FrequencyDomain Order Parameter for Synchronization Transition of Bursting

Frequency-Domain Order Parameter for Synchronization Transition of Bursting Neurons 1 Lim Woochang and Sang-Yoon 1 Department of Science Education, Daegu National University of Education 2 Research Division, LABASIS Co. Introduction Burstings with the Slow and Fast Time Scales Bursting: Neuronal activity alternates, on a slow timescale, between a silent phase and an active (bursting) phase of fast repetitive spikings Representative examples of bursting neurons: chattering neurons in the cortex, thalamocortical relay neurons, thalamic reticular neurons, hippocampal pyramidal neurons, Purkinje cells in the cerebellum, pancreatic -cells, and respiratory neurons in pre-Botzinger complex Synchronization of Bursting Neurons Two Different Synchronization Patterns Due to the Slow and Fast Time Scales of Bursting Activity Burst Synchronization: Synchrony on the Slow Bursting Timescale Temporal coherence between the active phase (bursting) onset or offset times of bursting neurons Spike Synchronization: Synchrony on the Fast Spiking Timescale Temporal coherence between intraburst spikes fired by bursting neurons in their respective active phases Inhibitory Population of Bursting Neurons Parameters in the single Hindmarsh-Rose (HR) neuron Parameters for the synaptic current Bursting Activity in the HR Neuron Bursting Transition in the Single Neuron Transition to bursting occurs IDC=I*DC (~1. 268) Characterization of Bursting Transition in Terms of Bursting Order Parameter Investigation of Population Bursting States via Separation of Slow Timescale Separation of the slow timescale from IPFR R via low-pass filtering (fc=10 Hz) IPBR Rb As D is increased, bursting bands in the raster plots becomes smeared and overlap. Amplitude of Rb decreases. Investigation of Population Bursting States in the Frequency Domain Power spectra of Rb Bursting Coherence Factor Hp and fp: Height and frequency of bursting peak fp: width of the bursting peak at the height of e-1/2 Hp. Frequency-Domain Bursting Order Parameter Unsynchronized Bursting State: N , then < b>r 0 Synchronized Bursting State: N , then < b>r Non-zero value Bursting Transition occurs for 2 Kim Characterization of Intraburst Spiking Transition Based on Rs Investigation of Intraburst Spiking States via Separation of Fast Time Scale and in the Frequency Domain IPSR Rs via band-pass filtering [lower and higher cut-off frequencies of 30 Hz (high-ass filter) and 90 Hz (low-pass filter)] As D is increased, stripes in the burst band becomes smeared and overlap. Amplitude of Rs decreases. Peak in the power spectra of Rs decreases. Frequency-Domain Spiking Order Parameter Unsynchronized Spiking State: N , then < s>r 0 Synchronized Spiking State: N , then < s>r Non-zero value Bursting Transition occurs for Characterization of Bursting Transition Based on Bursting Onset and Offset Times Investigation of Population Bursting States Based on Bursting Onset and Offset Times and in the Frequency Domain Another Raster plots of bursting onset and offset times and IPBR and As D is increased, bursting stripes in the raster plots becomes smeared and overlap. Amplitude of both and decreases. Peak in the power spectra of and of decreases. Frequency-Domain Bursting Order Parameter Unsynchronized Bursting State: N , then Synchronized Bursting State: N , then Non-zero value Bursting Transition occurs for Summary � Synchronization of Bursting Neurons: Burst and Spike Synchronizations Due to the Slow and Fast Timescales of Bursting Activity � Characterization of Burst and Spike Synchronizations via Separation of the Slow (Bursting) and Fast (Spiking) Time Scales by Frequency Filtering IPFR R IPBR Rb (Describing the Slow Bursting Behavior) and IPSR Rs (Describing the Fast Spiking Behavior) � Characterization of Burst Synchronization Based on Bursting Onset and Offset Times Direct Investigation of Bursting Behavior without Separation of Timescales � Characterization of Burst and Spike Synchronization in the Frequency Domain Power Spectrum: Practical Analysis Tools in the Experiments Frequency-Domain Order Parameter: Realistic Order Parameter Applicable in the Real Experiment (Raster Plots, IPFR, and Power Spectrum: Directly Obtained in the Experiments)