Deriving connectivity patterns in the primary visual cortex from spontaneous neuronal activity and feature maps Barak Blumenfeld, Dmitri Bibitchkov, Shmuel Naaman, Amiram Grinvald and Misha Tsodyks Department of Neurobiology, Weizmann institute of

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Deriving connectivity patterns in the primary
visual cortex from spontaneous neuronal activity
and feature maps Barak Blumenfeld, Dmitri
Bibitchkov, Shmuel Naaman, Amiram Grinvald and
Misha TsodyksDepartment of Neurobiology,
Weizmann institute of Science, Rehovot, Israel
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Abstract
Population activity across the surface of the
primary visual cortex exhibits well-known regular
patterns. The location and the shape of activity
patches depend on features of the stimulus such
as orientation. Recent studies have shown that
activity patterns generated spontaneously are
similar to those evoked by different orientations
of a moving grating stimulus Kenet, et. al.,
Nature 2003. This suggests the existence of
intrinsic preferred states of the cortical
network in this area of the brain. We deduce
possible connections in such a network from a set
of single condition orientation maps obtained by
voltage-sensitive dye imaging. We assume the maps
as attractor states of a recurrent neural network
and model the connectivity using a modified
version of the pseudo-inverse rule of the
Hopfield network. The results suggest a local
distance-dependent Mexican-hat shaped
connectivity. Long-range connections also exist
and depend mainly on the difference in
orientation selectivity of the connected pixels.
The strength of connections correlates strongly
with orientation selectivity of the neurons. The
dependence of the obtained synaptic weights on
the distance between neurons correlates with the
pattern of correlations in the spontaneous
activity, suggesting that intrinsic connectivity
in neuronal networks in this area of the brain
underlies the activity in both spontaneous and
evoked regimes.
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Experimental setup
Figure 2. Orientation single condition maps
obtained by voltage sensitive dye optical imaging
of a cat's area 17/18. The activity was evoked
by a moving grating stimulus with an orientation
of (A) 0 (horizontal), (B) 45, and (C) 90
(vertical). The direction of motion was
perpendicular to the stimulus orientation.
Figure 1. Experimental setup for the voltage
sensitive dye optical imaging.
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Topology of intrinsic states
Evoked
Spontaneous
PCA
Kohonen map
Templates
Figure 3. Projections of 24 single condition
orientation maps Mk corresponding to orientations
?k onto a plane spanned by the 1st two principle
components p1 ,p2. The data is fitted by a circle
(solid line).
Figure 4. Kohonen algorithm performs a
topological mapping of spontaneous activity
frames onto a set of templates on a ring. The
shapes of the learned templates resemble the
evoked orientation maps .
Selectivity
If orientation maps form a perfect ring
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Spontaneous activity patterns
Spontaneous
Evoked
Figure 6. Preferred orientation maps calculated
using evoked single condition maps (A) and
Kohonen templates of spontaneous spontaneous
activity (B) Kenet, et. al., 2003.
Figure 5. Activity patterns obtained by voltage
sensitive dye optical imaging. The pattern in (A)
was evoked by a 0 moving grating stimulus. It is
very similar to the spontaneous pattern (B).
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Network model with pseudo-inverse connectivity
Network dynamics
T
Network connectivity
Pattern correlation matrix
Fixed points of dynamics
For a linear gain function, the connectivity
results in a Hopfield network, which stores two
patterns corresponding to the principle
components of orientation maps
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Dependence of connectivity on orientation
selectivity
C
B
A
Figure 10. Connectivity of individual pixels. (A) Afferent synaptic weights of the pixel marked by the yellow dot. (B) Activity pattern evoked by a 90º stimulus. The yellow dot marks the same pixel as in (A). (C) Afferent synaptic weights of another pixel (close to a pinweel).
Figure 9. Average synaptic weights as a function
of the difference between preferred orientations
of the pre- and post synaptic neurons, for the
pseudo inverse connectivity .
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Dependence of connectivity on spatial separation
Figure 7. Average pixel-by-pixel correlation
coefficient of recorded spontaneous activity as a
function of distance between pixels on the
cortical surface. Solid line fit using a Mexican
hat function
Figure 8. Synaptic weights of the attractor
network as a function of distance between pre-
and post synaptic neuron, for the pseudo inverse
connectivity. The bin size was the size of one
pixel, which was 50µm.
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Network simulations
Figure 5.2 Simulations of the pseudo inverse
connectivity model with random initial activity.
Panels (A),(D) show the initial random activity
patterns for two trails. Panels (B),(E) show the
corrsponding stationary activity patterns
(t300). Panels (C),(F) show the corresponding
evoked activity pattern (C) 37.5º and (F)
112.5º. In all trails, the stationary activity
pattern was similar to one particular evoked
pattern, and was never a mixture of several
patterns evoked by different orientations. This
property is to be attributed to the non-linearity
of the gain function. By considering this type of
simulation as a model for spontaneous activity,
we conclude that the pseudo-inverse connectivity
can indeed produce the typical activity patterns
spontaneously.
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Conclusions

• Primary visual cortex has intrinsic activity
  states that emerge both spontaneously and due to
  visual stimulation and can originate from
  intra-cortical interactions in this area of the
  brain.
• Intrinsic states corresponding to
  orientation maps lie on a ring embedded into a
  high-dimensional space of neuronal activities.
• Attractor neural network with pseudo-inverse
  connectivity is capable to generate experimental
  activity patterns.
• The strength of modelled connections depends
  on the degree of selectivity of connected neurons
  and on the difference between their preferred
  orientations.

• References
• Kenet T., Bibitchkov D., Tsodyks M. ,
  Grinvald A. , Arieli A.  (2003) Spontaneously
  emerging cortical representations of visual
  attributes. Nature 425 954-956
• Personnaz L., Guyon I.I., Dreyfus G. (1986)
  Collective computational properties of neural
  networks New learning mechanisms. PHYS. REV. A.
  Nov34(5)4217-4228.