Optimal information processing in neural
populations.
Nigel Stocks
School of Engineering, University of Warwick, UK.
Collaborators:
A. Nikitin
R. P. Morse
M. D. McDonnell
- School of Engineering, University of Warwick, UK
- Aston University, Birmingham UK
- University of South Australia, Australia.
1
Sensory signal transduction
Cochlea
Inner Hair Cell
Data from H1 neuron of fly
(taken from ‘Spikes’, Rieke et al)
2
HAIR CELLS
(mechanical transducers)
K+
Stereocilia
(“hairs”)
Ca+
5 µm
3
Electron microscope image courtesy of Dr. David Furness, Keele University.
Noise sources
K+
Brownian motion of stereocilia, 2-3nm
rms (at threshold displacements of 0.3nm
can be detected).
Thermal noise of ion channels.
Stochastic nature of synaptic
transmission.
SNR ~ 0-10dB
Ca+
5 µm
4
Electron microscope images courtesy of Dr. David Furness, Keele University.
SNR ~ 0dB
SNR ~ 70dB
To understand performance need to
consider collective behaviour of neurons.
How do we maximise information flow
through a population of noisy neurons?
5
Array of N McCulloch-Pitts Neurons
Random
Gaussian
signal
2
Y = Number of units ‘on’
(discrete output)
Each unit has the transfer function given by
 1 if
yi = 
 0 if
S (x
t) + ηi > θ
i
S (x
t) + ηi < θ i
6
N=1 (single neuron)
Threshold=0
Threshold=2.83
σ =
noise power
signal power
7
Maximising Information for
identical thresholds
8
Array of N McCulloch-Pitts Neurons
(comparators)
Random
Gaussian
signal
Y = Number of units ‘on’
(discrete output)
Each unit has the transfer function given by
 1 if
yi = 
 0 if
S (x
t) + ηi > θ
i
S (x
t) + ηi < θ i
9
N>1 and {ϑi } = 0
Suprathreshold Stochastic Resonance (SSR)
Information, I (bits),
Threshold=0
Threshold=0
N. G. Stocks, Phys. Rev. Lett 84, 2310 (2000)
10
10 comparators without noise
Input signal
y1
y2
y3
y4
y5
y6
y7
y8
y9
y10
Output
response
11
10 comparators with noise
Input signal
y1
y2
y3
y4
y5
y6
y7
y8
y9
y10
Output
response
12
SSR in Real Neurons
13
Experiments with additive noise
Suprathreshold (+6 dB) signal.
1 second duration.
Same waveform for each presentation.
Stimulating
electrodes
Isolated sciatic
nerve
Current
source
Noise waveform, that differed for each presentation
14
Information transmission with
additive noise
Noise 1
Response 1
virtual fibre 1
Noise 2
Response 2
virtual fibre 2
Noise 3
Response 3
virtual fibre 3
Noise 4
Response 4
virtual fibre 4
Responses from 1 sciatic nerve fibre15
Experimental Results
SSR
Classical SR
0.3
Signal -6dB
Signal 6dB
0.5
Mutual information (bits)
M u tu al in fo rm atio n (b its)
0.6
0.4
0.3
1 fibre
2 fibres
4 fibres
8 fibres
16 fibres
20 fibres
0.2
0.1
0.0
-50
-40
-30
-20
-10
0
Noise level (dB re base level)
10
20
1 fibre
2 fibres
4 fibres
8 fibres
16 fibres
20 fibres
0.2
0.1
0.0
-50
-40
-30
-20
-10
0
10
20
Noise level (dB re base level)
16
Period histograms. Comparison of
single fibre acoustic data to LIF model
Model
Squirrel Monkey
Anderson D.J, J. Acoustic Soc. Of Am. 54, 361 (1973)
17
Information curves
Membrane noise
Signal 28dB
18
Information curves
Membrane noise
‘natural’ noise
Signal 28dB
19
1
Signal 6dB
0.5
1 neurone
4 neurones
8 neurones
16 neurones
0.8
0.4
I (bits)
0.6
0.3
0.4
1 fibre
2 fibres
4 fibres
8 fibres
16 fibres
20 fibres
0.2
0.1
0.2
0.0
-50
-40
-30
-20
-10
0
10
0
-60
20
-40
-20
0
20
40
σ (dB)
Noise level (dB re base level)
1
1 neurone
4 neurones
8 neurones
16 neurones
0.8
0.6
I (bits)
Mutual information (bits)
0.6
0.4
0.2
20
0
-60
-40
-20
0
20
40
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