Generalized Version of ISI Invariant for some Molecular Structures

2022 ◽  
Vol 1048 ◽  
pp. 221-226
Author(s):  
K. Pattabiraman ◽  
M. Kameswari ◽  
M. Seenivasan
Keyword(s):  
Generalized Inverse ◽  
Molecular Structures ◽  
Topological Invariants ◽  
Graph Invariants

Degree related topological invariants are the bygone and most victorioustype of graph invariants so far. In this article, we are interested in finding the generalized inverse indeg invariant of the nanostar dendrimers D[r],fullerene dendrimerNS4[r], and polymer dendrimerNS5[r]. Keywords: nanotubes; inverse indeg invariant; nanostar dendrimers; fullerene dendrimer; polymer dendrimer

scholarly journals On Realization and Characterization of Topological Indices

2019 ◽  
Vol 9 (1) ◽  
pp. 715-718
Keyword(s):  
Topological Index ◽  
Fixed Number ◽  
Topological Indices ◽  
Molecular Structures ◽  
Real Numbers ◽  
Graph Invariants ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory

In chemical graph theory, topological index is one of the graph invariants which is a fixed number based on structure of a graph. Topological index is used as one of the tool to analyze molecular structures and for proper and optimal design of nanostructure. In this paper we realize the real numbers that are topological indices such as Zagreb indices, Randic index, NK-index, multiplicative F-index and multiplicative Zagreb indices along with some characterizations.

scholarly journals Hosoya properties of the commuting graph associated with the group of symmetries

2021 ◽  
Vol 44 (1) ◽  
pp. 173-184
Author(s):  
Ghulam Abbas ◽  
Anam Rani ◽  
Muhammad Salman ◽  
Tahira Noreen ◽  
Usman Ali
Keyword(s):  
Combinatorial Chemistry ◽  
Algebraic Structure ◽  
Molecular Descriptors ◽  
Chemical Properties ◽  
Molecular Structures ◽  
Hosoya Index ◽  
Graph Invariants ◽  
Commuting Graph ◽  
Hosoya Polynomial ◽  
Group Of Symmetries

Abstract A vast amount of information about distance based graph invariants is contained in the Hosoya polynomial. Such an information is helpful to determine well-known distance based molecular descriptors. The Hosoya index or Z-index of a graph G is the total number of its matching. The Hosoya index is a prominent example of topological indices, which are of great interest in combinatorial chemistry, and later on it applies to address several chemical properties in molecular structures. In this article, we investigate Hosoya properties (Hosoya polynomial, reciprocal Hosoya polynomial and Hosoya index) of the commuting graph associated with an algebraic structure developed by the symmetries of regular molecular gones (constructed by atoms with regular atomic-bonding).

STATE SUM MODELS FOR TRIVALENT KNOTTED GRAPH INVARIANTS USING QUANTUM GROUP SLq(2)

1992 ◽  
Vol 01 (03) ◽  
pp. 253-278 ◽  
Author(s):  
SERGEY PIUNIKHIN
Keyword(s):  
Network Theory ◽  
Quantum Spin ◽  
Topological Invariants ◽  
Graph Invariants ◽  
Spin Network ◽  
Face Model ◽  
Polynomial Invariants ◽  
Root Of Unity ◽  
State Models ◽  
6J Symbols

Four approaches to construct polynomial invariants for trivalent knotted graphs in S3 are compared. The first approach is based on vertex model with R-matrices and Glebsh-Gordan coefficients, appearing in SLq(2)-representations theory, as Boltzman weights. The second approach is based on Kauffman's quantum spin network theory, the third one is based on Witten-Turaev area-coloring model (or face model) based on quantum 6j-symbols, where q is root of unity. The fourth approach is based on the same face (or area-coloring) model, but q is not root of unity. The coincidence (up to certain normalization) of topological invariants, arising from these four state models, is proved.

scholarly journals Molecular topological invariants of certain chemical networks

2021 ◽  
Vol 44 (1) ◽  
pp. 141-149
Author(s):  
Syed Ahtsham Ul Haq Bokhary ◽  
Muhammad Imran ◽  
Shehnaz Akhter ◽  
Sadia Manzoor
Keyword(s):  
Chemical Compounds ◽  
Topological Descriptors ◽  
Discrete Mathematics ◽  
Chemical Characteristics ◽  
Topological Invariants ◽  
Molecular Topology ◽  
Graph Invariants ◽  
Physico Chemical ◽  
Structure Relationship ◽  
Atom Bond

Abstract Topological descriptors are the graph invariants that are used to explore the molecular topology of the molecular/chemical graphs. In QSAR/QSPR research, physico-chemical characteristics and topological invariants including Randić, atom-bond connectivity, and geometric arithmetic invariants are utilized to corelate and estimate the structure relationship and bioactivity of certain chemical compounds. Graph theory and discrete mathematics have discovered an impressive utilization in the area of research. In this article, we investigate the valency-depended invariants for certain chemical networks like generalized Aztec diamonds and tetrahedral diamond lattice. Moreover, the exact values of invariants for these categories of chemical networks are derived.

Electron Microscopy in Molecular Biology

1967 ◽  
Vol 25 ◽  
pp. 2-3
Author(s):  
Cecil E. Hall
Keyword(s):  
Electron Microscopy ◽  
Molecular Biology ◽  
Noise Level ◽  
Molecular Structures ◽  
Material Structure ◽  
The Arts ◽  
Shadow Casting ◽  
Electron Image ◽  
High Degree ◽  
Very High

The visualization of organic macromolecules such as proteins, nucleic acids, viruses and virus components has reached its high degree of effectiveness owing to refinements and reliability of instruments and to the invention of methods for enhancing the structure of these materials within the electron image. The latter techniques have been most important because what can be seen depends upon the molecular and atomic character of the object as modified which is rarely evident in the pristine material. Structure may thus be displayed by the arts of positive and negative staining, shadow casting, replication and other techniques. Enhancement of contrast, which delineates bounds of isolated macromolecules has been effected progressively over the years as illustrated in Figs. 1, 2, 3 and 4 by these methods. We now look to the future wondering what other visions are waiting to be seen. The instrument designers will need to exact from the arts of fabrication the performance that theory has prescribed as well as methods for phase and interference contrast with explorations of the potentialities of very high and very low voltages. Chemistry must play an increasingly important part in future progress by providing specific stain molecules of high visibility, substrates of vanishing “noise” level and means for preservation of molecular structures that usually exist in a solvated condition.

Scanning tunneling microscopy (STM) of DNA and RNA

1989 ◽  
Vol 47 ◽  
pp. 34-35
Author(s):  
Patricia G. Arscott ◽  
Gil Lee ◽  
Victor A. Bloomfield ◽  
D. Fennell Evans
Keyword(s):  
Molecular Structures ◽  
Inorganic Materials ◽  
Resolving Power ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Form And Function ◽  
Dna And Rna ◽  
Calf Thymus ◽  
And Function ◽  
The Relationship

STM is one of the most promising techniques available for visualizing the fine details of biomolecular structure. It has been used to map the surface topography of inorganic materials in atomic dimensions, and thus has the resolving power not only to determine the conformation of small molecules but to distinguish site-specific features within a molecule. That level of detail is of critical importance in understanding the relationship between form and function in biological systems. The size, shape, and accessibility of molecular structures can be determined much more accurately by STM than by electron microscopy since no staining, shadowing or labeling with heavy metals is required, and there is no exposure to damaging radiation by electrons. Crystallography and most other physical techniques do not give information about individual molecules.We have obtained striking images of DNA and RNA, using calf thymus DNA and two synthetic polynucleotides, poly(dG-me5dC)·poly(dG-me5dC) and poly(rA)·poly(rU).

Molecular architecture and functions of the neuronal cytoskeleton

1990 ◽  
Vol 48 (3) ◽  
pp. 2-3
Author(s):  
Nobutaka Hirokawa
Keyword(s):  
Major Elements ◽  
Molecular Structures ◽  
Organelle Transport ◽  
Molecular Architecture ◽  
Neuronal Morphogenesis ◽  
Microtubule Associated Proteins ◽  
Associated Proteins ◽  
And Function ◽  
Small Clusters

In this symposium I will present our studies about the molecular architecture and function of the cytomatrix of the nerve cells. The nerve cell is a highly polarized cell composed of highly branched dendrites, cell body, and a single long axon along the direction of the impulse propagation. Each part of the neuron takes characteristic shapes for which the cytoskeleton provides the framework. The neuronal cytoskeletons play important roles on neuronal morphogenesis, organelle transport and the synaptic transmission. In the axon neurofilaments (NF) form dense arrays, while microtubules (MT) are arranged as small clusters among the NFs. On the other hand, MTs are distributed uniformly, whereas NFs tend to run solitarily or form small fascicles in the dendrites Quick freeze deep etch electron microscopy revealed various kinds of strands among MTs, NFs and membranous organelles (MO). These structures form major elements of the cytomatrix in the neuron. To investigate molecular nature and function of these filaments first we studied molecular structures of microtubule associated proteins (MAP1A, MAP1B, MAP2, MAP2C and tau), and microtubules reconstituted from MAPs and tubulin in vitro. These MAPs were all fibrous molecules with different length and formed arm like projections from the microtubule surface.

Toxicity of Heparinoids, with Special Reference to the Precipitation of Fibrinogen

1964 ◽  
Vol 12 (01) ◽  
pp. 232-261 ◽  
Author(s):  
S Sasaki ◽  
T Takemoto ◽  
S Oka
Keyword(s):  
Molecular Weight ◽  
Dextran Sulfate ◽  
Anticoagulant Activity ◽  
Molecular Structures ◽  
Severe Reaction ◽  
Clinical Use ◽  
Molecular Weights ◽  
Close Relationship

SummaryTo demonstrate whether the intravascular precipitation of fibrinogen is responsible for the toxicity of heparinoid, the relation between the toxicity of heparinoid in vivo and the precipitation of fibrinogen in vitro was investigated, using dextran sulfate of various molecular weights and various heparinoids.1. There are close relationships between the molecular weight of dextran sulfate, its toxicity, and the quantity of fibrinogen precipitated.2. The close relationship between the toxicity and the precipitation of fibrinogen found for dextran sulfate holds good for other heparinoids regardless of their molecular structures.3. Histological findings suggest strongly that the pathological changes produced with dextran sulfate are caused primarily by the intravascular precipitates with occlusion of the capillaries.From these facts, it is concluded that the precipitates of fibrinogen with heparinoid may be the cause or at least the major cause of the toxicity of heparinoid.4. The most suitable molecular weight of dextran sulfate for clinical use was found to be 5,300 ~ 6,700, from the maximum value of the product (LD50 · Anticoagulant activity). This product (LD50 · Anticoagulant activity) can be employed generally to assess the comparative merits of various heparinoids.5. Clinical use of the dextran sulfate prepared on this basis gave satisfactory results. No severe reaction was observed. However, two delayed reactions, alopecia and thrombocytopenia, were observed. These two reactions seem to come from the cause other than intravascular precipitation.

Factors Affecting Molecular Self-Assembly and Its Mechanism

2012 ◽  
Vol 9 (1) ◽  
pp. 43 ◽  
Author(s):  
Hueyling Tan
Keyword(s):  
Self Assembly ◽  
Building Blocks ◽  
Molecular Engineering ◽  
Molecular Structures ◽  
Polymer Science ◽  
New Approach ◽  
Factors Affecting ◽  
Dna Structures ◽  
Self Assembling ◽  
Wide Range

Molecular self-assembly is ubiquitous in nature and has emerged as a new approach to produce new materials in chemistry, engineering, nanotechnology, polymer science and materials. Molecular self-assembly has been attracting increasing interest from the scientific community in recent years due to its importance in understanding biology and a variety of diseases at the molecular level. In the last few years, considerable advances have been made in the use ofpeptides as building blocks to produce biological materials for wide range of applications, including fabricating novel supra-molecular structures and scaffolding for tissue repair. The study ofbiological self-assembly systems represents a significant advancement in molecular engineering and is a rapidly growing scientific and engineering field that crosses the boundaries ofexisting disciplines. Many self-assembling systems are rangefrom bi- andtri-block copolymers to DNA structures as well as simple and complex proteins andpeptides. The ultimate goal is to harness molecular self-assembly such that design andcontrol ofbottom-up processes is achieved thereby enabling exploitation of structures developed at the meso- and macro-scopic scale for the purposes oflife and non-life science applications. Such aspirations can be achievedthrough understanding thefundamental principles behind the selforganisation and self-synthesis processes exhibited by biological systems.

Visualizing 3D Molecular Structures Using an Augmented Reality App

2019 ◽  
Author(s):  
Kristina Eriksen ◽  
Bjarne Nielsen ◽  
Michael Pittelkow
Keyword(s):  
Augmented Reality ◽  
Small Molecules ◽  
Computer Modelling ◽  
Simple Procedure ◽  
3D Structure ◽  
Molecular Structures ◽  
Free Software ◽  
Programming Skills ◽  
2D Space ◽  
Made In

<p>We present a simple procedure to make an augmented reality app to visualize any 3D chemical model. The molecular structure may be based on data from crystallographic data or from computer modelling. This guide is made in such a way, that no programming skills are needed and the procedure uses free software and is a way to visualize 3D structures that are normally difficult to comprehend in the 2D space of paper. The process can be applied to make 3D representation of any 2D object, and we envisage the app to be useful when visualizing simple stereochemical problems, when presenting a complex 3D structure on a poster presentation or even in audio-visual presentations. The method works for all molecules including small molecules, supramolecular structures, MOFs and biomacromolecules.</p>

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