The Geometry of Biological Time: 12 (Interdisciplinary Applied Mathematics, 12) - Hardcover

Winfree, Arthur T.

Hardcover

ISBN 10: 0387989927 ISBN 13: 9780387989921

Publisher: Springer, 2001

Synopsis

From cell division to heartbeat, clocklike rhythms pervade the activities of every living organism. The cycles of life are ultimately biochemical in mechanism but many of the principles that dominate their orchestration are essentially mathematical. The Geometry of Biological Time describes periodic processes in living systems and their non-living analogues in the abstract terms of nonlinear dynamics. Enphasis is given in phase singularities, waves, and mutual synchronization in tissues composed of many clocklike units. Also provided are descriptions of the best-studied experimental systems such as chemical oscillators, pacemaker neurons, circadian clocks, and excitable media organized into biochemical and bioelectrical wave patterns in two and three dimensions. No theoretical background is assumed; the required notions are introduced through an extensive collection of pictures and easily understood examples. This extensively updated new edition incorporates the fruits of two decades' further exploration guided by the same principles. Limit cycle theories of circadian clocks are now applied to human jet lag and are understood in terms of the molecular genetics of their recently discovered mechanisms. Supercomputers reveal the unforeseen architecture and dynamics of three-dimensional scroll waves in excitable media. Their role in life-threatening electrical aberrations of the heartbeat is exposed by laboratory experiments and corroborated in the clinic. These developments trace back to three basic mathematical ideas.

About this title

Review:

"This book is a wonderful exposition about his life s work and is presented with such clarity that the reader gains an insight into details of his manner of thinking...the reader is taken on a quest to solve biological mysteries and travels from the intricate beginnings of formulating the questions, through the apices and troughs of analyzing, and on to the discovery of the holy grail, that which yields biological predictions and answers. One leaves with a sense of understanding that hopefully can be applied to one s own work...this book could easily serve a dual purpose. First, through the introduction of basic mathematical concepts such as topology combined with modeling, the book serves as an introduction helping the non-applied reader to see the beauty of mathematical modeling. Second, because Winfree explains the modeling process very thoroughly, instead of just presenting equations, the book can serve as a medium for the medical professional to acquire an understanding of the modeling process. A wonderful accomplishment...I am proud to have this book on my shelf and consider it...a seminal text in mathematical modeling. This is a text that every first year graduate student should look at in some detail." --Mathematical Reviews

Synopsis:

"Geometry of Biological Time" deals with dynamics of processes that repeat themselves regularly. Such rhythmic return through a cycle of change is an ubiquitous principle of organization in living systems. In this revised and updated edition, the author plans to extend the thread from 1980 to the present concentrating on areas which he personally feels have been interesting and where he feels there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities that the original book introduced. In particular, the work on excitability in cell membranes has been thoroughly updated as have the references throughout the book.

About this edition

• Publisher: Springer
• Publication date: 2001
• ISBN 10: 0387989927
• ISBN 13: 9780387989921
• Binding: Hardcover
• Edition number: 2
• Number of pages: 805