Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.     

Singular Sturm—Liouville problems with nonnegative and indefinite weights

This article is concerned with the oscillatory properties of the eigenfunctions of a class of singular Sturm—Liouville problems—(p y)+q y=w y on (a, b), where the weight functionw vanishes on a subinterval of positive measure, or where the weight functionw changes sign on (a, b).This work was supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.     

Homoclinic bifurcations at the onset of pulse self-replication

We establish a series of properties of symmetric, N-pulse, homoclinic solutions of the reduced Gray-Scott system: u^″=uv², v^″=v−uv², which play a pivotal role in questions concerning the existence and self-replication of pulse solutions of the full Gray-Scott model. Specifically, we establish the existence, and study properties, of solution branches in the (α,β)-plane that represent multi-pulse homoclinic orbits, where α and β are the central values of u(x) and v(x), respectively. We prove bounds for these solution branches, study their behavior as α→∞, and establish a series of geometric properties of these branches which are valid throughout the (α,β)-plane. We also establish qualitative properties of multi-pulse solutions and study how they bifurcate, i.e., how they change along the solution branches.     

Brownmillerites CaFeO2.5 and SrFeO2.5 as Catalyst Support for CO Oxidation

The support material can play an important role in oxidation catalysis, notably for CO oxidation. Here, we study two materials of the Brownmillerite family, CaFeO_2.5 and SrFeO_2.5, as one example of a stoichiometric phase (CaFeO_2.5, CFO) and one existing in different modifications (SrFeO_2.75, SrFeO_2.875 and SrFeO₃, SFO). The two materials are synthesized using two synthesis methods, one bottom-up approach via a complexation route and one top-down method (electric arc fusion), allowing to study the impact of the specific surface area on the oxygen mobility and catalytic performance. CO oxidation on ¹⁸O-exchanged materials shows that oxygen from SFO participates in the reaction as soon as the reaction starts, while for CFO, this onset takes place 185 °C after reaction onset. This indicates that the structure of the support material has an impact on the catalytic performance. We report here on significant differences in the catalytic activity linked to long-term stability of CFO and SFO, which is an important parameter not only for possible applications, but equally to better understand the mechanism of the catalytic activity itself.     

A Geometric Construction of Traveling Waves in a Bioremediation Model

Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil column. Using geometric singular perturbation theory, we construct traveling waves (TW) corresponding to the motion of a biologically active zone, in which the microorganisms consume both substrate and acceptor. For certain values of the parameters, the traveling waves exist on a three-dimensional slow manifold within the five-dimensional phase space. We prove persistence of the slow manifold under perturbation by controlling the nonlinearity via a change of coordinates, and we construct the wave in the transverse intersection of appropriate stable and unstable manifolds in this slow manifold. We study how the TW depends on the half-saturation constants and other parameters and investigate numerically a bifurcation in which the TW loses stability to a periodic wave.     

A commentary “on the periodic solutions of a forced second-order equation” by S. P. Hastings and J. B. McLeod

Summary We discuss the relationship of the shooting and perturbation methods used by Hastings and McLeod in the paper On the Periodic Solutions of a Forced Second-Order Equation to the geometrical techniques of nonlinear dynamical systems theory.     

A simple model of chaotic advection and scattering

In this work, we study a blinking vortex-uniform stream map. This map arises as an idealized, but essential, model of time-dependent convection past concentrated vorticity in a number of fluid systems. The map exhibits a rich variety of phenomena, yet it is simple enough so as to yield to extensive analytical investigation. The map's dynamics is dominated by the chaotic scattering of fluid particles near the vortex core. Studying the paths of fluid particles, it is seen that quantities such as residence time distributions and exit-vs-entry positions scale in self-similar fashions. A bifurcation is identified in which a saddle fixed point is created upstream at infinity. The homoclinic tangle formed by the transversely intersecting stable and unstable manifolds of this saddle is principally responsible for the observed self-similarity. Also, since the model is simple enough, various other properties are quantified analytically in terms of the circulation strength, stream velocity, and blinking period. These properties include: entire hierarchies of fixed points and periodic points, the parameter values at which these points undergo conservative period-doubling bifurcations, the structure of the unstable manifolds of the saddle fixed and periodic points, and the detailed structure of the resonance zones inside the vortex core region. A connection is made between a weakly dissipative version of our map and the Ikeda map from nonlinear optics. Finally, we discuss the essential ingredients that our model contains for studying how chaotic scattering induced by time-dependent flow past vortical structures produces enhanced diffusivities. (c) 1995 American Institute of Physics.