Analysis of the long-range effects was performed in terms of the response properties of the local circuitry. A module with one excitatory and one inhibitory population, which preserves the properties of the local circuitry, was considered and its responses to varying long range and thalamic inputs were studied (figure 4). This figure was generated by simulating a single module with 50 excitatory and 10 inhibitory cells (with the same cell properties as in the full model). Each cell projected to 30% of the other cells. The synaptic efficacies of the 4 types of projections were chosen so that the module approximated the average of a group of minicolumns in the full model. The strength of each projection depended on the two cell types only.

**Figure 4:**** Analysis of the
facilitation/suppression effect. **
* The green surface mesh shows the mean firing rates of excitatory cells
in a local excitatory and inhibitory population. The red curve is
the response for varying thalamic input, the blue curve is the response
for varying thalamic input and fixed long range influences. Biphasic
facilitation/supression will be present whenever the response surface exhibits
a steep decline along the inhibition axis for high input levels.*

The context dependent effect can be simply understood in this reduced model. Increasing thalamic input, such as that due to increasing the stimulus contrast, corresponds to a straight line in the input plane, where the slope of the line is equal to the ratio of synaptic efficacies of thalamic projections to excitatory and inhibitory cells. The effect of long range influences is to translate the whole line so that it starts at a point different from the origin, without affecting its slope. The new starting point is determined by the strength of long range inputs to the two populations in the module. Thus, a line in the input plane corresponds to thalamic input to the central region when the central contrast is varied and surround contrast is fixed (i.e. long range input is fixed). figure 4 shows the response curve of the module in the absence of long range inputs and when long range inputs are fixed to values similar to the full model. The two curves are shifted to the origin and projected on the back plane for comparison, demonstrating that the local analysis is enough to account for the facilitation/supression effect.

This effect of the long range connections is robust in the following sense: for most reasonable parameter settings of the local circuit, the inhibitory cells will start firing at some level of input and suppress the excitatory population, therefore the response surface will exhibit a decline along the inhibitory input axis as in figure 4. Then there is a wide range of possible values for the ratio of thalamic inputs to the two populations (slope of input line) and for the synaptic efficacy of the distant horizontal connection (displacement of input line) that will lead to the desired behavior. The magnitude of the context effect depends on the steepness of the 2D response surface.