Overcoming the boundary effects in surface spline interpolation

Surface spline interpolation when the domain is all of R^d isknown to converge much faster to the data function f than inthe case when the domain is the unit ball. This difference isunderstood to be due to boundary effects which, as will be shown,also affect the size of the surface spline's coefficients. Wepropose a modified form of surface spline interpolation which,to a great extent, overcomes these boundary effects. This modifiedsurface spline interpolant uses only the values of f at thegiven interpolation points.     

From homoleptic to heteroleptic double stranded Copper(I) helicates: the role of self-recognition in self-assembly processes

The ligands 2,9-bis[(6-methyl-2, 2'-bipyridin-6'-yl)methyleneoxymethylenyl]-1,10-phenanthroline (6), 6' ',6' "-bis[(6-methyl-2, 2'-bipyridin-6'-yl)methyleneoxymethylenyl)]-2' ',2' "-bipyridine (2), 5,5'-bis[(6-methyl-2,2'-bipyridin-6'yl)methyleneoxymethylenyl]-2, 2'-bithiophene (7), and 6,6'-bis[(6-methyl-2, 2'-bipyridin-6'-yl)methyleneoxymethylenyl]-2,2'-biphenyl (8) and their respective homo- and heteroleptic double-stranded copper(I) complexes were prepared and characterized in order to estimate the importance of self-recognition in the self-assembly processes of double-stranded copper complexes. The homoleptic double-stranded copper complexes of 2, 6, 7, and 8 were characterized by NMR, FAB-MS, and electrochemistry. It was found that 6 and 2 each form a single double-stranded helicate having the structure of [(L)(2)Cu(3)](3+) (L = 2 or 6), 7 forms two double-stranded [(7)(2)Cu(3)](3+) complexes, and 8 results in a mixture of at least two [(8)(2)Cu(2)](2+) complexes. The potential shift, DeltaE degrees (,) of the Cu(+)/Cu(2+) redox process of these complexes reflects the binding affinity of the different binding sites to the copper cation. The electrochemical data show that the central units have a higher affinity to Cu(+) as compared to the off-center binding sites. NMR was used to determine the actual complex composition obtained from different mixtures of 2, 6, or 7 with Cu(+). Interestingly, we have found that, although 6, 2, and 7 each form homoleptic double-stranded complexes, no heteroleptic double-stranded copper complexes were formed from the mixtures of 7 with either 6 or 2. However, when mixtures of 6 and 2 are used, helicate distributions seem to follow simple statistics. These results are discussed in terms of the relative importance of self-recognition in the self-assembly of double-stranded helicates.     

ALS-associated mutant SOD1<Superscript>G93A</Superscript> causes mitochondrial vacuolation by expansion of the intermembrane space and by involvement of SOD1 aggregation and peroxisomes

Background  

Amyotrophic lateral sclerosis (ALS) is an age-dependent neurodegenerative disease that causes motor neuron degeneration, paralysis and death. Mutations in Cu, Zn superoxide dismutase (SOD1) are one cause for the familial form of this disease. Transgenic mice expressing mutant SOD1 develop age-dependent motor neuron degeneration, skeletal muscle weakness, paralysis and death similar to humans. The mechanism whereby mutant SOD1 induces motor neuron degeneration is not understood but widespread mitochondrial vacuolation has been observed during early phases of motor neuron degeneration. How this vacuolation develops is not clear, but could involve autophagic vacuolation, mitochondrial permeability transition (MPT) or uncharacterized mechanisms. To determine which of these possibilities are true, we examined the vacuolar patterns in detail in transgenic mice expressing mutant SOD1^G93A.     

Dichlorocarbene Addition to

In contrast to the terminal phosphinidene complex PhPW(CO)(5) (2), which adds to [5]metacyclophane (1) in a 1,4-fashion, dichlorocarbene preferentially adds in a 1,2-fashion to the formal "anti-Bredt" type double bond of the aromatic ring of 1 to afford the norcaradiene 11b, which immediately rearranges to the bridged cycloheptatriene 12b and further by a [1,5] sigmatropic chlorine migration to the isomeric 13b as the first observable product. More slowly, the latter isomerizes via a dissociative mechanism to give 15b. A computational study supports the notion that the [1,5] chlorine migration in the rearrangement 12b --> 13b, for which an activation barrier of 70.2 kJ mol(-)(1) was calculated, is essentially concerted with minor charge separation. In contrast, the analogous [1,5] chlorine migration in the flat model compound 7,7-dichlorocycloheptatriene (12a) displays features of a dissociative pathway.