Stability of vertices in random boolean cellular automata

Based on computer simulations, Kauffman (Physica D, 10, 145-156, 1984) made several generalizations about a random Boolean cellular automaton which he invented as a model of cellular metabolism. Here we give the first rigorous proofs of two of Kauffman's generalizations: a large fraction of vertices stabilize quickly, consequently the length of cycles in the automaton's behavior is small compared to that of a random mapping with the same number of states; and reversal of the states of a large fraction of the vertices does not affect the cycle to which the automaton moves.     

The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

Combinatorial invariants for nets of conics in $$\mathrm {PG}(2,q)$$ PG ( 2 , q )

Designs, Codes and Cryptography - The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics...     

Generation and reactions of substituted phenide anions in an electrospray triple quadrupole mass spectrometer

Substituted benzoic acid anions undergo decarboxylation in the medium-pressure region of an electrospray ion source yielding in most cases the correspondingly substituted phenide anions in high yield. The location of the anionic center is specified by the position of the carboxylic group. The only exceptions are compounds with substituents containing acidic hydrogen atoms, like OH and NH(2) groups. For such compounds, either an intra- or an intermolecular (mediated by the molecules of methanol or water) proton transfer from the more acidic position to the benzene ring is observed. The generated anions can be selected using the first quadrupole for studying their ion-molecule chemistry in the second quadrupole of a triple quadrupole mass spectrometer. Their reactions with CO(2), O(2), CH(3)COCH(3) and CCl(4) may serve as typical examples. The general applicability of this method for the generation of phenide anions has been confirmed on three different mass spectrometers. Experiments performed using carboxylic acids other then benzoic acid and its derivatives show that this method is not limited to phenide anions and can be used for the generation of a much wider range of carbanions in the gas phase.     

The intermediacy of metathiophosphonate PhPSO in the reaction of N-tert-butyl-P-phenylphosphonamidothioic acid with alcohols

Kinetic studies of the reaction of N-tert-butyl-P-phenylphosphonamidothioic acid (1) with alcohols were carried out in CH2Cl2 by means of 31P NMR spectrometry. The reaction is of the first order with respect to thio acid 1. The first-order rate constant at 30 degrees C increases with increasing methanol concentration below 0.25 M, but otherwise the rate constants are either independent of alcohol concentration (MeOH above 0.25 M, BuOH) or decrease with increasing alcohol concentration (i-PrOH, t-BuOH). The effect of alcohols on the order of the reaction and parameters of activation, as well as results of competition experiments, lead us to the conclusion that reaction of 1 with alcohols occurs by an elimination-addition mechanism involving the association of the thio acid 1 and the alcohol and then formation in the rate-determining step of an encounter complex 2' ' involving metathiophosphonate 4, amine, and alcohol. Metathiophosphonate 4 reacts preferentially with the alcohol as the encounter complex (primary alcohols) or after diffusion apart as a "free" intermediate (hindered alcohols).     

Cornelian Cherry (Cornus mas L.) Extracts Exert Cytotoxicity in Two Selected Melanoma Cell Lines—A Factorial Analysis of Time-Dependent Alterations in Values Obtained with SRB and MTT Assays

Despite the fact that phytochemicals of Cornaceae species have long been discussed as possible auxiliary agents in contemporary treatment, the insights on their properties remain relatively scarce. This study focuses on Cornus mas L. (Cornelian cherry), the extracts of which are reported to exert a pleiotropic effect shown in both in vivo and in vitro studies. This study aimed to explore the cytotoxic effect of extracts from fruits of red (Cornus mas L. ‘Podolski’) and yellow (Cornus mas L. ‘Yantarnyi’ and ‘Flava’) Cornelian cherries on two melanoma cell lines (A375 and MeWo). The extracts were characterized in the context of the concentration of bioactive compounds of antioxidative properties. Cytotoxicity was investigated with the use of the following two assays: SRB and MTT. An additional, alternative protocol for the SRB assay was used in this study so as to account for possible bias. Cytotoxicity was assessed as a difference in the whole time series of cell viability, instead of analyzing differences in raw values (often found in the literature). Both extracts from Cornus mas L. induced cytotoxicity in both A375 and MeWo cell lines, although the response of these cells was different. Moreover, based on this study, there is no evidence for claiming a different magnitude of cytotoxicity between these two extracts.     

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.     

Classification of Polish Natural Bee Honeys Based on Their Chemical Composition

The targeted quantitative NMR (qNMR) approach is a powerful analytical tool, which can be applied to classify and/or determine the authenticity of honey samples. In our study, this technique was used to determine the chemical profiles of different types of Polish honey samples, featured by variable contents of main sugars, free amino acids, and 5-(hydroxymethyl)furfural. One-way analysis of variance (ANOVA) was performed on concentrations of selected compounds to determine significant differences in their levels between all types of honey. For pattern recognition, principal component analysis (PCA) was conducted and good separations between all honey samples were obtained. The results of present studies allow the differentiation of honey samples based on the content of sucrose, glucose, and fructose, as well as amino acids such as tyrosine, phenylalanine, proline, and alanine. Our results indicated that the combination of qNMR with chemometric analysis may serve as a supplementary tool in specifying honeys.     

Biochemical and Molecular Investigation of the Effect of Saponins and Terpenoids Derived from Leaves of Ilex aquifolium on Lipid Metabolism of Obese Zucker Rats

Ilex paraguariensis, the holly tree, is a plant with recognized biological properties, whose aqueous infusions are known as “Yerba mate”, that regulate lipid metabolism, reduce obesity, and improve brain stimulation. In the present study, the effect of standardized saponin and terpenoid fractions of a European taxon, Ilex aquifolium, on blood biochemical parameters in a rat model of metabolic disorder, (fa/fa) Zucker, are presented. The profiles of the volatile fractions of two species and six European varieties of Ilex were investigated. After selecting the best variety, the saponin and terpenoid fractions were isolated and standardized, and animals were fed 10 mg kg⁻¹ b.w. for 8 weeks. A statistically significant decrease in liver adiposity was observed, confirmed by histology and quantitative identification (gas chromatography–mass spectrometry analyses of hepatic lipids. RT-qPCR analysis of gene expression in the aorta revealed that the administration of the terpenoid fraction downregulated LOX-1, suggesting a reduction in atherosclerotic stimuli. In addition, a statistically significant reduction (p < 0.05) in PPARγ for the saponin fraction was observed in the liver. The expression of the ACAT-1 gene in the liver, responsible for the formation of cholesterol esters, increased significantly in the group receiving the terpenoid fraction compared to the control, which was also confirmed by the analysis of individual blood biochemical parameters. The opposite effect was observed for saponins. Taking the above into account, it is shown for the first time that Ilex aquifolium can be a source of compounds that positively influence lipid metabolism.