Models of Synaptic Transmission (2)

Models of synaptic transmission
part 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)

α (t ) = g NMDA e( − t /τ ↓
−e
− t /τ ↑
)⋅ g ∞ (V , [ Mg 2+ ]) ⋅ Θ (t )
τ ↓ = 40ms τ ↑ = 3ms

[Jahr and Stevens 1990]

10.08.2010 D. Bibichkov, AACIMP-2010

Chemical synapses

Excitatory neurons
• NMDA
voltage-dependent Mg2+- block (removed at V > - 50 mV)

α (t ) = g NMDA e ( − t /τ ↓
−e
− t /τ ↑
)⋅ g ∞ (V , [ Mg 2+ ]) ⋅ Θ (t )
1

0.9
τ ↓ = 40ms τ ↑ = 3ms
0.8

0.7
[ Mg 2+ ] − ε V − 1
0.6
g ∞ = (1 + e )
β
∞

0.5 0.01
g

0.1
0.4 1
10
0.3

0.2

0.1

0
-8 0 -6 0 -4 0 -2 0 0 20 40 60
V

[Gabbiani et.al 1994]


Activity-dependent recovery

Responses to regular spike trains at the calyx of Held.
Fit each frequency separately.
1
200Hz
0.9 100Hz
50Hz
0.8
n o rm a liz e d c u rre n t

20Hz
0.7 10Hz
5Hz
0.6
2Hz
0.5 1Hz
0.5Hz
0.4 0.2Hz
0.3

0.2

0.1
0 5 10 15 20 25
s p ike num b e r



Calcium accumulates during the trains of action potentials and
leads to increased recovery rates during high-frequency
stimulation
8

7

Effective recovery 6
rate:
r e c o v e r y r a te k , H z 5
mean recovery
rate over an ISI 4

3

2

1

0
0 .2 0 .5 1 2 5 10 20 50 100 200
in p u t f r e q u e n c y f, H z



activity dependence
no activity dependence

climbing fiber to Purkinje cell synapse Calyx of Held
[Dittmann and Regehr 1998] [Weis et.al. 1999]

Activity-dependent recovery increases the range of characteristic
frequencies towards the maximal recovery rate


Information Theory
Entropy of stochastic signal S: S R
amount of variability in the stimulus statistics synapse
(ISI) (PSC)
H ( S ) = − ∑ P ( s ) log 2 P ( s )
s

Conditional entropy of response R:
variability of the response to a given stimulus s
H ( R | s ) = − ∑ P (r | s ) log 2 P (r | s)
r
Noise entropy of response R: average response variability

H noise ( R ) = ∑
s
P ( s ) H ( R | s ) = − ∑ P ( s ) P (r | s ) log 2 P (r | s )
s ,r

Mutual information: reduction of uncertainty about the signal
due to the measurement of the response

I ( R, S ) = H ( S ) − H noise ( R)

Effects of synaptic dynamics on information transfer

• 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
synapse

ISI PSC

strong ‘optimal’
no depression
depression depression

Transmission is optimal when the input statistics spans the dynamic
range of possible responses.


Output entropy decreases with frequency

Deterministic model: I (S , R) = H ( R)


Output entropy decreases with frequency

Deterministic model: mutual information is equal to the differential
entropy of responses to Poisson spike trains :

-1
o u t p u t e n tr o p y

-2

-4 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 im )
0 .1 1 10 100
f, H z


Effect of facilitation on information transmission

[Fuhrmann et al 2002]

Facilitation sets an optimal range of frequency for information
transmission.


Stochastic model of release

• Number of available vesicles before spike: Nx

• Stochastic release of n ~ B(Nx,p) (binomial distribution)

 Nx  n
Pr( n released vesicles) = 
n   .p .( 1 − p)Nx − n
 
n = Nxp
• Depletion of releasable pool: x → x − n / N

• Stochastic postsynaptic response E ~ N(nq, nσ2)

• Stochastic recovery of vesicles according to a Poisson process
with rate k


Activity-dependent recovery extends the frequency range of effective
information transfer

Stochastic model:
0 .5 5
S t o c h a s t ic , τ = 4 . 7 2 s
S t o c h a s t ic , τ g lo b a l
0.5 eff
S t o c h a s t ic , τ (is i)
eff

0 .4 5

0.4
I(ISI,PSR)

0 .3 5

0.3

0 .2 5

0.2

1/8 1 8 32 128 512

f, Hz
[J. Bao, DB, EN]


Effect of facilitation on information transmission

D+F

D
[Jin Bao]

Facilitation increases information transmission for a range of
frequencies compared to synapses with pure depression.


Optimal recovery rate

12 e ff
− 0.6 τ r ( C a ly x )
τ opt ∝ f
10 o p t im a l τ

- 1 .6
8 τo p t ∼ r
τr ( s )

6

4

2

0
0 .1 1 8 128
input frequency (Hz)

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.

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]


Population spikes

fully connected recurrent network

Rate models

Integrate and fire neurons

[Loebel, Tsodyks 2002]


Population spikes

Dependinc on connection strength or ext. input strength
the network can be asynchronous or produce
synchronous activity patterns



Population spikes

Response to a tonic input elevation



Population spikes

Responses to
sharp stimuli of
different
frequencies



Short-term memory model

Facilitating synapse

τ F >> τ D

[Mongillo et. al 2008]


Sustained activity: short-term memory model

p

p

p



Sustained activity: short-term memory model

Robustness to noise and p

two-term memory

p

p

p



Self-organized criticality in neuronal cultures

• Power-law distribution of
avalanche sizes
• Exponent of -3/2
•Dynamics is stable over many
hours of recordings

[Beggs and Plenz 2003, 2004]


Self-organized ctiticality

Static synapses Depressing synapses

[Levina et. al 2007]


Attractor networks with synaptic depression

[Bibitchkov et.al 2002]


Ring model with synaptic depression

[York & van Rossum 2009]


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!!!!


Models of Synaptic Transmission (2)

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