Ma-Xu quantization rule and exact WKB condition for translationally shape invariant potentials

For translationally shape invariant potentials, the exact quantization rule proposed by Ma and Xu is a direct consequence of exactness of the modified WKB quantization condition proved by Barclay. We propose here a very direct alternative way to calculate the appropriate correction for the whole class of translationally shape invariant potentials

Bis(5,5,7,12,12,14-hexa­methyl-1,4,8,11-tetra­azacyclo­tetra­decane-κ4 N)(μ-l-mal­ato-κ4 O 1,O 2:O 4,O 4′)dinickel(II) bis(perchlorate) monohydrate

In the crystal structure of the title dinuclear compound, [Ni2(C4H4O5)(C16H36N4)2](ClO4)2·H2O, the bridg­ing di­car­box­yl­ate dianion O,O′-chelates to two Ni atoms, both of which are also chelated by the N-macrocylic ligand. The Ni atoms exhibit a distorted octa­hedral coordination. N—H⋯O and O—H⋯O hydrogen bonds link the cations and the uncoordinated water mol­ecules into a layer structure; the perchlorate anions occupy the space between adjacent layers, and are only weakly linked to the layers. One of the perchlorate anions is disordered over two sets of sites in a 3:2 ratio

[4-Carboxy­imidazole-5-carboxyl­ato(2–)-κ2 N 1,O 5](5,5,7,12,12,14-hexa­methyl-1,4,8,11-tetra­azacyclo­tetra­decane-κ4 N,N′,N′′,N′′′)nickel(II) monohydrate

The 4-carboxy­imidazole-5-carboxyl­ate(2−) dianion in the title compound, [Ni(C5H2N2O4)(C16H36N4)]·H2O, N,O′-chelates to the NiII atom, which shows an octa­hedral coordination. The macrocycle folds itself around the metal atom and binds to it through four secondary nitrogen atoms; adjacent molecules are linked by N—H⋯O hydrogen bonds into a linear chain. The water molecule is disordered over two positions

(Benzoato-κ2 O,O′)(5,5,7,12,12,14-hexa­methyl-1,4,8,11-tetra­azacyclo­tetra­decane-κ4 N,N′,N′′,N′′′)nickel(II) perchlorate benzoic acid solvate

In the title compound, [Ni(C7H5O2)(C16H36N4)]ClO4·C7H6O2, the Ni atom displays a distorted octa­hedral coordination geometry with four N atoms of the ligand rac-5,5,7,12,12,14-hexa­methyl-1,4,8,11-tetra­azacyclo­tetra­decane (L) in a folded configuration and two benzoate (bz) O atoms. The [Ni(rac-L)(bz)]+ complex cation, perchlorate anion and benzoic acid mol­ecules engage in hydrogen bonding, with N⋯O distances between 2.970 (3) and 3.123 (3) Å and an O⋯O distance of 2.691 (3) Å

A simple and scalable hydrogel-based system for culturing protein-producing cells

Recombinant protein therapeutics have become important components of the modern medicine. Majority of them are produced with mammalian cells that are cultured either through adherent culturing, in which cells are cultured on substrates, or suspension culturing, in which cells are suspended and cultured in agitated cell culture medium in a culture vessel. The adherent cell culturing method is limited by its low yield. In suspension culturing, cells need extensive genetic manipulation to grow as single cells at high density, which is time and labor-consuming. Here, we report a new method, which utilizes a thermoreversible hydrogel as the scaffold for culturing protein-expressing cells. The hydrogel scaffolds not only provide 3D spaces for the cells, but also act as physical barriers to prevent excessive cellular agglomeration and protect cells from the hydrodynamic stresses. As a result, cells can grow at high viability, high growth rate, and extremely high yield even without genetic manipulations. The cell yield in the hydrogels is around 20 times of the suspension culturing. In addition, the protein productivity per cell per day in the hydrogel is higher than the adherent culturing method. This new method is simple, scalable and defined. It will be of great value for both the research laboratories and pharmaceutical industry for producing proteins

cis-[(7R,14R)-5,5,7,12,12,14-Hexa­methyl-1,4,8,11-tetra­azacyclo­tetra­decane-κ4 N](oxalato-κ2 O,O′)nickel(II) oxalic acid solvate

Both mol­ecules of the title compound, [Ni(C2O4)(C16H36N4)]·C2H2O4, are located on a crystallographic twofold rotation axis. The NiII atom shows a distorted octa­hedral geometry. The crystal packing is stabilized by N—H⋯O and O—H⋯O hydrogen bonds

Evidence for gill slits and a pharynx in Cambrian vetulicolians: implications for the early evolution of deuterostomes.

BACKGROUND: Vetulicolians are a group of Cambrian metazoans whose distinctive bodyplan continues to present a major phylogenetic challenge. Thus, we see vetulicolians assigned to groups as disparate as deuterostomes and ecdysozoans. This divergence of opinions revolves around a strikingly arthropod-like body, but one that also bears complex lateral structures on its anterior section interpreted as pharyngeal openings. Establishing the homology of these structures is central to resolving where vetulicolians sit in metazoan phylogeny. RESULTS: New material from the Chengjiang Lagerstätte helps to resolve this issue. Here, we demonstrate that these controversial structures comprise grooves with a series of openings. The latter are oval in shape and associated with a complex anatomy consistent with control of their opening and closure. Remains of what we interpret to be a musculature, combined with the capacity for the grooves to contract, indicate vetulicolians possessed a pumping mechanism that could process considerable volumes of seawater. Our observations suggest that food captured in the anterior cavity was transported to dorsal and ventral gutters, which then channeled material to the intestine. This arrangement appears to find no counterpart in any known fossil or extant arthropod (or any other ecdysozoan). Anterior lateral perforations, however, are diagnostic of deuterostomes. CONCLUSIONS: If the evidence is against vetulicolians belonging to one or other group of ecdysozoan, then two phylogenetic options seem to remain. The first is that such features as vetulicolians possess are indicative of either a position among the bilaterians or deuterostomes but apart from the observation that they themselves form a distinctive and recognizable clade current evidence can permit no greater precision as to their phylogenetic placement. We argue that this is too pessimistic a view, and conclude that evidence points towards vetulicolians being members of the stem-group deuterostomes; a group best known as the chordates (amphioxus, tunicates, vertebrates), but also including the ambulacrarians (echinoderms, hemichordates), and xenoturbellids. If the latter, first they demonstrate that these members of the stem group show few similarities to the descendant crown group representatives. Second, of the key innovations that underpinned deuterostome success, the earliest and arguably most seminal was the evolution of openings that define the pharyngeal gill slits of hemichordates (and some extinct echinoderms) and chordates.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are