Feedforward networks

Complex Network

Simpler (but still complicated) Network

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Feedforward Network

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Hz

ms

Signal propagation through the network

on off

Hz

ms

“rate mode”Shadlen & Newsome, 1998Van Rossum et al., 2002

“synchrony mode”Abeles, corticonics, 1991Diesmann et al.,1999

Is synchrony robust ?

Why does synchrony develop ?

Is it useful for transmitting signals ?

Is it found in vivo?

Questions

Simulations with real neurons

Real neurons (God, unpublished results)

1000’s

Whole-cell recordings

Rats or mice are 18 days or older300-500 µm slices of somatosensory or auditory cortexmaintained at 32-34 degreesrecordings were from L5 pyramidal neurons and interneurons

Implementation of feedforward in vitro networks

1 2 3 m

1

2

n

individualspikes

histogram

0 200 400 600 800 1000 1200 1400

ms

cells

0 200 400 600 800 1000 1200 1400

ms

12008004000

L1

L2

L3

L4

L5

L6

L7

L8

L9

L10

L11

12008004000

L1

L2

L4

L11

L3

Network type:-> sparsely connected (10%)

L2

L3

L5

L4

L6

L7

L8

2.5

2.0

1.5

1.0

0.5

0.0

Norm

aliz

ed

CC

H a

rea

108642

Layer

10% connection

Quantification of Synchrony

ms

L1

0 100 200 300-100-200-300

Is synchrony robust ?

1. sparsely connected networks2. Poisson input3. heterogeneous networks4. excitatory & inhibitory networks5. extremely noisy6. sinusoidally-modulated inputs 7. NMDA-like EPSPs8. different initial conditions9. facilitating/depressing synapses

Various network configurations

Synchrony persists

Periodic

Poisson

Network type:-> sparsely connected (10%)-> Poisson input

cell Rn f/I slope

A 49 164B 54 227

C 28 134D 121 303

200 ms

50 mV

Network type:-> sparsely connected (10%)-> Poisson input-> heterogeneous

Heterogeneous Networks

12008004000

Time (ms)Time (ms)

Layer 2 Layer 6

12008004000

Excitatory & Inhibitory network

membrane voltage

Iexc

Iinh

net synaptic current = Iexc + Iinh

Isyn(t)= gsyn(t)*(V(t)-Esyn)

Iepsp = g * (V - E)

dynamic clamp

Ic-clamp(t)

Iipsp = g(t)*(V + 80 ) -62 mV

0.5 mV

50 ms

-62 mVIepsp =g(t)*(V - 0)

threshold

-58 mVEPSP rate: 28,000 HzIPSP rate: 12,000 Hz

200 ms

2 mV-58 mV

EPSP rate: 7000 HzIPSP rate: 3000 Hz

Chance, Abbott, Reyes 2002

Effects of conductance noise on membrane potential

excitatory cells

20 mV

200 ms

excitatory +inhibitory

layer 5

Network type:-> sparsely connected (10%)-> Poisson input-> heterogeneous-> excitatory + inhibitory

EPSPEPSP + IPSP

1 2 3 4 5 6

Network type:-> sparsely connected (10%)-> Poisson input-> heterogeneous-> epsp + ipsp-> ‘unphysiologically’ noisy

layer

CC

H a

rea

1 2 3 4 5 6 6

layer 2 layer 6

Why does synchrony develop ?

A simple model

counts

ms0 20 40 60 80 100

counts

ms

0 10 20 30 40 50

histogramsunitary synaptic

current

*

Composite current

1

2

3

4

experiment

12008004000

L1

L2

L4

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L3

0.0 0.4 0.8 1.0

seconds

A simple model

L1(t) ≡w(t) −αX (t),

τneg

dX / dt =−X +w(t).

⎧⎨⎪

⎩⎪

L1(t)L

1(0) =δ(t) −

β2τ

neg

e−t / τneg

∂P (u,X ,t)∂t

=−1τ

m

∂∂u

f0(u,R + R

0) −Gτ

s′R αX +

1τ

neg

∂∂X

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟P +

Gτs( )

2′R + R

0( )

2τm2

∂2P∂u2

+1

τneg

∂ XP( )∂X

+1

2τneg

2

′R + R1

′R∂2P∂X 2

+ Ju(X ,t)δ(u −U

reset)

∂p(u,t)∂t

=−1τ

m

∂∂u

GτsR +1 −eu

( )p+Gτ

s( )2R

2τm2

∂2p∂u2

+ Ju(t)δ(u −U

reset)

τ

m

dvdt

=− v −Vresting( ) −G(t)(v −V

E)

R =Nλ u = ln v / V

E−v( )( )

LIF:

FPE:

where

G(t) =Gτ

sNλ + NλL

1(t)( )

G(t) ≅Gτ

sNλ + Nλ w(t)( )

input:

G

1(t +T )G

1(t) = Gτ

s( )2λ(t)κ(T , λ(t))

κ(T , λ) =

12τ

s

e−T / τs +1

2τs

dxQ(x, λ)e−x−T / τs

−∞

∞

∫ −λ

Q̂(x,λ) =1 /xλθ

+1⎛

⎝⎜⎞

⎠⎟

θ

−1⎛

⎝⎜⎜

⎞

⎠⎟⎟

60504030200 10 70ms

0<G

(t)G

(0)>

60504030200 10 70

ms

G(t)G(0) = Gτ

s( )2 12τ

s

e−t / τs

autocorr: s(t)s(0) =λδ(t)

<G

(t)G

(0)>

Fokker-Planck Equations

Diesmann et al., Nature 1999

Is it useful for transmitting signals ?

Signal propagation through the network

on off

F1 F1F2 F2

1 nA

layer 6

25 mV

200 ms

layer 2

Fin = 25 Hz

55 Hz

55 Hz

25 Hz

Fin

25

20

15

10

5

0

1197531Layer

Avg

. ra

te (

Hz)

k

20

15

10

5

0Firi

ng R

ate

(H

z)

16008000Input rate (=N*Fpre)

123

N

Firing rate = Fpre

Flayer = k*N*Flayer-1

Input rate = N*Fpre

Frequency Frequency

20

10

30

0

654321

layer

avg. fi

ring r

ate

(H

z)

K*N < 1

K*N = 1

K*N > 1

FL = k*N*FL-1

Is it found in vivo ?

layer 6 (synchronous)

1 nA

25 mV

200 ms

layer 2 (asynchronous)

What to look for in vivo

10 mV

50 ms

In vivo intracellular recordings

Azouz & Gray, 1999

Lampl et al.,1999

0.5 mV

25 ms

Reyes & Sakmann, 1999

Brecht & Sakmann, 2002 10 mV

25 ms

wD4

Ikegaya et al., 2004

Is synchrony robust ?yes, for a wide range of physiological conditions

Why does synchrony develop ?Neurons become correlated at stimulus onset

Is it useful for transmitting signals ?Yes. In fact, it’s necessary!

In vivo evidence?Yes. Quite strong.

Summary

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3e

Feedforward Network

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0 40 80Hz

0 250Hz

0 40 80Hz

With inhib

pyramidals interneuron