Quadrature subunits in directionally selective simple cells: spatiotemporal interactions

I explore here whether linear mechanisms can explain directional selectivity (DS) in simple cells of the cat's striate cortex, a question suggested by a recent upswing in popularity of linear DS models. I chose a simple cell with a space-time inseparable receptive field (RF), i.e. one that shows gradually shifting latency across space, as the RF type most likely to depend on linear mechanisms of DS. However, measured responses of the cell to a moving bar were less modulated, and extended over a larger spatial region than predicted by two different popular "linear" models. They also were more DS in exhibiting a higher ratio of total spikes for the preferred direction. Each of the two models used for comparison has a single "branch" with a single spatiotemporally inseparable linear filter followed by a threshold, hence, a- "1-branch" model. Nonlinear interactions between pairs of bars in a 2-bar linear superposition test of the cell also disagreed in time-course with those of the 1-branch models. The only model whose 1-bar and 2-bar predictions matched the measured cell (including a complete "4-branch" motion energy model that matches complex cells) has two branches that differ in phase by about 90 deg, i.e. in quadrature. Each branch has its own threshold that helps define the preceding spatiotemporal unit as a subunit even after the outputs of the two branches are summed. As subunit phases differ by only 90 deg, flashing bar responses of the 2-subunit model are similar to those of the 1-subunit model. Therefore, the number of subunits is hidden from view when testing with a conventional stationary bar. In summary, movement responses and nonlinear interactions between pairs of bars in the measured cell matched those of the 2-subunit model, while they disagreed with the popular 1-subunit model. Thus, multiple nonlinear subunits appear to be necessary for DS, even in simple cortical cells.