Almost all models of orientation and direction selectivity in visual cortex are based on feedforward connection schemes, where genicu(cid:173) late input provides all excitation to both pyramidal and inhibitory neurons. The latter neurons then suppress the response of the for(cid:173) mer for non-optimal stimuli. However, anatomical studies show that up to 90 % of the excitatory synaptic input onto any corti(cid:173) cal cell is provided by other cortical cells. The massive excitatory feedback nature of cortical circuits is embedded in the canonical microcircuit of Douglas &. Martin (1991). We here investigate ana(cid:173) lytically and through biologically realistic simulations the function(cid:173) ing of a detailed model of this circuitry, operating in a hysteretic mode. In the model, weak geniculate input is dramatically ampli(cid:173) fied by intracortical excitation, while inhibition has a dual role: (i) to prevent the early geniculate-induced excitation in the null di(cid:173) rection and (ii) to restrain excitation and ensure that the neurons fire only when the stimulus is in their receptive-field. Among the 4 Humbert Suarez, Christo! Koch, Rodney Douglas insights gained are the possibility that hysteresis underlies visual cortical function, paralleling proposals for short-term memory, and strong limitations on linearity tests that use gratings. Properties of visual cortical neurons are compared in detail to this model and to a classical model of direction selectivity that does not include excitatory corti co-cortical connections. The model explain a num(cid:173) ber of puzzling features of direction-selective simple cells, includ(cid:173) ing the small somatic input conductance changes that have been measured experimentally during stimulation in the null direction. The model also allows us to understand why the velocity-response curve of area 17 neurons is different from that of their LG N affer(cid:173) ents, and the origin of expansive and compressive nonlinearities in the contrast-response curve of striate cortical neurons.

Behavioral experiments on insects (Hassenstein and Reichardt 1956; Poggio and Reichardt 1976) as well as psychophysical evidence from human studies (Van Santen and Sperling 1985; Adelson and Bergen 1985; Watson and Ahumada 1985) support the notion that short-range motion perception is mediated by a system with a quadratic type of nonlinearity, as in correlation (Hassenstein and Reichardt 1956), multiplication (Torre and Poggio 1978), or squaring (Adelson and Bergen 1985). However, there is little physiological evidence for quadratic nonlinearities in directionally selective cells. For instance, the response of cortical simple cells to a moving sine grating is half-wave instead of full-wave rectified as it should be for a quadratic nonlinearity (Movshon ef al. 1978; Holub and Morton-Gibson 1981) and is linear for low contrast (Holub and Morton-Gibson 1981). Complex cells have full-wave rectified responses, but are also linear in contrast. Moreover, a detailed theoretical analysis of possible biophysical mechanisms underlying direction selectivity concludes that most do not have quadratic properties except under very limited conditions (Grzywacz and Koch 1987). Thus, it is presently mysterious how a system can show quadratic properties while its individual components do not. We briefly discuss here a simple population encoding scheme offering a possible solution to this problem.