Representation of high
bandwidth sensory information
by small circuits in the whisker
system
Rasmus Petersen
Workshop on Computational Neuroscience, Warwick Dec 2008
Two views of neural coding
• Low bandwidth
e.g., visual cortex
• High bandwidth
e.g., fly H1
de Ruyter et al (1997)
A1
α
A2
A3
B1
β
A4
B2
B3
C1
γ
B4
C2
C3
D1
δ
C4
C6
C5
C7
D8
D7
D2
D3
D6
D5
D4
E9
E8
E7
E1
E6
E2
E3
E4
E5
SI
barrels
barreloids
Thalamus
Brainstem
barrelettes
Brecht (2007) COIN
Helmstaedter et al. (2007) Br Res Rev
Tansu Celikel
30 micron
grooves
smooth
1
2
3
4
5
A
Single whisker discrimination
B
C
D
E
Carvell & Simons (1990)
10000 neurons
per barrel
SI
250 neurons
per barreloid
Thalamus
Brainstem
250 neurons
per barrelette
150 receptors
per whisker
micromotions
free whisking
Whisker position
Whisker velocity
Whisker acceleration
object contact
• Experimentally measured
micromotions
• Importance of temporal domain
Arabzadeh et al. (2005)
Coding temporal signals
SI
Thalamus
Brainstem
1. Response question:
What is the ‘information-bearing
element’ of the neuronal response?
2. Stimulus question:
What stimulus features do the
information-bearing elements
signify?
The information-bearing element
of a spike train
Hypothesis 1. Firing rate
Hypothesis 2. Correlations between spikes
Firing rate vs temporal
correlations
• Effect of correlations on encoded information (Icorr)
How much does the presence of noise correlations change the
information compared to a hypothetical neural system where the
neuron has identical mean firing rate but zero noise
correlations? (eg Schneidman et al., 2003)
• Effect of correlations on decodable information (∆I)
If a hypothetical downstream decoding circuit attempts to
decode using a model that includes mean firing rates but
ignores noise correlations, how much information will be lost?
(Nirenberg et al., 2001)
Montemurro et al (2007) J Neurophysiol
Summary
• For VPM neurons stimulated by white
noise, key “information-bearing
element” is firing rate
• For most VPM neurons, higher order
temporal correlations have minor impact
What stimulus features does the
firing rate signify?
Approaches:
•Pseudolinear model:
•Spike-triggered averaging
•Non-linear models:
•Spike feedback (Paninski) model
•Spike-triggered covariance analysis
Linear Nonlinear Poisson (LNP)
Model
A
C
E
Position sensor
Velocity sensor
Acceleration sensor
0.8
0.3
0.5
k (t ) =
i=T / δt
‡” i = 0
s (t - i δ t
) f (i δ t )
r ( t ) = g [k ( t ) ]
Stim amplitude (SD)
0.7
0.6
0.5
0.4
0.2
0.3
0.1
0.2
0
0.1
-0.1
0.4
0
-0.2
-0.1
0.3
-0.3
-0.2
0.2
-0.3
-0.4
0.1
-0.4
-0.5
-0.5
0
30
20
10
0
-10
B
30
-0.6
20
10
0
-10
D
30
20
10
0
-10
F
0.4
0.45
Position
Velocity
Acceler.
r (t ) = g[ s (t )]
r (t ) = g[ s(t ) - s (t - δt )]
r (t ) = g[12 s (t ) - s (t - δt ) + 12 s (t - 2δt )]
Stim amplitude (SD)
0.4
0.2
0.3
0.1
0.35
0.2
0.3
0.1
0
0.25
-0.1
0
-0.2
0.2
-0.1
0.15
0.1
0.05
0
30 20 10
0 -10
Pre-spike tim e (m s)
-0.3
-0.2
-0.4
-0.3
-0.5
30 20 10
0 -10
Pre-spike tim e (m s)
30 20 10
0 -10
Pre-spike tim e (m s)
0.5
B
Firing rate (spikes/s)
Stim amp (SD)
A
0.4
0.3
0.2
0.1
0
40
20
0
Pre-spike tim e (m s)
C
20
15
10
5
-2
0
2
Feature coefficient (SD)
D
0.2
0
-0.2
-0.4
40
20
0
Pre-spike tim e (m s)
Firing rate (spikes/s)
0.4
Stim amp (SD)
25
60
50
40
30
20
10
0
-2
0
2
Feature coefficient (SD)
Petersen et al (in press) Neuron
How accurate is the LNP model?
• Non-linear approaches:
– Maximum likelihood fitting of spike
feedback (Paninski) model
– Spike-triggered covariance analysis
Petersen et al (in press) Neuron
B
0.8
Information (bits/spike)
Information (bits/spike)
A
0.6
0.4
0.2
0
0
0.8
0.6
0.4
0.2
0
10
20
Feature
C
0
10
20
Feature
D
12
1.2
10
1
Number units
STA information (bits/spike)
1.4
0.8
0.6
0.4
0.2
8
6
4
2
0
0
0.5
1
STC inform ation (bits/spike)
0
1
2
3
4
Inform ation ratio (STC/STA)
Petersen et al (in press) Neuron
LNP model
k (t ) =
‡”
r (t) = g
i= T / δ t
i= 0
[k
(t)
s (t - i δ t
) f (i δ t )
]
Petersen et al (in press) Neuron
Petersen et al (in press) Neuron
Petersen et al (in press) Neuron
Conclusions
• VPM neurons reliably encode complex whisker
motion
• Key information-bearing element of response is
firing rate on millisecond time-scale
• High reliability permits small subcortical circuits
to support demanding sensory processing
• Most VPM neurons can be described by LNP
models
• VPM exhibits a distributed code for whisker
motion
Acknowledgements
Michael Bale
Marco Brambilla
Andrea Alenda
Marcelo Montemurro
Liam Paninski
Stefano Panzeri
Miguel Maravall
EXTRA