Symmetry and the golden ratio in the analysis of a regular pentagon

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems.     

A Safety Strategy for Producing Poly(Acrylic Acid) of Low Molar Mass

The synthesis of poly(acrylic acid) (PAA) of low molar mass under safe conditions is difficult due to the high polymerization rate of acrylic acid (AA) and the fast heat generation. The aqueous‐solution “semibatch” polymerization of non‐ionized AA in almost starved conditions involves high initiator loads when low molar masses are required. This article proposes the simultaneous feeding of AA and nonconventional chain transfer agents (CTA) as a strategy aimed at controlling both the molar masses and the generated heat rate. Three CTAs are investigated: 2‐mercaptoethanol, thioglycolic acid, and isopropyl alcohol. Even when PAA of relatively low molar mass can be produced by adequately selecting the flow rates and concentrations of both AA and CTA, it is found that the nature of CTA can have a significant effect on the polymerizations kinetics. The mechanisms responsible for these effects are discussed with the help of a representative mathematical model.

     

The Biochemical Mechanisms of Antimicrobial Photodynamic Therapy†

The unbridled dissemination of multidrug-resistant pathogens is a major threat to global health and urgently demands novel therapeutic alternatives. Antimicrobial photodynamic therapy (aPDT) has been developed as a promising approach to treat localized infections regardless of drug resistance profile or taxonomy. Even though this technique has been known for more than a century, discussions and speculations regarding the biochemical mechanisms of microbial inactivation have never reached a consensus on what is the primary cause of cell death. Since photochemically generated oxidants promote ubiquitous reactions with various biomolecules, researchers simply assumed that all cellular structures are equally damaged. In this study, biochemical, molecular, biological and advanced microscopy techniques were employed to investigate whether protein, membrane or DNA damage correlates better with dose-dependent microbial inactivation kinetics. We showed that although mild membrane permeabilization and late DNA damage occur, no correlation with inactivation kinetics was found. On the other hand, protein degradation was analyzed by three different methods and showed a dose-dependent trend that matches microbial inactivation kinetics. Our results provide a deeper mechanistic understanding of aPDT that can guide the scientific community toward the development of optimized photosensitizing drugs and also rationally propose synergistic combinations with antimicrobial chemotherapy.     

In Vitro Cytotoxic Protective Effect of Alginate-Encapsulated Capsaicin Might Improve Skin Side Effects Associated with the Topical Application of Capsaicin

Chronic neuropathic pain, particularly peripheral pain, is a cause of great concern for diabetic patients. Current treatments include numerous agents such as capsaicinoids, a known deterrent of neuropathic pain despite the inconvenience associated with local side effects. In this context, the current work aims to elucidate the potential mechanisms involved in cytotoxicity by capsaicin and proposes an efficient formulation of capsaicin in alginate microcapsules, which significantly reduces side effects from capsaicin topical administration. For this, human dermal fibroblast cells were treated with alginate-microencapsulated capsaicin extracts and screened for potential cytotoxic effects produced by the treatment. Cell viability and morphology were examined, as well as oxidative stress status and anti-inflammatory potential. Our results show that the alginate encapsulated formulation of capsaicin exerted lower cytotoxic effects on human dermal fibroblasts as measured by cell viability and reactive oxygen species (ROS) production. Furthermore, the expression profiles of inflammatory cytokines were significantly altered by the treatment as compared with the control culture.     

Identification of a Prenyl Chalcone as a Competitive Lipoxygenase Inhibitor: Screening,Biochemical Evaluation and Molecular Modeling Studies

Cyclooxygenase (COX) and lipoxygenase (LOX) are key targets for the development of new anti-inflammatory agents. LOX, which is involved in the biosynthesis of mediators in inflammation and allergic reactions, was selected for a biochemical screening campaign to identify LOX inhibitors by employing the main natural product library of Brazilian biodiversity. Two prenyl chalcones were identified as potent inhibitors of LOX-1 in the screening. The most active compound, (E)-2-O-farnesyl chalcone, decreased the rate of oxygen consumption to an extent similar to that of the positive control, nordihydroguaiaretic acid. Additionally, studies on the mechanism of the action indicated that (E)-2-O-farnesyl chalcone is a competitive LOX-1 inhibitor. Molecular modeling studies indicated the importance of the prenyl moieties for the binding of the inhibitors to the LOX binding site, which is related to their pharmacological properties.     

Zn(ferulate)-LSH Systems as Multifunctional Filters

Excessive UV solar radiation exposure causes human health risks; therefore, the study of multifunctional filters is important to skin UV protective ability and also to other beneficial activities to the human organism, such as reduction of reactive oxygen species (ROS) responsible for cellular damages. Potential multifunctional filters were obtained by intercalating of ferulate anions into layered simple metal hydroxides (LSH) through anion exchange and precipitation at constant pH methods. Ultrasound treatment was used in order to investigate the structural changes in LSH-ferulate materials. Structural and spectroscopic analyses show the formation of layered materials composed by a mixture of LSH intercalated with ferulate anions, where carboxylate groups of ferulate species interact with LSH layers. UV-VIS absorption spectra and in vitro SPF measurements indicate that LSH-ferulate systems have UV shielding capacity, mainly UVB protection. The results of reactive species assays show the ability of layered compounds in capture DPPH^•, ABTS^•+, ROO^•, and HOCl/OCl⁻ reactive species. LSH-ferulate materials exhibit antioxidant activity and singular optical properties that enable their use as multifunctional filters.     

Wet-Chemically Prepared Porphyrin Layers on Rutile TiO2(110)

Porphyrins are large organic molecules that are interesting for different applications, such as photovoltaic cells, gas sensors, or in catalysis. For many of these applications, the interactions between adsorbed molecules and surfaces play a crucial role. Studies of porphyrins on surfaces typically fall into one of two groups: (1) evaporation onto well-defined single-crystal surfaces under well-controlled ultrahigh vacuum conditions or (2) more application-oriented wet chemical deposition onto less well-defined high surface area surfaces under ambient conditions. In this study, we will investigate the wet chemical deposition of 5-(monocarboxyphenyl)-10,15,20-triphenylporphyrin (MCTPP) on well-defined rutile TiO₂(110) single crystals under ambient conditions. Prior to deposition, the TiO₂(110) crystals were also cleaned wet-chemically under ambient conditions, meaning none of the preparation steps were done in ultrahigh vacuum. However, after each preparation step, the surfaces were characterized in ultrahigh vacuum with X-ray photoelectron spectroscopy (XPS) and the result was compared with porphyrin layers prepared in ultrahigh vacuum (UHV) by evaporation. The differences of both preparations when exposed to zinc ion solutions will also be discussed.     

Surface composition of PdCuAu ternary alloys: a combined LEIS and XPS study

PdCuAu ternary alloy samples with different composition were synthesized on top of ZrO₂‐modified porous stainless steel disks by the sequential electroless deposition technique. The structure, morphology and bulk composition of the samples were characterized by X‐ray diffraction (XRD), scanning electron microscopy and energy dispersive X‐ray spectroscopy (EDX). Complete alloy formation with a pure fcc phase for the Pd₇₁Cu₂₆Au₃, Pd₇₀Cu₂₅Au₅ and Pd₆₇Cu₂₄Au₉ samples and a bcc structure for the Pd₆₂Cu₃₆Au₂ and Pd₆₀Cu₃₇Au₃ samples were obtained upon annealing at 500 °C for 120 h as revealed by XRD. A combination of low‐energy ion scattering (LEIS) and X‐ray photoelectron spectroscopy (XPS) was used to investigate the surface properties of the PdCuAu alloys. XPS results confirmed alloy formation under the annealing conditions. XPS analysis also revealed that the near‐surface regions of the alloys became enriched in Pd with respect to the bulk composition determined by EDX. In contrast, LEIS and angle‐resolved XPS analyses showed that the top‐most surface layers in all samples were copper‐rich compared with the bulk composition. This high Cu surface concentration could impart resistance to bulk sulfide formation to the PdCuAu alloy membranes. Copyright © 2015 John Wiley & Sons, Ltd.     

Potential of prodendronic polyamines with modulated segmental charge density as novel coating for fast and efficient analysis of peptides and basic proteins by CE and CE‐MS

In this work, the suitability of a new polymer family has been investigated as capillary coatings for the analysis of peptides and basic proteins by CE. This polymer family has been designed to minimize or completely prevent protein–capillary wall interactions and to modify the EOF. These coating materials are linear polymeric chains bearing as side cationizable moiety a dentronic triamine derived from N,N,N’,N’‐tetraethyldiethylenetriamine (TEDETA), which is linked to the backbone through a spacer (unit labeled as TEDETAMA). Four different polymers have been prepared and evaluated: a homopolymer which comprised only of those cationizable repetitive units of TEDETAMA, and three copolymers that randomly incorporate TEDETAMA together with neutral hydrosoluble units of N‐(2‐hydroxypropyl) methacrylamide (HPMA) at different molar percentages (25:75, 50:50 and 75:25). It has been demonstrated that the composition of the copolymers influences the EOF and therefore the separation of the investigated biopolymers. Among the novel polymers studied, poly‐(TEDETAMA‐co‐HPMA) 50:50 copolymer was successfully applied as coating material of the inner capillary surface in CE‐UV and CE‐MS, providing EOF reversing together with fast and efficient baseline separation of peptides and basic proteins. Finally, the feasibility of the polymer‐coated capillary was shown through the analysis of lysozyme in a cheese sample.     

Influence of the Solvent on the “Casting” Methodology for MWCNT‐Modified Glassy Carbon and Platinum Electrodes

The choice of electrode material and surface preparation method are usually dictated by the suitability of the electrode to observe an electrochemical parameter, such as heterogeneous electron transfer rate, surface coverage, or redox potential. Thus, the glassy carbon (GC) and platinum (Pt) electrodes were modified with multiwalled carbon nanotubes (MWCNT) by direct “casting” modification using nine different aliquots of solvents. After drying at room temperature, the modified electrode showed distinct redox peaks corresponding to ferrocyanide oxidation/reduction. Using chemometrics, the cyclic voltammograms with higher current intensity were obtained for those in which ethanol, water and acetone as dispersing agents were used for GCE and dimethylformamide, water and acetone for Pt electrode modification.