Moth olfactory receptor neurons adjust their encoding efficiency to temporal statistics of pheromone fluctuations

Abstract

The efficient coding hypothesis predicts that sensory neurons adjust their coding resources to optimally represent the stimulus statistics of their environment. To test this prediction in the moth olfactory system, we have developed a stimulation protocol that mimics the natural temporal structure within a turbulent pheromone plume. We report that responses of antennal olfactory receptor neurons to pheromone encounters follow the temporal fluctuations in such a way that the most frequent stimulus timescales are encoded with maximum accuracy. We also observe that the average coding precision of the neurons adjusted to the stimulus-timescale statistics at a given distance from the pheromone source is higher than if the same encoding model is applied at a shorter, non-matching, distance. Finally, the coding accuracy profile and the stimulus-timescale distribution are related in the manner predicted by the information theory for the many-to-one convergence scenario of the moth peripheral sensory system.

Fig 1. Graphical abstract.

(A) Atmospheric turbulence governs the complicated non-homogeneous dispersion of a pheromone, which is detected by specialized olfactory receptor neurons (ORNs) located on the moth antennae (red circle). (B) A typical time course of the pheromone stimulation at a given distance from the source is intermittent. The signal consists of blanks, intervals of zero local concentration due to the passage of clean-air pockets, and of whiffs, intervals of pheromone presence. The statistics of blanks and whiffs describes the spatio-temporal structure of the turbulent plume. (C) A simple encoding model of a whiff encounter is given by the dependence of the firing rate (measured within a period after the whiff onset) on the preceding blank duration, the duration-rate relationship. The coding sensitivity of the whiff encounter is determined from the slope of the mean response and the response variability. In order to detect the pheromone optimally, the efficient coding hypothesis predicts the ORN to adjust its encoding sensitivity to the local stimulus conditions by adjusting the duration-rate relationship. (D) We observe that encoding properties of ORNs are adjusted to match the local distribution of blank durations. Particularly, i) the maximal sensitivity corresponds to the most frequent blank duration (stimulus timescale), cf. Figs 4 and 5; ii) the average decoding accuracy is largest for the matching stimulus-timescale distribution (Fig 6); and iii) the profile of the coding accuracy matches the stimulus-timescale distribution optimally from an information-theoretic point of view (Figs 7 and 8). (The figure is meant only as an illustration of the studied problem and does not represent the measured data.)

Fig 2. The temporal structure of the pheromone plume at a given downwind distance from the source (color) is characterized by the distribution of blanks and whiffs, which are independent.

(A) Distribution of blanks, intervals without pheromone detection. (B) Distribution of whiffs, intervals with detectable pheromone presence.

Fig 3. Responses of ORNs to pheromone encounter in dependence on the preceding blank duration (duration-rate relationships).

The response is the average firing rate in a 150 ms time window starting with the whiff onset. (A, B) Responses to two pheromone doses (10⁻³ ng and 10⁻¹ ng) at 16 m downwind distance from the pheromone source. Solid blue line represents the average, gray area indicates 95% confidence interval around the average. (C, D) Duration-rate relationships at 64 m downwind distance, the pheromone doses are same as in (A, B). Responses after longer blanks are more variable than responses preceded by shorter blanks. (E) Duration-rate relationship for all virtual distances with the pheromone dose 10⁻³ ng. The firing rate and the slope of duration-rate curves change systematically with the virtual distance, the variance is not affected much by the virtual distance.

Fig 4. ORN coding precision of pheromone encounters is adjusted to the statistics of blanks in the plume.

(Top row) Profiles of the coding accuracy (Fisher information) as a function of blank duration. The situation is shown for different pheromone doses (A–E) and virtual downwind distances from the source (color). Each Fisher information curve was individually scaled (normalized) to achieve that its maximum value is equal to 1. Stimulation by 10⁰ ng pheromone dose was not performed for 128 m. (Bottom row) The distributions of blanks for the corresponding distances. With the exception of the largest distance (128 m), the Fisher information profiles follow the distribution profiles, which means that the coding resources are distributed in agreement with the frequency of various blank durations. In particular, the maximal coding accuracy, indicated by the location of the maximum Fisher information, tends to occur at the mode of the corresponding distribution, cf. Fig 5. The adjustment results in an average coding accuracy optimized for the particular distance (Fig 6).

Fig 5. Positions of peaks in the ORN coding accuracy (mode of the Fisher information) tend to align with the most frequent duration of a blank.

The exact matching (dashed line) occurs for almost all measured cases with the exception of the largest distance (128 m) and the lowest pheromone dose (10⁻⁶ ng).

Fig 6. Overall coding accuracy (average Fisher information) is higher for the stimulus statistics of the matching distance than for mismatched statistics corresponding to shorter distances from the pheromone source.

(A) The ORNs exposed to the temporal statistics of pheromone plume at the distance of 16 m achieve different coding accuracy in dependence on the pheromone dose (color). The average coding accuracy when the encoding model for 16 m is applied to the correct stimulus-timescale statistics of 16 m (dashed line) is greater than the average coding accuracy of the same encoding model when assuming a mismatched stimulus-timescale statistics at 8 m, for all pheromone doses except 1 ng. (B–D) Analogous results for ORNs adjusted to statistics of other distances (dashed). The coding performance is always best for the matching distance. Virtual distances longer than the matching one could not be applied since the Fisher information is not defined for the whole range of possible blank durations.

Fig 7. The distribution of blanks predicted by the information theory for optimal encoding in high S/N scenario (color) is close to the real distribution in the natural environment (black).

The natural blanks distribution is very close to the Jeffreys prior (a distribution proportional to the square root of the Fisher information), suggesting that ORNs encode a whiff encounter optimally (transmit maximum information possible) if the simultaneous output of multiple independent ORNs is used for decoding. We speculate that such a setup is viable and in fact even corresponds to the basic anatomy of the moth peripheral olfactory system.

Fig 8. The stimulus-timescale distributions predicted by the information theory for optimal encoding in high S/N scenario (determined from the square root of the Fisher information, the Jeffreys prior), represented by their quantiles vs. quantiles of the real blank duration distributions (see also Fig 7).

The predicted quantiles (blue line) together with the 95% confidence interval (gray area) are very close to the real quantiles of blanks (dashed line), suggesting near-optimal information transmission.