Lee A. Segel - Böcker

In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.

As interest in theoretical biology grows, so does the need for an accessible link between these theories and experiments. The central purpose of this book is to illustrate the premise that examination of the kinetics of biological processes can give valuable information concerning the underlying mechanisms that are responsible for these processes. Topics covered range from co-operativity in protein binding, through receptor-infector coupling, to theories of biochemical oscillations in yeast and slime mould. In addition, an introduction to the explosively growing theoretical topic of chaos details attempts to apply this theory in physiology. The material of this book originally appeared as part of the volume Mathematical Models in Molecular and Cellular Biology (edited by L. A. Segel). However each article has been revised and updated.

Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.

The dynamic development of various processes is a central problem of biology and indeed of all the sciences. The mathematics describing that development is, in general, complicated, because the models that are realistic are usually nonlinear. Consequently many biologists may not notice a possible application of theory. They may be unable to decide whether a particular model captures the essence of a system, or to appreciate that analysis of a model can reveal important aspects of biological problems and may even describe in detail how a system works. The aim of this textbook is to remedy the situation by adopting a general approach to model analysis and applying it several times to problems (drawn primarily from molecular and cellular biology) of gradually increasing biological and mathematical complexity. Although material of considerable sophistication is included, little mathematical background is required - only some exposure to elementary calculus; appendixes supply the necessary mathematics and the author concentrates on concepts rather than techniques. He also emphasizes the role of computers in giving a full picture of model behavior and complementing more qualitative analysis. Some problems suitable for computer analysis are also included. This is a class-tested textbook suitable for a one-semester course for advanced undergraduate and beginning graduate students in biology or applied mathematics. It can also be used as a source book for teachers and a reference for specialists.

In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.

As interest in theoretical biology grows, so does the need for an accessible link between these theories and experiments. The central purpose of this book is to illustrate the premise that examination of the kinetics of biological processes can give valuable information concerning the underlying mechanisms that are responsible for these processes. Topics covered range from co-operativity in protein binding, through receptor-infector coupling, to theories of biochemical oscillations in yeast and slime mould. In addition, an introduction to the explosively growing theoretical topic of chaos details attempts to apply this theory in physiology. The material of this book originally appeared as part of the volume Mathematical Models in Molecular and Cellular Biology (edited by L. A. Segel). However each article has been revised and updated.