Near-Ultraviolet Circular Dichroism and Two-Dimensional Spectroscopy of Polypeptides

A fully quantitative theory of the relationship between protein conformation and optical spectroscopy would facilitate deeper insights into biophysical and simulation studies of protein dynamics and folding. In contrast to intense bands in the far-ultraviolet, near-UV bands are much weaker and have been challenging to compute theoretically. We report some advances in the accuracy of calculations in the near-UV, which were realised through the consideration of the vibrational structure of the electronic transitions of aromatic side chains.     

Substrates and Cyclic Peptide Inhibitors of the Oligonucleotide-Activated Sirtuin 7**

The sirtuins are NAD⁺-dependent lysine deacylases, comprising seven isoforms (SIRT1–7) in humans, which are involved in the regulation of a plethora of biological processes, including gene expression and metabolism. The sirtuins share a common hydrolytic mechanism but display preferences for different ϵ-N-acyllysine substrates. SIRT7 deacetylates targets in nuclei and nucleoli but remains one of the lesser studied of the seven isoforms, in part due to a lack of chemical tools to specifically probe SIRT7 activity. Here we expressed SIRT7 and, using small-angle X-ray scattering, reveal SIRT7 to be a monomeric enzyme with a low degree of globular flexibility in solution. We developed a fluorogenic assay for investigation of the substrate preferences of SIRT7 and to evaluate compounds that modulate its activity. We report several mechanism-based SIRT7 inhibitors as well as de novo cyclic peptide inhibitors selected from mRNA-display library screening that exhibit selectivity for SIRT7 over other sirtuin isoforms, stabilize SIRT7 in cells, and cause an increase in the acetylation of H3 K18.     

Nonstoichiometric,Protic Azolium Azolate Ionic Liquids Provide Unique Environments for N‐Donor Coordination Chemistry

Here we demonstrate that neat reactions of amphoteric azoles with more basic azoles give a family of finely tunable, nonstoichiometric liquids which are useful for N‐donor coordination chemistry. Reacting 4,5‐dicyanoimidazole (4,5‐DCNIm) with 1‐methylimidazole (1‐mim) gives new compounds with composition‐dependent speciation. Two crystalline compounds, a 1:1 protic salt, [H(1‐mim)][4,5‐DCNIm], and a 1:2 salt co‐crystal, [H(1‐mim)][4,5‐DCNIm]?4,5‐DCNIm, were isolated and structurally characterized, while differential scanning calorimetry revealed both suppression of crystallization and the presence of neutral and anionic species in the melt. Reactions of Cu(NO₃)₂?2.5 H₂O, CuO, and ZnO with the neat 2:1 1‐mim/4,5‐DCNIm melt resulted in the isolation of entirely N‐donor ligated complexes of the formula M(4,5‐DCNIm)₂(1‐mim)₄ (M=Cu, Zn).     

Dipolar Rotors Orderly Aligned in Mesoporous Fluorinated Organosilica Architectures

New mesoporous covalent frameworks, based on hybrid fluorinated organosilicas, were prepared to realize a periodic architecture of fast molecular rotors containing dynamic dipoles in their structure. The mobile elements, designed on the basis of fluorinated p‐divinylbenzene moieties, were integrated into the robust covalent structure through siloxane bonds, and showed not only the rapid dynamics of the aromatic rings (ca. 10⁸ Hz at 325 K), as detected by solid‐state NMR spectroscopy, but also a dielectric response typical of a fast dipole reorientation under the stimuli of an applied electric field. Furthermore, the mesochannels are open and accessible to diffusing in gas molecules, and rotor mobility could be individually regulated by I₂ vapors. The iodine enters the channels of the periodic structure and reacts with the pivotal double bonds of the divinyl‐fluoro‐phenylene rotors, affecting their motion and the dielectric properties.     

Stress in elastic plates reinforced by fibres lying in concentric circles

We Consider fibre-reinforced elastic plates with the reinforcement continuously distributed in concentric circles ; such a material is locally transversely isotropic, with the circumferential direction as the preferred direction. For an annulus bounded by concentric circles, the exact solution of the traction boundary value problem is obtained. When the extension modulus in the fibre direction is large compared to other extension and shear moduli, the material is strongly anisotropic. For this case a simpler approximate solution is obtained by treating the material as inextensible in the fibre direction. It is shown that the exact solution reduces to the inextensible solution in the appropriate limit. The inextensible theory predicts the occurrence of stress concentration layers in which the direct stress is infinite ; for materials with small but finite extensibility these layers correspond to thin regions of high stress and high stress gradient. A boundary layer theory is developed for these regions. For a typical carbon fibre-resin composite, the combined boundary layer and inextensible solutions give an excellent approximation to the exact solution. The theory is applied to the problem of an isotropic plate, under uniform stress at infinity, containing a circular hole which is strengthened by the addition of an annulus of fibre-reinforced material.     

Sharp Morawetz estimates

We prove sharp Morawetz estimates — global in time with a singular weight in the spatial variables — for the linear wave, Klein-Gordon, and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.     

On a canonical nine-body problem. Integrable Ermakov decomposition via reciprocal transformations

Here, a recently introduced nine-body problem is shown to be decomposable via a novel class of reciprocal transformations into a set of integrable Ermakov systems. This Ermakov decomposition is exploited to construct more general integrable nine-body systems in which the canonical nine-body system is embedded.