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1 Cycle 6: Synchronization by Oscillation

2 Introduction oscillation Resonator and oscillator Perturbation to an oscillator Network of oscillators oscillation (synchronization)?

3 What is an Oscillator? Neuronal oscillator : Limit cycle or Weakly chaotic oscillator Limit cycle Harmonic relaxation types (pulsatile oscillator) Slow accrual and fast release of energy Van der pol oscillator : integrate-and-fire oscillator : model of single neuron

4 Van der Pol circuit Tunnel Diode

5 <<1 Harmonic >>1 Relaxation oscillation Special case of FitzHugh-Nagumo

6 EEG Harmonic (sinusoid) Relaxation Active (Duty) Increase frequency Excitable Information transfer Harmonic (sinusoid)

7 Harmonic vs Relaxation 1. harmonic 2. Relaxation oscillator 1 synchrony

8 Resonator or oscillator? Transient oscillation oscillator resonator Beginning of stage Hz waves For 0.5 to 1.5 Oscillator : opposing forces and positive feedback Resonator : only opposing forces resonator

9 Oscillation and Resonance in Single Neurons Rodolfo Llinas : Active neuron Voltage gating: channel open/close depends on membrane potential Ligand gatig : neurotransmitters, drugs Ion-dependent gating : ex) Ca influx opens Kchannel Second-messenger gating

10 band-pass filters notch band-stop filter subthreshold oscillators etc Low-pass filter: passive neuron: Passive leak conductance and caacitance High-pass filter: active neuron: resting membrane potential voltage-gated currents

11 Preferred constellation of neuron 5Hz 30Hz Hz 20-40Hz 5-7Hz Pike et al. J.Physiol 2000 pp205

12 channel neuron Sejnowsky Nature vol pp363

13 Collective neuronal behavior can be established through synchrony Time window for coincidence 10msec : cortical pyramidal neuron Membrane time constant : integration of IPSP/EPSP Time constant input resistance (K channel) Time window for synchrony Harmonic : half of period Excitable period (harmonic ) excitable period neuron

14 External and internal sources of synchrony externally driven or self-generated Externally driven example of Albright Self-organized activity cognition?

15 Externally driven temporal coordination of ensemble synchrony Macaque middle temporal (MT) area 1bits/s ~29bits/s Thomas D. Albright Neuron vol

16 Stochastic Resonance Bistable system (neuron) Rhythmic input (below threshold) +White noise (below threshold) externally or internally by the brain Occasional action potential S/N Yerkes-Dodson law

17 Source of noise? Recycle the wasted action potential (population code) : single spike is reliable Chaotic behavior in brain Mixing of various oscillators cycle12

18 Emergence of cell assemblies through synchrony Cell assembly : Transient coalition of neuron Donald O. Hebb 1. Hebb s synaptic plasticity rule assembly 2. cell assembly 3. chain 4. 1 neuron assemblies

19 Example of Cell assembly Cell assembly Theta trough Trough depolarization spike Kenneth D Harris Nature pp552

20 Peer prediction method Optimal window : 10-30ms Duration of EPSP in pyramidal cells in vivo Period of gamma-frequency oscillations Most critical time window for Spike-timingdependent plasticity of synapse Resonance and subthreshold oscillations of layer 4 cortical neurons Peer prediction method neuron (place cell) spike train Rat spike spike Peer Prediction timescale (bin) spike bin size

21 Oscillatory synchrony is energetically cheap Maximum of the normalized correlation Average noise intensity 3s Nature vol pp849

22 Rules for oscillatory networks? Perturbation 1

23 Summary oscillation Oscillator : Limit cycle or weakly chaotic oscillator Relaxation oscillator : synchronize quickly Resonator : tuned by channels Collective behavior of oscillators : synchrony Stochastic resonance oscillation (synchronization)? Cell assembly : self-organization Metabolically cheap to exert a maximal impact

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