Introduction

Generalization allows learned responses to extend from a conditioned stimulus to similar cues, whereas discrimination enables animals to distinguish threat from safety. Adaptive behavior requires a balance between these processes, permitting defensive responses to potential danger while minimizing these responses to safe stimuli. Despite the importance of this balance for survival, how neural populations simultaneously support generalization and discrimination remains poorly understood. Two major theoretical frameworks have been proposed to explain these processes. Sensory similarity models posit that generalization arises primarily from overlap in sensory representations (Shepard, 1987). More recent work, however, suggests that sensory similarity alone cannot fully account for generalization. Instead, the brain is proposed to construct representations of learned threat-value, whereby neural activity reflects the estimated probability or magnitude of danger associated with different stimuli (Dunsmoor & LaBar, 2013; Laufer et al., 2016; Verra et al., 2026). Under this framework, sensory similarity provides the basis for evaluating novel stimuli, whereas associative learning determines their predicted threat-value. These models therefore make distinct predictions about neural activity. Sensory similarity models predict that neural activity is organized according to perceptual similarity, with generalized responses arising from overlapping neural representations and successful discrimination emerging from increasingly distinct representations, sometimes involving separate neuronal populations that encode threat and safety (Corches et al., 2019; Grosso et al., 2018). In contrast, threat-value models propose that neural activity reflects the learned threat value assigned to each stimulus, with generalization and discrimination represented along a continuum of expected danger rather than being determined solely by perceptual similarity (Levy & Schiller, 2021). In this study, we investigated how the prelimbic cortex (PL), a region implicated in fear expression and threat generalization (Burgos-Robles et al., 2009; Rosas-Vidal et al., 2025; Sierra-Mercado et al., 2011; Sotres-Bayon & Quirk, 2010; Stujenske et al., 2022), supports generalization and discrimination.

Previous studies have established that the prelimbic cortex is required for discriminating between threat and safety cues. During discriminative fear conditioning, transient inhibition of the PL causes animals to freeze similarly to conditioned threat and safe stimuli, resulting in overgeneralization (Likhtik et al., 2014). Likewise, disruption of endocannabinoid signaling in the PL abolishes the neuronal distinction between threat and neutral cues (Rosas-Vidal et al., 2025). Together, these findings indicate that the PL plays a critical role in organizing neural representations that support appropriate discrimination while limiting threat generalization. However, how individual PL neurons encode these computations remains unclear. Human neuroimaging studies have shown that medial prefrontal activity scales with gradients of learned threat, consistent with value-based representations (Lissek et al., 2014). In contrast, other studies suggest that activity in this region primarily reflects the representational similarity of affective or valence information (Chavez & Heatherton, 2015). Adding further complexity, PL neuronal activity is also strongly correlated with freezing behavior—a hallmark defensive response during fear retrieval—regardless of the specific cue predicting an aversive outcome (Casanova et al., 2024; Kyriazi et al., 2020). Consequently, it remains unclear whether PL population activity primarily reflects sensory similarity, learned threat value, or defensive behavior, and how these factors together shape threat generalization and discrimination.

An additional challenge in identifying the cortical neural codes underlying threat generalization and discrimination is that both episodic memory ensembles (DeNardo et al., 2019; Kitamura et al., 2017) and procedural memory ensembles (Do-Monte et al., 2015; Iqbal et al., 2026) undergo substantial reorganization across days—a hallmark of systems consolidation—even while learned behaviors remain remarkably stable. This dissociation between neuronal instability and behavioral persistence suggests that stable behavior can be supported by population-level representations despite continuous changes in their neuronal composition (Deitch et al., 2021; Gallego et al., 2020). Because threat generalization requires evaluating novel stimuli in relation to previously learned threat-value representations, often long after the original threat association has been acquired, it may be particularly sensitive to ongoing ensemble reorganization. These observations raise several important questions. Can stable population codes supporting threat generalization emerge despite continuous changes in their neural composition? Do distinct neuronal subpopulations differ in their long-term stability? If so, do stable and dynamic neuronal subpopulations differentially represent learned threat value, sensory similarity, or the expression of defensive behavior?

We hypothesized that the PL generates population-level representations of learned threat value that support threat generalization and discrimination, and that these representations are maintained through the complementary contributions of stable and dynamic neuronal ensembles despite ongoing ensemble reorganization. Furthermore, although freezing behavior was expected to account for a portion of the variance in neuronal activity, we predicted that learned threat value would explain substantially more of the neural response. To test these hypotheses, we combined longitudinal calcium imaging, computational clustering analyses, and a generalized linear model (GLMs) to characterize PL ensemble dynamics during auditory discriminative fear learning and memory retrieval in freely moving mice. Our results show that learned threat value is represented as graded neural responses at both the population and single-neuron levels despite extensive ensemble turnover. Moreover, population similarity across stimuli closely tracked behavioral generalization, suggesting that sensory similarity determines the overlap between population neuronal responses, whereas associative learning organizes these responses according to learned threat value. Finally, activity across cell types was better explained by learned threat value than by freezing behavior. Together, these findings provide a neural framework for understanding how the PL supports adaptive threat generalization and discrimination.

Results

Logarithmic tone separation predicts freezing level

To assess memory retrieval and generalization, GRIN-lens–implanted and non-implanted mice were trained in a differential auditory fear-conditioning paradigm (Fig. 1a). One tone (CS⁺; 80 dB) was paired with a mild foot shock (0.5 mA, 0.5 s), whereas a second tone (CS⁻; 80 dB) was never paired with shock. In one group, the CS⁺ was 15 kHz and the CS⁻ was 3 kHz (CS⁺15; N = 27; 7 implanted, 20 non-implanted); in a second group, contingencies were reversed (CS⁺3; N = 22; 5 implanted, 17 non-implanted). A no-shock control group was exposed to the same tones without shock (N = 13; 6 implanted, 7 non-implanted).

Figure 1.

Retrieval was assessed 1, 15, and 30 days after conditioning to probe recent, long-term, and remote memory (Bontempi et al., 1996). During each retrieval session, mice were tested in a novel context with the CS⁺, the CS⁻, and two intermediate frequencies (7 and 11 kHz), presented in a semi-random order with each tone repeated three times (Fig. 1a). The intermediate frequencies were selected to evaluate whether perceptual similarity predicts threat generalization. Although the separation between the CS⁺ and CS⁻ was identical in both groups (2.32 octaves), the spacing between the CS⁺ and the nearest intermediate frequency differed (0.45 octaves for 11–15 kHz versus 1.22 octaves for 3–7 kHz). Thus, if threat generalization is determined primarily by sensory similarity, freezing should generalize more strongly to 11 kHz in CS⁺15 mice than to 7 kHz in CS⁺3 mice.

In the CS⁺15 group, mice consistently discriminated between the CS⁺ and CS⁻. Although generalization to intermediate frequencies was broad on day 1, it became progressively restricted to 11 kHz—the frequency adjacent to the CS⁺—during long-term (day 15) and remote (day 30) retrieval (p < 0.05; Fig. 1b, left). CS⁺3 mice also discriminated between the CS⁺ and CS⁻; however, these animals exhibited greater freezing to the CS⁺ than to all intermediate frequencies across testing days (p < 0.05; Fig. 1b, center), indicating reduced generalization to the adjacent tone when the logarithmic separation was larger. No-shock control mice showed no significant differences in freezing across frequencies on any testing day (p > 0.05; Fig. 1b, right), confirming that the graded freezing patterns resulted from associative learning rather than the acoustic properties of the tones. Together, these results indicate that logarithmic spacing (i.e., frequency similarity), rather than simple proximity to the CS⁺, was the primary determinant of generalization.

Because our experimental design involved repeated retrieval testing over the course of a month, we examined whether repeated tone presentations produced extinction. We quantified stimulus discrimination using discrimination ratios (DRs), which measure discrimination between each tone and the CS+. As shown in Fig. S1, DRs increased over successive retrieval sessions in both conditioned groups. In CS+15 mice, significant increases were observed for the 3 and 7 kHz tones (p < 0.05), whereas persistent generalization remained only for the 11 kHz tone. Similarly, CS+3 mice exhibited significant increases in DRs for the CS− and all intermediate frequencies (p < 0.05, Fig. S1). Thus, repeated testing progressively sharpened discrimination rather than reducing conditioned responding. This pattern is inconsistent with extinction, which would be expected to flatten discrimination gradients, and instead agrees with previous studies showing that discrimination training narrows behavioral generalization gradients (Dunsmoor & LaBar, 2013; Herzog et al., 2021; Jenkins & Harrison, 1960; Lommen et al., 2017).

No sex differences were observed in CS⁺15 mice (11 females, 16 males) or (6 females, 7 males; p > 0.05). In CS⁺3 mice (11 females, 11 males), minor and inconsistent sex-related effects were detected on days 1 and 15, but these effects were absent by day 30 (Fig. S2). Accordingly, sex was not included as a factor in subsequent neural analyses. Behavioral performance did not differ between implanted and non-implanted mice on days 1 and 15 (p > 0.05). On day 30, a modest main effect of group was observed in the CS⁺3: group, reflecting higher overall freezing levels in implanted animals compared with non-implanted mice (p < 0.03). Importantly, both experimental groups exhibited robust frequency effects across days (p < 0.001), with no group × frequency interactions (p > 0.05), indicating preserved threat discrimination and generalization profiles.

PL sound-responsive ensembles exhibit dynamic properties over time

To examine the temporal evolution of PL neuronal responses, we performed longitudinal calcium imaging in CS⁺15 (N = 7), CS⁺3 (N = 5), and no-shock control mice (N = 6). Across groups, neurons were tracked during conditioning and all retrieval sessions. To assess registration quality, we used the conditioning session as a reference and measured the centroid shifts between matched neurons across retrieval sessions. For each animal, we generated histograms of these shifts (µm) and compared them with the median equivalent circular footprint diameter (Fig. S3). Across animals, 99–100% of registered neurons exhibited centroid shifts smaller than the median footprint diameter, indicating highly reliable cell registration. The proportion of registered neurons was equivalent across groups (Fig. S3). Fig. 1c illustrates the GCaMP6f viral injection strategy and representative histological sections showing the pattern of viral expression. Fig. 1d shows a representative raw calcium video frame, processed frames, and activity traces.

Sound-evoked responses were visualized using activity plots with calcium activity ranked across simultaneously recorded neurons (Fig. 2a). Across animals, we visualized distinct neuronal subpopulations showing positive modulation, negative modulation, mixed responses, or no consistent response to sound in each session (Fig. 2b). Sound-responsive neurons were identified using a sound responder statistical test that detected activity modulation relative to baseline, allowing reliable identification of sound responses while remaining robust to noise. This approach was effective for neurons exhibiting either brief calcium transients that rose and decayed rapidly or sustained activity throughout the tone presentation. Fig. 2c summarizes the proportions of response types pooled across animals and sessions.

Figure 2.

Given the ongoing debate over whether neocortical memory ensembles stabilize or remain dynamic over time (DeNardo et al., 2019; Kitamura et al., 2017; Kupke & Oliveira, 2025; Lopez et al., 2024; Mau et al., 2020; Rao-Ruiz et al., 2021; Refaeli et al., 2023; Terranova et al., 2023; Zaki & Cai, 2024), we next assessed the temporal stability of PL ensembles by tracking the cellular footprints of sound-responsive neurons across retrieval sessions. Ensemble stability was visualized using Venn diagrams (Fig. 2c). A moderate proportion of neurons was active across all retrieval sessions, with no differences between groups (p > 0.05). Likewise, there were no group differences in the proportion of neurons overlapping across only two sessions (p > 0.05). For neurons active in only a single session, control mice exhibited a higher proportion on day 30 compared with CS15+ mice (p < 0.05, Table S1), with no other differences observed. Overall, these data indicate that the majority of neurons overlapped across only a limited number of sessions or were transiently active, reflecting pronounced population-level dynamism over time.

Sound-modulated PL population responses encode generalization gradients

To assess population-level representations in response to conditioned and novel tones, calcium activity was averaged across three presentations for each frequency during a 10-s baseline, 20-s tone presentation, and 10-s post-stimulus interval. In CS⁺15 mice, positively modulated sound-responsive neurons exhibited graded tone activity reflecting learned contingency value across testing days (Fig. 3a, top). Area-under-the-curve (AUC) analyses obtained by averaging recorded cells per animal revealed the highest responses at 15 and 11 kHz, intermediate responses at 7 kHz, and the lowest at 3 kHz; with no difference between 11 and 15 kHz (p > 0.05) across testing days. This population level gradient mirrored behavioral generalization (Fig. 1b, left). By contrast, negatively modulated neurons showed overlapping responses across frequencies with no significant differences at any time point (p > 0.05; Fig. 3a, bottom). A complementary pattern was observed in CS⁺3 mice, with graded responses that peaked at 3 kHz (Fig. 3b). As in CS⁺15 mice, negatively modulated neurons exhibited overlapping responses across frequencies and days (p > 0.05). In no-shock controls, although both positive and negative responses were present, population activity was not modulated by tone frequency (p > 0.05; Fig. 3c, bottom panel), indicating that neuronal graded responses require associative learning.

Figure 3.

To determine how AUC varied across groups over time, we performed a three-way mixed-effects ANOVA with group (CS+15, CS+3, and no shock), frequency (3, 7, 11, and 15 kHz), and time (test days 1, 15, and 30) as factors, with repeated measures on frequency and time. For positive responder neurons, the analysis revealed significant main effects of group (p < 0.001) and time (p < 0.05), as well as a significant group × frequency interaction (p < 0.001), whereas the time × frequency and group × time × frequency interactions were not significant (p > 0.05; Table S2a). Tukey-corrected post hoc comparisons showed that, in the CS+15 group, AUC differed between all frequency pairs except 11 and 15 kHz (p < 0.05). In the CS+3 group, the AUC at 3 kHz differed from those at 7, 11, and 15 kHz (p < 0.05), whereas no significant frequency differences were observed in the no-shock controls (p > 0.05). For negative responder neurons, the only significant effect was a time × frequency interaction (p < 0.01). Tukey-corrected simple-effects analyses revealed that, on day 30, the AUC at 15 kHz differed from those at 3, 7, and 11 kHz (p < 0.05; Table S2b). Because this pattern was observed across all experimental groups, including the no-shock controls, it is unlikely to reflect associative learning. These results indicate that although the AUC exhibited modest changes over time, these changes were not group-specific and therefore do not support learning-dependent alterations in neuronal responses. Together, these results show that despite substantial neuronal turnover, PL population responses encode generalization gradients, closely matching behavioral expression.

Consistently active neurons preserve stable generalization gradients, whereas newly recruited neurons refine them over time

Longitudinal tracking of individual neurons revealed how subpopulations with distinct stability profiles shape the evolution of representations that parallel behavioral expression. We compared population responses across three stability types: consistently active neurons (active during conditioning and all retrieval sessions), emerging–retained neurons (recruited after conditioning and persisting through day 30), and transiently active neurons (only active during a single retrieval session). Consistently active, positively modulated neurons exhibited graded population responses reflecting a generalization gradient from day 1 onward in both experimental groups, which was quantified by calculating AUC per animal (p < 0.05; Fig. S4a–b, Table S3). In contrast, negatively responding neurons showed no graded tuning across days (p > 0.05), except for a day 1 difference between 15 and 3 kHz in CS⁺15 mice (p < 0.05). In control mice, positively and negatively modulated neurons displayed variable and inconsistent activity across frequencies in all cell categories (consistently active, emerging–retained, and transiently active). As a result, these neurons were not included in further cell-type analyses.

Emerging-retained neurons recruited after conditioning exhibited graded population responses when recruitment occurred after day 1 (Fig. S5a–b, Table S3). This category encompassed neurons that emerged on day 1 and persisted through day 30, as well as neurons that emerged on day 15 and remained active through day 30. In both experimental groups, graded tuning was absent on day 1 (p > 0.05) but emerged on days 15 and 30, when population responses closely mirrored behavioral generalization, with responses to 11 and 15 kHz becoming increasingly similar regardless of CS⁺ identity (p > 0.05). By contrast, emerging–retained negatively responding neurons showed no significant emotional tuning across days.

Finally, we examined transiently active neurons, defined as cells active only on a single retrieval session. Transiently positive responders showed no valence tuning when active on day 1 but exhibited clear graded population responses when recruited on days 15 or 30 in both experimental groups (Fig. S6a–b, Table S3). In contrast, transiently negative responders showed no significant frequency tuning at any time point (p > 0.05, Table S3). Together, these results indicate that consistently active neurons maintain stable generalization gradients across time, whereas neurons recruited after conditioning progressively sharpen their selectivity over time.

Tone identity is a stronger predictor of PL activity than freezing

Previous studies have shown that PL activity is associated with fear expression ((Burgos-Robles et al., 2009; Sierra-Mercado et al., 2011; Sotres-Bayon & Quirk, 2010), and more recent work has demonstrated that freezing can be decoded from PL neuronal activity (Casanova et al., 2024; Kyriazi et al., 2020). Because freezing covaries with learned threat value during fear generalization, however, it remains unclear whether PL neurons primarily encode behavioral expression or the learned threat value of auditory stimuli. Our experimental design provided a unique opportunity to dissociate these possibilities. The auditory stimuli were identical across sessions and animals, whereas freezing varied substantially across tones and retrieval sessions. Moreover, continuous acceleration extracted from the miniscope enabled probabilistic estimates of freezing without imposing an arbitrary threshold. To quantify the independent contributions of tone identity and freezing, we fitted a generalized linear model (GLM) to neuronal activity (calcium traces using tone identity and freezing probability as predictors.

We analyzed positively and negatively responsive neurons separately in the CS+15, CS+3, and control groups. For positively responsive neurons, freezing-corrected tone regression coefficients (β) exhibited opposite monotonic gradients that peaked at the CS+ in the two conditioning groups, whereas controls showed relatively flat coefficients (Fig. 4a; effect of groups: p < 0.01, group x frequency interaction: p < 0.001, Table S4a). To compare the relative contributions of tone identity and freezing, we calculated the freezing-to-tone β ratio. Across all groups, this ratio remained below 1 (Fig. 4b, Table S4b), indicating that tone identity contributed more strongly than freezing to neuronal activity. Consistent with this observation, only a modest fraction of neurons was classified as freezing-dominant, and this proportion remained stable across retrieval sessions, with no significant differences between groups (p > 0.05; Fig. 4c,d; Table S4c,d).

Figure 4.

Negatively responsive neurons displayed a different pattern. Tone β coefficients showed little evidence of graded tuning (p > 0.05; Table S4e; Fig. 4e), consistent with the population responses shown in Fig. 3. Although tone identity remained the stronger predictor overall, freezing contributed proportionally more than in positively responsive neurons, resulting in higher freezing-to-tone β ratios and a larger fraction of freezing-dominant cells (Fig. 4f–h), with no differences between groups (p > 0.05, Table S4f). There were no differences in the proportion of freezing dominant negative responders between groups (p > 0.05) and these proportions remain stable across time (p > 0.05, Table S4g, h). Together, these findings demonstrate that PL population activity is better explained by learned threat value than by freezing behavior, particularly among positively responsive neurons.

Population vector similarity at stimulus onset determines degree of generalization

The preceding results indicate that PL population activity is organized along generalization gradients, such that perceptually similar tones (i.e., adjacent frequencies) elicit similar population responses. However, the neural mechanisms that calibrate the similarity relationships remain unclear. Previous studies have shown that consistent neuronal responses across repeated stimulus presentations support stable population representations that facilitate generalization to similar cues (Hoshi et al., 2023). To assess population similarity within each retrieval session, we compared population activity across the three repeated presentations of each tone. Population activity was estimated using CASCADE, a validated spike-inference neural network (Rupprecht et al., 2021), and activity vectors were constructed from simultaneously recorded neurons. Response similarity between tone pairs was then quantified during stimulus presentation to assess the consistency of population activity across repeated trials.

Rate-based population similarity analysis revealed reliable, temporally structured responses for 3/3 kHz tone pairs in CS⁺3 mice and for 15/15 and 15/11 kHz tone pairs in CS⁺15 mice. In control mice high population similarity was absent for any frequency pair (Fig. 5a-d). Because population similarity peaked shortly after stimulus onset, we quantified similarity during the first 5 s after tone onset relative to the CS⁺. In CS⁺15 mice, early population similarity was highest for 15/15 and 15/11 tone pairs (p < 0.001), with no difference between them (p > 0.05), and was significantly greater than for 15/3 comparisons (p < 0.05, Fig. 5e). In CS⁺3 mice, early similarity was highest for 3/3 tone pairs (p < 0.004) and significantly lower for 11/3 and 15/3 comparisons (Fig. 5f; p < 0.05). The 3/3 and 3/7 comparisons showed a non-significant trend (p = 0.08). No differences were observed among 7/15, 11/15, and 15/15 tone pairs in either group (p > 0.05). These findings indicate that population-level similarity at stimulus onset scales with behavioral threat generalization. In summary, PL population responses form generalization gradients that correlate with behavioral expression and encode learned threat value, while perceptual similarity across repeated presentations of threat-associated stimuli promotes similar population responses, providing a potential neural mechanism for recognizing dangerous stimuli.

Figure 5.

Different subpopulations encode acoustic versus learned properties of sound association

Our previous analyses demonstrated that threat-value generalization gradients are represented at the population level. However, these findings do not reveal how these representations arise. Specifically, the observed population gradients could emerge either from the pooled activity of frequency-selective neurons that respond to individual tones or from neuronal subpopulations that integrate information across tones to encode their learned threat-value. To investigate these possibilities, we developed a clustering approach based on mutual information (MI), which captures both linear and nonlinear relationships between neuronal response profiles (Quian Quiroga & Panzeri, 2009). MI was used to group neurons with related activity patterns into functional subpopulations. Because MI does not preserve response polarity, neurons were subsequently classified by the sign of their pairwise correlations and re-clustered, consistently revealing two major response classes: positively and negatively modulated sound responders (Fig. 6a). Clustering was performed across all animals to derive global cluster identities and within each experimental and control group to identify learning-specific subpopulations (Figs. S7–S9).

Figure 6.

Clustering quality was assessed by sorting signed MI values by global cluster identity and comparing within-versus across-cluster correlations (Fig. 6b). The resulting box-diagonal structure indicated robust clustering, with comparable quality indices across groups (CS⁺15: 0.28; CS⁺3: 0.27; controls: 0.30). In all cases, within-cluster correlations exceeded across-cluster correlations, supporting the reliability of the approach (CS⁺15: 0.30 vs. −0.03; CS⁺3: 0.27 vs. −0.02; controls: 0.28 vs. −0.04).

Across all groups, we identified positively and negatively modulated clusters selective for individual frequencies, indicating that frequency-specific representations are present in PL independent of learning (Fig. 6c–d; Figs. S7–S9), consistent with a role in auditory processing (Hockley & Malmierca, 2024; Zikopoulos & Barbas, 2006). In contrast, clusters encoding graded patterns—characterized by neurons responding to all frequencies in a graded manner—were observed exclusively in trained animals (Fig. 7; Figs. S7–S8). Graded neurons peaking at 15 kHz were specific to the CS⁺15 group (Fig. 7a–b; Fig. S7), whereas neurons peaking at 3 kHz were unique to the CS⁺3 group (Fig. 7c–e; Fig. S8).

Figure 7.

If neurons encoding graded responses represent the learned contingencies, they should exhibit stability over time. To test this hypothesis, we quantified the proportion of registered neurons that retained their cluster identity across at least two retrieval sessions and compared these values to a shuffled null distribution (10,000 iterations), with multiple comparisons controlled using the Benjamini–Hochberg procedure. Only the positively modulated graded clusters showed significant identity stability across all retrieval intervals (days 1–15, 15–30, and 1–30; Fig. 7a-c).

In contrast, negatively modulated graded neurons and a smaller positively modulated cluster in the CS⁺3 group showed stability only between adjacent sessions (Fig. 7b, d, e, Table S5). These data demonstrate that graded clusters remain consistently active, retaining their neuronal profiles, at levels exceeding chance, providing a stable representation of learned contingencies and generalization gradients.

Activity changes in frequency selective neurons encode learned value

Graded clusters encode learned contingencies but represent only a subset of the active neuronal population. Nevertheless, population-level representations, which incorporate all active neurons, robustly preserve these gradients. This led us to hypothesize that dynamically recruited, frequency-selective neurons also contribute to threat-value representations through changes in response magnitude. Consistent with hippocampal studies showing that spatially selective neurons encode task contingencies via firing-rate modulation (Gagliardi et al., 2024; Huxter et al., 2003; Sanders et al., 2019), we tested whether dynamic, frequency-selective clusters exhibited firing-rate changes proportional to learned threat value. To do so, we quantified the normalized baseline-to-stimulus response ratio (BSR) of positively responding neurons within each cluster using CASCADE-inferred spikes (Rupprecht et al., 2021).

We found that although tone-selective clusters emerged independently of learning (i.e., they were present in both conditioned and control mice), their firing rates were shaped by associative learning. Specifically, 3-kHz-selective neurons exhibited higher BSR in both conditioned groups than in controls (p < 0.05), regardless of whether 3 kHz served as the CS⁺ or CS⁻. In contrast, 11-and 15-kHz-selective neurons displayed significantly higher BSR in the CS⁺15 group than in the CS⁺3 or control groups on days 15 and 30 (p < 0.05; Fig. S10, Table S6). Notably, in the CS⁺15 group, where 11 kHz elicited robust threat generalization, the 11- and 15-kHz-selective clusters exhibited similarly high BSRs to both tones. The higher activity rates observed for tones associated with threat or inducing generalization suggests that these neurons are shaped by the animal’s associative experience, including both conditioning and retrieval-dependent updating.

As expected, positively modulated graded neurons closely mirrored population responses, exhibiting the highest BSRs to the CS⁺ and strongly generalized tones and lower BSRs to discriminated tones (p < 0.05; Fig. 7h–i, Table S6). Together, these findings indicate that firing-rate modulation enables both graded and frequency-selective PL neurons to represent the learned contingencies.

Stable and dynamic neuronal subpopulations encode learned threat value beyond freezing

Our earlier GLM analysis established that tone identity explains neuronal activity more strongly than freezing in the overall PL population, we next asked whether this relationship differed among the neuronal subpopulations identified by our clustering analysis. We first examined frequency-selective (single-tone) neurons, assigning each neuron’s preferred tone according to its cluster identity. Summary statistics were calculated using animals as the experimental unit (CS+15: N = 7; CS+3: N = 5; controls: N = 6).

Among positively modulated single-tone neurons, freezing-corrected tone β coefficients increased monotonically toward the CS+ in opposite directions for the CS+15 and CS+3 groups, whereas coefficients remained relatively flat in controls (Fig. 8a; effect of groups: p < 0.001; group x frequency interaction: p < 0.002, Table S7a). Thus, although these neurons responded preferentially to a single frequency, their β coefficient magnitude scaled with the learned threat value of that tone rather than its absolute frequency.

Figure 8.

Consistent with the population GLM, freezing-to-tone β ratios remained well below 1 (median ≈ 0.4; Fig. 8b), indicating that tone β coefficients were approximately two-to threefold larger than freezing β coefficients. This effect, however, was larger in experimental groups (effect of groups: p < 0.001, Tukey comparisons: CS+15 vs control: p < 0.008, CS+3 vs control: p = 0.08, Table S7b). Likewise, within-cell comparisons showed larger median tone than freezing β coefficients across all groups for each animal (Fig. 8c; effect of group: p < 0.02; effect of state condition (tone vs freezing): p < 0.001; interaction: p < 0.002, Tukey multiple comparisons: Tone vs. freezing p < 0.001 for all groups; β coefficients for tone: CS+15 vs controls: p < 0.00, CS+15 vs CS+3: p < 0.03, Table S7c), and only a small, stable fraction of neurons was classified as freezing-dominant throughout retrieval, with no significant differences between groups across time (p > 0.005; Table S7d; Fig. 8d). Together, these findings indicate that positively modulated frequency-selective neurons primarily encode learned threat value despite their narrow frequency selectivity.

Negatively modulated single-tone neurons exhibited suppression at their preferred frequency but little evidence of systematic scaling with learned threat value (Fig. 8e, effect of groups: p < 0.001, interaction frequency x group: p > 0.05; Tukey multiple comparisons: CS+15 vs control: p < 0.001; Table S7e). Tone identity remained the stronger predictor of activity across groups, but freezing-to-tone β ratios were lower in the experimental groups than the control (Fig. 8f, effect of group: p < 0.001, Tukey multiple comparisons: CS+15 vs control: p < 0.001, CS+3 vs control: p < 0.006; Table S7f). Within-cell comparisons of tone and freezing β coefficients showed a difference in the experimental groups but not the controls (Fig. 8g, effect of groups: p < 0.05, condition (tone vs freezing): p < 0.001, interaction: p < 0.001, Tukey multiple comparisons: tone vs. freezing: CS+15: p < 0.001; CS+3: p < 0.01; control: p=0.977, Table S7g). Finally, the proportion of freezing-dominant neurons was highest in controls, although this difference reached significance only relative to the CS+15 group (Fig. 8h, effect of group: p < 0.005, Tukey tests: CS+15 vs control: p < 0.005, Table S7h). These findings suggest that negatively responsive frequency-selective neurons multiplex stimulus identity and behavioral state to a greater extent than positively responsive neurons.

We next applied the same analysis to neurons classified as graded (Fig. 7). Because graded clusters were absent in controls, this analysis included only the CS+15 and CS+3 groups. For each graded cell we obtained normalized freezing-corrected β coefficients by dividing each tone beta by the largest beta out of the 4. The normalized freezing-corrected β coefficients formed steep opposing monotonic gradients that tracked learned threat value in both conditioning groups (Fig. 8i; effect of groups: p < 0.001, interaction group x frequency: p < 0.001; Tukey multiple comparisons: CS+15 vs CS+3 for 3, 11, and 15 kHz: p < 0.001; CS+15 vs CS+3 for 7 kHz: p < 0.02, Table S7i). All freezing-to-tone β ratios remained well below 1 across time (Fig. 8j), with the ratios for the CS+15 being even lower than for CS+3 on days 2 and 30 (p < 0.05, Table S7j). The within-cell median β coefficients for freezing and tone were different in both experimental groups (p < 0.001; Fig. 8k), with the tone coefficients being higher in the CS+15 group (p <0.003, Table S7k). Only 4–7% of neurons were classified as freezing-dominant across retrieval sessions (Fig. 8l, Table S7l), a lower percentage than that observed in single-frequency neurons. Similar patterns were observed among negatively modulated graded neurons, although the difference between tone and freezing coefficients was smaller (Fig. 8m–p, Table 7Sm-Sp).

These analyses demonstrate that both dynamically recruited frequency-selective neurons and stable graded neurons encode learned threat value beyond freezing behavior. Graded neurons represented threat value with minimal influence of behavioral state, whereas frequency-selective neurons also encoded threat value, although their responses were more strongly modulated by freezing. Together, these complementary coding strategies likely enable PL populations to maintain stable representations of learned threat value despite ongoing changes in ensemble composition and behavioral state.

Discussion

Our findings suggest that sensory similarity and learned threat value are not competing explanations of threat generalization but complementary components of the neural code underlying this process. Associative learning generated graded population representations of learned contingencies and intermediate responses to novel tones that persisted despite substantial ensemble reorganization. Perceptually similar tones elicited similar population responses with the greatest consistency across stimulus presentations, indicating that sensory similarity promotes stable population representations of behaviorally significant stimuli. Importantly, these representations were not simply a reflection of freezing behavior. Although freezing contributed modestly to PL activity, GLM analyses showed that learned threat value associated with each tone explained substantially more variance in neuronal responses than freezing, with graded tone β coefficients persisting after accounting for freezing. This stable graded population code emerged through the complementary contributions of two neuronal populations: longitudinally stable graded neurons that consistently encoded learned threat value and dynamically recruited, frequency-selective neurons whose response magnitudes were modified by learning. Together, these findings suggest that the PL integrates sensory similarity with learned threat value to generate stable representations that support adaptive generalization and discrimination.

Generalization has traditionally been explained by perceptual similarity (Shepard, 1987), whereby stimuli resembling a conditioned cue recruit overlapping sensory representations and evoke similar behavioral responses (Corches et al., 2019; Grosso et al., 2018). Although perceptual similarity clearly influences the extent of generalization, accumulating evidence indicates that it cannot fully account for generalized responding (Verra et al., 2026). More recent frameworks propose that associative learning assigns learned value to novel stimuli by integrating their sensory similarity with previous experience, allowing behavior to scale according to predicted biological significance (Verra et al., 2026; Zaman et al., 2023). Our findings provide a neural framework consistent with these ideas. Sensory similarity promoted consistent neuronal population responses across tones, whereas associative learning organized these responses into graded representations that tracked learned threat value across the stimulus continuum. Thus, sensory similarity appears to define the neuronal substrate upon which associative learning constructs value-based representations that support graded behavioral generalization.

The ensemble turnover observed here is consistent with previous studies demonstrating dynamic reorganization of cortical activity patterns over time (DeNardo et al., 2019; Gallego et al., 2020; Kitamura et al., 2017; Tome et al., 2024). Such reorganization has been proposed to provide flexibility by allowing new information to be incorporated into existing cortical representations while preserving stable behavioral performance (Mau et al., 2020; Zaki & Cai, 2024). Several mechanisms could contribute to this turnover, including systems consolidation, retrieval-induced reconsolidation or memory updating, and repeated nonreinforced stimulus exposure (Lacagnina et al., 2019; Mau et al., 2020; Sangha, 2015; Zaki & Cai, 2024). Although our experiments cannot distinguish between the first two possibilities, the behavioral data argue against extinction as the primary explanation. Extinction is generally associated with the formation of new CS+-safety associations (Bouton et al., 2021), whereas discrimination ratios increased across retrieval sessions, indicating that animals progressively improved their discrimination between threat-associated and safe stimuli rather than acquiring generalized safety responses. This pattern is consistent with previous work showing that discrimination learning sharpens stimulus representations and narrows behavioral generalization gradients (Dunsmoor & LaBar, 2013; Herzog et al., 2021; Jenkins & Harrison, 1960; Lommen et al., 2017). Importantly, turnover was not uniform across the population. Graded neurons retained remarkably consistent response profiles across retrieval sessions, and their activity remained more strongly associated with learned threat value than with freezing behavior. These observations indicate that stable components of the population code can coexist with extensive reorganization of surrounding neuronal ensembles.

These findings also inform current views of systems consolidation and cortical plasticity (Frankland & Bontempi, 2005; Lopez et al., 2024). Classical models propose that memory initially depends on subcortical structures before gradually becoming stabilized within neocortical circuits (Moscovitch & Nadel, 1998; Nadel et al., 2000). In contrast, multiple-trace and related frameworks emphasize the rapid formation of cortical memory traces and continuous cortical reorganization throughout the lifetime of a memory (Moscovitch & Nadel, 1998; Nadel et al., 2000; Tonegawa et al., 2018). Our findings are consistent with elements of both views. Representations of learned threat value emerged shortly after conditioning and remained stable within a subset of neurons despite substantial reorganization of the broader ensemble. At the same time, narrower generalization gradients and improved discrimination across retrieval sessions suggests ongoing memory updating. These observations are consistent with contemporary theories proposing that systems consolidation and retrieval-dependent updating are complementary processes through which memories continue to evolve after learning (Mau et al., 2020; Tome et al., 2024; Zaki & Cai, 2024). Our results therefore suggest a mechanism by which stable cortical representations can be preserved despite continuous neuronal reorganization, providing both the stability required for long-term memory and the flexibility needed to generalize and discriminate newly encountered stimuli.

The persistence of graded neuronal responses despite extensive ensemble turnover also has implications for understanding long-term cortical coding. Although our experiments do not establish that the stable graded neurons are memory engrams or are causally required for memory expression, they demonstrate that stable representations of learned contingencies can coexist with pronounced changes in ensemble membership. Furthermore, the fact that the GLM analysis indicates that these neurons reflect learned threat value more than freezing behavior, suggests that they encode an abstract property of the learned stimulus rather than simply mirroring behavioral output. Future studies combining longitudinal imaging with selective manipulation of stable graded neurons will be needed to confirm whether these neurons are causally required for memory storage or retrieval and whether they constitute a persistent cortical memory trace.

Notably, frequency-selective neurons were present in both conditioned and control animals, indicating that these response properties likely reflect pre-existing sensory tuning within the PL rather than neuronal populations generated through learning (Hockley & Malmierca, 2024; Zikopoulos & Barbas, 2006). Associative learning instead appeared to modify the gain of these sensory-responsive neurons, producing progressively stronger responses to threat-associated than to safety-associated tones while preserving their underlying frequency selectivity. This suggests that the inferred firing rate of these neurons is shaped by the animal’s associative experience, including both conditioning and retrieval-dependent updating. This interaction between stable graded neurons and dynamically modulated sensory-responsive neurons provides a potential mechanism by which novel stimuli can be evaluated according to both their sensory similarity and their learned significance, thereby supporting flexible generalization and discrimination despite ongoing population reorganization.

In the auditory cortex, sound-evoked suppressive (“negative”) responses contribute to lateral inhibition by sharpening frequency tuning and improving sensory discrimination (Kato et al., 2017; Wehr & Zador, 2003). Although negative responders did not exhibit robust graded responses at the population level, we identified negatively graded clusters whose response profiles mirrored those of positively graded clusters across the stimulus continuum. These observations raise the possibility that suppressive neuronal populations provide complementary inhibitory contrast that enhances discrimination while preserving graded representations of learned threat value, although testing this hypothesis will require future causal experiments.

Together, our findings support a model in which sensory similarity and associative learning make complementary contributions to threat generalization. Sensory similarity determines the consistency between population responses produced by the same stimuli, whereas associative learning transforms these responses into graded representations of learned threat value that remain stable despite substantial ensemble turnover through the complementary contributions of stable graded and dynamic frequency-selective neurons. These findings provide a neural framework for understanding how the PL supports adaptive generalization and discrimination.

Methods

Subjects

Female and male C57BL/6J mice (IMSR_JAX:000664; Jackson Laboratory, Bar Harbor, ME), aged 8–10 weeks, were housed on a 12 h light/dark cycle. All experiments were conducted during the light phase of the cycle. Animal housing and care were consistent with standards set by the Association for Assessment and Accreditation of Laboratory Animal Care (AAALAC). All experimental procedures were approved by the University of Iowa Institutional Animal Care and Use Committee.

Discriminatory fear conditioning task

The training day, mice were placed in a square conditioning chamber (20 × 20 cm; Context A, Fig. 1a). The first 3 minutes served as a habituation period. Following habituation, experimental mice received presentations of a conditioned stimulus (CS⁺) tone (15 or 3 kHz, 80 dB, 20.5 s) that co-terminated with a mild foot shock (unconditioned stimulus, US; 0.5 s, 0.5 mA). Between CS⁺ presentations, animals were presented with a non-conditioned stimulus (CS⁻) tone (3 or 15 kHz, 80 dB, 20.5 s) that was never paired with shock. Mice received 10 CS+ tone–shock pairings and 10 CS− tone presentations. Intertrial intervals between CS⁺ and CS⁻ presentations alternated pseudo-randomly between 2, 4, and 6 minutes. Following the final CS⁻ presentation, mice remained in the chamber for an additional 60 s before being returned to their home cages. Control mice were exposed to the same auditory stimuli but did not receive foot shocks. On day 1, mice were placed in a novel context (Context B; 20 × 20 cm; see Fig. 1a) that differed from the training context in wall color, floor texture, and background scent. Animals were allowed to freely explore the chamber for 3 minutes, after which they were presented with auditory stimuli consisting of the conditioned tone (CS⁺) the non-conditioned tone (CS⁻), and two intermediate frequencies (7 and 11 kHz) spanning the same spectral range. These intermediate frequencies were spaced linearly rather than logarithmically. Tones were presented in a semi-random order, with three presentations per frequency and 3-min intertrial intervals. Following the final tone presentation, mice remained in the chamber for an additional 60 s period before being returned to their home cages.

Behavioral analysis

All behavioral sessions were video recorded using a mounted camera. Freezing behavior was defined as complete immobility except for respiratory movements and was quantified as a percentage of total trial time. Freezing was measured using FreezeFrame 5 software (Actimetrics, RRID:SCR_014429) for non-implanted mice and inertial measurement unit (IMU) data from the Inscopix miniscope system for implanted mice. This approach quantifies movement across three axes and circumvents visual occlusion introduced by the miniscope tether. To validate automated scoring, a subset of sessions from implanted and non-implanted mice were randomly selected and manually scored by an experimenter blind to experimental condition, following established criteria (Phillips & LeDoux, 1992; Wang et al., 2012). Automated and manual measurements were highly correlated (Pearson’s r = 0.98 and 0.96), confirming strong inter-method reliability. Freezing responses were analyzed across three retrieval sessions (days 1, 15, and 30). Two animals in the non-shock control group (JAM061 and JAM062) were excluded from repeated-measures analyses due to missing data on day 30 but were retained for day-specific comparisons.

Viral construct stereotaxic surgery

Mice were anesthetized with isoflurane (3% in oxygen at 1 L/min) and placed in a stereotaxic apparatus (David Kopf Instruments, Tujunga, CA). During surgery, anesthesia was maintained at 1.5%. The head was positioned to ensure a flat skull in both the anterior–posterior (AP) and medial–lateral (ML) planes. Rimadyl (5 mg/kg, s.c.) was administered preoperatively and for two consecutive days postoperatively for analgesia. For calcium imaging experiments, three injections (150 nL each) of AAV1-CaMKIIα-GCaMP6f-WPRE-SV40 (Addgene cat. # 100834) were delivered into the PL at the following stereotaxic coordinates relative to bregma: AP +1.95 mm, ML ±0.3 mm, and DV −1.7, −1.5, and −1.3 mm. Injections were performed at a rate of 50 nL/min. After each injection, the syringe was left in place for 5 minutes to allow for viral diffusion and to minimize backflow. Mice were allowed to recover for four weeks prior to implantation of the GRIN lens and baseplate assembly for in vivo imaging.

Miniendoscope baseplate placement

Following AAV-GCaMP6f injections, a gradient-index GRIN lens (Inscopix, diameter: 1.0 mm, length: 4.0 mm, numerical aperture: 0.5, model: 1050-004637) and baseplate assembly (Inscopix, Mountain View, CA) were implanted above the PL. Stereotaxic coordinates relative to bregma were AP +1.94 mm, ML ±0.3 mm, and DV −1.5 mm. The cortical surface was identified and set as the zero reference point. To create a tract for lens placement, a 26-gauge syringe needle was lowered to approximately two-thirds of the final depth (DV −1.0 mm) and then slowly retracted. The GRIN lens was subsequently lowered to the final DV coordinate (−1.5 mm) and secured in place with a thin layer of cyanoacrylate adhesive applied around the lens perimeter and over the exposed skull. Dental cement (Lang Dental) was used to further stabilize the baseplate and anchor it to the skull. Mice were allowed to recover for at least two weeks before the onset of behavioral training.

Calcium imaging analysis

Calcium imaging data acquired using the Inscopix nVoke 2.0 miniscope system were processed using Inscopix Data Processing Software (IDPS; Inscopix, Mountain View, CA). Raw recordings were first preprocessed using the standard IDPS pipeline, which included spatial downsampling, background subtraction, spatial filtering, and rigid motion correction to compensate for movement artifacts. Fluorescence signals were then normalized to ΔF/F, defined as the change in fluorescence relative to a baseline fluorescence level computed for each pixel, to quantify activity-dependent calcium dynamics. Following preprocessing, neuronal signals were extracted using a constrained non-negative matrix factorization approach optimized for one-photon calcium imaging (CNMF-E implemented by IDPS). This method decomposes the imaging data into spatial components corresponding to putative neurons and their associated temporal activity traces while accounting for background and neuropil contamination. Extracted components were manually curated to exclude non-neuronal signals and artifacts based on established morphological and activity criteria (Fig. 1d).

Neuronal activity was aligned to tone onset for all analyses, whereas signal representation, normalization, baseline correction, and temporal binning were adapted to the analytical objective. Sound responder classification, average stimulus-aligned traces, population trace analyses, stimulus response vectors, and the GLM were performed on ΔF/F fluorescence signals, whereas population similarity and baseline-to-stimulus ratio (BSR) analyses used CASCADE-deconvolved activity. Depending on the analysis, normalization consisted of either trial-wise or session-wise z-scoring, with baseline correction subsequently applied when quantifying stimulus-evoked responses. Analysis-specific processing steps are summarized in the table below and details provided in the relevant method subsections.

Sound responder classification

To quantify stimulus-evoked modulation of neuronal activity, we implemented a window-based sound response test (SRT) that detects changes in calcium activity relative to the pre-stimulus baseline while preserving the temporal structure of the response.

Data alignment and normalization

For each neuron, ΔF/F traces were aligned to tone onset and resampled onto a common relative time axis spanning a pre-stimulus baseline (10s before tone onset) and the 20-s stimulus period. All time points within that trial were normalized by subtracting the baseline mean and dividing by the standard deviation of that trial’s baseline across time. A small constant was added to the denominator to prevent division by zero. This within-trial normalization places all trials on a common scale prior to being combined and is distinct from the between-trial term described below, which standardizes the reliability of the baseline across trials.

Sliding window construction

To capture temporally localized stimulus responses, normalized traces were segmented into overlapping sliding windows spanning the stimulus period. Windows were defined by a fixed duration (1 s) and stride (0.1 s), with window boundaries determined directly from the sampling interval of the data. Only windows fully contained within the stimulus epoch were included. This approach enabled detection of responses with variable onset latencies and durations without assuming a fixed response time.

Window-wise response quantification

For each window, the median normalized activity was computed and compared with the corresponding trial baseline median. Baseline-subtracted responses were then averaged across trials to obtain a mean response magnitude for each window. Separately, to down-weight windows in cells whose baseline was unreliable across repetitions, a between-trial standardization was computed for each window as the mean baseline-subtracted response divided by the standard deviation of the per-trial baseline medians across trials. This computation indexes trial-to-trial baseline reliability rather than within-trial fluctuation, and was used only to gate which windows entered the significance test (see below); the response magnitude used to classify sound responders is the trial-averaged, baseline-relative response itself, already expressed in units of each trial’s baseline standard deviation. For single-trial cases, where a between-trial standard deviation is undefined, the trial-averaged baseline-relative response was used directly.

Statistical comparison to baseline

For each window, normalized activity values were compared with the pooled baseline distribution across trials using a two-sample Kolmogorov–Smirnov test. This nonparametric test was selected because it detects differences in both central tendency and distribution without assuming normality.

Identification of significant response epochs

A window was classified as significant if it met two criteria: (i) a p-value below a predefined threshold (typically p < 0.05) and (ii) a between-trial standardized response of at least one baseline standard deviation. Significant windows were classified as positive or negative according to the sign of the response, and contiguous windows of the same sign were merged into response epochs, allowing gaps of one window or less to account for noise. For each neuron and response direction, the longest response epoch was retained.

Summary response metrics

For each response epoch, we extracted the trial-averaged baseline-relative response and associated duration. Based on these metrics, responses were classified as positively modulated (trial-averaged baseline-relative response ≥ 3 and significant for at least 1 s) or negatively modulated (baseline-relative response ≤ −1.5 and significant for at least 1 s), where the response is expressed in units of each trial’s baseline standard deviation.

Mapping active ensembles across time

For longitudinal analyses, neuronal identity across imaging sessions was tracked using spatial footprint registration to identify putatively identical neurons across days. Spatial footprints of cells detected during conditioning were registered longitudinally using a probabilistic model implemented in CellReg [Inscopix, (Evangelidis & Psarakis, 2008)]. This algorithm aligns neurons based on the similarity of their spatial footprints, enabling consistent tracking of neuronal identity across imaging sessions. To evaluate registration quality, we used the conditioning session as the reference and measured the centroid distances between each neuron and its corresponding match in each retrieval session. For each animal, we generated histograms of these centroid shifts (expressed in micrometers) and compared their distributions with the median equivalent footprint diameter of the neurons. To estimate this value, we thresholded each neuronal footprint at half of its maximum intensity and calculated the diameter of an equivalent circle having the same area. Cells classified as consistently active were those reliably detected across all phases of conditioning and retrieval, including sessions on days 1, 15, and 30.

Average stimulus-aligned trace procedure

For each neuron and tone frequency, session z-scored ΔF/F traces were aligned to tone onset, and 40-s epochs (10 s pre-stimulus, 20 s stimulus, 10 s post-stimulus) were extracted. Epochs were linearly interpolated to a common time base (to allow for later averaging), after which the mean activity during the pre-stimulus period was subtracted to baseline-correct each epoch. Baseline-corrected epochs were then averaged across repetitions to generate a single average stimulus-aligned trace (ASAT) for each neuron and tone.

Generation of Population Sound-Response Curves

Population sound-response curves were generated by first averaging ASATs across neurons within each animal and condition and then averaging these animal-level traces across animals within each experimental group, representing the population response to each auditory stimulus.

Population similarity across repeated tone presentations

CASCADE-inferred firing rates were Gaussian-smoothed (2-s kernel), z-scored within each session, and averaged within overlapping 1-s windows (0.5-s overlap) to generate population activity vectors. Population similarity matrices were computed by correlating these vectors across independent presentations of the same tone (within-tone comparisons) and different tones (cross-tone comparisons). Similarity matrices were not symmetrized, preserving asymmetries arising from stimulus order (e.g., 11 vs. 3 kHz or 3 vs. 11 kHz), tone identity, and stimulus-evoked population dynamics. Matrix axes represent time relative to tone onset (−10 to 30 s), with tone presentation occurring from 0 to 20 s. The earlier tone presentation is plotted on the y-axis and the later presentation on the x-axis. To quantify similarity during stimulus onset, correlation values from the first 5 s of tone presentation were averaged for each animal and compared across tone pairs relative to the CS+ in each experimental group.al, focusing on tone pairs relative to the CS+ in each experimental group.

Classification of subpopulation tone-response patterns

Stimulus response vectors

For each neuron, baseline-corrected ΔF/F responses were extracted from 40-s stimulus-aligned epochs (10 s pre-stimulus, 20 s stimulus, 10 s post-stimulus), interpolated to a common time base, and averaged across repetitions for each tone frequency. Responses to the four frequencies were then concatenated in ascending order to generate a composite response vector for each neuron.

Mutual information matrix

For each pair of cells, we computed the mutual information (MI) between their stimulus response vectors to quantify the statistical dependence between their responses. MI measures the reduction in uncertainty about one variable given knowledge of another. In this context, low MI values indicate that the stimulus response vectors of two cells are largely independent, whereas high MI values indicate shared information or coordinated response structure. The MI values for all cell pairs were assembled into a symmetric matrix (n_cells × n_cells), with each entry representing the information shared between a given pair of cells. Separate MI matrices were computed for each experimental group (non-shock, CS+3, CS+15), pooling cells across recording days within each group. In what follows, “MI matrix” refers to one of these matrices.

Adjacency matrix construction

To transform the MI matrix into a network graph representation, we applied a summed top-k adjacency procedure. For each cell (matrix row), connections to other cells were ranked by MI strength, and only the top-k values were retained. Each retained connection was weighted by the reciprocal of its rank (1 / rank), favoring the strongest associations. The resulting matrix was symmetrized to represent an undirected network of functional connectivity (if cell A is functionally connected to cell B then this enforces that B is also functionally connected to A).

Spectral clustering

The adjacency matrix was analyzed using spectral clustering to identify functional subpopulations. Spectral clustering converts the adjacency matrix into a graph Laplacian, computes its eigenvalues and eigenvectors, and projects the data into a low-dimensional space in which clusters are more separable. K-means clustering was then applied to the eigenvector representations to delineate groups of highly connected neurons. This approach is well suited for detecting non-linear or irregular structures in neuronal co-activity subpopulations.

Hyperparameter selection

Two hyperparameters were determined: the top-k value and the number of clusters. We evaluated a range of top-k values (2 to 100) and, for each, computed the first 30 eigenvalues of the normalized graph Laplacian obtained during spectral clustering. Eigenvalues were averaged across top-k values to yield a single representative spectrum. The optimal cluster number was then determined using the eigengap method, defined as the largest gap between consecutive eigenvalues. The top-k values associated with this solution were averaged to obtain the final k.

Positively and negatively modulated subpopulations

Because MI is non-directional, it cannot distinguish between positively and negatively correlated responses. To separate these responses, Spearman’s correlation was computed for all pairs of cells within the cluster, and only the sign of each correlation was retained, resulting in a sign matrix of the same dimensions as the MI matrix. A signed MI matrix was then created by element-wise multiplication of the sign matrix by the MI matrix. The signed MI matrix was then used as input for another round of clustering, as previously described. Briefly, this involved generating a top-k adjacency matrix, computing eigenvalues from the normalized Laplacian, determining the optimal number of clusters using the eigengap method, and assigning cluster labels. Based on this procedure, one cluster was separated into three sub-clusters, while all other clusters were separated into two sub-clusters.

Global labels

Since our clustering method begins with a MI matrix, and each group has its own MI matrix and associated subclusters and subcluster labels, we performed a final cluster labeling step that allowed for comparison across groups. The results are such that, if a set of cells in group A have been assigned cluster label L, then the set of cells in group B having similar response patterns will be assigned the same cluster label L, allowing for comparison across groups.

Cluster Stability

To assess the stability and reorganization of functional clusters across days, we tracked registered cells that were detected on at least two of the three imaging sessions (day 1, day 15, and day 30). For each pair of days (A, B) and each cluster label L on day A, we quantified label stability (“percent_same”) — the percentage of cells that had label L on day A and retained the same label on day B:

where n_L is the number of cells assigned to label L on day A and n_same is the number of those cells that were assigned the same label on day B. Higher percent_same values indicate that a larger fraction of cells maintained the same cluster identity across days, suggesting that the corresponding functional cell assemblies were stable over time. Conversely, lower percent_same values reflect cluster reorganization, where individual cells changed their cluster membership between sessions.

Baseline-to-stimulus firing rate ratio (BSR)

For each neuron, the mean CASCADE-inferred firing rate during the 20-s stimulus period was divided by the mean firing rate during the 10-s prestimulus baseline. Ratios were then averaged across cells within each animal, cell type, and recording day.

Generalized linear model (GLM)

Freezing estimate

Movement was quantified using the inertial measurement unit (IMU) integrated into the head-mounted miniscope. Because the IMU provides band-limited body acceleration rather than locomotion speed, we fitted a two-component Gaussian mixture model to the distribution of log-transformed body-acceleration magnitude. The posterior probability that each imaging frame belonged to the low-movement (freezing) component, p_freeze(t) ∈ [0,1], was used as a continuous freezing regressor. Samples containing invalid or missing IMU values were identified using a validity mask and excluded from the analysis rather than being classified as freezing.

We used a continuous estimate of freezing instead of applying a binary threshold because it captures graded variations in immobility and uncertainty in behavioral state. Consequently, the GLM removes more behavior-related variance from the neural signal than would be expected with a binary freezing classifier. This provides a conservative test of tone encoding: if neuronal activity were primarily explained by freezing, the continuous regressor would account for more of that variance, making it more difficult—not easier—to detect an independent contribution of tone identity.

Freezing-controlled time-series GLM

We fitted a generalized linear model (GLM) to the z-scored ΔF/F time series of each neuron to estimate the independent contributions of tone identity and freezing behavior. The design matrix included four tone regressors (3, 7, 11, and 15 kHz), a continuous freezing regressor derived from IMU measurements (see previous subsection), and a trial-number regressor to account for within-session drift. The model was fitted without an intercept so that each tone coefficient represented activity relative to the inter-tone baseline. Standard errors were estimated using heteroskedasticity- and autocorrelation-consistent (HAC; Newey–West (Newly, 1987)) estimators because calcium activity exhibits substantial temporal autocorrelation, making conventional ordinary least squares standard errors anti-conservative. Autocorrelation was estimated within, but not across, trials by resetting the Bartlett kernel at trial boundaries, and the truncation lag was selected using the Newey–West plug-in rule, capped at the duration of a single trial. Statistical significance was assessed using two-sided t-tests based on the HAC standard errors.

To ensure that the effects of tone identity and freezing could be estimated independently, we assessed collinearity using the variance inflation factor (VIF). The freezing regressor exhibited minimal collinearity with the tone regressors (median VIF ≈ 1.1), confirming that the independent contributions of tone identity and freezing could be reliably estimated within the same model.

Derived per-cell metrics

From each fitted model we extracted the preferred-tone coefficient (β_pref), the freezing coefficient (β_freeze), the freezing-to-tone ratio (|β_freeze|/|β_pref|), and a binary freezing-dominant classification (|β_freeze|>|β_pref|, HAC p<0.05). A neuron was classified as freezing-dominant when the freezing coefficient was significant (HAC p < 0.05) and its absolute magnitude exceeded that of the corresponding tone coefficient.

For the general population GLM, in which neurons were not assigned to functional clusters, we used the same cells as used for the population curves and their associated beta tone values. i.e. If a cell contributed to a population response curve of a given tone, then we also used the same cell and its associated beta tone. For frequency-selective neurons, the preferred tone corresponded to the neuron’s preferred tone as determined by the mutual-information (MI) clustering analysis. For the graded neurons, each neuron generated four β tone values that were normalized by dividing by the maximum of the four.

Statistics

Behavioral and neural data were analyzed using one-or two-way analyses of variance (ANOVAs) with repeated measures. For one-way ANOVAs, tone frequency was treated as the repeated factor; for two-way ANOVAs, a between-subjects group factor (e.g., experimental vs. control) was additionally included. To evaluate the effects of frequency over time across all groups, we performed a three-way mixed-effects ANOVA with group (CS+15, CS+3, and control) as the between-subjects factor and frequency and time as within-subjects (repeated-measures) factors. When ANOVAs revealed significant main effects or interactions, post hoc comparisons were performed using Tukey multiple-comparisons test. Data normality was assessed using the Shapiro–Wilk test and homogeneity of variances with the Brown–Forsythe test prior to statistical analysis. When assumptions were violated, Friedman tests were used for repeated-measures analyses, and Kruskal–Wallis tests were used for comparisons without repeated measures. Rank-based tests were followed by Dunn’s post hoc multiple-comparison tests. Statistical significance was evaluated using a two-sided alpha level of 0.05. For analyses involving multiple cell-identity comparisons, p values were adjusted using the Benjamini–Hochberg false discovery rate procedure.

Histology

At the conclusion of experiments, mice were deeply anesthetized with isoflurane and transcardially perfused with phosphate-buffered saline (PBS), followed by 4% paraformaldehyde (PFA). Extracted brains were post-fixed in 4% PFA for 24 hours and subsequently transferred to a 20% sucrose solution containing sodium azide at 4 °C for an additional 24 hours. Frozen brains were coronally sectioned at 50 µm using a cryostat, and sections were mounted on Superfrost Plus microscope slides (Fisher Scientific). Histological verification was performed to confirm GCaMP expression and accurate lens placement within the PL.

Data availability

Datasets available at: https://data.mendeley.com/datasets/9yyn63g346/1

Supplementary figures and tables

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Table S1.

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Acknowledgements

This work has been funded by NSF (NSF/IOS 2303305 to IAM), NIH (R01 MH123260-01 to IAM; RISE GMO60655 to MRL).

Additional information

Author Contributions

MEN developed method to identify subpopulations, wrote code for analysis, and contributed to writing the manuscript, PMO collected data, conducted behavioral and in vivo recording experiments, and contributed to writing the manuscript, MRL contributed to experimental design, collected data, conducted behavioral and in vivo recording experiments. MMRA contributed to the statistical analysis. IAM supervised design, experiments, analysis, and writing of the manuscript.

Funding

National Science Foundation (NSF) (2303305)

• Isabel A Muzzio

National Institute of Mental Health and Neurosciences (NIMHANS) (MH123260-01)

• Isabel A Muzzio