Identification of phosphorylation sites of equine β‐casein isoforms

Equine β‐casein is phosphorylated at variable degrees and isoforms carrying 3 to 7 phosphate groups (3P–7P) have been found in milk, but the phosphorylated amino acid residues of each isoform are not yet identified. In the present work, the different phosphorylation variants were first isolated by ion‐exchange chromatography and then hydrolysed by trypsin to generate caseinophosphopeptides (CPPs), each containing all the potential phosphorylation sites. The equine CPPs were prepared by metal oxide affinity chromatography, a method based on the affinity of phosphate groups towards titanium dioxide immobilized onto a micro‐column. This method turned out to be an efficient tool to separate the CPPs Arg¹–Lys³⁴ and Glu⁴–Lys³⁴ from non‐phosphorylated peptides. Purification was achieved by reversed‐phase high‐performance liquid chromatography (RP‐HPLC) and each CPP was hydrolyzed by endoproteinase Glu‐C. Finally, the digests were analyzed by RP‐HPLC/electrospray ionization mass spectrometry (RP‐HPLC/ESI‐MS) and identified by nano‐electrospray ionization tandem mass spectrometry (nESI‐MS/MS) to locate the phosphorylated sites of the β‐casein isoforms 4P–7P with accuracy. Thus, the isoform 4P was found to be phosphorylated on residues Ser⁹, Ser²³, Ser²⁴, and Ser²⁵. Addition of phosphate groups on Ser¹⁸, Thr¹², and Ser¹⁰ led to the formation of the isoforms 5P–7P, respectively. The results indicated that the in vivo phosphorylation of the equine β‐casein follows a sequential way and is not randomly performed. Copyright © 2010 John Wiley & Sons, Ltd.     

Symmetries of the heat equation on the lattice

Discrete versions of the heat equation on two-dimensional uniform lattices are shown to possess the same symmetry algebra as their continuum limits. Solutions with definite symmetry properties are presented.     

Spherical goniometry and spacecraft attitude determination

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Spherical goniometry and spacecraft attitude determination

     

Contingent derivatives of set-valued maps and applications to vector optimization

In this paper we investigate contingent derivatives of set-valued maps and their lower and upper semidifferentiability properties. We provide also some calculus rules for these derivatives in infinite dimensional spaces. The concept of contingent derivatives is then applied to produce several necessary and sufficient conditions for vector optimization problems with set-valued objectives.This paper was written when the author was at the University of Erlangen-Nurnberg under a grant of the Alexander von Humboldt Foundation.On leave from the Institute of Mathematics, Hanoi, Vietnam.     

Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison

We address the output feedback stabilization problem of linearfinite-dimensional SISO systems. Limitations of static time-invariantoutput feedback on stabilizability are well known. We investigateand compare the possibilities of two recently proposed simplemodifications/generalizations of static time-invariant outputfeedback to remove such limitations. The first approach consistsof introducing a time-delay in the control law, which can betreated as an additional control parameter. The second approachconsists of making the gain time-varying. We show that bothapproaches are complementary. Existing theoretical results arebrought together in a unifying framework. Numerical proceduresfor the construction of the controllers are provided. Robustnessw.r.t. both parametric and delay uncertainty are dealt with.As an illustration the stabilizability of all second-order systemsis completely determined.     

Genetic analysis of the GRIK2 modifier effect in Huntington's disease

Background  

In Huntington's disease (HD), age at neurological onset is inversely correlated with the length of the CAG trinucleotide repeat mutation, but can be modified by genetic factors beyond the HD gene. Association of a relatively infrequent 16 TAA allele of a trinucleotide repeat polymorphism in the GRIK2 3'UTR with earlier than expected age at neurological onset has been suggested to reflect linkage disequilibrium with a functional polymorphism in GRIK2 or an adjacent gene.