Olfactory navigation and the receptor nonlinearity.

The demands on a sensory system depend not only on the statistics of its inputs but also on the task. In olfactory navigation, for example, the task is to find the plume source; allocation of sensory resources may therefore be driven by aspects of the plume that are informative about source location, rather than concentration per se. Here we explore the implications of this idea for encoding odor concentration. To formalize the notion that sensory resources are limited, we considered coding strategies that partitioned the odor concentration range into a set of discriminable intervals. Wedeveloped a dynamic programming algorithm that, given the distribution of odor concentrations at several locations, determines the partitioning that conveys the most information about location. We applied this analysis to planar laser-induced fluorescence measurements of spatiotemporal odor fields with realistic advection speeds (5-20 cm/s), with or without a nearby boundary or obstacle. Across all environments, the optimal coding strategy allocated more resources (i.e., more and finer discriminable intervals) to the upper end of the concentration range than would be expected from histogram equalization, the optimal strategy if the goal were to reconstruct the plume, rather than to navigate. Finally, we show that ligand binding, as captured by the Hill equation, transforms odorant concentration into response levels in a way that approximates information maximization for navigation. This behavior occurs when the Hill dissociation constant is near the mean odor concentration, an adaptive set-point that has been observed in the olfactory system of flies.