Functionality of divergence and convergence in a model of the insect olfactory system.

Recent studies have shown that the insect olfactory system uses a spatio-temporal encoding of odours in the population of projection neurons in the antennal lobe, and suggest that the information thus coded is spread across a large population of Kenyon cells in the mushroom bodies. At this stage, the temporal part of the code might be transformed into a spatial code, especially via the temporally sensitive mechanisms of paired-pulse facilitation and feedback inhibition with its possible associated rebound. We explore here a simple model of the olfactory system using a three-layer network of formal neurons, comprising a fixed number (three) of projection and inhibitory neurons, but a variable number of Kenyon cells. We show how enlarging the divergence of the network (i.e. the ratio between the number of Kenyon cells to the number of input - projection - neurons) alters the number of different output spatial states in response to a fixed set of spatio-temporal inputs, and may therefore improve its effectiveness in discriminating between these inputs. Such enlarged divergence also reduces the variation of this effectiveness among random realizations of the network connectivity. Our model shows that the discriminative effectiveness first increases with the divergence, and then plateaus for a divergence factor of approximately 20. The maximal average number of different outputs was 470.2, which was computed from some simulations with random realizations of connectivity and with a set of 512 possible inputs. The discriminative effectiveness of the network is sensitive to paired-pulse facilitation, and especially to inhibition with rebound.