Stochastic Burst Synchronization in A Scale-Free Neural Network with - - PowerPoint PPT Presentation

Stochastic Burst Synchronization in A Scale-Free Neural Network with Spike-Timing-Dependent Plasticity

S.-Y. Kim and W. Lim Institute for Computational Neuroscience Daegu National University of Education

Synaptic Plasticity

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• Spike-Timing-Dependent Plasticity (STDP)

Synaptic Plasticity: In real brains synaptic strengths may vary to adapt to environment (potentiated or depressed) STDP: Plasticity depending on the relative time difference between the pre-and the post-synaptic burst onset times

• Purpose of Our Study

Investigation of Effect of the STDP on the SBS in the Scale-Free Network (SFN)

• Stochastic Burst Synchronization (SBS)

Subthreshold neurons: Fire only with the help of noise and exhibit irregular discharges like Geiger counter Bursting: Neuronal activity alternates, on a slow timescale, between a silent phase and an active (bursting) phase of fast repetitive spikings SBS: Population synchronization between complex noise-induced burstings of subthreshold neurons & correlated with brain function of encoding sensory stimuli in the noisy environment Previous works on SBS: Synaptic strengths were static.

• Hebbian STDP

Update of coupling strengths: Additive nearest-burst pair-based STDP rule

Initial synaptic strengths: Mean J0=2.5 & standard deviation =0.02

Asymmetric time window for Jij tij > 0  LTP ,  tij < 0  LTD

Excitatory SFN of Subthreshold Izhikevich Neurons

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) (

ij ij ij ij

t J J J     

           

 

    

for for

/ / ij t ij t ij

t e A t e A J

ij ij

 

)] . 5 ( ), 0001 . ( [ 005 . ,

) ( ) (

      

h l ij pre j post i ij

J J J t t t 

• Scale-Free Network (SFN) of Subthreshold Izhikevich Neurons

Barabási-Albert SFN with symmetric attachment degree l*=10 (Growth and preferential directed attachment with lin incoming edges and lout

• utgoing edges; lin = lout = l*)

Subthreshold Izhikevich Neurons for the DC current IDC,i[3.55, 3.65]

. ) ( m sec, 30 m sec, 15 , 6 . , . 1        

    ij ij

t J A A  

• Raster Plots of Burst Onset Times

Appearance of stripes in the raster plot for synchronous case

SBS in the Absence of STDP

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Initial coupling strengths {Jij}: Gaussian distribution with mean J0=2.5 and standard deviation 0=0.02

• Thermodynamic Bursting Order Parameter:

Synchronized (desynchronized) state: Ob approach non-zero (zero) limit values for N SBS in via competition between the constructive and the destructive roles of noise.

) 4 . 18 ~ ( ) 1173 . ~ (

* * h l

D D D  

• Instantaneous Population Burst Rate (IPBR)

       

  



t e h t K t t K N t R

h t h N i n s i b h b

i

, 2 1 ) ( ; ) ( 1 ) (

2 2 2

/ 1 1 ) (



2

) ) ( ) ( ( t R t R

b b b

  O

• Histograms for Fraction of Synapses (Saturated limit value of Jij)

becomes larger (smaller) than the initial value for the case of LTP (LTD). The standard deviations are very larger than the initial one (=0.02).

• Time-Evolution of Population-Averaged Synaptic Strength <Jij>

D=0.3, 5, 9 and 13: <Jij> increases monotonically above its initial value J0 (=2.5), and it approaches a saturated limit value  LTP D=0.1175 and 17.5: <Jij> decreases monotonically below J0, and it approaches  LTD

Effect of the STDP on the SBS

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• Population-Averaged Limit Values of Synaptic Strengths

LTP occurs in In most range of the SBS LTP occurs, while LTD takes place only near both ends.

 

* ij

J  

* ij

J ]) 336 . 17 ~ [ ~ ], 1179 . ~ [ ~ (

h l

D D  

* ij

J

Initial : Gray & STDP Additiv e : Black

* ij

J

r ij

J  

*

• Raster Plots of Burst Onset Times

IPBR Rb(t)

LTP  The degrees of SBS are increased. LTD  The population states become desynchronized.

“Mathew” Effect of the STDP

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• Characterization of the Synchronization Degree via Statistical-Mechanical

Bursting Measure Mb

Pacing degree of the ith bursting stripe: averaging the contributions to Rb(t) of all microscopic burst onset times in the ith bursting stripe Bi: Number of burst onset times in the ith bursting stripe : global phase of burst onset time Nb: No. of bursting stripe LTP  Good burst synchronization gets better. LTD  Bad burst synchronization gets worse.





 

i

B k b k i b i

B P

1 ) ( ) (

cos 1







b

N i b i b b

P N M

1 ) (

1

) (b k



STDP

• f

Absence : Crosses & STDP Additiv e : circles Open

• Population-Averaged Histograms H(∆tij) for {∆tij} during t=0~saturation time

t* (=2000sec)

LTP (D=0.3, 5, 9, & 13): 3 peaks. One main central peaks (same bursting stripe) and two minor left and right peaks (different nearest-neighboring bursting stripes) LTD (D=0.1175 & 17.5): Single broad peak via a merging of the above main and minor peaks

Microscopic Investigation on Emergences of LTP and LTD

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LTD : Gray & LTP : Black

• Population-Averaged Synaptic Modification <<∆Jij>>r Obtained from H(∆tij)

Population-averaged limit values of synaptic strengths agree well with direct-obtained values.



    

bins ij ij ij r ij

t J t H J ) ( ) ( ~ ) (

* r ij r ij

J J J        

• Mathew Effect in Mc

Mc : Matthew effect also occurs.

• Time-Evolutions of <Jij> Obtained from H(tij)

D=13 (D=17.5): <Jij(t)> is positive (negative) <Jij(t)> approach 0 because H(tij) become symmetric.  LTP (LTD)

• Time-Evolutions of Normalized

Histogram H(tij) for {tij}

LTP: 3 peaks  Peaks become narrowed.  Main peak becomes symmetric. LTD: 3 peaks  Merged into the single broad peak  Peak becomes symmetric.

• Widths wb of Bursting Stripes

Strong (weak) Mc  wb decreases (increases)  Narrow (wide) distribution of tij  LTP (LTD)

Microscopic Cross-Correlations between Synaptic Pairs

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• Microscopic Correlation Measure Mc

Mc: Average “in-phase” degree between the pre- and the post-synaptic pairs

) ( ) ( ) ( ) ( ) ( , ) ( 1

2 2 , ) , ( ,

t r t r t r t r C C N M

j i j i j i j i j i syn c

      



 

LTD : Gray & LTP : Black

STDP

• f

Absence : Crosses STDP Additiv e : circles Open

Summary

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• Stochastic Burst Synchronization (SBS) in the Absence of STDP
• SBS between complex noise-induced burstings of subthreshold neurons:

Correlated with brain function of encoding sensory stimuli in the noisy environment.

• Occurrence of SBS in intermediated noise intensities via competition between

the constructive and the destructive roles of noise.

• Previous works on SBS: Synaptic strengths were static.
• Investigation of The Effect of STDP on the SBS
• Occurrence of “Matthew” effect in synaptic plasticity

 Good burst synchronization gets better via LTP , while bad burst synchronization gets worse via LTD.

• Emergences of LTP and LTD: Intensively investigated via microscopic studies

based on both the distributions of time delays between the pre- and the post-synaptic burst onset times and the pair-correlations between the pre- and the post-synaptic IIBRs.