The Geometry of Biological Time

Arthur T. Winfree

800 pages, parution le 01/06/2001 (2^eme édition)

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Résumé

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. Emphasis 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.

Table of contents

	Preface to the 2000 Edition
	Preface to the 1980 Edition
	Introduction
1	Circular Logic	1
2	Phase Singularities (Screwy Results of Circular Logic)	41
3	The Rules of the Ring	80
4	Ring Populations	101
5	Getting off the Ring	146
6	Attracting Cycles and Isochrons	161
7	Measuring the Trajectories of a Circadian Clock	198
8	Populations of Attracting-Cycle Oscillators	229
9	Excitable Kinetics and Excitable Media	258
10	The Varieties of Phaseless Experience: In which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways	303
11	The Firefly Machine	338
12	Energy Metabolism in Cells	347
13	The Malonic Acid Reagent ("Sodium Geometrate")	368
14	Electrical Rhythmicity and Excitability in Cell Membranes	411
15	The Aggregation of Slime Mold Amoebae	443
16	Numerical Organizing Centers	455
17	Electrical Singular Filaments in the Heart Wall	495
18	Pattern Formation in the Fungi	537
19	Circadian Rhythms in General	545
20	The Circadian Clocks of Insect Eclosion	592
21	The Flower of Kalanchoe	624
22	The Cell Mitotic Cycle	632
23	The Female Cycle	650
	Index of Author Citations and Publications	661
	Index of Subjects	761

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Arthur T. Winfree
Parution	01/06/2001
Édition	2^eme édition
Nb. de pages	800
Couverture	Relié
Intérieur	Noir et Blanc
EAN13	9780387989921
ISBN13	978-0-387-98992-1