Multistability and Clustering in a Population of Synthetic Genetic Oscillators via Phase-Repulsive Cell-to-Cell Communication

Ullner, Ekkehard; Zaikin, Alexey; Volkov, E.I.; García‐Ojalvo, Jordi

doi:10.1103/physrevlett.99.148103

Cited by 220 publications

(198 citation statements)

References 24 publications

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“…negative and positive) diffusive coupling also gives rise to AD [80]. AD has also been seen in parametrically modulated systems [81], phase repulsive communication [82], and by forcing [83] or gradient coupling [65].…”

Section: Linear Augmentation and Other Strategiesmentioning

confidence: 99%

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Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

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Section: Linear Augmentation and Other Strategiesmentioning

confidence: 99%

“…Diffusive coupling is not the only means of achieving amplitude death. Phase-repulsive coupling [82] also eliminate oscillations in a population of synthetic genetic clocks.…”

Section: Experiments and Applicationsmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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“…This regime occurs when a ho- * corresponding author: schoell@physik.tu-berlin.de mogeneous steady state splits into at least two distinct branches -upper and lower -which represent a newly created IHSS [25][26][27][28]. For a network of coupled elements oscillation death implies that its nodes occupy different branches of the IHSS.…”

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confidence: 99%

Chimera Death: Symmetry Breaking in Dynamical Networks

2014

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For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call chimera death. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations, and a direct abrupt transition for larger coupling strength. Spontaneous symmetry breaking in a complex dynamical system is a fundamental and universal phenomenon which occurs in diverse fields such as physics, chemistry, and biology [1]. It implies that processes occurring in nature favor a less symmetric configuration, although the underlying principles can be symmetric. This intriguing concept has recently gained renewed interest generated by the enormous burst of works on chimera states and on oscillation death, which have emerged independently. In this Letter we draw a relation between these two.Chimera states correspond to the situation when an ensemble of identical elements self-organizes into two coexisting and spatially separated domains with dramatically different behavior, i.e., spatially coherent and incoherent oscillations [2,3]. They have been the subject of intensive theoretical investigations, e.g. [4][5][6][7][8][9][10][11][12][13][14][15]. Experimental evidence of chimeras has only recently been provided for optical [16], chemical [17], mechanical [18] and electronic [19] systems. These peculiar hybrid states may also account for the observation of partial synchrony in neural activity [20], like unihemispheric sleep, i.e., the ability of some birds or dolphins to sleep with one half of their brain while the other half remains aware [21,22]. Chimera states have been initially found for phase oscillators [2], and they typically occur in networks with nonlocal coupling. Recently, for globally coupled oscillators it has been shown that such spatio-temporal patterns can be also connected to the amplitude dynamics (amplitude-mediated chimeras) [23,24]. However, the global coupling topology does not provide a clear notion of space, which is crucial for chimera states. A further open question is whether chimeras can be extended to more general symmetry breaking states.Another fascinating effect which requires the break-up of the system's symmetry as a crucial ingredient is oscillation death which refers to stable inhomogeneous steady states (IHSS) which are created through the coupling of self-sustained oscillators. This regime occurs when a ho- * corresponding author: schoell@physik.tu-berlin.de mogeneous steady state splits into at least two distinct branches -upper and lower -which represent a newly created IHSS [25][26][27][28]. For a network of coupled elements oscillation death ...

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“…As a basic unit, we consider a negative feedback loop consisting of three proteins that repress each other by blocking the associated genes, which Leibler and Elowitz termed the 'repressilator' [6]. Previously, others have studied coupled repressilators to investigate quorum sensing [7] and cell-to-cell communication [8]. As a further step, one might consider systems made up of regular arrays of cells interacting in a specific manner with neighboring cells.…”

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confidence: 99%

Repressor Lattice: Feedback, Commensurability, and Dynamical Frustration

Jensen¹,

Krishna²,

Pigolotti³

2009

Phys. Rev. Lett.

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We construct a hexagonal lattice of repressing genes, such that each node represses three of the neighbors, and use it as a model for genetic regulation in spatially extended systems. Using symmetry arguments and stability analysis we argue that the repressor-lattice can be in a nonfrustrated oscillating state with only three distinct phases. If the system size is not commensurate with three, oscillating solutions of several different phases are possible. As the strength of the interactions between the nodes increases, the system undergoes many transitions, breaking several symmetries. Eventually dynamical frustrated states appear, where the temporal evolution is chaotic, even though there are no built-in frustrations. Applications of the repressor-lattice to real biological systems are discussed.

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Multistability and Clustering in a Population of Synthetic Genetic Oscillators via Phase-Repulsive Cell-to-Cell Communication

Cited by 220 publications

References 24 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Chimera Death: Symmetry Breaking in Dynamical Networks

Repressor Lattice: Feedback, Commensurability, and Dynamical Frustration

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