Nonlinear directionally selective subunits in complex cells of cat striate cortex

Abstract

1. We have analyzed receptive fields (RFs) of directionally selective (DS) complex cells in the striate cortex of the cat. We determined the extent to which the DS of a complex cell depends on spatially identifiable subunits within the RF by studying responses to an optimally oriented, three-luminance-valued, gratinglike stimulus that was spatiotemporally randomized. 2. We identified subunits by testing for nonlinear spatial RF interactions. To do this, we calculated Wiener-like kernels in a spatial superposition test that depended on two RF positions at a time. The spatial and temporal separation of light and dark bars at these two positions varied over a spatial range of 8° and a temporal range of ±112 ms in increments of 0.5° and 16 ms, respectively. 3. DS responses in complex cells cannot be explained by their responses to single light or dark bars because any linear superposition of responses whose time course is uniform across space shows no directional preference. 4. Nonlinear interactions between a flashed reference bar that is fixed in position and a second bar that is flashed at surrounding positions help explain DS by showing multiplicative-type facilitation for bar pairs that mimic motion in the preferred direction and suppression for bar pairs that mimic motion in the null direction. Interactions in the preferred direction have an optimal space/time ratio (velocity), exhibited by elongated, obliquely oriented positive domains in a space-time coordinate frame. This relationship is inseparable in space-time. The slope of the long axis specifies the preferred speed, and its negative agrees with the most strongly suppressed speed in the opposite direction. 5. When the reference bar position is moved across the RF, the spatiotemporal interaction moves with it. This suggests the existence of a family of nearly uniform subunits distributed across the RF. We call the subunit interaction, as averaged across the RF, the 'motion kernel' because its spatial and temporal variables are those necessary to specify the velocity, the only parameter that distinguishes a moving image from a temporally modulated stationary image. The nonlinear interaction shows a spatial periodicity, which suggests a mechanism of velocity selectivity for moving extended images. 6. Our spatiotemporal interactions agree with the predictions of certain psychophysical models of movement perception and show that fully motion-opponent signals are not present in our DS neurons. We have developed a new kernel formulation that allows testing of separate light- and dark-bar effects. We find that the preferred direction for spatiotemporal interactions reverses when light-dark bar combinations are used, which agrees with results from psychophysical 'reversed-phi' tests and with predictions of their associated models. The inversion of the interaction for opposite-sign bars that is responsible for this effect suggests that the nonlinear interaction is closely related to the product of bar luminances. 7. Compared with a nondirectional member of the same (complex) cortical family, a DS complex cell exhibits three mechanisms that contribute to its DS: 1) between different RF regions, selectivity for asynchrony in stimulus onset that can exceed 80 ms, 2) facilitation, approximated by the product of the bar luminances, that enhances responses to motion in the preferred direction, and 3) suppression, approximated by the negative product of the bar luminances, perhaps through membrane nonlinear compressive interactions, that vetoes responses to motion in the null direction.