Representation of the molecular topology of cyclical structures by means of cycle graphs. 2. Application to clustering of chemical databases

The great size of chemical databases and the high computational cost required in the atom-atom comparison of molecular structures for the calculation of the similarity between two chemical compounds necessitate the proposal of new clustering models with the aim of reducing the time of recovery of a set of molecules from a database that satisfies a range of similarities with regard to a given molecule pattern. In this paper we make use of the information corresponding to the cycles existing in the structure of molecules as an approach for the classification of chemical databases. The clustering method here proposed is based on the representation of the topological structure of molecules stored in chemical databases through its corresponding cycle graph. This method presents a more appropriate behavior for others described in the bibliography in which the information corresponding to the cyclicity of the molecules is also used.     

A novel approach to the use of graph theory in structure–activity relationship studies. Application to the qualitative evaluation of mutagenicity in a series of nonfused ring aromatic compounds

In this article we describe a novel approach to the application of graph theory in structure–activity relationship studies. An information–theoretical topological index for the vertices of a molecular graph has been used for the qualitative evaluation of the mutagenic activity of a series of nonfused ring aromatic compounds. The use of a vertex index contrasts with the conventional approach of using a topological index for the entire molecule. The idea is to identify regions, or substructures in the molecules (molecular graphs) which may be used to determine certain biological activity of chemical compounds. The results obtained in this paper indicate that the present approach is capable of classifying the mutagenic activity of the compounds under consideration and may find useful application in structure–activity relationship studies of diverse bioactive compounds.     

计算机辅助结构解析中自同构群的生成算法

在结构解析过程中,自同构群的生成是必须的。通过全通道拓扑等价性算法,得到了化合物的自同构群,并比较了几种拓扑等价性算法,结果发现,全通道算法能够正确划分化合物的结构图,从而为ＥＳＥＳＯＣ系统的立体异构体穷举生成奠定了基础。     

三梯级和四梯级圆筒和Mbius分子的拓扑特性研究

Walba等以其卓越的工作,合成了三-THYME(C_(42)H_(72)O_(18))和四-THYME(C_(56)H_(96)O_(24))圆筒及其Mbius扭曲环带分子,被誉为拓扑学进入有机化学领域的奇迹,成为迄今为止拓扑立体化学研究的重要内容,但从拓扑学的观点探索分子图拓扑结构特性尚缺乏深入研究,本文作者考虑到一般性,曾将扭曲数T为偶数(0,2,4)的定义为Hckel型,扭曲数     

k-resonant benzenoid systems and k-cycle resonant graphs.

A benzenoid system (or hexagonal system) H is said to be k-resonant if, for 1 < or = t < or = k, any t disjoint hexagons of H are mutually resonant; that is, there is a Kekule structure (or perfect matching) K of H such that each of the k hexagons is an K-alternating hexagon. A connected graph G is said to be k-cycle resonant if, for 1 < or = t < or = k, any t disjoint cycles in G are mutually resonant. The concept of k-resonant benzenoid systems is closely related to Clar's aromatic sextet theory, and the concept of k-cycle resonant graphs is a natural generalization of k-resonant benzenoid systems. Some necessary and sufficient conditions for a benzenoid system (respectively a graph) to be k-resonant (respectively k-cycle resonant) have been established. In this paper, we will give a survey on investigations of k-resonant benzenoid systems and k-cycle resonant graphs.     

Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting statistics

We study Markovian stochastic motion on a graph with finite number of nodes and adiabatically periodically driven transition rates. We show that, under general conditions, the quantized currents that appear at low temperatures are a manifestation of topological invariants in the counting statistics of currents. This observation provides an approach for classification of topological properties of the counting statistics, as well as for extensions of the phenomenon of the robust quantization of currents at low temperatures to the properties of the counting statistics which persist to finite temperatures.     

Calculation of the average properties of atoms in molecules. II

This article describes an algorithm for the calculation of the average properties of an atom in a molecule. The atom is defined within the topological theory of molecular structure, a theory which defines atoms, bonds, structure, and structural stability in terms of the topological properties of a system's charge distribution. The average properties of the atom so defined are uniquely determined by quantum mechanics. Results for a number of hydrocarbon molecules, obtained by the program PROAIM (properties of atoms in molecules) which implements this algorithm, are given. In general, this program enables one to calculate the average energy of an atom in a molecule to an accuracy of ±1 kcal/mol.     

Topological indices for molecular fragments and new graph invariants

Whereas the internal fragment topological index (IFTI) is calculated in the normal manner as for any molecule, the external fragment topological index (EFTI) is calculated so as to reflect the interaction between the excised fragment F and the remainder of the molecule (G-F). For selected topological indices (TIs), a survey of EFTI values, formulas and examples is presented. Some requirements as to the fragment indices are formulated and examined. In the discussion of the results, it is shown that for some TIs regularities exist in the dependence of EFTI values upon the branching of fragment F, or upon the marginal versus central position of the fragment F in the graph G. New vortex invariants can be computed as EFTI values for one-atom fragments over all graph vertices; by iteration, it is in principle possible to devise an infinite number of now vertex invariants.     

Symmetry properties of chemical graphs. IX. The valence tautomerism in the P73− skeleton

We investigate the intramolecular rearrangement of the P₇^3? ion in which P? P bonds are continuously broken and reestablished resulting in a dynamic structure with all seven phosphorus atoms being chemically equivalent. This leads to 7/3 = 1680 valence tautomers. The P₇^3? ion is a typical fluctuating molecule, distantly related to C₁₀H₁₀ bullvalene. In order to determine the symmetry of the process we first consider the problem of the construction of the rearrangement graph. Initial steps toward this goal are illustrated, and additional characterizations of the graph are derived after its construction by computer. A number of properties of this rather complicated graph having 1680 vertices and 2520 edges are discussed: in particular the occurrence of various cycles, the maximal distance between vertices, the count of neighbors at different distance, and finally its symmetry.     

Understanding topological symmetry: a heuristic approach to its determination

An algorithm based on heuristic rules for topological symmetry perception of organic structures having heteroatoms, multiple bonds, and any kind of cycle, and configuration, is presented. This algorithm identifies topological symmetry planes and sets of equivalent atoms in the structure, named symmetry atom groups (SAGs). This approach avoids both the need to explore the entire graph automorphism groups, and to encompass cycle determination, resulting in a very effective computer processing. Applications to several structures, some of them highly symmetrical such as dendrimers, are presented.     

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). III. Topological,chemical, and stereochemical coding of molecular structure

A topological code is devised on the basis of the unique topological representation of the molecule described in the preceding two parts of this series.¹ By adding to the topological code additional chemical information on atoms and/or bonds, as well as stereochemical information, a chemical and respectively stereochemical code (SHOC) are also constructed. The advantages of the new linear codes are that they are convention-free codes, preserving the symmetry of molecular graph, and easily implemented either manually or by means of computer programs. By concentrating all topological, chemical, and stereochemical information, our code (SHOC) is more compact and more general than the codes based on several separate lists.     

Encoding of polycyclic Si-containing molecules for determining species uniqueness in automated mechanism generation

Automated mechanism generation is an attractive way to understand the fundamental kinetics of complex reaction systems such as silicon hydride clustering chemistry. It relies on being able to tell molecules apart as they are generated. The graph theoretic foundation allows molecules to be identified using unique notations created from their connectivity. To apply this technique to silicon hydride clustering chemistry, a molecule canonicalization and encoding algorithm was developed to handle complex polycyclic, nonplanar species. The algorithm combines the concepts of extended connectivity and the idea of breaking ties to encode highly symmetric molecules. The connected components in the molecules are encoded separately and reassembled using a depth-first search method to obtain the correct string codes. A revised cycle-finding algorithm was also developed to properly select the cycles used for ring corrections when thermodynamic properties were calculated using group additivity. In this algorithm, the molecules are expressed explicitly as trees, and all linearly independent cycles of every size in the molecule are found. The cycles are then sorted according to their size and functionality, and the cycles with higher priorities will be used to include ring corrections. Applying this algorithm, more appropriate cycle selection and more accurate estimation of thermochemical properties of the molecules can be obtained.     

The electrophoretic properties of a DNA cube and its substructure catenanes.

Electrophoretic properties have been measured for a DNA molecule whose helix axes have the connectivity of a cube. This molecule is a topologically bonded complex of six cyclic 80-mer molecules, in which each cycle corresponds to a face of the cube. Each cyclic molecule is doubly catenated to each of its four neighbors. Substructures of this molecule include a 5-cycle structure lacking one strand, two topoisomers of 4-cycle structures and two topoisomers of 3-cycle structures. One 4-cycle structure is a cyclic belt around the cube, lacking a top and a bottom, whereas the other lacks two catenated strands, such as the top and the front. One 3-cycle structure is a linear belt of three cycles, and the other corresponds to the three cycles that surround a corner. Each of these molecules is separable from the others under appropriate gel conditions. We have measured mobilities and calculated Ferguson plots for each of these molecules on polyacrylamide gels under both native and denaturing conditions. The measurements have been made with 1.25, 2.5, and 5% crosslinking of the gels. The data show that the higher-symmetry 3-cycle and 4-cycle structures migrate more slowly than their lower-symmetry isomers, under conditions where their Ferguson plots are parallel.