An application of Fourier series expansion of a function in a non-polar spherical coordinate system

Cubed sphere is one of the main tools used to avoid pole problems those arise in the selection of spherical polar coordinates. In this respect, earlier we considered a recently developed cubed sphere based on coordinate mapping over the cubed surface. The function on the sphere was treated as an ordered set of six-tuples. In that work, we established weakly orthogonal and completely orthogonal spherical harmonics of the system and developed corresponding symmetric and linear relations. Also, we found the norm of the orthogonal spherical harmonics. In this work, we explore the Fourier representation of a spherical function on this coordinate system in terms of weakly orthogonal spherical harmonics. The advantages of the linear relation between the two sets of spherical harmonics and diagonal property of the norm of the fully orthogonal spherical harmonics were in cooperated for this work. We also strength our work by giving an example to demonstrate how Fourier coefficients can be computed to represent a given spherical function in terms of the spherical harmonics of the coordinate system

Relational properties of weakly orthogonal and orthogonal spherical harmonics in cubed sphere

Numerical computations on the sphere in solving problems defined on the sphere suffer from many difficulties near the poles when using spherical polar coordinate system for the spherical surface. For example, in the computations of global weather prediction models, concentrated grid points near the poles increase the amount of computations in the pole region where quantities of interest are of less important than in other parts of the globe. Such problems are collectively called as the 'pole problems'. Avoiding pole problems have attracted some researches in the recent past. One of the recent development in this direction is to define grid meshes on the sphere which do not contain polar concentrated points. Among these the 'cubed sphere' defined from the surface of a unit cube has been used by some authors for approximating weather prediction models by finite difference and finite element methods. In a recent paper, one of the present authors has constructed weakly orthogonal spherical harmonics in a non-polar spherical co-ordinate system based on the cube sphere concept. This can be used for approximating functions on the sphere by spectral methods without the pole problems. In this work, we establish some Lin ear and recurrence relations between these two sets of spherical harmonics. We also exploit linear relations between harmonic components defined in the six faces of the cubed sphere

Native interface of the SAM domain polymer of TEL

BACKGROUND: TEL is a transcriptional repressor containing a SAM domain that forms a helical polymer. In a number of hematologic malignancies, chromosomal translocations lead to aberrant fusions of TEL-SAM to a variety of other proteins, including many tyrosine kinases. TEL-SAM polymerization results in constitutive activation of the tyrosine kinase domains to which it becomes fused, leading to cell transformation. Thus, inhibitors of TEL-SAM self-association could abrogate transformation in these cells. In previous work, we determined the structure of a mutant TEL-SAM polymer bearing a Val to Glu substitution in center of the subunit interface. It remained unclear how much the mutation affected the architecture of the polymer, however. RESULTS: Here we determine the structure of the native polymer interface. To accomplish this goal, we introduced mutations that block polymer extension, producing a heterodimer with a wild-type interface. We find that the structure of the wild-type polymer interface is quite similar to the mutant structure determined previously. With the structure of the native interface, it is possible to evaluate the potential for developing therapeutic inhibitors of the interaction. We find that the interacting surfaces of the protein are relatively flat, containing no obvious pockets for the design of small molecule inhibitors. CONCLUSION: Our results confirm the architecture of the TEL-SAM polymer proposed previously based on a mutant structure. The fact that the interface contains no obvious potential binding pockets suggests that it may be difficult to find small molecule inhibitors to treat malignancies in this way

Identification and Discrimination of Mycobacterium tuberculosis Complex with Traditional and Real-Time PCR in Different Specimens in Iraq

Background: Tuberculosis (TB) is a major public health issue and a main cause of global morbidity and mortality. TB is the world's ninth leading cause of death despite the numerous treatment strategies for managing the disease. Objective: To assess the traditional method (direct smear examination and culture) against real-time PCR as pulmonary and extrapulmonary tuberculosis laboratory diagnostic techniques. Cases and methods: Samples were collected from (612) TB cases, (409) of whom were pulmonary tuberculosis (PTB) and (203) were extrapolmonary tuberculosis (EPTB). The cases were seeking care at the Specialized Chest and Respiratory Disease Center/ National Reference Laboratory for Tuberculosis (NRL) in Baghdad, during the period 1st of May -1st of October 2019. Direct smear examination, Lowenstein-Jensen culture and Real Time PCR were used to diagnose TB. Results: Out of 612 samples received, 82(13.4%) were positive by smear microscopy, while 90(14.7%) were able to grow on Lowenstein-Jensen (LJ) media. Ninety DNA extracts from the samples which were positive on LJ media and 25 control specimens, were diagnosed with molecular analysis by using real time PCR to determine the species of Mycobacterium tuberculosis complex. The results revealed that the 71 samples (78.9%) were M. tuberculosis, three specimens (3.3%) were combined M. bovis and M. tuberculosis, and one M. tuberculosis, M. bovis, and M. bovis BCG, while15 (16.7%) were negative and subsequently excluded from study. Conclusion: The comparison between molecular diagnostic methods by using Real time PCR with conventional diagnostic methods, provides a new promising technique and is potentially a practical and rapid alternative to the slower traditional pulmonary and EPTB diagnostic culture. The results show M. bovis overall contribution on human TB in comparison to M. tuberculosis is minor among PTB and EPTB cases in the sample studied

Investigation of the N-terminus amino functional of Arg10-Teixobactin

Teixobactin is a recently described antimicrobial peptide that shows high activity against gram-positive bacteria as well as mycobacterium tuberculosis. Due to both its structure as a head-to-side chain cyclodepsipeptide and its activity, it has attracted the attention of several research groups. In this regard, a large number of analogs with substitutions in both the cycle and the tail has been described. Here, we report the contribution of the N-terminus residue, N-Me-d-Phe, to the activity of Arg10-teixobactin. On the basis of our findings, we conclude that the N-terminus accepts minimum changes but not the presence of long alkyl chains. The presence of a positive charge is a requirement for the activity of the peptide. Furthermore, acylation of the N-terminus leads to total loss of activity

Synthesis, X-ray structure, Hirshfeld surface analysis and antimicrobial assessment of tetranuclear s-triazine hydrazine Schiff base ligand

Funding: The Deputyship for Research and Innovation, “Ministry of Education”, King Saud University (IFKSUOR3-188-3), Saudi Arabia.The unexpected tetranuclear [Cu4(DPPT)2Cl6] complex was obtained by self-assembly of CuCl2.2H2O and (E)-2,4-di(piperidin-1-yl)-6-(2-(1-(pyridin-2-yl)ethylidene)hydrazinyl)-1,3,5-triazine, ( HDPPT ) in ethanol. In this tetranuclear [Cu4(DPPT)2Cl6] complex, the organic ligand acts as mononegative chelate bridging two crystallographically independent Cu(II) sites. The DPPT− anion acts as a bidentate ligand with respect to Cu(1), while it is a tridentate for Cu(2). The Cu(1)N2Cl3 and Cu(2)N3Cl spheres have square pyramidal and square planar coordination geometries with some distortion, respectively. Two of the chloride ions coordinating the Cu(1) are bridging between two crystallographically related Cu(1) sites connecting two [Cu2(DPPT)Cl3] units together, leading to the tetranuclear formula [Cu4(DPPT)2Cl6]. The packing of the [Cu4(DPPT)2Cl6] complex is dominated by C-H…Cl contacts, leading to one-dimensional hydrogen-bond polymeric structure. According to Hirshfeld surface analysis of molecular packing, the non-covalent interactions H…H, Cl…H, Cl…C, C…H, and N…H are the most significant. Their percentages are 52.8, 19.0, 3.2, 7.7, and 9.7%, respectively. Antimicrobial assessment showed good antifungal activity of the Cu(II) complex against A. fumigatus and C. albicans compared to Ketoconazole as positive control. Moreover, the [Cu4(DPPT)2Cl6] complex has higher activity against Gram-positive bacteria than Gentamycin as positive control. The opposite was observed when testing the tetranuclear [Cu4(DPPT)2Cl6] complex against the Gram-negative bacteria.Publisher PDFPeer reviewe

Elucidating glycosaminoglycan–protein–protein interactions using carbohydrate microarray and computational approaches

Glycosaminoglycan polysaccharides play critical roles in many cellular processes, ranging from viral invasion and angiogenesis to spinal cord injury. Their diverse biological activities are derived from an ability to regulate a remarkable number of proteins. However, few methods exist for the rapid identification of glycosaminoglycan–protein interactions and for studying the potential of glycosaminoglycans to assemble multimeric protein complexes. Here, we report a multidisciplinary approach that combines new carbohydrate microarray and computational modeling methodologies to elucidate glycosaminoglycan–protein interactions. The approach was validated through the study of known protein partners for heparan and chondroitin sulfate, including fibroblast growth factor 2 (FGF2) and its receptor FGFR1, the malarial protein VAR2CSA, and tumor necrosis factor-α (TNF-α). We also applied the approach to identify previously undescribed interactions between a specific sulfated epitope on chondroitin sulfate, CS-E, and the neurotrophins, a critical family of growth factors involved in the development, maintenance, and survival of the vertebrate nervous system. Our studies show for the first time that CS is capable of assembling multimeric signaling complexes and modulating neurotrophin signaling pathways. In addition, we identify a contiguous CS-E-binding site by computational modeling that suggests a potential mechanism to explain how CS may promote neurotrophin-tyrosine receptor kinase (Trk) complex formation and neurotrophin signaling. Together, our combined microarray and computational modeling methodologies provide a general, facile means to identify new glycosaminoglycan–protein–protein interactions, as well as a molecular-level understanding of those complexes

New Triazoloquinoxaline Ligand and its Polymeric 1D Silver(I) complex Synthesis, Structure, and Antimicrobial activity

The organic ligand 4-Benzyl-1-(N,N-dimethylamino)-[1,2,4]triazolo[4,3a]quinoxaline 1 (L) and its polymeric silver(I) complex, [Ag2L(NO3)2]n (2), have been synthesized and characterized. The organic ligand 1 crystallizes in the triclinic space group P¯1. The unit cell contains two parallel-stacked molecules. The complex [Ag2L(NO3)2]n (2) crystallizes in the monoclinic space group P21/n. The structure contains two different silver(I) ions. Ag(2) is coordinated by three oxygens (involving two nitrate groups) and to a nitrogen of the triazole ring of 1. These ligands form a strongly distorted tetrahedral, nearly planar coordination sphere. Ag(1) has an approximately tetrahedral geometry. It is bonded to one oxygen of a nitrate anion and a nitrogen of two different L; this aspect giving rise to an infinite chain structure. A final bond to Ag(1) involves the carbon of a phenyl group. It is more weakly bonded to the phenyl carbons on either side of this, so that the Ag(1)-phenyl bonding has aspects of an Ag-allyl bond. Ag(1) and Ag(2) participate in bonding to a common nitrate anion and alternate, the two distinct modes of bridging between them lead to a zig-zag chain structure. In addition to spectroscopic studies, the biological activities of the ligand and of the complex were scanned over a wide range of Gram positive and Gram negative flesh- and bone-eating bacteria. The results are discussed in comparison with well-known antibiotics