From Chemical Topology to Three-Dimensional Geometry

Transcription

1 From Chemical Topology to Three-Dimensional Geometry Edited by Alexandru T. Balaban Polytechnic University Bucharest, Romania and Academia Romänä Bucharest, Romania Plenum Press New York and London

2 Contents 1. From Chemical Graphs to 3D Molecular Modeling Alexandru T. Balaban 1.1. Constitutional Isomers, Stereoisomers, and Conformers Staggered Conformers of Alkanes and Diamond Hydrocarbons D and 3D Topological Indices Grid Coordinates and Molecular ID Numbers cis/trans Isomers of Alkenes, Cycloalkanes, and Congeners Molecular Topographie Indices and Configuration of Annulenes Data Bases for 3D Chemical Structures Similarity Searches in Files of 3D Chemical Structures D Protein Structure 18 References Descriptors of Molecular Shape in 3D Paul G. Mezey 2.1. Introduction Electronic Density, the Composite Nuclear Potential, and the Somoyai Function Three-Dimensional Shape Characterizations of Molecular Functions p(r), V n (r) and S(r,s) A Shape Representation of Macromolecules Shape-Energy Relations for the Computation of Forces and Geometry Optimization Based on Macromolecular Electronic Densities and the Electrostatic Theorem Summary 40 References 40 xi

3 xii Contents 3. 3D Molecular Design: Searching for Active Conformers in QSAR Ovanes G. Mekenyan and Gilman D. Veith 3.1. Introduction Algorithms for 3D Molecular Design D Input Geometry Approaches to 3D Molecular Design Interactive Methods Template-Based Methods Template-Free Methods Exhaustive Conformational Searching Methods Active Conformer Searches with the Dynamic Method Applications of the Dynamic Method Ah Receptor Binding Semicarbazide Toxicity in Frog Embryos Photoinduced Toxicity of a,a'-terthienyls Concluding Remarks 68 References Use of Graph-Theoretic and Geometrical Molecular Descriptors in Structure Activity Relationships Subhash C. Basak, Gregory D. Grunwald, and Gerald J. Niemi 4.1. Introduction Topological Indexes and QSAR Physicochemical Properties Boiling Point of Alkanes Boiling Point of Chlorofluorocarbons (CFCs) Lipophilicity of Diverse Sets of Compounds Chromatographie Retention Time of Alkanes, Alkylbenzenes Biomedicinal Properties Anesthetic Dose (AD 50 ) of Barbiturates Analgesie Potency (A-ED 50 ) of Barbiturates Enzymatic Acetyl Transfer Reaction Hill Reaction Inhibitory Potency of Triazinones Complement Inhibition by Benzamidines Binding of Barbiturates to Cytochrome P Toxicological Properties Nonspecific Narcotic Activity of Alcohols Nonspecific Toxicity of Esters to Pimephalespromelas Mutagenicity of Nitrosamines 82

4 Contents xiii Mutagenicity of Diverse Structures Toxicity of Monoketones Inhibition ofp-hydroxylation of Aniline by Alcohols Topological Approaches to Molecular Similarity Quantification of Similarity Using Path Numbers Quantification of Similarity Using Topological Indexes Quantification of Intermolecular Similarity Using Substructural Parameters Atom Pairs (APs) Similarity Methods Based on Substructures K Nearest-Neighbor (KNN) Method of Estimating Properties Geometrical/Shape Parameters in SAR van der Waals Volume (V w ) Physicochemical Properties Biomedicinal Properties Toxicological Properties Comparative Molecular Field Analysis (CoMFA) Approach Comparative Study of Topological versus Geometncal Descriptors in QSARs Property Data Bases Boiling Point Lipophilicity (logp, Octanol-Water) Mutagenicity (ln/j) Calculation of Parameters Computation of Topological Indexes Computation of Geometrical Parameters Computation of HB! Statistical Methods Index Selection Regression Analysis Results Boiling Point Lipophilicity (logp) Mutagenicity Discussion 111 References Recognition of Membrane Protein Structure from Amino Acid Sequence Bono Lucic, Nenad Trinajstic, and Davor Juretic 5.1. Introduction Investigations of the Structure of Membrane Proteins 119

5 xiv Contents Experimental Approaches The X-Ray Diffraction Method Electron Microscopy of 2D Crystals Experimental Methods for the Determination of the Topography and Topology of Membrane Protein Theoretical Approaches The Preference Functions Method Training and Testing Sets of Membrane Proteins Performance Measures Propensity Values Normal Approximation for Frequency Distribution of Amino Acid Residues over Local Sequence Environment The Definition of Preference Functions in the PREF Method (Version 2.0) Filtering the Prediction Results and Examples Illustrating the Prediction Accuracy Prediction Accuracy of the Transmembrane Segments on the Training and Testing Data Sets A Comparison of the Preference Functions Method with the Neural Network (NN) Method Predictions for Proteins with Known 3D Structure Insufficiently Reliable SWISS-PROT Structures of Membrane Proteins Predictions for Proteins for Which, According to the SWISS-PROT Data Bank, Structure and Topology Are Not Known Concluding Remarks 151 References On Characterization of 3D Molecular Structure Milan Randic and Marko Razinger 6.1. The Nature of the Chemical Structure Molecular Codes and Molecular Representation Molecular Graphs Molecular Invariants and Molecular Characterization Molecular Structure Basis Orthosimilarity Beyond Graph Theory D/D Matrices Linear Chains Conformations of «-Chains in a Plane Folding of Mathematical Curves 188

6 Contents xv Similarity Based on D/D Matrices Invanants Derived from the Molecular Geometry Molecular Profiles Bond Profiles Contour Profiles Shape Profiles Chromatographie Retention Indices Are Chromatographie Retention Indices Shape Dependent? Periphery Codes Similarity Derived from Periphery Codes Chirality 223 References Chemical Graph Theory of Fullerenes Patrick W. Fowler 7.1. Introduction The Isomer Problem What Is a Fullerene? How Many Fullerenes Are There? Fullerene NMR Spectra Electronic Structure The Model Types of Electronic Structure The Leapfrog Rule and Electron Deficiency The Carbon Cylinder Rule Sporadic Closed Shells Adequacy of the Electronic Model? Stability and Structure The Minimum Pentagon-Adjacency Rule Beyond the Isolated-Pentagon Rule Beyond the Hexagon-Neighbor Rule Perspective 259 References Recent Work on Toroidal and Other Exotic Fullerene Structures E. C. Kirby 8.1. Introduction Some General Principles and Definitions Types of Isomerism 267

7 xvi Contents 8.4. Some Useful Fundamental Relationships Conceptual Construction Folding and Gluing Toward a Characterization of the Planar Polyhex Precursor of a Toroidal Polyhex Stitching Tiling Modification of an Already Existing Lattice Isomorphism Enumeration The Drawing of Toroidal Fullerenes Some Particular Classes of Structure Toroidal Fullerenes A Three-Integer Code for Toroidal Polyhexes Properties of the 2x2 Toroidal Polyhex Matrix Klein Bottles Double Tori Helical Tubes Matters Relating to the Energy and Stability of Toroidal Fullerenes Adjacency Matrices and Their Eigenvalues for Toroidal Polyhexes Aspects of Hückel Spectrum Values Kekule Structures of Toroidal Polyhexes Fully Arenoids Ab Initio Calculations Molecular Mechanics The Effects on a Finite Lattice of Having No Periphery Concluding Remarks 293 References All-Conjugated Carbon Species Douglas J. Klein and Hongyao Zhu 9.1. Introduction History and Motivation Preview Graphico-Topological View of Chemical Structure General Three-Stage Description Examples Elaboration Invariants and Relations Graphico-Topological Invariants 307

8 Contents xvii Differential-Geometrie Invariants and Strain Curvature Mismatch Closed Surfaces General Theorematic Results Polyhedra Fullerenes Toroidal Surfaces Other Closed Surfaces Extended Structures Pure-Digonal One-Dimensionally Extended Structures Pure-Trigonal One-Dimensionally Extended Structures Pure-Trigonal Graphically Planar Sheets Pure-Trigonal Uniformly Negatively Curved Networks Transformations and Decorations Isomerizations and Stone-Wales Rearrangement Edge Deletions Leapfrog Transformations Transformation Algebra Poly-yne Replacements Joining Pairs of Cycles Face-to-Face Twist-Couplings Overview 334 References Applications of Topology and Graph Theory in Understanding Inorganic Molecules R. Bruce King Introduction Coordination Polyhedra Polyhedral Topology Atomic Orbitals and Their Quantum Numbers Polyhedra for Coordination Numbers from Four to Nine Polyhedral Isomerizations Polyhedral Boranes: 3D Aromaticity Graph Theory and Hückel Theory Application to the Deltahedral Boranes Fluxionality in Deltahedral Boranes Electron-Rich (Hyperelectronic) Polyhedral Boranes Tensor Surface Harmonie Theory Kekule-Type Structures in Polyhedral Boranes 376

9 xviii Contents Metal Carbonyl Clusters Metal Carbonyl Vertices and Electron Counting in Metal Carbonyl Clusters Electron-Poor (Hypoelectronic) Metal Carbonyl Clusters Metal Carbonyl Clusters Having Interstitial Atoms Metal Carbonyl Clusters Consisting of Fused Octahedra Coinage Metal Clusters Anisotropie Valence Orbital Manifolds in Coinage Metals and Other Post-Transition Elements Centered Gold Clusters Coinage Metal Alkyls and Aryls Coinage Metal Derivatives of Metal Carbonyls Post-Transition Element Clusters Bare Ionic Post-Transition Metal Clusters: Zintl Phases Polyhedral Clusters Containing the Heavier Congeners of Boron: Novel Hypoelectronic Polyhedra in Indium and Thallium Intermetallics Polyoxometalates: Binodal Orbital Aromaticity Structural Aspects of Polyoxometalates Binodal Orbital Aromaticity 408 References 410 Index 415