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 • 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. • 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) 1

Excitatory SFN of Subthreshold Izhikevich Neurons • Scale-Free Network (SFN) of Subthreshold Izhikevich Neurons Barabási -Albert SFN with symmetric attachment degree l * =10 (Growth and preferential directed attachment with l in incoming edges and l out outgoing edges; l in = l out = l * ) Subthreshold Izhikevich Neurons for the DC current I DC , i  [3.55, 3.65] • Hebbian STDP Update of coupling strengths: Additive nearest-burst pair-based STDP rule      ( post ) ( pre ) t t t , 0 . 005      ij i j J J J ( t ) ij ij ij ij    [ ( 0 . 0001 ), ( 5 . 0 )] J J J ij l h Initial synaptic strengths: Mean J 0 =2.5 & standard deviation  =0.02 Asymmetric time window for  J ij       t /   A e ij for t 0    ij  J      ij t /   A e ij for t 0   ij           A 1 . 0 , A 0 . 6 , 15 m sec, 30 m sec, J ( t 0 ) 0 .     ij ij  t ij > 0  LTP ,  t ij < 0  LTD 2

SBS in the Absence of STDP Initial coupling strengths { J ij } : Gaussian distribution with mean J 0 =2.5 and standard deviation  0 =0.02 • Raster Plots of Burst Onset Times Appearance of stripes in the raster plot for synchronous case • Instantaneous Population Burst Rate (IPBR) n N 1 1  i 2 2     2      ( i ) t / h R ( t ) K ( t t ) ; K ( t ) e , t b h b h  N 2 h   i 1 s 1 • Thermodynamic Bursting Order Parameter:   O 2 ( R ( t ) R ( t ) ) b b b Synchronized (desynchronized) state: O b approach non-zero (zero) limit values for N  SBS in via competition   * * D ( ~ 0 . 1173 ) D D ( ~ 18 . 4 ) l h between the constructive and the destructive roles of noise. 3

Effect of the STDP on the SBS • Time-Evolution of Population-Averaged Synaptic Strength < J ij > D =0.3, 5, 9 and 13: < J ij > increases monotonically above its initial value J 0 (=2.5), and it approaches a saturated limit value  LTP   * J ij D =0.1175 and 17.5: < J ij > decreases monotonically below J 0 , and it approaches  LTD   * J ij • Histograms for Fraction of Synapses (Saturated limit value of J ij ) * J ij becomes larger (smaller) than   * J Black : Additiv e STDP & Gray : Initial ij the initial value for the case of LTP (LTD). The standard deviations are very larger than the initial one (=0.02). • Population-Averaged Limit Values of Synaptic Strengths  J  * ij r ~ ~ LTP occurs in ( D [ ~ 0 . 1179 ], D [ ~ 17 . 336 ]) l h In most range of the SBS LTP occurs, while LTD takes place only near both ends. 4

“Mathew” Effect of the STDP • Raster Plots of Burst Onset Times IPBR R b ( t ) LTP  The degrees of SBS are increased. LTD  The population states become desynchronized. • Characterization of the Synchronization Degree via Statistical-Mechanical Bursting Measure M b Pacing degree of the i th bursting stripe: averaging the contributions to R b ( t ) of all microscopic burst onset times in the i th bursting stripe B i : Number of burst onset times in the i th bursting stripe B 1  i   ( b ) ( b ) : global phase of burst onset time P cos  ( b ) i k B k  k 1 i N 1  b  ( b ) N b : No. of bursting stripe M P b i N  i 1 b LTP  Good burst synchronization gets better. LTD  Bad burst synchronization gets worse. 5 Open circles : Additiv e STDP & Crosses : Absence of STDP

Microscopic Investigation on Emergences of LTP and LTD • Population-Averaged Histograms H (∆ t ij ) for {∆ t ij } during t =0~saturation time t * (=2000sec) LTP ( D =0.3, 5, 9, & 13): 3 peaks. One main central peaks (same bursting stripe) Black : LTP & Gray : LTD 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 • Population-Averaged Synaptic Modification <<∆ J ij >> r Obtained from H (∆ t ij ) Population-averaged limit values of synaptic strengths agree well with direct-obtained values.       J ~ H ( t ) J ( t ) ij ij ij ij r bins         * J ( J J ) ij r 0 ij r 6

Microscopic Cross-Correlations between Synaptic Pairs • Microscopic Correlation Measure M c M c : Average “in - phase” degree between the pre- and the post-synaptic pairs     ( ) ( ) r t r t 1     i j M C ( 0 ) , C ( ) c i , j i , j N   2 2 r ( t ) r ( t ) ( i , j ) syn i j • Widths w b of Bursting Stripes Strong (weak) M c  w b decreases (increases)  Narrow (wide) distribution of  t ij  LTP (LTD) Black : LTP & Gray : LTD • Time-Evolutions of Normalized Histogram H (  t ij ) for {  t ij } LTP: 3 peaks  Peaks become narrowed.  Main peak becomes symmetric. LTD: 3 peaks  Merged into the single broad peak  Peak becomes symmetric. • Time-Evolutions of <  J ij > Obtained from H (  t ij ) D =13 ( D =17.5): <  J ij ( t )> is positive (negative) <  J ij ( t )> approach 0 because H (  t ij ) become symmetric.  LTP (LTD) • Mathew Effect in M c Open circles : Additiv e STDP M c : Matthew effect also occurs. Crosses : Absence of STDP 7

Summary • 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. 8