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Oct 19, 2013 (3 years and 11 months ago)

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Stable Propagation of
Synchronous Spiking in Cortical
Neural Networks

Markus Diesmann, Marc
-
Oliver Gewaltig, Ad
Aertsen

Nature 402:529
-
533

Flavio Frohlich

Computational Neurobiology UCSD

La Jolla CA
-
92093

Outline


Background


Neural Code


Integrate&Fire Neuron


Motivation / Research Questions


Methods


Results


Discussion & Conclusions

The Neural Code

Stimulus
s
(
t
)

Neural

System

Neural Response

(
t
)

Stimulus

Neural Response

Coding

Given

To determine

Decoding

To determine

Given

The Neural Code


Independent
-
spike versus correlation
code.






Temporal versus rate code.


different

The Neural Code


Independent
-
spike code


Time
-
dependent firing rate
r
(
t
).


Probability distribution of spike times can be
computed from
r
(
t
) as inhomogenous Poisson
process.


Firing rate r(t)

contains all information about
stimulus.


Interspike intervals do not carry information.



The Neural Code


Correlation code


Correlation between spike times carry
information.


e.g. information about stimulus carried by
interspike intervals.



The Neural Code


Rate code


Assumption: independent
-
spike hypothesis fulfilled.


Firing rate
r
(
t
) “varies slowly with time”.


Temporal code


Assumption: independent
-
spike hypothesis fulfilled.


Firing rate
r
(
t
) “varies rapidly”.


“Information is carried by spike timing on a scale
shorter than fastest time characterizing variations of
stimulus.”


Requires precise spike timing


millisecond
precision possible for noisy neurons?


Motivation / Research Questions


High temporal accuracy observed
in vivo
(precisely timed action potentials related
to stimuli and behavioral events in awake
behaving monkey,
e.g. Abeles 1993
) and
in vitro
.


“Can instances of synchronous spiking be
successful transmitted/propagated by
subsequent group of neurons?”


“Under which conditions?”

Integrate & Fire Neuron I


No biophysical states (channel dynamics).


Integrate transmembrane currents.


If threshold reached:


Stipulate action potential (AP).


Reset membrane voltage below threshold.

Integrate & Fire Neuron II


Leaky integrate&fire (i&f) neuron:

Time constant

m

Membrane voltage
V

Steady state membrane voltage
E
L

Input resistance
R
m

Transmembrane current
I
E



Postsynaptic currents:

-
function:


Background firing (uncorrelated
stationary Poisson distribution)

Network Topology


Feedforward architecture.


Group = layer.

Group i

Group i+1


Each neuron: 20’000
synaptic inputs (88%
excitatory, 12%
inhibitory).


100 neurons/group.


10 groups.


Predictions


“Neurons that share a large enough pool
of simultaneously discharging input cells
tend to align their action potentials.”



“A group of neurons can reproduce its
synchronous input activity and act as the
source of synchronous shared input for
the following group.”


Synchronous spiking sustained or
not?

Input to Model Neuron


Pulse packet: spike
volley.


Activity
a
: number of
spikes in volley.


Temporal dispersion

: standard deviation
of underlying pulse
time distribution.


in

a = 20

Pulse packet

Output = Neuron(Input)


Input to model neurons:
pulse packets (pooling
from many neurons in
previous layer).

I&F Neuron

I&F Neuron

I&F Neuron


Output of model neuron:
at most one spike.


Spike probability



Standard deviation

out
.

Neural Transmission Function I

Input

dispersion

in

# input spikes

Spiking probability

Neural Transmission Function II

Input dispersion

# input spikes

Output dispersion


in
>

out


out
>

in

State Space Analysis

Stable attractor

Saddle point

State
-
space analysis
of propagating
spike synchrony.


State variables:

Activity
a

Dispersion



Trajectory
t
=
t
(
i
)
where
i

denotes
ordered group.

Size of Neuron Groups W

W = 80

W = 90

W = 100

W = 110

zero
-
isocline activity
a

zero
-
isocline dispersion


region of attraction


Increase W


Fixpoints

move apart.


Decrease W


Fixpoints
merge to saddle point.


Minimal group size W for
maintaining synchrony.

Discussion & Conclusions


Stable fixpoint


= 0.5 ms


temporal
precision matching cortical recordings.


Region of attraction guarantees
robustness.


Model parameters in congruence with
physiological data.