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Entraining synthetic genetic oscillators
Chaos, 2009
We propose a new approach for synchronizing a population of synthetic genetic oscillators, which consists in the entrainment of a colony of repressilators by external modulation. We present a model where the repressilator dynamics is affected by periodic changes in temperature. We introduce an additional plasmid in the bacteria in order to correlate the temperature variations with the enhancement of the transcription rate of a certain gene. This can be done by introducing a promoter that is related to the heat shock response. This way, the expression of that gene results in a protein that enhances the overall oscillations. Numerical results show coherent oscillations of the population for a certain range of the external frequency, which is in turn related to the natural oscillation frequency of the modified repressilator. Finally we study the transient times related with the loss of synchronization and we discuss possible applications in biotechnology of large-scale production coupled to synchronization events induced by heat shock.
PLoS ONE, 2011
Negative and positive transcriptional feedback loops are present in natural and synthetic genetic oscillators. A single gene with negative transcriptional feedback needs a time delay and sufficiently strong nonlinearity in the transmission of the feedback signal in order to produce biochemical rhythms. A single gene with only positive transcriptional feedback does not produce oscillations. Here, we demonstrate that this single-gene network in conjunction with a simple negative interaction can also easily produce rhythms. We examine a model comprised of two well-differentiated parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the dynamics of the oscillator are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this paper is that a simple and usual negative interaction, such as degradation, sequestration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene. This means that at the genetic level an explicit negative feedback loop is not necessary. The model needs neither cooperative binding reactions nor the formation of protein multimers. Therefore, our findings could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators.
A design principle underlying the synchronization of oscillations in cellular systems
Journal of Cell Science, 2010
Biological oscillations are found ubiquitously in cells and are widely variable, with periods varying from milliseconds to months, and scales involving subcellular components to large groups of organisms. Interestingly, independent oscillators from different cells often show synchronization that is not the consequence of an external regulator. What is the underlying design principle of such synchronized oscillations, and can modeling show that the complex consequences arise from simple molecular or other interactions between oscillators? When biological oscillators are coupled with each other, we found that synchronization is induced when they are connected together through a positive feedback loop. Increasing the coupling strength of two independent oscillators shows a threshold beyond which synchronization occurs within a few cycles, and a second threshold where oscillation stops. The positive feedback loop can be composed of either double-positive (PP) or double-negative (NN) interactions between a node of each of the two oscillating networks. The different coupling structures have contrasting characteristics. In particular, PP coupling is advantageous with respect to stability of period and amplitude, when local oscillators are coupled with a short time delay, whereas NN coupling is advantageous for a long time delay. In addition, PP coupling results in more robust synchronized oscillations with respect to amplitude excursions but not period, with applied noise disturbances compared to NN coupling. However, PP coupling can induce a large fluctuation in the amplitude and period of the resulting synchronized oscillation depending on the coupling strength, whereas NN coupling ensures almost constant amplitude and period irrespective of the coupling strength. Intriguingly, we have also observed that artificial evolution of random digital oscillator circuits also follows this design principle. We conclude that a different coupling strategy might have been selected according to different evolutionary requirements.
Marching along to an Offbeat Drum: Entrainment of Synthetic Gene Oscillators by a Noisy Stimulus
Modulation of biological oscillations by stimuli lies at the root of many phenomena, including maintenance of circadian rhythms, propagation of neural signals, and somitogenesis. While it is well established that regular periodic modulation can entrain an oscillator, an aperiodic (noisy) modulation can also robustly entrain oscillations. This latter scenario may describe, for instance, the effect of irregular weather patterns on circadian rhythms, or why irregular neural stimuli can still reliably transmit information. A synthetic gene oscillator approach has already proven to be useful in understanding the entrainment of biological oscillators by periodic signaling, mimicking the entrainment of a number of noisy oscillating systems. We similarly seek to use synthetic biology as a platform to understand how aperiodic signals can strongly correlate the behavior of cells. This study should lead to a deeper understanding of how fluctuations in our environment and even within our body may promote substantial synchrony among our cells. Specifically, we investigate experimentally and theoretically the entrainment of a synthetic gene oscillator in E. coli by a noisy stimulus. This phenomenon was experimentally studied and verified by a combination of microfluidics and microscopy using the real synthetic circuit. Stochastic simulation of an associated model further supports that the synthetic gene oscillator can be strongly entrained by aperiodic signals, especially telegraph noise. Finally, widespread applicability of aperiodic entrainment beyond the synthetic gene oscillator is supported by results derived from both a model for a natural oscillator in D. discoideum and a model for predator−prey oscillations.
A comparative analysis of synthetic genetic oscillators
Journal of The Royal Society Interface, 2010
Synthetic biology is a rapidly expanding discipline at the interface between engineering and biology. Much research in this area has focused on gene regulatory networks that function as biological switches and oscillators. Here we review the state of the art in the design and construction of oscillators, comparing the features of each of the main networks published to date, the models used for in silico design and validation and, where available, relevant experimental data. Trends are apparent in the ways that network topology constrains oscillator characteristics and dynamics. Also, noise and time delay within the network can both have constructive and destructive roles in generating oscillations, and stochastic coherence is commonplace. This review can be used to inform future work to design and implement new types of synthetic oscillators or to incorporate existing oscillators into new designs.
Entrainment as a means of controlling phase waves in populations of coupled oscillators
Physical Review E
We explore waves and entrainment in a model of coupled oscillators, inspired from the cellular oscillators in the presomitic mesoderm (PSM) of mice. The internal clock in each cell is based on a negative feedback loop which couples to the clocks of neighboring cells through a Notch mechanism. We investigate how a morphogen gradient in the mesoderm, which affects the period of oscillating cells, gives rise to phase waves traveling from the posterior to the anterior part of the PSM. We show that the phase waves can be entrained by an external periodic variation in this morphogen and also observe that multiple oscillatory solutions can coexist in the cell population. Together, these provide a way to potentially control phase waves and thereby manipulate somite patterning in embryos, based on entrainment properties of coupled nonlinear oscillators.
Analysis of coupled genetic oscillators with delayed positive feedback interconnections
2019 18th European Control Conference (ECC), 2019
Genetic oscillators have a fundamental role in the regulation not only of intracellular, but also of intercellular functions: for instance, in the segmentation clock, the synchronised oscillation of neighbouring cells generates spatial travelling waves that induce segmentation of precursors of the vertebral column. To investigate this type of phenomena, we consider the behaviour of two genetic negative feedback oscillators, each operating in a different cell, coupled by an intercellular positive-feedback interconnection with delays. The two coupled systems are nominally identical, but can be different due to noise and cell-to-cell variability. When they can be different in general, we study the effect of positive-feedback and of delay in inducing an oscillatory behaviour. When they are identical, we study how the intercellular feedback delay affects the phase difference between the two oscillators.
The ups and downs of biological timers
Theoretical Biology and Medical …, 2005
The need to execute a sequence of events in an orderly and timely manner is central to many biological processes, including cell cycle progression and cell differentiation. For selfperpetuating systems, such as the cell cycle oscillator, delay times between events are defined by the network of interacting proteins that propagates the system. However, protein levels inside cells are subject to genetic and environmental fluctuations, raising the question of how reliable timing is maintained.
Advances on biological rhythmic pattern generation: Experiments, algorithms and applications
Neurocomputing, 2015
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