From Chemical Topology To Three Dimensional Geometry

Even high-speed supercomputers cannot easily convert traditional two-dimensional databases from chemical topology into the three-dimensional ones demanded by today's chemists, particularly those working in drug design. This fascinating volume resolves this problem by positing mathematical and topological models which greatly expand the capabilities of chemical graph theory. The authors examine QSAR and molecular similarity studies, the relationship between the sequence of amino acids and the less familiar secondary and tertiary protein structures, and new topological methods.

Topology is becoming increasingly important in chemistry because of its rapidly growing number of applications. Here, its many uses are reviewed and the authors anticipate what future developments might bring. This work shows how significant new insights can be gained by representing molecular species as topological structures known as topographs. The text explores carbon structures, establishing how the stability of fullerene species can be accounted for and also predicting which fullerenes will be most stable. It is pointed out that molecular topology, rather than molecular geometry, characterizes molecular shape and various tools for shape characterization are described. Several of the fascinating ideas that arise from regarding topology as a unifying principle in chemical bonding theory are discussed, and in particular, the novel concept of the molecular topoid is shown to have numerous uses. The topological description of polymers is examined and the reader is gently guided through the realms of branched and tangled polymers. Overall, this work outlines the fact that topology is not only a theoretical discipline but also one that has practical applications and high relevance to the whole domain of chemistry.

As a result of new statistical and mathematical approaches, improved visualization tools, and recognition by international regulatory groups, quantitative structure-activity relationships (QSARs) now play important roles in pharmacology for the design of new drugs as well as in toxicology and ecotoxicology for hazard identification and risk assessm

Topological Indices and Related Descriptors in QSAR and QSPR reviews the state of the art in this field and highlights the important advances in the generation of descriptors calculated directly from the structure of molecules. This long-awaited comprehensive book provides all the necessary information to calculate and use these descriptors for deriving structure-activity and structure-property relationships. Written by leading experts in the field, this book discusses the physicochemical significance, strengths, and weaknesses of these indices and presents numerous examples of applications. This book will be a valuable reference for anyone involved in the use of QSAR and QSPR in the pharmaceutical, applied chemical, and environmental sciences. It is also suitable for use as a supplementary textbook on related graduate level courses.

The series Advances in Dendritic Macromolecules aims to cover the synthesis and supramolecular chemistry of dendritic or cascade super-molecules as well as their less perfect hyperbranched cousins. The field of hyperbranched macromolecules, specifically dendrimers, has continued to expand at an amazing rate. The synthetic aspects, which were assumed to be over several years ago, have opened new avenues into the mesomolecular regime. The synthetic ingenuity of chemical artists has afforded new monomers and their diverse combinations to give rise to (poly)functionalized materials that embrace new supramolecular concepts in areas such as molecular recognition, assembly, encapsulation, and inclusion; catalysts; coatings; drug delivery systems; and in essence opens up the field of suprasupermolecular chemistry. In chapter 1 the synthesis of organometallic and related transition metal-cotaining dendrimers is summarized and their novel properties and useful applications are described. Chapter 2 covers work on the commercial poly(propylene imine)s, including the "dendritic box", dendrimer-based superamphiphiles, and unimolecular inverse micelles. The next chapter looks at aspects of chirality in dendritic systems and this is followed by a look inside dendrimers from a molecular topologist's point-of-view.

Solved and Unsolved Problems of Structural Chemistry introduces new methods and approaches for solving problems related to molecular structure. It includes numerous subjects such as aromaticity—one of the central themes of chemistry—and topics from bioinformatics such as graphical and numerical characterization of DNA, proteins, and proteomes. It also outlines the construction of novel tools using techniques from discrete mathematics, particularly graph theory, which allowed problems to be solved that many had considered unsolvable. The book discusses a number of important problems in chemistry that have not been fully understood or fully appreciated, such as the notion of aromaticity and conjugated circuits, the generalized Hückel 4n + 2 Rule, and the nature of quantitative structure–property–activity relationships (QSARs), which have resulted in only partially solved problems and approximated solutions that are inadequate. It also describes advantages of mathematical descriptors in QSAR, including their use in screening combinatorial libraries to search for structures with high similarity to the target compounds. Selected problems that this book addresses include: Multiple regression analysis (MRA) Insufficient use of partial ordering in chemistry The role of Kekulé valence structures The problem of protein and DNA alignment Solved and Unsolved Problems of Structural Chemistry collects results that were once scattered in scientific literature into a thoughtful and compact volume. It sheds light on numerous problems in chemistry, including ones that appeared to have been solved but were actually only partially solved. Most importantly, it shows more complete solutions as well as methods and approaches that can lead to actualization of further solutions to problems in chemistry.

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Quantitative studies on structure-activity and structure-property relationships are powerful tools in directed drug research. In recent years, various strategies have been developed to characterize and classify structural patterns by means of molecular descriptors. It has become possible not only to assess diversities or similarities of structure databases, but molecular descriptors also facilitate the identification of potential bioactive molecules from the rapidly increasing number of compound libraries. They even allow for a controlled de-novo design of new lead structures. This is the most comprehensive collection of molecular descriptors and presents a detailed review from the origins of this research field up to present day. This practically oriented reference book gives a thorough overview of the different molecular descriptors representations and their corresponding molecular descriptors. All descriptors are listed with their definition, symbols and labels, formulas, some numerical examples, data and molecular graphs, while numerous figures and tables aid comprehension of the definitions. Cross-references throughout, a list of acronyms and notations allow easy access to the information needed to solve a specific research problem. Examples of descriptor calculations along with tables of descriptor values for a set of selected reference compounds and an up-to-date reference list add to the practical value of the book, making it an invaluable guide for all those dealing with bioactive molecules as well as for researchers.