Feedforward networks
Dec 20, 2015
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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
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
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
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
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
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
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
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
L11
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
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
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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Feedforward Network
1a
1b
1c
1d
1e
2a
2b
2c
2d
2e
3a
3b
3c
3d
3e
1a
1b
1c
1d
1e
2a
2b
2c
2d
2e
3a
3b
3c
3d
3e