Our project's outcomes show that today enough is known to make comprehensive computational models of the primary visual cortex, V1, that emulate its function in great detail, quantitatively. Our aim is to understand V1 function through computational modeling, and through understanding V1 to begin to understand cerebral cortex function in general. Our work has a strong focus on population dynamics not present in previous studies. To discover mechanisms, we study not only behaviors of individual model neurons but also how well the model's population behavior emulates population data obtained in the real V1.  Analysis of population activity in large-scale network models has the potential to yield new valuable information for theoretical neuroscience.

What was modeled was a small region of Layer 4Cα (L4), the input layer to V1 in the magnocellular pathway. In addition to L4, the model has two other components: 1) the magnocellular layers of the thalamic visual nucleus, the Lateral Geniculate Nucleus (LGN), which feeds forward to L4, and 2)  Layer 6 (L6) in V1, which feeds back to L4. The problem of feedback, a perennial headache for modelers, is solved in our models with a self-adjusted dynamic algorithm that represents the interactions between L4 and L6.

Here we present two major outcomes of the modeling work: 1) activity maps in the model that show the spatial distributions of firing rate across the cortical surface, and 2) population distributions of directional selectivity in the model that emulate the real cortex with great accuracy. There were many other theorecal results but the two presented here are representative outcomes of the grant.

Studying spatial maps of cortical activity on the cortical surface helps us to understand cortical function.  In the model as in real cortex, firing rates of cells in optimally driven domains climb steeply, while firing rates of cells in orthogonal domains are virtually unchanged. Thus, the firing rate profile across the cortical surface is extremely uneven, with tall peaks separated by deep valleys. How can such a wildly varying landscape of activity in mutually interacting neurons be stable? To answer this question, we present simulated activity maps in the model

Consider first the activity maps of E-cells (Fig 1, top row). Looking at the intended orientations map in Panel B, we see that the vertical preferring region is comprised of three diamonds stacked up vertically on the left side and three half-diamonds on the right side of the 9 HC model cortex. This means that when the vertical, or 0^o, grating is presented, one should expect these diamond-shaped regions to respond most vigorously. The top left panel of Fig 1 shows that this is indeed the case. But then consider the panel in A corresponding to the 45^o grating (middle of top row). As one can see in Panel B, there is no LGN template that prefers this orientation. There are, however, domains favoring 30^o and 60^o; the region in the model cortex that responded most vigorously to 45^o straddled those two regions evenly. We intentionally used 8 gratings with evenly spaced orientations, a number incommensurate with the 6 sets of LGN templates, to show that through dynamical interactions, both lateral and feedback, neurons in L4 are able to respond correctly to in- between orientations to produce a smooth orientation map.  

Activity maps for I-cells look different. Figure 1 second row, shows activity maps for I-cells. Observe that E- and I-cells are co-activated, and I-firing rates are 3-4 times higher than those of E-cells, consistent with data. Also, the regions of elevated I-spiking are larger than those for E-cells, and I-firing rates are above 20-30 spikes/sec virtually everywhere, unlike E-cells, which in orthogonal regions fire at or slightly above background level, i.e. at ~4 spikes/s.  

Each of the panels in Figure 1 represents a continuum of local equilibria, obtained through the dynamic balancing of excitation and inhibition. In the model as in real cortex, the circuitry of Layer 4Cα is roughly spatially homogeneous. The inputs received, on the other hand, vary from point to point depending on the stimulus, and activity maps are produced by the subtle changes in inputs together with cortico-cortical interaction.

Figure 2 shows the outcome of our modeling of Direction Selectivity (DS) in layer 4Cα based on dynamic differences in the ON and OFF LGN inputs to V1. Fig 2A shows distributions of Pref/Opp in layer 4Cα Simple cells (green, upper panel) and in model Simple cells (black, lower panel).  The two distributions have very similar medians (~3.5) and similar fractions of cells with very high DS, ie Pref/Opp>8. The cumulative distribution functions (CDFs) of DS of Simple and Complex cells in the model simulate those of the data very closely, also (Fig 2B). No other model has achieved this kind of agreement with cortical data on DS at the population level.

Last Modified: 10/04/2022
Modified by: Robert Shapley