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 Education2 Department of Physics Kangwon National University

Silent Brain Rhythms via Full Synchronization

Alpha Rhythm[H. Berger, Arch. Psychiatr Nervenkr.87, 527 (1929)]Slow brain rhythm (3~12Hz) with large amplitude during the contemplation with closing eyes

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Sleep Spindle Rhythm[M. Steriade, et. Al. J. Neurophysiol. 57, 260 (1987).]Brain rhythm (7~14Hz) with large amplitude during deep sleep without dream

Brain Rhythms for the Silent Brain

Individual Neurons: Regular Firings like ClocksLarge-Amplitude Slow Population Rhythm viaFull 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)

Silent Brain Rhythms via Full Synchronization

Behaving Brain Rhythms via Sparse Synchronization

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 behaviorIn contrast for the slow brain rhythm with large amplitude for silent brain

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Brain Rhythms for the Waking Brain

Gamma rhythm in visual cortex of behaving monkey

Individual Neurons: Intermittent and Stochastic Firings like Geiger CountersSmall-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

Behaving Brain Rhythms via Sparse Synchronization

Gamma Rhythm via Sparse Synchronization

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Gamma Rhythm in An Excitatory-Inhibitory Network

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

Population Coherent Rhythm ~ 40Hz Gamma Oscillation

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

Gamma Rhythm: Associated with Various Cognitive Functions such as Sensory Perception, Multisensory Binding, Selective Attention, & Working MemoryImpaired Gamma Rhythm: Neural Diseases associated with Cognitive Dysfunction (schizophrenia, autism spectrum disorder)

Globally-Coupled Inhibitory Morris-Lecar Neurons

Coupled Morris-Lecar (ML) Neurons

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N

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:Coupling Synaptic Global

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:receptors) GABAby (mediated Synapse Inhibitory1-1-

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Firings in the Single Type-I ML Neuron

Type-I Excitability(act as an integrator)

Regular Firing of the Suprathreshold casefor IDC=41

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

Excitability of the Single ML Neuron

Type-II Excitability(act as a resonator)

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

Homogeneous Population of Inhibitory Subthreshold ML Neurons

Incoherent State: N, then O0Coherent State: N, then O Non-zero value

Inhibitory Synchronization

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

Investigation of Inhibitory Synchronization (Population Synchronization via Synaptic Inhibition) Using a Thermodynamic Order Parameter:

(VG: Ensemble-Averaged Membrane Potential)

22 ))()(()( tVtVV GGG O

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Heterogeneous Population of Subthreshold and Suprathreshold Neurons

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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)

Hz8.13Gf Hz3.14Gf Hz6.13Gf Hz2.14Gf

8,20 DJ

8,20 DJ

Firing Patterns of Suprathreshold and Subthreshold Neurons

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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.

Hz6.3sf Hz8.2sf Hz3.2sf Hz8.1sf

Subthreshold Neurons (hopping synchronization) By virtue of coherent inhibition of sparsely synchronized suprathreshold neurons, occurrence of hopping synchronization between the potentials of subthreshold neurons

8,20 DJ

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

Characterization of Sparse Spike Synchronization

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

Occupation Degree Oi

Pacing Degree Pi

8,20 DJ

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:

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

Spiking Coherence Measure

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

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)

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