An egalitarian network model for the emergence of simple and complex cells in visual cortex

Abstract

We explain how simple and complex cells arise in a large-scale neuronal network model of the primary visual cortex of the macaque. Our model consists of Ϸ4,000 integrate-and-fire, conductance-based point neurons, representing the cells in a small, 1-mm 2 patch of an input layer of the primary visual cortex. In the model the local connections are isotropic and nonspecific, and convergent input from the lateral geniculate nucleus confers cortical cells with orientation and spatial phase preference. The balance between lateral connections and lateral geniculate nucleus drive determines whether individual neurons in this recurrent circuit are simple or complex. The model reproduces qualitatively the experimentally observed distributions of both extracellular and intracellular measures of simple and complex response. Simple and complex cells may have different tasks in visual perception. Cortical cells must represent spatial properties such as surface brightness and color and the perceptual spatial organization of a scene that is the basis of form. Simple cells are necessary for all of these functions because they are the visual cortical neurons that are able to respond monotonically to signed edge contrast. Complex cells, being insensitive to spatial phase, cannot provide a cortical representation of signed contrast, but they are sensitive to texture, firing at elevated rates in response to stimuli within their receptive fields.Although long-standing and with functional implications, the simple͞complex classification is hardly sharp. Recent work by Ringach et al. (2) analyzes the extracellular responses of neurons across many experiments in macaque V1. They find that many V1 cells are neither wholly simple nor wholly complex but lie somewhere in between. And although most cells in V1 might be classified as complex, the cortical layer that receives the bulk of lateral geniculate nucleus (LGN) excitation, 4C, has simple and complex cells in approximately equal proportion.Associated with the simple͞complex classification is the influential hierarchical model of Hubel and Wiesel (1), shown schematically in Fig. 1a, wherein simple cells receive geniculate drive and the pooling of their phase-specific outputs drives the phase invariant responses of complex cells. As we argue in Results, this conception seems difficult to reconcile with recent experimental evidence. Chance, Nelson, and Abbott (3) have put forward a very different model that investigates the possible role of recurrent excitation in creating complex cells. In their model, the phase-specific outputs of excitatory simple cells drive cells coupled together in an excitatory recurrent network (Fig. 1b). Realizing this architecture by using a rate model for network activity, they find phase invariant, complex responses when recurrent excitation in the network dominates that of the simple cell inputs.Here, we study a large-scale model of the neuronal dynamics in layer 4C␣ of macaque V1, whose architecture is known better than for almost any other cortical area. Ou...

Orientation selectivity in visual cortex by fluctuation-controlled criticality

“…1b shows an intracellular antecedent, the F1͞F0 distribution of the intracellular effective reversal potential V S . Again, in agreement with experimental observation (19) and our previous model (13), this distribution is plainly unimodal, which in the model reflects the egalitarian nature of the basic connectivity (see also ref. 20).…”

“…Recent intracellular measurements of cells near pinwheel centers have also shown misalignments (16) of firing and conductance peaks. In general, the effect of the haphazard, sparser coupling in our model is to improve the tuning of complex cells near pinwheel centers (13) while reducing the relatively better tuning of simple cells near pinwheel centers seen in ref. 11.…”

“…2 a-d shows the tuning properties of four sample excitatory neurons near pinwheel cen- Near pinwheel centers, the cortical conductances come from a population of cells with broadly distributed preferred orientations. In our previous models (11,13), which were densely coupled, this scheme led to cortical conductances that were very nearly independent of stimulus orientation. One consequence was that simple cells were especially selective near pinwheel centers because of the interaction of excitatory conductances dominated by tuned geniculate input (that is, tuned in its non-mean components) with a cortical inhibition that was independent of orientation.…”

“…Previously, we studied how simple and complex cell responses arise in a large-scale neuronal network model of an input layer 4C␣ of macaque V1 (11)(12)(13). The model represents a 1-mm 2 local patch with four orientation hypercolumns containing O(10 4 ) conductance-based, integrate-and-fire (I&F) neurons: 75% excitatory and 25% inhibitory.…”

“…In its published form, this model operated in a regime where its membrane conductances and potential had large fluctuations over its mean (see figures 4 and 5 of ref. 13). Indeed, it was these fluctuations that drove the network activity because the trial-averaged membrane potential was below the firing threshold, ʈ as has also been observed experimentally (14).…”