Symmetry operation measures

We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.     

Convenient Synthesis of the Food Mutagen 2-Amino-3-Methylimidazo[4,5-f]Quinoline (IQ), and IQ-D3

The title compounds (5 and 10) were each prepared in four steps from commercially available 5-amino-6-nitroquinoline (1) in 41% overall yield. The key step was the displacement of the methylsulfonyl group of 4 by sodamide.     

Barotropic elliptical dipoles in a rotating fluid

Barotropic f-plane dipolar vortices were generated in a rotating fluid and a comparison was made with the so-called supersmooth f-plane solution which—in contrast to the classical Lamb–Chaplygin solution—is marked by an elliptical separatrix and a doubly continuously differentiable vorticity field. Dye-visualization and high-resolution particle-tracking techniques revealed that the observed dipole characteristics (separatrix aspect ratio, cross-sectional vorticity distribution and vorticity versus streamfunction relationship) are in close agreement with those of the supersmooth f-plane solution for the entire lifespan of the dipolar vortex.     

Dynamics of charge solitons in 1-D arrays of Josephson junctions

A 1-D array of Josephson coupled superconducting grains whose kinetic inductance dominates over the Josephson inductance is studied. We show that in this limit excess Cooper pairs in the array give rise to charge solitons via polarization of the grains. We analyze the dynamics of these macroscopic topological excitations, and find that their classical relativistic motion leads to saturation branches in the I-V characteristic of the array. When the dephasing length of the charge soliton is larger than the length of the array, we expect that it behaves quantum mechanically. We study the dynamics of quantum charge solitons in a ring-shaped array biased by an external flux, and show that they can exhibit phenomena like persistent current and coherent current oscillations.     

Sharp ULP rounding error bound for the hypotenuse function

The hypotenuse function, , is sometimes included in math library packages. Assuming that it is being computed by a straightforward algorithm, in a binary floating point environment, with round to nearest rounding mode, a sharp roundoff error bound is derived, for arbitrary precision. For IEEE single precision, or higher, the bound implies that and . Numerical experiments indicate that this bound is sharp and cannot be improved.

     

Antibody for Serine 65 Phosphorylated Ubiquitin Identifies PLK1-Mediated Phosphorylation of Mitotic Proteins and APC1

Deciphering the protein posttranslational modification (PTM) code is one of the greatest biochemical challenges of our time. Phosphorylation and ubiquitylation are key PTMs that dictate protein function, recognition, sub-cellular localization, stability, turnover and fate. Hence, failures in their regulation leads to various disease. Chemical protein synthesis allows preparation of ubiquitinated and phosphorylated proteins to study their biochemical properties in great detail. However, monitoring these modifications in intact cells or in cell extracts mostly depends on antibodies, which often have off-target binding. Here, we report that the most widely used antibody for ubiquitin (Ub) phosphorylated at serine 65 (pUb) has significant off-targets that appear during mitosis. These off-targets are connected to polo-like kinase 1 (PLK1) mediated phosphorylation of cell cycle-related proteins and the anaphase promoting complex subunit 1 (APC1).