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Cognitive Brain Rhythms via Sparse Synchronization Inhibitory Synchronization in A Heterogeneous Population of Subthreshold and Suprathreshold Type-I Neurons. Woochang Lim 1 and Sang-Yoon Kim 2 1 Department of Science Education Daegu National University of Education

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Cognitive Brain Rhythms via Sparse Synchronization


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slide1

Cognitive Brain Rhythms

via Sparse Synchronization

Inhibitory Synchronization in A Heterogeneous Population

of Subthreshold and Suprathreshold Type-I Neurons

Woochang Lim1 and Sang-Yoon Kim2

1 Department of Science Education

Daegu National University of Education

2 Department of Physics

Kangwon National University

slide2

Silent Brain Rhythms via Full Synchronization

 Brain Rhythms for the Silent Brain

Sleep Spindle Rhythm

[M. Steriade, et. Al. J. Neurophysiol. 57, 260 (1987).]

Brain rhythm (7~14Hz) with large amplitude during deep sleep without dream

Alpha Rhythm

[H. Berger, Arch. Psychiatr Nervenkr.87, 527 (1929)]

Slow brain rhythm (3~12Hz) with large amplitude during the contemplation with closing eyes

 Silent Brain Rhythms via Full Synchronization

Individual Neurons: Regular Firings like Clocks

Large-Amplitude Slow Population Rhythm via

Full Synchronization of Individual Regular Firings

Investigation of this Huygens mode of full synchronization using coupled oscillators model

 Coupled Suprathreshold Neurons (without noise or with small noise)

1

slide3

Behaving Brain Rhythms via Sparse Synchronization

 Brain Rhythms for the Waking Brain

Gamma Rhythm

[G. Buzsaki & XJ. Wang, Annu. Rev. Neurosci. 35, 203 (2012)]

Desynchronized EEG: Appearance of fast brain

rhythm (30~80Hz) with small amplitude

in the EEG of the Waking Brain during behavior

In contrast for the slow brain rhythm with large

amplitude for silent brain

Gamma rhythm in visual cortex of behaving monkey

 Behaving Brain Rhythms via Sparse Synchronization

  • Individual Neurons: Intermittent and Stochastic Firings
  • like Geiger Counters
  • Small-Amplitude Fast Population Rhythm via Sparse
  • Synchronization of Individual Complex Firings
  • Coupled oscillators model: Inappropriate for investigation
  • Of the behaving brain rhythm via sparse synchronization
  • Coupled Subthreshold and/or Suprathreshold Neurons

in the Presence of Strong Noise

  • They exhibit noise-induced complex firing patterns

2

slide4

Gamma Rhythm via Sparse Synchronization

 Gamma Rhythm in An Excitatory-Inhibitory Network

[N. Brunel and XJ. Wang, J. Neurophysiol. 90, 415 (2003)]

Pyramidal cells and interneurons show intermittent and irregular firing patterns like Geiger counters

Population Coherent Rhythm ~ 40Hz  Gamma Oscillation

Gamma Rhythm: Associated with Various Cognitive Functions such as

Sensory Perception, Multisensory Binding, Selective Attention,

& Working Memory

Impaired Gamma Rhythm: Neural Diseases associated with Cognitive Dysfunction

(schizophrenia, autism spectrum disorder)

3

slide5

Globally-Coupled Inhibitory Morris-Lecar Neurons

[S.-Y. Kim, D.G. Hong, J. Kim and W. Lim, J. Phys. A 45, 155102 (2012).]

 Coupled Morris-Lecar (ML) Neurons

 Excitability of the Single ML Neuron

Type-II Excitability

(act as a resonator)

Type-I Excitability

(act as an integrator)

 Firings in the Single Type-I ML Neuron

Noise-Induced Firing of the Subthreshold case for IDC=39 and D=20

Regular Firing of the Suprathreshold case

for IDC=41

4

slide6

Homogeneous Population of Inhibitory Subthreshold ML Neurons

 Inhibitory Synchronization

Investigation of Inhibitory Synchronization

(Population Synchronization via Synaptic Inhibition)

Using a Thermodynamic Order Parameter:

(VG: Ensemble-Averaged Membrane Potential)

Incoherent State: N, then O0

Coherent State: N, then O Non-zero value

No Inhibitory Synchronization for the case of type-I integrators,

in contrast to the case of type-II resonators

Type-I, J=20

Type-II, J=20

5

slide7

Heterogeneous Population of Subthreshold and Suprathreshold Neurons

  • Investigation of Inhibitory Synchronization
  • in A Heterogeneous Population

by Increasing the Fraction of

Suprathreshold Neurons

Appearance of Inhibitory Synchronization for Psupra > P*supra (~0.16)

Appearance of Partially Occupied Stripes in the Raster Plot

 Emergence of Sparsely-Synchronized Small-Amplitude Fast Oscillation (Beta rhythm)

6

slide8

Firing Patterns of Suprathreshold and Subthreshold Neurons

  • Suprathreshold Neurons

(sparse spike synchronization)

  • Individual potentials:
  • sparsely synchronized spikings
  • (multi-peaked ISI histogram) +
  • coherent small-amplitude hoppings
  •  Role of Coherent Inhibitor for the
  • Emergence of Inhibitory Sync.
  • Subthreshold Neurons

(hopping synchronization)

By virtue of coherent inhibition of

sparsely synchronized suprathreshold

neurons, occurrence of hopping

synchronization between the

potentials of subthreshold neurons

Multi-Peaked ISI Histogram & Firing Freq. of Individual Neurons << Population Rhythm Freq.

7

slide9

Characterization of Sparse Spike Synchronization

[W. Lim and S.Y. Kim, J. Comput. Neurosci. 31, 667 (2011).]

Sparse Synchronization: Well Seen in Partially-Occupied Stripes in the Raster Plot of Neural Spikes

Measuring the Degree of Sparse Spike Synchronization in terms of a Statistical-Mechanical

Spike-Based Measure by Considering the Occupation Pattern and the Pacing Degree of Spikes

in the Stripes:

  • Occupation Degree Oi

Representing the Density of the ith Stripe in terms of Fraction of Spiking Neurons

 Sparse Synchronization

 Pacing Degree Pi

Denoting the Smearing of The ith Stripe by Taking into Consideration of Average Contribution of Microscopic Individual Spikes to The Macroscopic Global Potential

 Spiking Coherence Measure

8

slide10

Summary

  • Sparse Spike Synchronization in Heterogeneous Population of Inhibitory

Suprathreshold and Subthreshold Type-I Neurons

  • Homogeneous population of Inhibitory Subthreshold Type-I (Integrating) Neurons
  •  No Synchronization (in contrast to the case of type-II resonating neurons)
  • Occurrence of Sparse Synchronization for Psupra > P*supra
  •  Suprathreshold neurons (showing sparse spike synchronization:
  • mean firing rate ~ 2Hz) play the role of coherent inhibitors
  • for the emergence of inhibitory synchronization in the
  • whole population (subthreshold neurons: hopping synchronization)
  • Emergence Small-Amplitude Fast Population Rhythm (~15Hz)

9