The Geometry of Biological TimeSpringer Science & Business Media, 08/06/2001 - 779 من الصفحات 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. |
المحتوى
Circular Logic | 1 |
Mappings | 4 |
Phase Singularities of Maps | 24 |
Technical Details on Application to Biological Rhythms | 30 |
Phase Singularities Screwy Results of Circular Logic | 41 |
Examples | 42 |
Counterexamples | 75 |
The Word Singularity | 77 |
Wave Phenomena | 377 |
Excitation in Nonoscillating Medium | 382 |
Wave Patterns in Twoand ThreeDimensional Context | 383 |
Pacemakers | 406 |
Electrical Rhythmicity and Excitability in Cell Membranes | 411 |
Rephasing Schedules of Pacemaker Neurons | 413 |
Mutual Synchronization | 422 |
Waves in One Dimension | 428 |
The Rules of the Ring | 80 |
Dynamics on the Ring | 83 |
Derivation of PhaseResetting Curves | 88 |
Historical Appendix | 97 |
Ring Populations | 101 |
Communities of Clocks | 119 |
Spatially Distributed Independent Simple Clocks | 134 |
Ring Devices Interacting Locally | 138 |
Getting off the Ring | 146 |
Deducing the Topology | 147 |
The Simplest Models | 149 |
Mathematical Redescription | 151 |
Graphical Interpretation | 155 |
Summary | 159 |
Attracting Cycles and Isochrons | 161 |
Perturbing an AttractingCycle Oscillator | 177 |
Unsmooth Kinetics | 188 |
Measuring the Trajectories of a Circadian Clock | 198 |
The Time Machine Experiment | 200 |
Unperturbed Dynamics | 206 |
The Impact of Light | 213 |
Deriving the Pinwheel Experiment | 216 |
So What? | 220 |
In Conclusion | 228 |
Populations of AttractingCycle Oscillators | 229 |
Collective Rhythmicity in a Population of Independent Oscillators How Many Oscillators? | 230 |
Collective Rhythmicity in a Community of AttractingCycle Oscillators | 231 |
Spatially Distributed Independent Oscillators | 236 |
AttractingCycle Oscillators Interacting Locally in TwoDimensional Space | 250 |
Excitable Kinetics and Excitable Media | 258 |
Rotors | 264 |
ThreeDimensional Rotors | 291 |
The Varieties of Phaseless Experience In which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways | 303 |
The Physical Nature of Diverse States of Ambiguous Phase | 304 |
The Singularities of Unsmooth Cycles | 333 |
Transition to Bestiary | 336 |
The Firefly Machine | 338 |
Results | 341 |
Historical | 344 |
Energy Metabolism in Cells | 347 |
The Dynamics of Anaerobic Sugar Metabolism | 348 |
The Pasteur Effect | 350 |
Goldbeters PFK Kinetics | 351 |
Phase Control by ADP | 353 |
More PhaseResetting Experiments | 354 |
Results The Time Crystal | 355 |
A Repeat Using Divalent Cations | 359 |
A Repeat Using Acetaldehyde | 360 |
Phase Compromise Experiments | 366 |
The Malonic Acid Reagent Sodium Geometrate | 368 |
Mechanism of the Reaction | 371 |
Rotating Waves in Two Dimensions | 432 |
The Aggregation of Slime Mold Amoebae | 443 |
Questions of Continuity | 446 |
Cell Chemistry and CellCell Coupling | 449 |
Phase Resetting by a cAMP Pulse | 451 |
Historical Note | 453 |
Numerical Organizing Centers | 455 |
Scroll Filaments in Two Dimensions | 456 |
Scroll Rings Shrink and Drift | 467 |
Linked and Knotted Ring Anatomy | 469 |
Linked and Knotted Ring Dynamics | 472 |
Efforts to Analytically Derive and Numerically Confirm the Laws of Filament Dynamics | 474 |
The Discovery of Persistent Ring Configurations | 483 |
For the Future | 490 |
Transition to Chapter 17 About Heart Muscle | 492 |
Electrical Singular Filaments in the Heart Wall | 495 |
Rotors in a Field of Coupled Oscillators | 498 |
The Pinwheel Experiment | 505 |
Pinwheel Experiment Revisited PER | 518 |
Two vs ThreeDimensional Instabilities of the Singular Filament in Heart Muscle | 525 |
A Quick Summary of the April 1997 Experiments | 532 |
Whats Next? | 533 |
Pattern Formation in the Fungi | 537 |
Breadmold with a Circadian Clock | 538 |
Breadmolds in TwoDimensional Growth | 539 |
Pattern Polymorphism in Bourrets Nectria | 540 |
Integration of Pattern | 543 |
Circadian Rhythms in General | 545 |
Some Characteristics of Circadian Rhythms | 561 |
Clock Evolution | 576 |
The Multioscillator View of Circadian Rhythms | 585 |
The Orcadian Clocks of Insect Eclosion | 592 |
Phase and Amplitude Resetting in Drosophila pseudoobscura | 606 |
Other Diptera | 620 |
The Flower of Kalanchoë | 624 |
Resetting Data at Many Stimulus Magnitudes | 627 |
A Phase Singularity | 630 |
Amplitude Resetting | 631 |
The Cell Mitotic Cycle | 632 |
Three Basic Concepts and Some Models | 634 |
Regulation of Mitosis by the Circadian Clock | 640 |
Further Developments in the Area of Circadian Rhythms Applied Back to the Cell Cycle | 642 |
Physarum Polycephalum | 644 |
The Female Cycle | 650 |
Statistics Am I Overdue? | 653 |
Rephasing Schedules | 655 |
The Question of Smoothness | 657 |
Circadian Control of Ovulation | 658 |
Index of Author Citations and Publications | 661 |
761 | |