Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

Lanthanide modulation of the orientation of macromolecules induced by purple membrane.

Addition of Tb3+ to purple membrane (PM) suspensions changes the orientation of the menbrane normal from parallel to perpendicular with respect to the magnetic field. Residual dipolar couplings measured in protein L in the presence of PM are scaled by a factor of -1/2. NMR line broadening and cross-correlation effects induced by the addition of PM are partially reversed by Tb3+ but not by Tm3+ that has no effect on the orientation of PM. This is interpreted as the result of anisotropically restricted motion of protein L in the transiently PM-bound form.     

An effective enantioselective approach to the securinega alkaloids: total synthesis of (-)-norsecurinine

[reaction: see text] A highly versatile approach to the enantioselective synthesis of securinega alkaloids is presented. Crucial steps are a palladium-catalyzed enantioselective imide alkylation, a vinylogous Mannich reaction, and a ring-closing metathesis process. Through this strategy, the synthesis of (-)-norsecurinine has been accomplished in nine steps and 11% overall yield.     

Discovering the dynamics of smart business networks

This paper describes a simple diffusion process whereby to discover the dynamics of emergent smart business network structures and their performance in view of business collaboration patterns over time. They include the destabilizing effects of business relationship tie-up’s or break-downs, and are discussed various partner evaluation, filtering and self-preference strategies. Three real life cases of business network dynamics are discussed based on data from the high tech sector. Lessons learnt from such cases are reported regarding overall smart network dynamic parameters with respect to local interaction strategies.     

Multiple Stable Conformations Account for Reversible Concentration‐Dependent Oligomerization and Autoinhibition of a Metamorphic Metallopeptidase

Molecular plasticity controls enzymatic activity: the native fold of a protein in a given environment is normally unique and at a global free‐energy minimum. Some proteins, however, spontaneously undergo substantial fold switching to reversibly transit between defined conformers, the “metamorphic” proteins. Here, we present a minimal metamorphic, selective, and specific caseinolytic metallopeptidase, selecase, which reversibly transits between several different states of defined three‐dimensional structure, which are associated with loss of enzymatic activity due to autoinhibition. The latter is triggered by sequestering the competent conformation in incompetent but structured dimers, tetramers, and octamers. This system, which is compatible with a discrete multifunnel energy landscape, affords a switch that provides a reversible mechanism of control of catalytic activity unique in nature.     

Dissolving Hydroxyolite: A DNA Molecule into Its Hydroxyapatite Mold

In spite of the clinical importance of hydroxyapatite (HAp), the mechanism that controls its dissolution in acidic environments remains unclear. Knowledge of such a process is highly desirable to provide better understanding of different pathologies, as for example osteoporosis, and of the HAp potential as vehicle for gene delivery to replace damaged DNA. In this work, the mechanism of dissolution in acid conditions of HAp nanoparticles encapsulating double‐stranded DNA has been investigated at the atomistic level using computer simulations. For this purpose, four consecutive (multi‐step) molecular dynamics simulations, involving different temperatures and proton transfer processes, have been carried out. Results are consistent with a polynuclear decalcification mechanism in which proton transfer processes, from the surface to the internal regions of the particle, play a crucial role. In addition, the DNA remains protected by the mineral mold and transferred proton from both temperature and chemicals. These results, which indicate that biomineralization imparts very effective protection to DNA, also have important implications in other biomedical fields, as for example in the design of artificial bones or in the fight against osteoporosis by promoting the fixation of Ca²⁺ ions.     

Volatile Constituents of Achillea ligustica All. by HS-SPME/GC/GC-MS. Comparison with Essential Oils Obtained by Hydrodistillation from Corsica and Sardinia

The volatile components extracted from the headspace (HS) of Achillea ligustica All. samples and their separated organs using solid phase microextraction (SPME) were investigated by gas chromatography and gas chromatography-mass spectrometry. Fiftyseven compounds were identified, the main components were camphor (14.2–29.8%), artemisia ketone (0.3–26.7%), santolina alcohol (0.5–9.4%), camphene (3.0–9.0%) and trans-sabinyl acetate (1.6–5.5%). Moreover, the chemical composition of Corsican and Sardinian A. ligustica oils obtained from flowers and leafy stems harvested in four regions of both islands, were investigated. Two collective oils of A. ligustica were also investigated, comparison between both oils as well as from data literature were reported. A comparison of hydrodistillation and HS-SPME extraction of volatile components in term of isolation time, plant-consuming and chemical composition was discussed. HS-SPME technique was clearly fast in contrast to hydrodistillation (90 min/300 min). HS extraction was performed with a much smaller amount of plant than hydrodistillation. Although the aromatic profiles of HS-fractions and oils showed several quantitative differences HS-SPME can be applied to routine control analysis of aromatic and medicinal plants.