Novel topological index F based on incidence matrix

Based on incidence matrix W, the novel topological index F is defined by the matrices L, W, X as F = LWX. The properties, the chemical environments, and the interaction of the vertexes in a molecule are taken into account in this definition. Several good QSPR models in the hetero-atom-containing organic compounds and inorganic compounds are obtained. Moreover, based on the definition of F and the values C(i) of the vertexes or the values (m)F(ij) of the chemical bonds, we have obtained serial indices, (m)F(v), (m)F(b), and F(w). They are successfully applied to QSPR models and good correlation results have been obtained as well.     

Fidelity of the protein structure reconstruction from inter-residue proximity constraints

Inter-residue proximity constraints obtained in such experiments as cross-linking/mass spectrometry are important sources of information for protein structure determination. A central question in structure determination using these constraints is, What is the minimal number of inter-residue constraints needed to determine the fold of a protein? It is also unknown how the different structural aspects of constraints differentiate their ability in determining the native fold and whether there is a rational strategy for selecting constraints that feature higher fidelity in structure determination. To shed light on these questions, we study the fidelity of protein fold determination using theoretical inter-residue proximity constraints derived from protein native structures and the effect of various subsets of such constraints on fold determination. We show that approximately 70% randomly selected constraints are sufficient for determining the fold of a domain (with an average root-mean-square deviation of 相似文献   

Molecular topology. IV. Regressive vertex degrees (new graph invariants) and derived topological indices

New local graph invariants, “regressive vertex degrees” (which are slightly augmented vertex degrees) are introduced on the basis of decreasing contributions of more remote vertexes to the classical vertex degrees. Several such invariants are proposed (BR, ER, SR) where t (either t = 1 or t = 2) is an operator expressing the attenuation with increasing topological distance, according to formula (1) or (2). With the aid of these new local invariants, new topological indices (global graph invariants), Y (namely BY, EY or SY) are introduced and exemplified. Their ability to express the branching and to order alkanes is investigated. An appendix gives some recursive relationships for computing these indices.     

The multiplicative version of the Wiener index

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, pi(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the pi index are established and its possible physicochemical applications examined. In the case of alkanes, pi and W are highly correlated; a slightly curvilinear correlation exists between In pi and W.     

Application to QSAR studies of 2-furylethylene derivatives

A quantitative structure–activity relationship (QSAR) is a mathematical model that relates a molecular structure to a physicochemical property or a biological activity. The log P of a set of 38 of 2-furylethylenes, biologically active substances exhibiting a broad spectrum of antimicrobial, antiparasitic, cytotoxic, carcinogenic and mutagenic activities, was modeled by using topological indices provided by TOPOCLUJ and DRAGON software packages. The models derived showed good stability and predictability (as given by the leave-one-out LOO cross-validation data). The results are compared with those reported in literature, obtained by different methodology.     

Surface immobilization and mechanical properties of catanionic hollow faceted polyhedrons

We report here for the first time on surface immobilization of hollow faceted polyhedrons formed from catanionic surfactant mixtures. We find that electrostatic interaction with the substrate dominates their adhesion behavior. Using polyelectrolyte coated surfaces with tailored charge densities, polyhedrons can thus be immobilized without complete spreading, which allows for further study of their mechanical properties using AFM force measurements. The elastic response of individual polyhedrons can be locally resolved, showing pronounced differences in stiffness between faces and vertexes of the structure, which makes these systems interesting as models for structurally similar colloidal scale objects such as viruses, where such effects are predicted but cannot be directly observed due to the smaller dimensions. Elastic constants of the wall material are estimated using shell and plate deformation models and are found to be a factor of 5 larger than those for neutral lipidic bilayers in the gel state. We discuss the molecular origins of this high stiffness.     

Some novel neighborhood degree sum-based versus degree-based topological indices in QSPR analysis of alkanes from n-butane to nonanes

The topological indices are reported to be very useful in various QSPR studies as these indices can be utilized as a tool to predict the physicochemical properties of a diverse set of chemical compounds. The objective of this communication is twofold. First, to introduce some neighborhood degree sum-based topological indices and perform a comparative QSPR analysis of the indices with their corresponding degree-based topological indices to analyze the usefulness of the new indices. Second, to investigate isomer discrimination ability of the newly defined indices on the basis of degeneracy test. Neighborhood degree sum-based topological indices not only consider the degree of each atom in the molecule but also the degrees of its neighboring atoms. Moreover, these indices are expected to provide information about how connected and dense the neighborhoods of atoms are within the molecule. In this study, we observe that the proposed neighborhood degree sum-based topological indices exhibit better correlation with some physicochemical properties of Octane Isomers and 66 alkanes as compared to their corresponding degree-based topological indices. Also, the supremacy in terms of sensitivity of the neighbourhood degree sum-based topological indices as compared to the classical degree-based ones is established.     

Ad hoc optimal topological indices for QSPR

Optimal topological indices for particular physicochemical properties can be designed using the chemical structure matrix. Taking the alkane boiling points as examples, the extrapolation properties of some well-known topological indices were compared with those of the optimal topological indices designed ad hoc. The advantages of the new indices are shown. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1454–1461, September, 2006.     

Analytical expressions for topological properties of polycyclic benzenoid networks

Quantitative structure‐activity and structure‐property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure‐based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure‐activity and structure‐property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex‐degree and edge‐based topological indices such as edge‐Wiener, vertex‐edge Wiener, vertex‐Szeged, edge‐Szeged, edge‐vertex Szeged, total‐Szeged, Padmakar‐Ivan, Schultz, Gutman, Randić, generalized Randić, reciprocal Randić, reduced reciprocal Randić, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom‐bond connectivity, harmonic, sum‐connectivity, and geometric‐arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram‐like polycyclic benzenoid networks.     

Description of oxygen permeability in various high polymers using a graph theoretical approach

Graph theory methods are shown to complement group additivity methods of predicting oxygen permeability in certain types of polymers. Graph theory is a topological approach that assigns a set of indices to a molecule to describe its structure. Since many physical properties of molecules depend upon their structure, graph theory indices can be used to describe important properties of molecules. In this work a set of graph theory indices are used to describe the property of a polymer based on a modified representation of the monomer unit. More specifically, Randic indices are used to describe the log of the oxygen permeability with 3.2% average relative error. Polymers comprising the basis set contain backbones of sp², sp³, or aromatic carbons, oxygen, or silicon and have substituents that contain chloride, fluoride, alkyl groups, hydrogen, oxygen, aromatic carbons, or chloro and/or fluoro substituted alkyl groups. The correlation coefficient (R²) (0 ≤ R² ≤ 1) of a nonlinear model is 0.91. The graph theory method for describing the oxygen permeability of these selected groups of polymers is in good agreement with that predicted by the permachor model. The permachor method makes oxygen permeability predictions based upon group additivity and distinguishes the degree of crystallinity of a polymer by empirically assigning different permachor (π) values to identical groups based upon the polymer crystallinity. The inability of graph theory to explain the remaining 9% of the scatter in the data is probably due to failure to incorporate into the graph theory model terms which quantify crystallinity.     

Structural interpretation of the topological index. 2. The molecular connectivity index, the Kappa index, and the atom-type E-State index

The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type E-State index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type E-State indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.