Bistability of bursting and silence regimes in a model of a leech heart interneuron

Malashchenko, Tatiana; Shilnikov, Andrey; Cymbalyuk, Gennady

doi:10.1103/physreve.84.041910

Cited by 31 publications

(35 citation statements)

References 41 publications

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“…We chose the leak current conductance as the continuation parameter because it is present in vast majority of biophysically meaningful models of neurons. In our previous work [10], [17], [26], we have shown its importance in shaping multistable behavior in leech heart neuron models.…”

Section: Resultsmentioning

confidence: 94%

“…The mechanisms underlying multistability can be thoroughly studied by applying the theory of dynamical systems [5], [6]–[8], [11], [16], [17], [54], [57]–[63]. A key ingredient of a description of a mechanism is the identification of the unstable regime(s) which creates the boundary separating observable regimes.…”

Section: Discussionmentioning

confidence: 99%

“…Application of the theory of dynamical systems allows mapping the transitions between the regimes by using bifurcation diagrams [10], [17], [18], [27]. Through the use of numerical continuation of stationary states, we incorporated information about stable and unstable stationary states into the database developed in [25].…”

Section: Introductionmentioning

confidence: 99%

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High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

et al. 2013

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Flexibility in neuronal circuits has its roots in the dynamical richness of their neurons. Depending on their membrane properties single neurons can produce a plethora of activity regimes including silence, spiking and bursting. What is less appreciated is that these regimes can coexist with each other so that a transient stimulus can cause persistent change in the activity of a given neuron. Such multistability of the neuronal dynamics has been shown in a variety of neurons under different modulatory conditions. It can play either a functional role or present a substrate for dynamical diseases. We considered a database of an isolated leech heart interneuron model that can display silent, tonic spiking and bursting regimes. We analyzed only the cases of endogenous bursters producing functional half-center oscillators (HCOs). Using a one parameter (the leak conductance ()) bifurcation analysis, we extended the database to include silent regimes (stationary states) and systematically classified cases for the coexistence of silent and bursting regimes. We showed that different cases could exhibit two stable depolarized stationary states and two hyperpolarized stationary states in addition to various spiking and bursting regimes. We analyzed all cases of endogenous bursters and found that 18% of the cases were multistable, exhibiting coexistences of stationary states and bursting. Moreover, 91% of the cases exhibited multistability in some range of . We also explored HCOs built of multistable neuron cases with coexisting stationary states and a bursting regime. In 96% of cases analyzed, the HCOs resumed normal alternating bursting after one of the neurons was reset to a stationary state, proving themselves robust against this perturbation.

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Section: Resultsmentioning

confidence: 94%

Section: Discussionmentioning

confidence: 99%

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High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

et al. 2013

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“…Because dq dt is positive (negative) over (under) the q-nullcline, the system state transits the spiking state, or the limit cycle, and the silent state, or the equilibrium, alternately. Autonomous bursting cells in the pre-Bötzinger complex [35] and heart interneurons in Leech [36] are known to have this kind of dynamics, square-wave bursting. The Hindmarsh-Rose (1984) model [37], a qualitative neuron model, also has such dynamics.…”

Section: An Analog Silicon Neuronmentioning

confidence: 99%

Silicon neuronal networks towards brain-morphic computers

Kohno

Aihara

2014

NOLTA

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Neuromorphic systems are designed by mimicking or being inspired by the nervous system, which realizes robust, autonomous, and power-efficient information processing by highly parallel architecture. It is a candidate of the next-generation computing system that is expected to have advanced information processing ability by power-efficient and parallel architecture. A silicon neuronal network is a neuromorphic system with a most detailed level of analogy to the nervous system. It is a network of silicon neurons connected via silicon synapses; they are electronic circuits to reproduce the electrophysiological activity of neuronal cells and synapses, respectively. There is a trade-off between the proximity to the neuronal and synaptic activities and simplicity and power-consumption of the circuit. Power-efficient and simple silicon neurons assume uniform spikes, but biophysical experimental data suggest the possibility that variety of spikes given to a synapse is playing a certain role in the information processing in the brain. In this article, we review our design approach of silicon neuronal networks where uniform spikes are not assumed. Simplicity of the circuits is brought by mathematical techniques of qualitative neuronal modeling. Though it is neither simpler nor low-power consuming than above silicon neurons, it is expected to be more appropriate for silicon neuronal networks applied to brain-morphic computing.

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“…A canonical model of the HN accurately reproduces experimental results [1,2]. It also exhibits bistability of bursting and silence in single HNs and the HCO [1,3]. The single HN and HCO model have been expanded into a family of models that satisfy biological constraints [2].…”

mentioning

confidence: 99%

Protective role of the half-center oscillator connectivity against external perturbations

2013

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Bistability of bursting and silence regimes in a model of a leech heart interneuron

Cited by 31 publications

References 41 publications

High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

Silicon neuronal networks towards brain-morphic computers

Protective role of the half-center oscillator connectivity against external perturbations

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