PMID: 708805Sep 28, 1978Paper

Biological oscillators can be stopped--topological study of a phase response care

Biological cybernetics
M Kawato, R Suzuki

Abstract

Many biological oscillators are stable against noise and perturbation (e.g. circadian rhythms, biochemical oscillators, pacemaker neurons, bursting neurons and neural networks with periodic outputs). The experiment of phase shifts resulting from discrete perturbation of stable biological rhythms was developed by Perkel and coworkers (Perkel et al., 1964). By these methods, they could get important insights into the entrainment behaviors of biological rhythms. Phase response curves, which are measured in these experiments, can be classified into two types. The one is the curve with one mapping degree (Type 1), and the other is that with zero mapping degree (Type 0) (Winfree, 1970). We define the phase response curve mathematically, and explain the difference between these two types by the homotopy theory. Moreover, we prove that, if a Type 0 curve is obtained at a certain magnitude of perturbation, there exists at least one lower magnitude for which the phase response curve cannot be measured. Some applications of these theoretical results are presented.

References

Nov 1, 1975·Journal of Theoretical Biology·E Harth, N S Lewis
Aug 1, 1979·Biological cybernetics·J YamanishiR Suzuki
Aug 19, 1977·Science·A T Winfree
Sep 1, 1970·Journal of Theoretical Biology·A T Winfree
Jul 3, 1964·Science·D H PERKELJ P Segundo
Sep 1, 1975·Journal of Mathematical Biology·J Guckenheimer

Citations

Jan 1, 1980·Biological cybernetics·J YamanishiR Suzuki
Aug 1, 1979·Biological cybernetics·J YamanishiR Suzuki
Oct 1, 1979·Biological cybernetics·M KawatoR Suzuki
Jan 1, 1982·Biological cybernetics·D L YpeyG de Bruin
Aug 26, 2014·Neural Computation·Yasuomi D Sato, Kazuyuki Aihara
Sep 26, 2009·Epilepsy & Behavior : E&B·Steven C SchachterSummit Contributors
Sep 15, 2004·Journal of Theoretical Biology·T Krogh-MadsenM R Guevara
Nov 5, 2013·The Journal of Physical Chemistry. a·Tomáš VeberIgor Schreiber
Jun 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Nomura, Leon Glass
Feb 28, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Leon GlassStanley Nattel
Feb 1, 2021·Computers in Biology and Medicine·Naoki TomiiIchiro Sakuma

Related Concepts

Acclimatization
Metazoa
Oscillators, Biological
Mathematics
Neurons
Periodicity

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