Animals must modulate early sensory processing to optimize navigation of their environment (Baker et al., 2018; Pakan et al., 2018). This experience-dependent shaping involves an interplay between sensory input, behavioral state, arousal and motor activity. Neuronal activity, temporally organized by local field potential (LFP) oscillations, carries distinct information at different phases of each cycle (Jensen, 2001; Kepecs et al., 2006; Lisman and Jensen, 2013). For example, in the hippocampus different phases of the theta LFP (2–12 Hz) preferentially encode present and future spatial locations, illustrating temporal ‘chunking’ of information (Amemiya and Redish, 2018; Siegle and Wilson, 2014). Place cell preferred fields are encoded temporally through phase precession in relation to hippocampal theta oscillations (Buzsaki, 2004; Lisman, 2005; O'Keefe and Recce, 1993; Skaggs et al., 1996). Additionally, LFP oscillations in different frequency bandwidths can be related through cross frequency coupling (CFC), which can further enhance information carrying capacity (Canolty and Knight, 2010; Engel et al., 1999; Florin and Baillet, 2015; Fries, 2005).

One example of CFC is PAC, wherein the amplitude of a faster oscillation (e.g. gamma, 35–95 Hz) is related to the phase of a slower oscillation (e.g. theta, 2–12 Hz) (Chrobak and Buzsáki, 1998; Soltesz et al., 1993). PAC occurs during task engagement in rodent hippocampus (Bragin et al., 1995; Lisman and Idiart, 1995; Soltesz et al., 1993), rodent orbitofrontal cortex (van Wingerden et al., 2014), macaque auditory cortex (Márton et al., 2019), human hippocampus (Lega et al., 2016) and human visual cortex (Daume et al., 2017; Seymour et al., 2017). Interestingly, van Wingerden et al. (2014) described how theta-gamma PAC strengthens in rat orbitofrontal cortex with learning for trials in which the correct decision was made in the olfactory go no-go task.

The study of PAC in the earliest sensory processing brain areas is virtually non-existent. The olfactory bulb (OB) is an ideal location to study whether PAC is relevant to sensory processing; its intrinsic oscillatory activity is linked to odorant signal processing (Doucette et al., 2011; Gschwend et al., 2012; Li et al., 2015; Smear et al., 2011). The rhythmic activation of olfactory sensory neurons (OSNs) through breathing generates a theta-frequency (2–12 Hz) respiratory-related LFP in the target region of the OSNs, the OB, that is coherent with oscillations in downstream processing areas such as piriform cortex (PC) and hippocampus (Gourévitch et al., 2010; Heck et al., 2019; Nguyen Chi et al., 2016; Tort et al., 2018). Interestingly, PAC is present in human PC, and the respiratory phase for presentation of stimuli modulates the ability to retrieve episodic memory (Zelano et al., 2016). Downstream neural networks receiving olfactory information from the OB could be tuned to respond to sensory input at certain phases of this theta LFP (Buzsáki, 2010; Jensen, 2001) and could send back modulatory signals during other phases (Kay, 2015; Kepecs et al., 2006).

Decades of work have characterized LFP activity in the OB in various states of wakefulness (Adrian, 1950; Chery et al., 2014; Li et al., 2012) and olfactory task engagement (Gourévitch et al., 2010; Martin and Ravel, 2014). Surprisingly, this LFP signal changes in response to prior experience (Courtiol and Wilson, 2017; Gire et al., 2013). Work in the go no-go operant conditioning task where the animal learns to respond to the reinforced odorant for a water reward has revealed broadband LFP power changes for the rewarded versus the unrewarded odorant with discrimination learning (Beshel et al., 2007; Martin et al., 2004; Ramirez-Gordillo et al., 2018; Stopfer and Laurent, 1999). Additionally, changes in the balance of sensory and corticofugal inputs to OB interneurons can alter timing of beta and gamma oscillatory states, suggesting that information transfer from the OB is influenced by top-down signaling (David et al., 2015). Also, these investigators posited that slower theta oscillations gate temporal windows for sensory and centrifugal inputs to ascend and descend, respectively, suggesting an important role for PAC in gating information transfer. Since PAC exists in the OB in anesthetized (Buonviso et al., 2003) and awake, idle rats (Rojas-Líbano et al., 2014), we wondered whether PAC changes with learning, reflecting unsupervised Bayesian learning or supervised learning through top-down modulation sensory information (Hiratani and Latham, 2019), and whether encoding this information by the power of high frequency oscillations differs as a function of the phase of the theta LFP.

Here, thirsty mice implanted with tetrodes in the OB learned to associate an odorant with water reward in the go no-go task, discriminating between two monomolecular odorants (e.g. between isoamyl acetate vs acetophenone, IAAP) or between a monomolecular odorant and an odorant mixture (between ethyl acetate and a mixture of ethyl acetate and propyl acetate, EAPA). LFP was analyzed over task learning for changes in PAC and for the ability of theta phase-referenced high frequency oscillatory power—termed phase referenced power (PRP) hereafter—to encode for the perceived contextual identity of the odorant.

We demonstrate that the strength of PAC, quantified as the modulation index (Tort et al., 2010), changes for the rewarded odorant (S+) as the animals learn. Interestingly, the variance of the angle of theta with the strongest gamma oscillation (peak angle) increases for the unrewarded odorant (S-) over the course of learning. These changes in PAC raised the question whether a downstream observer focused on high frequency oscillations at different theta phases would find a difference in stimulus prediction with learning. We found that the ability to decode stimulus identity by PRP improves with task proficiency and the dimensionality, a measure of separable representation within signals, decreased as the animal learned to differentiate the odorants, suggesting that a stable and unambiguous representation of odor identity arises in PRP after learning.

The experiments were designed to study encoding of odorant identity by cross-frequency coupling. We report data obtained in two different sets of experiments that we name Exp1 and Exp2. As shown in Supplementary file 1-Table S1 the two experiments differed in electrode locations, mouse genotype, device implantation (tetrode vs. optetrode), and odorant pairs used (see also Materials and methods). Mice learned to discriminate between rewarded (S+) and unrewarded odorants (S-) presented in pseudorandomized order in the go no-go olfactory task (Figure 1A–C). The dataset is comprised of 119 recording sessions in 30 mice. The odorant pairs tested were different volatile compounds (or mixtures) whose nomenclature addresses the odorant names and the experimental set (e.g. IAAPexp1, see Supplementary file 1-Table S1 for the nomenclature). Supplementary file 1-Table S2 enumerates the total number of sessions per odorant pair, mouse, and experiment.

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In the go-no go task mice start the trial spontaneously by poking their nose into the odor spout and licking on the lick port. The odorant is delivered at a random time 1–1.5 s after nose poke (the time course for odorant concentration is shown in Figure 1—figure supplement 1). The mice must decide to either lick a waterspout at least once during each 0.5 s bin in the 2 s response area (green blocks in Figure 1B) to obtain a water reward for the rewarded odorant or refrain from licking for the unrewarded odorant (Figure 1C). We did not punish for licking for the unrewarded odorant, and mice refrain because of the effort it takes to lick. Behavioral performance was termed naïve or proficient when their performance estimated in a 20-trial window was ≤65% for naïve and ≥80% for proficient. After three 20-trial blocks of proficient performance, the session was ended; valence was reversed the next day or another odorant was tested. We recorded the LFP using four tetrodes (16 electrodes) implanted in the OB, and we analyzed the data to determine whether information carried by cross-frequency coupling can encode for the contextual identity of the odorant for naïve or proficient mice. Importantly, reversal experiments from previous studies where we switched the rewarded and unrewarded odorants have shown that the power of the LFP in the OB and mitral/tufted cell spiking encodes for the contextual identity of the odorant (is the odorant rewarded?) (Doucette et al., 2011; Doucette and Restrepo, 2008; Li et al., 2015; Ramirez-Gordillo et al., 2018). Therefore, when we refer to identity in this publication we do not mean the chemical identity of the odorant, we mean whether the odorant is rewarded or unrewarded. Finally, to evaluate the statistical significance of differences in oscillatory parameters estimated in this study the estimates were either averaged in the time period of odorant application (0.5 to 2.5 s after diverting the odorant to the odor delivery spout) or the statistical significance was evaluated for the entire time course with time points every 0.1 s using a generalized linear model (GLM, see Materials and methods). Furthermore, we complement testing of statistical significance using p values with estimation of bootstrapped confidence intervals (Halsey et al., 2015).

Peak angle variance for Theta/high gamma phase amplitude coupling increases for S- when the animals learn to differentiate odorants in the go-no go task

We proceeded to ask whether the strength of PAC, quantified by MI, and the peak angle change as the animal learns to differentiate odorants in the go-no go task. Figure 2A–F illustrates theta/high gamma PAC for all S+ and S- odorant trials in one session for a mouse proficient in differentiating the odorants. The phase amplitude plots for all the trials are shown in pseudocolor in Figure 2A, behavioral performance is shown in Figure 2B, and the corresponding normalized phase amplitude plots are shown in Figure 2C, while the mean average theta LFP is shown for one cycle in Figure 2D. There is clear (biphasic) theta phase coupling for high gamma amplitude with maxima at ~120° and 270° for S+ (Figure 2Ai and red line in 2C). This strong PAC is reflected by an MI with a mean of 0.02 with small trial to trial variance (Figure 2E, red circles), and small variation in peak phase (Figure 2F, red polar histogram). In contrast, PAC displays variable strength and phase for S- in this session (Figure 2Aii, blue line in 2E and blue polar histogram in 2F). For S- the average MI is smaller and displays large variance ranging from 0 to 0.06 (mean MI 0.014, Figure 2E, blue circles). The peak angle for S+ takes place slightly above 90 degrees and varies significantly for S- (Figure 2F). The MI and peak angle variance differ significantly between S+ and S- (MI: ranksum p value < 0.001, peak angle variance: ranksum p value < 0.05, n = 50 S- trials, 49 S+ trials).

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Browsing through PAC data for different sessions, plotted as in the example shown in Figure 2A–F, raised the question whether PAC changes over the course of learning in the go-no go olfactory discrimination task—as reported by mean MI and peak angle variance. We noticed that in sessions where the mouse learned to differentiate the odorants the phase of the peak angle became highly variable when the animal became proficient. An example is shown in Figure 2—figure supplement 1 where a mouse started the session performing close to 50% correct, and became proficient during the last portion of the session. The phase of the peak angle is highly variable for the last 20 S- trials. We proceeded to estimate mean MI and peak angle variance for all mice. The mean MI and peak angle variance was estimated as the mean in all trials within either the naïve or proficient periods for S+ and S-, calculated between 0 and 2.5 s after odorant application. Figure 2G illustrates cumulative histograms for the mean MI (i,iii) and peak angle variance (ii,iv) for theta/beta (i,ii) and theta/high gamma PAC (iii,iv) for the APEBexp1 odorant for S+ and S- odorants for trial ranges when the mice were naïve or proficient. The cumulative histograms for mean MI measured per electrode (Figure 2Gi, iii) show small yet statistically significant changes in PAC strength for both the theta/beta and theta/high gamma as the animal learns to discriminate between odorants (GLM analysis, indicates that the differences in mean MI in terms of proficiency and the event type are significant p<0.001, 896 degrees of freedom, d.f., for theta/beta and theta/high gamma, 16 electrodes per mouse, 14 mice). In addition, the circles in Figure 2Gi, iii show the per mouse mean MI. A GLM analysis did not yield significant changes for the per mouse average MI as a function of either event type or proficiency for theta/beta PAC (p>0.05, 52 d.f., 14 mice). Per mouse average MI was significant for both event type and proficiency for theta/high gamma PAC (p<0.05, 52 d.f., 14 mice). Finally, for the APEBexp1 odorant pair we found a substantial decrease in peak angle variance for S+ and an increase in peak angle variance for S- for both the theta/beta and theta/high gamma PAC (Figure 2Gii, iv GLM analysis for changes in peak angle variance for both proficiency and event type yield p<0.001, 892 d.f. for both theta/beta and theta/high gamma, 16 electrodes per mouse, 14 mice). The changes were also statistically significant when a GLM was computed for the average peak angle variance per mouse (circles in Figure 2Gii, iv, GLM p value < 0.01 for theta/beta and p<0.001 for theta/high gamma for both event type and proficiency with 52 d.f.,14 mice).

Similar differences between S+ and S- and changes when the animal became proficient were found for peak angle variance for the other odorant pairs (Supplemental Information and Figure 2—figure supplement 2). Furthermore, we evaluated the changes in PAC strength quantified as MI and peak angle variance by analyzing per-experiment mean values (averaged over odorant pairs, Figure 2H). GLM yielded significant p values for peak angle variance for theta/high gamma PAC for S+ vs. S- (<0.01, 16 d.f.) and for the interaction between S+ vs. S- and proficiency (p<0.05, 16 d.f.) (Figure 2Hiv). For a downstream observer focused on the LFP power at the peak of PAC for the rewarded odorant these changes in peak angle variance may reflect a mechanism by which the unrewarded stimulus is devalued while the rewarded odorant is valued. To our knowledge, this is the first demonstration of dynamic cross frequency interactions changing with learning for early processing in sensory systems.

Peak phase referenced power increases for S+ and decreases for S- over learning

The existence and evolution of PAC over learning alone do not demonstrate its potential utility to the animal in its decision-making process. In order to assess whether high frequency LFP power at the peak of theta oscillations changes as the animal learns we performed wavelet analysis to extract the power of high gamma (and beta) LFP referenced to specific PAC phases of theta—peak and trough (as defined in Figure 1E). We term this analysis phase-referenced (high-frequency) power, or PRP. PRP analysis allows answering the question whether the power of burst high frequency LFP evaluated at a specific phase for PAC changes as the animal learns to differentiate the odorants in the go-no go task.

In Figure 3A–C, we show how this PRP analysis was performed. Figure 3A shows Morlet wavelet LFP power analysis (Chery et al., 2014; David et al., 2015) for a single S+ trial characterized by strong, persistent theta power during and after odor delivery (related to respiration and olfactory investigation) accompanied by higher frequency power bursts whose periodicity reflects PAC. Figure 3B shows the theta (6–14 Hz)-filtered waveform (Figure 3Bi) and the Hilbert-extracted phase (Figure 3Bii; Tort et al., 2010) co-registered to the one-second epoch extracted from the wavelet LFP power plot shown in Figure 3Aii. We proceeded to extract the value of the power (in decibels) referenced to the peak or the trough of PAC measured in S+ trials (peak and trough are defined in Figure 1E). The red line in Figure 3Ci shows a clear odor-induced increase in the peak-referenced wavelet power for high gamma/theta PAC in this single trial example (Figure 3Ci, red line). In contrast, there was little change in power referenced to the trough of PAC (Figure 3Ci, blue line). Figure 3Cii shows the time course for the average peak (red) and trough (blue) PRP calculated for all trials in this go-no go session for a mouse that was performing proficiently in differentiation of the two odorants.

Figure 3

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In order to assess whether PRP changes with learning we performed this analysis for all sessions for naïve and proficient periods. Figure 3D shows cumulative histograms for the peak and trough PRP for all mice for the odor period for all go-no go sessions with the IAAPexp2 odorant pair for theta/high gamma PAC. Over the course of learning, peak-related high gamma power increases for S+ and decreases for S- (Figure 3D top). In contrast, the changes elicited by learning in trough PRP are smaller (Figure 3D bottom). The differences were statistically significant between peak and trough, S+ and S- and naïve and proficient (GLM p values < 0.001, 1016 d.f.). The summary of PRP for peak and trough for theta/high gamma PAC for the odor period are shown for all odorant pairs in Figure 3E (peak PRP) and 3F (trough PRP). For all odorant pairs peak PRP increases for S+ over learning and decreases for S-. Trough PRP is weaker yet follows the same trend as the animal learns to discriminate the odorant as peak PRP (GLM p value < 0.001, 6386 d.f. for S+ vs. S-, peak vs. trough, naïve vs. proficient). In addition, the learning-induced changes in PRP are larger for Exp2 (GLM p value < 0.001 for experiment, 6386 d.f.). Similar changes were found for PRP for theta/beta PAC, but there was no difference between peak and trough (not shown).

Finally, we found that theta peak phase-referenced power decreases for S- and increases for S+ regardless of the chemical identity of the odorant. Figure 4A shows that after the valence of the odorant is reversed the animal learns to respond to the new rewarded odorant. We asked the question whether odorant-induced changes in peak PRP would change when odorant valence was reversed. Figure 4B and C show that in proficient mice peak PRP increases when the mouse responds to the rewarded odorant regardless of the chemical identity of the odorant, and PRP decreases when the mouse responds to the unrewarded odorant. GLM analysis yields significant changes for odorant, reversal and the interaction of reversal and odorant (p<0.001, 1051 d.f.). These data show that as the animal learns to differentiate between odorants in the go-no go task there is an increase in rewarded odorant-induced peak PRP and a decrease in unrewarded-odorant peak PRP.

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Linear discriminant analysis classifies stimuli using PRP

The finding that LFP power referenced to the peak of the theta oscillation increases for S+ and decreases for S- when the animal learns to differentiate the odors (naïve vs. proficient) raises the question whether a downstream reader evaluating peak power could decode which stimulus is presented. To assess decoding of olfactory stimuli using PRP, a linear discriminant analysis (LDA) was used to set a decision boundary hyper-plane between binary stimulus classes (S+ versus S-) (Vizcay et al., 2015) using PRP data referenced to the peak (or the trough) of theta/beta or theta/high gamma PAC. LDA was trained with PRP from each electrode for each mouse (16 electrodes per mouse) for all trials except one (the training dataset) and then the missing trial (test data) was classified as S+ or S- using the PRP data from that trial. This was performed separately for trials where the mouse was naïve or proficient to odorant discrimination, for each 0.1 s time point throughout the trial and was repeated for all trials. As a control we shuffled the identity of trials in the training set. In addition, we performed a complementary principal component analysis (PCA) of the PRP to visualize the odor-induced divergence in the time course of the first principal component (PC1).

Figure 5A shows for theta/beta (i and ii) and theta/high gamma (iii and iv) the time course for PC1 calculated for S+ and S- odorants for naïve (i and iii) and proficient (ii and iv) mice calculated with the PRP for 16 electrodes for one example odorant pair (APEBexp1). In the naïve state PC1 diverged between S+ and S- shortly after water reinforcement for peak and trough theta/beta PRP (Figure 5Ai) and for peak theta/high gamma PRP (Figure 5Aiii, with a smaller change for trough). However, when the animal became proficient PC1 diverged between S+ and S- shortly after odorant addition for theta/beta PRP (Figure 5Aii) and theta/high gamma PRP (Figure 5Aiv). This analysis suggests that for the proficient animal PRP LFP carries information on the rewarded odorant.

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In order to quantify the accuracy for decoding odorant identity using PRP LFP we performed LDA analysis (Figure 5B). For naïve animals the LDA could not classify stimulus identity using peak or trough PRP for either theta/beta (Figure 5Bi) or theta/high gamma (Figure 5Biii). In contrast, when the animal was proficient the precision of the LDA classifier increased shortly after odorant application from chance to values above 70%, significantly higher than the 95% confidence interval of the LDA performed with shuffled trials for both theta/beta (Figure 5Bii) and theta/gamma (Figure 5Biv) (GLM analysis p value for learning <0.001, 104 d.f.). For theta/beta, both peak and trough PRP LDA performed significantly better than shuffled data for proficient mice (Figure 5Bii, GLM p value < 0.001, 104 d.f.). However, for theta/high gamma in proficient animals (Figure 5Biv, bottom) LDA discriminated the identity of the stimulus more effectively using peak PRP (GLM p value < 0.001, 104 d.f.).

The difference in LDA performance between peak and trough PRP was further evaluated by calculating the area under the curve (AUC) for LDA performance during the odor application window (0.5–2.5 s after odorant valve opening). AUC is a statistical method to quantify differences between the distributions of values of two variables (Green and Swets, 1988). The AUC was normalized and it ranged from zero (random decoding at 50%, Figure 5—figure supplement 1Ai) to 1 (100% decoding during the odor period, Figure 5—figure supplement 1Aii). AUC is plotted for all odorant pairs for peak and trough PRP in Figure 5C for theta/beta (i and ii) and theta/high gamma (iii and iv) for naïve (i,iii) and proficient (ii,iv) conditions. In the proficient state, AUC for peak PRP LDA for high gamma was significantly higher than AUC for trough PRP LDA (Figure 5Civ, GLM for AUC peak vs. trough p value < 0.001, 104 d.f.). AUC for beta PRP LDA did not differ between peak and trough (Figure 5Cii). Furthermore, Figure 5D shows that the AUC was larger for Exp2 (GLM p value < 0.001 for experiment, 6386 d.f.).

Finally, we asked the question whether decoding performance differs when mice make mistakes in the go-no go task. If PRP encodes for the chemical identity of the odorant we would expect that decoding performance would be similar between Hit/Miss and CR/FA during the first second of the trial when the animal keeps their head in the odor port. If PRP encodes for contextual odorant identity decoding performance would differ between correct responses (Hit and CR) and mistakes (Miss, FA) shortly after the animal detects the odorant. Figure 5E shows the results of the per trial analysis of decoding performance for LDA with theta/beta PRP (i) and theta/high gamma PRP (ii) sorted by behavioral outcome. Interestingly, shortly after addition of the odorant there is a divergence in decoding performance between trials with correct decision (Hit, CR) and mistakes (Miss, FA). Shortly after addition of the odorant decoding performance for FA drops below 50% (it tends to encode for the opposite odor), and for Miss trials the decoder performs like the shuffled trials. Decoder performance increases above 50% for both FA and Miss towards the end of the trial. Taken together with the shift of PRP in the reversal experiments (Figure 4) the difference in LDA encoding between correct trials and mistakes is further evidence that PRP encodes for the contextual identity of the odorant (as opposed to the chemical identity). A GLM analysis indicates that there are significant differences between all behavioral outcomes except for Hit vs. CR for theta/high gamma (p<0.001 for all outcome pairs, except for Hit vs CR for theta/beta PRP that has p<0.01 and Hit vs. CR for theta/high gamma that has p>0.05, 2110 d.f.). There is no significant difference between experiments (GLM p>0.05, 2110 d.f.).

To our knowledge, this is the first demonstration of high gamma phase-referenced LFP power developing differential information carrying capacity in early sensory systems with learning.

Decision-making takes place at the same time for peak PRP LDA and licks

After learning that using peak PRP LDA can decode stimulus identity, we wondered how decision-making times estimated based on either the behavioral response of the animal in the go-no go task (licks) or classification of the stimulus by PRP LDA relate to each other. In addition, we asked whether the decision-making time calculated with peak PRP LDA differed from decision-making time estimated using trough PRP LDA. Decision-making time was defined as the time when there is a statistically significant difference between S+ and S- in odorant classification (estimated separately for licks and LDA).

Figure 6A–B show examples of licks by a mouse in the go-no go task for the EAPAexp2 odorant pair. Figure 6A shows the licks detected at the waterspout for 25 S+ trials when the animal was performing proficiently while Figure 6B shows the lick traces for 25 S- trials in the same session. As in previous studies (Doucette and Restrepo, 2008), we estimated the p value for lick decision-making by computing in each 0.1 s time bin the ranksum test for the difference between licks (scored 0 for no lick vs. one for lick). An example of the time course of the p value for licks for mice performing the go-no go task for EAPAexp2 is shown by the green line in Figure 6Ci. The p value drops below 0.05 ~ 250 msec after odorant addition. We defined the lick decision-making time as the time point when the p value for difference in licks between S+ and S- falls and stays below 0.05 after odor application.

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LDA decision-making time was estimated in a similar manner by computing the p value for a ranksum test for the difference between predictions (scored one for correct prediction vs. 0 for incorrect prediction) for PRP LDA decisions evaluated after pooling data for all mice for each odor pair. As explained under supplemental information (Figure 6—figure supplement 1) pooled animal data were used as opposed to per animal PRP LDA because this resulted in consistent estimation of earlier decision-making times. Examples of the time courses of the p values for PRP LDA performing the go-no go task for EAPAexp2 are displayed in Figure 6Ci for theta/high gamma PAC (red line: peak, blue line: trough). Before odorant presentation the p value fluctuates and sometimes falls below 0.05 transiently, while after odor presentation the p values for peak PRP fall below 0.05 sharply and continuously at approximately the same time as lick p value (~250 msec). Trough PRP p value for LDA decoding performance drops below 0.05 later (~950 msec) and the p values are higher than peak p values (compare red and blue lines in Figure 6Ci). Thus, in this example lick decision-making time is similar for licks and peak PRP LDA, and is slower for trough PRP LDA.

We proceeded to calculate decision-making times for licks and peak PRP LDA for all odorant pairs. Decision-making times for LDA decoding performance via peak PRP and lick for all odorant pairs for pooled mouse data are shown in Figure 6D for naïve (Figure 6Di) an proficient (Figure 6Dii) mice. Decision times were reduced significantly with task learning (GLM p value < 0.001, 44 d.f.). However, decision-making times did not differ between lick and peak PRP LDA (GLM p value > 0.05, 44 d.f.).

Dimensionality of PRP LFP space decreases when the animal learns to discriminate the odorants

Figure 7A shows the change in the scatter pattern of the first two principal components (PCs) of the theta/high gamma peak PRP calculated for pooled data from all mice as the animals learn to differentiate the two odorants for the EAPAexp1 odorant pair. Figure 7Ai shows that when the mice are naïve S+ (red) and S- (blue) points are mixed in the 2D PC space before and during odorant application. In contrast, Figure 7Aii shows that the 2D PC patterns become clearly separable when the animals are proficient. There appears to be a change in the geometrical arrangement of the points in principal component space suggesting that there is a change in dimensionality as the animal learns to differentiate the odorants (Litwin-Kumar et al., 2017).

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In order to provide a more nuanced analysis of whether the number of independent signals in the PRP LFP data measured by the 16 electrodes changes as the animals learn to discriminate between odorants we calculated a quantitative measure that characterizes dimensionality in the PRP LFP space (see Materials and methods). The 16 electrodes are closely spaced (12.5 μm diameter electrodes in the same tetrode are directly abutted against each other and tetrodes are separated by 100–200 μm in both preparations: Exp1 with optetrodes and Exp2 with tetrodes). Because of this close proximity the extracellular field potentials would not be expected to differ greatly (Gold et al., 2006) and therefore the dimensionality of the PRP LFP space would be expected to be close to one. Interestingly, when the dimensionality was calculated on a per mouse basis where the maximum dimensionality (M) is 16 we found that the average dimensionality for theta/high gamma PRP LFP for electrodes in Exp2 was indeed close to one, but it was significantly higher (2-4) in Exp1, with the highest dimensionality for PRP LFP trough (Figure 7—figure supplement 1Ai, GLM p value < 0.001 for peak vs. trough and Exp1 vs. Exp2, 379 d.f.). We found similar differences in dimensionality between Exp1 and Exp2 for theta/beta PRP LFP, but in this case there was no difference between peak and trough dimensionality (Figure 7—figure supplement 1Aii, GLM p value < 0.001 for Exp1 vs. Exp2 and >0.05 for peak vs. trough, 379 d.f.). This indicates that even when measured using electrodes located within 100–200 μm the LFP carries information on multiple independent components.

Interestingly, the dimensionality for peak PRP LFP for theta/high gamma calculated on a per mouse basis decreased after addition of the odorant for both experiments and the decrease in dimensionality was larger for proficient mice. Examples of the dimensionality time course for peak PRP LFP for theta/high gamma calculated on a per mouse basis are shown for two odorant pairs in Figure 7—figure supplement 1Bi (Exp1) and Figure 7—figure supplement 1Bii (Exp2). A GLM analysis of the dimensionality for peak PRP LFP calculated on a per mouse basis for all odorant pairs indicates that there are significant differences in theta/high gamma peak PRP LFP dimensionality for proficient vs. naïve, time course, experiments, and for interactions of these factors (except for the interaction of experiments x proficient vs. naïve) (GLM p values < 0.001, 6098 d.f.). For theta/beta peak PRP LFP dimensionality we found similar results with the exception that there was no difference between peak and trough (Figure 7—figure supplement 1Ci and Cii, GLM p values < 0.001, 6098 d.f.).

Finally, when the dimensionality for peak PRP LFP was calculated for LFPs recorded from all mice the difference in the decrease in dimensionality between naïve and proficient became more evident. Time courses for pooled mouse peak PRP LFP dimensionality for theta/high gamma are shown in Figure 7B for Exp1 (7Bi) and Exp2 (7Bii). Peak theta/high gamma PRP LFP dimensionality decreases markedly when the odorant is delivered for both Exp1 and Exp2 for proficient mice and this decrease is larger for proficient compared to naïve mice (compare naïve vs. proficient in Figure 7Bi and ii). A GLM analysis indicates that there are significant differences for time course, proficient vs. naïve, experiments and peak vs. trough, and for interactions of these factors (GLM p values < 0.001, 1688 d.f.). For theta/beta peak PRP LFP dimensionality for pooled mice we found similar results (Figure 7Ci and 7Cii), but there was no difference between peak and trough. GLM analysis found statistically significant differences for time course, and proficient vs. naïve, and for interaction of these factors (GLM p values < 0.001, 1688 d.f.), and a statistically significant difference between experiments (GLM p value < 0.01, 1688 d.f.). However, was no difference between peak and trough (GLM p value > 0.05, 1688 d.f). Therefore, for both the per animal and the pooled animal PRP LFP space there is a decrease in dimensionality as the animal learns to discriminate between odorants, but this difference is more evident for the pooled animal data. This is evidence for a learned tightening of dimensionality for the odor representation manifold (defined as the independent neural components representing the odor).

We asked whether information carried by high frequency oscillations in brain regions involved in early sensory processing changes when observed at different phases of theta frequency oscillations. Specifically, we asked whether information on contextual odorant identity conveyed by LFP power of high gamma and beta frequency oscillations of the OB differs when the downstream observer filters the input through different theta LFP phase windows. We focused on the OB where it has been suggested that amplitude modulation may be used by higher-order processing centers such as PC to decode stimulus identity (Freeman and Schneider, 1982; Heck et al., 2019). We found that identity could not be decoded from beta or high gamma OB LFP power when the mouse was naïve to the identity of the reinforced odorant (left panels in Figure 5B). However, the contextual identity of the odorant could be decoded from the PRP after the animal learned to discriminate between the odorants (right panels in Figure 5B). Furthermore, decoding was more accurate when the high gamma LFP power was observed at the peak of the theta oscillation, but it was similar at both the peak and trough phases for beta LFP oscillations. LDA correctly identified the stimulus with a time course for decision-making similar to the behavioral readout (licking on the water-delivery spout, Figure 6). Thus, stimulus representation by theta phase-referenced beta and high gamma oscillations of the OB evolves over the course of learning. Importantly, our findings were replicated in two different experiments (Exp1 and Exp2) differing in genotype, electrode location, device implanted (tetrode or electrode) and odorant pairs used (see Supplementary file 1-Table S1). We did find differences in measured parameters between experiments, and these are likely due to methodological differences between Exp1 and Exp2 such as electrode location and genotype. Regardless of the reason for differences between experiments it is important for this study that the findings on PRP are found for both experiments under substantially different experimental conditions. To our knowledge this is the first demonstration that decoding of stimulus identity from theta phase-referenced high gamma oscillations, reflecting synchronized neuronal firing, changes with learning in brain areas involved in early sensory processing.

The importance of PAC in information processing is based on the notion that different information is carried at different phases of the slow carrier oscillation. This discretization of information is a potential mechanism for encoding short-term memories (Lisman and Idiart, 1995) and more broadly as a neural communication protocol, the theta-gamma neural code (Hopfield, 1995; Lisman and Jensen, 2013). Circuit activation at theta frequency was discovered to be essential for long-term potentiation in the rabbit hippocampus (Bliss and Lomo, 1973), arguing that neural information transfer may go beyond mean rate codes and involve spike timing with respect to oscillatory timekeepers. Subsequent studies indicated that temporal windows set by theta cycles allow for local circuit interactions and a considerable degree of computational independence in subdivisions of the entorhinal cortex-hippocampal loop (Mizuseki et al., 2009). For CA1, it was hypothesized that theta partitions the encoding of new information versus the retrieval of stored information (Hasselmo et al., 2002). Indeed, optogenetic recruitment of fast spiking inhibition in CA1 delivered at specific theta phases altered murine performance in a spatial navigation task (Siegle and Wilson, 2014). When the mice were encoding a location, triggering of inhibition of CA1 at theta peaks improved performance, whereas inhibition at theta troughs improved performance during the retrieval phase. Recently, age related cognitive decline in working memory in humans was reversed temporarily via transcranial alternating-current stimulation frequency-tuned to the endogenous theta peak frequency of each individual’s frontotemporal network (Reinhart and Nguyen, 2019). It appears that working memory is undergirded by theta-gamma PAC and that inter-regional communication is facilitated by theta phase coherence (Daume et al., 2017; Reinhart and Nguyen, 2019). Thus, the theta LFP which has been cited as one of the most global oscillations in the brain acts as a timekeeper (Siegle and Wilson, 2014) that is coherent across numerous cortical and subcortical structures arguing for its role in transfer of discrete chunks of information (Buzsáki, 2002).

Here we asked whether odor identity information was carried at different phases of theta. Our study of PAC in the OB involved learning of odor discrimination in the go no-go task. In orbitofrontal cortex, Van Wingerden et al. (van Wingerden et al., 2014) showed that this task elicited strongest theta/gamma PAC during odor sampling preceding correct decision-making, which they attributed to temporal coordination between cell assemblies responsible for stimulus representation and reward association. The OB circuit is characterized by beta and gamma oscillations nested in a slower theta carrier wave pertaining to respiration (Buonviso et al., 2003; Heck et al., 2019; Kay, 2005; Kepecs et al., 2006; Rebello et al., 2014; Rojas-Líbano et al., 2014). However, Granger directionality analysis shows that the theta oscillation in the OB is also influenced by hippocampal slow oscillations indicating that the origin of OB slow carrier oscillations is complex, involving both respiration and centrifugal input from downstream brain regions whose relative contribution likely changes under different behavioral states (Nguyen Chi et al., 2016). Cyclical activation of OSNs through respiration (Adrian, 1950; Bressler, 1988; Rosero and Aylwin, 2011; Zhuang et al., 2019) provides input to mitral/tufted (M/T) cells, and coordinated activity by M/T cells in the OB caused by mitral cell-granule cell reciprocal dendrodendritic interactions establishes gamma oscillations (Arnson and Strowbridge, 2017; Osinski and Kay, 2016; Pouille and Schoppa, 2018; Schoppa, 2006; Stopfer et al., 1997) (see review by Heck et al., 2019). Gamma LFP is thought to represent the stimulus identity (Bathellier et al., 2006; Beshel et al., 2007; Li and Cleland, 2017; Rojas-Líbano and Kay, 2008) and beta LFP oscillations (15–35 Hz) have been linked to learned reward (Martin et al., 2006). However, the classification of these two bandwidths as carrying learning vs. odor identity information is not always appropriate, and Frederick et al. (2016) proposed that they represent different cognitive states that vary depending on particular behavioral demands. PAC is present in the OB (Buonviso et al., 2003; Rojas-Líbano et al., 2014) and it may be of great albeit relatively unexplored utility. We contributed to the understanding of which information is carried by different frequency oscillations by asking whether the high gamma and beta oscillations carry different information when they are observed within particular phase windows of the theta carrier wave (Figure 5). We hypothesized that PAC may be used to convey olfactory stimulus information to theta phase-synchronized downstream regions like PC (Kepecs et al., 2006; Lisman and Buzsáki, 2008).

We demonstrate that PAC changes in the OB during associative learning (Figure 2). Peak angle variance increased for the unrewarded odorants with learning. The theta phase-referenced PRP of the high gamma and beta LFPs also follows this trend (Figure 3), increasing for S+ and decreasing with S- over learning. The changes in PRP correlating with learning may reflect contrast enhancement that facilitates the discrimination between similar stimuli by a downstream observer. Neuronal adaptation to facilitate contrast enhancement has been shown at the level of the OSNs (Haney et al., 2018), the glomerular layer (Cavarretta et al., 2016), and the granule cell layer (Adams et al., 2019) of the OB. We speculate that the concurrent increase in PRP for S+ and decrease in PRP for S- reflects adaptational mechanisms in the OB to enhance contrast between similar stimuli with different associated values. Finally, given that there is coordination of oromotor actions through brainstem circuits (Moore et al., 2014), and that studies have shown development of coordinated sniffing and licking as rodents learn to differentiate odorants (Jordan et al., 2018; Lefèvre et al., 2016; Rosero and Aylwin, 2011) it is likely that the changes found in PRP as the animals learn to differentiate the odorants reflect an interaction with changes in licking and sniffing.

To quantify whether these changes in PAC increased discriminability between odorants using PRP we asked whether the stimulus that was delivered could be decoded from PRP data. Previous investigations have decoded olfactory stimuli from spike counts aligned to sniffing in the mouse (Cury and Uchida, 2010; Gschwend et al., 2012), in the antennal lobe of the locust (Stopfer and Laurent, 1999), and M/T neural activity assayed through calcium transients in mice (Chu et al., 2016), but trial classification via PAC remains unexplored. Here, we performed LDA on PRP data to determine whether a single hyperplane could differentiate between stimuli as the animals learned the task. Figure 5B indicates that the identity of the stimuli cannot be decoded from PRP recorded in the naïve mice, but that the stimuli can be decoded when the mice learn to discriminate the odorants. Furthermore, decoding the stimuli from peak high gamma PRP is significantly better than trough PRP. Thus, decoding of the odorant identity by downstream observer using a phase window for the slow carrier oscillation could detect the identity of the odorants after the animal learns to differentiate between odors in the go no-go task. Finally, this study contributes to the mounting evidence that the OB is an important locus for learning-related activity changes (Abraham et al., 2014; Doucette et al., 2011; Doucette and Restrepo, 2008; Koldaeva et al., 2019; Li et al., 2015).

We wondered how timing for decision-making would relate comparing stimulus decoding with PRP with decision-making estimated from the behavioral readout of the olfactory-driven decision in the go no-go task (differential licking between the two odorants). The time course for the behavioral decision, reflected in the graph of p value for differential licks, is overlaid by the p value time course for peak PRP decoding (Figure 6C, right) with trough PRP lagging behind. Neither beta nor high gamma peak PRP p values are discriminable from lick p values in terms of decision time in this task. As shown in Figure 6D, for proficient animals licking differs between odorants within about 0.5 s from stimulus onset, at the same time that PRP decoding becomes significant. This is slower than discrimination times for odorant responses recorded in mice performing two alternative forced choice odorant discrimination or receiving odors passively where discrimination takes place within the first respiratory cycle (~250 ms) after stimulus onset (Cury and Uchida, 2010; Short and Wachowiak, 2019; Shusterman et al., 2011). However, the 0.5 s decision-making time is consistent with studies with the go no-go task where there is not a strong motivation for the animal to stop licking for the unrewarded odorant (Abraham et al., 2004; Doucette and Restrepo, 2008; Jordan et al., 2018; Rinberg, 2006)—with the exception of rapid detection of optogenetic activation of glomerular input in the go no-go task (Smear et al., 2011). Thus, we conclude that PRP is an accurate reflection of decision-making in olfactory discrimination.

Interestingly, in contrast with theta/high gamma PRP where the decoding performance for peak and through differ substantially, for theta/beta PRP there is no difference in decoding performance between peak and trough (compare Figure 5Bii and 5Biv). Increases in OB beta LFP for rodents engaged in odorant discrimination tasks take place after the onset of changes in gamma LFP and it has been postulated that beta LFP represents systemwide coherent states perhaps conveying centrifugal modulation from downstream brain areas to the OB (David et al., 2015; Frederick et al., 2016; Kay, 2014). If beta oscillations indeed represent centrifugal feedback our findings suggest that centrifugal modulation does not differ through phases of the theta oscillation and would therefore excerpt modulation on high frequency circuit activity occurring at different theta phases. Here we show that peak-referenced high gamma oscillation power encodes for the contextual identity of the odorant (is the odorant rewarded?). What information could be conveyed at other theta phases is an open question. Perhaps asynchronous M/T firing carries chemical odorant information in the theta trough.

Finally, we turn to dimensionality. The measurements in the experiments presented here are inherently low dimensional because: 1) The animal is discriminating between two odors, and the behavior is constrained by the go no-go task (Gao et al., 2017) and 2) While the number of independent degrees of freedom for inputs to the OB is potentially large (~2000 glomeruli), the four tetrodes are close together and they should sample a small subset of these input dimensions. Indeed, because the tetrodes are within 200 μm of each other (and electrodes are adjacent within tetrodes), the LFP recorded from each electrode is likely to be similar, assuming that the cellular milieu around the electrodes does not separate the inputs (Gold et al., 2006). Interestingly, the dimensionality measured from the 16 electrodes (four tetrodes) varies between 1 and 6 suggesting that subsets of electrodes are detecting different signals (Figure 7—figure supplement 1A). However, when the mice learn to discriminate the dimensionality decreases in the presence of the relevant odorant (Figure 7 and Figure 7—figure supplement 1B and C), suggesting that population representation is a modifiable aspect of OB processing. This likely reflects experience-dependent, attention (Canas and Jones, 2010; Niv et al., 2015). In the naïve state, relevant (rewarded) dimensions are unknown to the mouse, and a downstream structure sampling from the recorded population would receive ambiguous signaling in the presence of the rewarded odorant without decoding or reducing the input information. We find a large decrease in dimensionality post-learning, suggesting that OB now enhances a relevant and invariant signal to allow for unambiguous odor detection. Attention, guided by reward prediction error, likely biases/constrains the learning to the relevant dimensions (Leong et al., 2017)—in this task, odor identity.

The changes in signal processing elicited by learning, habituation, and passive odorant exposure in the OB, the earliest processing center in the olfactory system, are remarkable. Why is processing in this circuit so plastic and influenced by centrifugal input from downstream targets, such as PC, and from a variety of neuromodulatory centers (Gire et al., 2013; Linster and Cleland, 2016)? Likely the reason is that this processing center receives massive parallel glomerular input and projects M/T output of high dimensionality to downstream brain processing areas (Chae et al., 2019). Furthermore, unsupervised learning modifying cellular interactions in the OB would increase dimensionality (Hiratani and Latham, 2019). Therefore, odors must be identified in the midst of a high dimensionality cocktail party (Rokni et al., 2014). Based on the present data showing a large increase in the accuracy for decoding of contextual odor identity from the PRP as the animal learns to differentiate the odorants we speculate that when a subset of the degrees of freedom of the sensory input become behaviorally relevant, centrifugal feedback elicits supervised learning that results in a decrease in dimensionality of the output from the OB to downstream brain areas. Thus, the fact that peak theta-referenced high gamma power encodes information on whether the odorant is rewarded may simply reflect the fact that the transfer of sensory information on the rewarded odorant is being prioritized in the OB circuit. This would result in more accurate discrimination of the input channels that are relevant to the current task. Whether (and how) supervised learning-induced OB circuit plasticity results in a decrease in dimensionality of the output remains to be determined.

The Matlab code used for data analysis has been deposited to https://github.com/restrepd/drgMaster (copy archived at https://github.com/elifesciences-publications/drgMaster-52583). Data have been deposited to GigaDB (https://doi.org/10.5524/100699).

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Author details

1. Justin Losacco (deceased)

   1. Neuroscience Graduate Program, University of Colorado Anschutz Medical Campus, Aurora, United States
   2. Department of Cell and Developmental Biology, University of Colorado Anschutz Medical Campus, Aurora, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Methodology

   Contributed equally with

   Daniel Ramirez-Gordillo

   Competing interests

   No competing interests declared

2. Daniel Ramirez-Gordillo

   Department of Cell and Developmental Biology, University of Colorado Anschutz Medical Campus, Aurora, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Validation, Investigation, Methodology

   Contributed equally with

   Justin Losacco

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8189-6069

3. Jesse Gilmer

   1. Neuroscience Graduate Program, University of Colorado Anschutz Medical Campus, Aurora, United States
   2. Department of Physiology and Biophysics, University of Colorado Anschutz Medical Campus, Aurora, United States

   Contribution

   Software

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5778-1061

4. Diego Restrepo

   1. Neuroscience Graduate Program, University of Colorado Anschutz Medical Campus, Aurora, United States
   2. Department of Cell and Developmental Biology, University of Colorado Anschutz Medical Campus, Aurora, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Project administration

   For correspondence

   diego.restrepo@cuanschutz.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4972-446X

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