Sniff Invariant Odor Coding

Odor concentration perception does not depend on sniff duration

To test whether odor intensity perception depends on sniff duration, we trained rats to classify odor concentrations in a two-alternative choice task (Fig. 1A,B). On each trial, we presented randomly one of eight odor concentrations. Rats were trained to go to the left water port for four higher concentrations and to go to the right water port for the four lower concentrations (Fig. 1A). Rats performed on average ∼700–800 trials per session which results in ∼80–100 trials per each concentration. We estimated behavioral performance using psychometric functions (Fig. 1C) with three parameters: μ, the decision boundary between high and low concentrations; σ, the curve slope, which corresponds to odor concentration discriminability (sensitivity); and γ , lapse rate, the percentage of trials on which the animal guessed the answer (Eqs. 1, 2; Wichmann and Hill, 2001a).

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Figure 1.

Behavioral discrimination of odor concentrations is sniff frequency invariant. A, Two-alternative choice odor discrimination task. Rats initiate trials by poking into an odor port (OP), which activates presentation of one out of eight odor concentrations. After being exposed to one of four low/high concentrations, rats are rewarded for poking into right/left water port (WP). Light brown bars above the water ports represent the different concentrations the rat must discriminate. B, Task trial structure and pressure signal. Downward and upward deflections of the pressure signal reflect inhalation and exhalation, respectively. Light brown shading marks odor presentation time interval. C, Average concentration classification performance (n = 4 rats). Error bars denote SDs across all sessions for all rats. The continuous line is an error function fit to the data. D, Example performance during a single session for fast (black) and slow (red) sniff cycles. Each point denotes probability of going left (high concentration). Each inset is a sniff duration histogram for a given concentration. E, Differences in psychometric parameters between fast and slow sampling for decision boundary, δμ = μ_fast - μ_slow, and sensitivity, δσ = σ_fast - σ_slow: histograms for all sessions (top) and values for individual sessions (bottom). Lines are 95% confidence intervals assessed via bootstrap. Sessions from different animals are presented in alternating black and gray colors.

At the first sniff after odor exposure, rats exhibited a broad range of sniff durations (across all rats: median: 143 ms, range: 74–441 ms; Fig. 1D, insets). To quantify the dependence of animal performance on sniff duration we split all trials into two groups: with fast/slow sniffs (sniff duration was shorter/longer than the median sniff duration for a given rat). We fit psychometric functions independently for each group of trials (Fig. 1D). The differences between groups for the decision boundaries , sensitivities , and lapse rates did not statistically differ from zero (δμ: p = 0.77, δσ: p = 0.18 δ γ : p = 0.36, Wilcoxon signed-rank test Table 1). These results suggest that neither concentration sensitivity, σ, nor biases in perceived concentration, μ, depend on the sniff duration. Therefore, behavioral performance in this concentration discrimination task does not depend on sniff duration. The accompanying study yielded identical results on mice (Jordan et al., 2018)

Odor responses vary with sniff duration

To investigate which features of neural code are invariant to variations in sniff pattern, we exploited the natural variability in the sniffing pattern of awake animals. We recorded MT cell responses (13 mice, 200 cells) to different odorants and different concentrations of the same odor in head-restrained mice (Fig. 2A; see Materials and Methods). Sniffing was monitored via an intranasal pressure cannula (Fig. 2A). Responses of each MT cell were recorded typically to 5–10 odorants, making in total 1409 cell-odor pairs. Out of 200 MT cells, 134 cells were recorded in sessions with a presentation of multiple odor concentrations (548 unit-odor-concentration triplets). Out of all responses, 28% demonstrated initially excitatory activity and 28% initially inhibitory (Fig. 2B; see Materials and Methods).

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Figure 2.

Differences in MT cell responses between fast and slow sniff cycles. A, Schematic of the experiment. A head-fixed mouse implanted with intranasal cannula and a multi-electrode chamber was positioned in front of the odor delivery port. Left, Pressure wave form of a typical breathing cycle. Red dots indicate the inhalation onsets and offsets. The blue line is the parabolic fit to the first minimum after the inhalation onset. The sniff offset was defined as the second zero crossing of the parabolic fit. The gray shaded area marks the inhalation interval. B, Distribution of different response types observed in the data. Next to the pie chart are examples of initially excitatory (red) and initially inhibitory (blue) responses. Gray lines represent spontaneous activity. C, Sniff duration histogram for all mice averaged across multiple sessions for the 1st odorized sniff cycle. Sniffs are split into two groups: fast (<221 ms; orange) and slow (>221 ms; blue). D, Raster (top panels) and PSTH (bottom panels) plots of the first odorized sniff cycle for four MT cells in response to an odor stimulus. Trials in the raster plots are ordered bottom to top by the increase in the duration of sniff cycle. Gray line shows end of the sniff cycle. Raster plots and PSTHs for fast and slow sniffs are marked by orange and blue colors, respectively. Gray PSTHs are average spontaneous activity of MT cells during all unodorized sniffs.

To visualize MT cell odor response dependence on sniff duration, we aligned responses by the beginning of the first inhalation after the onset of odor presentation. Trials in the raster plots were ordered by the duration of the first odorized sniff cycle. These raster plots reveal the clear dependence of MT cell responses on sniff frequency (Fig. 2D). While earlier temporal features of MT response are preserved across different sniff durations, the later features are often absent on trials with short sniff cycles (Fig. 2D). Thus, the temporal pattern across the full sniff cycle depends on the sniff duration.

Amplitude and latency of the response but not spike count depend on sniff duration

Visual inspection of the raster plots (Fig. 2D) suggests that responses during the early part of the sniff cycle are more similar for fast and slow sniffs than the later part. To quantify this observation, we estimated the distribution of sniff durations for all mice and all sessions and divided the sniffs into two groups, fast sniff trials with the sniff duration in the left third of the distribution, and slow - in the right two thirds of the distribution (Fig. 2C). The boundary between these groups was 221 ms (see Materials and Methods; Fig. 2C). MT cell activity during short and long sniff cycles was averaged separately (Fig. 2D). MT cell responses during slow sniff cycles contain on average 2.3 times more spikes than responses during fast sniff cycles. However, the average spike count during the first 221 ms remains almost the same (Fig. 3A). The distribution of the spike count differences for fast and slow sniffs for all cell-odor pairs is centered around zero (Fig. 3A, inset; p = 0.43, Wilcoxon signed-rank test). Thus, spike count over this early time window is invariant to changes in sniff frequency.

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Figure 3.

Comparison of response features for fast and slow sniff durations. A–C, Comparison scatter plots of average spike count during the first 221 ms (A), average peak amplitude (B), and average response latency (C) for fast versus slow sniff cycles. Each dot represents comparison for a single cell-odor pair. Diagonal plots are distributions of differences of corresponding values. Spike counts are statistically indistinguishable for slow and fast sniffs. On average, peak amplitudes are larger (p = 0.013; Wilcoxon signed-rank test) and latencies are shorter (p = 0.007; Wilcoxon signed-rank test) for fast sniffs compared to slow sniffs. D, Shift in latency of responses between slow and fast sniffs as function of response latency. Red solid line is a linear regression fit to the data. Red dashed lines mark the limits of the 95% confidence interval (slope = 0.35). See also Extended Data Figure 3-1.

Integration of spiking activity over a long time widow (∼200 ms) may not serve as an informative cue for many odor driven behavioral decisions, which are often relatively fast (Resulaj and Rinberg, 2015; Wilson et al., 2017). Thus, we looked into finer features of MT cell responses, such as the amplitude of the response, which is a combined characteristic of instantaneous firing rate and spike timing precision, and the latency of the response (Fig. 2D). We calculated these parameters for fast and slow sniffs separately. We present the data for individual cell-odor pairs as scatter plots of peak amplitudes (Fig. 3B) and peak latencies (Fig. 3C) for fast and slow sniffs. The response amplitude is slightly lower for slow sniffs than that for fast sniffs (Fig. 3B, inset; δA = 5.7 Hz, p = 0.013, Wilcoxon signed-rank test). The response latencies also differ between fast and slow sniffs: fast sniff latencies are slightly shorter that those of slow sniffs (Fig. 3C, inset; δτ =10.4 ms, p = 0.007, Wilcoxon signed-rank test; see also Jordan et al., 2018). Further analysis of the response latencies showed that latency differences δτ between slow and fast sniffs increases with latency (Fig. 3D; regression parameters: slope = 0.36 ± 0.11, intercept = –22.6 ± 11.2). Thus, fine temporal features of the odor response vary with the sniff duration.

How significant are these sniff duration-dependent differences in response latency and peak amplitude? To answer this question, we compare the time and amplitude changes due to sniff variability to those due to concentration changes. Based on our previous work (Sirotin et al., 2015), a time difference of δτ ≈ 10 ms corresponds to a 3-fold concentration change, and an amplitude difference of δA ≈ 6 Hz corresponds to a 2-fold concentration change. So, the temporal features of MT cell responses vary with sniff duration as much as they vary for 2–3-fold concentration differences.

These observations raise two questions. First, what is the mechanism responsible for the sniff wave form dependent variability? And second, is there a representation of the odor response which is invariant to the sniff duration? These two questions are related: defining the mechanism will allow us to find a better representation, and vice versa: finding a better representation will help reveal the mechanism. To address these questions, we formulate a simple model based on the FD of odor propagation in the nasal cavity which may explain the sniff dependent variability. We then compare our model with the previously proposed representations described above. For quantitative comparison, we propose a metric of how well these representations reduce sniff wave form related odor response variability. Lastly, we discuss the applicability of such transformations for analysis of olfactory coding.

FD model

We observed that faster sniffs evoke earlier odor responses with higher amplitude. Also, on average, faster sniffs have larger pressure amplitude changes (Extended Data Fig. 3-1; Youngentob et al., 1987; Walker et al., 1997). We assume that the pressure measured via cannula is a good proxy of the air velocity inside the nasal cavity. Given this assumption, we propose a FD-based model which can explain the dependence of response latency on a sniff waveform.

Let us assume that response latency, τ , of a MT cell odor response consists of two terms: first is a FD term that depends on the sniff wave form, where, is an averaged across nostril cross-section instantaneous air velocity wave form, and square brackets symbolize the dependence on the whole wave form function, rather than instantaneous values. Here, for simplicity, we ignore non-uniform distribution of air velocity. Second term, is the delay due to neural processing which may depend on the odor and a specific MT cell, but is independent of the sniff wave form: (12)

To model the dependence of on the sniff wave form, we propose that odor is carried into the nose by an air flux with time-dependent velocity (Fig. 4A). Suppose, the receptors are located at an approximate distance L from the nasal opening. Then the relationship between air velocity and distance L is following: (13)

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Figure 4.

A FD model explaining latency of MT cell activation. A, Simple physical model of odor molecules delivery to the receptors. During inhalation, odorized air (yellow) is drawn into the nose with velocity u(t). The OSNs (green) are located at an average distance L from nasal opening. Air velocity is proportional to pressure measured via cannula u(t) ∼ P(t). B, A schematic of pressure signal temporal profiles, P(t) for three representative sniff cycles. C, Integrals of pressure signals: . Left panel, A schematic distribution of values of integrals over the whole inhalation interval normalized to their mean value, . For a given value of an integral, for example, λ=0.5 in normalized coordinates, we estimate time points for which: , here are normalized pressure traces. D, Raster plots of spiking data from a representative cell, aligned to different values of λ. Black line shows end of the inhalation. See also Extended Data Figures 4-1, 4-2.

In our model, L does not depend on the sniff wave form, and the velocity is proportional to the measured pressure: (Zwicker et al., 2018). The pressure changes due to the air flow have two main terms, the first one is due to the viscosity of the air is a narrow tube, i.e., it is a drag term which is proportional to the air velocity. The second is FD Bernoulli term which is proportional to velocity square: ( ρ is air density ∼1.2 kg/m³). Typical peak velocity during inhalation is ∼1 m/s (Youngentob et al., 1987), which corresponds to ∼1 Pa pressure difference. This is significantly smaller than the peak pressure deviation measured in our system ∼50 Pa. We consider that we can neglect non-linear velocity dependencies. Under these conditions, during faster sniff cycles, air velocity is higher, therefore it takes less time to odor molecules to pass the same distance L. While L is unknown, we can treat it as a model parameter which is estimated by minimizing neural response variability. The detailed procedure is shown in Figure 4B,C and in Materials and Methods. Briefly, for a given fraction, of normalized length, ( ), and for each sniff i , we find the FD time, . Then we estimate an average FD delay across all trials and shift spiking activity during trial i by a time interval . We repeat this procedure for different values of Lambda between 0 and 1. Then, using log-likelihood estimation, we find the value of λ that minimizes trial-by-trial variability of the neural response. The transformation of spike trains for different values of λ is shown in Figure 4D for one cell-odor pair (Extended Data Fig. 4-1). On average, the best transformation of odor responses is achieved for λ = 0.3 (Extended Data Fig. 4-2).

This model-based procedure reduces odor response variability compared to an original representation in time relative to the onset of inhalation, which corresponds to λ = 0. In sensory systems, neuronal responses are often tightly locked to the time of stimulus presentation (Richmond et al., 1990). In olfaction, this time may be the moment when odor concentration crosses a receptor’s threshold. This timing varies with the sniff pattern. Although our model is oversimplified, it may allow us to remove the influence of sniffing on spike pattern and better understand sniff invariant odor processing. Next, we perform model-based comparison of different representations to find a transformation that best describes sniff invariant odor representation.

Model comparison

To infer the best sniff invariant odor representation, we apply different models to transform individual spike trains based on the corresponding waveforms and estimate an average odor response. The optimal transformation should minimize trial to trial response variability. Using maximum likelihood estimation (MLE), we evaluate which of the average responses better fits experimental data (see Materials and Methods). We consider the following spike time transformations, most of which were previously discussed in the literature, while the last one is proposed here (Fig. 5A):

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Figure 5.

Model comparison of different alignment methods. A, left, Schematics of the effect of each of the transformation on sniff cycles. Right: raster plots of responses of two cell-odor pairs aligned according to each schematic. B, Log-likelihood of each model across the population of responses. Pairwise comparisons were done using the Wilcoxon signed-rank test (FD vs time comparison, p = 5.7e-19; FD vs phase comparison, p = 9.5e-04; FD vs two interval phase comparison, p = 9.9e-03; FD vs inhalation proportional comparison, p = 3.5e-02). See also Extended Data Figure 5-1.

(1) Time model: spike times aligned to onset of inhalation, with no further transformation. (2) Phase model: spike times relative to onset of inhalation are scaled proportionally to the duration of the whole sniff cycle. (3) Two-interval phase model: the sniff cycle is split into the inhalation interval and the rest of the cycle. Spike times during the inhalation interval are scaled proportionally to the duration of the inhalation, while spikes times occurring in the rest of the sniff cycle are scaled proportionally to the duration of that interval (Shusterman et al., 2011). (4) Inhalation proportional model: spike times during the whole sniff cycle are scaled proportionally to the duration of the inhalation (Arneodo et al., 2017). (5) FD-based model: spike times are shifted by a specific value determined by the sniff waveform integral in that trial (Fig. 4). Note that only this model has an additional adjustable parameter, optimization of this parameter was done using the same MLE procedure.

An example of transformation for all five models of two cell-odor responses is shown in Figure 5A. To fit each model, we transform the spike trains in individual trials according to that model's alignment rule (Fig. 5A) and calculate PSTHs using the transformed spike trains (Extended Data Fig. 5-1). To evaluate the goodness of fit of different models, we evaluate their average log-likelihood in held out sniff cycles. To this end, we first inversely transform each model’s PSTH according to the duration parameters of a given sniff cycle using interpolation. We then evaluate the Poisson process log-likelihood, given the inversely transformed PSTH, for the spike train during that sniff cycle (Fig. 5B). Finally, we average the calculated single-sniff log-likelihoods for a model over all sniffs to obtain that model’s average log-likelihood. We performed this analysis on 192 excitatory responses each consisting of at least 30 trials per response. On average, the FD model better predicted the time course of instantaneous firing rates than any of the other models (Fig. 5B; for details, see Materials and Methods). Pairwise comparisons were done using the Wilcoxon signed-rank test on population log-likelihoods (FD vs time comparison, p = 5.7e-19; FD vs phase comparison, p = 9.5e-04; FD vs two interval phase comparison, p = 9.9e-03; FD vs inhalation proportional comparison, p = 3.5e-02). Since the FD model has an extra fitting parameter, we tested models performances on held out data to ensure that better performance is not trivial consequence of overfitting. Among other models the best is two-interval phase model, which we used previously in our studies to discover higher temporal precision of odor responses (Shusterman et al., 2011). The difference between two-interval phase and inhalation proportional models is insignificant (p = 0.12) and may be different for different datasets (Arneodo et al., 2017).

Decoding of odor concentration in FD transformation is better than in real time

If a model-based transformation of spike trains reduces sniff wave form related variability, then stimulus decoding using that transformation should be improved. Response profiles of the same cell across odorants are highly diverse (Shusterman et al., 2011). Therefore, odor identity can be decoded with high success rate irrespective of how or whether they are transformed (Bathellier et al., 2008; Cury and Uchida, 2010; Shusterman et al., 2011). In contrast, the type of transformation should play a more significant role in decoding odor concentration, which is encoded mainly by the fine temporal structure of spike trains (Bolding and Franks, 2017). As we pointed out above, sniff wave form-related variability is similar to a 2–3-fold uncertainty in concentration estimation. To test if the FD alignment allows for better decoding of odor concentration than time alignment, we evaluated the accuracy with which responses of MT cells to two odor concentrations (Fig. 6A,B) can be discriminated in each alignment, on a trial-by-trial basis (see Materials and Methods). We performed this analysis on 93 cell-odor-concentration triplets. On average, discrimination success rate between odor concentrations is better after FD transformation than in time coordinates: 70.2% versus 78.3% (t test, p = 8e-03; Fig. 6C).

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Figure 6.

Discrimination among odor concentrations by MT cells in time versus FD transformation. A, B, Raster and PSTH plots of MT cell responses to high (blue) and low (red) odor concentrations in time and in FD transformation. C, Concentration discrimination performance across the population in time (yellow) and FD (green) alignments. Gray dots and lines show discrimination performance for odor concentration pairs from A, B. The horizontal dashed line is chance level performance.