The behavior of differential forms under purely inseparable extensions

Let F be a field of characteristic 2. In this paper we give a complete computation of the kernel of the homomorphism $H_2^{m+1}(F)?H_2^{m+1}(L)$ induced by scalar extension, where $L/F$ is a purely inseparable extension (of any degree), $H_2^{m+1}(F)$ is the cokernel of the Artin–Schreier operator $?:{\mathrm{\Omega }}_F^m?{\mathrm{\Omega }}_F^m/\mathrm{d}{\mathrm{\Omega }}_F^{m?1}$ given by: $x\frac{\mathrm{d}{x}_1}{x_1}\wedge ?\wedge \frac{\mathrm{d}{x}_m}{x_m}?(x^2?x)\frac{\mathrm{d}{x}_1}{x_1}\wedge ?\wedge \frac{\mathrm{d}{x}_m}{x_m}+\mathrm{d}{\mathrm{\Omega }}_F^{m?1}$, where ${\mathrm{\Omega }}_F^m$ is the space of absolute m-differential forms over F and d is the differential operator. Other related results are included.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Study of Endogen Substrates,Drug Substrates and Inhibitors Binding Conformations on MRP4 and Its Variants by Molecular Docking and Molecular Dynamics

Multidrug resistance protein-4 (MRP4) belongs to the ABC transporter superfamily and promotes the transport of xenobiotics including drugs. A non-synonymous single nucleotide polymorphisms (nsSNPs) in the ABCC4 gene can promote changes in the structure and function of MRP4. In this work, the interaction of certain endogen substrates, drug substrates, and inhibitors with wild type-MRP4 (WT-MRP4) and its variants G187W and Y556C were studied to determine differences in the intermolecular interactions and affinity related to SNPs using protein threading modeling, molecular docking, all-atom, coarse grained, and umbrella sampling molecular dynamics simulations (AA-MDS and CG-MDS, respectively). The results showed that the three MRP4 structures had significantly different conformations at given sites, leading to differences in the docking scores (DS) and binding sites of three different groups of molecules. Folic acid (FA) had the highest variation in DS on G187W concerning WT-MRP4. WT-MRP4, G187W, Y556C, and FA had different conformations through 25 ns AA-MD. Umbrella sampling simulations indicated that the Y556C-FA complex was the most stable one with or without ATP. In Y556C, the cyclic adenosine monophosphate (cAMP) and ceefourin-1 binding sites are located out of the entrance of the inner cavity, which suggests that both cAMP and ceefourin-1 may not be transported. The binding site for cAMP and ceefourin-1 is quite similar and the affinity (binding energy) of ceefourin-1 to WT-MRP4, G187W, and Y556C is greater than the affinity of cAMP, which may suggest that ceefourin-1 works as a competitive inhibitor. In conclusion, the nsSNPs G187W and Y556C lead to changes in protein conformation, which modifies the ligand binding site, DS, and binding energy.     

Anticancer SAR establishment and novel accruing signal transduction model of drug action using biscoumarin scaffold

In this paper, we have established methylenebis (4-hydroxy-2H-chromen-2-one) as a promising anticancer scaffold with kinesin spindle protein (KSP) inhibitory activity under malignant condition. A series of biscoumarin derivatives (MN1 to MN30) with different substituent were synthesized, and their anticancer activity was explored. Six biscoumarin derivatives that were found active were further selected to formulate organic nanoparticles (ONPs). Anticancer activity of both the forms (viz conventional and ONPs) was compared. MN30 was found most potent whereby MN10 showed good anticancer activity in both, i.e., conventional and ONP form; the structural activity relationship (SAR) study has been established. Computational investigation revealed biscoumarin scaffold as a suitable pharmacophore to bind against KSP protein. Molecular dynamics simulation studies revealed protein-ligand stability and dynamic behavior of biscoumarin-KSP complex. Finally, accruing signal transduction model was formulated to explain the observed MTT trend of conventional and ONP form. The model seems useful towards solving population specific varied results of chemotherapeutic agents. According to the model, MN10 and MN30 derivatives have good pharmacodynamics inertia and therefore, both the molecules were able to provide dose-dependent cytotoxic results.     

New organoruthenium metallates containing ferrocenecarboxalidine thiosemicarbazones and their nucleic acid/albumin binding and in vitro cytotoxicity

A string of four new hetero binuclear Ru(III) complexes of ferrocenecarboxaldehyde-4(N)-substituted thiosemicarbazones were synthesized and characterized by various spectral (infrared, ultraviolet–visible, Electron Paramagnetic Resonance (EPR) and High Resolution Mass Spectrometry (HR-MS) techniques. The binding abilities of the ligands/complexes with nucleic acid (calf thymus DNA, CT-DNA) and bovine serum albumin (BSA) were analyzed by absorption and emission titration methods. The complexes exhibited better DNA binding affinity than their parent ligands. The interaction with CT-DNA was found to be intercalative and with BSA static quenching mechanism was observed. All the synthesized Ru(III) complexes were subjected to study their in vitro cytotoxicity against MCF-7 (human breast cancer) and HT-29 (human colon cancer) cell lines. Among the four complexes, complex 3 [RuCp (FF-etsc)PPh₃]Cl exhibited the highest cytotoxicity in MCF-7 cells and complex 4 [RuCp (FF-ptsc)PPh₃]Cl was the most active on HT-29 cells.     

Thermodynamic study of transthyretin association (wild‐type and senile forms) with heparan sulfate proteoglycan: pH effect and implication of the reactive histidine residue

The tetramer destabilization of transthyretin into monomers and its fibrillation are phenomena leading to amyloid deposition. Heparan sulfate proteoglycan (HSPG) has been found in all amyloid deposits. A chromatographic approach was developed to compare binding parameters between wild‐type transthyretin (wtTTR) and an amyloidogenic transthyretin (sTTR). Results showed a greater affinity of sTTR for HSPG at pH 7.4 compared with wtTTR owing to the monomeric form of sTTR. Analysis of the thermodynamic parameters showed that van der Waals interactions were involved at the complex interface for both transthyretin forms. For sTTR, results from the plot representing the number of protons exchanged vs pH showed that the binding mechanism was pH‐dependent with a critical value at a pH 6.5. This observation was due to the protonation of a histidine residue as an imidazolium cation, which was not accessible when TTR was in its tetrameric structure. At pH >6.5, dehydration at the binding interface and several contacts between nonpolar groups of sTTR and HSPG were also coupled to binding for an optimal hydrogen‐bond network. At pH <6.5, the protonation of the His residue from sTTR monomer when pH decreased broke the hydrogen‐bond network, leading to its destabilization and thus producing slight conformational changes in the sTTR monomer structure. Copyright © 2014 John Wiley & Sons, Ltd.     

Large offset far infrared laser lines generation from the C-O stretching Q-branch of 13CD3OD

2 laser of wide tunability to pump ¹³CD₃OD we could observe 10 new far infrared laser lines ranging from 109 μm to 472 μm. The lines were generated by pumping infrared absorbing transitions of large offset appertaining to the C-O stretching Q-branch. All lines were characterised in wavelength, polarisation, optimum pressure of operation and precise offset measurements. Received: 17 September 1996/Revised version: 18 November 1996     

Double Michael Additions of Lithium Enolate of 1,4-Dioxaspiro[4.5]dec-6-en-8-One to Acrylates

Double Michael additions of lithium enolaie of 1,4-dioxaspiro[4.5]dec-6-en-8-one to four acrylates afforded bicyclo[2.2.2]octan-2-ones with high regio- and stereoselectivities in moderate yields.     

Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity

The interferometric intensity patterns from a 2D shearing interferometer are shown and discussed. The intensity patterns can be obtained in two different approaches incorporating differential and extended wavefront controlled displacements. The reliable directional sensitivity of this interferometer allows the optimization of the measurement parameters to estimate the wavefront of the intensity patterns by regularization techniques.