Cognitive Brain Rhythms via Sparse Synchronization

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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