Diffusion of Calcium and Metabolites in Pancreatic Islets: Killing Oscillations with a Pitchfork

Tsaneva-Atanasova, Krasimira; Zimliki, Charles L.; Bertram, Richard; Sherman, Arthur

doi:10.1529/biophysj.105.078360

Cited by 88 publications

(81 citation statements)

References 46 publications

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“…There exist various biological applications, e.g. neural networks [26], genetic oscillators [27], calcium oscillators [28] or stem cell differentiation [29] where it has been proposed as a basic mechanism for morphogenesis and cellular differentiation. Consequently, there has also been theoretical interest in oscillation death and it has been shown to exist for special time-delayed [30] and repulsive [31,32] types of coupling as well as coupling through conjugate or dissimilar variables [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Stable and transient multicluster oscillation death in nonlocally coupled networks

et al. 2015

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In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation which works well for large coupling ranges but fails for coupling ranges which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.

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Section: Introductionmentioning

confidence: 99%

Stable and transient multicluster oscillation death in nonlocally coupled networks

et al. 2015

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“…Oscillation death is inherent in various systems and its existence has been confirmed experimentally, e.g., in chemical reactors [29], chemical oscillators [30], chemical droplets [31], electronic circuits [32] and thermokinetic oscillators [33]. Moreover, it is especially significant in the light of applications to biological systems like neuronal networks [34], genetic oscillators [35], calcium oscillators [26], and it has been proposed as a basic mechanism for morphogenesis and cellular differentiation, for instance, stem cell differentiation [36]. Oscillation death has been shown to exist for special timedelayed [37] and repulsive [38] types of coupling as well as coupling through conjugate [39,40] or dissimilar variables [41].…”

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confidence: 98%

“…For a network of coupled elements oscillation death implies that its nodes occupy different branches of the IHSS. Oscillation death is inherent in various systems and its existence has been confirmed experimentally, e.g., in chemical reactors [29] [26], and it has been proposed as a basic mechanism for morphogenesis and cellular differentiation, for instance, stem cell differentiation [36]. Oscillation death has been shown to exist for special timedelayed [37] and repulsive [38] types of coupling as well as coupling through conjugate [39,40] or dissimilar variables [41].…”

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confidence: 99%

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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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“…However, in CaD modes, voltage coupling with high calcium coupling causes desynchronization in voltage. This is reminiscent of the work on coupled cells in [16], where adding calcium permeability between cells leads to a desynchronization of voltage via a pitchfork bifurcation. These results help us to better understand how calcium is organized in pancreatic islets in the process of insulin secretion.…”

Section: Discussionmentioning

confidence: 89%

The Interaction of Calcium and Metabolic Oscillations in Pancreatic Beta-cells

Aronne¹,

Clapp²,

Jung³

et al. 2017

SPORA

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Diabetes is a disease characterized by an excessive level of glucose in the bloodstream, which may be a result of improper insulin secretion. Insulin is secreted in a bursting behavior of pancreatic β-cells in islets, which is affected by oscillations of cytosolic calcium concentration. We used the Dual Oscillator Model to explore the role of calcium in calcium oscillation independent and calcium oscillation dependent modes and the synchronization of metabolic oscillations in electrically coupled β-cells. We implemented a synchronization index in order to better measure the synchronization of the β-cells within an islet, and we studied heterogeneous modes of coupled β-cells. We saw that increasing calcium coupling or voltage coupling in heterogeneous cases increases synchronization; however, in certain cases increasing both voltage and calcium coupling causes desynchronization. To better represent an islet, we altered previous code to allow for a greater number of cells to be simulated.

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Diffusion of Calcium and Metabolites in Pancreatic Islets: Killing Oscillations with a Pitchfork

Cited by 88 publications

References 46 publications

Stable and transient multicluster oscillation death in nonlocally coupled networks

Stable and transient multicluster oscillation death in nonlocally coupled networks

Chimera Death: Symmetry Breaking in Dynamical Networks

The Interaction of Calcium and Metabolic Oscillations in Pancreatic Beta-cells

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