Extremal families of cubic Thue equations

We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form $F(x,y)=1$ with at least $5$ such solutions. Our approach combines elementary arguments, with lower bounds for linear forms in logarithms and lattice-basis reduction

Corporate separateness

Banking structure ; Bank affiliates ; Bank holding companies

\u3cem\u3eArabidopsis thaliana\u3c/em\u3e GLX2-1 Contains a Dinuclear Metal Binding Site, but Is Not a Glyoxalase 2

In an effort to probe the structure and function of a predicted mitochondrial glyoxalase 2, GLX2-1, from Arabidopsis thaliana, GLX2-1 was cloned, overexpressed, purified and characterized using metal analyses, kinetics, and UV–visible, EPR, and 1H-NMR spectroscopies. The purified enzyme was purple and contained substoichiometric amounts of iron and zinc; however, metal-binding studies reveal that GLX2-1 can bind nearly two equivalents of either iron or zinc and that the most stable analogue of GLX2-1 is the iron-containing form. UV–visible spectra of the purified enzyme suggest the presence of Fe(II) in the protein, but the Fe(II) can be oxidized over time or by the addition of metal ions to the protein. EPR spectra revealed the presence of an anti-ferromagnetically-coupled Fe(III)Fe(II) centre and the presence of a protein-bound high-spin Fe(III) centre, perhaps as part of a FeZn centre. No paramagnetically shifted peaks were observed in 1H-NMR spectra of the GLX2-1 analogues, suggesting low amounts of the paramagnetic, anti-ferromagnetically coupled centre. Steady-state kinetic studies with several thiolester substrates indicate that GLX2-1 is not a GLX2. In contrast with all of the other GLX2 proteins characterized, GLX2-1 contains an arginine in place of one of the metal-binding histidine residues at position 246. In order to evaluate further whether Arg246 binds metal, the R246L mutant was prepared. The metal binding results are very similar to those of native GLX2-1, suggesting that a different amino acid is recruited as a metal-binding ligand. These results demonstrate that Arabidopsis GLX2-1 is a novel member of the metallo-β-lactamase superfamily

Spectroscopic Studies on \u3cem\u3eArabidopsis\u3c/em\u3e ETHE1, a Glyoxalase II-like Protein

ETHE1 (ethylmalonic encephalopathy protein 1) is a β-lactamase fold-containing protein that is essential for the survival of a range of organisms. In spite of the apparent importance of this enzyme, very little is known about its function or biochemical properties. In this study Arabidopsis ETHE1 was over-expressed and purified and shown to bind tightly to 1.2 ± 0.2 equivalents of iron. 1H NMR and EPR studies demonstrate that the predominant oxidation state of Fe in ETHE1 is Fe(II), and NMR studies confirm that two histidines are bound to Fe(II). EPR studies show that there is no antiferromagnetically coupled Fe(III)Fe(II) center in ETHE1. Gel filtration studies reveal that ETHE1 is a dimer in solution, which is consistent with previous crystallographic studies. Although very similar in terms of amino acid sequence to glyoxalase II, ETHE1 exhibits no thioester hydrolase activity, and activity screening assays reveal that ETHE1 exhibits low level esterase activity. Taken together, ETHE1 is a novel, mononuclear Fe(II)-containing member of the β-lactamase fold superfamily