Computer Simulations of Neuronal Signal Transduction: The Role of Nonlinear Dynamics and Noise

Braun, Hans; Huber, Martin; Dewald, M.; Schäfer, Klaus; Voigt, Karlheinz

doi:10.1142/s0218127498000681

Cited by 140 publications

(116 citation statements)

References 33 publications

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“…In addition, stochastic fluctuations, which are naturally present due to the inherent noisiness of neurons, play an important role for the response behavior. When oscillations operate close to the spike threshold, the noise can essentially determine whether a spike is triggered or not and even little stochastic fluctuations can initiate action potential generation [8,[12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

Huber

Braun

2006

Phys. Rev. E

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Marburg, 22.09.2005 We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation.On depolarization by an applied current, the model exhibits subthreshold oscillatory activity with occasional spike generation when oscillations reach the spike threshold. We consider how the amount of applied current, the noise intensity, variation of maximum conductance values and scaling to different temperature ranges alter the responses of the model with respect to voltage traces, interspike intervals and their statistics and the mean spike frequency curves. We demonstrate that subthreshold oscillatory neurons in the presence of noise can sensitively and also selectively be tuned by stimulus-dependent variation of model

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Section: Introductionmentioning

confidence: 99%

“…This is because electrical stimuli rather selectively modulate the spiking probability whereas temperature alters both the spiking probability and the frequency. Such temperature-dependent effects on neuronal oscillations are also known from temperatureencoding by peripheral themoreceptors [12,13,16,19,20].…”

Section: Introductionmentioning

confidence: 99%

Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

Huber

Braun

2006

Phys. Rev. E

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“…The parameters used in the simulations are those used by Braun et al (1998) and Masoller et al (2008): , and the number of neurons is N = 2, 3, 5, 10 from top to bottom for both the columns. The dashed line shows the natural oscillation amplitude of the uncoupled neuron.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of globally delay-coupled neurons displaying subthreshold oscillations

Masoller

Torrent

García‐Ojalvo

2009

Phil. Trans. R. Soc. A.

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We study an ensemble of neurons that are coupled through their time-delayed collective mean field. The individual neuron is modelled using a Hodgkin-Huxley-type conductance model with parameters chosen such that the uncoupled neuron displays autonomous subthreshold oscillations of the membrane potential. We find that the ensemble generates a rich variety of oscillatory activities that are mainly controlled by two time scales: the natural period of oscillation at the single neuron level and the delay time of the global coupling. When the neuronal oscillations are synchronized, they can be either in-phase or out-of-phase. The phase-shifted activity is interpreted as the result of a phase-flip bifurcation, also occurring in a set of globally delay-coupled limit cycle oscillators. At the bifurcation point, there is a transition from in-phase to out-of-phase (or vice versa) synchronized oscillations, which is accompanied by an abrupt change in the common oscillation frequency. This phase-flip bifurcation was recently investigated in two mutually delay-coupled oscillators and can play a role in the mechanisms by which the neurons switch among different firing patterns.

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“…Depending on the parameters, it exhibits a 64 variety of firing patterns including irregular, tonic regular, bursting and chaotic 65 firing [12,32]. Based on the Huber & Braun (HB) thermoreceptor model [11], it will be 66 referred to as the HB+I h model. Examples of the chaotic and non-chaotic oscillations 67 are plotted in Fig 1 at different combinations of conductance parameters.…”

Section: /19mentioning

confidence: 99%

“…The first type of chaotic dynamics in neural systems is typically 14 accompanied by microscopic chaotic dynamics at the level of individual oscillators. The 15 presence of this chaos has been observed in networks of Hindmarsh-Rose neurons [8] and 16 biophysical conductance-based neurons [9][10][11][12]. The second type of chaotic firing pattern 17 is the synchronous chaos.…”

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confidence: 92%

Is chaos making a difference? Synchronization transitions in chaotic and nonchaotic neuronal networks

Maidana

Castro

et al. 2017

Preprint

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Chaotic dynamics of neural oscillations has been shown at the single neuron and network levels, both in experimental data and numerical simulations. Theoretical studies over the last twenty years have demonstrated an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to relevant network behavior and whether the dynamical richness of neural networks are sensitive to the dynamics of isolated neurons, still remain open questions. We investigated transition dynamics of a medium-sized heterogeneous neural network of neurons connected by electrical coupling in a small world topology. We make use of an oscillatory neuron model (HB+I h ) that exhibits either chaotic or non-chaotic behavior at different combinations of conductance parameters. Measuring order parameter as a measure of synchrony, we find that the heterogeneity of firing rate and types of firing patterns make a greater contribution than chaos to the steepness of synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in process of network synchronization transitions. Moreover, the macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as the multi-stable behavior, where the network dynamically switches between a number of different semi-synchronized, metastable states.

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Computer Simulations of Neuronal Signal Transduction: The Role of Nonlinear Dynamics and Noise

Cited by 140 publications

References 33 publications

Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

Dynamics of globally delay-coupled neurons displaying subthreshold oscillations

Is chaos making a difference? Synchronization transitions in chaotic and nonchaotic neuronal networks

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