Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP 3

Falcke, Martin; Huerta, Ramón; Rabinovich, M. I.; Abarbanel, Henry D. I.; Elson, Robert C.; Selverston, Allen I.

doi:10.1007/s004220050604

Cited by 85 publications

(62 citation statements)

References 24 publications

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“…Indeed, it is well known that individual neurons can express either irregular or regular forms of burst firing as a result of specific sets of voltage-dependent conductances and intracellular signal cascades that can be activated and modified by neuromodulatory transmitters (Canavier et al, 1994;Turrigiano et al, 1994;Lechner et al, 1996;Falcke et al, 2000). Although in the context of the present study the pattern-initiating B63 neurons themselves are obvious candidates for such modulatory control, the possible contribution of modifications to the burst-generating properties of other buccal Conversely, continuous hyperpolarizing current (Ϫ2 nA) injected into the B63 neurons of contingent preparations (middle gray bar) significantly decreased the rate of motor patterns compared with that occurring spontaneously (middle black bar; W ϭ 21).…”

Section: Cellular Loci For Operant Learningmentioning

confidence: 99%

Behavioral andIn VitroCorrelates of Compulsive-Like Food Seeking Induced by Operant Conditioning inAplysia

Nargeot¹,

Petrissans²,

Simmers³

2007

J. Neurosci.

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Motivated behaviors comprise appetitive actions whose occurrence results partly from an internally driven incentive to act. Such impulsive behavior can also be regulated by external rewarding stimuli that, through learning processes, can lead to accelerated and seemingly automatic, compulsive-like recurrences of the rewarded act. Here, we explored such behavioral plasticity in Aplysia by analyzing how appetitive reward stimulation in a form of operant conditioning can modify a goal-directed component of the animal's food-seeking behavior. In naive animals, protraction/retraction cycles of the tongue-like radula are expressed sporadically with highly variable interbite intervals. In contrast, animals that were previously given a food-reward stimulus in association with each spontaneous radula bite now expressed movement cycles with an elevated frequency and a stereotyped rhythmic organization. This rate increase and regularization, which was retained for several hours after training, depended on both the reward quality and its contingency because accelerated, stereotyped biting was not induced in animals that had previously received a less-palatable food stimulus or had been subjected to nonassociative reward stimulation. Neuronal correlates of these learning-induced changes were also expressed in the radula motor pattern-generating circuitry of isolated buccal ganglia. In such in vitro preparations, moreover, manipulation of the burst frequency of the bilateral motor pattern-initiating B63 interneurons indicated that the regularization of radula motor pattern generation in contingently trained animals occurred separately from an increase in cycle rate, thereby suggesting independent processes of network plasticity. These data therefore suggest that operant conditioning can induce compulsive-like actions in Aplysia feeding behavior and provide a substrate for a cellular analysis of the underlying mechanisms.

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Section: Cellular Loci For Operant Learningmentioning

confidence: 99%

Behavioral andIn VitroCorrelates of Compulsive-Like Food Seeking Induced by Operant Conditioning inAplysia

Nargeot¹,

Petrissans²,

Simmers³

2007

J. Neurosci.

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“…Irregular activity in neuronal models has been associated with the presence of deterministic chaos [39][40][41]. Nevertheless, the main cause of irregularities in our model is the amplification of stochastic phenomena by the transient dynamics.…”

Section: Discussionmentioning

confidence: 90%

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

et al. 2014

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First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network reveals irregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior.We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine-tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained, and can approximate several possible sources of noise, e.g. random channel gating or synaptic bombardment.The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).

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“…So the irregular behavior, found to be related to nonlinear and chaotic properties of the cells (Falcke et al 2000;Rabinovich et al 1997), is structurally stable in a high-dimensional experimental parameter space, where the neurons are subject to small fluctuations not only in intrinsic properties but also in several other external parameters, such as temperature, ionic concentrations of the saline, etc.…”

Section: Introductionmentioning

confidence: 99%

Whole Cell Stochastic Model Reproduces the Irregularities Found in the Membrane Potential of Bursting Neurons

Carelli

Reyes²,

Sartorelli³

et al. 2005

Journal of Neurophysiology

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. Whole cell stochastic model reproduces the irregularities found in the membrane potential of bursting neurons. J Neurophysiol 94: 1169 -1179, 2005. First published March 30, 2005 doi:10.1152/jn.00070.2005. Irregular intrinsic behavior of neurons seems ubiquitous in the nervous system. Even in circuits specialized to provide periodic and reliable patterns to control the repetitive activity of muscles, such as the pyloric central pattern generator (CPG) of the crustacean stomatogastric ganglion (STG), many bursting motor neurons present irregular activity when deprived from synaptic inputs. Moreover, many authors attribute to these irregularities the role of providing flexibility and adaptation capabilities to oscillatory neural networks such as CPGs. These irregular behaviors, related to nonlinear and chaotic properties of the cells, pose serious challenges to developing deterministic Hodgkin-Huxley-type (HHtype) conductance models. Only a few deterministic HH-type models based on experimental conductance values were able to show such nonlinear properties, but most of these models are based on slow oscillatory dynamics of the cytosolic calcium concentration that were never found experimentally in STG neurons. Based on an up-to-date single-compartment deterministic HH-type model of a STG neuron, we developed a stochastic HH-type model based on the microscopic Markovian states that an ion channel can achieve. We used tools from nonlinear analysis to show that the stochastic model is able to express the same kind of irregularities, sensitivity to initial conditions, and low dimensional dynamics found in the neurons isolated from the STG. Without including any nonrealistic dynamics in our whole cell stochastic model, we show that the nontrivial dynamics of the membrane potential naturally emerge from the interplay between the microscopic probabilistic character of the ion channels and the nonlinear interactions among these elements. Moreover, the experimental irregular behavior is reproduced by the stochastic model for the same parameters for which the membrane potential of the original deterministic model exhibits periodic oscillations.

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Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP 3

Cited by 85 publications

References 24 publications

Behavioral andIn VitroCorrelates of Compulsive-Like Food Seeking Induced by Operant Conditioning inAplysia

Behavioral andIn VitroCorrelates of Compulsive-Like Food Seeking Induced by Operant Conditioning inAplysia

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

Whole Cell Stochastic Model Reproduces the Irregularities Found in the Membrane Potential of Bursting Neurons

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