Signal amplification and information
transmission in neural systems
Benjamin Lindner
Department of
Biological Physics
Max-Planck-Institut für Physik
komplexer Systeme Dresden
Tuesday, January 26, 2010
mpipks group
Stochastic Processes
in Biophysics
Outline
• Dynamics of coupled hair bundles enhanced signal amplification by means of coupling-induced noise reduction
- Intro
- Numerical simulation approach
- Experimental approach
- Analytical approach
spike trains
• Effects of short-term plasticity on neural information transfer
- Intro
- Broadband coding of information for
a simple rate-coded signal
- different presynaptic populations:
0
frequency-dependent info transfer
0
1
time
by additional noise
.
-Summary
.
Tuesday, January 26, 2010
.
2
3
PART 1
• HAIRBUNDLE DYNAMICS
Tuesday, January 26, 2010
Range of frequencies
and frequency resolution
Hearing range: 20Hz - 20kHz
Two neighboring piano keys
Difference of 6%
Perceptible difference in hearing < 1% changes in frequency
Tuesday, January 26, 2010
Range of sound amplitudes
Wide dynamic range (6 orders
of magnitude in sound pressure)
0 dB sound pressure level (SPL)
absolute hearing threshold for humans
−9
20 ∗ 10
% of the normal air pressure
120 dB sound pressure level (SPL) Loud rock group
20 ∗ 10
Tuesday, January 26, 2010
−3
% of the normal air pressure
www.vestibular.org
Tuesday, January 26, 2010
Sound elicits a traveling wave of the basilar membrane
Position of maximum vibration
depends on frequency
“tonotopic mapping”
http://www1.appstate.edu/~kms/classes/psy3203/Ear/
Neurotransmitter causes action potentials that are sent to the brain
Tuesday, January 26, 2010
The response of the basilar membrane to pure tones
normal air
pressure
Change in
pressure
2p
5
0
-5
p=200 µPa
Basilar 5
membrane
vibrations 0
[nm] -5
p=2000 µPa
5
0
-5
p=200 mPa
time
Tuesday, January 26, 2010
(χ)vib) log10(BM vib)
logExponent
(χ) loglog
(BM
Local
Local Exponent
10
10 10
1
0.5
1/4
The response
~P of the basilar membrane to pure tones
0
-0.5
1
1
0.5
0
0
-0.5
-1
-0.5
-1.5
1
0
0.5
0
-0.5
-0.5
-1
-1
-1.5
-1.5
-2
0
~P
Nonlinear compression
1/4
~P
~P
-3/4
~P
Output
-3/4
~P
Sensitivity=Output/Input
-1
0
1
2
log10(P/P0)
-0.5
-1
-1.5
-2
Tuesday, January 26, 2010
guinea pig: data from
-1
0
log10(P/P0)
1
2
Robles & Ruggero Physiol. Rev. 2001
The response of the basilar membrane to pure tones
Basilar membran vibration [a.u.]
Sharp tuning
3
10
10
2
1
10
10
0
0
10
20
Frequency [kHz]
30
guinea pig: data from
Robles & Ruggero Physiol. Rev. 2001
Tuesday, January 26, 2010
The big question
What is the active mechanism which
underlies frequency selectivity and
nonlinear compression?
Tuesday, January 26, 2010
Basilar membrane vibrations are transduced by hair cells
into an electric current which is signaled to the brain
Neurotransmitter causes action potentials that are sent to the brain
Tuesday, January 26, 2010
Hair cells are an essential part of the
cochlear amplifier
inner hair
cells
basilar
membrane
outer hair cells
from Dallos et al. The Cochlea
Tuesday, January 26, 2010
from the Cochlea homepage
Experimental model system:
hair bundle from the sacculus of bullfrog
Martin et al. J. Neurosci. 2003
Tuesday, January 26, 2010
Martin et al. PNAS 2001
A single hair bundle shows tuning and
nonlinear compression
f −2/3
Martin & Hudspeth PNAS 2001
Tuesday, January 26, 2010
A stochastic model of a single hair
bundle reproduces these features
Tuesday, January 26, 2010
Spontaneous activity of the hair bundle
Tuesday, January 26, 2010
Stimulated activity of the hair bundle analytical results vs experiment
Two-state theory
noisy Hopf oscillator
Power spectrum
Experiment
Theory
Simulations
8
6
4
2
0.6
0.8
1
ω
χ"
χ'
10
Clausznitzer, Lindner, Jülicher & Martin
Phys. Rev. E (2008)
Tuesday, January 26, 2010
1.2
1.4
Theory
Simulations
5
0
0
6
4
2
0
-2
-4
-6
0
0.5
0.5
1
1.5
2
1
1.5
2
frequency
Jülicher, Dierkes, Lindner, Prost, & Martin
Eur. Phys. J. E (2009)
A single hair bundle shows tuning and
nonlinear compression
f −2/3
... but only precursors
(compared with the cochlea!)
Martin & Hudspeth PNAS 2001
Tuesday, January 26, 2010
Coupling by membranes
cochlea
Tuesday, January 26, 2010
tectorial membrane
Numerical approach
λẊ i,j = fX (X i,j , Xai,j ) + Fext (t) + η i,j (t)
−
1
!
"
∂U (X
i,j
,X
i+k,j+l
k,l=−1
i,j
λa Ẋa
Tuesday, January 26, 2010
= fXa (X
i,j
i,j
, Xa )
+
i,j
ηa (t),
)/∂X
i,j
Tuesday, January 26, 2010
Coupling among hair cells
results in refined frequency tuning...
1000
1x1
3x3
4x4
6x6
9x9
Sensitivity [nm/pN]
1
0.5
100
0
-2
0
HBs
HBs
HBs
HBs
HBs
2
10
-2
-1
0
1
Frequency mismatch [Hz]
2
Dierkes, Lindner & Jülicher PNAS (2008)
Tuesday, January 26, 2010
Coupling among hair cells
results in refined frequency tuning
and enhanced signal compression
1x1
3x3
4x4
6x6
9x9
3
Sensitivity [nm/pN]
10
10
2
~F
1
10
10
HBs
HBs
HBs
HBs
HBs
-0.88
0
-2
10
-1
10
0
10
1
10
F [pN]
2
10
3
10
Dierkes, Lindner & Jülicher PNAS (2008)
Tuesday, January 26, 2010
Coupling among hair cells
results in refined frequency tuning
and enhanced signal compression
through noise reduction!
Sensitivity [nm/pN]
10
2
~F
1
10
10
1x1
3x3
4x4
6x6
9x9
HBs
HBs
HBs
HBs
HBs
3
10
Sensitivity [nm/pN]
coupled system
3
10
-0.88
0
10
-2
-1
10
Tuesday, January 26, 2010
0
10
1
10
F [pN]
2
10
10
3
2
1
10
10
10
single hair bundle
with reduced noise
decrease of intrinsic
noise by 1/N
0
-2
10
-1
10
0
10
1
10
F [pN]
2
10
10
3
Experimental approach
Tuesday, January 26, 2010
Experimental confirmation:
coupling a hair bundle to two cyber clones
X
X1
X
No coupling
X2
Real-time
simulation
FEXT
Cyber
bundle 1
FEXT
Hair
bundle
FINT F2
FEXT
Cyber
bundle 2
K = 0.4 pN/nm
100 ms
20 nm
F1
Cyber
clone 1
Hair
bundle
Cyber
clone 2
Δ
Experiments by Jérémie Barral & Kai Dierkes in the lab of Pascal Martin (Paris)
Tuesday, January 26, 2010
Experimental confirmation:
coupling enhances response to periodic
stimulus
coupled
hair bundle
isolated
hair bundle
Experiments by Jérémie Barral & Kai Dierkes in the lab of Pascal Martin (Paris)
Tuesday, January 26, 2010
Analytical approach
ρ!d f
ρd +
d ln(|χ|)
=f
α=
d ln(f )
D
!
I0 (f ρd /D) I1 (f ρd /D)
−
I1 (f ρd /D) I0 (f ρd /D)
"
−2
f ρd /D ! 1 ⇒ α ≈ 0
D
! f ! ρd (5Cρ4d + 3Bρ2d + r) ⇒ α ≈ −1
ρd
f ≥
Tuesday, January 26, 2010
ρd (5Cρ4d
+
3Bρ2d
+ r) ⇒ α ≈
!
−2/3
−4/5
:
:
supercritical
subcritical
Coupled system equivalent to a single
oscillator with reduced noise
Sensitivity [nm/pN]
10
2
~F
1
10
10
HBs
HBs
HBs
HBs
HBs
3
10
Sensitivity [nm/pN]
1x1
3x3
4x4
6x6
9x9
3
10
-0.88
0
10
1
10
10
-2
10
-1
10
Tuesday, January 26, 2010
0
10
1
10
F [pN]
2
10
10
3
2
decrease of intrinsic
noise by 1/N
0
-2
10
-1
10
0
10
1
10
F [pN]
2
10
10
3
A generic oscillator: Hopf normal form
ż = −(r + iω0 )z − B|z|2 z − C|z|4 z +
√
2Dξ(t) + f e−iωt
2
Im(z)
1
0
-1
-2
-2
Tuesday, January 26, 2010
-1
0
Re(z)
1
2
Amplitude and phase dynamics
ż = −(r + iω0 )z − B|z|2 z − C|z|4 z +
Polar coordinates
√
2Dξ(t) + f e−iωt
(!(z), "(z)) ⇒ (ρ, φ)
Phase difference between oscillator and driving phases
ψ(t) = φ(t) + ωt
Mean output is
Sensitivity is
Tuesday, January 26, 2010
!z(t)" = !ρeiφ(t) " = !ρeiψ "e−iωt
|!ρeiψ "|
|χ| =
f
Amplitude and phase dynamics
ż = −(r + iω0 )z − B|z|2 z − C|z|4 z +
√
2Dξ(t) + f e−iωt
Phase difference between oscillator and driving phases
ψ(t) = φ(t) + ωt
f
ψ̇ = ∆ω − sin(ψ) +
ρ
√
2D
ξ(t)
ρ
Amplitude dynamics
3
5
ρ̇ = −rρ − Bρ − Cρ + f cos(ψ) + D/ρ +
Tuesday, January 26, 2010
√
2Dξρ (t)
Amplitude and phase dynamics
ż = −(r + iω0 )z − B|z|2 z − C|z|4 z +
√
2Dξ(t) + f e−iωt
Phase difference between oscillator and driving phases
ψ(t) = φ(t) + ωt
√
f
2D
ψ̇ = ∆ω −
sin(ψ) +
ξ(t)
ρd
ρd
Amplitude dynamics
for r<0 and weak noise we can approximate
0 = −rρd − Bρd 3 − Cρd 5 + f " cos(ψ)#
Tuesday, January 26, 2010
Amplitude and phase dynamics
ż = −(r + iω0 )z − B|z|2 z − C|z|4 z +
√
2Dξ(t) + f e−iωt
Phase difference between oscillator and driving phases
ψ(t) = φ(t) + ωt
√
f
2D
ψ̇ = ∆ω −
sin(ψ) +
ξ(t)
ρd
ρd
Δω ψ−(f/ρd)cos(ψ)
!eiψ " =
ψ
Tuesday, January 26, 2010
I1+i∆ωρ2d /D (f ρd (f )/D)
Ii∆ωρ2d /D (f ρd (f )/D)
Haken et al. Z. Phys. 1967
Solution for the sensitivity
!e
−iψ
"=
0 = −rρd −
I1+i∆ωρ2d /D (f ρd (f )/D)
Ii∆ωρ2d /D (f ρd (f )/D)
3
Bρd
−
5
Cρd
+ f "#e
−iψ
$
!
!
!
!
2
I
(f
ρ
(f
)/D)
d
ρd (f ) ! 1+i∆ωρd /D
!
|χ| =
!
!
f ! Ii∆ωρ2d /D (f ρd (f )/D) !
Lindner, Dierkes & Jülicher Phys.Rev.Lett. (2009)
Tuesday, January 26, 2010
Instead of fitting power laws ...
... let’s calculate the local exponent (∆ω = 0 )
ρ!d f
ρd +
d ln(|χ|)
=f
α=
d ln(f )
D
!
I0 (f ρd /D) I1 (f ρd /D)
−
I1 (f ρd /D) I0 (f ρd /D)
"
−2
f ρd /D ! 1 ⇒ α ≈ 0
D
! f ! ρd (5Cρ4d + 3Bρ2d + r) ⇒ α ≈ −1
ρd
f ≥
ρd (5Cρ4d
+
3Bρ2d
+ r) ⇒ α ≈
!
−2/3 : supercritical
−4/5 : subcritical
Lindner, Dierkes & Jülicher Phys.Rev.Lett. (2009)
Tuesday, January 26, 2010
Exponents for ∆ω = 0 ...
-2
10
0
-0.2
"
α
-0.4
-0.6
-0.8
-1
-6
10
2
10
~f
-4
-2/3
D = 10
-3
D = 10
0 = 10-2
D
-1
D = 10
10
-2
4
10
-2/3
-0.6
-2/3
-4 -2
10 10
f
-2 0
1010
02
10
10
10
0
-0.2
-0.4
-0.6
-0.8
-1
f [pN]
-1
-1
2
10
-6
10
(b)
-4/5
0
-0.8
-1
~f
10
-0.2
-0.4
~f
(b)
-1
2
00
0
-4
Tuesday, January 26, 2010
-4
2
# = 10
10-3
# = 10
# = 10 -2
-1
0
# = 10
10 0
# = 10
10
0
-0.2
-0.4
-0.6
-0.8
-1
10
|!| [nm/pN]
10
(a) (a)
-1
"
0
~f
4
10
|χ|
|χ|
10
10
Stochastic
Hair bundle model
SUBCRITICAL
OP 2
α
2
|!| [nm|/pN]
4
10
Noisy
normal form
SUPERCRITICAL
OP 1
4
-4
10
0
0
-4/5
-1
-4-2
10
10
f
10 -2
10
0
2
10100
f [pN]
-1
2
10
Comparison to the hair bundle model
Exponents of nonlinear compression
subcritical Hopf oscillator
from formula
HB model
numerically from sensitivity curves
1e+00
0.2
1e+00
LR
LR
NC
1e-01
NC
1e-01
D
0.0
-0.2
D
1e-02
-0.4
SNC
SNC
1e-03
1e-02
1e-01
1e+00
f
Tuesday, January 26, 2010
1e+01
1e+02
1e+03
-0.6
LR
1e-02
-0.8
1e-03
1e-02
1e-01
1e+01
1e+00
f
1e+02
1e+03
-1.0
Summary
•sharp tuning and high exponents of nonlinear
compression through coupling-induced noise
reduction
•numerical, experimental, and analytical results give a
unique picture of small groups of coupled hair bundles
as an essential part of the cochlear amplifier
Tuesday, January 26, 2010
PART 2
• SHORT-TERM PLASTICITY AND INFORMATION TRANSFER
Tuesday, January 26, 2010
Setting
dynamic synapses
(short-term plasticity)
output spikes
synaptic
background
+
signals
Central question
How do dynamic synapses affect
the transfer of time-dependent
signals and noise?
Tuesday, January 26, 2010
Short-term plasticity (STP)
Change in the released transmitter by incoming spikes
Increase in efficacy = synaptic facilitation
Decrease in efficacy = synaptic depression
[Markram & Tsodyks 1997, Abbott et al. 1997, Zucker & Regehr 2002]
EPSCs
Field potentials
depression
facilitation
1mV
100ms
facilitation
Abbott & Regehr Nature. (2004)
Tuesday, January 26, 2010
facilitation
Lewis &Maler J. Neurophysiol. (2002)
Facilitation & depression add an
amplitude to each spike
Synaptic
facilitation and
depression
spike trains
F-D
0
0
1
time
2
3
.
.
.
.
.
.
0
Synaptic
input
spike trains
input spike
trains
0
0
1
time
2
3
2
3
.
.
.
F-D
0
1
!
time
2
δ(t − ti,j )
Tuesday, January 26, 2010
3
0
0
!
1
time
Ai,j δ(t − ti,j )
Known effects of dynamic synapses
•
•
Single neurons
Network level
sensory adaptation and decorrelation
(Chung et al. 2002)
•shift in response times to population
input compression
(Tsodyks & Markram 1997,
Abbott et al. 1997)
•network oscillations
•
switching between different neural codes
(Tsodyks & Markram 1997)
•
spectral filtering
(Fortune & Rose 2001, Abbott et al. 1997)
•
synaptic amplitude can keep info about
the presynaptic spike train seen so far
(e.g. Fuhrmann et al. 2001)
Tuesday, January 26, 2010
bursts Richardson et al. (2005)
Marinazzo et al. Neural Comp. 2007
•self-organized criticality
Levina et al. Nature Physics 2007
•working memory
Mongillo et al. Science 2008
Here:
information transmission
across dynamic synapse
Model
(similar to phenomenological models by
Abbott et al. and Tsodyks & Markram)
Tuesday, January 26, 2010
Model
Postsynaptic
amplitude
1mV
100ms
Aj = Fj Dj
Dynamics for facilitation
and depression
Dittman et al. J. Neurosci. (2000), Lewis &Maler J. Neurophysiol. (2002,2004)
Tuesday, January 26, 2010
Conductance and voltage dynamics
Presynaptic spike trains
Synaptic inputs
!
δ(t − ti,j )
Conductance dynamics
Membrane voltage dynamics
[postsynaptic spiking with fire&reset rule (LIF)]
Tuesday, January 26, 2010
Effect of FD dynamics on the temporal
structure of the postsynaptic activity
dynamic synapses
output spikes
Poissonian spike trains
synaptic input,
postsynaptic conductance
Power spectra
Tuesday, January 26, 2010
spike trains
Power spectra
0
1
time
2
3
.
.
.
Correlation function or
power spectra?
0
Tuesday, January 26, 2010
0
0
1
2
3
power spectra
Power spectra
constant amplitude
60
40
dominating depression
dominating facilitation
Theory
20
0
Tuesday, January 26, 2010
0
10
1
Frequency
10
10
8
6
4
2
0
r=1Hz
r=1Hz
0.01
60
40
20
0
100
DDR
FDR
theory
0.0015
0.001
0.0005
0
r=10Hz
0.005
r=10Hz
0
0.004
r=100Hz
r=100Hz
0.002
50
0
10
0
10
1
frequency
10
0
10
1
Voltage power spectrum
spike train power spectrum
Power spectra
0
frequency
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
Model with rate modulation
Modulation of the input firing
rate by a periodic signal
Tuesday, January 26, 2010
R(t) = r · [1 + εs(t)]
Model with rate modulation
Modulation of the input firing
rate by a periodic signal
R(t) = r · [1 + εs(t)]
SNR largely independent of frequency !
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
Model with rate modulation
Modulation of the input firing
rate by a band-limited Gaussian
white noise (0-100Hz)
R(t) = r · [1 + εs(t)]
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
Spectral measures
Fourier transform
1
x̃ = √
T
!T
dt e
2πif t
x(t)
0
Cross spectra of synaptic input/voltage and input signal
SXs = !X̃ s̃ "
∗
Sgs = !g̃s̃ "
2
|Sgs |2
=
Sgg Sss
∗
Coherence functions
CXs
Tuesday, January 26, 2010
|SXs |
=
Sss SXX
Cgs
Why the coherence?
Relation to information theoretic measures
Lower bound on mutual
! information
ILB = −
df log2 [1 − C(f )]
Error of linear reconstruction
!
!=
Tuesday, January 26, 2010
df Sss [1 − C(f )]
Coherence functions for various
parameter sets
CXs
|SXs |2
=
Sss SXX
broadband coding
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
Cross spectra
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
Coherence functions for various
parameter sets
CXs
|SXs |2
=
Sss SXX
broadband coding
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
Why is the coherence flat ?
1
CX,R
N −1
1 1
1
=
+
N C!xi ",R
N Cxi ,R
Coherence between rate and
time-dependent mean value of the
single FD modulated spike train
Coherence between rate and the
single FD modulated spike train
C!xi ",R ≈ 1
Merkel & Lindner submitted (2009)
Tuesday, January 26, 2010
Coherence for a single synapse
pure facilitation
pure depression
0.04
Simulation
Theory
0.1
A
~|cross 2
spectrum|
~|cross 2
spectrum|
0.2
0.1
B
0.02
Simulation
Theory
0.01
0.03
B
0.02
0.01
0.00
coherence
coherence
0.0
0.004
0.004
0.002
0.000
A
0.00
~power
spectrum
~power
spectrum
0.0
0.03
0.002
C
0.1
1
10
frequency [Hz]
CRx (f )
≈
1+
ε2 rSRR (f )
[1+(2πf τF )2 ]·∆2lin rτF /2
(F1 +∆lin rτF )2 +(2πf τF )2 ·F12
with F1 = F0,lin + Dlin rτF
Tuesday, January 26, 2010
0.000
C
0.1
1
10
frequency [Hz]
!
F02 rτD
2
CRx (f ) ≈ ε rSRR (f ) · 1 −
2β
Merkel & Lindner submitted (2009)
"
Coherence for a single synapse
simulation value
(theoretical value)
Merkel & Lindner submitted (2009)
Tuesday, January 26, 2010
Why is the coherence flat ?
1
CX,R
N −1
1 1
1
=
+
N C!xi ",R
N Cxi ,R
Coherence between rate and
time-dependent mean value of the
single FD modulated spike train
Coherence between rate and the
single FD modulated spike train
C!xi ",R ≈ 1
Merkel & Lindner submitted (2009)
Tuesday, January 26, 2010
Coherence-dependence on the number N
of synapses
1
N=10000
coherence CRX
0.1
0.01
0.001
N=1000
N=100
N=10
N=1
0.0001
0.01
Simulation
Theory
0.1
1
10
frequency [Hz]
Merkel & Lindner submitted (2009)
Tuesday, January 26, 2010
Extension I
Postsynaptic spiking
Tuesday, January 26, 2010
LIF output spike train
+µ
if V = −65mV then ti = t & V = −70mV
Tuesday, January 26, 2010
Coherence for static synapses and
different I&F models
1
A
γ 2 /c
0.8
B
C
PIF
LIF
QIF
0.6
0.4
0.2
0
-2
-1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
1
D
γ 2 /c
0.8
F
E
0.6
0.4
Perfect IF
0.2
0
-2
-1
0
1
10 10 10 10
1
-2
-1
10
0
10
1
10
-2
10
G
0.8
γ 2 /c
Coherence functions
always low-pass !
10
-1
10
0
10
1
10
H
QuadraticIF
I
0.6
Leaky IF
0.4
0.2
0
-2
10
-1
0
10
10
f
Tuesday, January 26, 2010
1
10
-2
10
-1
0
10
10
f
1
10
-3
10
-2
10
-1
10
f
0
10
1
10
Vilela & Lindner
Phys. Rev. E (2009)
Coherence -LIF output spike train
Lindner, Gangloff, Longtin & Lewis J. Neurosci. (2009)
Tuesday, January 26, 2010
So far: one presynaptic population with
one rate modulation
dynamic synapses
output spikes
R(t) = r · [1 + εs(t)]
synaptic input,
postsynaptic conductance,
output spike train
Info about R(t)
broadband coding
Tuesday, January 26, 2010
Extension II
Extra Noise channel
Tuesday, January 26, 2010
Extra noise
spikes with
constant rate
(just noise)
facilitation-dominated synapses
output spikes
spikes with rate
modulation R(t)
Tuesday, January 26, 2010
depression-dominated synapses
Extra noise
40
=
CRX (f )
1
N
spectra [Hz]
A
·
1
CRxi (f )
1
+N
30
20
10
·
+
40
spectra [Hz]
1
1
Sηη
NSxx
30
20 )
CRxi (f
10
·
·
1
CR"x # (f )
i
Sηη (f )
N Sxi xi (f )
Sηη
NSxx
0
0
B
0.02
CRX (Simulation)
CRX (Theory)
0.01
0.00
0.01
0.1
0.25
coherence
coherence
N −1
N
0.2
0.15
CRX (Theory)
CRX (Simulation)
0.1
0.05
1
10
frequency [Hz]
Facilitating synapses for signal
Depressing synapses for noise
0
0.01
0.1
1
10
frequency [Hz]
Depressing synapses for signal
Facilitating synapses for noise
Merkel & Lindner in preparation (2009)
Tuesday, January 26, 2010
Extra noise
spikes with
constant rate
(just noise)
facilitation-dominated synapses
output spikes
synaptic input,
postsynaptic conductance,
output spike train
spikes with rate
modulation R(t)
depression-dominated
synapses
Tuesday, January 26, 2010
Info about R(t)
low or highpass coding
possible
Summary
‣
analytical results for FD dynamics under Poissonian stimulation
‣
“information filtering” not affected by FD dynamics broadband coding at the level of the conductance dynamics
‣
“information filtering” possible if additional noise channels
are present
Tuesday, January 26, 2010