Dynamics of excitable elements with time-delayed coupling

Rüdiger, Stephan; Schimansky‐Geier, Lutz

doi:10.1016/j.jtbi.2009.01.030

Cited by 13 publications

(8 citation statements)

References 16 publications

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“…The small number of channels and their proximity lead to stochastic but cooperative openings concerted by local diffusion of Ca 2þ and calcium-induced calcium release between adjacent channels (5,6). It has been argued that the different coupling strength between channels within the same cluster and those in different clusters is responsible for the hierarchical occurrence of puffs and cell-global release (7)(8)(9). According to this picture, global release occurs from clusters across the ER membrane at spacings of a few micrometers and requires synchronization of many clusters to form global oscillations and waves (4,(10)(11)(12).…”

Section: Introductionmentioning

confidence: 99%

Calcium Domains around Single and Clustered IP3 Receptors and Their Modulation by Buffers

Rüdiger

Nagaiah

Warnecke

et al. 2010

Biophysical Journal

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We study Ca(2+) release through single and clustered IP(3) receptor channels on the ER membrane under presence of buffer proteins. Our computational scheme couples reaction-diffusion equations and a Markovian channel model and allows our investigating the effects of buffer proteins on local calcium concentrations and channel gating. We find transient and stationary elevations of calcium concentrations around active channels and show how they determine release amplitude. Transient calcium domains occur after closing of isolated channels and constitute an important part of the channel's feedback. They cause repeated openings (bursts) and mediate increased release due to Ca(2+) buffering by immobile proteins. Stationary domains occur during prolonged activity of clustered channels, where the spatial proximity of IP(3)Rs produces a distinct [Ca(2+)] scale (0.5-10 microM), which is smaller than channel pore concentrations (>100 microM) but larger than transient levels. While immobile buffer affects transient levels only, mobile buffers in general reduce both transient and stationary domains, giving rise to Ca(2+) evacuation and biphasic modulation of release amplitude. Our findings explain recent experiments in oocytes and provide a general framework for the understanding of calcium signals.

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Section: Introductionmentioning

confidence: 99%

Calcium Domains around Single and Clustered IP3 Receptors and Their Modulation by Buffers

Rüdiger

Nagaiah

Warnecke

et al. 2010

Biophysical Journal

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“…This corresponds to the generation of a second-time scale, namely, the slow decay of spiking activity studied in Ref. [6].…”

Section: B Transition Regime: Echo Wavesmentioning

confidence: 94%

“…There, as explained in Ref. [6], delay originates from the finite distance between dynamically active channel clusters, which is about ten times larger than the actual size of the cluster. Between clusters one can assume absence of channels and thus a purely passive behavior of the medium.…”

Section: Motivation For Time-delay Coupling and Model Equationsmentioning

confidence: 99%

“…In this direction, we took as initial point of research Ref. [6], where we compared the time-delay coupling with the diffusive one in order to show that the former could explain certain properties of spatiotemporal patterns displayed by the intracellular release of calcium. This system provides an important cell-physiological process, where recent experimental and modeling evidence strongly suggests excitable behavior [7].…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [6], different behaviors were observed in the dynamics of arrays of excitable elements according to the nature of the coupling, either diffusive or time delayed. In the case of time-delayed coupling, signals from neighboring elements were shown to serve as mutual excitations, resulting in a prolonged signal duration.…”

Section: Introductionmentioning

confidence: 99%

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Traveling echo waves in an array of excitable elements with time-delayed coupling

et al. 2011

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We study time-delayed coupling in one-dimensional arrays of discrete excitable FitzHugh-Nagumo elements. For small time delays in an excitatory coupling, noise-triggered spikes undergo a slight prolongation. For larger delay times, the coupling to adjacent elements leads to a splitting of spikes and an "echo" effect that produces dampened series of spikes. For very large delay times, a transition to a stationary regime appears, as the spikes are sustained by mutual excitations, resulting in antiphase synchronization of all elements. We characterize several features exhibited by the system, such as speed and duration of pulses as well as bifurcations leading to the stationary regime.

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Control of bursting behavior in neurons by autaptic modulation

Wang

Zeng

2013

Neurol Sci

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Firing properties of biological neurons have long been recognized to be determined by extrinsic synaptic afferents that neurons receive and intrinsic ionic mechanisms that neurons possess, however, previous researches have also demonstrated that firing behavior of single neurons can be modulated by the neurons themselves, realized by the autapses. Thus in this investigation, we argued that how autaptic modulations shape the bursting behavior of biological neurons. We considered the issue from the following two aspects: autaptic-excitation and -inhibition. Our results suggested that for autaptic-excitation, under the condition of relatively weak stimulus, regular bursting was more incline to occur when the autaptic strength was weak, while regular spiking was more likely to appear when the autaptic strength was strong. However, larger stimulus would diminish the portion of bursting, but increase the portion of spiking. For autaptic-inhibition, under relatively weak stimulus, a wide range of regular bursting emerges when the autaptic strength was small, but when stronger stimulus were applied, the range of regular bursting shrinked into a small region. Meanwhile, we observed that synaptic delays have no obvious effects in the case of autaptic-excitation, while a subtle effect of synaptic delays was observed in the case of autaptic-inhibition. These results showed that bursting behavior of neurons could be controlled and modulated by the autaptic mechanisms that biological neurons intrinsically possess, and the final results may further promote the understanding in the generation of various neuronal firing patterns.

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Dynamics of excitable elements with time-delayed coupling

Cited by 13 publications

References 16 publications

Calcium Domains around Single and Clustered IP3 Receptors and Their Modulation by Buffers

Calcium Domains around Single and Clustered IP3 Receptors and Their Modulation by Buffers

Traveling echo waves in an array of excitable elements with time-delayed coupling

Control of bursting behavior in neurons by autaptic modulation

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