53 research outputs found
Oscillations and temporal signalling in cells
The development of new techniques to quantitatively measure gene expression
in cells has shed light on a number of systems that display oscillations in
protein concentration. Here we review the different mechanisms which can
produce oscillations in gene expression or protein concentration, using a
framework of simple mathematical models. We focus on three eukaryotic genetic
regulatory networks which show "ultradian" oscillations, with time period of
the order of hours, and involve, respectively, proteins important for
development (Hes1), apoptosis (p53) and immune response (NFkB). We argue that
underlying all three is a common design consisting of a negative feedback loop
with time delay which is responsible for the oscillatory behaviour
Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks
The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semidiscretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production
Oscillations and temporal signalling in cells
ArXiv pre-print: http://arxiv.org/abs/q-bio/0703047.-- Final full-text version of the paper available at: http://dx.doi.org/10.1088/1478-3975/4/2/R01.PMID: 17664651The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show ultradian oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-κB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.SK, MHJ and KS acknowledge support from the Danish National Research Foundation and Villum Kann Rasmussen Foundation. GT acknowledges support from the FIRB 2003 program of the
Italian Ministry for University and Scientific Research
Mathematical modelling of p53 signalling during DNA damage response: a survey
No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage
Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks
The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semidiscretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production
Robust dynamical pattern formation from a multifunctional minimal genetic circuit
<p>Abstract</p> <p>Background</p> <p>A practical problem during the analysis of natural networks is their complexity, thus the use of synthetic circuits would allow to unveil the natural mechanisms of operation. Autocatalytic gene regulatory networks play an important role in shaping the development of multicellular organisms, whereas oscillatory circuits are used to control gene expression under variable environments such as the light-dark cycle.</p> <p>Results</p> <p>We propose a new mechanism to generate developmental patterns and oscillations using a minimal number of genes. For this, we design a synthetic gene circuit with an antagonistic self-regulation to study the spatio-temporal control of protein expression. Here, we show that our minimal system can behave as a biological clock or memory, and it exhibites an inherent robustness due to a quorum sensing mechanism. We analyze this property by accounting for molecular noise in an heterogeneous population. We also show how the period of the oscillations is tunable by environmental signals, and we study the bifurcations of the system by constructing different phase diagrams.</p> <p>Conclusions</p> <p>As this minimal circuit is based on a single transcriptional unit, it provides a new mechanism based on post-translational interactions to generate targeted spatio-temporal behavior.</p
Are physiological oscillations 'physiological'?
Despite widespread and striking examples of physiological oscillations, their
functional role is often unclear. Even glycolysis, the paradigm example of
oscillatory biochemistry, has seen questions about its oscillatory function.
Here, we take a systems approach to summarize evidence that oscillations play
critical physiological roles. Oscillatory behavior enables systems to avoid
desensitization, to avoid chronically high and therefore toxic levels of
chemicals, and to become more resistant to noise. Oscillation also enables
complex physiological systems to reconcile incompatible conditions such as
oxidation and reduction, by cycling between them, and to synchronize the
oscillations of many small units into one large effect. In pancreatic beta
cells, glycolytic oscillations are in synchrony with calcium and mitochondrial
oscillations to drive pulsatile insulin release, which is pivotal for the liver
to regulate blood glucose dynamics. In addition, oscillation can keep
biological time, essential for embryonic development in promoting cell
diversity and pattern formation. The functional importance of oscillatory
processes requires a rethinking of the traditional doctrine of homeostasis,
holding that physiological quantities are maintained at constant equilibrium
values, a view that has largely failed us in the clinic. A more dynamic
approach will enable us to view health and disease through a new light and
initiate a paradigm shift in treating diseases, including depression and
cancer. This modern synthesis also takes a deeper look into the mechanisms that
create, sustain and abolish oscillatory processes, which requires the language
of nonlinear dynamics, well beyond the linearization techniques of equilibrium
control theory
Oscillations in well-mixed, deterministic feedback systems: beyond ring oscillators
A ring oscillator is a system in which one species regulates the next, which regulates the next and so
on until the last species regulates the first. In addition, the number of the regulations which are negative, and so result in a reduction in the regulated species, is odd, making the overall feedback in the
loop negative. In ring oscillators, the probability of oscillations is maximised if the degradation rates of
the species are equal. When there is more than one loop in the regulatory network, the dynamics can
be more complicated. Here, a systematic way of organising the characteristic equation of ODE models of
regulatory networks is provided. This facilitates the identification of Hopf bifurcations. It is shown that
the probability of oscillations in non-ring systems is maximised for unequal degradation rates. For example, when there is a ring and a second ring employing a subset of the genes in the first ring, then the
probability of oscillations is maximised when the species in the sub-ring degrade more slowly than those
outside, for a negative feedback subring. When the sub-ring forms a positive feedback loop, the optimal
degradation rates are larger for the species in the sub-ring, provided the positive feedback is not too
strong. By contrast, optimal degradation rates are smaller for the species in the sub-ring, when the positive feedback is very strong. Adding a positive feedback loop to a repressilator increases the probability
of oscillations, provided the positive feedback is not too strong, whereas adding a negative feedback loop
decreases the probability of oscillations. The work is illustrated with numerical simulations of example
systems: an autoregulatory gene model in which transcription is downregulated by the protein dimer and
three-species and four-species gene regulatory network examples
- …