The optimal odor-receptor interaction network is sparse in olfactory systems: Compressed sensing by nonlinear neurons with a finite dynamic range

There are numerous different odorant molecules in nature but only a relatively small number of olfactory receptor neurons (ORNs) in brains. This “compressed sensing” challenge is compounded by the constraint that ORNs are nonlinear sensors with a finite dynamic range. Here, we investigate possible optimal olfactory coding strategies by maximizing mutual information between odor mixtures and ORNs’ responses with respect to the bipartite odor-receptor interaction network (ORIN) characterized by sensitivities between all odorant-ORN pairs. We find that the optimal ORIN is sparse – a finite fraction of sensitives are zero, and the nonzero sensitivities follow a broad distribution that depends on the odor statistics. We show that the optimal ORIN enhances performances of downstream learning tasks (reconstruction and classification). For ORNs with a finite basal activity, we find that having a basal-activity-dependent fraction of inhibitory odor-receptor interactions increases the coding capacity. All our theoretical findings are consistent with existing experiments and predictions are made to further test our theory. The optimal coding model provides a unifying framework to understand the peripheral olfactory systems across different organisms.