Rapid Long-Range Disynaptic Inhibition Explains the Formation of Cortical Orientation Maps

Competitive interactions are believed to underlie many types of cortical processing, ranging from memory formation, attention and development of cortical functional organization (e.g., development of orientation maps in primary visual cortex). In the latter case, the competitive interactions happen along the cortical surface, with local populations of neurons reinforcing each other, while competing with those displaced more distally. This specific configuration of lateral interactions is however in stark contrast with the known properties of the anatomical substrate, i.e., excitatory connections (mediating reinforcement) having longer reach than inhibitory ones (mediating competition). No satisfactory biologically plausible resolution of this conflict between anatomical measures, and assumed cortical function has been proposed. Recently a specific pattern of delays between different types of neurons in cat cortex has been discovered, where direct mono-synaptic excitation has approximately the same delay, as the combined delays of the disynaptic inhibitory interactions between excitatory neurons (i.e., the sum of delays from excitatory to inhibitory and from inhibitory to excitatory neurons). Here we show that this specific pattern of delays represents a biologically plausible explanation for how short-range inhibition can support competitive interactions that underlie the development of orientation maps in primary visual cortex. We demonstrate this statement analytically under simplifying conditions, and subsequently show using network simulations that development of orientation maps is preserved when long-range excitation, direct inhibitory to inhibitory interactions, and moderate inequality in the delays between excitatory and inhibitory pathways is added.