e-book

A primer on mathematical models in biology

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It was on a placid canoe trip at a Gordon Conference in 2002 that Lee Segel told me that
he was writing a new book in mathematical biology. In the prime of his health and at the
peak of his mathematical career, Lee asked me to agree to act as shepherd to this book “in
case” anything happened to prevent his completion of the project. The request was purely
“academic” at that time, and I agreed to this formal arrangement with the certainty that it
would require no actual work. It came as a great shock that Lee Segel passed away on
January 31, 2005, after a sudden and devastating illness. This was a great loss to his many
friends, students, coworkers, and admirers in the applied mathematics and mathematical
biology communities.

Lee Segel had collected material that he had taught over several years at theWeizmann
Institute of Science. Some of it (e.g., biochemical kinetics, neurophysiology) is “classic,”
and part of a solid core of knowledge in mathematical biology. Other parts are newer
additions to this “folklore.” I have endeavored to present Lee’s philosophy and pedagogy
mostly in his own words in Chapters 1, 8–11, and parts of Chapters 2 and 13 with some
insertions, deletions, reordering, editing, and rearranging of the original text. Material that
I deemed to be too specialized or more technical has been moved to Chapter 14 (“For further
study”) at the end of the book, and extended exercises that Lee Segel had composed for
course examinations are now part of a collection in Chapter 15. Some of these problems are
suitable for term projects, and most of them are mentioned in the list of exercises in each
chapter.

I have added new material, including Chapters 3–7. This has made the analysis of
differential equation models and phase plane methods more central to the book. Some
parts of Chapters 3 and 7 were destined by Lee Segel for Appendices, but I have elected
to expand and weave these into the development of the course. Chapter 6 gives one complete
“case study” where the mathematical tools are illustrated on a clear-cut traditional
problem of disease dynamics. This way, the student gains familiarity with working tools
of the trade, and then sees the benefits of these methods in the deeper analysis possible in
Chapters 11–12 of models for excitable systems, bistable switches, and cell cycle oscillations.
In one respect I have changed the flavor of the text considerably, by including some
focus on exploring problems and models with simple simulations. In making or remaking
many of the original figures, I have used simple simulation files (for a popular current
simulation platform, XPP1). These program files are included in Appendix E and online
at www.siam.org/books/SegelLEK. A number of exercises are built on encouraging such
explorations. Students or researchers who use alternative simulation platforms will find
these useful nevertheless, as all needed information (equations, parameter values, initial
conditions, etc.) are preserved for the figures so constructed.

A few difficult decisions had to be made. For instance, a detailed chapter on models
of the cell cycle that Lee Segel had written was out of date and difficult to follow. I replaced
that material with a shorter and slightly modernized approach emphasizing the stepwise
approach to constructing such models and the insights gained through bifurcations and phase
plane simulations. This is now a smaller part of a new chapter on biochemical modules
in Chapter 12. Here I have tried to “pull together the threads” of the book: that is, show
how a number of ideas in previous chapters (enzyme kinetics, dimerization, cooperativity,
bistability, excitable systems, limit cycles, and bifurcations) come together in a few simple
but elegant recent models in cellular and molecular biology. For this reason, the chapter is
placed after material on neurophysiology that Lee had written (but see below for suggestions
on how to use this book that abbreviates some of the above).

When Lee Segel was conceiving and creating this book, the analysis of genetic and
biochemical networks was emerging as a novel hot area of research. He had written two
chapters on discrete networks and Boolean models that spanned some 50 pages. As yet, this
field of computational biology is young, and it is not entirely clear (at least to a nonexpert
like me) which works and ideas will stand the test of time, to become classics. Moreover,
fitting the discrete and continuous approaches together in this book was a challenge. In
deference to Lee, I kept some of this material in a slightly abbreviated version in Chapter 13.

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Ketersediaan

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

New York : Society for Industrial and Applied Mathematics., 2013

Deskripsi Fisik

QH323.5.S43 - 570.1’13--dc23

Bahasa

English

ISBN/ISSN

978-1-611972-49-8

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

BIOLOGI
MODEL MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

Versi lain/terkait

Lampiran Berkas

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