A 13C NMR study of pyridoxal-5′-phosphate oxime

Pyridoxal-5′-phosphate amino-oxy acetate oxime was titrated in water, over the pH range 4–12, and the changes followed using ¹³C NMR. The results were compared to those of analogous Schiff's bases presented in the literature. The chemical shifts and titration curves of the oxime were appreciably different from those of the Schiff's bases, and the differences are explained as being due to the absence of ketoenamine-enolimine tautomerism in the oxime. The low chemical shift value and the large changes of the oxime azomethine carbon during titration, as compared to the Schiff's bases, are discussed. The high stability of the oximes in water makes them suitable as model compounds for some tautomeric forms of the Iess stable Schiff's bases.     

Upper and lower error bounds for plate-bending finite elements

Summary. We compare the robustness of three different low-order mixed methods that have been proposed for plate-bending problems: the so-called MITC, Arnold-Falk and Arnold-Brezzi elements. We show that for free plates, the asymptotic rate of convergence in the presence of quasiuniform meshes approaches the optimal O(h) for MITC elements as the thickness approaches 0, but only approaches for the latter two. We accomplish this by establishing lower bounds for the error in the rotation. The deterioration occurs due to a consistency error associated with the boundary layer – we show how a modification of the elements at the boundary can fix the problem. Finally, we show that the Arnold-Brezzi element requires extra regularity for the convergence of the limiting (discrete Kirchhoff) case, and show that it fails to converge in the presence of point loads. Received June 9, 1998 / Published online December 6, 1999     

Quasi-nearly subharmonic functions in locally uniformly homogeneous spaces

We define nonnegative quasi-nearly subharmonic functions on so called locally uniformly homogeneous spaces. We point out that this function class is rather general. It includes quasi-nearly subharmonic (thus also subharmonic, quasisubharmonic and nearly subharmonic) functions on domains of Euclidean spaces \mathbbRⁿ{{\mathbb{R}}^n}, n ≥ 2. In addition, quasi-nearly subharmonic functions with respect to various measures on domains of \mathbbRⁿ{{\mathbb{R}}^n}, n ≥ 2, are included. As examples we list the cases of the hyperbolic measure on the unit ball B ⁿ of \mathbbRⁿ{{\mathbb{R}}^n}, the M{{\mathcal{M}}}-invariant measure on the unit ball B ²ⁿ of \mathbbCⁿ{{\mathbb{C}}^n}, n ≥ 1, and the quasihyperbolic measure on any domain D ì \mathbbRⁿ{D\subset {\mathbb{R}}^n}, D 1 \mathbbRⁿ{D\ne {\mathbb{R}}^n}. Moreover, we show that if u is a quasi-nearly subharmonic function on a locally uniformly homogeneous space and the space satisfies a mild additional condition, then also u ^p is quasi-nearly subharmonic for all p > 0.     

Fluorescent small molecule probe to modulate and explore α2β1 integrin function

Collagen binding integrins are an important family of cell surface receptors that mediate bidirectionally signals between the interior of the cell and the extracellular matrix. The protein-protein interactions between cells and collagen are necessary for many physiological functions, but also promote diseases. For example, the interaction of α2β1 integrin and collagen has been shown to have an important role in thrombus formation and cancer spread. The fact that the discovery of small molecules that can block such protein-protein interactions is highly challenging has significantly hindered the discovery of pharmaceutical agents to treat these diseases. Here, we present a rationally designed novel fluorescent molecule that can be synthesized in just a few minutes from commercially available starting materials. This molecule blocks the protein-protein interaction between α2β1 integrin and collagen, and due to its fluorescent properties, it can be employed in wide variety of biological applications.     

Thermal and IR-induced conformer interconversion processes for 2-chloroallyl alcohol in Low-temperature matrices: Wavelength-dependent conformer steady states

2-chloroallyl alcohol has been studied in low-temperature Ar, Kr, Xe, N₂ and CH₄ matrices. An IR-induced process was found in all media except CH₄ and resulted in a steady state dependent on the Wavelength of the irradiation. At elevated temperatures thermal conformer interconversions occurred. The energetics of the processes are discussed and their potential barriers determined. No mode selectivity was found.     

Molecular Pacman: folding, inclusion, and X-ray structures of tri- and tetraamino piperazine cyclophanes

Reaction of piperazine and 1,3-bis(bromomethyl)-2-nitrobenzene under high-dilution conditions yields cyclic trimeric trinitro, tetrameric tetranitro, and pentameric pentanitro piperazine cyclophanes. Reduction of the nitro groups with SnCl(2) under acidic conditions produces the corresponding triamino and tetraamino piperazine cyclophanes. The solution studies of both nitro and amino piperazine cyclophanes at 30 degrees C by (1)H NMR spectroscopy shows symmetrical structures owing to the fast conformational exchange, whereas the low temperature studies of the tetraamino piperazine cyclophane reveals interesting dynamic behavior that indicates additional intramolecular interactions. Careful crystallizations of the trimeric trinitro and triamino and the tetrameric tetraamino cyclophanes resulted in crystals suitable for X-ray diffraction studies. In the crystalline state the amino-functionalized cyclophanes manifest an extraordinary circular intramolecular hydrogen-bonding network that leads to a fixed 3D structure. Hydrogen bonding in the triamino trimer leads to orientation of all three of the amino groups on the same side of the macrocycle, namely, the rcc conformation, whereas the tetraamino tetramer folds into a more compact shell-like conformation. During the crystallization process one acetonitrile guest is enclosed into the cavity of the tetraamino cyclophane, which gives a crystalline inclusion complex with remarkable resemblance to the famous Pacman motif. The folding, which mimics the behavior of some cyclic peptides and pyrroles, is induced by intramolecular hydrogen bonding from the amino groups to the tertiary amine groups of the piperazines. The cavity of the tetraamino tetramer is markedly smaller than in the corresponding, but nonfolded, tetranitro tetramer and the guest/host volume ratio (packing coefficient) for the acetonitrile and the cavity is approximately 50 %, which indicates a good size match for acetonitrile inclusion.     

Fuzzy expectation values in multistage optimization problems

The study demonstrates the use of fuzzy expectation values in problems of multistage optimization under uncertainty. A practicable procedure is presented for the case where the optimization objective can be decomposed into a series of single-stage decision goals. Instead of probability theory, the uncertainty resolution is accomplished by fuzzy expectation values. In essence, then, the risk aversion is emboided in the selection of the fuzzy integration measure. If for example, the primary goal of the optimization is to achieve a strict cost minimum, then in the lack of information, a weaker goal can be introduced that corresponds to balancing the anticipated costs to the risk of exceeding these in reality. In a number of common optimization problems the method proposed facilitates a rapid solution with clear information on the risk involved.     

On cube-free ω-words generated by binary morphisms

Let h be a morphism satisfying h(a) = ax for a letter a and a nonempty word x. Then h defines an infinite word (an ω-word) when applied iteratively starting from a. Such ω-words are considered in a binary case. It is shown that only biprefixes can generate cube-free ω-words, i.e. words which do not contain a word υ³, with υ ≠ λ, as a subword. The same does not hold true for fourth power-free ω-words, the counterexample being the ω-word defined by the Fibonaccimorphism: h(a) = ba, h(b) = a.As the main result it is proved that it is decidable whether a given morphism of the above form generates a cube-free ω-word. Moreover, it is shown that no more than 10 steps of iterations are needed to solve the problem.