Can topological indices transmit information on properties but not on structures?

SummaryA survey of several topological indices (TIs) is provided according to the nature (integers or real numbers) of the local vertex invariants (LOVIs) and of the resulting molecular descriptor (TI). The 1st generation TIs such as the Wiener index when both the LOVIs and the TI are integers have a very high degeneracy. This fact can become an asset for the problem under discussion: when confronted with the “inverse problem” (reverse engineering) such indices lead to a combinatorial explosion of possible solutions. On the other extreme, TIs with very low degeneracy may also offer the possibility to transmit information on properties but not on structures, because they may be too difficult to lend themselves to reverse engineering in a reasonable amount of time. Several such indices are discussed: the novel second-generation index G (derived from the average distance-based connectivity index J in order to include a dependence on graph size and cyclicity), and third-generation indices such as the triplet TI denoted by DN2S(4) or the Kier–Hall index TOTOP. The intercorrelation of these indices is discussed: G is almost linearly-correlated with DN2S(4), and shows a different type of correlation with TOTOP.

[1]  Alexandru T. Balaban,et al.  Chemical graphs , 1979 .

[2]  David T. Stanton,et al.  Evaluation and Use of BCUT Descriptors in QSAR and QSPR Studies , 1999, J. Chem. Inf. Comput. Sci..

[3]  Ovidiu Ivanciuc,et al.  Design of Topological Indices. Part 10.1 Parameters Based on Electronegativity and Covalent Radius for the Computation of Molecular Graph Descriptors for Heteroatom-Containing Molecules , 1998, J. Chem. Inf. Comput. Sci..

[4]  Vladimír Kvasnička,et al.  An improved version of the constructive enumeration of molecular graphs with prescribed sequence of valence states , 1993 .

[5]  P. Schleyer.  Encyclopedia of computational chemistry , 1998 .

[6]  Jean-Loup Faulon,et al.  Isomorphism, Automorphism Partitioning, and Canonical Labeling Can Be Solved in Polynomial-Time for Molecular Graphs , 1998, J. Chem. Inf. Comput. Sci..

[7]  Jean-Loup Faulon,et al.  Stochastic Generator of Chemical Structure. 1. Application to the Structure Elucidation of Large Molecules , 1994, Journal of chemical information and computer sciences.

[8]  L. Hall,et al.  Molecular connectivity in chemistry and drug research , 1976 .

[9]  Sunil Gupta,et al.  Eccentric distance sum: A novel graph invariant for predicting biological and physical properties , 2002 .

[10]  L. Hall,et al.  Molecular Structure Description: The Electrotopological State , 1999 .

[11]  Yu. M. Kiselev,et al.  “Matrix” Stabilization of RhVIIons in the Structure of MIIEVIO4(E = Cr, Mo, W) , 2001 .

[12]  Steven H. Bertz,et al.  Branching in graphs and molecules , 1988, Discret. Appl. Math..

[13]  A. Balaban,et al.  New vertex invariants and topological indices of chemical graphs based on information on distances , 1991 .

[14]  A. Balaban,et al.  Topological Indices for Structure-Activity Correlations , 1983, Steric Effects in Drug Design.

[15]  M. Karelson.  Molecular descriptors in QSAR/QSPR , 2000 .

[16]  F. Burden.  Molecular identification number for substructure searches , 1989, J. Chem. Inf. Comput. Sci..

[17]  Costas D. Maranas,et al.  Optimization in product design with properties correlated with topological indices , 1998 .

[18]  C. Raychaudhury,et al.  Discrimination of isomeric structures using information theoretic topological indices , 1984 .

[19]  Jiri Pospichal,et al.  Simulated Annealing Construction of Molecular Graphs with Required Properties , 1996, J. Chem. Inf. Comput. Sci..

[20]  Igor I. Baskin,et al.  Inverse problem in QSAR/QSPR studies for the case of topological indexes characterizing molecular shape (Kier indices) , 1993, J. Chem. Inf. Comput. Sci..

[21]  Subhash C. Basak,et al.  Topological Indices: Their Nature and Mutual Relatedness , 2000, J. Chem. Inf. Comput. Sci..

[22]  S. Unger.  Molecular Connectivity in Structure–activity Analysis , 1987 .

[23]  Robert S. Pearlman,et al.  Metric Validation and the Receptor-Relevant Subspace Concept , 1999, J. Chem. Inf. Comput. Sci..

[24]  Jiri Pospichal,et al.  Canonical indexing and constructive enumeration of molecular graphs , 1990, J. Chem. Inf. Comput. Sci..

[25]  A. K. Madan,et al.  Prediction of Carbonic Anhydrase Activation by Tri-/Tetrasubstituted-pyridinium-azole Compounds: A Computational Approach using Novel Topochemical Descriptor , 2004 .

[26]  Subhash C. Basak,et al.  Determining structural similarity of chemicals using graph-theoretic indices , 1988, Discret. Appl. Math..

[27]  Alexandru T. Balaban,et al.  Topological indices based on topological distances in molecular graphs , 1983 .

[28]  Jean-Loup Faulon,et al.  The Signature Molecular Descriptor. 2. Enumerating Molecules from Their Extended Valence Sequences , 2003, J. Chem. Inf. Comput. Sci..

[29]  Alexandru T. Balaban,et al.  A new approach for devising local graph invariants: Derived topological indices with low degeneracy and good correlation ability , 1987 .

[30]  Alexandru T. Balaban,et al.  Chapter 5 – A Comparison Between Various Topological Indices, Particularly Between the Index J and Wiener's Index W , 2002 .

[31]  A K Madan,et al.  Topochemical model for prediction of anti-HIV activity of HEPT analogs. , 2005, Bioorganic & medicinal chemistry letters.

[32]  S C Basak,et al.  Complexity of chemical graphs in terms of size, branching, and cyclicity , 2006, SAR and QSAR in environmental research.

[33]  Jean-Loup Faulon,et al.  Stochastic Generator of Chemical Structure, 2. Using Simulated Annealing To Search the Space of Constitutional Isomers , 1996, J. Chem. Inf. Comput. Sci..

[34]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[35]  Subhash C. Basak,et al.  Interrelationship of Major Topological Indices Evidenced by Clustering , 2004 .

[36]  Jean-Loup Faulon,et al.  Developing a methodology for an inverse quantitative structure-activity relationship using the signature molecular descriptor. , 2002, Journal of molecular graphics & modelling.

[37]  Manjit Singh,et al.  Applications of graph theory: Relationship of molecular connectivity index and atomic molecular connectivity index with anti-HSV activity , 2001 .

[38]  Lemont B. Kier,et al.  Design of molecules from quantitative structure-activity relationship models. 3. Role of higher order path counts: Path 3 , 1993, J. Chem. Inf. Comput. Sci..

[39]  Nikolai S. Zefirov,et al.  General methodology and computer program for the exhaustive restoring of chemical structures by molecular connectivity indexes. Solution of the inverse problem in QSAR/QSPR , 1990 .

[40]  Lemont B. Kier,et al.  Determination of Topological Equivalence in Molecular Graphs from the Topological State , 1990 .

[41]  A K Madan,et al.  Topological models for prediction of anti-inflammatory activity of N-arylanthranilic acids. , 2004, Bioorganic & medicinal chemistry.

[42]  Danail Bonchev,et al.  Information theoretic indices for characterization of chemical structures , 1983 .

[43]  M. Leonor Contreras,et al.  Exhaustive generation of organic isomers. 2. Cyclic structures: new compact molecular code , 1992, J. Chem. Inf. Comput. Sci..

[44]  Jean-Loup Faulon,et al.  Stochastic Generator of Chemical Structure. 3. Reaction Network Generation , 2000, J. Chem. Inf. Comput. Sci..

[45]  Lemont B. Kier,et al.  Design of molecules from quantitative structure-activity relationship models. 2. Derivation and proof of information transfer relating equations , 1993, J. Chem. Inf. Comput. Sci..

[46]  E Uriarte,et al.  Recent advances on the role of topological indices in drug discovery research. , 2001, Current medicinal chemistry.

[47]  Vladimír Kvasnička,et al.  Constructive enumeration of molecular graphs with prescribed valence states , 1991 .

[48]  Giuseppe Lancia,et al.  Algorithmic strategies in combinatorial chemistry , 2000, SODA '00.

[49]  M. Randic.  Characterization of molecular branching , 1975 .

[50]  H. Hosoya.  Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons , 1971 .

[51]  Jean-Loup Faulon,et al.  The signature molecular descriptor. 3. Inverse-quantitative structure-activity relationship of ICAM-1 inhibitory peptides. , 2003, Journal of molecular graphics & modelling.

[52]  N. Trinajstic,et al.  Information theory, distance matrix, and molecular branching , 1977 .

[53]  Lemont B. Kier,et al.  Design of molecules from quantitative structure-activity relationship models. 1. Information transfer between path and vertex degree counts , 1993, J. Chem. Inf. Comput. Sci..

[54]  A. K. Madan,et al.  Predicting anti-HIV activity of phenethylthiazolethiourea (PETT) analogs: computational approach using Wiener's topochemical index , 2004 .

[55]  Roberto Todeschini,et al.  Handbook of Molecular Descriptors , 2002 .

[56]  A. Balaban.  Highly discriminating distance-based topological index , 1982 .

[57]  Igor I. Baskin,et al.  On the Basis of Invariants of Labeled Molecular Graphs , 1995, J. Chem. Inf. Comput. Sci..

[58]  Igor I. Baskin,et al.  INVERSE PROBLEM IN THE STRUCTURE-PROPERTY RELATIONSHIP ANALYSIS FOR THE CASE OF INFORMATION TOPOLOGICAL INDICES , 1997 .

[59]  D. Rouvray,et al.  Topology in Chemistry: Discrete Mathematics of Molecules , 2002 .

[60]  F. Harary,et al.  Chemical graphs—V : Enumeration and proposed nomenclature of benzenoid cata-condensed polycyclic aromatic hydrocarbons , 1968 .

[61]  M. Leonor Contreras,et al.  Exhaustive generation of organic isomers. 1. Acyclic structures , 1992, J. Chem. Inf. Comput. Sci..

[62]  Vladimir A. Palyulin,et al.  Inverse Structure–Property Relationship Problem for the Case of a Correlation Equation Containing the Hosoya Index , 2001 .

[63]  J P Doucet,et al.  Application of topological descriptors in QSAR and drug design: history and new trends. , 2002, Current drug targets. Infectious disorders.

[64]  Gilles Klopman,et al.  Vertex indexes of molecular graphs in structure-activity relationships: a study of the convulsant-anticonvulsant activity of barbiturates and the carcinogenicity of unsubstituted polycyclic aromatic hydrocarbons , 1990, J. Chem. Inf. Comput. Sci..

[65]  L. Pogliani.  From molecular connectivity indices to semiempirical connectivity terms: recent trends in graph theoretical descriptors. , 2000, Chemical reviews.

[66]  A. Balaban,et al.  Topological Indices and Related Descriptors in QSAR and QSPR , 2003 .

[67]  Robert D. Carr,et al.  The Signature Molecular Descriptor. 4. Canonizing Molecules Using Extended Valence Sequences , 2004, J. Chem. Inf. Model..