Neural Networks with Short-Term Synaptic Dynamics

(Leiden, May 23 2008)

Misha Tsodyks, Weizmann Institute

• Mathematical Models of Short-Term Synaptic plasticity

• Computations in Neural Networks with Short-Term Synaptic Plasticity

Experiments: Henry Markram, Eli NelkenTheory: Klaus Pawelzik, Alex Loebel

Multineuron Recording

Principles of Time-Dependency of Release

AP onset

Facilitation

Depression

Synaptic Facilitation

Synaptic Depression

Three Laws of ReleaseLimited Synaptic Resources

Release Dependent Depression

Release Independent Facilitation

Four Parameters of Release

•Absolute strength

•Probability of release

•Depression time constant

•Facilitation time constant

A Phenomenological Approach to Dynamic Synaptic Transmission

• 4 Key Synaptic Parameters– Absolute strength

– Probability of release

– Depression time constant

– Facilitation time constant

Phenomenological model of synaptic depression (deterministic)

(1 )( )

( )

sp

I s

r

p

dR RRu

Au

t tdt

I I R t t

.

.

.

Stochastic transmission

Binomial model of synaptic release

, , , rP Q N

Loebel et al, submitted

The fitting process (deterministic model)

, , rA U

,mem I

Testing the Model

experiment

model

experiment

model

Frequency-dependence of post-synaptic response

(1 )( )sp

r

dR Ru R t t

dt

Frequency-dependence of post-synaptic response

(1 )( )sp

r

dR Ru R t t

dt

/ /1

/ /1 1

(1 ) 1

(1 ) (1 )

r r

r r

T Tn n

T Tn n

R R u e e

E E u e E e

Frequency-dependence of post-synaptic response

(1 )( )sp

r

dR Ru R t t

dt

/ /1

/ /1 1

(1 ) 1

(1 ) (1 )

r r

r r

T Tn n

T Tn n

R R u e e

E E u e E e

/

1 /

1

1 (1 )

r

r

T

st T

eE E

u e

Frequency-dependence of post-synaptic response

(1 )( )sp

r

dR Ru R t t

dt

/ /1

/ /1 1

(1 ) 1

(1 ) (1 )

r r

r r

T Tn n

T Tn n

R R u e e

E E u e E e

/1

1 /

1

1 (1 )

r

r

T

st Tr r

Ee AE E

u e u f f

Tsodyks et al, PNAS 1997

The 1/f Law of Release

Redistribution of Synaptic Efficacy

RSERSE

Shifting the Distribution of Release Probabilities

Population signal

1( )

( )

r

I

RR Ru E t

I I AuRE t

Tsodyks et al, Neural Computation 1998

Population signal

1( )

( ) ( )r

RR Ru E t

I t AuRE t

Population signal

1( )

( ) ( )r

RR Ru E t

I t AuRE t

‘High-pass filtering’ of the input rate

Steady-state signal

1

1

1

r

r

Ru E

EI Au

u E

Tsodyks et al PNAS 1997

Synchronous change in pre-synaptic rates

1 2E E E E

Synchronous change in pre-synaptic rates

1 2E E E E

1 2exp( / )recI AuR E t R

Synchronous change in pre-synaptic rates

1 2E E E E

1 2 2exp( / ) exp( / )rec rec

EI AuR E t R t R

E

Abbott et al Science 1997

Modeling synaptic facilitation (deterministic)

(1 ) ( )

1( )

( )

sf

sr

I s

u Uu U u t t

RR uR t t

I I AuR t t

Markram, Wang & Tsodyks PNAS 1998

FacilitationFacilitation

Frequency-dependence of post-synaptic response

(1 ) ( )

1( )

sf

sr

u Uu U u t t

RR uR t t

Frequency-dependence of post-synaptic response

/1

/ /1

/ /1 1

(1 )

(1 ) 1

(1 ) (1 )

f

r r

r r

Tn n

T Tn n n

T Tn n n n

u u U e U

R R u e e

E E u e Au e

(1 ) ( )

1( )

sf

sr

u Uu U u t t

RR uR t t

Frequency-dependence of post-synaptic response

/1

/ /1

/ /1 1

(1 )

(1 ) 1

(1 ) (1 )

f

r r

r r

Tn n

T Tn n n

T Tn n n n

u u U e U

R R u e e

E E u e Au e

/

/

/

1 (1 )

1

1 (1 )

f

r

r

st T

T

st st Tst

Uu

U e

eE Au

u e

(1 ) ( )

1( )

sf

sr

u Uu U u t t

RR uR t t

Population signal

(1 ) ( )

1( )

( ) ( )

f

r

u Uu U u E t

RR Ru E t

I t AuRE t

Tsodyks et al 1998

Steady-state signal

1

1

1

1

1

f

f

r

r

Eu U

U E

Ru E

EI AuRE Au

u E

A Small Circuit

Recurrent networks with synaptic depression

Tsodyks et al, J. Neurosci. 2000Loebel & Tsodyks JCNS 2002Loebel, Nelken & Tsodyks, Frontiers in Neurosci. 2007

Simulation of Network Activity

Simulation of Network Activity

Origin of Population Spikes

Network response to stimulation

Experimental evidence for population spikes

DeWeese & Zador 2006

Simplified model )no inhibition, uniform connections, rate equations(

1ei

Ne

J J

The rate model equations

There are two sets of equations representing the excitatory units firing rate, E , and their

depression factor, R :

1

[ ]N

ii j j i

j

dE JE E R e

dt N

1i i

i ir

dR RuR E

dt

Tone

The tonic stimuli is represented by a constant shift of the {e}’s, that, when large enough, causes the network to spike and reach a new steady state

DeWeese, …, Zador 2003

(Nelken et al, Nature 1999)

0

Noi

se a

mpl

itude

Extended model

Loebel, Nelken & Tsodyks, 2007

Rotman et al, 2001

Forward suppression

Network response to complex stimuli

Network response to complex stimuli

Neural Network Models of Working Memory

Misha Tsodyks

Weizmann Institute of Science

Barak Blumenfeld, Son Preminger & Dov Sagi

Gianluigi Mongillo & Omri Barak

Delayed memory experiments – sample to match

Miyashita et al, Nature 1988

Persistent activity (Fuster ’73)

Miyashita et al, Nature 1988

Neural network models of associative memory (Hopfield ’82)

Memories are represented as attractors (stable states) of network dynamics. Attractor = internal representation (memory) of a stimulus in the form

of stable network activity pattern Synaptic modifications => Changes in attractor landscape = long-

term changes in memory Convergence to an attractor = recall of item from long-term memory

into a working form

Associative memory model

Hopfield Model (1982):

1

( 1) ( ( ))N

i ij j

j

S t sign J S t

1iS Neurons:

Synaptic connections: ijJ

Network dynamics:

Memory patterns: 1i

Associative memory model

Hopfield Model (1982):

1iS Neurons: Memory patterns: 1i

Synaptic modifications : ij ij i jJ J

Associative memory model

Hopfield Model (1982):

1iS Neurons: Memory patterns: 1i

1

P

ij i jJ

Synaptic modifications : ij ij i jJ J

Associative memory model

Hopfield Model (1982):

1iS Neurons: Memory patterns: 1i

1

P

ij i j i iJ A

Synaptic modifications : ij ij i jJ J

(for each )

Amit, Guetfriend and Sompolinsky et al 1985if 0.14P N

Network dynamics: Convergence to an attractor

Memory#

Ove

rlap

Network dynamics: Convergence to an attractor

Memory#

Ove

rlap

Context-dependent representations: gradual change in the pattern

… …

Long-term memory for faces

Non Friends

Friends

Preminger, Sagi & Tsodyks, Vision Research 2007

Experiment – Terminology

• Basic Friend or Non-Friend task (FNF task)– Face images of faces are flashed for 200 ms – for each image the subject is asked whether the

image is a friend image (learned in advance) or not. – 50% of images are friends, 50% non-friends, in

random order; each friend is shown the same number of times. No feedback is given

F/NF

?

200ms

F/NF

?F/NF

?

200ms 200ms 200ms 200ms 200ms 200ms 200ms 200ms

1 … 20

Source(friend)

Target(unfamiliar)

… 40 … 60 … 80 100…

Morph sequence

Subject HL -------- (blue-green spectrum) days 1-18

Morph effect

Bin number

Nu

mb

er o

f ‘F

rien

d’

resp

on

ses

Preminger, Sagi & Tsodyks, Vision Research 2007

Morphed patterns – Hopfield model

Continuous set of patterns 0 1

{ } (0 1)

Morphed patterns – Hopfield model

Continuous set of patterns

0 1

ij i jJ

1

( 1) ( ( ))N

i ij j

j

S t sign J S t

0 1 { } (0 1)

* 0.5i iA

Blumenfeld et al, Neuron 2006

Network dynamics: Convergence to the common attractor

Ove

rlap

Network dynamics: Convergence to the common attractor

Ove

rlap

Working memory in biologically-realistic networks (D. Amit ‘90)

Working memory in biologically-realistic networks (D. Amit ‘90)

Working memory in biologically-realistic networks (D. Amit ‘90)

Brunel & Wang, J. Comp. Neurosci 2001

Working memory in biologically-realistic networks

Brunel & Wang, J. Comp. Neurosci 2001

Multi-stability in recurrent networks

( )I t

( )E t J( )dE

E g JE Idt

Multi-stability in recurrent networksF

iring

rat

e (H

Z)

Synaptic strength (J)

( )I t

( )E t J

Persistent activity is time-dependent.

Rainer & Miller EJN 2002

A Phenomenological Approach to Dynamic Synaptic Transmission

• 4 Key Synaptic Parameters– Absolute strength– Probability of release– Depression time constant– Facilitation time constant

• 2 Synaptic Variables– Resources available (x)– Release probability (u)

Markram, Wang & Tsodyks PNAS 1998

(1 ) ( )

1( )

spf

spd

du u UU u t t

dt

dx xux t t

dt

Synaptic diversity in the pre-frontal cortex

Wang, Markram et al, Nature Neuroscience 2006

New idea

• To hold short-term memories in synapses too, with pre-synaptic calcium level.

• Use spiking activity only when the memory is needed for processing, and/or to refresh the synapses (smth like ‘rehearsal’).

Mongillo, Barak & Tsodyks 2008

Bifurcation diagram

Attractors in networks with synaptic facilitation

Integrate and fire network simulations

Integrate and fire network simulations

Integrate and fire network simulations

Robustness and multi-item memory

Robustness and multi-item memory

Random overlapping populations

Predictions

• Increased pre-synaptic calcium concentration during the delay period, disassociated from increased firing rate

• Resistance to temporal cessation of spiking

• Synchronous spiking activity during the delay period

• Slow oscillations during the delay period (theta rhythm?).

Correlated spiking activity during delay period

Constantinidis et al, J. Neurosci. 2001

Theta oscillations and working memory

Lee et al, Neuron 2005

Barak Blumenfeld)WIS, Rehovot(

Son Preminger)WIS, Rehovot(

Dov Sagi)WIS, Rehovot(

Omri Barak)WIS, Rehovot(

Gianluigi Mongillo)ENS, Paris(