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This textbook grew out of a course that the highly respected
applied mathematician Lee Segel taught at the Weizmann Institute.
This book represents the unique perspective on mathematical biology
of Segel and his co-author Leah Edelstein-Keshet (author of the
popular SIAM book, Mathematical Models in Biology). It introduces
differential equations, biological applications, and simulations,
with emphasis on molecular events (biochemistry and enzyme
kinetics), excitable systems (neural signals), and small protein
and genetic circuits. The exposition combines clear and useful
mathematical methods with plenty of applications to illustrate the
power of such tools, along with many exercises in reasoning,
modelling and simulation. The reader will also find suggestions for
further study and appendices containing useful background material.
These features make the book ideal for students at the advanced
undergraduate or graduate level in both biology and mathematics who
wish to experience the application of mathematical techniques to
the biological sciences.
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.
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.
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.
A classroom-tested introduction to model analysis of dynamic phenomena that takes a general approach and applies it several times to problems of gradually increasing biological and mathematical complexity.
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.
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