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The paper presents an analytical study on different theoretical aspects regarding the construction of the tetrahedron. It covers some of the particular construction cases which use descriptive geometry methods. Starting from these cases, one can also construct other particular cases. The matter seems simple enough, yet some of the cases require more complex solutions.

The paper presents an analytical study on different theoretical aspects regarding the construction of the tetrahedron. It covers some of the particular construction cases which use descriptive geometry methods. Starting from these cases, one can also construct other particular cases. The matter seems simple enough, yet some of the cases require more complex solutions.

DNA not only plays a vital role in nature as fundamental hereditary material for storing genetic material, but also serves as well-defined functional material, for example, building blocks for the assembly of nanoscale bio-architectures by Watson-Crick base-pairing interaction. With the development of molecular biology, biotechnology and nanoscience, structural DNA nanotechnology has achieved numerous advances, contributing to the construction of various DNA nanostructures ranging from discrete objects to one dimensional (1D), two dimensional (2D), and three dimensional (3D) architectures. Among them, DNA tetrahedral nanoarchitecture is intensively studied because of simple 3D structure, easy design and unique properties, such as high rigidity, desirable biostability and efficient cellular uptake without auxiliary species. This review summarizes the research progress in the assembly of DNA tetrahedral objects and outlines the applications in biosensing, drug delivery and targeted therapy. Moreover, the dependence of biological activity of biomolecules on DNA tetrahedron-mediated spatially-controlled arrangement and great potential applications are discussed. In addition, the challenges in the design and clinic applications of DNA tetrahedron-based platforms are described, the perspectives towards biomedical applications are foreseen, and our understandings on further studies of DNA tetrahedron are provided, aiming to motivate the development of DNA nanotechnology and interdisciplinary research. Features of DNA tetrahedron and potential applications in biomarker detection, drug delivery and targeted therapy are discussed. The challenges and corresponding solutions are indicated, promoting the development of DNA nanotechnology. [Display omitted] •Challenges and prospects of DNA tetrahedral as bioassay probes and drug vehicles, promoted the DNA nanotechnology and clinical translation.

Conway established the following geometric fact: If the sides and of a triangle  are prolonged beyond the point by the length of the opposite side and the same is done with the vertices and , then the so-constructed 6 points lie on the sole circle whose center coincides with the center of the inscribed circle. V.A. Alexandrov found a spatial analog of the Conway circle. Namely, if in a tetrahedron we mark three points on the prolongations of the edges , , and  beyond the vertex  at distance from  to the half-perimeter of the opposite face and then do the same with the remaining vertices , , and  then the so-constructed 12 points lie on the same sphere if and only if is a frame tetrahedron. We address the multidimensional version of the fact for a simplex in the Euclidean space  .

Structural DNA nanotechnology enables DNA to be used as nanomaterials for novel nanostructure construction with unprecedented functionalities. Artificial DNA nanostructures can be designed and generated with precisely controlled features, resulting in its utility in bionanotechnological and biomedical applications. A tetrahedral DNA nanostructure (TDN), the most popular DNA nanostructure, with high stability and simple synthesis procedure, is a promising candidate as nanocarriers in drug delivery and bioimaging platforms, particularly in precision medicine as well as diagnosis for cancer therapy. Recent evidence collectively indicated that TDN successfully enhanced cancer therapeutic efficiency both in vitro and in vivo. Here, we summarize the development of TDN and highlight various aspects of TDN applications in cancer therapy based on previous reports, including anticancer drug loading, photodynamic therapy, therapeutic oligonucleotides, bioimaging platforms, and other molecules and discuss a perspective in opportunities and challenges for future TDN‐based nanomedicine. This review summarizes the development of tetrahedral DNA nanostructure (TDN) and highlights various aspects of TDN applications in cancer therapy based on previous reports, including anticancer drug loading, photodynamic therapy, therapeutic oligonucleotides, and bioimaging platforms, and discuss a perspective in opportunities and challenges for future TDN‐based nanomedicine.

Yanghao Zhou,1 Qiang Yang,1 Feng Wang,1 Zunjie Zhou,1 Jing Xu,1 Si Cheng,2 Yuan Cheng1 1Department of Neurosurgery, The Second Affiliated Hospital of Chongqing Medical University, Chongqing, 400010, People's Republic of China; 2Department of Orthopedics, The Second Affiliated Hospital of Chongqing Medical University, Chongqing, 400010, People's Republic of ChinaCorrespondence: Yuan ChengDepartment of Neurosurgery, The Second Affiliated Hospital of Chongqing Medical University, Chongqing, 400016, People's Republic of ChinaEmail chengyuan@hospital.cqmu.edu.cnSi ChengDepartment of Orthopedics, The Second Affiliated Hospital of Chongqing Medical University, Chongqing, 400010, People's Republic of ChinaEmail 304238@cqmu.edu.cnIntroduction: RNA interference is a promising therapy in glioma treatment. However, the application of RNA interference has been limited in glioma therapy by RNA instability and the lack of tumor targeting. Here, we report a novel DNA tetrahedron, which can effectively deliver small interfering RNA to glioma cells and induce apoptosis.Methods: siRNA, a small interfering RNA that can suppress the expression of survivin in glioma, was loaded into the DNA tetrahedron (TDN). To enhance the ability of active targeting of this nanoparticle, we modified one side of the DNA nanostructure with aptamer as1411 (As-TDN-R), which can selectively recognize the nucleolin in the cytomembrane of tumor cells. The modified nanoparticles were characterized by agarose gel electrophoresis, dynamic light scattering, and transmission electron microscopy. The serum stability was evaluated by agarose gel electrophoresis. Nucleolin was detected by Western blot and immunofluorescence, and targeted cellular uptake was examined by flow cytometry. The TUNEL assay, flow cytometry, and Western Blot were used to detect apoptosis in U87 cells. The gene silencing of survivin was examined by qPCR, Western Blot, and immunofluorescence.Results: As-TDN-R alone showed better stability towards siRNA, indicating that TDN was a good siRNA protector. Compared with TDN alone, there was increased intercellular uptake of As-TDN-R by U87 cells, evidenced by overexpressed nucleolin in glioma cell lines. TUNEL assay, flow cytometry, and Western Blot revealed increased apoptosis in the As-TDN-R group. The downregulation of survivin protein and mRNA expression levels indicated that As-TDN-R effectively silenced the target gene.Conclusion: The novel nanoparticle can serve as a good carrier for targeting siRNA delivery in glioma. Further exploration of the DNA nanostructure can greatly promote the application of DNA-based drug systems in glioma.Keywords: DNA tetrahedron, nanomedicine, tumor targeting, aptamer, apoptosis, RNA interference

Catalysts make alcohols more reactive by taking away hydrogen to create carbonyl compounds and then returning the hydrogen to the final products. Alcohols are relatively common starting materials for chemical reactions, even though they are quite unreactive. For example, reactions that would substitute another functional group (a nucleophile) for OH often fail because the hydroxide group (HO − ) is difficult to displace—it is a poor leaving group. Alcohols are usually activated by turning the hydroxide into a better leaving group, either by protonating the alcohol or by converting it into a sulfonate or halide. However, both of these activation methods have some disadvantages ( 1 ). The acidic environment required for protonating the alcohol also protonates and deactivates the incoming nucleophile, especially amines. Conversion of the alcohol into a sulfonate or halide can lead to toxicity problems; many alkyl halides and alkyl sulfonates are mutagenic.

Nearly all high–energy density cathodes for rechargeable lithium batteries are well-ordered materials in which lithium and other cations occupy distinct sites. Cation-disordered materials are generally disregarded as cathodes because lithium diffusion tends to be limited by their structures. The performance of Li1.211Mo0.467Cr0.3O2 shows that lithium diffusion can be facile in disordered materials. Using ab initio computations, we demonstrate that this unexpected behavior is due to percolation of a certain type of active diffusion channels in disordered Li-excess materials. A unified understanding of high performance in both layered and Li-excess materials may enable the design of disordered-electrode materials with high capacity and high energy density.

To promote the utilization of rare earth resources in metallurgical rare-earth-containing slag, the effect of P 2 O 5 on the morphology and structure of the rare earth crystalline phase in the CaO–SiO 2 –CaF 2 –La 2 O 3 slag was studied. The La 2 O 3 content being greater than 15%, the amount of rare earth crystal phase in the slag increased with the addition of P 2 O 5 . Due to the addition of P 2 O 5 , the crystal structure of the rare earth crystal phase changed to phosphosilicate. The relationship between phosphorus structures and the crystal structure of the rare earth phase was studied by Raman spectroscopy. The presence of interactions between the silicate network and the phosphate network was studied. La 3+ preferentially acted as a depolymerization agent for the silicate network rather than for the phosphate network structure. For the La 2 O 3 content of less than 10%, it is clear that P 2 O 5 promotes the crystal growth of the rare earth phase in the CaO–SiO 2 –CaF 2 –La 2 O 3 slag.