On permutation properties in groups and semigroups

A semigroupS satisfiesPPn, thepermutation property of degree n (n≥2) if every product ofn elements inS remains invariant under some nontrivial permutation of its factors. It is shown that a semigroup satisfiesPP3 if and only if it contains at most one nontrivial commutator. Further a regular semigroup is a semilattice ofPP3 right or left groups, and a subdirect product ofPP3 semigroups of a simple type. A negative answer to a question posed by Restivo and Reutenauer is provided by a suitablePP3 group.     

Physicochemical and biological characterization of ceramide-containing liposomes: paving the way to ceramide therapeutic application

Ceramides mediate antiproliferative responses, and it has been proposed that increasing the level of ceramides in cancer cells may have a therapeutic antitumor effect. However, ceramides, because of their high "packing parameter" (PP), do not form lipid assemblies that can be dispersed in a form suitable for intravenous administration. We found that nanoliposomes containing short- or medium-chain ceramides are unstable because of their very high (>1.3) PP. To overcome this major obstacle, we included the lipopolymer 2kPEG-DSPE, which reduces the additive PP. The presence of PEG-DSPE allows the formation of highly stable (>1 year) ceramide (Cer)-containing nanoliposomes suitable for systemic administration. Using tumor cell lines, we found that the ceramide cytotoxicity was not impaired by their inclusion in nanoliposomes. The use of 14C-labeled ceramides shows that the C6Cer, but not C16Cer, was transferred from the nanoliposomes to the cells and metabolized efficiently. The difference between the two ceramides is related to the large difference between their critical aggregation concentration and was correlated with the much higher cytotoxity of liposomal C6Cer. The activity of 2kPEG-DSPE as a steric stabilizer (as previously shown for Doxil) was also confirmed for C6Cer-containing nanoliposomes. The 2kPEG-DSPE lipopolymer significantly reduced the desorption rate of the ceramide from the liposome bilayer, thereby allowing liposomes containing C6Cer to reach the tumor site and to demonstrate therapeutic efficacy.     

Application of the “proportionate partitioning” method suggested by Poulovassilis and Kargas (2000) for determination of the domain distribution function

The soil water hysteresis model proposed by Poulovassilis and Kargas (Soil Sci. Soc. Am. J. 64:1947–1950, 2000) is considered in the present study. According to this model, the bivariate domain density distribution function f can be derived by partitioning the slopes of either of two main curves proportionally to the slopes of another. Accordingly, there are two possible ways of deriving function f. The basic claim of Poulovassilis and Kargas is that both possibilities lead to the same resultant function f, which can be evaluated using integral equation presented by them. The present study shows that the above two ways of determining function f actually lead to two incompatible partitioning models yielding different domain density distribution functions. Moreover, none of these two partitioning models can reproduce the measured hysteresis loop used for calibration. Whether the partitioning of the main wetting curve slopes proportionally to the main drying curve slopes or vice versa is applied, most of the predicted primary scanning curves deviate considerably from the measured ones, cross out the measured boundary loop and do not converge at an appropriate edge of the loop. The present study reveals that the above-mentioned integral equation, presented by Poulovassilis and Kargas, appears to be at variance with both partitioning models. It is shown herein that this integral equation unambiguously follows from Mualem (Water Resour. Res. 9:1324–1331, 1973) similarity hypothesis and, accordingly, the correspondent domain density distribution function derived as the unique analytical solution of this equation is evidently identical to that obtained by Mualem (1973). The predicted curves presented by Poulovassilis and Kargas are not obtained when any of the two partitioning models is applied, but when using the integral equation of Mualem’s (1973) model.     

Amidothionophosphates: Novel Antioxidant Molecules

Abstract

This work describes the synthesis and characterization of a new family of antioxidants. The molecules have the same active group, but different oil-to-water and octanol-to-water partition coefficients due to different substituents. Three new molecules were synthesized based on the chemical structure of the primary amide attached to a thiophosphate group forming an amidothionophosphate. The amidothionophosphate molecules were exposed to the oxidative stress of hydrogen peroxide and sodium hypochlorite, and the chemical changes following the exposure were monitored by 31P NMR. The reaction constants with reactive oxygen species such as hydroxyl radical and superoxide radical were also calculated and found to be 1.5?109 M-1 and 8.1?102 M-1S-1, respectively. In order to elucidate the ability of amidothionophosphates to act as antioxidants in protecting lipids and proteins, we examined damage prevention in Bovine serum albumin, egg phosphatidyl choline liposomes and lipid emulsions following oxidative smss. Amidothionophosphate showed unique protection properties in these models. In contrast to other antioxidant molecules (ascorbic acid, cystine, and a-tocopherol) the new group did not have any pro-oxidative effects as measured by oxygen consumption from buffer solutions containing amidothionophosphates and cupric sulfate as a redox-active metal. Amidothionophosphates reduced significantly and in a dose-dependent manner the oxidative burst in human neutrophils as measured by luminol-dependent chemiluminescence, and they also markedly depressed the killing of human fibroblasts by mixtures of glucose oxidase and streptolysin S. The toxicity of these molecules was tested by i.p. injection of up to 1000 mg/kg to white Sabra mice. No mortality was observed 30 days after administration of up to 500 mg/kg.     

The size of chordal,interval and threshold subgraphs

Given a graphG withn vertices andm edges, how many edges must be in the largest chordal subgraph ofG? Form=n ²/4+1, the answer is 3n/2?1. Form=n ²/3, it is 2n?3. Form=n ²/3+1, it is at least 7n/3?6 and at most 8n/3?4. Similar questions are studied, with less complete results, for threshold graphs, interval graphs, and the stars on edges, triangles, andK ₄'s.     

Influence of lipid composition on the thermotropic behavior and size distribution of mixed cationic liposomes

Cationic liposomes are studied mainly as nonviral nucleic acid delivery systems and to a lesser extent as carriers/adjuvants of vaccines and as low-molecular-weight drug carriers. It is well established that the performance and the biological activity of liposomes in general are strongly related to their physicochemical properties. We investigated the thermotropic behavior and the size distribution of mixed cationic liposomes formulated with different percentages of 1,2 dimyristoyl-sn-glycero-3-phosphatidylcholine and one of four cationic amphiphiles characterized by a pyrrolidinium headgroup with the aim of achieving a better understanding of how the molecular structure of the cationic amphiphile and its mole percentage affect the physicochemical properties of the liposomes. Multilamellar vesicles and large unilamellar vesicles were studied by differential scanning calorimetry and turbidity, respectively, to characterize the thermotropic behavior and lipid phase, whereas dynamic light scattering was used to determine size distribution. This study shows that subtle modifications in the cationic amphiphile's molecular structure and in liposome composition may have dramatic effects on the organization of the liposome bilayer and hence on the morphological and physicochemical features of the liposomes, thus being highly relevant to the biological features investigated previously.     

Selective Terminal Functionalization of Linear Alkanes**

A two-step sequential strategy involving a biocatalytic dehydrogenation/remote hydrofunctionalization, as a unified and versatile approach to selectively convert linear alkanes into a large array of valuable functionalized aliphatic derivatives is reported. The dehydrogenation is carried out by a mutant strain of a bacteria Rhodococcus and the produced alkenes are subsequently engaged in a remote functionalization through a metal-catalyzed hydrometalation/migration sequence that subsequently react with a large variety of electrophiles. The judicious implementation of this combined biocatalytic and organometallic approach enabled us to develop a high-yielding protocol to site-selectively functionalize unreactive primary C−H bonds.