The Thermal Diastereomerization of the Tryptophane-Derived Green Fluorescent Protein Chromophore

Summary. Two model compounds for the tryptophane variant of the green fluorescent protein chromophore containing a 3-indolyl and 2-pyrrolyl moiety were prepared. For the first one the (Z)-diastereomer was found to be more stable than the (E)-diastereomer by 5.7 kJ mol⁻¹. It could be photo-diastereomerized and its thermal equilibration was studied, whereas the second one underwent photo-destruction. From an Arrhenius plot an activation barrier for the (E) to (Z) diastereomerization of 85.6 kJ mol⁻¹ could be determined. Thus, it could be demonstrated that in contrast to the corresponding phenyl derivative studied recently the tyrosine- and tryptophane-derived chromophores of the green fluorescent protein are amenable to fast thermal diastereomerization, which is of fundamental importance for the fluorescence and photoswitching processes in the corresponding proteins.     

On the Chemistry of the Resveratrol Diastereomers

Summary.  The (E)- and (Z)-diastereomers of resveratrol were investigated with respect to their photochemical and thermal diastereomerization reactions. The free enthalpy difference between the two diastereomers was estimated to be in the order of common stilbenes, with the (E)-diastereomer more stable by about 11–14 kJ mol⁻¹. The Arrhenius activation barrier of about 280 kJ mol⁻¹ was found to be quite high and implies that thermal equilibration cannot account for the (Z)-diastereomer found in nature. A preparative access to the (Z)-diastereomer by photodiastereomerization is described. The ¹H and ¹³C NMR spectra of the two diastereomers were assigned and their absorption spectra and fluorescence quantum yields of the neutral and monodeprotonated species were determined. Corresponding author. E-mail: heinz.falk@jku.at Received October 15, 2002; accepted November 7, 2002 Published online February 20, 2003     

A note on generalized Pareto distributions and thek upper extremes

Summary Denote byD(n, k) the maximum distance between the distribution function of thekth-largest order statistic in aniid sample of sizen, equally standardized ink, and of its corresponding limiting extreme value distribution.Suppose that the underlying distribution function is ultimately continuous and strictly increasing. It is shown in the present paper thatD(n,k) converges to zero for any sequencek=k (n) with if and only if the underlying distribution is ultimately a generalized Pareto distribution. ThusgPds do not only yield the best rate of joint convergence of extremes, but they are also the only distributions where there actually is convergence.     

The vanishing ideal of a finite set of closed points in affine space

Given a finite set of closed rational points of affine space over a field, we give a Gröbner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the Buchberger-Möller algorithm, but in contrast to that, we determine the set of leading terms of the ideal without solving any linear equation but by induction over the dimension of affine space. The elements of the Gröbner basis are also computed by induction over the dimension, using one-dimensional interpolation of coefficients of certain polynomials.     

On the cohomology of flows of stochastic and random differential equations

We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise. Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001     

Concerning the Absorption and Photochemical Properties of an ω-4-Dimethylaminobenzal Hypericin Derivative

Summary.  A hypericin derivative containing ω,ω ′-4-dimethylaminobenzal residues was shown to undergo an intramolecular [2 + 2] cycloaddition upon irradiation leading to a cyclobutane derivative whose main absorption band is hardly shifted as compared to hypericin. The corresponding ω-substituted derivative displayed a 34 nm bathochromic shift and a strongly reduced fluorescence quantum yield rendering it a nice candidate for a photodynamic therapy agent. Unfortunately, however, it produced virtually no photosensitized active oxygen species, making it thus unsuited for this purpose. Received July 11, 2001. Accepted July 18, 2001     

On the anionic homo‐ and copolymerization of ethyl‐ and butyl‐2‐cyanoacrylates

Ethyl‐(ECA) and butyl‐2‐cyanoacrylate (BCA) monomers of high purity and acidic stabilization were synthesized and anionically polymerized to homo‐ and copolymers in two different ways: by piperidine‐catalyzed bulk polymerization leading to transparent, brittle films (method A) and by polymerization in aqueous medium in the presence of sodium bicarbonate to obtain white powders (Method B). The molecular structure of the synthesized monomers, homopolymers and copolymers were corroborated by spectral methods. The polymers were studied further by thermal gravimetric analysis (TGA), differential scanning calorimetry (DSC), size exclusion chromatography (SEC) and proton nuclear magnetic resonance (¹H NMR). Controlling the composition of the monomer feed and the way the polymerization was performed, it was possible to obtain phase separated or homogeneous cyanoacrylate copolymers with glass transitions varying between the T_g of polyECA and that of polyBCA. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5142–5156, 2008