Do oscillations in the OB encode odorant concentration ranges and does the accuracy of encoding change as mice learn to discriminate in the go-no go task? We used tetrodes to record LFP oscillations in the OB of mice learning to associate a range of odorant concentrations with a water reward (go-no go odor concentration range task). In this task, mice which licked at least once in each of four 0.5 s time segments when the rewarded stimulus (S+) was presented received a water reward and the response was classified as a Hit (Figures 1A–C). A lack of licking in any of the time segments in the S+ segment was classified as a Miss. The mouse did not receive a reward if it licked for the unrewarded (S-) stimulus. Licking during S- was classified as a false alarm (FA), and correctly refraining from licking during S- trials was classified as a correct rejection (CR) (Figure 1C). We presented the animal with six different odorant concentrations generated by bubbling air into mineral oil containing different liquid dilutions (c_liq) of either isoamyl acetate or acetophenone (0.033, 0.1, 0.33, 1, 3.3, and 10%). The rewarded stimulus was either the higher concentrations (1–10% c_liq, Figure 1C) or the lower concentrations (0.033–0.33%). Figure 1D shows examples of behavioral performance in this go-no go task. Behavioral performance was quantified by the percent correct responses (both Hits and CRs) computed in a sliding window of 20 trials (see Methods). Mice learned to differentiate between concentration ranges regardless of whether the rewarded stimulus was the high (Figure 1Di) or the low concentration range (Figure 1Dii, also see Supplementary Figure 1). We focused on characterizing differences in OB oscillations between naïve animals (≤65% correct behavioral performance, green points in Figure 1D) and proficient mice (≥80% correct, magenta points in Figure 1D).

Previous studies of LFP oscillations found strong coupling of gamma and beta oscillation bursts within specific phases of the lower frequency theta oscillations (Buonviso et al., 2003; Rojas-Libano et al., 2014; Losacco et al., 2020) and that these theta phase-amplitude coupled (PAC) gamma/beta oscillations encode for odorant contextual identity (Losacco et al., 2020). To quantify these phase-coupled oscillations we performed PAC analysis (Tort et al., 2010). We extracted the phase of the low frequency theta oscillation using a Hilbert transform of the theta-filtered LFP trace, thereby identifying the peak and trough of theta (Figures 1E,F,ii,iii). We estimated the amplitude of the theta-referenced fluctuations of beta and gamma oscillations by computing the theta envelope of the beta and gamma LFP using a Hilbert transform (Figures 1E,F,iv, yellow line).

We have previously shown that tPAC changes as an animal learns to discriminate two distinct odors (Losacco et al., 2020). Here, we surveyed tPAC in the OB in response to odor concentrations and we found a difference in the strength of tPAC between the rewarded and unrewarded concentrations once the animals became proficient. Figure 2A shows in pseudocolor the amplitude of the gamma oscillations as a function of theta phase for the different trials in a session where the animal was proficient (percent correct ≥ 80%, see Figure 2B for percent correct as function of trial for this session). For this session the amplitude of the gamma oscillations peaked at about 280° for S+, while for S- the peak of the gamma amplitude shifted from trial to trial (red peak in Figure 2A and peak angle in Figure 2D). The strength of tPAC appeared to be stronger for S+ than for S- (Figure 2A). We quantified tPAC using the modulation index, a measure of how localized high frequency firing is within the phase of theta oscillations (Tort et al., 2010). In previous studies using a go-no go odor discrimination task, tPAC modulation index fell between 0.005 and 0.04 for the OB (Losacco et al., 2020). For this example session, we found that the modulation index was larger for the rewarded stimulus (in this case the high concentration range) (Figure 2C). A gerneralized linear model (GLM) analysis for the modulation index indicated that there was a statistically significant difference between S+ and S- (p < 0.001, 77 trials, 71 d.f., F-Statistic 18.3, p-value for the model <0.001, Supplementary Table 1). Furthermore, as shown in Figures 2A,D, the theta phase for the largest amplitude for the gamma oscillation (the peak angle) appeared to vary to a larger extent for the unrewarded stimuli. This means that a downstream observer quantifying the amplitude of gamma oscillations at a specific fixed theta phase (e.g., 280°) would be detecting high amplitude gamma power for the S+ odorant compared to S- because of the higher modulation index and the lower peak angle variance for the rewarded stimulus.

We next analyzed whether the modulation index changed as the animal learned to discriminate odorant concentration ranges in the go-no go task. For both beta and gamma tPAC we found that the modulation index increased when the animals learned to differentiate the concentration ranges and differed between rewarded and unrewarded concentration (Figures 2E,F, also see Supplementary Figure 2 for an example of tPAC for a session where the mouse was naïve). For the beta tPAC, a GLM found significant differences between odorant concentrations and between rewarded vs. unrewarded stimuli and for the interaction between naïve vs. proficient and concentration (Figure 2E, p < 0.001, 2,784 observations, 2,776 d.f., F-statistic = 61.2, p < 0.001, nine mice, Supplementary Table 2). The statistical significance of the interaction between naïve vs. proficient and concentration indicates that the effect of one causal variable on an outcome depends on the state of a second causal variable (e.g., in this case in Figure 2E the difference between naïve and proficient for S+:high is larger for the lower concentrations). For beta tPAC there was no significant difference between naïve and proficient (p > 0.05). For gamma tPAC, a GLM found significant differences for the modulation index between odorant concentrations, between rewarded vs. unrewarded stimuli, and between naïve vs. proficient mice (Figure 2F, p < 0.001, 2,784 observations, 2,776 d.f., F-statistic = 47.5, p < 0.001, nine mice, Supplementary Table 3). Finally, we quantified the variation in the peak angle to determine whether the peak angle shifted on a trial by trial basis as found for S- in Figure 2A. Peak angle variance was higher for the unrewarded odorant concentration range for both beta and gamma tPAC (Figures 2G,H). For the beta tPAC, a GLM finds for the peak angle variances statistically significant differences between odorant concentrations, between naïve vs. proficient and between rewarded vs. unrewarded stimuli (Figure 2G, p < 0.001, 2,784 observations, 2,776 d.f., F-statistic = 100, p < 0.001, nine mice, Supplementary Table 4). For gamma tPAC, a GLM finds statistically significant differences between odorant concentrations, naïve vs. proficient and between rewarded vs. unrewarded stimuli (Figure 2H, p < 0.001, 2,784 observations, 2,776 d.f., F-statistic = 99.2, p < 0.001, nine mice, Supplementary Table 5).

Therefore, the strength of tPAC and peak angle variance changed as the animal learned to discriminate between odor concentration ranges. Gamma tPAC tends to become stronger for the rewarded stimuli as the animal learns and the peak angle variance became larger for the unrewarded stimuli compared to the rewarded odorant concentrations. For beta tPAC, we found similar changes in the peak angle variance, and tPAC tended to become stronger for the unrewarded odorant. These observations raised the question of whether the power of beta or gamma oscillations within a theta phase window could be used to discriminate between concentration ranges.

In earlier studies of the go-no go task where the animal learned to differentiate odorants we found that peak gamma tPRP conveyed more information on the rewarded stimulus than trough gamma tPRP (Losacco et al., 2020). We proceeded to quantify the power for beta and gamma oscillations referenced to the peak or trough of the theta LFP in the go-no go concentration task. Upper panels in Figure 3 show examples of the time course per trial for the power distribution estimated using a Morlet wavelet analysis. A Morlet wavelet is defined as a sine wave tapered by a Gaussian, and in the Morlet wavelet analysis LFP oscillations are fit to subsets of Morelet wavelets of different frequencies thereby quantifying the contribution of these wavelets to the oscillations. As performed with fast Fourier transform wavelet analysis allows evaluation of the power of LFP oscillations at different frequencies. However, unlike fast Fourier transform wavelet analysis is able to follow changes in power that occur in the theta frequency. The bottom panels show the gamma power referenced to the peak (red traces) or the trough (blue traces) of the theta LFP oscillation. Two stimuli belonging to either the unrewarded low concentration range (0.1% c_liq of acetopheonone) or the rewarded high concentration range (3.3% c_liq) elicited relatively small changes in tPRP for the naïve animal (Figures 3A,B). In contrast, for the proficient animal the rewarded 3.3% c_liq stimulus elicits a substantial increase in peak-referenced tPRP (Figure 3D, red trace) and the unrewarded 0.1% c_liq stimulus elicits a decrease in tPRP (Figure 3C, red trace), while the trough-referenced changes in tPRP are small (blue traces in Figures 3C,D). Similar results are shown in Figures 3E–H for a session where the rewarded stimuli were the low concentration odorants.

We proceeded to evaluate the difference in odorant-elicited changes in tPRP between naïve and proficient mice for beta and gamma tPRP. Furthermore, we asked whether these changes in tPRP were similar when the rewarded odorant was either the high or the low concentration range of odorant stimuli. When the high concentration range was rewarded there was a clear increase in beta tPRP for the rewarded stimulus, and a decrease for the unrewarded stimulus for proficient compared to naïve animals (Figure 4A). These changes in beta tPRP were similar for peak- and trough-referenced tPRP (Figure 4Ai vs. Figure 4Aii). When the rewarded stimulus was the low concentration range there was also a clear decrease in beta peak or trough-referenced tPRP for the unrewarded stimuli (in this case the high concentration odorants), but for the unrewarded high concentration range the proficient vs. naïve difference increased as the concentration increased, and there was not a substantial difference in tPRP between naïve and proficient for the rewarded low concentration range (S+, Figure 4B). For beta tPRP we found statistically significant differences between rewarded vs. unrewarded stimuli, proficient vs. naïve and for concentration (GLM, p < 0.001, 5,568 observations, 5,552 d.f., F-statistic = 525, p < 0.001, nine mice, Supplementary Table 6, Figures 4A,B), and there was no statistical significance between peak and trough tPRP (GLM, p > 0.05, 5,568 observations, 5,552 d.f., F-statistic = 525, p < 0.001, nine mice). Post-hoc ranksum or t-tests yielded differences between naïve and proficient for all concentrations for the experiments where the high concentrations were rewarded, but did not yield significant difference for the lowest two concentrations when the low concentrations were rewarded (asterisks in Figures 4A,B, p-values < pFDR. pFDR was 0.044 for peak beta tPRP, 0.043 for trough beta tPRP).

In contrast, there was a clear difference between peak-referenced and trough-referenced gamma tPRP in their dependence on learning (Figures 4C,D). When the high concentration range was rewarded there was a clear increase for peak gamma tPRP for the rewarded stimulus, and a decrease for the unrewarded stimulus as the animal learned to discriminate odorant concentrations (Figure 4Ci). Interestingly, the learning induced changes in gamma tPRP did not take place for trough-referenced tPRP (Figure 4Cii). Similar to theta-beta tPRP, when the rewarded stimulus was the low concentration range there was also a clear decrease in peak-referenced gamma tPRP for the unrewarded stimuli, and the proficient vs. naïve difference increased as the concentration increased (Figure 4Di). There were small changes in trough-referenced gamma tPRP (Figure 4Dii). For the gamma tPRP (Figures 4C,D) there was a significant differences between rewarded vs. unrewarded stimuli, proficient vs. naïve, concentration and peak vs. trough (Figures 4C,D, GLM, p < 0.001, 5,568 observations, 5,552 d.f., F-statistic = 525, p < 0.001, nine mice, Supplementary Table 7).

Thus, as the animal learns to discriminate rewarded and unrewarded odor concentration ranges (transitions from naïve to proficient), both beta and gamma tPRP increase. This raises the question whether the proficient animal's tPRP encodes the identity of the rewarded stimulus irrespective of odor concentration. Surprisingly, when the rewarded stimulus is the low concentration range the tPRP depends on odorant concentration, whereas we did not see this effect when the rewarded stimulus is the high odorant concentration range.

We proceeded to evaluate the discriminability of per trial tPRP values comparing tPRP for trials with rewarded stimuli vs. trials with unrewarded stimuli using receiver operating characteristic (ROC) analysis (Fawcett, 2006). Figures 5A,B show ROC analysis for two concentration pairs for a proficient mouse engaged in a go-no go session where the high concentration range was the rewarded stimulus. First, we checked whether animals could differentiate between odor concentrations within the rewarded concentration range. The gamma peak tPRP histograms for 10 and 3.3% c_liq (both S+) overlap (Figure 5A) and, as expected, the ROC curve falls along the diagonal, indicating that tPRP can not be used to distinguish these two concentrations. In contrast, for c_liq 10% (S+) and 0.033% (S-) the gamma peak tPRP histograms are largely non-overlapping, reflecting better ability to discriminate as the ROC curve rises away from the diagonal. We defined the area under the ROC curve (auROC) as 0 when the curve falls along the diagonal and the stimuli cannot be differentiated and 0.5 when it lays along the top left axes, when the tPRP values are distinct for the two stimuli. For the ROC in Figure 5A the auROC is 0.02 and for the ROC in Figure 5B it is 0.38. Thus, ROC quantifies the extent of overlap between the two distributions.

To quantify the difference between tPRP distributions for all combinations of two odorant concentrations we calculated auROC for each electrode, for each of nine mice for trials when the mouse was naïve or proficient. The average auROC values for all combinations of odorant concentrations for theta-gamma tPRP are shown in pseudocolor in Figures 5C–F. To gauge the differences in auROC for different pairs of odorant concentrations, we display the average auROC in a bar graph and individual auROCs per electrode per mouse in a violin plot (Figures 5G,H). We group concentration pairs in the bar graph/violin plot as those within the high or low concentration ranges (labeled “within high” and “within low”) or the pairs with one concentration belonging to the high or low concentration ranges (labeled “between”). We found a large increase in auROC for both beta and gamma for the between group when the animals become proficient (compare Figures 5C–F panels i,iii with panels ii,iv and in Figures 5G,H compare green with magenta bars). Interestingly, the auROC does not differ between within low and within high when the rewarded stimulus is the high concentration range (left panels in Figures 5Gi,ii,Hi,ii). However, within high auROCs are higher than within low auROCs when the rewarded stimulus is the low concentration range (left panels in Figures 5Gi,ii,Hi,ii). This indicates that in the latter case there is information on concentration in the within high group tPRP. When we asesssed beta tPRP auROC scores with a GLM, we noted significant differences for proficient vs. naïve and high S+ vs. low S+ (Figure 5G, p < 0.001, 17,888 observations, 17,964 d.f., F-statistic = 1,180, p-value for F-statistic < 0.001, Supplementary Table 8). There was no significant difference between peak and trough (p > 0.05). A GLM for the gamma tPRP auROC yielded significant differences for proficient vs. naïve, peak vs. trough and high S+ vs. low S+ (Figure 5H, p < 0.001, 17,888 observations, 17,964 d.f., F-statistic = 880, p-value for F-statistic < 0.001, Supplementary Table 9). Asterisks in Figures 5E,F denote significant post-hoc statistical difference assessed with either t-test or ranksum tests corrected for multiple comparisons (pFDR = 0.039 for Ei, 0.04 for Eii, 0.036 for Fi and 0.045 for Fii).

In summary, auROC analysis indicates that as the animal learns the tPRP for rewarded vs. unrewarded stimuli become different. In addition, when the low concentration odorants are the reinforced stimuli the tPRP values within the high concentration (S-) odorants maintain discriminability, albeit with a lower auROC compared to auROCs quantified for concentrations belonging to the rewarded and unrewarded groups. The fact that there were differences in auROC when the rewarded stimulus was either the high or low concentration range raised the question whether there were differences in decoding accuracy between these conditions.

If changes in tPRP are strongly related to learning, a simple classifier should be able to accurately discriminate between rewarded and unrewarded conditions. To test this, we used linear discriminant analysis (LDA). LDA places a hyperplane in n dimensional space to separate different categories. We trained the LDA algorithm to differentiate between rewarded and unrewarded stimuli using the tPRP recorded by the 16 electrodes in all trials minus one, and then asked whether the trial that was left out belonged to the reinforced stimulus group. As a control, the algorithm was trained after shuffling the identity of reinforced stimulus for each trial. Figures 6A,B show the time course for the performance of the LDA decoder for beta and gamma tPRP (n = 7 mice). The performance diverged strongly from the shuffled control shortly after odorant addition for proficient animals and reached levels above 70% by the end of odorant presentation (Figures 6Aii,Bii). In contrast, LDA performance did not increase appreciably during odorant exposure when the mice were naïve (Figures 6Ai,Bi). Decoding performance was higher for peak tPRP for the gamma tPRP, but not for the beta tPRP (compare Figures 6Aii,Bii). We quantified the performance of the decoder by calculating the area under the performance curve (AUC) normalized such that when the performance remains at 50% the AUC is zero and when the performance increases to 100% when the odorant is added the AUC is one. AUC values are shown for all conditions in Figure 6C (beta) and Figure 6D (gamma). AUC LDA performance for beta tPRP was significantly different (Figure 6C) for proficient vs. naïve or shuffled (P < 0.001) and for high S+ vs. low S+ (GLM, p < 0.05, 88 observations, 76 d.f., F-statistic = 34.3, p-value for F-statistic < 0.001, n = 8 mice, Supplementary Table 10). Peak and trough differences were not significantly different (GLM, p > 0.05). AUC for the LDA calculated for the gamma tPRP (Figure 6D) yielded significant differences for proficient vs. naïve or shuffled and peak vs. trough (GLM, p < 0.001, 88 observations, 76 d.f., F-statistic = 29.2, p-value for F-statistic < 0.001, Supplementary Table 11), but not for and high S+ vs. low S+ (GLM, p > 0.05).

We complemented the analysis of the performance of the LDA decoder by asking whether the decision time differs between the behavior (differential licking for the rewarded vs. unrewarded odorants) and the decoder (differential classification of the stimulus as rewarded vs. unrewarded by the LDA algorithm). As in previous studies we assessed the difference in licks or decoder classification by calculating the p-value for the difference between reinforced stimulus trials and unreinforced stimulus trials with a ranksum test (Losacco et al., 2020). Figures 6E,F show the time course for this p-value calculated for licks (black), peak tPRP (red), and trough tPRP (blue) when the reinforced stimulus was the high concentration range. As expected, the p-value for licks dropped quickly below 0.05 after addition of the odorant when the mice were proficient (Figure 6Eii or Figure 6Fii, black line). In contrast, when mice were naïve the p-value for licks dropped slowly after odorant addition and dropped more sharply after the mice were reinforced with water (Figure 6Ei or Figure 6Fi, black line). For beta tPRP decoding both the peak and trough tPRP p-values displayed a similar sharp drop below p = 0.05 after odorant addition when the animal was proficient (Figure 6Eii, red and blue lines), while the drop below 0.05 was more pronounced for the p-values calculated with the peak gamma tPRP (Figure 6Fii, red and blue lines).

The decision time was estimated as the time when the p-value for the ranksum test dropped below 0.05. The p-value was calculated with a ranksum test for licks (scored 1 for lick and 0 for no lick) for all trials for each time point. This allows for a reliable determination of decision time when the p-value falls monotonically below 0.05 (Doucette and Restrepo, 2008). We found that decision times for both licks and peak or trough tPRP decoding became shorter when the mice became proficient. A GLM for the decision times for the LDA calculated for the beta tPRP yielded significant differences for proficient vs. naïve and for the interaction between proficient and naïve and for high S+ vs. low S+ (Figure 6G, P < 0.001, 87 observations, 75 d.f., F-statistic = 26.6, p-value for F-statistic < 0.001, n = 8 mice, Supplementary Table 12), but did not yield a statistical significance between peak and trough (p > 0.05). When comparing decision times for the LDA calculated for the gamma tPRP were significantly different for proficient vs. naïve conditions (GLM, p < 0.001, 87 observations, 75 d.f., F-statistic = 19.6, p-value for F-statistic < 0.001, Supplementary Table 13). Interestingly, for proficient mice, post-hoc t or ranksum tests indicated that there was a significant difference for decision times calculated for tPRP decoding compared to lick decision times when the reinforced stimulus was the low concentration range, but not when the reinforced stimulus was the high concentration range Figures 6G,H. Thus, the speed of decision making differs when the rewarded stimulus is the low or high concentration range.

The differences in tPRP and decoding performance between sessions where the rewarded stimulus were the high vs. the low concentration odorants (Figures 4–6) raised the question whether the responses of the animals to the different odorant concentrations also differed. When we plotted the percent correct responses in the go-no go task as a function of odorant concentration we found that when the high concentration range was rewarded there were small differences in behavioral performance between the high and low odorants (vermillion bars in Figure 7A). In contrast, when the low concentration odorants were rewarded, the performance was high for the low concentration odorants, and changed as a function of concentration for the high concentration range with the lowest performance being the 1% c_liq (sky blue bars in Figure 7A). There was a significant difference for the interaction between reward for concentration and odorant dilution (GLM, p < 0.001, 84 observations, 80 d.f., F-statistic 4.98, p < 0.01, n = 6 mice, Supplementary Table 14). Interestingly, when we plotted the performance for decoding the stimulus from tPRP averaged between 2 and 2.5 s after odorant addition we found the same trend for theta-referenced beta and gamma LFP power (Figure 7B through Figure 7E). Thus, when the high concentration odorants were rewarded there were small differences in performance (vermillion bars in Figure 7B through Figure 7E) while when the low concentration odorants were rewarded there was a decreased performance for the 1 and 3.3% c_liq (sky blue bars in Figure 7B through Figure 7E). For the trough-referenced beta tPRP (Figure 7B) there was a significant difference for reward for high vs. low concentration (GLM, p < 0.05) and odorant dilution (GLM, p < 0.05) and for the interaction between reward for high vs. low concentration and odorant dilution (GLM, p < 0.01, 84 observations, 80 d.f., F-statistic 4.7, p < 0.01, n = 6 mice, Supplementary Table 15). For the peak-referenced beta tPRP (Figure 7C) there was a significant difference for reward for high vs. low concentration (GLM, p < 0.01) and odorant dilution (GLM, p < 0.05) and for the interaction between reward for high vs. low concentration and odorant dilution (GLM, p < 0.01, 84 observations, 80 d.f., F-statistic 4.7, p < 0.01, n = 6 mice, Supplementary Table 16).

Trough-referenced gamma tPRP had no statistical differences (GLM, p > 0.05, 84 observations, 80 d.f., F-statistic 0.37, p > 0.05, n = 6 mice, Supplementary Table 17) and there were no significant differences in post-hoc t or ranksum tests corrected for multiple comparisons (p < pFDA = 0.0004). For the peak-referenced tPRP there was a significant difference for reward for high vs. low concentration (GLM, p < 0.01, 84 observations, 80 d.f., F-statistic 2.8, p < 0.05, n = 6 mice, Supplementary Table 18). Finally, we found a linear relationship between decoding performance and behavioral performance (Figures 7F,G) indicating that tPRP signal processing in the OB may contribute to behavioral performance in the go-no go odorant concentration task.

We found an asymmetry in the false alarm rates between the high and low concentration rewarding conditions, which is reflected in the OB activity (Figure 7). To gain insights on the underlying mechanism, we constructed a simple model of the concentration discrimination task. In the model, the perceived intensity follows a Gaussian distribution centered around the true intensity (curves in Figure 8A). In the S+: high condition, for instance, the model makes a go decision if the perceived intensity is larger than the boundary shown in vermilion line, or vice versa (cyan line). Here, we used different boundaries for high/low rewarded conditions, and the variance in the perceived intensity was set to scale with the mean intesntiy (blue to yellow curves).

The model reproduced the behavioral result well-upon parameter fitting (Figure 8B). In particular, it qualitatively reproduced the asymmetry between the correct rejection rates in the two task conditions, though it overestimated the correct rejection rate under a very low odor concentration. The model supports the hypothesis that animals use a single boundary for concentration discrimination task, but it also suggests that, in go/no-go tasks, the boundary should be different depending on whether high or low concentrations are rewarded.

The study was performed with male 6–11 months old OMP-hChR2V mice (Li et al., 2014) (eight mice) and one C57BL/6 mouse (Jackson stock number: 000664). All animal procedures were performed under approval from the Institutional Animal Care and Use Committee (IACUC) at the University of Colorado Anschutz Medical Campus under guidelines from the National Institutes of Health.

Surgery was performed under approval from the Institutional Animal Care and Use Committee (IACUC) at the University of Colorado Anschutz Medical Campus, using aseptic technique. As per Li et al. (2015), tetrode boards (EIB-16, Neuralynx) were populated with four tetrodes consisting of four 12.5 μm nichrome wires coated with polyimide (Sandvik RO800). Electrode tips were electroplated to 0.2–0.4 MΩ impedance.

Two-months-old male mice were anesthetized with 5% isoflurane in oxygen. Intraperitoneal ketamine/xylazine (100 and 10 mg/kg, respectively) was then administered along with 100 μl of 2% lidocaine injected subcutaneously over the skull. After the mouse was found to be unresponsive to a toe pinch, the animal's head was then secured in the stereotaxic apparatus (Narishige SR-5M-HT) and the skull was leveled (≤50 μm difference DV between bregma and lambda). Gentamycin ophthalmic ointment was applied to the eyes to maintain hydration. After incising the skin overlaying the skull, the periosteum was cleared with 15% H₂O₂. A manipulator (Sutter MP-285) was zeroed at bregma and midline and the target location for OB implantation was marked with respect to bregma (AP +4.28 mm, ML +0.5 mm).

A craniotomy performed at this site (Marathon III drill) exposed dura mater which was removed prior to implantation. Another craniotomy was performed more caudally for implantation of one ground screw (Plastics1 00-96 × 1/16). The tetrode was positioned above the craniotomy over the OB while the ground wire was wrapped around the ground screw with the connection coated in silver paint (SPI Flash-Dry silver conductive paint). After securing the ground screw to the skull, the tetrodes were lowered into position at the rate of 1 mm/minute (AP +4.28 mm, ML +0.5 mm, and DV 1.0 mm). After reaching the target depth, the tetrode was adhered to the skull with C&B Metabond, followed by Teets “Cold Cure” dental cement. After curing (10 min), the tetrode was detached from the manipulator, the animal was removed from the stereotax and received subcutaneous injections of carprofen (10 mg/kg) and buprenorphine (0.05 mg/kg) and recovered on a heating pad kept at 37°C. The mice were monitored daily and received additional carprofen injections daily for the first 2 days postoperatively.

Mice were water deprived until they reached 80% normal body mass. Then they were placed into the Slotnick olfactometer (Bodyak and Slotnick, 1999; Li et al., 2015) chamber where they could move freely. All mice were first trained to lick the water spout to obtain water in the presence of odor (1% isoamyl acetate in mineral oil, v/v) in the “begin” task (Slotnick and Restrepo, 2005). Training in the begin task required 2–5 sessions of 50–200 trials. Each session was run until the animal became satiated. Subsequently they learned to discriminate 1% isoamyl acetate (S+) vs. mineral oil (S-) in the “go no-go” task (Doucette et al., 2011; Li et al., 2015), followed by learning to discriminate high from low odorant concentrations. For the go-no go odorant concentration discrimination task one of six odorant concentrations was presented randomly in each trial. Odorized air was generated by bubbling air at 50 ml/min through mineral oil with either isoamyl acetate or acetophenone diluted in six logarithmically-spaced v/v liquid dilution (c_liq): 10, 3.3, 1, 0.33, 0.1, and 0.033% (Wojcik and Sirotin, 2014). The high odorant concentration range was 10, 3.3, and 1% c_liq and the low odorant concentration range was 0.33, 0.1, and 0.033% c_liq.

The go-no go task was performed as described by Losacco et al. (2020) with the exception that the rewarded stimulus was either the high or low concentration odorants. Mice self-initiated trials by poking their head into the odor delivery port, breaking a photodiode beam (Figure 1A). During reinforced odorant delivery (lasting 2.5 s) they must lick a water delivery spout at least once during each of four 0.5 s-long response areas in order to register the decision as a Hit (Figure 1B). Licks were detected as electrical connectivity between the water spout and the ground plate on which they stand (Slotnick and Restrepo, 2005). If the mice licked during a rewarded odorant trial, they received ~10 μl water reinforcement. The mice learn to refrain from licking for the unrewarded odorant due to the unrewarded effort of sustained licking. This task was not designed to require the mouse to respond as soon as possible. The proficient mouse starts licking at the beginning of the trial and for correct rejections the last lick that takes place 0.3–0.7 s after odorant onset (Figures 6E,F). Rather, this task was designed to make the mouse aware that the two stimuli have different valences, and allow the mouse to take it's time to make the decision.

Mice were presented blocks of 20 trials, with 10 S+ and 10 S- trials presented at random. Animals performed as many as 10 blocks per session. Sessions were terminated when animals demonstrated satiety/disengagement from the task or when they performed at or above 80% correct discrimination in three or more blocks in a session. Supplementary Figure 1 shows which of the two odorants (isoamyl acetate or acetophenone) and which odorant group (high vs. low concentrations) was the reinforced stimulus for each go-no go session for each of the nine mice. Data were analyzed for all odorant sessions. Data were analyzed within two performance windows: when the animal was performing below 65% (naïve) or above 80% (proficient). The results obtained with the two odorants were similar and the results from both odorants were merged for data analysis.

Odor stimulus delivery time was measured with a photoionization detector (miniPID, Aurora Scientific). Figure 1, Supplementary Figure 1 of Losacco et al. (2020) shows the time course for odorant concentration measured at the odor spout. The time difference between valve opening and detection of odor at the odor port was between 66 and 133 ms, depending on which olfactometer was used. The minimum intertrial interval in all the sessions for this study was 13.5 s. Using an multi exponential fit of the time course for odorant concentration measured with the PID we estimate that the largest residual odorant is equivalent to a 0.00008% c_liq, two orders of magnitude smaller than the smallest c_liq used in the concentration series indicating that the olfactometer does not compromise concentration delivery. Finally, after valve opening the odorant raised sharply (0.12 s half time) and then increased more slowly for the rest of the odorant application interval (2.16 s half time) (Figure 1, Supplementary Figure 1 in Losacco et al. (2020). As a result, the mouse is making a decision on the dynamic change in concentration as opposed to a step change in concentration.

Extracellular potentials from the four tetrodes were captured and digitized at 20 kHz on the RHD2216 amplifier of the Intan RHD2000 Evaluation System with a 1–750 Hz bandpass filter. Information on behavioral events (valve times, mouse presence at the odor port) was sent through a digital line from the Slotnick olfactometer to the Intan board. Licks detected by the Slotnick olfactometer were recorded as an analog signal by the Intan board and were digitized at 20 kHz.

PAC data were processed using the Hilbert transform method described by Tort et al. (2010). Briefly, data were bandpass filtered with a 20th order Butterworth filter using Matlab's filtfilt function with zero phase shift to extract LFP in the low frequency oscillation used for phase estimation (theta, 2–14 Hz, Figures 1Eiii,Fiii) and the high frequency oscillation used for estimation of the amplitude of the envelope (either beta, 15–30 Hz, or gamma, 65–95 Hz, Figures 1E,F). Hilbert transform established the theta phase (Figures 1Eiii,Fiii) and, separately, the envelope for beta or gamma (red line in Figures 1Eiv,Fiv). To quantify the strength of tPAC we calculated the modulation index (MI) estimating the KL distance to quantify the difference between the observed beta/gamma amplitude distribution along the phase of theta from a uniform distribution. If tPAC is non-existent, MI = 0, meaning the mean amplitude is distributed uniformly over theta phases, and if tPAC is a delta function MI = 1. MI for signals measured in brain areas such as the hippocampus typically fall between 0 and 0.03 (Tort et al., 2010).

tPRP was calculated as detailed in Losacco et al. (2020) using custom Matlab code. Briefly, tPAC was calculated using the approach documented by Tort et al. (2010), as described above and summarized in Figure 1. Peak and trough theta phases are defined as the phase for maxima and minima of the tPAC distribution measured for the S+ trials. A continuous Morlet wavelet transform was used to estimate the power for the high frequency oscillations (Buonviso et al., 2003). tPRP was estimated as the power of the high frequency oscillations (beta or gamma) measured at the peak or trough of tPAC. The Matlab code used for data analysis has been deposited to https://github.com/restrepd/drgMaster.

Statistical analysis was performed in Matlab. tPAC parameters and tPRP were calculated separately per electrode (16 electrodes per mouse) for all electrodes per mouse. Statistical significance for changes in measured parameters for factors such as learning and odorant identity was estimated using generalized linear model (GLM) analysis, with post-hoc tests for all data pairs corrected for multiple comparisons using false discovery rate (Curran-Everett, 2000). The post hoc comparisons between pairs of data were performed either with a t-test, or a ranksum test, depending on the result of an Anderson-Darling test of normality. GLM is a general statistical method that includes regression and analysis of variance. Degrees of freedom and statistical significance have the same meaning in GLM as in analysis of variance and regression (Agresti, 2015). In addition, as a complementary assessment of significant differences (Halsey et al., 2015) we display 95% confidence intervals (CIs) shown in the figures as vertical black lines were estimated by bootstrap analysis of the mean by sampling with replacement 1,000 times.

Classification of trials using tPRP was accomplished via LDA in Matlab whereby tPRP for every trial except one were used to train the LDA, and the missing trial was classified by the LDA prediction. LDA, lick ranksum differences and lick rate were computed in 0.1 s bins. This was repeated for all trials and was performed separately for peak and trough tPRP, and for analysis where the identity of the odorants was shuffled. LDA and dimensionality analysis were performed either on a per-mouse basis where the input was the tPRP recorded from 16 electrodes, or on pooled mouse data where the input was the tPRP recorded from 16 × N electrodes where N is the number of mice. For pooled mouse analysis a pooled response vector was therefore created by concatenating across animals and the number of trials n, was determined by the session with the lowest number of trials for a single odorant (Chu et al., 2016). LDA decoding was not calculated for mice that did not have more than 20 trials for both naïve and proficient mice.

For a given concentration c_k∈{0.033, 0.1, 0.33, 1.0, 3.3, 10}, we modeled the perceived intensity by a random Gaussian variable x ~ N(μ_k, σ_k²), where the mean and the variance are given as μ_k = log(c_k/c_min) and σ_k² = a₁μ_k + a₂μ_k², This is because the OB activity roughly scales logarithmically with the concentration (Bolding and Franks, 2018), and its variance scales linearly with the firing rate if the activity is Poisson, and potentially more steeply if bursty (Pillow and Scott, 2012). Suppose an animal decides whether the concentration is high or low using a fixed threshold θ (Wojcik and Sirotin, 2014), the probability that the animal judges the concentration as low is given by a Gaussian cumulative distribution function Φ[(θ - μ_k)/σ_k].

We fitted this model to the behavioral data, by minimizing the mean squared error between the estimated performance from the model and the mean performance over all the mice. Minimization was performed with gradient descent from various different initial states, which robustly converged onto c_min = 0.015, a₁ = 0, a₂ = 0.0478, and the thresholds for the low and the high tasks were converged to θ_low = 4.357 and θ_high = 3.378, respectively. The simulation code is deposited at https://github.com/nhiratani/odor_concentration_classification.