Inextensible domains

We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that origin-symmetric inextensible domains are exactly the origin-symmetric convex domains with a circle of outer billiard triangles. We address a conjecture by Genin and Tabachnikov about convex domains, not necessarily symmetric, with a circle of outer billiard triangles, and show that it follows immediately from a result of Sas.     

Tracking Conformational Changes in Calmodulin in vitro,in Cell Extract,and in Cells by Electron Paramagnetic Resonance Distance Measurements

It is an open question whether the conformations of proteins sampled in dilute solutions are the same as in the cellular environment. Here we address this question by double electron-electron resonance (DEER) distance measurements with Gd(III) spin labels to probe the conformations of calmodulin (CaM) in vitro, in cell extract, and in human HeLa cells. Using the CaM mutants N53C/T110C and T34C/T117C labeled with maleimide-DOTA-Gd(III) in the N- and C-terminal domains, we observed broad and varied interdomain distance distributions. The in vitro distance distributions of apo-CaM and holo-CaM in the presence and absence of the IQ target peptide can be described by combinations of closed, open, and collapsed conformations. In cell extract, apo- and holo-CaM bind to target proteins in a similar way as apo- and holo-CaM bind to IQ peptide in vitro. In HeLa cells, however, in the presence or absence of elevated in-cell Ca²⁺ levels CaM unexpectedly produced more open conformations and very broad distance distributions indicative of many different interactions with in-cell components. These results show-case the importance of in-cell analyses of protein structures.     

New developments in the spatial encoding of spin interactions for single‐scan 2D NMR

Single‐scan 2D NMR relies on a spatial axis for encoding the indirect‐domain internal spin interactions. Various strategies have been demonstrated for fulfilling the needs underlying this procedure. All such schemes use gradient‐echoed sequences that leave at their conclusion solely the effects of the internal interactions along the indirect domain; they also include a real‐time scheme that though simple, yields in general mixed‐phase line shapes. The present paper introduces two new proposals geared up for easing the spatial encoding underlying single‐scan 2D NMR methodologies. One of these is capable of delivering dispersive‐free peaks along the indirect domain, and thereby purely‐absorptive 2D line shapes, in amplitude‐encoded experiments. The other demonstrates for the first time, the possibility to obtain single‐scan 2D spectra without echoing the effects of the encoding gradient–simply by applying a single‐pulse frequency sweep to encode the interactions. Both of these modes are compatible with homo‐ and heteronuclear correlations, and exhibit a number of complementary features vis‐à‐vis encoding alternatives that have so far been presented. The overall principles underlying these new spatially encoding protocols are derived, and their performance demonstrated with single‐scan 2D NMR TOCSY and HSQC experiments on model compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

The Strong Influence of Structure Polymorphism on the Conductivity of Peptide Fibrils

Peptide fibril nanostructures have been advocated as components of future biotechnology and nanotechnology devices. However, the ability to exploit the fibril functionality for applications, such as catalysis or electron transfer, depends on the formation of well‐defined architectures. Fibrils made of peptides substituted with aromatic groups are described presenting efficient electron delocalization. Peptide self‐assembly under various conditions produced polymorphic fibril products presenting distinctly different conductivities. This process is driven by a collective set of hydrogen bonding, electrostatic, and π‐stacking interactions, and as a result it can be directed towards formation of a distinct polymorph by using the medium to enhance specific interactions rather than the others. This method facilitates the detailed characterization of different polymorphs, and allows specific conditions to be established that lead to the polymorph with the highest conductivity.     

Hybrid Volatolomics and Disease Detection

This Review presents a concise, but not exhaustive, didactic overview of some of the main concepts and approaches related to “volatolomics”—an emerging frontier for fast, risk‐free, and potentially inexpensive diagnostics. It attempts to review the source and characteristics of volatolomics through the so‐called volatile organic compounds (VOCs) emanating from cells and their microenvironment. It also reviews the existence of VOCs in several bodily fluids, including the cellular environment, blood, breath, skin, feces, urine, and saliva. Finally, the usefulness of volatolomics for diagnosis from a single bodily fluid, as well as ways to improve these diagnostic aspects by “hybrid” approaches that combine VOC profiles collected from two or more bodily fluids, will be discussed. The perspectives of this approach in developing the field of diagnostics to a new level are highlighted.     

Spatially encoded NMR and the acquisition of 2D magnetic resonance images within a single scan

An approach that enables the acquisition of multidimensional NMR spectra within a single scan has been recently proposed and demonstrated. The present paper explores the applicability of such ultrafast acquisition schemes toward the collection of two-dimensional magnetic resonance imaging (2D MRI) data. It is shown that ideas enabling the application of these spatially encoded schemes within a spectroscopic setting, can be extended in a straightforward manner to pure imaging. Furthermore, the reliance of the original scheme on a spatial encoding and subsequent decoding of the evolution frequencies endows imaging applications with a greater simplicity and flexibility than their spectroscopic counterparts. The new methodology also offers the possibility of implementing the single-scan acquisition of 2D MRI images using sinusoidal gradients, without having to resort to subsequent interpolation procedures or non-linear sampling of the data. Theoretical derivations on the operational principles and imaging characteristics of a number of sequences based on these ideas are derived, and experimentally validated with a series of 2D MRI results collected on a variety of model phantom samples.     

Homogeneous Orthogonally Additive Polynomials on Banach Lattices

The main result in this paper is a representation theorem forhomogeneous orthogonally additive polynomials on Banach lattices.The representation theorem is used to study the linear spanof the set of zeros of homogeneous real-valued orthogonallyadditive polynomials. It is shown that in certain lattices everyelement can be represented as the sum of two or three zerosor, at least, can be approximated by such sums. It is also indicatedhow these results can be used to study weak topologies inducedby orthogonally additive polynomials on Banach lattices. 2000Mathematics Subject Classification 46G25, 46B42, 47B38.     

Anion-binding properties of the tripyrrolemethane group: a combined experimental and theoretical study

Tripyrrolemethane- and bistripyrrolemethane-containing systems were recently reported to be efficient and selective hosts for anions. Nevertheless, the basic intrinsic properties of tripyrrolemethane as a ligand for anions have not yet been explored. Here we report the study of the anion-binding properties of the tripyrrolemethane group. We applied a combined experimental and theoretical approach to determine the affinity of the tripyrrolemethane system for different anions in the gas phase, in solution and in the crystalline state. In the crystal, the tripyrrolemethane group forms a number of different complexes with the bromide ion, some involving the participation of more than one ligand species. Despite the very similar basicity of fluoride and dihydrogen phosphate, the tripyrrolemethane ligand exhibits a clear preference for the fluoride anion in solution, which indicates an anion-binding system and not merely deprotonation. Although the affinity of the tripyrrolemethane ligand for other ions was negligible in solution, gas-phase studies show that complexation with larger halide ions is favoured over complexation with fluoride.