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Among visual cortical neurons, simple cells are, undoubtedly, those on which has been written the most and whose properties have been studied the deepest [5,23,29,52,53,59,61,70,71,72,87,122]. Although much has been done in analyzing the properties of simple cells, how those cells acquire their RFs remains one of the most intriguing question in neuroscience.
In this paper, we have investigated the mechanisms by which recurrent intracortical inhibition may influence the final profile of simple cell RFs. We can argue that intracortical inhibition may well be the substrate for a variety of influences observed between the RF center and its surround, including the refining of orientation and the spatial-frequency tuning of simple cells, and the emergence of the Gabor-like profiles of their RFs. In this context, we evidenced how the geometrical organization of inhibitory couplings is fundamental. In fact, regular spatial alternation of excitatory and inhibitory subregions arises spontaneously as an effect of recurrent inhibitory couplings among clustered populations of neurons, while we observed no oscillations when inhibitory connections are uniformly distributed in the horizontal plane. A careful examination of the functionality of the inhibitory mechanisms has revealed that they are almost independent of the choice of the orientation map and therefore of any highly-specific interaction among orientations. Indeed, we have obtained highly regular RFs for the most of orientation maps considered, provided that they are characterized by a non-random arrangement of orientations. The number of subregions exceeding that due to thalamic afferents, depends both on the size/strength of the initial geniculate bias, respect to the extension of inhibition, and on the strength of inhibitory couplings. Thus, we stress on the possibility that there might be a common strategy that leads to Gabor-like profiles in both periodic and non-periodic simple cell RFs. This disagrees with those models which justify periodic RFs as a spatial summation of many non-periodic RFs (e.g., a cell collecting the output of many non-periodic simple cells) [48,59,87,88,96] It is worthy to note that, in our model, periodic RFs demand the cooperation of a large set of surrounding cells and thus the stimulation of a rather wide portion of visual cortex. The horizontal contributions may be inadequate to elicit a response in a cell, but if such cell has been already brought above threshold by thalamic inputs, they are able to modulate the response to stimuli over an area larger than the ``classical'' RF, as defined by simple stimuli [4,14,25,28,57,74,81,116]. This is in accordance with the fact that the physiological and psychophysical observation of the additional sidebands in real simple cells [29,120] require functional stimulation such as gratings, rather than more traditional ones such as luminous bars or edges.
In conceiving our model and carrying on the analysis we stressed more on the extrapolation of computational principles than on the details of anatomical facts. For that reason, the present study can be though not as a realistic biological model of primary visual cortex, rather as an attempt to set forth some average structural/functional principles of intracortical connectivity and to relate them to the underlying single-cell properties. Specifically, since our model is based on the average anatomy of a given cortical area, it cannot represent the individual behavior of single cortical cells. It can only indicate properties probably common to all or most neuron within the averaging area. The principles so outlined may induce experimental validations of the drawn conclusions and/or lead to the exploitation of such structural/functional paradigms to develop neuromorphic architectures for artificial visual systems [130,131,132]. We have completely disregarded, in this study, excitatory corticocortical connections and the simultaneously presence of ON and OFF subsystems. Moreover our model is time invariant. Further improvements to the model can, therefore be achieved including also positive feedback circuits [32,90,103] and a competitive interaction between ON and OFF channels, according to the so called push-pull models [35,83,89,113] and considering also the temporal domain [30, 68, 135].