Chaotic Resonance in Coupled Inferior Olive Neurons with the Llinás Approach Neuron Model

It is well known that cerebellar motor control is fine-tuned by the learning process adjusted according to rich error signals from inferior olive (IO) neurons. Schweighofer and colleagues proposed that these signals can be produced by chaotic irregular firing in the IO neuron assembly; such chaotic resonance (CR) was replicated in their computer demonstration of a Hodgkin-Huxley (HH)-type compartment model. In this study, we examined the response of CR to a periodic signal in the IO neuron assembly comprising the Llinás approach IO neuron model. This system involves empirically observed dynamics of the IO membrane potential and is simpler than the HH-type compartment model. We then clarified its dependence on electrical coupling strength, input signal strength, and frequency. Furthermore, we compared the physiological validity for IO neurons such as low firing rate and sustaining subthreshold oscillation between CR and conventional stochastic resonance (SR) and examined the consistency with asynchronous firings indicated by the previous model-based studies in the cerebellar learning process. In addition, the signal response of CR and SR was investigated in a large neuron assembly. As the result, we confirmed that CR was consistent with the above IO neuron’s characteristics, but it was not as easy for SR.

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Electrical Coupling Controls Dimensionality and Chaotic Firing of Inferior Olive Neurons

SSRN Electronic Journal ◽

10.2139/ssrn.3403331 ◽

2019 ◽

Author(s):

Huu Hoang ◽

Eric J. Lang ◽

Yoshito Hirata ◽

Isao T. Tokuda ◽

Kazuyuki Aihara ◽

...

Keyword(s):

Inferior Olive ◽

Electrical Coupling ◽

Inferior Olive Neurons

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Electrical coupling controls dimensionality and chaotic firing of inferior olive neurons

PLoS Computational Biology ◽

10.1371/journal.pcbi.1008075 ◽

2020 ◽

Vol 16 (7) ◽

pp. e1008075

Author(s):

Huu Hoang ◽

Eric J. Lang ◽

Yoshito Hirata ◽

Isao T. Tokuda ◽

Kazuyuki Aihara ◽

...

Keyword(s):

Inferior Olive ◽

Electrical Coupling ◽

Inferior Olive Neurons

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Electrical coupling controls dimensionality and chaotic firing of inferior olive neurons

10.1101/542183 ◽

2019 ◽

Cited By ~ 1

Author(s):

Huu Hoang ◽

Eric J. Lang ◽

Yoshito Hirata ◽

Isao T. Tokuda ◽

Kazuyuki Aihara ◽

...

Keyword(s):

Degrees Of Freedom ◽

Inferior Olive ◽

Electrical Coupling ◽

Training Sample ◽

Firing Frequency ◽

Effective Coupling ◽

Neural Learning ◽

Inferior Olive Neurons ◽

Coupling Strengths

SUMMARYOne of the main challenges facing online neural learning systems with numerous modifiable parameters (or “degrees-of-freedom”) such as the cerebellum, is how to avoid “overfitting”. We previously proposed that the cerebellum controls the degree-of-freedoms during learning by gradually modulating the electric coupling strength between inferior olive neurons. Here, we develop a modeling technique to estimate effective coupling strengths between inferior olive neurons from in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions. We show that high coupling strengths induce synchronous firing and decrease the dimensionality of inferior olive firing dynamics. In contrast, intermediate coupling strengths induce chaotic firing and increase the dimensionality of firing dynamics. Our results thus support the hypothesis that effective coupling controls the dimensionality of inferior olive firing, which may allow the olivocerebellar system to learn effectively from a small training sample set despite the low firing frequency of inferior olive neurons.

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Adaptive coupling of inferior olive neurons in cerebellar learning

Neural Networks ◽

10.1016/j.neunet.2012.12.006 ◽

2013 ◽

Vol 47 ◽

pp. 42-50 ◽

Cited By ~ 20

Author(s):

Isao T. Tokuda ◽

Huu Hoang ◽

Nicolas Schweighofer ◽

Mitsuo Kawato

Keyword(s):

Inferior Olive ◽

Inferior Olive Neurons ◽

Adaptive Coupling ◽

Cerebellar Learning

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Encoding of Oscillations by Axonal Bursts in Inferior Olive Neurons

Neuron ◽

10.1016/j.neuron.2009.03.023 ◽

2009 ◽

Vol 62 (3) ◽

pp. 388-399 ◽

Cited By ~ 135

Author(s):

Alexandre Mathy ◽

Sara S.N. Ho ◽

Jenny T. Davie ◽

Ian C. Duguid ◽

Beverley A. Clark ◽

...

Keyword(s):

Inferior Olive ◽

Inferior Olive Neurons

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Low-Amplitude Oscillations in the Inferior Olive: A Model Based on Electrical Coupling of Neurons With Heterogeneous Channel Densities

Journal of Neurophysiology ◽

10.1152/jn.1997.77.5.2736 ◽

1997 ◽

Vol 77 (5) ◽

pp. 2736-2752 ◽

Cited By ~ 134

Author(s):

Yair Manor ◽

John Rinzel ◽

Idan Segev ◽

Yosef Yarom

Keyword(s):

Inferior Olive ◽

Electrical Coupling ◽

The Other ◽

Sustained Oscillation ◽

Large Coupling ◽

Model Based ◽

Subthreshold Oscillations ◽

Coupling Current ◽

Low Amplitude ◽

Inferior Olivary

Manor, Yair, John Rinzel, Idan Segev, and Yosef Yarom. Low-amplitude oscillations in the inferior olive: a model based on electrical coupling of neurons with heterogeneous channel densities. J. Neurophysiol. 77: 2736–2752, 1997. The mechanism underlying subthreshold oscillations in inferior olivary cells is not known. To study this question, we developed a single-compartment, two-variable, Hodgkin-Huxley-like model for inferior olive neurons. The model consists of a leakage current and a low-threshold calcium current, whose kinetics were experimentally measured in slices. Depending on the maximal calcium and leak conductances, we found that a neuron model's response to current injection could be of four qualitatively different types: always stable, spontaneously oscillating, oscillating with injection of current, and bistable with injection of current. By the use of phase plane techniques, numerical integration, and bifurcation analysis, we subdivided the two-parameter space of channel densities into four regions corresponding to these behavioral types. We further developed, with the use of such techniques, an empirical rule of thumb that characterizes whether two cells when coupled electrically can generate sustained, synchronized oscillations like those observed in inferior olivary cells in slices, of low amplitude (0.1–10 mV) in the frequency range 4–10 Hz. We found that it is not necessary for either cell to be a spontaneous oscillator to obtain a sustained oscillation. On the other hand, two spontaneous oscillators always form an oscillating network when electrically coupled with any arbitrary coupling conductance. In the case of an oscillating pair of electrically coupled nonidentical cells, the coupling current varies periodically and is nonzero even for very large coupling values. The coupling current acts as an equalizing current to reconcile the differences between the two cells' ionic currents. It transiently depolarizes one cell and/or hyperpolarizes the other cell to obtain the regenerative response(s) required for the synchronized oscillation. We suggest that the subthreshold oscillations observed in the inferior olive can emerge from the electrical coupling between neurons with different channel densities, even if the inferior olive nucleus contains no or just a small proportion of spontaneously oscillating neurons.

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Electrophysiological Properties of Inferior Olive Neurons: A Compartmental Model

Journal of Neurophysiology ◽

10.1152/jn.1999.82.2.804 ◽

1999 ◽

Vol 82 (2) ◽

pp. 804-817 ◽

Cited By ~ 77

Author(s):

Nicolas Schweighofer ◽

Kenji Doya ◽

Mitsuo Kawato

Keyword(s):

Calcium Current ◽

Potassium Current ◽

Inferior Olive ◽

Sodium Current ◽

Electrical Coupling ◽

Biophysical Model ◽

Delayed Rectifier ◽

High Threshold ◽

Electrophysiological Properties

As a step in exploring the functions of the inferior olive, we constructed a biophysical model of the olivary neurons to examine their unique electrophysiological properties. The model consists of two compartments to represent the known distribution of ionic currents across the cell membrane, as well as the dendritic location of the gap junctions and synaptic inputs. The somatic compartment includes a low-threshold calcium current ( I Ca_l), an anomalous inward rectifier current ( I h), a sodium current ( I Na), and a delayed rectifier potassium current ( I K_dr). The dendritic compartment contains a high-threshold calcium current ( I Ca_h), a calcium-dependent potassium current ( I K_Ca), and a current flowing into other cells through electrical coupling ( I c). First, kinetic parameters for these currents were set according to previously reported experimental data. Next, the remaining free parameters were determined to account for both static and spiking properties of single olivary neurons in vitro. We then performed a series of simulated pharmacological experiments using bifurcation analysis and extensive two-parameter searches. Consistent with previous studies, we quantitatively demonstrated the major role of I Ca_l in spiking excitability. In addition, I h had an important modulatory role in the spike generation and period of oscillations, as previously suggested by Bal and McCormick. Finally, we investigated the role of electrical coupling in two coupled spiking cells. Depending on the coupling strength, the hyperpolarization level, and the I Ca_l and I hmodulation, the coupled cells had four different synchronization modes: the cells could be in-phase, phase-shifted, or anti-phase or could exhibit a complex desynchronized spiking mode. Hence these simulation results support the counterintuitive hypothesis that electrical coupling can desynchronize coupled inferior olive cells.

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Noise and Coupling Affect Signal Detection and Bursting in a Simulated Physiological Neural Network

Journal of Neurophysiology ◽

10.1152/jn.00223.2002 ◽

2002 ◽

Vol 88 (5) ◽

pp. 2598-2611 ◽

Cited By ~ 33

Author(s):

William C. Stacey ◽

Dominique M. Durand

Keyword(s):

Signal Detection ◽

Epileptiform Activity ◽

Electrical Coupling ◽

Periodic Signal ◽

Physiological Noise ◽

Ca1 Neurons ◽

Ca1 Region ◽

Noise Characteristics ◽

Hippocampal Ca1

Signal detection in the CNS relies on a complex interaction between the numerous synaptic inputs to the detecting cells. Two effects, stochastic resonance (SR) and coherence resonance (CR) have been shown to affect signal detection in arrays of basic neuronal models. Here, an array of simulated hippocampal CA1 neurons was used to test the hypothesis that physiological noise and electrical coupling can interact to modulate signal detection in the CA1 region of the hippocampus. The array was tested using varying levels of coupling and noise with different input signals. Detection of a subthreshold signal in the network improved as the number of detecting cells increased and as coupling was increased as predicted by previous studies in SR; however, the response depended greatly on the noise characteristics present and varied from SR predictions at times. Careful evaluation of noise characteristics may be necessary to form conclusions about the role of SR in complex systems such as physiological neurons. The coupled array fired synchronous, periodic bursts when presented with noise alone. The synchrony of this firing changed as a function of noise and coupling as predicted by CR. The firing was very similar to certain models of epileptiform activity, leading to a discussion of CR as a possible simple model of epilepsy. A single neuron was unable to recruit its neighbors to a periodic signal unless the signal was very close to the synchronous bursting frequency. These findings, when viewed in comparison with physiological parameters in the hippocampus, suggest that both SR and CR can have significant effects on signal processing in vivo.

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