Bilateral Alignment of Receptive Fields in the Olfactory Cortex

A new method for unilateral odor delivery

A major goal of this study was to compare the bilateral odor receptive fields of OC neurons of awake mice. To do so, we needed a way to reliably deliver odors to one nostril at a time. Previous studies have used two different techniques to achieve such unilateral odor stimulations. Either a piece of tubing was inserted in each nostril (Wilson, 1997) or the two nostrils were separated by a plastic septum (Kikuta et al., 2008, 2010). Since mice have very sensitive muzzles, neither of these approaches is applicable to awake animals.

We developed a new facial mask for unilateral odor delivery in awake mice (Fig. 1B). On each side of the mask, close to the nostrils, we used a computer-controlled olfactometer to deliver 15 monomolecular odors, one at the time, to the left or the right nostril (Extended Data Fig. 1-1A,B). The mask was connected to an airflow sensor for respiration monitoring (Extended Data Fig. 1-1C–F). We aligned all neuronal odor-evoked activity to the first sniff after odor onset (see Materials and Methods).

We tested the side selectivity of the mask through two methods. First, we simultaneously monitored the glomerular activity at the surface of the OBs of OMP-GCaMP3 mice (Isogai et al., 2011) through calcium imaging while delivering odors to either nostril (Fig. 1C; n = 155 glomeruli, six OBs, three mice). When odors were presented on the contralateral nostril, glomeruli showed little to no response (Fig. 1D–F).

We also performed extracellular recordings of M/T cells in the OB of awake mice using chronically implanted tetrodes (n = 42 single units isolated from four mice; Fig. 1G; Extended Data Fig. 1-1G–L; Extended Data Table 1-1). M/T cells hardly responded to contralateral odor presentations: out of the 42 isolated neurons, 32 responded to ipsilateral stimulations, while 10 showed significant contralateral responses (Fig. 1H; Extended Data Fig. 1-1M). Furthermore, while the ipsilateral M/T cell responses were largely positive, the few contralateral responses were always negative (Fig. 1H).

The ratio of contra- to ipsilateral response magnitude elicited by odors presented within the mask was 0.12 in our glomerular imaging data (ΔF/F magnitude; average ± SEM; ipsilateral, 7.9 ± 0.025%; contralateral, 0.93 ± 7.0 × 10⁻³%; Fig. 1I) and 0.10 in our M/T recordings (response magnitude; average ± SEM; ipsilateral, 1.6 ± 0.019 Hz; contralateral, 0.16 ± 2.1 × 10⁻³ Hz; Fig. 1J). Therefore, on average, odor responses were 8–10 times stronger on the ipsilateral side of the mask, compared with the contralateral side. In addition, by systematically lowering the concentration of odor stimuli presented to the two nostrils, we found that the glomerular responses to contralateral stimuli were comparable with presenting a 10-fold lower-intensity ipsilaterally (Extended Data Fig. 1-3). Finally, we further evaluated potential cross-contamination by imaging the glomerular activity of awake mice after naris occlusion while presenting odors through our mask (Extended Data Fig. 1-4). This experiment confirmed our other controls: when considering the odor-evoked activity of the OB contralateral to the occlusion (i.e., the OB on the unoccluded side), the glomerular responses were >10 times when stimulating the open nostril, compared with puffing odors on the occluded naris (Extended Data Fig. 1-4C).

Previous work has indicated that M/T cell responses to a given odor at a concentration of 0.1% were quite similar to the same odor at a concentration of 1% (Bolding and Franks, 2017, 2018). Since the M/T cell responses we observed are substantially smaller for contralateral presentations, the effective odor concentration in the ipsilateral nostril, when odors are presented contralaterally, is likely to be much <10% of the initial concentration from ipsilateral presentations.

Together, these results confirmed that odors, when delivered to one nostril through our custom-built mask, activate sensory neurons in the other nostril at least an order of magnitude less than ipsilateral activation.

Unilateral odor tuning of neurons in different regions of the OC

We next used our unilateral odor delivery system to characterize how the OC responds to unilateral odor presentations. To do so, we monitored the activity of the AON and APC through extracellular recordings in awake mice (n = 7 mice; 1,316 neurons total; AON, 3 mice, 385 neurons; APC, 4 mice, 931 neurons; Fig. 2A; Extended Data Fig. 2-1; Extended Data Table 1-1).

Overall, neurons in the OC had low spontaneous activity (Fig. 2B), in accordance with previous studies (Litaudon et al., 2003; Zhan and Luo, 2010; Bolding and Franks, 2017). Spontaneous activity in the AON was significantly higher than in the APC (average spontaneous activity ± SEM; AON, 3.9 ± 0.012 Hz; APC, 2.8 ± 3.6 × 10⁻³ Hz; rank-sum test; p < 0.0001).

We found a diversity of responses to ipsi- as well as contralateral odor stimulations in both the AON and APC, including neurons that responded to odors presented to either one or the other nostril or to both nostrils (Fig. 2C,D). Importantly, in both OC regions, a sizeable fraction of neurons responded to contralateral odor presentations (fraction of neurons significantly responding to at least one odor presented on the ipsilateral nostril; AON, 86%; APC, 81%; contralateral side, AON, 87%; APC, 83%), expanding earlier anesthetized observations to the awake OC (Wilson, 1997; Kikuta et al., 2008, 2010).

OC neurons typically responded to at most a few odors from our odor panel (Fig. 2E), as previously reported with bilateral odor stimulations (Bolding and Franks, 2017; Iurilli and Datta, 2017). We found a wide range of response magnitudes across the OC, and contralateral responses were as strong as ipsilateral ones in the APC and slightly weaker in the AON (Fig. 2F; Wilcoxon signed-rank test, ipsi- vs contralateral distribution; AON, p = 8.2 × 10⁻³; APC, p = 0.94).

An idiosyncratic feature of olfactory cortical responses is that a neuron that responds to a particular odor with an increase in the firing rate tends to exhibit increases in firing rates for any other odor it responds to; similarly, a neuron having inhibitory response to an odor is also inhibited by any other odor it responds to (Kikuta et al., 2008; Zhan and Luo, 2010; Otazu et al., 2015; Bolding and Franks, 2017; Hu et al., 2017). We find that this feature applies to both cortical regions we examined (Fig. 2G).

Overall, we found reliable odor responses in the OC to unilateral stimulation through both the ipsi- and contralateral nostrils.

Strong bilateral correlations in the OC

Our data indicate that the OC receives robust contralateral odor information, but it is unclear whether this information is similar to that arriving ipsilaterally. To examine this issue, we related the average odor-evoked responses to ipsilateral against contralateral presentations.

First, we plotted the ipsi- versus contralateral odor responses for each neuron individually. Given the prevalent view of OC connectivity as largely random, we expected OC neurons to show little to no match between their ipsi- and contralateral odor response profiles. To our surprise, we found many neurons with bilaterally correlated odor responses (Fig. 3A; F test; significance of the linear model, from left to right neuron; top row, p = 0.41; p = 0.84; p = 0.54; p = 0.59; bottom row, p = 5.3 × 10⁻⁶; p = 5.5 × 10⁻⁴; p = 6.6 × 10⁻³; p = 2.2 × 10⁻⁴; see also Fig. 2D, neurons with an asterisk). Overall, for each mouse recorded in the OC, we consistently found a sizeable fraction of bilaterally-correlated neurons (BCNs) (Fig. 3B).

We used a bootstrap strategy to determine that the fraction of BCNs in each mouse was significantly higher than what one would expect from chance. In brief, for each mouse, each neuron, we randomly shuffled odor identities on each nostril separately. We repeated this shuffling for all neurons and calculated the resulting percentage of BCNs. We reiterated this procedure 10,000 times in order to build a “chance” distribution. Finally, we compared this distribution with the actual fraction of BCNs. In all mice recorded in the OC, the fraction of BCNs was greater than one would expect from chance (Fig. 3B,C; Extended Data Fig. 3-1A–D).

While our initial estimates of the fraction of BCNs include all neurons recorded (Fig. 3B; Extended Data Fig. 3-1A), we verified that our conclusions remained true when selecting only the significantly responding (Extended Data Fig. 3-1B,C).

We performed additional analysis to determine the extent to which response variability masks response correlations. We generated individual trials from a Poisson process with rates determined from our recordings. We then enquired how correlated responses would be for two independent sets of seven trials generated with the same set of data. A large number of such sampling revealed that the fraction of (simulated) neurons that show significant response correlations was on the order of 40–80%. Therefore, even when excluding virtually all variability sources except for the neurons’ trial-to-trial variability, we still cannot reach a perfect correlation (100%). In other words, response variability probably lowers the apparent bilateral correlations we observe (Extended Data Fig. 3-1D). This analysis indicates that the fraction of significantly correlated neurons in the AON observed in our recordings may underestimate the real fraction of BCNs.

In addition, for each mouse, each side, and each neuron, we randomly split the seven trials into two groups of three and four, to calculate the correlation between the two groups of trials. We then computed the percentage of bilateral correlations among all neurons. We repeated this process for all the possibilities of trial splits. The goal of this test was to estimate an upper bound for the percentage of bilateral correlations one could expect in each mouse. The correlations obtained through this method were visually similar to the actual percentages. This suggests that the variability across mice in the actual data comes, at least partly, from the trial-to-trial response variability and/or overall weak odor responses, rather than a sizable difference of fraction of BCNs across mice. The analysis also suggests that the percentages of BCNs that were obtained in each mouse are rather close to the maximum correlation one could expect (Extended Data Fig. 3-1E).

Overall, the bilateral correlations were strong (Fig. 3D), with mostly positive slopes (Fig. 3E), and a distribution of intercepts centered on zero (Fig. 3F). In other words, BCNs appear to respond to unilateral odor presentations in a mostly side-invariant way, with their ipsi- and contralateral odor responses similar in sign and amplitude. The distribution of slopes was similar between the bilateral correlations originating from the AON and APC (mean ± SEM; AON, 0.79 ± 0.025; APC, 0.69 ± 0.036; Wilcoxon rank-sum test; p = 0.25). In addition, we found minimal but significant differences between the distribution of coefficients of determination (mean ± SEM; AON, 0.60 ± 0.017; APC, 0.54 ± 0.016; Wilcoxon rank-sum test; p = 0.013), as well as intercepts (mean ± SEM; AON, −0.24 ± 0.11; APC, 0.37 ± 0.16; Wilcoxon rank-sum test; p = 3.9 × 10⁻³) between the two regions.

We wondered if the bilaterally matched responses occurred preferentially in a particular neuron type. We used a classic method for identifying putative excitatory and inhibitory neurons—the width of extracellular action potentials (Suzuki and Smith, 1985; Gur et al., 1999; Frank et al., 2001; Swadlow, 2003; Povysheva et al., 2006; Hassani et al., 2009; Weir et al., 2015). Most of the BCNs in the AON and APC had broader spikes and lower spontaneous activity (Extended Data Fig. 3-1F–I), suggesting they are excitatory.

When testing our mask for cross-contamination (Fig. 1), we estimated that at most 10% of odors puffed on one side of the mask could reach the contralateral nostril. Can this cross-contamination alone explain the side-invariant responses we observed in the OC? To test this hypothesis, we first determined how much each odor from our panel needed to be diluted in the solvent to elicit a PID signal 10 times weaker than our initial dilution (5% volume/volume; Extended Data Fig. 3-1J). We then recorded individual neurons in the AON of awake mice (n = 2 mice; 120 neurons) while delivering odors on either side of the mask, both at initial (5%) and new dilutions (i.e., dilutions resulting in PID signals 10 times weaker; Extended Data Fig. 3-1K). On average, for a given side of the mask, new dilutions elicited neuronal responses 6–7 times weaker than our initial dilutions (neuronal response; mean ± SEM; for ipsilateral presentations; initial dilution, 2.1 ± 0.023 Hz; final dilution, 0.34 ± 2.7 × 10⁻³ Hz; for contralateral presentations; initial dilution, 2.5 ± 0.031 Hz; final dilution, 0.37 ± 2.5 × 10⁻³ Hz). In other words, since weak ipsilateral presentation generates responses that are much weaker than the contralateral responses we measured, contralateral cross-contamination in the mask, if any, is not sufficient to explain the presence of side-invariant odor responses.

Finally, we compared the ipsilateral and contralateral population representation in the two OC regions recorded for each odor (Fig. 3G; Extended Data Fig. 3-2A–C). Consistent with our analysis of individual BCNs, we found that unilateral population representations were significantly and strongly correlated for all odors tested in the AON and APC (Extended Data Fig. 3-2A,B; see Extended Data Table 1-2 for detailed statistics). Analyzing population correlations for each odor individually ensures that the correlations we observe are not driven by few neurons responding strongly and similarly to all odors, which would otherwise create an artificially strong positive correlation. Furthermore, a bootstrap analysis similar to what we described above confirmed that the strong correlation we observed for each odor individually was unlikely to occur by chance (Extended Data Fig. 3-2C,D). When considering each mouse separately, our conclusions held true for most odors (Extended Data Fig. 3-2E).

Together, these data indicate that the odor information arriving contralaterally to the OC strongly matches that arriving ipsilaterally.

Accurate decoding of odor identity from contralateral activity

Odor selectivity in the OC allows a population representation of odor identity, and odor identity can be decoded from the activity of a sufficient number of neurons (Bolding and Franks, 2017). If odor responses are similar for ipsi- and contralateral presentations, decoding of identity should be transferrable. To formally test this, we asked a linear classifier to decode odor identity from OC responses to stimuli in one nostril, after we trained it with OC responses to stimuli in the opposite nostril.

In brief, at each instance we created a training set by randomly removing one trial per odor (Bolding and Franks, 2017). If we were testing on the same side as we trained (e.g., train ipsilaterally, test ipsilaterally), then we tested the classifier on the trials outside of the training set. If we were testing on the opposite side (e.g., train ipsilaterally, test contralaterally), then one trial per odor from the opposite side was randomly chosen to form the test set (Fig. 4A). We performed all our decoding analyses over an odor response window of 2 s, as it maximized performance of odor decoding on the same side (Extended Data Fig. 4-1A).

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Figure 4.

Decoding odor identity and laterality. A, Diagram of the odor decoding process. B,C, Odor identity decoding per region. Mean ± SEM over 200 repetitions of the decoding process. For B, the decoder was trained with data from ipsilateral presentations. For C, the decoder was trained on contralateral odor responses. D, Side identity decoding per region. Mean ± SEM over 200 repetitions of the decoding process. For B–D, gray dotted line, Chance. See also Extended Data Figures 4-1 and 3-3.

In both the AON and APC, the decoder performed with similarly high levels of accuracy when tested on data from the same or the opposite side (Fig. 4B,C). In other words, odor identity decoding optimized with responses to stimulation from one nostril transfers very well to stimulation of the other side.

Note that the seeming decrease of decoding performance from AON to APC is most probably due to variability across mice (Extended Data Fig. 4-1B). More precisely, the three mice with overall weaker and fewer odor-evoked responses (i.e., mice AON2, APC1, and APC2) showed lower odor decoding performances, no matter the side tested (Extended Data Fig. 3-3). In addition, AON2 is the mouse from which we isolated the fewest neurons (73 neurons, while all other OC recorded mice have over a hundred neurons each; Extended Data Table 1-1). Predictably, in these same three mice, the fractions of BCNs, while significantly higher than chance, were the lowest.

Rodents are able to determine the direction of the odor stimulation at short distances (Rajan et al., 2006; Rabell et al., 2017). We asked whether population activity in a single hemisphere differs sufficiently for stimulation of ipsi- and contralateral nostril to allow decoding of intensity differences between the two sides. Side identity, or laterality, could indeed be decoded with high accuracy (Fig. 4D), which confirms that odor representations from both sides, despite similarities, remain distinct and separable.

In addition, we asked whether the way we compute odor responses could influence the decoder's results. To do so, we replicated the decoding results from Figure 4B,D, using odor responses calculated with no blank trial subtraction (Extended Data Fig. 4-2). Overall, the decoding results obtained with and without blank subtraction are very similar, suggesting that the way we built our initial metric had little impact on the decoder's performance.

Finally, we tested how BCNs affected the decoding results, by performing the decoding analysis described in Figure 4 while varying the proportion of BCNs in the dataset fed to the decoder (Extended Data Fig. 4-3). Decoding performance degraded as we removed BCNs from the dataset, which indicates that BCNs are the main drivers of the high performances of our odor decoder. In addition, same-side decoding was also affected by the removal of BCNs. This suggests that BCNs carry a sizable fraction of the total odor information, presumably because of stronger responses. Lastly, side identity could be decoded with high accuracy, even in the absence of BCNs, which confirms that the odor response profiles from both sides remain distinct, even in the noncorrelated population.

Together, our data indicate that odor decoding is transferrable across sides. Ipsi- and contralateral odor representations, while distinct, share a high degree of similarity.

A computational model of bilateral matching in the OC

How does one OC respond so similarly to inputs from two distinct routes/nostrils? So similarly, in fact, that a linear classifier trained on one set of representations can decode the other?

An appealingly simple resolution might suggest itself based on recent theoretical work. It has been shown that if two correlated representations are projected through the same random matrix, the output representations are also correlated (Babadi and Sompolinsky, 2014; Schaffer et al., 2018). Thus, one could hypothesize that any interhemispheric projection between two OCs could preserve the structure inherited from the underlying OB representations, hence explaining the similarity. However, this argument is insufficient, as illustrated in Figure 5. The correlations in glomerular neural representations of the 15 odors used in our study are shown in Figure 5B. These correlations are partially preserved when projected through two different random matrices (to represent the OB to OC projections of each hemisphere; Fig. 5C, top and bottom block diagonals). However, the two OC hemispheres connected with random projections will not yield correlated responses to the same odor presented to the left or right side (Fig. 5C). In the extended data (Extended Data Note 5-1) we show that, even in the limiting case where the response of ipsi- and contralateral cortices are identical, unstructured interhemispheric connectivity ensures that the responses of one cortex to odors presented in different nostrils will be uncorrelated. Hence, there must exist some structured connectivity that is aligning the cortical responses (Fig. 5D; note the much higher similarity values in the two off-diagonal blocks).

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Figure 5.

Structure is necessary for alignment between responses to different nostrils. A, Odor tuning of 50 randomly selected glomeruli. B, The OB odor–odor cosine similarity matrix measured using calcium imaging. Color scale at right applies to panels B–D. C, We modeled the two OCs and connected them using a random matrix (see Materials and Methods), the correlations between odors from the same nostril are preserved, but correlations between nostrils are completely lost (quadrants pointed to by red arrows and red dotted squares). D, Including a structured cross-cortical connectivity produces correlations between ipsi- and contralateral odors. See also Extended Data Note 5-1.

We then asked what type of structured interhemispheric connectivity is sufficient to achieve the observed tight alignment of responses from different nostrils. Through computational modeling, we tested a simple and plausible model for structured matching, a Hebbian connectivity matrix that links together the same-odor representations in each hemisphere. We combined this Hebbian matrix (G_Struct) with a random matrix (G_Rand), which models unstructured elements of connectivity and whose elements are drawn independently from a Gaussian distribution. We vary the degree of structure using a parameter α. Explicitly,G=αGStruct+(1−α)GRand. The parameter α took values between 0 and 1 with α = 0 corresponding to purely random connectivity and α = 1 to purely structured connectivity. The random and Hebbian components were scaled appropriately such that α represents the proportion of contralateral input magnitude that is formed by structured connectivity.

Our modeling strategy began by creating a cortical representation of odors presented in the ipsilateral nostril, based on the AON. Random OB-to-OC connectivity indicates that each cortical olfactory neuron samples a random subset of glomeruli. This implies that the input to each cortical neuron is statistically independent and that the response of one cortical neuron to different odorants can be modeled as a thresholded multivariate Gaussian whose covariance matrix can be extracted from activities in the OB (Fig. 6A; see Materials and Methods). We validated this model of a single AON against neuronal recordings: our model replicated the population statistics remarkably well with minimal parameter adjustment (Fig. 6B–D; Extended Data Fig. 6-1A–C).

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Figure 6.

Modeling olfactory cross-cortical connections. A, Diagram of the model. B–D, Model validation. Contralateral odor responses from the model are overlaid with actual contralateral AON responses (Extended Data Fig. 2E–G). E–J, Various measurements of cross-cortical alignment from the model. E, Contra- versus ipsilateral responses for random (α = 0) and semistructured (α = 0.42) projections. F, Contra- versus ipsilateral response correlations R for various α values. G, The percentage of BCNs for various α values. H, Odor decoding accuracy for random (α = 0) and semistructured (α = 0.42) projections. Red, Same as Figure 3B, AON, “test contra.” I, Odor decoding accuracy for various α values. J, Side decoding accuracy for various α values. For E–H, measurements from the model were calculated by sampling 385 neurons 200 times. The best fit α (0.42) was found by comparing to AON data (n = 385 neurons from 3 mice). See also Extended Data Figures 6-1 and 6-2.

We then linked two simulated AONs using the connectivity matrix G. The computational analog of the cortical representations of an odor presented contralaterally is the representation after mapping through the interhemispheric matrix, G. Thus, by comparing the simulated and measured alignment of ipsi- and contralaterally presented odors as we vary α, we can ask if this simple Hebbian structure is sufficient to recapture the degree of alignment observed.

We compared the alignment using four metrics: the overall correlation of odor population representation across sides (Fig. 6E,F; similar to Fig. 3G), the fraction of BCNs (Fig. 6G; similar to Fig. 3B), the accuracy of odor identity decoding (Fig. 6H,I and Extended Data Fig. 6-1D; similar to Fig. 4B,C), and the accuracy of side identity decoding (Fig. 6J; similar to Fig. 4D).

The four computed measurements best matched our actual AON neuronal recordings with a nonzero α (∼0.4). This result held true, even when we fitted each animal separately (AON1 α = 0.3; AON2 α = 0.1; AON3 α = 0.3; APC1 α = 0.1; APC2 α = 0.1; APC3: α = 0.25; APC4 α = 0.35). In summary, for all animals, α was greater than zero.

This result did not vary when we changed the size of the modeled OC population (Extended Data Fig. 6-1E–H). This suggests that a significantly Hebbian connectivity between cortices is sufficient to explain the observations.

We chose this particular structured connectivity, the 15 odor Hebbian matrix G_Struct, for its appealing simplicity and biological plausibility. For example, early in life, the animal might have smelt these odors in both nostrils and associatively matched the responses between hemispheres. However, there are many other sufficient alignment schemes that do not rely on having experienced specifically these 15 odors; we implemented two such examples in the supplementary material. The first uses a set of Hebbian matching experiences that span the subspace in which the 15 odorants lie. Roughly six of these are needed to achieve similar levels of alignment (Extended Data Fig. 6-2G–J) showing that a smaller number of more general early learning experiences could also explain the alignment seen in the data. The second technique uses singular value decomposition to create a low-rank approximation of G_Struct; again, a rank of about 7 is necessary to match the data (Extended Data Fig. 6-2C–F). Effectively, any connectivity that links same-odor representations in each hemisphere together will be able to match the alignment seen in the data.