Statistical Encounters with Complex B-Splines

Complex B-splines as introduced in Forster et al. (Appl. Comput. Harmon. Anal. 20:281–282, 2006) are an extension of Schoenberg’s cardinal splines to include complex orders. We exhibit relationships between these complex B-splines and the complex analogues of the classical difference and divided difference operators and prove a generalization of the Hermite–Genocchi formula. This generalized Hermite–Genocchi formula then gives rise to a more general class of complex B-splines that allows for some interesting stochastic interpretations.      

A multiplicity result for a special class of gradient-type systems with non-differentiable term

We prove the existence of multiple solutions of certain systems of hemivariational inequalities, using a recent minimax result of B. Ricceri. We apply both our main theorem and the principle of symmetric criticality to obtain multiple solutions of systems of hemivariational inequalities defined on certain Sobolev spaces.     

Synthesis and characterization of new semifluorinated linear and hyperbranched poly(arylene ether phosphine oxide)s through B2 + A2 and AB2 approaches

A new phosphorus containing trifluoromethyl-activated bisfluoro B₂ monomer has been synthesized successfully by coupling reaction of 4-methoxyphenylphosphonic dichloride and the Grignard salt of 5-bromo-2-fluorobenzotrifluoride. This monomer was converted to linear poly(arylene ether phosphine oxide)s by nucleophilic displacement of the fluorine atom on the benzene ring with several diphenols. The B₂ monomer was further demethylated to form an AB₂ monomer which on self condensation yielded hyperbranched poly(arylene ether phosphine oxide) with identical phosphorous containing moiety. The products obtained exhibit weight-average molecular weights as high as 600,000 g mol⁻¹ in SEC. These linear and hyperbranched poly(arylene ether phosphine oxide)s showed thermal stability as high as 516 °C for 10% weight loss in TGA in nitrogen and showed glass transition temperatures up to 253 °C in DSC. All the polymers were soluble in a wide range of organic solvents, e.g., CHCl₃, THF, NMP and DMF, however, the hb sample showed a significant lower solution viscosity compared to linear samples of similar molar mass. Transparent thin films of linear poly(arylene ether phosphine oxide)s casted from dichloromethane exhibited tensile strengths up to 50 MPa, a modulus of elasticity up to 0.95 GPa and elongation at break up to 36% depending on their exact repeating unit structures. No free standing films could be prepared from the hb analogue due to the missing entanglements, but stable thin polymer films on silicon wafers with high hydrophobicity were formed which showed water contact angles as high as 91°.     

Cluster analysis application identifies muscle characteristics of importance for beef tenderness

Background

Unsaturated fatty acids are susceptible to oxidation and damaged chains are removed from glycerophospholipids by phospholipase A₂. De-acylated lipids are then re-acylated by lysophospholipid acyltransferase enzymes such as LPCAT1 which catalyses the formation of phosphatidylcholine (PC) from lysoPC and long-chain acyl-CoA.

Results

Activity of LPCAT1 is inhibited by Ca²⁺, and a Ca²⁺-binding motif of the EF-hand type, EFh-1, was identified in the carboxyl-terminal domain of the protein. The residues Asp-392 and Glu-403 define the loop of the hairpin structure formed by EFh-1. Substitution of D³⁹² and E⁴⁰³ to alanine rendered an enzyme insensitive to Ca²⁺, which established that Ca²⁺ binding to that region negatively regulates the activity of the acyltransferase amino-terminal domain. Residue Cys-211 of the conserved motif III is not essential for catalysis and not sufficient for sensitivity to treatment by sulfhydryl-modifier agents. Among the several active cysteine-substitution mutants of LPCAT1 generated, we identified one to be resistant to treatment by sulfhydryl-alkylating and sulfhydryl-oxidizer agents.

Conclusion

Mutant forms of LPCAT1 that are not inhibited by Ca²⁺ and sulfhydryl-alkylating and ?Coxidizing agents will provide a better understanding of the physiological function of a mechanism that places the formation of PC, and the disposal of the bioactive species lysoPC, under the control of the redox status and Ca²⁺ concentration of the cell.     

Kinetics of the production of chain-end groups and methanol from the depolymerization of cellulose during the ageing of paper/oil systems. Part 2: Thermally-upgraded insulating papers

In order to go further in demonstrating that methanol can be used as a universal cellulose degradation indicator in power transformers, the ageing study of standard wood kraft specimens in oil in the range of 60–130 °C (Gilbert et al. in Cellulose 16:327–338, 2009) has been extended to thermally-upgraded (TU) papers. The kinetic model that best tracks the ageing patterns was shown to be a function that can accelerate or decelerate the pseudo-zero kinetics by the adjustment of a free parameter. The results showed a non-negligible contribution of 1,4-β-glycosidic bond breaking in the crystalline regions suggesting that the degradation at this level is not necessary occurring through a quantum mode mechanism. The results also showed a significant error in the determination of the rate constants when obtained from isotherms of varying degree of depolymerization. In the case of TU papers, provided that there is a sufficient amount of stabilizers in the fibrous structure, not only could the self-catalyzing nature of the cellulose ageing process as well as the effect of an external supply of catalysts be lost but the chain-breaking could decrease to nearly zero for an undetermined period well before reaching the levelling-off degree of polymerization. The initial rate constants (k _1o) for the depolymerization and methanol formation of these papers were found to be very near those of standard cellulose (giving about the same activation energy), which indicates that they are obtained from the ageing patterns well before the retardant action has fully taken place. The life extension of TU papers is achieved by a reduction with time of the frequency at which the bonds are ruptured. Moreover, the production of methanol and chain-end groups showed about the same value for the frequency factor, which introduces the possibility that the rate of production of CH₃OH from chopped chains is much higher than the rate of depolymerization, so that the latter becomes the rate determining step of the overall reaction. On the other hand, the apparent yield of CH₃OH molecules per scission is seen to increase substantially with the amount of stabilizers (from ~0.4 to 0.8 and to 1.4 for a paper containing 0 to 1.15 and to 3.9% (w/w) N₂) and to a lesser extent, with the moisture in the specimens. However, these variations could either be attributed to a modification of the CH₃OH paper/oil partitioning by the stabilizers and moisture in fibrous structure. Finally, pre-aged systems (130 °C for 168 h) conditioned at 20 °C for variable lengths of time provided further evidence that O₂ is not necessarily involved in CH₃OH production.     

Non-innocent ligands in bioinorganic chemistry—An overview

This review touches the most common instances where non-innocent (“suspect”) behaviour of redox-active ligands, either substrates or supporting components, is observed in a biochemical context. These ligands include the O₂/O₂^?/O₂^2?, NO⁺/NO/NO^?, o-quinone/o-semiquinone/catecholate and tyrosyl/tyrosinate redox systems, the tetrapyrrole (porphyrinic) ligands, the pterins and flavins, and the dithiolene/ene-dithiolate ligands in molybdo- and tungstopterin. These non-innocent ligands are discussed in their interaction with biological iron, copper, manganese, molybdenum or tungsten centers.     

Photobleaching induced damage of biomolecules: Streptavidin as ‘bio’-photoresist

2-dimensional patterning of surfaces in order to address biological questions is of central interest for the investigation of cell–surface interactions and biosensing.Here we report on an approach which makes use of photobleaching of fluorescently-labelled surface-immobilized streptavidin as ‘bio’-photoresist in order to locally in situ interact with surfaces. Reactive oxygen created during the photobleaching process is likely to be involved in this novel surface manipulation process and its effect on surface-immobilized moieties was investigated by Optical Waveguide Lightmode Spectroscopy (OWLS) and on pre-patterned surfaces using fluorescent microscopy. The creation of bio-patterns as an application of this effect was demonstrated by locally exchanging streptavidin and phospholipid vesicles.This novel surface modification method is interesting from the engineering point of view since no harsh conditions are required and therefore the ‘bio’-photoresist streptavidin allows for the manipulation of surfaces in situ in aqueous solutions e.g., for cell studies.