models of synaptic transmission (2)
TRANSCRIPT
Models of synaptic transmissionpart II
Dmitry Bibichkov Max Planck Institute for Biophysical Chemistry Göttingen, Germany
Bernstein Center for Computational Neuroscience Göttingen , Germany
Chemical synapses
Excitatory neurons• NMDA voltage-dependent Mg2+- block (removed at V > - 50 mV)
[Jahr and Stevens 1990]
ms3=↑τms40=↓τ( ) )(])[,()( 2// tMgVgeegt tt
NMDA Θ⋅⋅−= +∞
−− ↑↓ ττα
10.08.2010 D. Bibichkov, AACIMP-2010
Chemical synapses
Excitatory neurons• NMDA voltage-dependent Mg2+- block (removed at V > - 50 mV)
( ) )(])[,()( 2// tMgVgeegt ttNMDA Θ⋅⋅−= +
∞−− ↑↓ ττα
12
)][1( −−+
∞ += VeMgg ε
β
[Gabbiani et.al 1994]
-8 0 -6 0 -4 0 -20 0 2 0 4 0 600
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1
V
g ∞
0 .0 1
0 .1 1
1 0
ms3=↑τms40=↓τ
10.08.2010 D. Bibichkov, AACIMP-2010
Activity-dependent recovery
Responses to regular spike trains at the calyx of Held. Fit each frequency separately.
0 5 10 15 20 250.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
s p ike num b e r
norm
aliz
ed c
urre
nt
200Hz100Hz
50Hz
20Hz
10Hz 5Hz
2Hz
1Hz
0.5Hz0.2Hz
10.08.2010 D. Bibichkov, AACIMP-2010
Activity-dependent recovery
0 . 2 0 . 5 1 2 5 1 0 2 0 5 0 1 0 0 2 0 00
1
2
3
4
5
6
7
8
i n p u t f r e q u e n c y f , H z
reco
very
rat
e k
, H
z
Effective recovery rate:mean recovery rate over an ISI
Calcium accumulates during the trains of action potentials and leads to increased recovery rates during high-frequency stimulation
10.08.2010 D. Bibichkov, AACIMP-2010
Activity-dependent recovery
Calyx of Held[Weis et.al. 1999]
Activity-dependent recovery increases the range of characteristic frequencies towards the maximal recovery rate
climbing fiber to Purkinje cell synapse[Dittmann and Regehr 1998]
activity dependenceno activity dependence
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Entropy of stochastic signal S: amount of variability in the stimulus statistics
∑−=s
sPsPSH )(log)()( 2
Noise entropy of response R: average response variability
∑∑ −==rss
noise srPsrPsPsRHsPRH,
2 )|(log)|()()|()()(
Mutual information: reduction of uncertainty about the signal due to the measurement of the response
)()(),( RHSHSRI noise−=
synapseS R
Conditional entropy of response R: variability of the response to a given stimulus s
∑−=r
srPsrPsRH )|(log)|()|( 2
(ISI) (PSC)
Information Theory
10.08.2010 D. Bibichkov, AACIMP-2010
• Optimal inputs maximizing response entropy and mutual information for estimated synaptic parameters ? • Optimal synaptic parameters for given input statistics ?
Effects of synaptic dynamics on information transfer
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ISI PSC
no depression strongdepression
‘optimal’depression
Transmission is optimal when the input statistics spans the dynamic range of possible responses.
synapseEffects of synaptic dynamics on information transfer
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Output entropy decreases with frequency
Deterministic model: )(),( RHRSI =
10.08.2010 D. Bibichkov, AACIMP-2010
Output entropy decreases with frequency
Deterministic model: mutual information is equal to the differential entropy of responses to Poisson spike trains :
0 . 1 1 1 0 1 0 0
- 1
- 2
- 4
f , H z
outp
ut e
ntro
py
F D R ( t h e o r )
τ = 4 . 7 ( t h e o r ) F D R ( s im )
τ = 4 . 7 ( s i m )
10.08.2010 D. Bibichkov, AACIMP-2010
Effect of facilitation on information transmission
Facilitation sets an optimal range of frequency for information transmission.
[Fuhrmann et al 2002]
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Stochastic model of release
• Number of available vesicles before spike: Nx
• Stochastic release of n ~ B(Nx,p) (binomial distribution)
• Depletion of releasable pool:
• Stochastic postsynaptic response E ~ N(nq, nσ2)
• Stochastic recovery of vesicles according to a Poisson process with rate k
Nnxx /−→Nxpn
p).(.pnNx
n nNxn
=
−
= −1) Pr( vesiclesreleased
10.08.2010 D. Bibichkov, AACIMP-2010
Activity-dependent recovery extends the frequency range of effective information transfer
Stochastic model:
1 / 8 1 8 3 2 1 2 8 5 1 2
0 . 2
0 . 2 5
0 . 3
0 . 3 5
0 . 4
0 . 4 5
0 . 5
0 . 5 5
f, Hz
I(IS
I,PS
R)
S t o c h a s t i c , τ= 4 . 7 2 s
S t o c h a s t i c , τe f f g l o b a l
S t o c h a s t i c , τe f f ( i s i )
[J. Bao, DB, EN]
10.08.2010 D. Bibichkov, AACIMP-2010
Effect of facilitation on information transmission
Facilitation increases information transmission for a range of frequencies compared to synapses with pure depression.
[Jin Bao]D
D+F
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Optimal recovery rate
0 . 1 1 8 1 2 80
2
4
6
8
1 0
1 2
input frequency (Hz)
τr (
s)
τe f fr
( C a l y x )
o p t i m a l τ
τo p t ∼ r - 1 . 6
6.0−∝ foptτ
The parameters of the Calyx of Held synapse which fit the responses to the regular trains are close to the optimal in terms of transmission of information.
10.08.2010 D. Bibichkov, AACIMP-2010
Network effects
1. Generation of population spikes in network with recurrent excitation and depressing synapses [Loebel, Tsodyks 2002]
2. Generation of sustained activity by calcium-dependent facilitation: short-term memory model [Mongillo et. al 2008]
3. Self-organized criticality in networks with synaptic depression [Levina et.al 2007]
4. Capacity modulation and sequence storage in associative memory networks [Bibitchkov et.al 2002]
5. Stabilization of activity, oscillations and pattern switching in recurrent networks with "ring-like" structure [van Rossum 2009]
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Population spikes
[Loebel, Tsodyks 2002]
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fully connected recurrent network
Rate models
Integrate and fire neurons
Population spikes
[Loebel, Tsodyks 2002]
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Dependinc on connection strength or ext. input strength the network can be asynchronous or produce synchronous activity patterns
Population spikes
[Loebel, Tsodyks 2002]
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Response to a tonic input elevation
Population spikes
[Loebel, Tsodyks 2002]
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Responses tosharp stimuli ofdifferentfrequencies
Short-term memory model
[Mongillo et. al 2008]
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Facilitating synapse
DF ττ > >
Sustained activity: short-term memory model
p
p
p
[Mongillo et. al 2008]
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Sustained activity: short-term memory model
p
p
p
p
Robustness to noise and
two-term memory
[Mongillo et. al 2008]
10.08.2010 D. Bibichkov, AACIMP-2010
Self-organized criticality in neuronal cultures
[Beggs and Plenz 2003, 2004]
• Power-law distribution of avalanche sizes
• Exponent of -3/2
•Dynamics is stable over many hours of recordings
10.08.2010 D. Bibichkov, AACIMP-2010
Self-organized ctiticality
Static synapses Depressing synapses
[Levina et. al 2007]
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Attractor networks with synaptic depression
[Bibitchkov et.al 2002]
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Acknowledgements
J.Michael Herrmann (University of Edinburgh)Misha Tsodyks (Weizmann Institute)Barak Blumenfeld (Weizmann Institute)Erwin Neher (MPI for Biophysical Chemistry, Göttingen)Holger Taschenberger (MPI for Biophysical Chemistry, Göttingen)Jin Bao (MPI for Biophysical Chemistry, Göttingen)I-Wen Chen (MPI for Biophysical Chemistry, Göttingen*)Kun-Han Lim (MPI for Biophysical Chemistry, Göttingen)Anna Levina (MPI for Dynamics and Self-Organization Göttingen)Mark van Rossum (University of Edinburgh)
ORGANIZERS!!!!
10.08.2010 D. Bibichkov, AACIMP-2010