Multidimensional Numbers and the Genomatrices of Hydrogen Bonds

2010 ◽  
pp. 193-206
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Hydrogen Bonds ◽  
Genetic Code ◽  
Structural Features ◽  
Hyperbolic Type ◽  
Complex Numbers ◽  
Hypercomplex Numbers ◽  
Molecular Systems ◽  
Natural Systems ◽  
Double Numbers ◽  
Mathematical Properties

This chapter returns to the kind of numeric genetic matrices, which were considered in Chapter 4-6. This kind of genomatrices is not connected with the degeneracy of the genetic code directly, but it is related to some other structural features of the genetic code systems. The connection of the Kronecker families of such genomatrices with special categories of hypercomplex numbers and with their algebras is demonstrated. Hypercomplex numbers of these two categories are named “matrions of a hyperbolic type” and “matrions of a circular type.” These hypercomplex numbers are a generalization of complex numbers and double numbers. Mathematical properties of these additional categories of algebras are presented. A possible meaning and possible applications of these hypercomplex numbers are discussed. The investigation of these hyperbolic numbers in their connection with the parameters of molecular systems of the genetic code can be considered as a continuation of the Pythagorean approach to understanding natural systems.

scholarly journals The Genetic Code, Algebraic Codes and Double Numbers

2020 ◽  
Author(s):  
Sergey V. Petoukhov
Keyword(s):  
Genetic Code ◽  
Communication Technologies ◽  
Structural Features ◽  
Rna Molecules ◽  
Doubly Stochastic ◽  
Dna And Rna ◽  
Double Numbers ◽  
Algebraic Codes ◽  
Living Organisms ◽  
Algebraic Code

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

scholarly journals Crystal structure of 1,2-bis[(2-tert-butylphenyl)imino]ethane

2015 ◽  
Vol 71 (6) ◽  
pp. o385-o386
Author(s):  
Alexandre C. Silvino ◽  
Juliana M. Torres
Keyword(s):  
Hydrogen Bonds ◽  
Structural Features ◽  
Angular Deviation ◽  
Aromatic Rings ◽  
Acta Cryst ◽  
Compound C ◽  
Angle Deviation ◽  
Steric Factors ◽  
Diimine Ligand ◽  
Intramolecular Hydrogen

The whole molecule of the title compound, C22H28N2, (I), is generated by inversion symmetry. The molecule is rather similar to that of 2,3-bis[(2-tert-butylphenyl)imino]butane, (II), a diimine ligand comprising similar structural features [Ferreiraet al.(2006).Acta Cryst.E62, o4282–o4284]. Both ligands crystallize with the –N=C(R)—C(R)=N– group around an inversion centre, in atransconfiguration. Comparing the two structures, it may be noted that the independent planar groups in both molecules [the central link, –N=C(R)—C(R)=N–, and the terminal aromatic ring] subtend an angle of 69.6 (1)° in (II) and 49.4 (2)° in (I). Ferreira and co-workers proposed that such angle deviation may be ascribed to the presence of two non-classical intramolecular hydrogen bonds and steric factors. In fact, in (I), similar non-classical hydrogen bonds are observed, and the larger angular deviation in (II) may be assigned to the presence of methyl groups in the diimino fragment, which can cause steric hindrance due to the presence of bulkytert-butyl substituents in the aromatic rings. The C=N bond lengths are similar in both compounds and agree with comonly accepted values.

scholarly journals Bis(3-carbamoylpyridin-1-ium) phosphite monohydrate

2018 ◽  
Vol 74 (9) ◽  
pp. 1295-1298
Author(s):  
Jan Fábry
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Water Molecule ◽  
Secondary Amine ◽  
Symmetry Plane ◽  
Structural Features ◽  
Water Molecules ◽  
Amine Groups

Two of the constituent molecules in the title structure, 2C6H7N2O+·HPO3 2−·H2O, i.e. the phosphite anion and the water molecule, are situated on a symmetry plane. The molecules are held together by moderate N—H...O and O—H...N, and weak O—H...O and C—H...Ocarbonyl hydrogen bonds in which the amide and secondary amine groups, and the water molecules are involved. The structural features are usual, among them the H atom bonded to the P atom avoids hydrogen bonding.

scholarly journals The Effects of the Solvents on the Macrocyclic Structures: From Rigid Pillararene to Flexible Crown Ether

2021 ◽  
Author(s):  
Shuangshuang Wang ◽  
Yanzhen Yin ◽  
Jian Gao ◽  
Xingtang Liang ◽  
Haixin Shi
Keyword(s):  
Hydrogen Bonds ◽  
Structural Design ◽  
Structural Features ◽  
Intermolecular Hydrogen Bonds ◽  
Intramolecular Hydrogen Bonds ◽  
Effect Of Solvents ◽  
Dynamics Simulations ◽  
Intramolecular Hydrogen ◽  
Macrocyclic Molecules ◽  
Polarity Of Solvents

The differences in the macrocyclic structures lead to different flexibilities, and yet the effect of solvents on the conformations is not clear so far. In this work, the conformations of four representational macrocyclic molecules (pillar[5]arene, p-tert-butyl calix[6]arene, benzylic amide macrocycle and dibenzo-18-crown-6) in three solvents with distinct polarity have been studied by all-atom molecular dynamics simulations. The structural features of the macrocycles in the solvents indicate that the conformations are related to the polarity of the solvents and the formation of hydrogen bonds. For the pillar[5]arene, the benzylic amide macrocycle and the dibenzo-18-crown-6, that cannot form intramolecular hydrogen bonds, the polarity of solvents is the major contributing factor in the conformations. The formation of intramolecular hydrogen bonds, in contrast, determinates the conformations of the calix[6]arene. Furthermore, the slight fluctuations of the structures will result in tremendous change of the intramolecular hydrogen bonds of the macrocycles and the intermolecular hydrogen bonds between the macrocycles and the solvents. The current theoretical studies that serve as a basis for the macrocyclic chemistry are valuable for the efficient structural design of the macrocyclic molecules.

scholarly journals Synthesis and crystal structures of a bis(3-hydroxy-cyclohex-2-en-1-one) and two hexahydroquinoline derivatives

2020 ◽  
Vol 76 (2) ◽  
pp. 125-131
Author(s):  
Scott A. Steiger ◽  
Chun Li ◽  
Christina Gates ◽  
Nicholas R. Natale
Keyword(s):  
Hydrogen Bonds ◽  
Title Compound ◽  
Crystal Packing ◽  
Structural Features ◽  
Boat Conformation ◽  
Two Dimensional ◽  
Aryl Group ◽  
Dimensional Network ◽  
A Chain ◽  
Intramolecular Hydrogen

The title compound I, 2,2′-[(2-nitrophenyl)methylene]bis(3-hydroxy-5,5-dimethylcyclohex-2-enone), C23H27NO6, features a 1,3-ketone–enol conformation which is stabilized by two intramolecular hydrogen bonds. The most prominent intermolecular interactions in compound I are C—H...O hydrogen bonds, which link molecules into a two-dimensional network parallel to the (001) plane and a chain perpendicular to (1\overline{1}1). Both title compounds II, ethyl 4-(4-hydroxy-3,5-dimethoxyphenyl)-2,7,7-trimethyl-5-oxo-1,4,5,6,7,8-hexahydroquinoline-3-carboxylate, C23H29NO6, and III, ethyl 4-(anthracen-9-yl)-2,7,7-trimethyl-5-oxo-1,4,5,6,7,8-hexahydroquinoline-3-carboxylate, C29H29NO3, share the same structural features, such as a shallow boat conformation of the dihydropyridine group and an orthogonal aryl group attached to the dihydropyridine. Intermolecular N—H...O bonding is present in the crystal packing of both compound II and III.

Molecular assembly at surfaces: progress and challenges

2017 ◽  
Vol 204 ◽  
pp. 9-33 ◽  
Author(s):  
R. Raval
Keyword(s):  
Building Blocks ◽  
Covalent Bonding ◽  
Molecular Assembly ◽  
Theoretical Modelling ◽  
Top Down ◽  
Molecular Systems ◽  
Natural Systems ◽  
Surfaces And Interfaces ◽  
Macromolecular Systems ◽  
Determine System

Molecules provide versatile building blocks, with a vast palette of functionalities and an ability to assemble via supramolecular and covalent bonding to generate remarkably diverse macromolecular systems. This is abundantly displayed by natural systems that have evolved on Earth, which exploit both supramolecular and covalent protocols to create the machinery of life. Importantly, these molecular assemblies deliver functions that are reproducible, adaptable, finessed and responsive. There is now a real need to translate complex molecular systems to surfaces and interfaces in order to engineer 21st century nanotechnology. ‘Top-down’ and ‘bottom-up’ approaches, and utilisation of supramolecular and covalent assembly, are currently being used to create a range of molecular architectures and functionalities at surfaces. In parallel, advanced tools developed for interrogating surfaces and interfaces have been deployed to capture the complexities of molecular behaviour at interfaces from the nanoscale to the macroscale, while advances in theoretical modelling are delivering insights into the balance of interactions that determine system behaviour. A few examples are provided here that outline molecular behaviour at surfaces, and the level of complexity that is inherent in such systems.

scholarly journals Structural insights into the specific anti-HIV property of actinohivin: structure of its complex with the α(1–2)mannobiose moiety of gp120

2012 ◽  
Vol 68 (12) ◽  
pp. 1671-1679 ◽  
Author(s):  
M. Mominul Hoque ◽  
Kaoru Suzuki ◽  
Masaru Tsunoda ◽  
Jiandong Jiang ◽  
Fang Zhang ◽  
...  
Keyword(s):  
Hydrogen Bonds ◽  
Open Space ◽  
Tandem Repeats ◽  
Specific Binding ◽  
Structural Features ◽  
Hydroxyl Groups ◽  
Mannose Residue ◽  
Specific Affinity ◽  
Anti Hiv ◽  
Hiv 1

Actinohivin (AH) is an actinomycete lectin with a potent specific anti-HIV activity. In order to clarify the structural evidence for its specific binding to the α(1–2)mannobiose (MB) moiety of the D1 chains of high-mannose-type glycans (HMTGs) attached to HIV-1 gp120, the crystal structure of AH in complex with MB has been determined. The AH molecule is composed of three identical structural modules, each of which has a pocket in which an MB molecule is bound adopting a bracket-shaped conformation. This conformation is stabilized through two weak C—H...O hydrogen bonds facilitated by the α(1–2) linkage. The binding features in the three pockets are quite similar to each other, in accordance with the molecular pseudo-threefold symmetry generated from the three tandem repeats in the amino-acid sequence. The shape of the pocket can accept two neighbouring hydroxyl groups of the O3and O4atoms of the equatorial configuration of the second mannose residue. To recognize these atoms through hydrogen bonds, an Asp residue is located at the bottom of each pocket. Tyr and Leu residues seem to block the movement of the MB molecules. Furthermore, the O1atom of the axial configuration of the second mannose residue protrudes from each pocket into an open space surrounded by the conserved hydrophobic residues, suggesting an additional binding site for the third mannose residue of the branched D1 chain of HMTGs. These structural features provide strong evidence indicating that AH is only highly specific for MB and would facilitate the highly specific affinity of AH for any glycoprotein carrying many HMTGs, such as HIV-1 gp120.

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