Course 2 Understanding neuronal dynamics by geometrical dissection of minimal models

Borisyuk, Alla; Rinzel, John

doi:10.1016/s0924-8099(05)80008-3

Cited by 48 publications

(39 citation statements)

References 53 publications

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“…In contrast, no changes were observed in the spike waveform before the pause, suggesting that the pauses are probably not triggered by intrinsic processes such as slow inactivation of sodium currents. The biophysical dynamics of burst and bistability cellular phenomena have been studied at many different levels (Bertram et al, 1995;Izhikevich, 2000;Borisyuk and Rinzel, 2005). The lack of consistent changes in discharge rate before the pause rules out square-wave and parabolic but not elliptic bursting behavior.…”

Section: Relationships Between Discharge Parameters and Pausesmentioning

confidence: 99%

Statistical Properties of Pauses of the High-Frequency Discharge Neurons in the External Segment of the Globus Pallidus

Elias¹,

Joshua²,

Goldberg³

et al. 2007

J. Neurosci.

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The neurons of many basal ganglia nuclei, including the external and internal globus pallidus (GPe and GPi, respectively) and the substantia nigra pars reticulata (SNr) are characterized by their high-frequency (50 -100 spikes/s) tonic discharge (HFD). However, the high firing rate of GPe neurons is interrupted by long pauses. We studied the extracellularly recorded spiking activity of 212 well-isolated HFD GPe and 52 GPi/SNr neurons from five monkeys during different states of behavioral activity. An algorithm that maximizes the surprise function was used to detect pauses and pauser cells ("pausers"). Only 6% of the GPi/SNr neurons versus as many as 56% of the GPe neurons were classified as pausers. The GPe average pause duration equals 0.62 s. The interpause intervals follow a Poissonian distribution with a frequency of 13 pauses/minute. No linear relationship was found between pause parameters (duration or frequency) and the firing rate of the cell. Pauses were preceded by various changes in firing rate but not dominantly by a decrease. The average amplitude and duration of the spike waveform was modulated only after the pause but not before it. Pauses of pairs of cells that were recorded simultaneously were not correlated. The probability of GPe cells to pause spontaneously was extremely variable among monkeys (30 -90%) and inversely related to the degree of the monkey's motor activity. These findings suggest that spontaneous GPe pauses are related to low-arousal periods and are generated by a process that is independent of the discharge properties of the cells.

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Section: Relationships Between Discharge Parameters and Pausesmentioning

confidence: 99%

Statistical Properties of Pauses of the High-Frequency Discharge Neurons in the External Segment of the Globus Pallidus

Elias¹,

Joshua²,

Goldberg³

et al. 2007

J. Neurosci.

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“…The abstraction of qualitative motifs from these sub-models encoded well-known insights into the sodium-potassium action potential (Na/K AP). For instance, we observe that the derived R I -R II correspond to Phases 1-2 (upstroke and then plateau) of Borisyuk and Rinzel (2005); R III and R IV constitute two parts of Phase 3 (downstroke); and R V corresponds to Phase 4 (recovery). The mechanistic roles of the fast sodium and slow (rectifying) potassium currents were shown to persist in models with different excitability properties and in the context of strong modulatory currents.…”

Section: Discussionmentioning

confidence: 90%

Encoding the fine-structured mechanism of action potential dynamics with qualitative motifs

Clewley

2010

J Comput Neurosci

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This work presents a neuroinformatic method for deriving mechanistic descriptions of fine-structured neural activity. This is a new development in the computer-assisted analysis of dynamics in conductance-based models, which is illustrated using single compartment models of an action potential. A sequence of abstract, qualitative motifs is inferred from this analysis, forming a template that is independent of the specific equations from which they were abstracted. The template encodes the assumptions behind the model reduction steps used to derive the motifs, and so specifies quantitative information about their domains of validity. The template representation of a mechanism is converted to a hybrid dynamical system, which is simulated as a sequence of low-dimensional reduced models (in this example, phase plane models) with appropriate switching conditions taken from the motifs. We demonstrate the validity of the template on a detailed single neuron model of spiking taken from the literature, and show that the corresponding hybrid system simulation closely mimics the spiking dynamics of the full model.

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“…With this fast-slow decomposition, we can understand the maintenance of wake and sleep states, as well as the transitions between them, by the solutions of Eqn. (2.1) governed by the nullclines of the (v i , w i ) phase plane (see also [7]). We provide a description of the sleep/wake cycle (see Fig.…”

Section: Resultsmentioning

confidence: 98%

“…On the contrary, when vnullclines sit low (indicating strong inhibitory or low excitatory drive), they cross the w-nullcline on the left branch defining a "stable fixed point" of low activity. Finally, when v-nullclines cross the w-nullcline on the middle branch, they define an "unstable fixed point" and a "stable limit cycle" of periodic activity and inactivity naturally occurs (see [7]). …”

Section: Resultsmentioning

confidence: 99%

Effects of Thermoregulation on Human Sleep Patterns: A Mathematical Model of Sleep–Wake Cycles with REM–NREM Subcircuit

Bañuelos

Best

Huguet

et al. 2015

The IMA Volumes in Mathematics and Its Applications

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Abstract. In this paper we construct a mathematical model of human sleep/wake regulation with thermoregulation and temperature effects. Simulations of this model show features previously presented in experimental data such as elongation of duration and number of REM bouts across the night as well as the appearance of awakenings due to deviations in body temperature from thermoneutrality. This model helps to demonstrate the importance of temperature in the sleep cycle. Further modifications of the model to include more temperature effects on other aspects of sleep regulation such as sleep and REM latency are discussed.

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Course 2 Understanding neuronal dynamics by geometrical dissection of minimal models

Cited by 48 publications

References 53 publications

Statistical Properties of Pauses of the High-Frequency Discharge Neurons in the External Segment of the Globus Pallidus

Statistical Properties of Pauses of the High-Frequency Discharge Neurons in the External Segment of the Globus Pallidus

Encoding the fine-structured mechanism of action potential dynamics with qualitative motifs

Effects of Thermoregulation on Human Sleep Patterns: A Mathematical Model of Sleep–Wake Cycles with REM–NREM Subcircuit

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