Direct observation of phenylalanine orientations in statherin bound to hydroxyapatite surfaces

Extracellular biomineralization proteins such as salivary statherin control the growth of hydroxyapatite (HAP), the principal component of teeth and bones. Despite the important role that statherin plays in the regulation of hard tissue formation in humans, the surface recognition mechanisms involved are poorly understood. The protein-surface interaction likely involves very specific contacts between the surface atoms and the key protein side chains. This study demonstrates for the first time the power of combining near-edge X-ray absorption fine structure (NEXAFS) spectroscopy with element labeling to quantify the orientation of individual side chains. In this work, the 15 amino acid N-terminal binding domain of statherin has been adsorbed onto HAP surfaces, and the orientations of phenylalanine rings F7 and F14 have been determined using NEXAFS analysis and fluorine labels at individual phenylalanine sites. The NEXAFS-derived phenylalanine tilt angles have been verified with sum frequency generation spectroscopy.     

Monoidal Categories and Multiextensions

We associate to a group-like monoidal grupoid a principal bundle E satisfying most of the axioms defining a biextension. The obstruction to the existence of a genuine biextension structure on E is exhibited. When this obstruction vanishes, the biextension E is alternating and a trivialization of E induces a trivialization of . The analogous theory for monoidal n-categories is also examined, as well as the appropriate generalization of these constructions in a sheaf-theoretic context. In the n-categorial situation, this produces a higher commutator calculus, in which some interesting generalizations of the notion of an alternating biextension occur. For n=2, the corresponding cocycles are constructed explicitly, by a partial symmetrization process, from the cocycle describing the n-category.     

An example concerning unions of two starshaped sets in the plane

LetS be a closed, simply connected subset of the plane,J a line segment (or a one-pointed set),J⊂S. If for every three points ofS there is a point ofJ seeing at least two of these points viaS, thenS is a union of two starshaped sets. IfJ⊈S or ifS is not simply connected, the result fails.     

Increasing unions of starlike sets

Let S be an arbitrary set in R². Every three points of cl S are clearly visible via S from a common point of cl S if and only if each bounded subset of S may be extended to a starlike set in S. When this occurs, set S is expressible as an increasing union of starlike sets.     

A Helly-type theorem for intersections of orthogonally starshaped sets in \mathbb R^d

Let $\mathcal K$ be a finite family of orthogonal polytopes in $\mathbb R^d$ such that, for every nonempty subfamily $\mathcal K^\prime $ of $\mathcal K, \cap \{K : K$ in $\mathcal K^\prime \}$ , if nonempty, is a finite union of boxes whose intersection graph is a tree. Assume that every $d + 1$ (not necessarily distinct) members of $\mathcal K$ meet in a (nonempty) staircase starshaped set. Then $S \equiv \cap \{ K : K$ in $\mathcal K\}$ is nonempty and staircase starshaped.     

Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

A decomposition theorem form-convex sets

LetS be a closedm-convex subset of the plane,m≧2,Q the set of points of local nonconvexity ofS, with convQ ⊆S. If there is some pointp in [(bdryS) ∩ (kerS)] ∼Q, thenS is a union ofm−1 closed convex sets. The result is best possible for everym.     

Principal ideals in the semigroup of binary relations on a finite set: What happens when one element is added to the set

The principal ideals in the semigroup of binary relations on a finite set X form a partially ordered set under inclusion. When the cardinality of the set X is increased by one, some of the covering relations present in the original set will be preserved and some will not. This article describes the difference.     

Steric effects in 31P NMR spectra: ‘Gamma’ shielding in aliphatic phosphorus compounds

An examination of published ³¹P NMR spectral data for aliphatic phosphorus compounds has revealed that chain lengthening and branching effects on the chemical shift can be interpreted in terms similar to those used for ¹³C and ¹⁵N shifts. For six families of phosphorus compounds, a β-carbon substituent was shown to deshield phosphorus, while a γ-carbon caused shielding. The effects are additive, and good agreement was obtained between ³¹P shifts calculated with the appropriate constants and the experimental values. Shielding by γ-carbon is indicative of the operation of a steric influence on ³¹P chemical shifts, not heretofore articulated. The γ-effect is also useful in explaining the unusually large shielding found in six-membered cyclic phosphines.