scholarly journals Hexagonal projected symmetries

2015 ◽  
Vol 71 (5) ◽  
pp. 549-558 ◽  
Author(s):  
Juliane F. Oliveira ◽  
Sofia B. S. D. Castro ◽  
Isabel S. Labouriau
Keyword(s):  
Pattern Formation ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Crystallographic Group ◽  
Two Dimensional ◽  
Thin Domains ◽  
Crystallographic Groups ◽  
Physical Systems ◽  
Eye Pattern

In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern.

Three-Dimensional Structure of Cloned T3 Connector Protein at 1.6nm Resolution

1990 ◽  
Vol 48 (1) ◽  
pp. 282-283
Author(s):  
José L. Carrascosa ◽  
José M. Valpuesta ◽  
Hisao Fujisawa
Keyword(s):  
Dna Sequences ◽  
Expression Vector ◽  
Three Dimensional ◽  
Deae Cellulose ◽  
Dna Packaging ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Freezing And Thawing ◽  
Three Dimensional Structure ◽  
Dimensional Reconstruction

The head to tail connector of bacteriophages plays a fundamental role in the assembly of viral heads and DNA packaging. In spite of the absence of sequence homology, the structure of connectors from different viruses (T4, Ø29, T3, P22, etc) share common morphological features, that are most clearly revealed in their three-dimensional structure. We have studied the three-dimensional reconstruction of the connector protein from phage T3 (gp 8) from tilted view of two dimensional crystals obtained from this protein after cloning and purification.DNA sequences including gene 8 from phage T3 were cloned, into Bam Hl-Eco Rl sites down stream of lambda promotor PL, in the expression vector pNT45 under the control of cI857. E R204 (pNT89) cells were incubated at 42°C for 2h, harvested and resuspended in 20 mM Tris HC1 (pH 7.4), 7mM 2 mercaptoethanol, ImM EDTA. The cells were lysed by freezing and thawing in the presence of lysozyme (lmg/ml) and ligthly sonicated. The low speed supernatant was precipitated by ammonium sulfate (60% saturated) and dissolved in the original buffer to be subjected to gel nitration through Sepharose 6B, followed by phosphocellulose colum (Pll) and DEAE cellulose colum (DE52). Purified gp8 appeared at 0.3M NaCl and formed crystals when its concentration increased above 1.5 mg/ml.

Televisualization: An Aid To Collaborative Research In Molecular Structure Biology

1998 ◽  
Vol 4 (S2) ◽  
pp. 32-33
Author(s):  
M. F. Schmid ◽  
P. Matsudaira ◽  
M. T. Dougherty ◽  
M. B. Sherman ◽  
C. Henn ◽  
...  
Keyword(s):  
Image Processing ◽  
Actin Filaments ◽  
Collaborative Research ◽  
Horseshoe Crab ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
Limulus Polyphemus ◽  
Dimensional Structure ◽  
Cross Linking ◽  
Tilt Series

Collaboration between local microscopists and image processing specialists, and their remote biological colleagues, has been hampered by the difficulty of i) transferring the three-dimensional reconstructions of macromolecules resulting from the cryomicroscopy and image processing, ii) viewing the results in a meaningful way, and iii) communicating the results and the interpretations derived therefrom to each other.The acrosomal process is an intracellular quasi-crystalline organelle in the head of the sperm of the horseshoe crab Limulus polyphemus. It consists of 100 - 130 actin-scruin filaments packed together in a pseudo-hexagonal lattice and is up to 60 μm long with a diameter of 0.1 μm. Scruin-scruin interactions are responsible for cross-linking the actin filaments together in the bundle. Our goal was to reveal interfilament interactions in the bundle. We have taken tilt series images in the electron microscope to reconstruct its three-dimensional structure at 45 Å resolution.

scholarly journals Mechanochemical Synthesis of a Mercury(II) Metal-Organic Framework Reveals a Two-Dimensional Polymorph Stabilized by Weak Interactions

2019 ◽  
Author(s):  
Isaiah R. Speight ◽  
Igor Huskić ◽  
Mihails Arhangelskis ◽  
Hatem M. Titi ◽  
Robin Stein ◽  
...  
Keyword(s):  
Density Functional ◽  
Weak Interactions ◽  
Metal Organic Framework ◽  
Three Dimensional ◽  
Density Functional Theory Calculations ◽  
Dimensional Structure ◽  
Reaction Monitoring ◽  
Two Dimensional ◽  
Functional Theory ◽  
Metal Organic

Solid-state mechanochemistry revealed a novel polymorph of the mercury(II) imidazolate framework, based on square-grid (sql) topology layers. Reaction monitoring and periodic density functional theory calculations show that the sql-structure is of higher stability than the previously reported three-dimensional structure, with the unexpected stabilization of a lower dimensionality structure explained by contributions of weak interactions, which include short C-H···Hg contacts.

Pattern re-establishment — transplantation and regeneration of the leg in the cricket Teleogryllus commodus (Walker)

Development ◽  
1981 ◽  
Vol 61 (1) ◽  
pp. 87-101
Author(s):  
Robert J. Biggin
Keyword(s):  
Pattern Formation ◽  
Three Dimensional ◽  
External Morphology ◽  
Dimensional Structure ◽  
Three Dimensional Structure ◽  
Teleogryllus Commodus ◽  
Cuticular Structures

Regeneration and grafting experiments were carried out on the prothoracic leg of the cricket Teleogryllus commodus (Walker) to examine the precision with which surface cuticular structures and internal epidermal derivatives are reformed. By comparing regenerated and grafted limbs with normal limbs it was found that the three-dimensional structure of epidermal derivatives is not restored. This is despite the fact that regenerated and grafted limbs appear similar in their external morphology to normal limbs. The implication of these results are discussed in the context of theories of pattern formation.

Poly[deca-μ2-cyanido-dicyanidobis(μ2-ethylenediamine)bis(ethylenediamine)tricadmium(II)dicobalt(III)]: a two-dimensional coordination polymer

2009 ◽  
Vol 65 (3) ◽  
pp. m118-m120
Author(s):  
Olha Sereda ◽  
Helen Stoeckli-Evans
Keyword(s):  
Coordination Polymer ◽  
Network Structure ◽  
General Position ◽  
Rotation Axis ◽  
Three Dimensional ◽  
The Other ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Asymmetric Unit ◽  
Dimensional Network

The title coordination polymer, [Cd3Co2(CN)12(C2H8N2)4]n, has an infinite two-dimensional network structure. The asymmetric unit is composed of two crystallographically independent CdIIatoms, one of which is located on a twofold rotation axis. There are two independent ethylenediamine (en) ligands, one of which bis-chelates to the Cd atom that sits in a general position, while the other bridges this Cd atom to that sitting on the twofold axis. The Cd atom located on the twofold rotation axis is linked to four equivalent CoIIIatomsviacyanide bridges, while the Cd atom that sits in a general position is connected to three equivalent CoIIIatomsviacyanide bridges. In this way, a series of trinuclear, tetranuclear and pentanuclear macrocycles are linked to form a two-dimensional network structure lying parallel to thebcplane. In the crystal structure, these two-dimensional networks are linkedviaN—H...N hydrogen bonds involving an en NH2H atom and a cyanide N atom, leading to the formation of a three-dimensional structure. This coordination polymer is only the second example involving a cyanometallate where the en ligand is present in both chelating and bridging coordination modes.

A new two-dimensional managnese(II) coordination polymer constructed by 2,2′-(1,2-phenylene)bis(1H-imidazole-4,5-dicarboxylate)

2018 ◽  
Vol 74 (5) ◽  
pp. 599-603 ◽  
Author(s):  
Yan-Ju Liu ◽  
Di Cheng ◽  
Ya-Xue Li ◽  
Xiang-Ru Meng ◽  
Huai-Xia Yang
Keyword(s):  
Solid State ◽  
Coordination Polymer ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Coordination Geometry ◽  
Two Dimensional ◽  
Carboxylate Ligands ◽  
Rich Variety ◽  
Distorted Octahedral ◽  
Solvothermal Conditions

In recent years, N-heterocyclic carboxylate ligands have attracted much interest in the preparation of new coordination polymers since they contain N-atom donors, as well as O-atom donors, and have a rich variety of coordination modes which can lead to polymers with intriguing structures and interesting properties. A new two-dimensional coordination polymer, namely poly[[μ3-2,2′-(1,2-phenylene)bis(4-carboxy-1H-imidazole-5-carboxylato)-κ6 O 4,N 3,N 3′,O 4′:O 5:O 5′]manganese(II)], [Mn(C16H8N4O8)] n or [Mn(H4Phbidc)] n , has been synthesized by the reaction of Mn(OAc)2·4H2O (OAc is acetate) with 2,2′-(1,2-phenylene)bis(1H-imidazole-4,5-dicarboxylic acid) (H6Phbidc) under solvothermal conditions. In the polymer, each MnII ion is six-coordinated by two N atoms from one H4Phbidc2− ligand and by four O atoms from three H4Phbidc2− ligands, forming a significantly distorted octahedral MnN2O4 coordination geometry. The MnII ions are linked by hexadentate H4Phbidc2− ligands, leading to a two-dimensional structure parallel to the ac plane. In the crystal, adjacent layers are further connected by N—H...O hydrogen bonds, forming a three-dimensional structure in the solid state.

scholarly journals Structural diversity induced by ligand geometry: From two-dimensional to three-dimensional coordination polymers with pyridine

2020 ◽  
pp. 174751982096816
Author(s):  
Fang-Kuo Wang ◽  
Shi-Yao Yang ◽  
Hua-Ze Dong
Keyword(s):  
Coordination Polymers ◽  
Three Dimensional ◽  
Structural Diversity ◽  
Dimensional Structure ◽  
Layer By Layer ◽  
Two Dimensional ◽  
Guest Molecules ◽  
X Ray ◽  
Benzenedicarboxylic Acid ◽  
Benzenetricarboxylic Acid

Two coordination polymers with two-dimensional and three-dimensional structures are, {[Zn3(bdc)3(py)2]·2NMP}n (1) (H2bdc = 1,4-benzenedicarboxylic acid) and [Zn2(NO3−)(btc)(nmp)2(py)]n (2) (H3btc = 1,3,5-benzenetricarboxylic acid), synthesized by hot-solution reactions of Zn(NO3)2·6H2O, pyridine (py) and two different ligands in N-methylpyrrolidone (NMP). {[Zn3(bdc)3(py)2]·2NMP}n exhibits two-dimensional networks with trizinc subunits [Zn3(COO)6py2] stacking with a layer-by-layer alignment, and there are strong π–π interactions involving py from adjacent layers. [Zn2(NO3−)(btc)(nmp)2(py)]n has a three-dimensional structure containing two independent zinc ions, tetrahedral ZnO4 and octahedral ZnNO5. Based on X-ray studies, the coordination polymers {[Zn3(bdc)3(py)2]·2NMP}n (1) have a porous structure with NMP guest molecules. In contrast, X-ray studies revealed that coordination polymer [Zn2(NO3−)(btc)(nmp)2(py)]n (2) had a larger void that was inhabited by coordinated py and NMP. In addition, the form of the two coordination polymers changed from two-dimensional to three-dimensional with transformation of the ligand geometry.

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