The Liouville property and a conjecture of De Giorgi

We consider bounded entire solutions of the nonlinear PDE Δu + u − u³ = 0 in ℝ^d and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes. The proof uses a Liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form operator. © 2000 John Wiley & Sons, Inc.     

Separation and identification of positively charged and neutral nucleoside adducts by capillary electrochromatography-microelectrospray mass spectrometry

Capillary electrochromatography (CEC) is shown to be capable of separating mixtures containing both positively charged and neutral styrene oxide–adenosine adducts. In a study of the mechanism of deamination of positively charged 1-(2-hydroxy-1-phenylethyl) adenosine using ¹⁸O-labeled water, possible contamination of the chromatographically purified deamination product, 1-(2-hydroxy-1-phenylethyl) inosine, with the positively charged 1-(2-hydroxy-1-phenylethyl) adenosine was observed. Because the deamination product and the presumed contamination have the same molecular weights and similar structures, CEC-microelectrospray mass spectrometry (CEC-μESI/MS) was used to confirm the presence and identity of the suspected impurity. A trace amount of the positively charged 1-(2-hydroxy-1-phenylethyl) adenosine, which could not be observed by either HPLC-UV or CEC-UV, was detected by CEC-μESI/MS. This discriminatory ability of CEC-μESI/MS is attributed to the fact that positive ion mode ESI-MS is a more sensitive detector for a positively charged compound than a UV detector, and that the combination of electroosmotic and electrophoretic flows and hydrophobic interactions with the stationary phase contributes to the separation of the positively charged compound. As a result, the positively charged compound was observed to elute much earlier and with much sharper peaks than the neutral compounds for which electroosmotic flow is the only “pumping” force for the solvent.     

Decoding the components of dynamics in three‐domain proteins

In this study, we examine the feasibility and limitations of describing the motional behavior of three‐domain proteins in which the domains are linearly connected. In addition to attempting the determination of the internal and overall reorientational correlation times, we investigate the existence of correlations in the motions between the three domains. Since in linearly arranged three‐domain proteins, there are typically no experimental data that can directly report on motional correlation between the first and the third domain, we address this question by dynamics simulations. Two limiting cases occur: (1) for weak repulsive potentials and (2) when strong repulsive potentials are applied between sequential domains. The motions of the terminal domains become correlated in the case of strong interdomain repulsive potentials when these potentials do not allow the angle between the sequential domains to be smaller than about 60°. Using the model‐free (MF) and extended MF formalisms of Lipari and Szabo, we find that the motional behavior can be separated into two components; the first component represents the concerted overall motion of the three domains, and the second describes the independent component of the motion of each individual domain. We find that this division of the motional behavior of the protein is maintained only when their timescales are distinct and can be made when the angles between sequential domains remain between 60° and 160°. In this work, we identify and quantify interdomain motional correlations. © 2013 Wiley Periodicals, Inc.     

A cube in a tetrahedron: microwave-assisted synthesis of an octametallic Fe(III) cluster

The microwave-assisted reaction of Fe(O2CMe)2 with salicylaldoxime (saoH2) in pyridine produces an octametallic cluster in crystalline form in 2 min. The core describes a cube encapsulated in a tetrahedron, while sao2- exhibits a novel coordination mode.     

Investigating the solid state hosting abilities of homo- and hetero-valent [Co7] metallocalix[6]arenes

A family of homo-valent [Co(II)(7)(OH)(6)(L(1))(6)](NO(3))(2) (1), [(MeOH)(2) is a subset of Co(II)(7)(OH)(6)(L(1))(6)](NO(3))(2) (2) (where L(1)H = 2-iminomethyl-6-methoxyphenol) and hetero-valent [(NO(3))(2) is a subset of Co(III)Co(II)(6)(OH)(6)(L(2))(6)](NO(3))·3MeCN (4) (where L(2)H = 2-iminophenyl-6-methoxyphenol) complexes possess metallic skeletons describing planar hexagonal discs. Their organic exteriors form double-bowl shaped topologies, and coupled with their 3-D connectivity, this results in the formation of molecular cavities in the solid state. These confined spaces are shown to behave as host units in the solid state for guests including solvent molecules and charge balancing counter anions. Magnetic susceptibility measurements on 2 and 4 reveal weak ferro- and ferrimagnetism, respectively. The utilisation of other Co(II) salt precursors gives rise to entirely different species including the mononuclear and trinuclear complexes [Co(II)(L(2))(2)] (5) and [Co(III)(2)Na(I)(1)(L(3))(6)](BF(4)) (6) (where L(3)H = 2-iminomethyl-4-bromo-6-methoxyphenol).     

Calixarene-supported rare-earth clusters: heteroatom bridge influences cluster composition

Rare-earth octahedra have been previously synthesised using p-tert-butylcalix[4]arene as a cluster support. Introduction of a heteroatom bridge in the calixarene framework, with concomitant alteration to the nature of the metal binding pocket, influences lanthanide composition in the cluster.