The eye faithfully maps visual space to different positions on the retina. This retinotopy is preserved as the signal is forwarded from retinal ganglion cells to the LGN, then to V1, and onwards. Cells which are physically adjacent on a retinotopic map have receptive fields corresponding to similar positions in space. More generally, properties like orientation, direction and spatial frequency selectivity are organized  topographically on the cortical surface.

This simple fact has deep and important consequences. This is because neurons tend to receive inhibitory and excitatory input from other neurons which are quite close to them physically. So this combination of regular topography and local processing is a very strong constraint on cortical processing.

Kerlin et al. (2010) is great example of this idea. They looked at the direction, orientation and spatial frequency tuning of different subtypes of mouse V1 neurons. Specifically, they identified and characterized excitatory neurons as well as 4 different subtypes of inhibitory neurons. Overall, excitatory neurons had sharper orientation and spatial frequency tuning than all subtypes of inhibitory neurons. In fact, a large proportion of inhibitory neurons were essentially untuned for orientation.

This is interesting, because in other species, like the cat, inhibitory neurons are well tuned in primary visual cortex. Cat primary visual cortex has an orderly orientation map (shown above). Mouse V1 doesn’t; rather, the orientation selectivity of adjacent excitatory neurons is more or less independent. This is often called “salt-and-pepper” organization.

If you assume that an inhibitory neuron pools from the output of several excitatory neurons in its close (horizontal) vicinity, the inhibitory neuron should be orientation tuned if there is an orderly local orientation map, as in the cat, but untuned if there isn’t, as in the mouse.

The data is consistent with this idea (above). The authors computed the average tuning curves of excitatory neurons within each imaged volume. These volumes being spatially limited (150 x 150 x 45 microns), the mean tuning curves differed slightly from volume to volume. The tuning curves of inhibitory neurons closely matched that of the mean tuning curve of excitatory neurons in the same volume. This shows that the tuning of inhibitory neurons can be understood simply in terms of local topography and local wiring schemes.

We can also look at the inverse question: given an excitatory neuron, where does it get its inhibitory inputs from? Using optogenetic techniques, Kätzel at al. (2010) examined this idea. They found that regardless of whether they recorded in mouse V1, M1 or S1, excitatory neurons received inhibition from horizontal circuits spanning at most 550 microns. This turns our to be equal to the size of 3 barrels in barrel cortex (S1), which are easily visualized columns associated with whiskers. So basically an excitatory cell gets its inhibitory input from its own column as well as next-neighbor columns. As the authors state:

Inhibitory connections thus seem to follow a pericolumnar ‘center-surround’ arrangement, which provides an anatomical substrate by which activity in one column can suppress that of its immediate neighbors.

Again, you have this same motif: topography + local wiring rules = function. In this case the function is center-surround antagonism. Pretty sick.

Forwarding a topographic map from one area to the next can lead to interesting effects. I discussed previously Dario Ringach’s idea that V1 orientation columns are generated by the convergence of interfering  ON- and OFF- retinal ganglion cell hexagonal maps.

Another application of this idea is the paper by Motter (2009) examining the relationship between V4 and V1 retinotopic maps. What he found is that the size and shape of V4 receptive fields could be explained very straightforwardly by assuming that each V4 cell takes its inputs from within a circular area about 15 mm across on the surface of V1 (above).

It would be interesting to see if this idea generalizes further. For example, primate V1 has orderly retinotopy and orientation domains. So if you pool the output of a small area of V1 cortex, the resulting receptive field should not only be contiguous, but it should also be selective for a relatively small number of orientations. Thus, much like Dario’s idea that orientation selectivity in V1 could be seeded from the hexagonal topography of RGCs, so the curvature or conjunction selectivity of V2/V3 and V4 could be seeded from the orientation/retinotopic maps of V1. Just a hunch.

Kerlin, A., Andermann, M., Berezovskii, V., & Reid, R. (2010). Broadly Tuned Response Properties of Diverse Inhibitory Neuron Subtypes in Mouse Visual Cortex Neuron, 67 (5), 858-871 DOI: 10.1016/j.neuron.2010.08.002

Kätzel, D., Zemelman, B., Buetfering, C., Wölfel, M., & Miesenböck, G. (2010). The columnar and laminar organization of inhibitory connections to neocortical excitatory cells Nature Neuroscience, 14 (1), 100-107 DOI: 10.1038/nn.2687

Motter, B. (2009). Central V4 Receptive Fields Are Scaled by the V1 Cortical Magnification and Correspond to a Constant-Sized Sampling of the V1 Surface Journal of Neuroscience, 29 (18), 5749-5757 DOI: 10.1523/JNEUROSCI.4496-08.2009