protein synthesis and protein degradation in the individual cells, and are reinforced
by electrical coupling between the cells, resulting in a very robust multicellular
circadian oscillator.
Physics has developed powerful conceptual and mathematical tools to understand the behavior of physical oscillators, such as pendula. Remarkably, the
analogies from the physical world have proven to be useful in describing, modeling
and understanding the behaviors and dynamics of biological oscillators. Physics
offers much to the biologist, providing formal descriptions of systems that are too
complex to be understood intuitively, and predictive power, which is required to
turn discovery into application. Whilst useful, there are challenges in applying
concepts from the physical world to biological oscillators. Physical descriptions of
oscillators are often applied to designed mechanical or electronic systems in which
the components and connections are known and well understood. Often, in studying
biological oscillators, the number of components, the nature of the components, the
network of interactions between the components and the mechanisms by which
these interactions occur are either assumed, or known for only a few of the components that make up the oscillator.
Biological oscillators can be formed by very simple systems comprising only
two components, but are often formed of very complex networks that can be nearly
fully connected and therefore have a high degree of feedback. For example, the
mutual gene regulatory networks that are part of the 24-hour circadian oscillator of
plant cells involve mutual regulation between at least 30 genes in a nearly fully
connected network. This means it is often difficult to obtain a model of the interactions in the network in which one can have full confidence. The nature of the
oscillatory dynamics in biological systems can be complex, involving many
changes in state, abundance and location of the components. In the plant circadian
oscillator as an example, feedback between components can occur through
protein-DNA interactions regulating the expression of component parts, phosphorylation to affect protein activity, ubiquitination to affect protein stability and
translocation between the cytoplasm and nucleus to regulate accessibility of transcriptional regulators to DNA.
One of the most challenging features of biological oscillators, compared to those
designed by humans, is that at different times in the oscillatory cycle, the network of
regulatory connections in the oscillator can change. For example, in the circadian
oscillators that drive 24 hour rhythms in plants and humans, the proteins that form
the regulatory network vary greatly in their abundance over the cycle because of
oscillations in protein translation and breakdown, which are the basis of the
oscillatory dynamics. Thus, theoretical and mathematical descriptions of biological
oscillators must describe not only the dynamics and properties of the oscillator, but
also how those change through the oscillatory cycle. This is a particular challenge
when considering non-autonomous oscillators that respond to external inputs,
which probably represents most biological oscillators, because regulation by an
external signal can be affected by the state and availability of a component in the
oscillator, meaning that regulatory inputs are subject themselves to feedback control
from the oscillator.
vi
Foreword by Alex A. R. Webb
by electrical coupling between the cells, resulting in a very robust multicellular
circadian oscillator.
Physics has developed powerful conceptual and mathematical tools to understand the behavior of physical oscillators, such as pendula. Remarkably, the
analogies from the physical world have proven to be useful in describing, modeling
and understanding the behaviors and dynamics of biological oscillators. Physics
offers much to the biologist, providing formal descriptions of systems that are too
complex to be understood intuitively, and predictive power, which is required to
turn discovery into application. Whilst useful, there are challenges in applying
concepts from the physical world to biological oscillators. Physical descriptions of
oscillators are often applied to designed mechanical or electronic systems in which
the components and connections are known and well understood. Often, in studying
biological oscillators, the number of components, the nature of the components, the
network of interactions between the components and the mechanisms by which
these interactions occur are either assumed, or known for only a few of the components that make up the oscillator.
Biological oscillators can be formed by very simple systems comprising only
two components, but are often formed of very complex networks that can be nearly
fully connected and therefore have a high degree of feedback. For example, the
mutual gene regulatory networks that are part of the 24-hour circadian oscillator of
plant cells involve mutual regulation between at least 30 genes in a nearly fully
connected network. This means it is often difficult to obtain a model of the interactions in the network in which one can have full confidence. The nature of the
oscillatory dynamics in biological systems can be complex, involving many
changes in state, abundance and location of the components. In the plant circadian
oscillator as an example, feedback between components can occur through
protein-DNA interactions regulating the expression of component parts, phosphorylation to affect protein activity, ubiquitination to affect protein stability and
translocation between the cytoplasm and nucleus to regulate accessibility of transcriptional regulators to DNA.
One of the most challenging features of biological oscillators, compared to those
designed by humans, is that at different times in the oscillatory cycle, the network of
regulatory connections in the oscillator can change. For example, in the circadian
oscillators that drive 24 hour rhythms in plants and humans, the proteins that form
the regulatory network vary greatly in their abundance over the cycle because of
oscillations in protein translation and breakdown, which are the basis of the
oscillatory dynamics. Thus, theoretical and mathematical descriptions of biological
oscillators must describe not only the dynamics and properties of the oscillator, but
also how those change through the oscillatory cycle. This is a particular challenge
when considering non-autonomous oscillators that respond to external inputs,
which probably represents most biological oscillators, because regulation by an
external signal can be affected by the state and availability of a component in the
oscillator, meaning that regulatory inputs are subject themselves to feedback control
from the oscillator.
vi
Foreword by Alex A. R. Webb