4
P. V. E. McClintock and A. Stefanovska
ular, on localised modes where only parts of the chain oscillate. They relate their
model to the mechanical oscillations of trees, where the branches move but usually
not the trunk. Chapter 10 by Ben-Tal presents some thoughts on the (sometimes
controversial) question of how non-autonomous model systems can be converted to
autonomous ones by application of an appropriate transformation. The author discusses the procedure, not only for periodic forcing, but also for other special cases.
In Chap. 11, Stankovski offers an overview of the coupling functions that can be
used to model the interactions between oscillatory systems and which mediate the
non-autonomous effects seen in a particular system under examination. He focuses
on the use and suitability of coupling functions in neuroscience and their use in
accounting for neuronal oscillations and brain (EEG) waves. The final contribution
to Part II, Chap. 12 by Gengel and Pikovsky, tackles one of the central questions
confronting an experimentalist making measurements on an oscillatory system, not
necessarily a biological one: how best can the recorded time series be analysed to
illuminate understanding of the underlying dynamics? The authors show that iterated
Hilbert transform embedding provides a good reconstruction of the phase dynamics,
provided that the amplitude variations are relatively small.
1.3 Biological Oscillations
Although the biological oscillators of Part III are not the only examples of nonautonomous oscillatory systems, they are overwhelmingly the most widespread and
important. Living systems are inherently non-autonomous on account of the internal
interactions between their component parts, in addition to the influence of the external
environment. Each oscillator affects some of the other oscillators, thus giving rise
to the time-variations in frequency and amplitude that are observed. Furthermore,
living systems are never stationary but, rather, are in a state of continuous evolution
from birth until death, with corresponding evolution of their characteristic parameter
values.
Chapter 13 by Folke Olsen and Lunding is devoted to oscillations in yeast glycolysis. These have been known about for over six decades, but their mechanism remains
uncertain and their purpose is still a mystery. The authors present experimental evidence that many variables, seemingly unrelated to glycolysis, oscillate in synchrony
with glycolytic intermediates. They suggest that the function of metabolic oscillations is to maintain the cell in a state of constant low entropy. In Chap. 14 Lloyd
provides a general discussion of biological oscillations, including yeast cell oscillations, and he too considers what their purpose may be. He discusses a model in
which ultradian (faster than circadian) rhythms are the synchronizing signatures that
organize the coherence of the living state. Chapter 15 by Amemiya et al. addresses
glycolytic oscillations in cancer cells. It reviews the first direct observation of glycolytic oscillations in HeLa cervical and DU145 prostate cancer cells. The authors
propose a mathematical model to account for the oscillation mechanism, show that
it can reproduce the experimental results, and consider the wider implications. They
P. V. E. McClintock and A. Stefanovska
ular, on localised modes where only parts of the chain oscillate. They relate their
model to the mechanical oscillations of trees, where the branches move but usually
not the trunk. Chapter 10 by Ben-Tal presents some thoughts on the (sometimes
controversial) question of how non-autonomous model systems can be converted to
autonomous ones by application of an appropriate transformation. The author discusses the procedure, not only for periodic forcing, but also for other special cases.
In Chap. 11, Stankovski offers an overview of the coupling functions that can be
used to model the interactions between oscillatory systems and which mediate the
non-autonomous effects seen in a particular system under examination. He focuses
on the use and suitability of coupling functions in neuroscience and their use in
accounting for neuronal oscillations and brain (EEG) waves. The final contribution
to Part II, Chap. 12 by Gengel and Pikovsky, tackles one of the central questions
confronting an experimentalist making measurements on an oscillatory system, not
necessarily a biological one: how best can the recorded time series be analysed to
illuminate understanding of the underlying dynamics? The authors show that iterated
Hilbert transform embedding provides a good reconstruction of the phase dynamics,
provided that the amplitude variations are relatively small.
1.3 Biological Oscillations
Although the biological oscillators of Part III are not the only examples of nonautonomous oscillatory systems, they are overwhelmingly the most widespread and
important. Living systems are inherently non-autonomous on account of the internal
interactions between their component parts, in addition to the influence of the external
environment. Each oscillator affects some of the other oscillators, thus giving rise
to the time-variations in frequency and amplitude that are observed. Furthermore,
living systems are never stationary but, rather, are in a state of continuous evolution
from birth until death, with corresponding evolution of their characteristic parameter
values.
Chapter 13 by Folke Olsen and Lunding is devoted to oscillations in yeast glycolysis. These have been known about for over six decades, but their mechanism remains
uncertain and their purpose is still a mystery. The authors present experimental evidence that many variables, seemingly unrelated to glycolysis, oscillate in synchrony
with glycolytic intermediates. They suggest that the function of metabolic oscillations is to maintain the cell in a state of constant low entropy. In Chap. 14 Lloyd
provides a general discussion of biological oscillations, including yeast cell oscillations, and he too considers what their purpose may be. He discusses a model in
which ultradian (faster than circadian) rhythms are the synchronizing signatures that
organize the coherence of the living state. Chapter 15 by Amemiya et al. addresses
glycolytic oscillations in cancer cells. It reviews the first direct observation of glycolytic oscillations in HeLa cervical and DU145 prostate cancer cells. The authors
propose a mathematical model to account for the oscillation mechanism, show that
it can reproduce the experimental results, and consider the wider implications. They