There are a number of possible sources for push-pull inhibition with the properties predicted by Troyer et al. (1998)'s model. One possible source is direct input from inhibitory geniculate relay cells (Carandini and Heeger, 1994). The receptive fields of these relay cells would have the same arrangement into elongated rows as that proposed by Hubel and Wiesel for the excitatory input. Were they to exist, they would fit exactly the criteria of a contrast response function similar to that of the relay cells, and complementary spatial organization to the excitatory input. Unfortunately, no physiological evidence for direct inhibition from relay cells has been found (Ferster and Lindström, 1983, Martin and Whitteridge, 1984), though some anatomical evidence has been reported (Einstein et al., 1987).
Thus, it is more realistic to fashion push-pull inhibition out of input from cortical inhibitory interneurons. An obvious problem, however, is that most cortical cells are strongly orientation selective. The inhibitory simple cells, if they were like the cortical cells most often recorded, would not normally fire in response to an orthogonally oriented stimulus, and so they would fail to counteract the non-zero baseline in the orientation tuning curves of Figure 4D.
One fix would be to arrange for each simple cell to receive inhibition from a large pool of other simple cells of all preferred orientations. At the preferred orientation of the postsynaptic cell, the subfields of the inhibitory interneurons would be aligned with those of the postsynaptic cell but have opposite response polarity, and so generate the observed push-pull arrangement. These interneurons would provide strong inhibition. At non-preferred orientations, many different interneurons with many different receptive field locations would counterbalance the relay cell input evoked by a bar of any orientation and location. [Note that this pool of inhibitory inputs would need to provide a signal that is subtracted from the feedforward geniculate input, rather than dividing it as in ``normalization'' models (Carandini and Heeger, 1994) discussed below.] Compared to the push-pull inhibition at the preferred orientation, which is known to be quite strong, these interneurons would provide only weak inhibition at the orthogonal orientation, in accordance with the inhibition observed in simple cells. The inhibition would only need to be strong enough to overcome the relatively small relay-cell excitation predicted by the feedforward model to come from the relay cells in response to orthogonal stimuli.
A second possibility has been proposed by (Troyer et al., 1998). In their model, the interneurons providing push-pull inhibition to simple cells all have preferred orientations similar to that of the postsynaptic cell (), but respond much like the uncompensated feedforward input itself. These interneurons, unlike the classical simple cell, would respond much like the one depicted in Figure 4B and D. For stimuli of the preferred orientation, they would act like normal simple cells, responding in the normal, position sensitive way only when bright stimuli were located in an ON region and/or dark stimuli were in an OFF region. For stimuli of the non-preferred orientation, these cells would show weak responses that grow with contrast, much like the LGN input in Figure 4B and D. The orientation tuning of these inhibitory simple cells, then, would not be invariant with contrast. They would retain the properties of the pure feedforward input.
While these inhibitory interneurons are themselves not contrast invariant in orientation, they would be in a position to generate contrast invariance in their neighbors. Consider a group of simple cells with a given preferred orientation. A high-contrast stimulus orthogonal to this preferred orientation will provide LGN input strong enough to evoke a response in simple cells unless the simple cells are sufficiently inhibited. In the model, some of the simple cells in the group -- the postulated interneurons -- do respond, and provide the inhibition that prevents the remainder of the cells from firing.
A critical prediction of this model is the existence of inhibitory interneurons in layer 4 with simple receptive fields that respond to stimuli of the non-preferred orientation in a manner that increases with increasing stimulus contrast. These interneurons would respond more or less as predicted by the feed-forward model in its simplest form (Hubel and Wiesel, 1962). It is difficult, however, to assess from current data whether or not these neurons exist. A large number of simple cells have been described in extracellular studies of the cortex. About 10-15% of visually responsive neurons in cat V1 are poorly tuned or non-selective for orientation (earlier work reviewed in Fregnac and Imbert (1984); Maldonado et al. (1997)). This percentage could easily include the postulated layer 4 interneurons, which are probably underrepresented in the sample. Interneurons form only 15-20% of cortical cells and, being small, are likely to have been recorded less frequently than excitatory cells. Nor is it often possible to identify interneurons from extracellular recordings. A few interneurons have been identified intracellularly, and are reported to have simple receptive fields with orientation tuning, though details of tuning were not reported (Gilbert and Wiesel, 1979). A recent such study of 8 identified interneurons found, suggestively, that all respond to orientations orthogonal to their preferred (Azouz et al., 1997). Unfortunately, no interneurons have yet been studied thoroughly enough to determine whether they possess all the properties predicted by Troyer et al. (1998). A search for the proposed interneurons remains a key experiment with which to test the model.