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Fast odour dynamics are encoded in the olfactory system and guide behaviour

This article has been updated


Odours are transported in turbulent plumes, which result in rapid concentration fluctuations1,2 that contain rich information about the olfactory scenery, such as the composition and location of an odour source2,3,4. However, it is unclear whether the mammalian olfactory system can use the underlying temporal structure to extract information about the environment. Here we show that ten-millisecond odour pulse patterns produce distinct responses in olfactory receptor neurons. In operant conditioning experiments, mice discriminated temporal correlations of rapidly fluctuating odours at frequencies of up to 40 Hz. In imaging and electrophysiological recordings, such correlation information could be readily extracted from the activity of mitral and tufted cells—the output neurons of the olfactory bulb. Furthermore, temporal correlation of odour concentrations5 reliably predicted whether odorants emerged from the same or different sources in naturalistic environments with complex airflow. Experiments in which mice were trained on such tasks and probed using synthetic correlated stimuli at different frequencies suggest that mice can use the temporal structure of odours to extract information about space. Thus, the mammalian olfactory system has access to unexpectedly fast temporal features in odour stimuli. This endows animals with the capacity to overcome key behavioural challenges such as odour source separation5, figure–ground segregation6 and odour localization7 by extracting information about space from temporal odour dynamics.

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Fig. 1: Sub-sniff detection of odour signals in olfactory bulb inputs.
Fig. 2: Mice can discriminate odour correlation structure at frequencies up to 40 Hz.
Fig. 3: Odour correlation structure is encoded by OB output neurons.
Fig. 4: Source separation using correlations of odour concentration fluctuations.

Data availability

Data related to the OSN model (Extended Data Fig. 1) are available at Data related to the glomerular classifier analysis (Extended Data Fig. 6) are available at The remaining data that support the findings of this study will be made available by the authors upon request.

Code availability

All custom Python scripts to generate pulses (PyPulse, PulseBoy) are available at and Code for controlling AutonoMouse is available at Code related to the OSN model is available at Code related to the glomerular classifier analysis is available at

Change history

  • 12 May 2021

    This Article was amended to correct the linking to Supplementary Videos 1 and 2.


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We thank the animal facilities at the National Institute for Medical Research and the Francis Crick Institute for animal care and technical assistance, the mechanical and electronic workshops in MPI Heidelberg (N. Neef, K. Schmidt, M. Lukat, R. Roedel, C. Kieser) and London (A. Ling, A. Hurst, M. Stopps) for support during development and construction, the Aurora Scientific team for suggestions for adapting the miniPID, T. Margrie for discussion, V. Murthy for discussions and suggestions on the OSN imaging experiments, and A. Fleischmann, K. Franks, F. Guillemot, M. Hausser, F. Iacaruso, R. Jordan, J. Kohl, T. Mrsic-Flogel, V. Pachnis, A. Silver, and P. Znamenskiy for comments on earlier versions of the manuscript. We thank the members of the Odor2Action NeuroNex network, in particular J. Victor, J. Crimaldi, B. Smith, M. Schmucker, and J. Verhagen for discussions. This work was supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001153), the UK Medical Research Council (FC001153), and the Wellcome Trust (FC001153); by the UK Medical Research Council (grant reference MC_UP_1202/5); a Wellcome Trust Investigator grant to A.T.S. (110174/Z/15/Z), a BIF doctoral fellowship to A.C.M., and a DFG postdoctoral fellowship to T.A.

Author information

Authors and Affiliations



A.T.S. conceived the project; T.A., A.E., D.D. and A.T.S. designed experiments with input from A.C.M., T.P.A.W., J.J.H., and S.T.; T.A. (in vivo imaging, plume measurements), A.E. (plume measurements, frequency and correlation behaviour), D.D. (plume measurements, whole-cell recordings), A.C.M. (source separation behaviour), T.P.A.W. (unit recordings), S.T. (analysis for OSN imaging) and J.J.H. (source separation behaviour) performed experiments and analysed data; I.F. contributed tools and to experimental design; S.T. performed simulations; and T.A., A.E. and A.T.S. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Andreas T. Schaefer.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks Venkatesh Murthy and Diego Restrepo for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Distinguishing fast odour stimuli with slow OSNs.

a, Membrane voltage relative to baseline of a single model OSN in response to a 10-ms odour pulse. Black traces are individual trials; red trace is average over 20 trials. OSN spike threshold has been set high enough to prevent spiking to illustrate the subthreshold voltage time course. b, Membrane voltages (grey traces) of ten OSNs from a population of 5,000 in response to a paired odour pulse with pulse width 10 ms and PPI of 25 ms. The voltage time course for one example OSN is in black. Several OSNs reach the OSN spike threshold (dashed red line) and are temporarily reset to the refractory voltage of −1. The population average membrane voltage (red) reveals membrane charging in response to odour stimulation and the subsequent discharging and refractory period. c, Raster showing the spike times (dots) of the full population from b and the corresponding mean firing rate (trace) estimated in 1-ms bins. d, Mean firing rates computed over 20 trials in response to paired odour pulses of width 10 ms and PPIs of 10 ms (green) and 25 ms (black). e, Model calcium signals are produced by squaring the instantaneous mean firing rate and filtering the result with a calcium imaging kernel. f, Model calcium responses to the paired odour stimulus with a PPI of 10 ms (green) and 25 ms (black). Thin traces are single trials, thick traces are averages over 15 trials. g, Schematic of the OSN model. Variables in dashed bounding boxes are changed for each glomerulus (Methods). h, Linear classifier analysis over an increasing subset size of glomeruli (1–100; plotted is mean ± s.d., 256 repeats for random subsets of n glomeruli generating 256 unshuffled and 256 shuffled accuracies).

Extended Data Fig. 2 Sub-sniff odour information in the olfactory bulb input layer.

a, GCaMP6f fluorescence recorded in OB glomeruli in an anaesthetized OMP-cre: Ai95(RCL-GCaMP6f)-D mouse (maximum projection of 8,200 frames, glomerulus marked with red asterisk corresponds to first example trace shown in b). Scale bar, 50 μm. b, Example calcium traces in response to 10 and 25 ms PPI odour stimuli (mean of 50 trials ± s.e.m.). Bottom, example respiration traces. P values derived from unpaired two-sided t-tests comparing responses of individual trials integrated over 2-s windows to paired odour pulse stimulation. c, Classifier accuracy over an increasing number of glomeruli when a linear classifier was trained on several response windows (colour-coded; black, shuffle control) to PPI 10 versus 25 ms stimuli (mean ± s.d. of up to 93 glomeruli from 4 individual animals; 500 repetitions). di, Classifier accuracy when trained on all glomeruli in response to PPI 10 versus 25 ms stimuli recorded in anaesthetized animals (n = 93 glomeruli, mean ± s.d. from 4 individual animals) with a sliding window of different durations (colour-coded; black, shuffle control; 100 repetitions) starting at 2 s before odour onset (left) and time period between −0.5 and 0.5 s from odour onset shown at higher magnification (right). dii, Same as di for awake animals (n = 100 glomeruli, mean ± s.d. from 5 individual animals). e, f, Odour (e) and flow (f) signals integrated over 2 s for PPI 10 ms and PPI 25 ms stimuli (10 repeats each; odour, P = 0.1841; flow, P = 0.1786; unpaired two-sided t-test). g, Correlation coefficients of glomerular calcium responses to PPI 10 versus 25 ms in anaesthetized (n = 93 glomeruli from 4 individual animals) and awake (n = 100 glomeruli from 5 individual animals) mice (P = 0.3187, unpaired two-sided t-test, measured as in Fig. 1 from OMP-Cre: Ai95(RCL-GCaMP6f)-D mice). Violin plots show the median as a black dot and the first and third quartiles by the bounds of the black bar. hi, Example respiration traces recorded using a flow sensor from awake mice. Inhalation goes in the upwards direction, exhalation downwards. hii, Average instantaneous sniff frequency from one example animal plotted as a function of time (n = 24 trials, mean ± s.e.m.). The odour stimulus consisted of two 10-ms odour pulses either 10 or 25 ms apart (Fig. 1c). hiii, Distribution of sniff intervals during a 2-s window before (grey) and a 5-s window after (blue) odour stimulus onset (P = 1.02 × 10−189, two-sample Kolmogorov–Smirnov test). hiv–vi, Same as top row but for the anaesthetized condition (P = 0.3952, two-sample Kolmogorov–Smirnov test). i, Mean odour signal for PPI 10 and 25 ms for 10 increasing concentration steps defined by modulating valve pulse duty (Methods and Supplementary Fig. 1). There were no significant differences in odour concentration between both stimuli (unpaired two-sided t-tests). j, Modelled response integrals to PPI 10 versus 25 ms stimulations over a tenfold concentration range pooled over all 20 trials and 100 glomeruli (Methods). Box plots show median and extend from the 25th to 75th percentiles, whiskers extend to the 5th and 95th percentiles. ki, Confusion matrix of SVM-based classification results of modelled glomerular signals in response to a range of ten odour concentrations ranked and colour-coded (n = 100 glomeruli). kii, Shuffle control with labels assigned randomly. kiii, Confusion matrix showing the ranked and colour-coded results of glomerular responses independently classified for 10 ms versus 25 ms PPI and across the range of ten odour concentrations. kiv, shuffle control for kiii with labels assigned randomly. l, As in j but with 2-s response integrals derived from Ca2+ imaging data (10 repeats for each concentration). m, As in k for Ca2+ imaging data (n = 57 glomeruli, from 2 individual animals, 10 repeats for each concentration). Note that 10 ms PPI could be reliably distinguished from 25 ms PPI with only few instances where a response to, for example, a 10 ms PPI stimulus was misclassified as 25 ms or vice versa (compare light red quadrants to light green quadrants). n, Shifting the position of 10 ms PPI within a single inhalation. PPI 10 ms at position 1 (ni) or at position 2 (nii) of three 10-ms odour pulses. Odour pulses as recorded with a PID shown in red, valve commands are shown in dark grey. Light grey area shows additional compensatory blank valve command to keep the flow profile indistinguishable between stimuli. niii, Total odour concentration was independent of the pulse profile (10 repeats, P = 0.57, unpaired two-sided t-test). o, The 10 ms PPI at both position 1 (oi) and position 2 (oii) are presented during the inhalation phase (respiration shown in black, inhalation upwards, exhalation downwards). p, Example calcium traces in response to 10 ms PPI at position 1 (black) and position 2 (red), shown is the mean of 10 trials ± s.e.m. P values derived from unpaired t-tests comparing 2 s integrated responses of individual trials to odour pulses. q, Classifier accuracy over increasing number of glomeruli when a linear classifier was trained on the 2-s response to PPI 10 ms at position 1 versus position 2 (mean ± s.d. of up to 57 glomeruli, from 2 individual animals, 500 repetitions; blue: PPI 10 ms at position 1 versus position 2; black: shuffle control). For box plots, boxes indicate 25th–75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers (Methods).

Extended Data Fig. 3 Frequency discrimination experiments.

a, Frequency discrimination stimuli are produced by alternating presentation of two odours to generate a desired odour change frequency. During odour delivery, valves are not held open but rather are randomly opened and closed over time to produce slight variation in odour amplitude for each pulse. This means that odour concentration cannot be used as a cue to learn the task and odour switching frequency is the primary stimulus signal. Furthermore, valve clicking is randomized to minimize any acoustic cues. b, Replacing one odour channel with blank, un-odourized air and recording the frequency stimuli with a PID reveals that the desired odour pulse frequency is being produced. c, Mice readily learn to discriminate 2 versus 20 Hz pulse frequency stimuli in a go/no-go task. Replacing the odours with blank channels results in chance-level performance (no odour), which recovers when odours are replaced (recovery), showing that mice were probably discriminating the odour switching frequency rather than any extraneous cues such as valve noise. The order of odour presentation in the stimuli had no effect on behaviour as when it was shifted (phase switch) no decrease in performance was observed. Additionally, performance was dependent on the alternation between different odours, as when the experiment was repeated with the same odours in each channel (equal odours) performance was at chance level. d, To determine the perceptual limit of frequency discrimination, the floor frequency used in the task over successive experiments was increased such that the difference in frequency between the stimuli progressively narrowed. Overall performance decreased as the difference in frequency grew smaller, reaching near-chance level with a frequency difference of 10 Hz (10 versus 20 Hz). Switching back to the original discrimination (2 versus 20 Hz) recovered performance quickly, showing that the drop in discrimination ability was truly due to the frequency difference rather than general deterioration of performance over time. ei, Example uncorrelated stimuli. Combinations of odour 1 (red) and odour 2 (blue) valves are opened with temporal offsets and randomized pulse timing resulting in a correlation of 0 (Methods). Blank (black) valves are used to keep total airflow constant throughout the stimulus. eii, Higher magnification of the area shaded in grey. f, Animals show similar average accuracy as shown in Fig. 2k when probed to discriminate correlated from uncorrelated odour pulses at 10 Hz (n = 19 mice, mean ± s.e.m. of average accuracy = 0.6506 ± 0.0016; after scrambling stimulus identity: 0.4997 ± 0.0032; P = 0.0175, unpaired two-sided t-test). g, Animals show similar average accuracy when discriminating the correlation structure of a different odour pair (acetophenone versus cineol) at 10 Hz (n = 19 mice, mean ± s.e.m. of average accuracy = 0.6558 ± 0.0026; after scrambling stimulus identity: 0.5165 ± 0.0048; P = 0.0129, unpaired two-sided t-test). Grey dots mark average performance of individual animals. Boxes in f, g indicate 25th–75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers (Methods).

Extended Data Fig. 4 AutonoMouse stimulus and experimental design.

a, Detailed schematic of stimulus production; odour presentation (odour 1: blue, odour 2: red) is always offset by clean air (mineral oil: grey) valves at the same flow levels, to ensure that total flow during the stimulus is constant. b, Schematic of the use of valve subsets to produce the desired stimulus. t1 and t2 represent valve openings at the corresponding time points shown in a. c1 (left) and c2 (middle) represent two possible configurations that could be used to produce the same resulting stimulus at the two time points. Opacity in the colours represents total concentration contribution to the resulting stimulus at the time point. For example, to produce the dual odour pulse at t1, configuration c1 can be used where odour 1 (blue) is delivered from one valve and odour 2 (red) from another valve. During t2 two valves contribute clean air. Alternatively, configuration c2 can be used in which during t1 odour 1 (blue) is generated by 50% opening of two valves, with odour 2 (red) produced by 70%–30% opening of two other valves. Right, scramble control: valve maps (represented by arrow colour) are maintained compared to the training condition but odour vial positions are scrambled resulting in odour stimuli that are uninformative about reward association while maintaining any non-odour cue such as putative sound or flow contributions. c, Predicted accuracy for animals in the case that they use solely olfactory temporal correlations (black) and in the case that they use extraneous non-olfactory cues or non-intended olfactory cues (for example, contaminations, clicking noises) (violet). Note that when switching stimulus preparations to a new set of valves (as in Fig. 2i and ik), such non-intended cues would not provide any information about stimulus–reward association, so accuracy would transiently drop back to chance. di, Average flow recordings (mean ± s.d.) of 2 Hz correlated (black, n = 75) and anti-correlated (red, n = 70) trials taken from the AutonoMouse odour port. dii, Fourier transform of the flow plots from di, showing the power of the signal over a range of 1 kHz. diii, An expanded view over the range of 10 Hz indicated by the dotted box in dii. div, Mean accuracy of a series of linear classifiers trained on an increasing window of the integrated signal starting from 1 s before trial shown in di. Classifiers were tested on two withheld trials, one correlated and one anti-correlated, and repeated 100 times. e, As in d but for 40 Hz trials (n = 69 correlated and n = 72 anti-correlated). fi, Average audio recording trace (mean ± s.d.) of 2 Hz stimuli using a microphone placed in close proximity to the AutonoMouse odour port. fii, fiii, Fourier transforms of the audio signal from fi. Note, although there are notable peaks at specific frequencies, these are present in both correlated and anti-correlated trials. fiv, Accuracy of a series of linear classifiers as shown in d but using the modulus of the audio signal. g, As in f but for 40 Hz trials. Note, whereas the sound profile and the Fourier transforms are different between 2 and 40 Hz, there is no difference detectable between correlated and anti-correlated trials. h, Example traces of odour signal (ethyl butyrate, isoamyl acetate, PID recorded) during correlated (top) and anti-correlated trials (middle). Simulated maximum accuracy based on differences in mean odour signal (bottom). Simulated accuracy was calculated as the fraction of trials correctly identified as correlated or anti-correlated based on a decision threshold set at some level between the minimum and maximum mean signal. Simulated accuracy was calculated for multiple decision thresholds, increasing the decision threshold from minimum odour signal to maximum odour signal in steps of 1/5,000th of the range between minimum and maximum. i, Detailed schematic of correlated (top left) and anti-correlated (top right) stimulus production before (middle) and after (bottom) switching valves. For the switch control, a set of previously unused odour valves is introduced to rule out potential bias towards a specific valve combination when performing the odour correlation discrimination task. j, Trial map of five representative animals during 2 Hz (ji) and 12 Hz (jii) correlation discrimination tasks before and after the introduction of control valves (n = 12 trials before and 12 trials after new valve introduction, which is indicated by black vertical dotted line. Each row corresponds to an animal, each column represents a trial. Light green: hit, dark green: correct rejection, light red: false alarm, dark red: miss. ki, Boxplots of mean accuracy for animals (n = 5 mice) pre- and post-control for 2 Hz (left) and 12 Hz (right). Box indicates 25th–75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers; Methods. P values derived from unpaired t-tests. kii, Summary histograms of performance change for all animals during all ‘valve switch’ control tests (Methods), indicating that discrimination accuracy was based on intended olfactory cues. The five animals with the best performance before the valve switch or bottle change (and thus the largest potential to drop in performance) were analysed. l, Discrimination accuracy (n = 33 animals, mean ± s.e.m.) for rewarded S+ (left) and unrewarded S− (right) trials when odours were presented using standard training valve configurations (black) and scrambled valve identity (red), data from Fig. 2k. Note that frequencies above 40 Hz were presented predominantly in the last block of the training schedule and reduced licking in the control group (decreased S+ performance and increased S− performance) might be due to decreased motivation at that point.

Extended Data Fig. 5 Respiration recordings, stimulus onset model and reaction time for correlation discrimination experiments.

a, An overhead camera was used to image a head-fixed mouse during a sequence of odour presentations. Simultaneously, a flow sensor was placed close to one nostril to monitor respiration to establish the validity of motion imaging-based respiration recording. Phase-based motion amplification was used to magnify motion on the animal’s flank to capture body movements associated with respiration. Right, example of simultaneous respiration measurement with motion imaging (red) and flow sensor (black; Methods and Supplementary Video 2). b, Three further example trials with respiration rate extracted from motion imaging (red) and simultaneous flow sensor recording (black). Below, instantaneous sniff frequencies calculated from either sensor were tightly correlated. c, Correlation between respiration traces extracted from motion imaging and respiration captured by flow sensor (n = 26 trials, 10 s duration each). Violin plot shows the median as a black dot and the first and third quartiles by the bounds of the black bar. d, e, Probability distributions of inter-sniff intervals for odour presentations (isoamyl acetate versus ethyl butyrate, 2 Hz and 20 Hz) for freely moving animals in AutonoMouse before stimulus onset (d) and during 2 s odour stimulation (e; n = 605 sniffs for 2 Hz and n = 668 sniffs for 20 Hz, two-sample Kolmogorov–Smirnov test). f, Heat map of accuracy difference between a model in which animals rely on onset information only (Methods) and actual animal accuracies across a range of sniff frequencies and inhalation fractions (n = 10 mice). No matter the assumed sniff frequency and inhalation frequency, the ‘onset model’ deviates substantially from the accuracy measured in the behavioural experiments (h, i). g, Difference between a model in which animals use the entire stimulus structure (Methods) and actual behavioural accuracies across different stimulus sampling times (n = 10 repeats, mean ± s.d.). The ‘whole stimulus’ model accurately describes animal behaviour, indicating that mice do not base a decision about the correlation structure of a stimulus predominantly on the onset. Note the different scales in f and g. h, Schematic of experimental stimuli in which the first stimulus pulse was disrupted when presented on probe trials. Top, normal stimulus design; bottom, ‘onset disrupt’ stimuli, in which the first pulse in a correlated stimulus is disrupted to be anti-correlated; and vice versa for an anti-correlated stimulus. i, Animals were trained on standard (non-probe) correlation discrimination stimuli (f = 10 Hz) but onset disrupt (probe) stimuli were presented randomly on probe trials with a 1/10 probability. Accuracy was only slightly degraded on probe trials (mean ± s.d. of accuracy for non-probe trials 75.8 ± 4.4%; for probe trials 67.8 ± 6.1%; P = 0.001, paired two-sided t-test, n = 9 mice) but did not drop below chance (P = 7.3 × 10−6, paired t-test). Notably, accuracy on probe trials was consistent with whole-structure prediction (70.3 ± 3.5%, P = 0.13, paired t-test of comparison to probe trials) and differed significantly from the accuracy of onset-only prediction (41.6 ± 1.5%; P = 1.02 × 10−6, paired t-test of comparison to probe trials). j, Mean reaction time (time from stimulus onset to first lick in S+ trials) plotted as a function of stimulus pulse frequency for the three animals with the best (left) and the worst (right) global accuracy (mean accuracy across all trials). Better-performing animals tend to increase their reaction time as stimulus pulse frequency increases. k, Scatter plot of mean accuracy versus mean reaction time for each animal and stimulus pulse frequency condition (averaged over blocks of 100 trials). Points are colour-coded according to stimulus pulse frequency. Accuracy was significantly positively correlated with reaction time, suggesting that mice that sampled a greater portion of the stimulus made more accurate decisions about its correlation structure (Pearson correlation coefficient R = 0.49, P < 1.1 × 10−112). l, Accuracy (mean ± s.e.m.) is plotted as in Fig. 2k, but only trial blocks with reaction times above or below a certain threshold (colour code) are included in the analysis. Where only longer reaction times are considered, global performance is higher than the case in which only shorter reaction times are included, again suggesting that longer stimulus sampling improves discrimination of odour correlation structure across all stimulus pulse frequencies.

Extended Data Fig. 6 OSN imaging in response to correlated versus anti-correlated odour stimulation.

ai, Four example fields of view (FOVs) recorded from the dorsal olfactory bulb of individual mice. aii, Number of individual glomeruli per FOV in all experimental mice (n = 15). The number of individually delineated glomeruli ranges from 20 to 36 with an average of 28 glomeruli per FOV. Labelled data points (1–4) correspond to FOVs shown in ai. Scale bars, 50 μm. Centre line is median, the edges of the box are the 25th and 75th percentiles, and the whiskers extend to the most extreme data points not considered as outliers; Methods. b, Example glomerulus response from OMP-Cre: Ai95(RCL-GCaMP6f)-D mice to presentation of individual odours plotted pairwise (AB, CD, EF; mean ± s.e.m. of 6 trials). Stimulation period (1 s) is indicated by vertical bar (blue, green and yellow). Bottom, typical example respiration trace. P values derived from unpaired two-sided t-tests comparing 2-s integrated responses between paired odours. c, Averaged calcium transients from all glomeruli (n = 145 from 5 individual animals) in response to individual odours, plotted as colour maps sorted by response magnitude. d, Difference between glomerulus responses to individual odours plotted pairwise as colour maps. Glomeruli are sorted by average magnitude of response difference. e, Example glomerulus response to presentation of correlated versus anti-correlated odour pairs fluctuating at 2 Hz (mean ± s.e.m. of 12 trials). Bottom, typical example respiration trace. P values derived from unpaired two-sided t-tests comparing 2-s integrated responses of individual trials to correlated and anti-correlated odour stimulation. f, Difference between glomerulus responses to 2 Hz correlated and anti-correlated odours as colour maps, sorted as in d. g, h, As in e, f but for 20 Hz correlated versus anti-correlated stimuli. Example glomerulus from b, e, g indicated with an asterisk in colour maps in c, d, f, h. i, Left, P values derived from comparing trials of the summed 2-s response to correlated versus anti-correlated odour stimulation at 2 Hz (unpaired two-sided t-tests) for three odour pairs (colour-coded) as a function of glomerulus selectivity to individual odours (n = 145 glomeruli). Selectivity is calculated as the difference between the absolute response to single odours scaled by the summed absolute response. A threshold is set at 0.5 to define glomeruli as low- or high-selective. Dot size represents magnitude of the summed response. Middle, comparison of P values between low- and high-selective glomeruli (P < 0.05, unpaired two-sided t-test). Violin plots show the median as a white dot and the first and third quartiles by the bounds of the grey bar. Right, cumulative distribution function of P values for low- and high-selective glomeruli (P < 0.01 for all pairwise comparisons, two-sample Kolmogorov–Smirnov test). j, As in i but for 20 Hz (n = 145 glomeruli). k, Top, mean ± s.d. of classifier accuracy over 100 repetitions when trained on all responsive glomeruli (n = 145 available, from 5 individual animals, Methods) to discriminate 2 Hz correlated versus anti-correlated stimuli, trained separately for each of the three odour pairs and within sliding windows of different widths (colours); x-coordinates indicate latest extent of each window. Bottom, same as top row but with labels shuffled as control. l, As in k for 20 Hz correlated versus anti-correlated odours. Some data points in k, l are absent because not all time points had responsive ROIs for every window size (Methods).

Extended Data Fig. 7 Odour correlation structure is encoded in dendrites of olfactory bulb output neurons.

a, GCaMP6f fluorescence from mitral and tufted cells and their dendrites recorded in the dorsal portion of the olfactory bulb of a Tbet-cre: Ai95(RCL-GCaMP6f)-D mouse (maximum projection of 8,000 frames). Dendritic ROIs are superimposed in colour. Four dendritic segments (1–4) are shown in higher magnification; scale bars, 20 μm. b, Four example calcium traces extracted from dendritic segments shown in a that show differential response kinetics to correlated (black) and anti-correlated (red) stimulation (mean ± s.e.m. of 24 trials, f = 20 Hz). In total, 24% of dendritic segments showed significantly different integral responses (0–5 s after odour onset, P < 0.01, unpaired two-sided t-test; 121/514) to the two stimuli. c, Average calcium transients as colour maps for correlated (left) and anti-correlated stimuli (middle) and the difference between the two (right) of all analysed dendritic segments (n = 514, from 6 individual animals). d, Classifier accuracy over an increasing number of dendritic ROIs trained on several response windows (colour-coded) to discriminate correlated versus anti-correlated stimuli at 20 Hz (n = up to 514, mean ± s.d. from 6 individual animals, black: shuffle control). e, Method of aligning calcium traces to first inhalation after odour stimulus onset. ei, Representative respiration traces recorded using a flow sensor placed in front of the nostril contralateral to the imaging window. The first inhalation peaks were detected and the time (Δt) to the first inhalation after odour onset was calculated for each trial individually. eii, Representative calcium transients in response to a single odour presentation (here: 20 Hz correlated). eiii, Transients are shifted according to Δt. eiv, Individual calcium transients (faint colours, 24 trials) in response to 20 Hz correlated odour presentations with the average calcium signal (thick traces) superimposed. Top, before aligning to first inhalation after odour onset; bottom, after alignment. Blue bar represents the odour presentation phase (approximate for the aligned data). f, Distribution of odour response integrals from all recorded ROIs (n = 514) for correlated (grey) and anti-correlated (red) stimulation. Box indicates 25th–75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers; Methods. g, Histogram of the difference between correlated and anti-correlated odour responses. Box plot as in f. h, Comparison of correlated and anti-correlated odour responses of all dendritic ROIs (f = 20 Hz, n = 514 dendrites). i, Classifier accuracy when trained on all dendritic ROIs recorded with a sliding window of different durations starting 2 s before odour onset (colour-coded; black, shuffle control; n = 514 from 6 individual animals; mean ± s.d., 100 repetitions). jm, As in fi but for projection neuron somata (f = 20 Hz, n = 680 cells; Fig. 3).

Extended Data Fig. 8 Projection neuron unit recordings in response to correlated versus anti-correlated stimulation and short odour pulse combinations.

a, Data from unit recordings as in Fig. 3h–k. Average waveforms across all channels of two isolated units shown in bi,ii. Each waveform represents the average waveform for the unit on a specific channel. Red waveform indicates the channel with the largest average waveform for the unit. Scale bars, 100 μV (vertically) and 1 ms (horizontally). b, Additional example single unit odour responses to correlated (black) and anti-correlated (red) stimuli shown as raster plots (top) and PSTHs (mean ± s.e.m. of 64 trials for each condition) of spike times before (second from top) and after baseline subtraction (second from bottom), and the differential PSTHs for correlated and anti-correlated stimuli (bottom, blue). Average spike waveforms shown as insets in bi,ii. Duration of odour presentation (2 s) is indicated in light blue. P values derived from a two-sided Mann–Whitney U test comparing the spike time distributions of correlated and anti-correlated trials during the 4 s after odour onset. c, Average baseline firing rate for all units (n = 97 from 6 individual animals). Baseline firing rates were calculated from 4 s to 0 s before odour onset for each of the 1,312 trials presented during all recordings. Violin plot shows the median as a black dot and the first and third quartiles by the bounds of the black bar. di, Classifier accuracy when trained on all baseline-subtracted units in response to 20 Hz correlated versus anti-correlated stimulation (n = 97 units, mean ± s.d. from 6 individual animals) with a sliding window of different durations (colour-coded; black, shuffle control; 100 repetitions) starting at 2 s before odour onset. Time along the x-axis represents the end time of the window. dii, Time period between −0.5 and 0.5 s from odour onset shown at higher magnification (n = 97 units, mean ± s.d. from 6 individual animals). e, To take the entire temporal structure of responses into account we performed a PCA on the temporal evolution of the firing rate responses (Methods). Shown here is the accuracy for linear SVM classifiers (mean ± s.d.) trained on increasing numbers of PCs. Classifiers were trained on all but two trials (one correlated, one anti-correlated). Training and testing were repeated 1,000 times. The colour code represents the same window sizes as in d. f, The first (fi), second (fii), and third (fiii) PCs found from PCA for different rolling window sizes (colour code as in d). In the second and third PCs, the windows have been split as to better compare the similarities in PCs for different window sizes. g, Average classifier accuracy of a set of classifiers trained on the PC weights of increasing number of units. Classifiers were trained on all but two trials (one correlated, one anti-correlated). The number of PCs used for each window was selected by the peak accuracies in e (colour-coded; n = up to 97 units from 6 individual animals; mean ± s.d. of 1,000 classifier repetitions). h, Schematic of odour pulse stimulus timings in relation to the respiration cycle. Three combinations were presented, with each trial 120 ms in length. For example, 11000 (top) consisted of a 40-ms odour pulse (light blue) followed by 80 ms of blank odourless air (grey). All trials were triggered at the onset of inhalation. i, PSTHs from four example units (ii–iv) showing their average firing rate before, during, and after odour presentation (light blue vertical bar). Responses are to either 11000 trial (black) or 10100 odour presentation (red). The instantaneous firing rate was calculated by summing the number of detected spikes in 10-ms windows and multiplying the value by 100 to get Hz. j, Accuracy of linear classifiers as a function of the number of units available for training or testing (mean ± s.d. of n = up to 145 units from 8 individual anaesthetized animals). Each classifier was trained on the summed spike count of the available units in a window of 500 ms starting at odour onset. The classifiers were trained on all but two trials (one 11000 and one 10100 trial) and the number of repeats between animals varied between 11 and 30. To account for this and to minimize the variability of the training set, trial number was bootstrapped to 1,000 repeats. This was achieved by randomly selecting a repetition for each unit independently. The test set was isolated from the responses before bootstrapping and thus was not seen by the classifier until it was tested on it. Each classification was repeated 500 times with a different selection of units, and a different test set. The shuffled control (black) was accomplished by shuffling the training labels during each iteration of the classifier without shuffling test labels. k, As in j but classifying all three odour pulse combinations shown in h. l, Confusion matrix showing the fractions that each trial type was classified as (n = 145 units from 8 individual animals). True labels are shown on the x-axis and labels predicted by the classifier on the y-axis. Accuracies correspond to maximum unit count shown in c, d. The classifiers can readily separate between trials containing a single 40-ms odour pulse. Accuracy is lower when distinguishing between an intermission of 20 or 40 ms but remains above chance (chance = 0.33).

Extended Data Fig. 9 Whole-cell recordings of projection neurons in response to correlated versus anti-correlated odour stimulation.

a, Schematic of the whole-cell patch-clamp recording approach. b, c, Distributions of input resistance (b) and recording depth (c) as measured from all recorded projection neurons (n = 31). d, Left, example recordings from single cells with consecutive presentations of correlated (black) and anti-correlated (red) odour stimulus at 2 Hz. Duration of odour presentation (2 s) is indicated in light blue. Right, baseline-subtracted and spike-clipped subthreshold voltage response from a single cell to odour 1 (green) and odour 2 (blue) for 2 Hz. e, As in d but for 20 Hz odour stimulation. f, Voltage response from three example cells for correlated (black) and anti-correlated (red) odour stimuli for 2 Hz (top) and 20 Hz (bottom). The cell shown in fi corresponds to the cell shown in d, e. The grey overlaid traces correspond to the arithmetic sum estimated from the response to individual odours. Bottom, linear prediction histogram calculated by thresholding the arithmetic sum of the subthreshold responses to the individual odours. Differences here suggest that correlation can be calculated at the single-cell level if the two individual odours engage overlapping OSN populations. P values are derived from a paired two-sided t-test of the membrane potential and the firing rate in the first 500 ms after odour onset. g, h, Average change in voltage (gi) and in instantaneous spike frequency (gii) in the first 500 ms after odour onset from baseline membrane potential for 2 Hz (g) and 20 Hz (h) correlated versus anti-correlated odour presentation. Each marker corresponds to a single cell; error bars represent s.e.m. Data points in black represent cells where P < 0.05 between correlated and anti-correlated conditions. P values are derived from a paired t-test of the membrane potential and the firing rate in the first 500 ms after odour onset. Indicators i, ii and iii represent cells shown in f. i, Pie charts depicting the proportions of cells showing significant difference as described above (blue) in subthreshold membrane potential (left) and spike frequency (right) for all 2 Hz (top) and 20 Hz (bottom) cells. P values are derived from a paired t-test of the membrane potential and the firing rate in the first 500 ms after odour onset.

Extended Data Fig. 10 Odour plume generation and additional analysis of source separation experiments.

a, Power spectrum of all recorded odour plumes (mean ± s.d. of log power, n = 132 plumes). b, Cross-correlation of all recordings at different lateral separation distances. c, Correlation coefficients over all recordings for odours from the same source and for odour sources separated by 50 cm in a controlled laboratory environment with complex airflow (indoors; ethyl valerate (EV) versus tripropylamine (TPA); n = 25 for same source, n = 27 for sources separated by 50 cm; P < 0.0001, unpaired two-sided t-test). Box indicates 25th–75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers; Methods. d, As in Fig. 4b (for α-terpinene and ethyl butyrate) but for radial distances to the PID of 20 cm and 60 cm (P < 0.0001, unpaired two-sided t-test). e, As in d but measured outdoors (n = 7 for same source, 10 for sources separated by 50 cm; P < 0.001, unpaired t-test; indoors versus outdoors, one source: P = 0.0060, s = 50 cm: P = 0.0632, unpaired two-sided t-test). f, Example plume structures originating from the same source or separated sources as recorded with a PID (blue) and replayed with the multi-channel high bandwidth odour delivery device (orange). g, Correlation coefficients over all recordings of replayed plumes for one source (n = 53 plumes) and for sources separated by 50 cm from each other (n = 74 plumes; P = 2.27 × 10−41, unpaired two-sided t-test). h, Odour signals integrated over 2 s for all recordings of replayed plumes for one source (n = 53 plumes) and for sources separated by 50 cm (n = 74 plumes; P = 0.75, unpaired two-sided t-test). i, Odour plume signals integrated over 2 s for rewarded and unrewarded trials (n = 150 trials each; odour 1: P = 0.4739, odour 2: P = 0.0923, unpaired two-sided t-test). j, Overlaid power spectra (mean ± s.d. of log power) of all plumes (n = 127 plumes) recorded in complex, natural airflow conditions (blue) and replayed plumes (orange). k, Schematic of plume reproduction. First, a 2-s window is selected from the PID recording, starting around the middle of the trace and such that odour is present during the first 500 ms. Second, the trace is normalized between 0 and 1. Third, the trace is converted into a series of binary opening and closing commands directly related to the value of the normalized signal. A value of 1 translates to a continuous opening, and a value of 0 translates to continuously closed. This series of commands is relayed to an odour valve and an inverted version of the commands is relayed to a mineral oil valve to generate a compensatory airflow. The resulting output resembles the original plume, as measured with a PID, and there is constant airflow throughout the trial, as measured with a flow meter. The same procedure is then applied to the accompanying odour, to create both plumes needed for each trial. l, Group learning curves (mean ± s.d.) for the two groups of animals trained on the virtual source separation task, but on different sets of valves. Group 1 (n = 6 mice, blue) were trained on the task from the start, whereas group 2 (n = 6 mice, cyan) were first exposed to a scrambled version of the task and were later transferred to the same plumes as group 1. This served as a control that the cue required for learning is indeed olfactory information contained in the odour plumes. For the third stage of learning, the plumes were refined to ensure odour was always present in the first 500 ms of the trial and performance stabilized for the two groups. Mice progressed through these learning stages as a group, based on time elapsed from the beginning of training. Therefore, some mice performed more trials than others. The last trial performed by a mouse in each phase is represented by a colour-coded circle above the plot. Accuracy is calculated over a 100-trial sliding window. m, Rejection fraction (fraction of trials the mouse abstained from licking) calculated for each plume pair plotted in relation to the correlation between the two odour traces in that plume pair. Animals are trained to lick (expected low rejection fraction) for source-separated trials (low correlation) and abstain from licking (high rejection fraction) for one-source trials (high correlation). n, Difference in lick rates in response to source-separation training trials (n = 9 mice, mean ± s.d.), calculated for each mouse as lick rate (licks per 100 ms) in response to S+ trials minus the lick rate in response to S− trials, normalized to averaged lick rate for all trials across the corresponding time period. o, Reaction times for each mouse, calculated as the time point when the difference in lick rate for each mouse crossed a threshold (mean + 3 s.d. over the baseline, defined as the first 200 ms of the trace, when odour was not present). Box indicates 25th–75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers; Methods. p, Trial map of all animals during virtual source separation tasks before and after introduction of control valves similar to Extended Data Fig. 4 (n = 40 trials before and 40 trials after new valve introduction, which is indicated by black vertical line). Each row corresponds to an animal, each column represents a trial. Light green, hit; dark green, correct rejection; light red, false alarm; dark red, miss. q, Mean performance of animals (n = 11 mice) that reached performance criterion during training during before and after control. r, Discrimination accuracy split by stimulus valence (green, S+; black, S−) for odour correlation fluctuation frequencies 2, 20 and 40 Hz (Fig. 4e; n = 9 mice, data are mean ± s.d., unpaired two-sided t-test). s, Group performance for the square pulse probe trials at different frequencies, in animals trained on the source separation task (blue dots, n = 9 mice, data are mean ± s.d.), compared to group performance where animals were trained on correlated and anti-correlated square pulse trains (from Fig. 2k, black line and s.e.m. band, n = 33 mice; 2 Hz: P = 0.0018, 20 Hz: P = 0.19, 40 Hz: P = 0.94, unpaired two-sided t-test). Violin plots in gi show the median as a black dot and the first and third quartiles by the bounds of the black bar.

Supplementary information

Supplementary Tables

This file contains Supplementary Table 1: Parameters of the olfactory sensory neuron population model; and Supplementary Table 2: Parameters of the olfactory sensory neuron population model that were varied.

Reporting Summary

Supplementary Figure 1

Characterization of odorants presented with a high-speed odour delivery device. a, Calculated signal fidelities for seven different odours (colours, see legend in b) pulsed for 2 s over a frequency range of 2 to 100 Hz at 50% pulse duty (n = 5 repeats for each condition, mean ± SEM). b, Amount of released odour (n = 5 repeats for each condition, mean ± SEM). Odours are: AA (isoamyl acetate), ACP (acetophenone), AT (α-Terpinene), CN (cineol), EB (ethyl butyrate), Hex (2-hexanone), PEA (phenylethyl alcohol). c, Left: Schematic of the pulse-width modulation (PWM) method. For any period of odour release, maximum final concentration is achieved by keeping the valve open for the entire time (top). The amount of odour released can be reduced by cycling the valve at a high frequency (here 500 Hz) with a different level of PWM (middle and bottom panel). Right: Odours were released over a 2 s period with different PWM duties at 500 Hz (n = 5 repeats for each condition, mean ± SEM). The resulting amount of released odour is normalised to the maximum release (PWM = 1). d, Average PID signal of single 100 ms pulses (pulse indicated in blue) for seven different odours (n = 60 pulses for each odour, mean ± SEM). e, Summary table: delay (time from start of the odour pulse to 5% of maximum signal amplitude), rise (time from 5% to 95% of maximum signal amplitude), decay (time for the signal to decay back to 5% of maximum amplitude after the end of the odour pulse). f, Effect of tubing length attached to the valve manifold on signal fidelity at different pulse frequencies pulsed for 2 s at 50% pulse duty (ethyl butyrate).

Supplementary Figure 2

Dual-energy fast photoionisation detection (defPID). a, Schematic of the dual-energy fast photoionisation detection method. Two odours are recorded simultaneously by two PIDs with different ionizing energies (different wavelength UV light sources). The odours are chosen such that one odour (odour 2 (ethyl butyrate), 9.5 eV) has an ionization energy greater than the low energy PID bulb, but less than the high energy PID bulb, thus only being detectable by the high energy PID. The other odour (odour 1 (α-Terpinene), 7.9 eV) is chosen such that its ionization energy is lower than both PID bulbs (detectable by both PIDs, see also e). b, Method of decomposing odour signals. Top panel: high energy PID signal (grey: recorded signal, blue: calculated signal due to odour 1, red: calculated signal due to odour 2). Bottom panel: low energy PID signal (green: recorded signal, red: calculated signal due to odour 2; the entire signal is due to odour 1). c, Single data points of the PID signal evoked by α-Terpinene in the two PIDs. The slope of the linear fit serves as a scaling factor to map the low energy PID to the high energy PID signal. d, Histogram of R-squared values of all dual-PID α-Terpinene recordings to define the scaling factor (n = 59 recordings). e, Summary of signal combinations for defPID recordings. The scaling factor for the PIDlow signal is determined by the slope in c. f, Schematic of outdoors odour plume recording setup. PIDs and odour delivery system were used to record for multiple trials at different lateral distances (s) between odours held in ceramic crucibles. Data was collected on a day with low wind (~8-12 mph, equivalent to ~3-5 m/s, recorded with a 2-axis ultrasonic wind sensor at the height of the PID inlet. Outdoor experiments were performed on a ~6 m x 10 m wooden patio structure surrounded by trees. There was >300 cm of unobstructed space on an artificial grass mat in front of the PIDs to capture air movements. g, Indoor setup: A digitally controlled fan was placed at a distance of 325 cm facing the PID inlet. An exhaust line was situated behind the PID inlet to ensure the direction of air from the fan towards the PID inlet. During a recording, the fan was set to maximum speed such that it pushed approximately 552 cf/min (cubic feet per minute, ~260 l/s) of air towards the PID inlet. A 25x25x25 cm Thermocool box was placed 200 cm downwind of the fan acting as an obstacle to air movement, promoting complex air movement patterns at the PID location. The pump at the PID was set to ~0.02 l/s suction speed, unlikely to perturb overall airflow dynamics substantially.

Supplementary Video 1

Automated operant conditioning system (“AutonoMouse”) equipped with high speed odour delivery device.

Supplementary Video 2

Comparison between original video-based respiration recording and phase-based motion amplification (red trace) in head-fixed condition on the animal’s flank to capture body movements associated with respiration. Simultaneously, respiration was recorded with a flow sensor placed in front of one nostril (black trace). Odour stimulus highlighted with blue bar.

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Ackels, T., Erskine, A., Dasgupta, D. et al. Fast odour dynamics are encoded in the olfactory system and guide behaviour. Nature 593, 558–563 (2021).

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