Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators

Taylor, Annette F.; Tinsley, Mark R.; Wang, Fang; Huang, Zhaoyang; Showalter, Kenneth

doi:10.1126/science.1166253

Cited by 389 publications

(376 citation statements)

References 26 publications

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“…In a large variety of chemical and biological systems, moving entities synchronize an internal degree of freedom: examples include mobile catalytic beads exhibiting the oscillatory Belousov-Zhabotinsky (BZ) reaction [1] as well as the BZ reaction in vortical flow [2], synthetic genetic oscillators [3], motile cells synchronizing intracellular oscillations during embryonic somitogenesis [4][5][6], quorum sensing of signaling amoebae [7] and the coordinated motion of myxobacteria regulated by the oscillatory Frz-signaling system [8][9][10]. Furthermore, it has been speculated that the flagellar beating of active microswimmers synchronizes by hydrodynamic interaction thus affecting the rheology of active suspensions [11,12].…”

Section: Introductionmentioning

confidence: 99%

Superdiffusion, large-scale synchronization, and topological defects

2016

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We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby introducing an additional, independent source of fluctuations, thus constituting the intrinsic nonequilibrium nature of the temporal dynamics. We employ this paradigmatic model system to discuss how the emergence of order is affected by motion of individual entities. In particular, we consider both, normal diffusive motion and superdiffusion. A non-Hamiltonian field theory including multiplicative noise terms is derived which describes the nonequilibrium dynamics at the macroscale. This theory reveals a defect-mediated transition from incoherence to quasi long-range order for normal diffusion of oscillators in two dimensions, implying a power-law dependence of all synchronization properties on system size. In contrast, superdiffusive transport suppresses the emergence of topological defects, thereby inducing a continuous synchronization transition to long-range order in two dimensions. These results are consistent with particle-based simulations.

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Section: Introductionmentioning

confidence: 99%

Superdiffusion, large-scale synchronization, and topological defects

2016

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“…Unlike the cases of interacting excitable cells where the oscillation is treated as a collective phenomenon [1]- [6], in the case of a fixed network specific signalling pathways can be more readily identified. The networks studied here share some essential features with brains, and it is plausible that the mechanism described here plays a role in epileptic seizures.…”

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confidence: 99%

Self-sustaining oscillations in complex networks of excitable elements

McGraw

Menzinger

2011

Phys. Rev. E

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Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently random. In the oscillating state, signals propagate in a single direction and one or a few network loops are selected as driving loops in which the excitation circulates periodically. We analyze the mechanism, describe the oscillating states, identify the pacemaker loops and explain key features of their distribution. This mechanism may play a role in epileptic seizures.PACS numbers: 89.75. Hc, 05.65.+b, 87.19.lj, 87.19.xm The coherent oscillation (CO) of a collection of units that are non-oscillatory on their own is relevant to biological and physical sciences: CO has been identified and analyzed in populations of excitable biological cells ( [7]. In contrast with well-studied synchronization phenomena of self-oscillating units [8], in these cases the ability to oscillate derives from the interactions of the elements. CO can occur also on complex networks if the nodes are excitable [9][10] or even monostable [9], provided that the network contains loops, and that the directional symmetry of couplings is somehow broken to allow a signal to propagate in a single direction around a loop [10].Networks of these types include some neural [11][12] and genetic regulatory networks.[9] Some studies of excitable networks have been inspired by target and spiral waves in continuous media. [13][7] [10] In complex networks, loops are both generic and abundant. [15][14] While short loops of length L ≪ N (where N is the network size) are rare in large random networks, ones with L ln N occur generically in numbers growing exponentially with N . Their number also grows roughly exponentially with L up to a maximum at a length L m ∼ N.[15] [14] In this letter we show that random excitable networks readily self-organize into a CO state following a transient phase during which one or a few loops are dynamically selected as driving (or pacemaker) loops. We describe the mechanism of signal propagation and gain an understanding of the resulting distributions of the oscillating states and associated driving loops.We consider networks of diffusively coupled, excitable elements with dynamics described by the Bär model [16] N is the number of nodes, u i and v i are dynamical variables, D is the coupling strength, and A ij is the adjacency matrix. a, b, and ε are parameters, for which we adopt the values a = 0.84, b = 0.07, and ε = 0.04. In the absence of coupling, the individual nodes display excitable dynamics, with a stable equilibrium at (u, v) = (0, 0) and an excitation threshold u th ≈ 0.1. The dynamical equations were integrated numerically using a fourth-order Runge-Kutta algorithm with time step ∆t = 0.1. For the topology, we chose the undirected random regular network of degree 3 (RRN3), where nodes are randomly and symmetrically connected with the constraint that all have the same degr...

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“…The essential elements required for synchronization typically include some form of coupling between components of the oscillating systems which can exert an influence on the phase of the oscillations, enabling the frequency of one system to be entrained by another into a constant ratio (on average), typically of simple integers. Such systems have been widely studied for many years with diverse applications in both discrete and continuum systems, such as in networks of physical or biological systems (e.g., Watts andStrogatz, 1998 andArenas et al, 2008), ensembles of chemical oscillators (e.g., Taylor et al, 2009), lasers (e.g., Van Wiggeren and Roy 1998), cardiac and circadian rhythms (Glass 2001), reaction-diffusion systems, and in mechanically oscillating systems among many others (e.g., see Pikovsky et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

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Morice-Atkinson

Allen

et al. 2017

Chaos

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A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to timedependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction d of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and d was varied over the range 0:1 d 1. Reducing d was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at d ¼ 0:1. Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles. Synchronization is commonly discussed in the context of discrete, coupled oscillators which may be periodic or chaotic. But under some circumstances, extended nonlinear systems which are formally infinite-dimensional, such as fluid flows, may exhibit discrete oscillations and behave as if they consisted of discrete oscillating components. We study such an example in the laboratory, consisting of amplitude-modulated, azimuthally travelling baroclinic waves in a thermally driven, rotating annulus experiment. Earlier experiments showed that, under conditions in which the unperturbed travelling waves are spontaneously (either periodically or weakly chaotically) modulated in time, the amplitude modulation of the waves can be phase-locked and synchronized with periodic perturbations of the applied (axisymmetric) temperature difference between the inner and outer cylinders of the experiment. We use this potentially synchronized system to explore what happens if the periodic perturbations are applied for only a given fraction of each cycle-i.e., for a duty cycle <100%. Our systematic exploration of variations in both the duty cycle and detuning (difference in period between the natural oscillation period and that of the imposed boundary temperature variations) shows that the duty cycle acts in the same way as a variable coupling coefficient, demonstrating a narrowing of the frequency interval over which complete phase synchronization is observed as ...

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Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators

Cited by 389 publications

References 26 publications

Superdiffusion, large-scale synchronization, and topological defects

Superdiffusion, large-scale synchronization, and topological defects

Self-sustaining oscillations in complex networks of excitable elements

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

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