Canard cycles in aircraft ground dynamics

The loss of lateral stability of an aircraft turning on the ground is associated with a rapid transition from small-amplitude oscillations to large-amplitude relaxation oscillations over a very small parameter range. This phenomenon is shown to correspond to a canard explosion, which is known to be an important feature of systems that exhibit a separation of time scales. While the industry-tested model of aircraft ground dynamics that we consider does not feature an explicit splitting of time scales, we show that, locally near the transition from stable turning to laterally unstable behaviour, the forward speed of the aircraft acts as a slow variable. The associated family of canard cycles is identified, and the canard explosion is shown to be directly related to the successive saturation of tyre forces at the two main landing gears. We present a canonical two-dimensional slow–fast vector field model that captures the key features of this type of canard explosion; it differs from the canard explosion in the archetypical Van der Pol system in terms of the shape of the associated critical manifold.     

The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions

Freezing-point and vapor-pressure osmometry data are reported for aqueous sodium decanoate (NaD) solutions and aqueous NaD + NaCl solutions. The derived osmotic coefficients are analyzed with a mass-action model based on the micelle formation reaction qNa(+) + nD(-) = (Na(q)D(n))(q-n) and Guggenheim equations for the micelle and ionic activity coefficients. Stoichiometric activity coefficients of the NaD and NaCl components and the equilibrium constant for micelle formation are evaluated. Illustrating the remarkable but not widely appreciated nonideal behavior of ionic surfactant solutions, the micelle activity coefficient drops to astonishingly low values, below 10(-7) (relative to unity for ideal solutions). The activity coefficients of the Na(+) and D(-) ions, raised to large powers of q and n, reduce calculated extents of micelle formation by up to 15 orders of magnitude. Activity coefficients, frequently omitted from the Gibbs equation, are found to increase the calculated surface excess concentration of NaD by up to an order of magnitude. Inflection points in the extent of micelle formation, used to calculate critical micelle concentration (cmc) lowering caused by added salt, provide unexpected thermodynamic evidence for the elusive second cmc.     

Inner-sphere mechanism for molecular oxygen reduction catalyzed by copper amine oxidases

Copper and topaquinone (TPQ) containing amine oxidases utilize O2 for the metabolism of biogenic amines while concomitantly generating H2O2 for use by the cell. The mechanism of O2 reduction has been the subject of long-standing debate due to the obscuring influence of a proton-coupled electron transfer between the tyrosine-derived TPQ and copper, a rapidly established equilibrium precluding assignment of the enzyme in its reactive form. Here, we show that substrate-reduced pea seedling amine oxidase (PSAO) exists predominantly in the Cu(I), TPQ semiquinone state. A new mechanistic proposal for O2 reduction is advanced on the basis of thermodynamic considerations together with kinetic studies (at varying pH, temperature, and viscosity), the identification of steady-state intermediates, and the analysis of competitive oxygen kinetic isotope effects, (18)O KIEs, [kcat/KM((16,16)O2)]/[kcat/KM((16,18)O2)]. The (18)O KIE = 1.0136 +/- 0.0013 at pH 7.2 is independent of temperature from 5 degrees C to 47 degrees C and insignificantly changed to 1.0122 +/- 0.0020 upon raising the pH to 9, thus indicating the absence of kinetic complexity. Using density functional methods, the effect is found to be precisely in the range expected for reversible O2 binding to Cu(I) to afford a superoxide, [Cu(II)(eta(1)-O2)(-I)](+), intermediate. Electron transfer from the TPQ semiquinone follows in the first irreversible step to form a peroxide, Cu(II)(eta(1)-O2)(-II), intermediate driving the reduction of O2. The similar (18)O KIEs reported for copper amine oxidases from other sources raise the possibility that all enzymes react by related inner-sphere mechanisms although additional experiments are needed to test this proposal.     

The first crystal structure of a monomeric phenoxyl radical: 2,4,6-tri-tert-butylphenoxyl radical

Crystals of the 2,4,6-tri-tert-butylphenoxyl radical have been isolated and characterized by X-ray diffraction, and calculations have been performed that give the distribution of spin density in the radical.     

Selective chemical imaging of static actin in live cells

We have characterized rationally designed and optimized analogues of the actin-stabilizing natural products jasplakinolide and chondramide C. Efficient actin staining was achieved in fixed permeabilized and non-permeabilized cells using different combinations of dye and linker length, thus highlighting the degree of molecular flexibility of the natural product scaffold. Investigations into synthetically accessible, non-toxic analogues have led to the characterization of a powerful cell-permeable probe to selectively image static, long-lived actin filaments against dynamic F-actin and monomeric G-actin populations in live cells, with negligible disruption of rapid actin dynamics.     

Mechanisms of electron transfer in catalysis by copper zinc superoxide dismutase

Activated oxygen intermediates during copper zinc superoxide dismutase (SOD) catalysis were investigated using an isotope fractionation technique and natural abundance reagents. Competitive oxygen kinetic isotope effects (KIEs) are reported for the enzyme-catalyzed disproportionation of superoxide as well as the stoichiometric reaction of reduced SOD with molecular oxygen. Analysis within the context of quantum mechanical electron transfer theory provides evidence against an outer-sphere mechanism for O2*- oxidation. A CuII-O2-I intermediate is, therefore, proposed. The SOD-catalyzed oxidation of O2*- is characterized by an inverse (<1) KIE which is similar to those determined for the analogous reactions of synthetic copper compounds. An inverse kinetic isotope effect upon the enzymatic reduction of O2*- is also observed and proposed to arise from rate-determining proton transfer which leads to the formation of HO2* in the SOD active site.     

Tailored polymers by free radical processes

This paper describes a versatile and effective method for the control of free radical polymerization and its use in the preparation of narrow polydispersity polymers of various architectures. Living character is conferred to conventional free radical polymerization by the addition of a thiocarbonylthio compound of general structure S=C(Z)SR, for example, S=C(Ph)SC(CH₃)₂Ph. The mechanism involves Reversible Addition-Fragmentation chain Transfer and, for convenience of referral, we have designated it the RAFT polymerization. The process is compatible with a very wide range of monomers including functional monomers such as acrylic acid, hydroxyethyl methacrylate, and dimethylaminoethyl methacrylate. Examples of narrow polydispersity (≤1.2) homopolymers, copolymers, gradient copolymers, end-functional polymers, star polymers, A-B diblock and A-B-A triblock copolymers are presented.