Philip K. Maini - Böcker

Very Short Introductions: Brilliant, Sharp, Inspiring Why are English Premier League football shirt patterns very similar to animal coat markings? And what do invasive species have in common with cancer cells in the body? Mathematical biology develops models which answer these questions, as they are applied to processes from the spread of a gene in a population, to predator-prey dynamics in an ecosystem, to the growth of tumours. In this Very Short Introduction Philip K. Maini describes the art of modelling, what it is, why we do it, and illustrates how the abstract way of thinking that is the essence of mathematics enables us to transfer knowledge from one area of research to another. Using numerous examples, he explains how the same fundamental ideas have been used in different fields, and shows how mathematics is the language of science. The author also points to cases in science where the traditional scientific modelling approach - verbal reasoning - is incorrect and shows how mathematics can uncover, and correct, such flawed reasoning while, at the same time, enhance our intuition. This book provides a guide to the trajectory of mathematical biology from a niche subject in the 1970s to a well-established, popular subject that is truly inter-disciplinary, and points to exciting future challenges.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

The formation of patterns in developing biological systems involves the spatio-temporal coordination of growth, cell-cell signalling, tissue movement, gene expression and cell differentiation. The interactions of these complex processes are generally nonlinear, and this mathematical modelling and analysis are needed to provide the framework in which to compute the outcome of different hypothesis on modes of interaction and to make experimentally testable predictions. This collection contains papers exploring several aspects of the hierarchy of processes occurring during pattern formation. A number of papers address the modelling of cell movement and deformation, with application to pattern formation within a collection of cells in response to external signalling cues. The results are considered in the context of pattern generation in Dictyostelium discoideum and bacterial colonies. A number of models at the macroscopic level explore the possible mechanisms underlying spatio-temporal pattern generation in early development, focussing on primitive streak, somitogenesis, vertebrate limb development and pigmentation patterning.The latter two applications consider in detail the effects of growth on patterning. The potential of models to generate more complex patterns are considered and models involving different modes of cell-cell signalling are investigated. Pattern selection is analyzed in the context of chemical Turing patterns, which serve as a paradigm for morphogenesis and a model for vegetation patterns is presented.

The Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences.

This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro­ grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em­ phasis on "Theoretical Problems in Developmental Biology and Immunol­ ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro­ gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro­ gram possible.

This volume contains the proceedings of the NATO ARW on 'Biological Pattern Formation' held at Merton College, University of Oxford, on 27-31 August, 1992. The objective of the workshop was to bring together a select group of theoreticians and experimental biologists to present the latest results in the area of biological pattern formation and to foster interactiqn across dis- plines. The workshop was divided into 5 main areas: (i) limb development, (ii) Dictyostelium discoideum, (iii) Drosophila, (iv) cell movement, (v) g- eral pattern formation. We thank all the participants for their contributions, enthusiasm, and willingness to collaborate. There was a genuine, open, and extremely fru- ful interaction between the experimentalists and theoreticians which made the workshop a success. We also thank The Welcome Trust for providing additional funding. The local organization fell mainly on Denise McKittrick and Beverley Bhaskhare at the Mathematical Institute, Oxford, and Jeanette Hudson and the staff of Merton College. We greatly appreciate their help and patience. We also thank Jonathan Sherratt, Wendy Brandts and Debbie Benson for helping out in the conference and for providing a happy welcome to parti- pants on a typically cold, wet and windy English summer day.