The maximal denumerant of a numerical semigroup

Given a numerical semigroup S=〈a ₀,a ₁,a ₂,…,a _t 〉 and n∈S, we consider the factorization n=c ₀ a ₀+c ₁ a ₁+?+c _t a _t where c _i ≥0. Such a factorization is maximal if ∑c _i is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.     

Rolling circle amplification-templated DNA nanotubes show increased stability and cell penetration ability

DNA nanotubes hold promise as scaffolds for protein organization, as templates of nanowires and photonic systems, and as drug delivery vehicles. We present a new DNA-economic strategy for the construction of DNA nanotubes with a backbone produced by rolling circle amplification (RCA), which results in increased stability and templated length. These nanotubes are more resistant to nuclease degradation, capable of entering human cervical cancer (HeLa) cells with significantly increased uptake over double-stranded DNA, and are amenable to encapsulation and release behavior. As such, they represent a potentially unique platform for the development of cell probes, drug delivery, and imaging tools.     

Efflux Pump Inhibitor Potentiates Antimicrobial Photodynamic Inactivation of Enterococcus faecalis Biofilm

Microbial biofilm architecture contains numerous protective features, including extracellular polymeric material that render biofilms impermeable to conventional antimicrobial agents. This study evaluated the efficacy of antimicrobial photodynamic inactivation (aPDI) of Enterococcus faecalis biofilms. The ability of a cationic, phenothiazinium photosensitizer, methylene blue (MB) and an anionic, xanthene photosensitizer, rose bengal (RB) to inactivate biofilms of E. faecalis (OG1RF and FA 2-2) and disrupt the biofilm structure was evaluated. Bacterial cells were tested as planktonic suspensions, intact biofilms and biofilm-derived suspensions obtained by the mechanical disruption of biofilms. The role of a specific microbial efflux pump inhibitor (EPI), verapamil hydrochloride in the MB-mediated aPDI of E. faecalis biofilms was also investigated. The results showed that E. faecalis biofilms exhibited significantly higher resistance to aPDI when compared with E. faecalis in suspension (P < 0.001). aPDI with cationic MB produced superior inactivation of E. faecalis strains in a biofilm along with significant destruction of biofilm structure when compared with anionic RB (P < 0.05). The ability to inactivate biofilm bacteria was further enhanced when the EPI was used with MB (P < 0.001). These experiments demonstrated the advantage of a cationic phenothiazinium photosensitizer combined with an EPI to inactivate biofilm bacteria and disrupt biofilm structure.     

Low‐level Laser (Light) Therapy Increases Mitochondrial Membrane Potential and ATP Synthesis in C2C12 Myotubes with a Peak Response at 3–6 h

Low‐level laser (light) therapy has been used before exercise to increase muscle performance in both experimental animals and in humans. However, uncertainty exists concerning the optimum time to apply the light before exercise. The mechanism of action is thought to be stimulation of mitochondrial respiration in muscles, and to increase adenosine triphosphate (ATP) needed to perform exercise. The goal of this study was to investigate the time course of the increases in mitochondrial membrane potential (MMP) and ATP in myotubes formed from C2C12 mouse muscle cells and exposed to light‐emitting diode therapy (LEDT). LEDT employed a cluster of LEDs with 20 red (630 ± 10 nm, 25 mW) and 20 near‐infrared (850 ± 10 nm, 50 mW) delivering 28 mW cm² for 90 s (2.5 J cm²) with analysis at 5 min, 3 h, 6 h and 24 h post‐LEDT. LEDT‐6 h had the highest MMP, followed by LEDT‐3 h, LEDT‐24 h, LEDT‐5 min and Control with significant differences. The same order (6 h > 3 h > 24 h > 5 min > Control) was found for ATP with significant differences. A good correlation was found (r = 0.89) between MMP and ATP. These data suggest an optimum time window of 3–6 h for LEDT stimulate muscle cells.     

The Effect of Charge on Cellular Uptake and Phototoxicity of Polylysine Chlorine6Conjugates

Abstract— The effect of charge on the cellular uptake, localization and phototoxicity of conjugates between chlorin_e6 ( c _e6) and poly-L-lysine was studied in vitro. These conjugates (average MW35–55 kDa) were synthesized to have polycationic, polyanionic or neutral charges. Two human cell lines (A431 epidermoid carcinoma cells and EA.hy926 hybrid endothelial cells) were studied and the cellular uptake of c _e6 delivered by the conjugates of varying charge and free c _e6 was measured at conjugate c _e6 equivalent concentrations up to 0.4 μM. Uptake was time and concentration dependent and temperature dependent in the case of neutral and anionic conjugates. Relative uptake at 6 h for A431 cells was 73:15:4:1 and for EA. hy926 cells was 63:11:3:1 for cationic, anionic, neutral and free c _e6, respectively, but EA. hy926 cells took up 1.5-2 times as much c _e6 from all the conjugates as A431 cells. Localization as studied by fluorescence microscopy indicated that the cationic conjugate was in aggregates bound to the plasma membrane, while the other forms were internalized in organelles and membranes. Phototoxicity was measured by 3-(4,5-dimethylthiazol-2-yl)-diphenyltetra-zolium bromide (MTT) assay after irradiation with5–20 J cm⁻²of 666 nm light. In contrast to the uptake, the order of phototoxicity for both cell types per mole of c _e6 uptake per cell was neutral ≫ anionic > cationic > free c _e6. Polymeric c _e6 conjugates bearing positive, negative and neutral charges may have different tissue-localizing properties and could play a role in photodynamic therapy.     

Synthesis and characterization of positively charged pentacationic [60]fullerene monoadducts for antimicrobial photodynamic inactivation

We designed and synthesized two analogous pentacationic [60]fullerenyl monoadducts, C??(>ME?N??C?) (1) and C??(>ME?N??C?) (2), with variation of the methoxyethyleneglycol length. Each of these derivatives bears a well-defined number of cationic charges aimed to enhance and control their ability to target pathogenic Gram-positive and Gram-negative bacterial cells for allowing photodynamic inactivation. The synthesis was achieved by the use of a common synthon of pentacationic N,N′,N,N,N,N-hexapropylhexa(aminoethyl)amine arm (C?N??) having six attached propyl groups, instead of methyl or ethyl groups, to provide a well-balanced hydrophobicity-hydrophilicity character to pentacationic precursor intermediates and better compatibility with the highly hydrophobic C?? cage moiety. We demonstrated two plausible synthetic routes for the preparation of 1 and 2 with the product characterization via various spectroscopic methods.     

Linezolid and Vancomycin Decrease the Therapeutic Effect of Methylene Blue‐Photodynamic therapy in a Mouse Model of MRSA Bacterial Arthritis

We previously reported that photodynamic therapy (PDT) using intra‐articular methylene blue (MB) could be used to treat arthritis in mice caused by bioluminescent methicillin‐resistant Staphylococcus aureus (MRSA) either in a therapeutic or in a preventative mode. PDT accumulated neutrophils into the mouse knee via activation of chemoattractants such as inflammatory cytokines or chemokines. In this study, we asked whether PDT combined with antibiotics used for MRSA could provide added benefit in controlling the infection. We compared MB‐PDT alone, systemic administration of either linezolid (LZD) alone or vancomycin (VCM) alone or the combination of PDT with either LZD or VCM. Real‐time noninvasive imaging was used to serially follow the progress of the infection. PDT alone was the most effective, whereas LZD alone was ineffective and VCM alone showed some benefit. Surprisingly the addition of LZD or VCM reduced the therapeutic effect of PDT alone (P < 0.05). Considering that PDT in this mouse model stimulates neutrophils to be antibacterial rather than actively killing the bacteria, we propose that LZD and VCM might inhibit the activation of inflammatory cytokines without eradicating the bacteria, and thereby reduce the therapeutic effect of PDT.     

Ultra-low-frequency dust-electromagnetic modes in self-gravitating magnetized dusty plasmas

Obliquely propagating altra-low-frequency dust-electromagnetic waves in a self-gravitating, warm, magnetized, two fluid dusty plasma system have been investigated. Two special cases, namely, dust-Alfvén mode propagating parallel to the external magnetic field and dustmagnetosonic mode propagating perpendicular to the external magnetic field have also been considered. It has been shown that effects of self-gravitational field, dust fluid temperature, and obliqueness significantly modify the dispersion properties of these ultra-low-frequency dust-electromagnetic modes. It is also found that in parallel propagating dust-Alfvén mode these effects play no role, but in obliquely propagating dust-Alfvén mode or perpendicular propagating dust-magnetosonic mode the effect of self-gravitational field plays destabilizing role whereas the effect of dust/ion fluid temperature plays stabilizing role.     

Solvable Groups Satisfying the Two-prime Hypothesis,Part I

In this paper, finite solvable groups satisfying the “-prime hypothesis” are considered. Specifically, a bound on the number of irreducible character degrees of such a group is obtained when . The general situation is also considered, and generalizations of the -prime hypothesis are analyzed. Presented by A. Verschoren.