Second-order neurons across species demonstrate two common properties: flat average response of the population and diverse response shapes of individual neurons.

(A) Illustration of the early olfactory circuit across species. (B–D) Example responses of second-order neurons in locust (to odor geraniol), zebrafish (phenylalanine), and mice (valeraldhyde), respectively. Top: individual neuron response curves across concentrations. Middle: mean population responses across concentrations. Bottom: polar histogram showing the distribution of individual neuron response shapes for all odors combined. The x-axis shows the slope between neuron response at concentration level 1 (lowest) to concentration level 3, and the y-axis shows the slope from concentration level 2 to concentration level 4 (highest). The angle of the bar shows the direction of the vector formed by these two slopes, and the length of the bar shows the percentage of neurons with the same angle. Top right quadrant: monotonically increasing responses; top left quadrant: decreasing then increasing; bottom left quadrant: monotonically decreasing; bottom right quadrant: increasing then decreasing. (E) Fitted slopes for mean population responses across concentrations for first- and second-order neurons. Each dot represents a single odor. First two columns show data collected in mice, and dashed lines connect the same odor. The third column shows all odors tested in locust and zebrafish combined. T-test is performed between the slopes formed by first- and second-order neurons; *** p-value < 0.001.

Responses of simulated second-order neurons recapitulate the two common properties.

(Ai–Aii) Example experimentally measured responses of first-order neurons in fruit flies (apple odor) and mice (heptanal). (Bi–Bii) Simulated responses of corresponding second-order neurons after applying divisive normalization (DN) to first-order neurons. The top two rows show results of a single example odor, while the bottom row (the polar plots) show all odors combined. (Ci–Cii) Same as B but after applying subtractive normalization (SN). (Di–Dii) Same as B after applying intraglomerular gain control (IGC). (Ei–Eii) Fitted slopes for the mean population response across concentrations for first-order neurons, as well as simulated second-order neurons after IGC, SN, or DN is applied. Each dot represents an odor. Dashed lines connect the same odor across normalization methods. Paired t-test is performed between the slopes formed by first- and second-order neurons; *** p-value < 0.001, ** p-value < 0.01.

Sufficient conditions to generate diverse concentration response shapes using divisive normalization.

(A–B) Simulated response curves of first-order neurons across concentration levels. Two classes of first-order responses are considered: those with cross-overs and those without cross-overs. Left: single neuron response curves and population average across four simulated concentration levels. Center: polar histogram for the shapes of response curves. Right: rank order of neuron activities at each concentration level (neurons are sorted according to response strength at the lowest nominal concentration, and the same indexing is preserved across the higher concentrations). (C–D). Same as A and B but showing the responses of simulated second-order neurons after divisive normalization is applied to first-order neurons.

Divisive normalization reformats concentration representations in the rate and time domains.

(A) Accuracy for concentration classification using experimental responses of second-order neurons (left: locust; center: zebrafish; right: mice). The concentration levels of each odor are classified independently per odor. Reported are the average accuracy across all odors, and error bars show standard deviations. Dashed line shows the accuracy level for random guess (0.2 for locust and zebrafish, 0.25 for mice). (B) Same as A but for experimental first-order neurons in fruit flies and mice. (C) Same as A but after divisive normalization applied to first-order responses in B. (D) The temporal response curves of simulated first-order neurons to an odor. Neurons with different affinity to this synthetic odor are highlighted (high affinity: blue; medium affinity: red; low affinity: cyan). (E) Same as D, after divisive normalization is applied. (F) Jaccard similarity between the sets of the 50 earliest-responding neurons for each pair of concentration levels. The value of Jaccard similarity ranges between 0 and 1; 1 means the two sets of neurons contain identical neurons, and 0 means they share no neurons in common. (G) The time when the 50 earliest-responding neurons respond under each concentration level. The neurons are sorted by their peak time under low concentration. (H) Rank of neurons under low concentration based on their time of peak response (y-axis) vs. rank of neurons under high concentration (x-axis).

A parallel olfactory pathway in land vertebrates provides improved concentration decoding.

(A) Top: concentration response curves of individual tufted cells to a single odor (valeraldhyde). Bottom: average population responses for mitral (MC, blue) and tufted (TC, red) cells. (B) Polar histogram showing the distribution of concentration response shapes MCs and TCs for all five odors combined. (C) Left: Cartoon illustration for the odor localization task. Right: estimated decrease in odor concentration as distance from the odor source increases. (D) Change in average population neuron activities across all pairs of concentrations. The x-axis shows the absolute value of difference in the relative dilution (in order of magnitude) between the two concentration levels. The y-axis shows the change in activity. Results are averaged over five odors, and the shaded area shows the 95% confidence intervals. (E) Estimated change of neural activities as the distance between the odor source and the animal’s location increases for mitral cells (left) and tufted cells (right). Each dot shows a particular concentration for an odor. There are 20 dots in total (4 concentrations x 5 odors). Each opaque line is a linear regression calculated based on all concentrations of a given odor, and the darker lines are the average over all odors. (F) Slopes for the linear regression lines shown in E. Each dot represents an odor. The value of the slope is an estimate of neural sensitivity to the change in distance to the odor source. The higher the slope, the higher the sensitivity.