Maintenance of spatially localized, persistent activity with short-range inhibition and long-range excitation and relation between the profile of synaptic connectivity and the tuning widths of activity. A, Negative correlation between tuning widths and width of synaptic connections in negative-derivative feedback networks. The spatial profiles of the excitatory and inhibitory connections in this example were Gaussian, and the widths of both the excitatory and inhibitory connections were varied. To obtain the tuning widths of the activity of the excitatory and inhibitory populations, the activity was fit by the sum of constant and Gaussian functions and the tuning width was defined as the width of the Gaussian function during the delay period as in Constantinidis and Goldman-Rakic, (2002). B, Experimentally observed broader tuning of inhibitory neurons than of excitatory neurons during the different task epochs of a delayed saccade task. (Adapted from Constantinidis and Goldman-Rakic, 2002). C–E, Spatial profile of excitatory (blue; same for the E-to-E and E-to-I connections) and inhibitory (red; same for the I-to-E and I-to-I connections) connectivity with broader inhibitory connections (C), broader excitatory connections (D), or broader tuned component of excitatory than inhibitory connections but with inhibitory connections additionally having a nonselective (constant) component (E). Spatial profiles of synaptic connectivity are normalized by their maximum height. F–H, Activity patterns of excitatory (blue) and inhibitory (red) populations in response to a stimulus centered at θ = 0, illustrated 3 s into the delay period. Firing rates were normalized for comparison by subtracting off the minimum activity and scaling the resulting firing rates to unit amplitude. A broader tuned component of the inhibitory connections (C) results in a narrower profile of the inhibitory population activity (F). A broader tuned component of excitatory connections, with (E) or without (D) an additional nonselective component of inhibitory projections, results in a narrower profile of sustained excitatory activity (G, H). I–K, Spatial profiles of balanced excitatory (blue) and inhibitory (red) synaptic inputs coming into an excitatory neuron. Inputs are normalized by the maximum of the excitatory inputs.