Deriving Connectivity Patterns in the Primary Visual Cortex from Neuronal Activity

1. Deriving connectivity patterns in the primary visual cortex from spontaneous neuronal activity and feature mapsBarak Blumenfeld, Dmitri Bibitchkov, Shmuel Naaman, Amiram Grinvald and Misha TsodyksDepartment of Neurobiology, Weizmann institute of Science, Rehovot, Israel

2. 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.

3. A B C 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.

4. Topology of intrinsic states Evoked Spontaneous PCA Kohonen map Templates Figure 3.Projections of 24 single condition orientation maps Mk corresponding to orientations θkonto 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:

5. Spontaneous A B 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).

6. Recurrent neural network with functional maps as attractors: 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:

7. 5 4 3 2 -3 -3 x 10 x 10 1 2 2 0 1 1 -1 0 0 -2 -1 -1 -2 -2 -3 -4 Dependence of connectivity on orientation selectivity B C A 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 .

8. 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.

9. Simulation Experiment Initial Stationary A B C Experiment Simulation Initial Stationary D E F 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 (t=300). 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.

10. 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. , ArieliA.  (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. Nov;34(5):4217-4228.