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Estrada Index
In chemical graph theory, the Estrada index is a topological index of protein folding. The index was first defined by Ernesto Estrada as a measure of the degree of folding of a protein, which is represented as a path-graph weighted by the dihedral or torsional angles of the protein backbone. This index of degree of folding has found multiple applications in the study of protein functions and protein-ligand interactions. The name "Estrada index" was introduced by de la Peña et al. in 2007. Derivation Let G=(V,E) be a graph of size , V, =n and let \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n be a non-increasing ordering of the eigenvalues of its adjacency matrix In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simp ... A. The Estrada index is defined as : \operatorname(G)=\sum_^n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Graph Theory
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo Hosoya, Milan Randić and Nenad Trinajstić (also Harry Wiener and others). In 1988, it was reported that several hundred researchers worked in this area, producing about 500 articles annually. A number of monographs have been written in the area, including the two-volume comprehensive text by Trinajstić, ''Chemical Graph Theory'', that summarized the field up to mid-1980s. The adherents of the theory maintain that the properties of a chemical graph (i.e., a graph-theoretical representation of a molecule) give valuable insights into the chemical phenomena. Others contend that graphs play only a fringe role in chemical research.D.H. Rouvray, "Combinatorics in Chemistry", pp. 1955-1982, in: Ronald Graham, Martin Grötschel, László Lovász (E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Index
In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. Calculation Topological descriptors are derived from hydrogen-suppressed molecular graphs, in which the atoms are represented by vertices and the bonds by edges. The connections between the atoms can be described by various types of topological matrices (e.g., distance or adjacency matrices), which can be mathematically manipulated so as to derive a single number, usually known as grap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Protein Folding
Protein folding is the physical process by which a protein chain is translated to its native three-dimensional structure, typically a "folded" conformation by which the protein becomes biologically functional. Via an expeditious and reproducible process, a polypeptide folds into its characteristic three-dimensional structure from a random coil. Each protein exists first as an unfolded polypeptide or random coil after being translated from a sequence of mRNA to a linear chain of amino acids. At this stage the polypeptide lacks any stable (long-lasting) three-dimensional structure (the left hand side of the first figure). As the polypeptide chain is being synthesized by a ribosome, the linear chain begins to fold into its three-dimensional structure. Folding of many proteins begins even during translation of the polypeptide chain. Amino acids interact with each other to produce a well-defined three-dimensional structure, the folded protein (the right hand side of the figure), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernesto Estrada (scientist)
Ernesto Estrada (born 2 May 1966) is a Cuban-Spanish scientist. He has been Senior ARAID Researcher at the Institute of Mathematics and Applications at the University of Zaragoza, Spain since 2019. Before that he was the chair in Complexity Science, and full professor at the Department of Mathematics and Statistics of the University of Strathclyde, Glasgow, United Kingdom. He is known by his contributions in different disciplines, including mathematical chemistry and complex network theory. Birth and education Estrada was born in the city of Sancti Spiritus, in the central region of Cuba. Since the age of 11 he studied in a school which specialized in exact sciences. He later studied for a technical degree in Analytical chemistry in the technological institute IPQI Mártires de Girón Havana. At the age of 18 years, and before entering the university, he presented his first scientific paper in an international congress together with his mentor, Dr. Jose F. Fernández-Bertr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torsional Angle
A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. The planes of a flying machine are said to be at positive dihedral angle when both starboard and port main planes (commonly called wings) are upwardly inclined to the lateral axis. When downwardly inclined they are said to be at a negative dihedral angle. Mathematical background When the two intersecting planes are described in terms of Cartesian coordinates by the two equations : a_1 x + b_1 y + c_1 z + d_1 = 0 :a_2 x + b_2 y + c_2 z + d_2 = 0 the dihedral angle, \varphi between them is given by: :\cos \varphi = \frac and satisfies 0\le \varphi \le \pi/2. Alternatively, if an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency Matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory. The adjacency matrix of a graph should be distinguished from its incidence matrix, a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix, which contains information about the degree of each vertex. Definition For a simple graph with vertex set , the adjacency matrix is a square matrix such that its element is one when there is an edge from vertex to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Chemistry
Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Mathematical chemistry has also sometimes been called computer chemistry, but should not be confused with computational chemistry. Major areas of research in mathematical chemistry include chemical graph theory, which deals with topology such as the mathematical study of isomerism and the development of topological descriptors or indices which find application in quantitative structure-property relationships; and chemical aspects of group theory, which finds applications in stereochemistry and quantum chemistry. Another important area is molecular knot theory and circuit topology that describe the topology of folded linear molecules such as proteins and Nucleic Acids. The history of the approach may be traced back to the 19th century. Georg Helm published a treatise titled "The Principles of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cheminformatics
Cheminformatics (also known as chemoinformatics) refers to use of physical chemistry theory with computer and information science techniques—so called "''in silico''" techniques—in application to a range of descriptive and prescriptive problems in the field of chemistry, including in its applications to biology and related molecular fields. Such ''in silico'' techniques are used, for example, by pharmaceutical companies and in academic settings to aid and inform the process of drug discovery, for instance in the design of well-defined combinatorial libraries of synthetic compounds, or to assist in structure-based drug design. The methods can also be used in chemical and allied industries, and such fields as environmental science and pharmacology, where chemical processes are involved or studied. History Cheminformatics has been an active field in various guises since the 1970s and earlier, with activity in academic departments and commercial pharmaceutical research and dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
