On the mechanism underlying bursting in the Aplysia abdominal ganglion R15 cell

Plant, Richard E.; Kim, M.

doi:10.1016/0025-5564(75)90022-x

Cited by 44 publications

(26 citation statements)

References 16 publications

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“…A theorem due to Tikhonov (1950, presented in English by Plant and Kim 1975) describes the dynamics of a system in terms of fast and slow components. The dynamics of a system can be measured by the time required, Tr, to return to the attractor following a small perturbation.…”

Section: Metastabilitymentioning

confidence: 99%

A hierarchical framework for the analysis of scale

1989

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Landscapes are complex ecological systems that operate over broad spatiotemporal scales. Hierarchy theory conceptualizes such systems as composed of relatively isolated levels, each operating at a distinct time and space scale. This paper explores some basic properties of scaled systems with a view toward taking advantage of the scaled structure in predicting system dynamics. Three basic properties are explored:(1) hierarchical structuring, (2) disequilibrium, and (3) metastability. These three properties lead to three conclusions about complex ecological systems. First, predictions about landscape dynamics can often be based on constraints that directly result from scaled structure. Biotic potential and environmental limits form a constraint envelope, analogous to a niche hypervolume, within which the landscape system must operate. Second, within the constraint envelope, thermodynamic and other limiting factors may produce attractors toward which individual landscapes will tend to move. Third, because of changes in biotic potential and environmental conditions, both the constraint envelope and the local attractors change through time. Changes in the constraint structure may involve critical thresholds that result in radical changes in the state of the system. An attempt is made to define measurements to predict whether a specific landscape is approaching a critical threshold.

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Section: Metastabilitymentioning

confidence: 99%

A hierarchical framework for the analysis of scale

1989

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“…This bifurcation occurs in the fast 3D (V, h, n)-subspace of the model and is modulated by the 2D slow dynamics in the (Ca, x)-variables, which are determined by slow oscillations of the intracellular calcium concentration [Plant & Kim, 1975, 1976. The unfolding of this codimension-one bifurcation includes an onset of a stable equilibrium, which is associated with a hyperpolarized phase of bursting, and on the other end, an emergent stable periodic orbit that is associated with tonic spiking phase of bursting.…”

Section: Methods: the Plant Model Of Parabolic Burstingmentioning

confidence: 99%

“…This observation indicates the type of neuronal models to be employed to describe network cores. Our model of choice for parabolic bursting is the Plant model [Plant & Kim, 1975, 1976Plant, 1981]. The Plant model has been developed to accurately describe the voltage dynamics of the R15 neuron in a mollusk Aplysia Californica, which has turned out to be an endogenous burster [Levitan & Levitan, 1988].…”

Section: Introductionmentioning

confidence: 99%

Making a Swim Central Pattern Generator Out of Latent Parabolic Bursters

Alaçam

Shilnikov

2015

Int. J. Bifurcation Chaos

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“…These range from the simple model of Hindmarsh and Rose (1984) to the more complex models of Plant and Kim (1975) and Plant (1978). Although these models generate a bursting oscillation, they do not make use of the ionic mechanism (described above) that is now thought to be responsible for the oscillation in R15.…”

Section: Introductionmentioning

confidence: 97%

A computational study of the effects of serotonin on a molluscan burster neuron

Bertram

1993

Biol. Cybern.

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Abstract. A mathematical model of burster neuron R15from the abdominal ganglion of Aplysia is presented. This is an improvement over earlier models in that the bursting mechanism is more accurately represented. The improved model allows for simulated application of the neurotransmitter serotonin, which has been reported to have profound effects on the voltage waveform produced by Rl5. Computational analysis indicates that the serotonin-induced modulation of the waveform can be explained in terms of competition between stationary, bursting, and beating attractors. Analysis also indicates that, as a result of this competition, serotonin increases the sensitivity of the neuron to synaptic perturbations. This may have important consequences with regard to water balance in the Aplysia, particularly during egg laying.

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On the mechanism underlying bursting in the Aplysia abdominal ganglion R15 cell

Cited by 44 publications

References 16 publications

A hierarchical framework for the analysis of scale

A hierarchical framework for the analysis of scale

Making a Swim Central Pattern Generator Out of Latent Parabolic Bursters

A computational study of the effects of serotonin on a molluscan burster neuron

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