The path from relatively unstructured egg to full organism is one of the most fascinating trajectories in the biological sciences. Its complexity calls for a very high level of organization, with an array of subprocesses in constant communication with each other. These notes introduce an interleaved set of mathematical models representative of research in the last few decades, as well as the techniques that have been developed for their solution. Such models offer an effective way of incorporating reliable data in a concise form, provide an approach complementary to the techniques of molecular biology, and help to inform and direct future research. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Combinatorial chemistry has taken the pharmaceutical industry by storm over the past ten to fifteen years. There has been a massive investment in automation by pharmaceutical companies and a demand for graduates/PhDs with experience and knowledge of combinatorial chemistry. These days the academic education of chemists and biologists is gradually converging, so those entering the pharmaceutical industry need to be not only chemistry graduates but also biologists applying their biological knowledge to chemistry. Many chemists, however, still require experience in biological methods and similarly biologists have not yet realized the power of chemical methods. This book will therefore help ease the transition from biology into chemistry and vice versa, for those working in the combinatorial chemistry field. Because combinatorial chemistry evolved from the requirements of the biology field, the authors have written this book with both biologists and chemists in mind. Combinatorial chemistry is a new and highly influential area of modern synthetic chemistry based on efficient, parallel synthesis of molecules, as opposed to the use of several synthetic steps, to produce many sets of compounds for biological evaluation. The techniques used in this area are key to the discovery of new drug compounds in the pharmaceutical and agrochemical industries. Combinatorial Methods in Chemistry and Biology describes the origins, basics and techniques used both in combinatorial chemistry and molecular biology. Key features: * First book to cover combinatorial methods in both chemistry and biology - ideal for those with either a chemical or biological background. * Introductory text - ideal for newcomers to the field. * Covers a wide swathe of techniques and topics - providing beginners with a complete overview of the field. * Contains chapters on supporting material and linkers, two important areas in the field. * Up-to-date and topical. This volume will be of key interest to technicians/scientists working in the pharmaceutical industry with backgrounds in either biology or chemistry. It will also be invaluable to students - postgraduates studying chemistry and molecular biology or those chemistry/molecular biology undergraduates at universities where combinatorial chemistry is taught as a module.

This IMA Volume in Mathematics and its Applications Applications of Combinatorics and Graph Theory to the Biological and Social Sciences is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with the application of combinatorial ideas to the social and biological sciences. A vner Friedman Willard Miller APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL AND SOCIAL SCIENCES: SEVEN FUNDAMENTAL IDEAS FRED S. RoBERTS* Abstract. To set the stage for the other papers in this volume, seven fundamental concepts which arise in the applications of combinatorics and graph theory in the biological and social sciences are described. These ideas are: RNA chains as "words" in a 4 letter alphabet; interval graphs; competition graphs or niche overlap graphs; qualitative stability; balanced signed graphs; social welfare functions; and semiorders. For each idea, some basic results are presented, some recent results are given, and some open problems are mentioned.

Since the publication of the best-selling Handbook of Molecular and Cellular Methods in Biology and Medicine, the field of biology has experienced several milestones. Genome sequencing of higher eukaryotes has progressed at an unprecedented speed. Starting with baker's yeast (Saccharomyces cerevisiae), organisms sequenced now include human (Homo sa

The enormous complexity of biological systems at the molecular level must be answered with powerful computational methods. Computational biology is a young field, but has seen rapid growth and advancement over the past few decades. Surveying the progress made in this multidisciplinary field, the Handbook of Computational Molecular Biology of

Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the interrelationship between the principal options for encoding phylogenetic trees: split systems, quartet systems and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and are at the basis of much of phylogenetic data processing. This book highlights how each one provides a unique perspective for viewing and perceiving the combinatorial structure of a phylogenetic tree and is, simultaneously, a rich source for combinatorial analysis and theory building. Graduate students and researchers in mathematics and computer science will enjoy exploring this fascinating new area and learn how mathematics may be used to help solve topical problems arising in evolutionary biology.

The cumulative death toll from AIDS has reached 16.3 million individuals, and more than 33 million persons are currently living with HIV-1. Although it is one of the most-widely studied viruses, many mysteries remain about this pathogen. In this comprehensive two-volume set, HIV-1: Molecular Biology and Pathogenesis, leading investigators in HIV research present a timely picture of the molecular mechanisms which guide HIV-1 expression and replication and provide the most current clinical strategies for combating this virus. Twenty-six teams of experts unravel structure-function interactions of HIV-1 with host cells and the resulting pathological consequences, review strategies fo treatment, and describe ongoing progress in developing animal models and prophylactic vaccines.The two volumes, covering viral mechanisms and clinical applications, respectively, are written by an international collection of AIDS expers from North America, Europe, Australia, and Asia. - Detailed insights into viral packaging, expression, and assembly - Mechanistic understanding of how HIV interacts with receptors and infects cells - Delineation of virally encoded regulatory processes unique to HIV - Clinical Applications: - An updated review of current chemotherapeutics for HIV - New concepts in the discovery and design of novel anti-HIV drugs - The latest developments in HIV-vaccine research

This volume features highlights from the DIMACS Special Year on "Mathematical Support for Molecular Biology". Top researchers presented both new research results and comprehensive overviews on the use of mathematics (especially discrete mathematics) and theoretical computer science in molecular biology. The book provides a unique "snapshot" of this growing area of study. It will be of interest to both experts and novices seeking information on the state of the research.