Models of Synaptic Transmission (2)

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


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



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



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


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


• 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


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


Output entropy decreases with frequency

Deterministic model: )(),( RHRSI =


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 )


Effect of facilitation on information transmission

Facilitation sets an optimal range of frequency for information transmission.

[Fuhrmann et al 2002]


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


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]


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


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.


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

[Loebel, Tsodyks 2002]


fully connected recurrent network

Rate models

Integrate and fire neurons

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 tosharp stimuli ofdifferentfrequencies

Short-term memory model

[Mongillo et. al 2008]


Facilitating synapse

DF ττ > >

Sustained activity: short-term memory model

p

p

p



Sustained activity: short-term memory model

p

p

p

p

Robustness to noise and

two-term memory



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


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]


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!!!!


Education

Models of Synaptic Transmission (2)