Simple cells of mammalian striate cortex drew the attention of neuroscientists because of their receptive fields (RFs) composed of elongated, separate, and parallel subregions, alternately driven by stimuli of opposite contrast that make them selective to bars and gratings, drifting or flashing within restricted portions of the visual field and at specific angles of orientation. The number of subregions usually ranges from one to three, but many authors [29,88,120] reported the observation of simple cell RFs with multiple sidebands which are often referred to as ``periodic'' RFs. Independently of the number of the subregions, the spatial response profile of simple cells appears as an extremely regular structure for its smooth isotropic decay, for the symmetrical spacing of the zero-crossings, and for the relationships among the amplitudes of neighboring subregions, to such a point that it resembles a sine wave weighted by a two-dimensional Gaussian envelope. Functional implications of this surprising RF organization have been widely investigated in terms of cortical image representation, by modeling simple cell RFs with families of two-dimensional spatial functions, such as Gaussian derivatives [128,129], Gabor functions [22,23,69,77] or differences of offset Gaussians [52,53], and by formulating the computational capabilities of such Gabor-like RFs in relation to communication theory [23,43,69,106]. The question however arises as which are the anatomical and physiological processes that underlie such peculiar RF profiles. Some authors identify these processes with functional projections going from lateral geniculate nucleus (LGN) to layer IV of the striate cortex and, from there, up to deeper cortical layers, as originally proposed by Hubel and Wiesel in their hierarchical model . According to this model, an elongated subfield of a simple cell RF is generated directly by synaptic inputs from a row of geniculate neurons whose RF centers overlap the subregion, and, likewise, a periodic RF may be constructed hierarchically by the merging of lower order simple cells, i.e. the more common simple cells whose RFs are composed of one to three subregions. Although it is widely acknowledged the importance of Hubel and Wiesel's original hypothesis in establishing orientation preference in cortical simple cells [18,110], it is difficult to prove that the origin of the detailed structure of their RFs depends exclusively on the spatial organization of the geniculocortical connections. In principle, indeed, all of the response properties of cortical cells can be explained with models that postulate a high degree of feed-forward connection specificity. However, establishing highly specific connections requires large amounts of information, which might be more than what can be determined genetically or learned by experience . Alternatively, other authors suggest that the origin of the final shape of simple cell RFs should be searched in the organization of intracortical inhibitory inputs. Several studies, indeed, reported that the response selectivity of simple cells can be reduced and even suppressed by the superposition of non-specific visual stimulation [20,86], as well by neurochemical manipulation [3,10,80,101,119].
When assessing the role of inhibition in cortical function, one important issue concerns the spatial localization of inhibitory influences. In this paper, we will evidence how tangential (e.g., horizontal) inhibitory processes with a non-local clustered character can give rise to cooperative inhibitory effects that result in the regular shape of Gabor-like RFs. The analysis will be carried out within a linear framework in which we assume a linear superposition of geniculate (feed-forward) and intracortical (feed-back) contributions. A systematic parametric study of the effect of the strength of inhibition and of its spatial localization on the sharpness of orientation selectivity and on the narrowness of spatial frequency tuning will be presented. Moreover, although the emphasis in this work is on the exploration of general principles, rather than to the detailed modeling of neurophysiological observations, consistencies and divergences between our results and the experimental data available in the literature will be evidenced.