vegetables could be efficient iodine carriers. However, the conditions of the impregnation process are crucial for fortification efficiency, particularly the degree of hydration and the temperature of the impregnated samples before drying. The results showed that the lowest iodine content was in samples fortified at 4 °C and 1:4 hydration. On the other hand, the highest reproducibility of iodine was for the following fortification conditions: temperature of −76 °C and hydration of 1:1. The studies confirmed the higher stability of iodine in KIO₃ form compared to KI. To increase recovery of the introduced iodine in the product after drying, using the conditioning step at 4 °C is not recommended. We recommend freezing vegetables immediately after the impregnation process     

Buckwheat Hull-Enriched Pasta: Physicochemical and Sensory Properties

This work aimed to evaluate the effect of partial replacement of semolina with 0, 1, 5, 10, 15, and 20% of ground buckwheat hull (BH) on the chemical composition, antioxidant properties, color, cooking characteristics, and sensory properties of wheat pasta. Pasta samples were prepared by dough lamination (tagliatelle shape) and dried at 55 °C until the moisture content was 11–12% (wet basis). Analyses of samples showed that the addition of BH caused an increase in fiber content in pasta from 4.31% (control pasta) to 14.15% (pasta with 20% of BH). Moreover, the brightness and yellowness of BH-enriched products were significantly decreased compared to the control sample, and the total color difference ranged from 23.84 (pasta with 1% of BH) to 32.56 (pasta with 15% BH). In addition, a decrease in optimal cooking time, as well as an increased weight index and cooking loss, was observed in BH-enriched pasta samples. Furthermore, BH-enriched cooked pasta had significantly higher total phenolic content and antioxidant activity but an unpleasant smell and taste, especially if the level of BH was higher than 10%.     

Acid–Base Equilibrium and Self-Association in Relation to High Antitumor Activity of Selected Unsymmetrical Bisacridines Established by Extensive Chemometric Analysis

Unsymmetrical bisacridines (UAs) represent a novel class of anticancer agents previously synthesized by our group. Our recent studies have demonstrated their high antitumor potential against multiple cancer cell lines and human tumor xenografts in nude mice. At the cellular level, these compounds affected 3D cancer spheroid growth and their cellular uptake was selectively modulated by quantum dots. UAs were shown to undergo metabolic transformations in vitro and in tumor cells. However, the physicochemical properties of UAs, which could possibly affect their interactions with molecular targets, remain unknown. Therefore, we selected four highly active UAs for the assessment of physicochemical parameters under various pH conditions. We determined the compounds’ pK_a dissociation constants as well as their potential to self-associate. Both parameters were determined by detailed and complex chemometric analysis of UV-Vis spectra supported by nuclear magnetic resonance (NMR) spectroscopy. The obtained results indicate that general molecular properties of UAs in aqueous media, including their protonation state, self-association ratio, and solubility, are strongly pH-dependent, particularly in the physiological pH range of 6 to 8. In conclusion, we describe the detailed physicochemical characteristics of UAs, which might contribute to their selectivity towards tumour cells as opposed to their effect on normal cells.     

Novel C60 Fullerenol-Gentamicin Conjugate–Physicochemical Characterization and Evaluation of Antibacterial and Cytotoxic Properties

This study aimed to develop, characterize, and evaluate antibacterial and cytotoxic properties of novel fullerene derivative composed of C₆₀ fullerenol and standard aminoglycoside antibiotic–gentamicin (C₆₀ fullerenol-gentamicin conjugate). The successful introduction of gentamicin to fullerenol was confirmed by X-ray photoelectron spectroscopy which together with thermogravimetric and spectroscopic analysis revealing the formula of the composition as C₆₀(OH)₁₂(GLYMO)₁₁(Gentamicin)_0.8. The dynamic light scattering (DLS) revealed that conjugate possessed ability to form agglomerates in water (size around 115 nm), while Zeta potential measurements demonstrated that such agglomerates possessed neutral character. In vitro biological assays indicated that obtained C₆₀ fullerenol-gentamicin conjugate possessed the same antibacterial activity as standard gentamicin against Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, and Escherichia coli, which proves that combination of fullerenol with gentamicin does not cause the loss of antibacterial activity of antibiotic. Moreover, cytotoxicity assessment demonstrated that obtained fullerenol-gentamicin derivative did not decrease viability of normal human fibroblasts (model eukaryotic cells) compared to control fibroblasts. Thus, taking into account all of the results, it can be stated that this research presents effective method to fabricate C₆₀ fullerenol-gentamicin conjugate and proves that such derivative possesses desired antibacterial properties without unfavorable cytotoxic effects towards eukaryotic cells in vitro. These promising preliminary results indicate that obtained C₆₀ fullerenol-gentamicin conjugate could have biomedical potential. It may be presumed that obtained fullerenol may be used as an effective carrier for antibiotic, and developed fullerenol-gentamicin conjugate may be apply locally (i.e., at the wound site). Moreover, in future we will evaluate possibility of its applications in inter alia tissue engineering, namely as a component of wound dressings and implantable biomaterials.     

Leptin in Human Milk—One of the Key Regulators of Nutritional Programming

Breast milk is the optimal food for infants and toddlers, providing basic nutrients. It is also a source of many biologically active substances. Among them are hormones responsible for metabolic balance. One of the hormones taken in with breast milk by a breastfed baby is leptin. This hormone is involved in the regulation of appetite, informing the brain about the body’s energy resources. Having the correct mechanisms related to the action of leptin is a factor reducing the risk of obesity. The natural presence of leptin in the composition of breast milk suggests that it has a specific role in shaping the health of a breastfed child. Obesity as a disease of civilization affects more and more people, including children. The development of this disease is multifaceted and determined by many factors, including genetic and environmental factors such as eating habits and low physical activity. Behind obesity, there are complex mechanisms in which many elements of the human body are involved. Understanding the effects of breastfeeding as a natural source of leptin can help prevent childhood obesity and development of this disease in future life.     

Gold Nanoparticles as Effective ion Traps in Poly(dimethylsiloxane) Cross-Linked by Metal-Ligand Coordination

At this time, the development of advanced elastic dielectric materials for use in organic devices, particularly in organic field-effect transistors, is of considerable interest to the scientific community. In the present work, flexible poly(dimethylsiloxane) (PDMS) specimens cross-linked by means of ZnCl₂-bipyridine coordination with an addition of 0.001 wt. %, 0.0025 wt. %, 0.005 wt. %, 0.04 wt. %, 0.2 wt. %, and 0.4 wt. % of gold nanoparticles (AuNPs) were prepared in order to understand the effect of AuNPs on the electrical properties of the composite materials formed. The broadband dielectric spectroscopy measurements revealed one order of magnitude decrease in loss tangent, compared to the coordinated system, upon an introduction of 0.001 wt. % of AuNPs into the polymeric matrix. An introduction of AuNPs causes damping of conductivity within the low-temperature range investigated. These effects can be explained as a result of trapping the Cl⁻ counter ions by the nanoparticles. The study has shown that even a very low concentration of AuNPs (0.001 wt. %) still brings about effective trapping of Cl⁻ counter anions, therefore improving the dielectric properties of the investigated systems. The modification proposed reveals new perspectives for using AuNPs in polymers cross-linked by metal-ligand coordination systems.     

Comparison of Physical Adsorption and Covalent Coupling Methods for Surface Density-Dependent Orientation of Antibody on Silicon

The orientation of antibodies, employed as capture molecules on biosensors, determines biorecognition efficiency and bioassay performance. In a previous publication we demonstrated for antibodies attached covalently to silicon that an increase in their surface amount Γ, evaluated with ellipsometry, induces changes in their orientation, which is traced directly using Time-of-Flight Secondary Ion Mass Spectroscopy combined with Principal Component Analysis. Here, we extend the above studies to antibodies adsorbed physically on a 3-aminopropyltriethoxysilane (APTES) monolayer. Antibodies physisorbed on APTES (0 ≤ Γ ≤ 3.5 mg/m²) reveal the Γ ranges for flat-on, side-on, and vertical orientation consistent with random molecular packing. The relation between orientation and Γ is juxtaposed for silicon functionalized with APTES, APTES modified with glutaraldehyde (APTES/GA) and N-hydroxysuccinimide-silane (NHS-silane). Antibody reorientation occurs at lower Γ values when physisorption (APTES) is involved rather than chemisorption (APTES/GA, NHS-silane). At high Γ values, comparable proportions of molecules adapting head-on and tail-on vertical alignment are concluded for APTES and the NHS-silane monolayer, and they are related to intermolecular dipole–dipole interactions. Intermolecular forces seem to be less decisive than covalent binding for antibodies on the APTES/GA surface, with dominant head-on orientation. Independently, the impact of glutaraldehyde activation of APTES on vertical orientation is confirmed by separate TOF-SIMS measurements.