A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

一种新型双吡啶悬臂Mn(Ⅱ)配合物的合成、晶体结构及DNA结合能力研究

通过3,3′-((乙烷-1,2-二基双(2-甲基吡啶杂氮二基)双(亚甲基))双(2-羟基-5-甲基苯甲醛)与2-羟基-1,3-丙二胺的缩合反应得到一种具有双吡啶悬臂的双核锰配合物。通过X射线单晶衍射确定了该配合物结构,结果显示其分子式为[Mn₂(C₃₇H₄₃N₆O₆)]·(ClO₄)₂。该配合物属于单斜晶系,P2₁/c空间群,晶胞参数为:a=1.096 50(19) nm, b=1.419 5(3) nm, c=3.109 4(5) nm, β=108.153(5)°。进一步分析表明两个二价锰离子分别与(N_amine)₂(N_imine)₂O₃和(N_imine)₂O₄体系配位,它们与配位原子形成的几何构型分别是十面体和扭曲的八面体。两个中心锰离子距离为0.331 6 nm,由酚氧原子和醋酸根共同桥联。另外,本文也利用伏安法和黏度法对该配合物与小牛胸腺DNA的结合能力进行研究,实验结果表明它们之间的结合方式为弱的插入作用。     

Design,synthesis and evaluation of novel dehydroabietic acid-dithiocarbamate hybrids as potential multi-targeted compounds for tumor cytotoxicity

In the present study, novel representatives of the important group of biologically-active, dehydroabietic acid-bearing dithiocarbamate moiety, were synthesized and characterized by ¹H NMR, ¹³C NMR, HR-MS. The in vitro antiproliferative activity evaluation (MTT) indicated that these compounds exhibited potent inhibitory activities in various cancer cell lines (HepG-2, MCF-7, HeLa, T-24, MGC-803). Particularly, compound III-b possessed extraordinary cytotoxicity with low micromolar IC₅₀ values ranging from 4.07 to 38.84 µM against tested cancer cell lines, while displayed weak cytotoxicity on two normal cell lines (LO-2 and HEK 293 T). Subsequently, the potential mechanisms of representative compound III-b were elementarily investigated by Transwell experiment, which showed III-b can inhibit cancer cells migration. Annexin-V/PI dual staining showed that the compound can induce HepG-2 cells apoptosis in a dose-dependent manner. Meanwhile this apoptosis may be related to the upregulated protein expression of cleaved-caspase 3, cleaved-caspase 9, Bax and downregulated of Bcl-2 indicated by Western Blot. Later study further confirmed that ROS levels in HepG-2 cells increased significantly with the rise of concentrations. In addition, through the network pharmacology data analyzing, the core targets and signaling pathways of compound III-b for treatment of liver neoplasms were forecasted. Molecular docking model showed that compound III-b had high affinity with hub targets (CASP3, EGFR, HSP90AA1, MAPK1, ERBB2, MDM2), suggesting that compound III-b might target the hub protein to modulate signaling activity. Taken together, these data indicated that dehydroabietic acid structural modification following the “Molecular hybridization” principle is a feasible way to discover the potential multi-targeted antitumor compounds.     

A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Determination of Anti-Parkinson Drug Pramipexole Using a Label-free Biosensor and Evaluation of its Interaction with ds-DNA

In this study, we fabricated an effective and sensitive DNA biosensor based on flower-like Pt/NiCo₂O₄ modified carbon paste electrode (FL-Pt/NiCo₂O₄/CPE) for detection of pramipexole (PPX). Spectrophotometry, differential pulse voltammetry (DPV) and docking methods were employed to evaluate the interaction of DNA-PPX. Moreover, the DPV technique was chosen to monitor the electrochemical response of guanine on the DNA biosensor. The relationship between the concentration of PPX and the oxidation signal of guanine was linear in the range of 0.4 to 310.0 μM and a limit of detection (LOD) of 0.09 μM was calculated.     

Melatonin Rescues the Dendrite Collapse Induced by the Pro-Oxidant Toxin Okadaic Acid in Organotypic Cultures of Rat Hilar Hippocampus

The pro-oxidant compound okadaic acid (OKA) mimics alterations found in Alzheimer’s disease (AD) as oxidative stress and tau hyperphosphorylation, leading to neurodegeneration and cognitive decline. Although loss of dendrite complexity occurs in AD, the study of this post-synaptic domain in chemical-induced models remains unexplored. Moreover, there is a growing expectation for therapeutic adjuvants to counteract these brain dysfunctions. Melatonin, a free-radical scavenger, inhibits tau hyperphosphorylation, modulates phosphatases, and strengthens dendritic arbors. Thus, we determined if OKA alters the dendritic arbors of hilar hippocampal neurons and whether melatonin prevents, counteracts, or reverses these damages. Rat organotypic cultures were incubated with vehicle, OKA, melatonin, and combined treatments with melatonin either before, simultaneously, or after OKA. DNA breaks were assessed by TUNEL assay and nuclei were counterstained with DAPI. Additionally, MAP2 was immunostained to assess the dendritic arbor properties by the Sholl method. In hippocampal hilus, OKA increased DNA fragmentation and reduced the number of MAP2(+) cells, whereas melatonin protected against oxidation and apoptosis. Additionally, OKA decreased the dendritic arbor complexity and melatonin not only counteracted, but also prevented and reversed the dendritic arbor retraction, highlighting its role in post-synaptic domain integrity preservation against neurodegenerative events in hippocampal neurons.     

Insights into the Structure and Energy of DNA Nanoassemblies

Since the pioneering work of Ned Seeman in the early 1980s, the use of the DNA molecule as a construction material experienced a rapid growth and led to the establishment of a new field of science, nowadays called structural DNA nanotechnology. Here, the self-recognition properties of DNA are employed to build micrometer-large molecular objects with nanometer-sized features, thus bridging the nano- to the microscopic world in a programmable fashion. Distinct design strategies and experimental procedures have been developed over the years, enabling the realization of extremely sophisticated structures with a level of control that approaches that of natural macromolecular assemblies. Nevertheless, our understanding of the building process, i.e., what defines the route that goes from the initial mixture of DNA strands to the final intertwined superstructure, is, in some cases, still limited. In this review, we describe the main structural and energetic features of DNA nanoconstructs, from the simple Holliday junction to more complicated DNA architectures, and present the theoretical frameworks that have been formulated until now to explain their self-assembly. Deeper insights into the underlying principles of DNA self-assembly may certainly help us to overcome current experimental challenges and foster the development of original strategies inspired to dissipative and evolutive assembly processes occurring in nature.