ch 9. rhythms and synchrony 9.7 adaptive cooperative systems, martin beckerman, 1997. summarized by...

Ch 9. Rhythms and SynchronyCh 9. Rhythms and Synchrony9.79.7

Adaptive Cooperative Systems, Adaptive Cooperative Systems, Martin Beckerman, 1997.Martin Beckerman, 1997.

Summarized by M.-O. Heo

Biointelligence Laboratory, Seoul National Universityhttp://bi.snu.ac.kr/

2(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/

ContentsContents

9.7 Oscillations and Synchrony in the Visual Cortex and Hippocampus 9.7.1 Mean-Field Model of Cortical Oscillations 9.7.2 Delay Connections and Nearest-Neighbor Interactions 9.7.3 Burst Synchronization 9.7.4 Rhythmic Population Oscillations in the Hippocampus 9.7.5 Feature Integration

Mean-Field Model of Cortical OscillationsMean-Field Model of Cortical Oscillations

How limit cycle oscillations may arise in a single cortical column in response to external stimuli?


Dynamic Equations for the cortical column activities


Mean firing rate of excitatory neurons

Mean firing rate of inhibitory neurons

# of Excitatory neurons# of Inhibitory neurons

Sigmoidal response fct.

External inputs to the excitatory cells(No input to the Inhibitory neurons)

Taylor Expansionwith τ=0, r=0

Sum over the index i

A stable fixed point characterizes the system at low-stimulus intensities.

There is a transition to limit cycle activity once the stimulus intensity increases beyond a critical value.


By coupling together a number of excitatory-inhibitory clusters

Introducing the phase variable through the deviations of the activities from the unstable fixed points


If η is weak…

The couplings proportional to η

Oscillator Freq.

Delay Connections and Nearest-Neighbor Delay Connections and Nearest-Neighbor InteractionsInteractions Delay connections in a simplified oscillator unit obeying the

followings.

Results When the time delays are either too small or too large, a system of

two coupled units will relax to a stable fixed point. There is a broad range of delays in the vicinity of 4 to 5 ms for

which the system will exhibit stable limit cycle behavior. Desynchronization was promoted by adding a second set of delay

connections operating between next nearest neighbors.

7

Delay

Damping Constant Noise inputs

Burst SynchronizationBurst Synchronization

Bush & Douglas A network composed of excitatory pyramidal and inhibitory basket

(smooth) neurons. Showing a rapid onset of synchronous bursting with randomly varying

interburst intervals. Koch & Schuster

Simplified Bush & Douglas Model One containing all-to-all excitatory binary (McCulloch-Pitts) neurons A single global inhibitor.

Generating burst synchronization without frequency locking The neural circuitry functions as a coincidence detector Inhibition improves frequency locking and determines the frequency

of the oscillatory firing pattern.


Rhythmic Population Oscillations in the Rhythmic Population Oscillations in the HippocampusHippocampus Hippocampus exhibits several different types of rhythmicity

and has a number of possibly redundant mechanisms for inducing collective responses. Hippocampal cells extend out widely arborizing axon collaterals those

provide the connectivity to generate recurrent excitation. GABAergic interneurons are present.

Inhibitory postsynaptic potentials (IPSP) are consistent with the timing required for recurrent inhibition.

Cells are capable of repetitive bursting The membrane potential of single pyramidal cells can oscillate in the

4~10 Hz range. Oscillatory cells in the entorhinal cortex projecting to hippocampal

neurons can also drive cells into 4~10 Hz oscillations. The 40-Hz oscillations

are a collective behavior of the network of inhibitory interneurons in the hippocampus. Mutual inhibition plays a key role for this.

Are from the intrinsic 40-Hz oscillatory interneurons.9(C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Computational studies for the characteristics of hippocampal rhythmicity. Traub et al.

200 excitatory neurons in a two-dimensional array 10 inhibitory neurons uniformly distributed across the array.

– Two types: fast inhibition, slow one When fast inhibition is present the bursting neurons self-organize

into clusters of synchronously firing cells. When fast inhibition is blocked, most of the cells in the population

burst coherently.


Constant speed traveling waves of activity Observed in EEG recordings

– 9000 model excitatory cells, each contacted 22 neurons; 20 of these excitatory, 2 of these inhibitory

– 900 inhibitory ones, each communicated 220 neurons;200 excitatory, 20 inhibitory

– Typical cell received 20 excitatory inputs and 20 inhibitory inputs. Connection probability

– Decreased exponentially with distance at a rate determined by space constants for excitatory and inhibitory units.


Feature IntegrationFeature Integration

Binding problem How attributes are integrated to produce a segmentation of the

scene into its component surfaces and a segregation of objects from their backgrounds.

Candidate mechanisms Through a convergence of low-level inputs into a small number of

higher-level neurons called grandfather or cardinal cells located in object-specific cortical areas.

Through assembly coding - through flexible associations of large numbers of simultaneously active neurons.

– Bound together by their synchronous firing– Experimental evidence that clusters of synchronously discharging

cells form within one or more columns and in different cortical regions and hemispheres.


Assembly coding and MRF-based integration-by-labeling are self-organizing processes that reinforce and improve the integration of features from one iteration to the next and are robust against noise.

Visual cortical areas were built from feature selective cells arranged topographically into cortical columns.

Assembly coding has been identified with gamma-band rhythmicity.


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