Quadratic and adaptive computations yield an efficient representation of song in Drosophila auditory receptor neurons

Sensory neurons transform stimuli through multiple adaptive and nonlinear computations. In Drosophila, auditory receptor neurons adapt to the mean and intensity of acoustic stimuli, shift their frequency tuning with sound intensity, and employ a quadratic nonlinearity. Although each of these computations is thought to improve sensory encoding, their combination could produce a highly ambiguous neural code from which behaviorally relevant information is difficult to extract. Here, we combine electrophysiology and computational modeling to determine how these computations jointly encode natural acoustic signals such as courtship song. We show that a model consisting of a quadratic filter followed by divisive normalization accurately reproduces population responses to both artificial and natural sounds. The model further localizes adaptive temporal filtering to antennal mechanics and variance adaptation to divisive normalization downstream of the receptor mechanics. For arbitrary broadband stimuli, these computations generate an ambiguous representation from which carrier frequency and amplitude cannot be reliably recovered. In contrast, the representation of courtship song is simple and robust. Quadratic filtering enhances encoding of the song envelope while preserving a straightforward temporal code for the carrier through frequency doubling. Divisive normalization removes slow intensity fluctuations arising during social interactions while preserving the rapid envelope fluctuations that define song structure. Together, our results show that adaptive and nonlinear computations that appear to complicate sensory coding for arbitrary stimuli instead generate a robust and easily decoded representation of behaviorally relevant signals by exploiting their natural statistics.