We first developed a novel discrimination–avoidance task, tailored to investigate action-based complex associative learning in mice. In this task, animals learn to discriminate between two auditory cues that predict context-dependent footshocks. Specifically, sounds A and B signal electric shocks in rooms A and B of a shuttle box at sound terminations, respectively (Figure 1A; Figure 1—figure supplement 1). This design requires animals to either ‘stay’ in the current room or ‘shuttle’ to the adjacent room during sound presentations to avoid shocks (Figure 1—videos 1 and 2). During inter-trial intervals, animals are free to explore either room without consequence.

Notably, the auditory cues are not inherently associated with positive or negative valence; instead, their meaning is dynamically determined by the animal’s current location (room A or B) at the time of cue presentation, signaling either safety or shock. Thus, this task, which requires discrimination of sensory cues and environmental contexts, as well as the integration of cues, actions, and outcomes, serves as an ideal tool to study complex associative learning. Our results showed that mice gradually learned the task, achieving an average success rate of 76.7% in avoiding shocks by the 10th training session (Figure 1B). An additional five training sessions yielded a modest improvement, increasing the average success rate to 82.5% on the 15th session (Figure 1—figure supplement 2).

Given that the task requires two distinct behavioral responses, we separated the trials into shuttle and stay trials for further analysis. In shuttle trials, mice must move to the adjacent room before the sound ends to avoid shocks. Across training sessions, correct shuttles increased markedly, whereas incorrect shuttles decreased only modestly (Figure 1C; Figure 1—figure supplement 2). This pattern suggests that animals choose to shuttle primarily when they are confident in the outcome (i.e., safety); otherwise, they remain in place. Consistent with this notion, in stay trials, where mice must remain in their current room to avoid shocks, incorrect stays decreased markedly across training sessions, mirroring the improvement in correct shuttle performance. By contrast, correct stays increased only modestly (Figure 1C; Figure 1—figure supplement 2).

We also compared shuttle response latencies between correct and incorrect trials during the late stages of training. On average, the shuttle response latency was 6.5 s during correct shuttles, providing a 3.5-s temporal separation between actions (shuttles) and outcomes (safety or shocks; Figure 1D). This clear temporal distinction allows us to compare how information is coded during the action vs. outcome periods. The longer shuttle latency during incorrect shuttles suggests that last-second responses are more likely to be incorrect (Figure 1D).

Next, we conducted multi-channel in vivo electrophysiology recordings from the ACC (Figure 2A; Figure 1—figure supplement 2) in mice performing the discrimination–avoidance task after they had completed 10 training sessions and achieved a success rate of 70% or above. We initially observed robust changes in ACC activity following shuttle responses (Figure 2B, C). While many ACC neurons showed changes in activity during the shuttle period, the majority of these changes persisted well after shuttle termination, with some lasting up to 30 s after the initial response (Figure 2C, E; Figure 1—figure supplement 2). In contrast, the same ACC neurons showed no or limited activity changes during stay trials in response to the auditory cues (Figure 2D, F).

To assess ACC neuronal population activity dynamics, we performed principal component analysis (PCA) on simultaneously recorded ACC neurons across correct-shuttle and correct-stay trials (Figure 3A). The first three principal components (PCs) revealed pronounced changes in population activity during shuttle trials, whereas activity remained relatively stable during stay trials (Figure 3B; Figure 3—figure supplement 1). Quantifying the maximum trajectory distance within the 3D PC space revealed consistent, prominent changes in population activity during shuttle responses across animals in five representative sessions (Figure 3C). The pronounced ACC activity during and following shuttles, coupled with minimal activity in response to cues, suggests that ACC neurons primarily encode action and post-action variables. Such sustained post-action activity may support complex associative learning by linking temporally separated action- and outcome-relevant information.

To assess whether ACC activity has a role in encoding pre-action variables, we examined ACC activity aligned to shuttle initiations, defined as locomotion velocity exceeding 1 SD above baseline (Figure 4A). Our results revealed diverse response properties of the ACC neuronal population (Figure 4B), which frequently persisted beyond the shuttle response window (~1–3 s between shuttle initiations and terminations; Figure 4A). PCA classified these responses into three major categories (Figure 4C, D). Pre-shuttle ramping activity was mainly observed in a small subset of neurons (Types 3b and 3c, ~16% of the population), indicating a limited role of the ACC in pre-action information coding, including decision-making and planning processes. The remaining ACC neurons primarily displayed sustained activity after initiation, either activation (Types 1a, 1b, and 3a) or inhibition (Types 2a and 2b), highlighting the predominant role of the ACC in post-action information processing. Overall, despite aligning to shuttle crossings or initiations, the extended analysis windows largely captured post-action ACC activity.

To determine which shuttle event (initiation, crossing, or termination) captured the most acute changes in ACC neuronal firing, we conducted an event-locked modulation analysis (Figure 4—figure supplement 1). Our results showed that shuttle crossing was associated with the largest fraction of significantly modulated ACC neurons, particularly when comparing short windows (250–1000 ms) between pre- and post-event ACC activity (Figure 4—figure supplement 1). These findings suggest that shuttle crossing represents the most prominent event for ACC engagement during shuttle behaviors.

Given that the post-action ACC activity is often prolonged and outlasts shuttle termination, we hypothesized that this activity is distinct from locomotion encoding. To test this, we analyzed ACC activity in relation to movement speed. Each task session included a 5-min free exploration period before trials began, allowing us to assess if ACC activity is associated with basic motor functions. We found that only a small portion of neurons showed speed-correlated activity, with either positive (7.7%) or negative correlation (6.9%), indicating that the majority of the neurons are not tuned to movement speed (Figure 5A–C). This is consistent with our observation of sustained post-shuttle ACC activity in the absence of movement, which is distinct from locomotion encoding. Nevertheless, it remains unclear whether this small fraction of speed-related neurons represents a distinct subpopulation within the ACC or reflects recordings from nearby motor cortex. Postmortem examination of the recording sites suggests that most neurons were recorded from the ACC, while a small subset was located at the border between the ACC and motor cortex (Figure 1—figure supplement 2). Therefore, it is possible that the speed-related neurons originated from the motor cortex.

To determine if the post-action ACC activity encodes information related to outcomes, we analyzed ACC neuronal activity across three distinct conditions: correct shuttles, incorrect shuttles, and post-shock shuttles (Figure 6A; post-shock shuttles are defined as shuttles following footshocks received during incorrect-shuttle and incorrect-stay trials). Our results revealed that ACC neurons exhibited similar activity patterns across all three conditions, regardless of outcomes (presumed safety vs. uncertainty vs. safety; Figure 6B). Specifically, both activity strength (Figure 6C) and activity pattern (Figure 6D) were significantly correlated across conditions, indicating outcome-independent responses in ACC neurons. Consistently, we found that ACC neurons showed limited responses to footshocks during incorrect trials (Figure 6—figure supplement 1). Together, these findings suggest that ACC neurons monitor actions independent of outcomes or values associated with these actions.

Since post-action ACC activity was outcome-independent, we next asked which other features of the task ACC activity might differentiate. Leveraging the two distinct shuttle responses within the task, we examined whether ACC neurons responded differently between rooms A → B shuttles (in response to sound A) and rooms B → A shuttles (in response to sound B). Our analyses identified two major groups of ACC neurons based on their responses to these shuttles. The first group showed indiscriminate responses, exhibiting either increased or decreased activity without differentiating between A → B and B → A shuttles (Figure 7: Neurons 1 and 2). We propose that these ACC neurons encode an action state, a variable representing the change of behavioral state in response to the auditory cues.

In contrast, the second group of ACC neurons exhibited discriminative responses between rooms A → B and B → A shuttles. These neurons either responded selectively in one set of shuttles or showed different levels of responses (activation or inhibition) between the two sets of shuttles (Figure 7: Neurons 3 and 4; Figure 7—figure supplement 1). We propose that these ACC neurons encode action content, a variable representing distinct action information (i.e., shuttling from rooms A → B vs. B → A).

To quantify action-state and action-content neurons, we performed a generalized linear model (GLM)-based analysis of ACC activity surrounding shuttle responses (see Methods). Based on coefficient β or Δβ value differences, most ACC neurons were classified as either action-content neurons (54.5%; Categories 1 and 2) or action-state neurons (19.1%; Categories 3 and 4; Figure 7C–E). These findings suggest a prominent role for post-action ACC activity in encoding rich information about preceding action state and action content.

Notably, ACC activity does not resemble place cell activity observed in the hippocampus (Moser et al., 2008), as evidenced by our analysis of spike activity from the intertrial-interval periods (Figure 7—figure supplement 2). This aligns with prior findings that ACC neurons do not simply encode spatial information (Kennerley and Wallis, 2009), although action-content ACC neurons likely incorporate spatial variables, given their shuttle-route response selectivity.

To determine if the post-action ACC neuronal population activity can decode shuttle contents (rooms A → B vs. B → A shuttles), we implemented a machine-learning approach. Specifically, we trained binary support vector machine (SVM) classifiers and performed cross-validations (Figure 8A). Our results revealed that the post-shuttle population ACC activity was highly effective in decoding the animal’s preceding actions of either A → B vs. B → A shuttles, reaching a decoding accuracy close to 90% on average (Figure 8B). Although the pre-shuttle ACC activity can also decode the shuttle content, it did so with much lower accuracy (Figure 8B). Importantly, decoding accuracy was reliant on action-content neurons, as their removal significantly reduced decoding accuracy, whereas removal of non-action-content neurons had no effect (Figure 8C). These results persisted even when neuron category counts were matched across sessions in a pseudo-ensemble decoding analysis (Figure 8—figure supplement 1). Only action-content neurons could reliably decode shuttle content, confirming a functional dissociation at the population level (Figure 8—figure supplement 1). These findings provide compelling evidence supporting post-action ACC activity in encoding detailed information about the animal’s preceding actions.

We next investigated whether post-action ACC activity following a trial influenced performance on the subsequent trial, which occurred ~1 min later. Specifically, we divided correct-shuttle trials into two groups (Figure 9A): those followed by correct trials (including both correct stays and shuttles), and those followed by incorrect trials (including incorrect stays and shuttles). Our results revealed that post-action ACC activity was notably higher when it preceded correct trials rather than incorrect ones (Figure 9B). The strength of post-shuttle ACC activity may reflect task engagement, with greater engagement facilitating learning. Statistically, the top one third of the most responsive ACC neurons exhibit significantly higher activity that preceded correct trials than incorrect ones (Figure 9C). This correlation between higher ACC activity and future correct performance suggests that post-action ACC activity may contribute to trial-to-trial behavioral adjustment that underlies associative learning (Sheth et al., 2012).

As a control, we also examined whether the status of the preceding trial influenced post-action ACC activity in the current trial. Specifically, we divided correct-shuttle trials into two groups: those preceded by correct trials, and those preceded by incorrect ones (Figure 9D). Our results showed no difference in post-action ACC activity between the two conditions (Figure 9E, F). This finding was expected, as both positive and negative reinforcement can similarly contribute to associative learning and neural plasticity.

Male C57BL/6 mice (Jackson Laboratory, stock #000664) were used in this study. The mice were 8–10 weeks old at the start of discrimination–avoidance task training. All mice were group-housed (2–4 mice per cage; 40 × 20 × 25 cm) with corn cob bedding and cotton nesting material, except that after electrode implantation surgery, mice were singly housed. They were maintained on a 12-hr light/dark cycle with ad libitum access to food and water.

All experimental procedures were approved by the Institutional Animal Care and Use Committees at Drexel University (Protocol # LA-23-740) and adhered to the National Research Council’s Guide for the Care and Use of Laboratory Animals.

Two 10 s auditory cues, 5 kHz tone at ~75 dB and white noise at ~65 dB, were chosen for sound discrimination. Both sounds included 50 ms shaped rise and fall times to reduce abruptness and minimize potential startle responses. The shuttle box used in the experiment was a square chamber measuring 25 × 25 × 32 cm, with a 36 bar shock grid floor, illuminated by lights inside sound-attenuating cubicles (64 × 75 × 36 cm) equipped with speakers (Med Associates). The shuttle box was divided at the midline by a plastic divider into two rooms. These two rooms were slightly modified for discrimination purposes: one had two black walls, one white wall, and one transparent wall, while the other room had two white walls, one metal wall, and one transparent wall (Figure 1—figure supplement 1). The divider had a 2-inch opening in the center to allow the mice to move freely between the rooms. Animals’ behaviors were recorded using Video Freeze software (Med Associates) (Anagnostaras et al., 2010).

Prior to training, all mice underwent two daily handling sessions (~10 min each). Once training began, the mice received one training session per day, 5 days per week. In the task, the mice were trained to discriminate between two distinct sounds (A and B) and shuttle between two adjacent rooms (A and B) within a shuttle box to avoid potential footshocks. Specifically, sounds A and B signaled electric shocks in rooms A and B, respectively (Figure 1A). During training, the mice were first allowed to freely explore the shuttle box for 2 min before trials began, except on the first day of training, where the free exploration period was extended to 10 min.

The training procedure consisted of two phases: pre-training and training. Pre-training phase: mice underwent five daily sessions of sound alternation trials 5/5 (AAAAABBBBB …). Mice that did not exhibit shuttling responses during the first session were excluded from further training. Training phase: mice underwent 10 daily sessions (5 sessions per week) of alternation trials in a pseudorandom order (ABBABAAB …).

Each training session comprised 50 trials, 60 s apart. On incorrect trials, up to 10 scrambled electric shocks (0.5 mA; 0.1 s) were administered starting at sound terminations and continued for an additional 18 s (1 shock every 2 s), except during the pre-training phase, where up to 20 scrambled electric shocks were administered. Shocks were terminated once the mice navigated to the adjacent safe room. The mouse’s success rate in avoiding shocks at sound terminations was defined as: Success rate (%) = (Correct stays + Correct shuttles)/All trials.

We employed MATLAB functions to detect animal location and subsequently control shock administration (Figure 1—figure supplement 1). Specifically, Med Associates Video Freeze software recorded real-time video footage of the animal’s behaviors (Anagnostaras et al., 2010). During each trial, MATLAB captured screenshots of the ongoing video at sound terminations and every 2 s thereafter during the shock period. MATLAB then performed background extraction on the captured images to determine which room the mouse was located in. To deliver a shock, MATLAB sent a ‘shock’ signal to an Arduino UNO circuit board, which relayed that signal to Med Associates, triggering shock administration.

Mice that had completed 10 training sessions and surpassed a success rate of 70% during discrimination–avoidance tasks were used for surgery. In brief, mice were anesthetized with a ketamine/xylazine mixture (∼100/10 mg/kg, i.p.) and maintained on a heating pad at 37°C. Following that, mice received an intra-ACC implantation of a custom-made electrode array (eight tetrodes) (Lin et al., 2006; Liu et al., 2024), and the implant was secured to the skull with stainless screws and resin ionomer (DenMat). The coordinates used were AP 1.0 mm, ML 0.4 mm, and DV 1.0 mm.

We used tetrodes for recording (Lin et al., 2006; Liu et al., 2024). Each tetrode consisted of four wires (90% platinum, 10% iridium; ~18 μm diameter; California Fine Wire). Neural signals were preamplified, digitized, and recorded using a Blackrock Neurotech CerePlex, while the animals’ behaviors were simultaneously recorded. Spikes were digitized at 30 kHz and filtered between 600–6000 Hz. The recorded spikes were manually sorted using Plexon Offline Sorter (Wang and Tsien, 2011; Wang et al., 2011), with key datasets verified by a second experimenter. Tetrode arrays were gradually lowered through a microdrive (Wang et al., 2015; Opalka et al., 2020) to record at multiple depths within the ACC, with 2–4 depths from each animal (DV ~1.0–1.3) used for analysis.

Overall, ACC spikes from five mice across 15 sessions were analyzed, with neuron counts of 20/23/29/32 (mouse #1; 4 sessions), 17/20/22 (mouse #2; 3 sessions), 28/24 (mouse #3; 2 sessions), 33/25/21/27 (mouse #4; 4 sessions), and 22/25 (mouse #5; 2 sessions), respectively. The total number of correct/incorrect shuttles used for analysis are 19/5, 19/4, 21/5, 20/4 (mouse #1); 20/7, 23/7, 20/7 (mouse #2); 19/4, 16/2 (mouse #3); 26/4, 23/4, 17/6, 25/5 (mouse #4); and 20/5, and 17/4 (mouse #5), respectively. For Figures 2—5, 7, and 8, all recorded neurons (n = 376) from the 15 sessions were included in the analyses. For Figures 6 and 9, however, one or two sessions were excluded because they contained too few trials of certain types (n ≤ 3).

The discrimination–avoidance task was similar to that during the training phase, except that five direct-current electric shocks, which minimize electromagnetic artifacts, were administered starting at sound terminations and continued for 8 s. This shorter shock period allowed the mice more time to move freely within the shuttle box during the 42 s inter-trial intervals, when no consequences were administered. Additionally, each task session included a 5-min free exploration period before trials began. In some sessions, a small number of trials were excluded from analysis, partly due to the electrode implant or recording cable occasionally interfering with the animal’s shuttle responses.

We used DeepLabCut (Mathis et al., 2018) to analyze animals’ locations during discrimination–avoidance tasks, with all locations determined based on body center positions. Shuttle crossing was defined as the body center crossing the midline opening of the shuttle box. Shuttle initiations and terminations were defined as the time points when the animal’s movement velocity deviated 1 SD above the mean (Figure 4A).

We used PCA to analyze the major activity patterns of ACC neuronal populations. The first three PCs were used for 3D visualizations. Specifically, the activity of each ACC neuron was first averaged during shuttle responses (bin size, 0.1 s) and z-scored. The z-scored activity of ACC neurons was then processed with PCA (pca, MATLAB).

Neural activity was aligned to shuttle initiations, crossings, or terminations following standard peri-event procedures. For each neuron, firing-rate modulation (ΔFR) was computed as the difference between post-event (0 to W ms) and pre-event (−W to 0 ms) windows (W = 250–2000 ms), similar to prior event-related analyses (Ito et al., 2015). For each event, significance was assessed using an empirical sliding-window null distribution generated within a baseline period (−20 to −10 s). Two-sided empirical p-values were computed, and neurons were considered significantly modulated if p < 0.01 and effect size |Δ| ≥ 0.6. Neurons were classified as event-specific, crossing-only, both, or non-significant based on the overlap of significant modulation. Differences in modulation prevalence were evaluated using exact McNemar tests (Hung et al., 2005).

Speed tuning was assessed using neural and behavioral data collected during a ~5-min period of free movement in the shuttle box prior to task onset. During this period, animals freely explored the environment and exhibited a broad range of instantaneous running speeds. Running speed was extracted from behavioral tracking data and sampled at 50 Hz. Spike trains from individual neurons were binned at 20-ms resolution and converted to firing rates. Firing-rate time series were smoothed using a Gaussian kernel with a 250-ms window. To reduce potential confounds associated with immobility-related network states, time points with running speed below 2 cm/s were excluded from the analysis, following established procedures (Kropff et al., 2015). For each neuron, a speed score was defined as the Pearson correlation coefficient between the smoothed firing rate and the valid portion of the instantaneous running speed.

Statistical significance was assessed using a circular time-shift shuffle procedure. For each neuron, spike times were circularly shifted by a random offset greater than 30 s, preserving the temporal structure of firing while disrupting its alignment with behavior. The firing rate–speed correlation was recomputed for each shuffle, and this procedure was repeated 100 times to generate a null distribution of speed scores. Neurons were classified as speed-modulated if their observed speed score exceeded the 99th percentile or fell below the 1st percentile of the shuffle distribution (two-sided criterion). All analysis procedures were adapted from previous studies of speed-modulated neurons (Kropff et al., 2015).

We used PCA to classify major types of ACC neurons based on their activity in reference to shuttle initiation. Specifically, the activity of each ACC neuron was first averaged surrounding shuttle responses (−5 to 5 s; bin size, 25 ms) and z-scored. The first three PCs were used in a hierarchical clustering algorithm (Linkage) to find the similarity (Euclidean distance) between all pairs of activity patterns in PC space, iteratively grouping the activity patterns into larger and larger clusters based on their similarity. Lastly, we set a distance-criterion to extract major clusters from the hierarchical tree (Liu et al., 2021).

For each neuron, we computed peri-event firing rates using 25 ms bins and normalized activity relative to a baseline window from −30 to −20 s preceding shuttle onset. Post-shuttle activity (0–5 s) was analyzed using a GLM with separate regressors for each event. Specifically, for Event 1 (shuttle A → B) and Event 2 (shuttle B → A) trials, we fit the modelr(t)=β1⋅Event1(t)+β2⋅Event2(t),\begin{document}$$\displaystyle \rm r(t) = \beta 1 \cdot Event1(t) + \beta 2 \cdot Event2(t),$$\end{document}

using a normal distribution with an identity link (glmfit, constant = ‘off’, MATLAB). We estimated coefficients β₁ and β₂ (corresponding to shuttle A → B and shuttle B → A, respectively) and assessed their significance using Wald tests against zero. To quantify event selectivity, we tested the contrast: Δβ = β₁ − β₂. Resulting p-values were corrected for multiple comparisons using Bonferroni correction across regressors and neurons (α_bonf = 0.01/(3N), where N is the number of neurons in a session). Neurons were classified as action-content neurons if the corrected p-value for Δβ was significant and the absolute effect size exceeded a predefined threshold (∣Δβ∣\begin{document}$\mid \mathrm{\Delta }\beta \mid $\end{document}>0.5). Neurons were classified as action-state neurons if Δβ was not significant but both β₁ and β₂ were individually significant after correction. All analysis procedures were adapted from previous studies (Truccolo et al., 2005; Vaccari et al., 2021; Peer et al., 2022).

We used SVM classifiers to train ACC neuronal population activity to decode shuttle content (rooms A → B vs. B → A shuttles) and subsequently performed 10-fold cross-validations. Specifically, the total number of spikes from each ACC neuron, calculated during either the pre-shuttle (−5 to 0 s) or post-shuttle period (0 to 5 s), were used for training and testing the SVM classifier. For each dataset, we performed SVM classification training and cross-validation 100 times (fitcsvm and crossval, MATLAB), assigning the mean correct classification rate as the decoding accuracy. Notably, using shorter or longer time windows surrounding shuttle responses, such as 2.5 or 10 s, yielded similar conclusions (Figure 8—figure supplement 2). Additionally, ACC neuronal population activity moderately decoded Room-A vs. Room-B stays (Figure 8—figure supplement 2; SVM training and cross-validation repeated 500 times).

To assess the contribution of action-content neurons to decoding performance, neurons were progressively removed in 20% increments (Figure 8C). Within each session, action-content neurons were ranked by ∣Δβ∣\begin{document}$\mid \mathrm{\Delta }\mathrm{\beta }\mid $\end{document} in descending order, and the top fraction was removed at each step prior to re-estimating decoding accuracy. As a control, the same number of neurons was randomly removed from the Δβ\begin{document}$\mathrm{\Delta }\mathrm{\beta }$\end{document} non-significant pool. At each removal fraction, decoding accuracies obtained after action-content neuron removal were compared to control accuracies across sessions using a paired, two-sided, Wilcoxon signed-rank test.

To quantify population-level encoding of action contents, we performed pseudo-ensemble decoding using trial-level firing rates. For each neuron, firing rate was computed separately for each trial within the post-shuttle window (0–5 s). For a given ensemble size (N neurons), pseudo-population vectors were constructed by randomly sampling one trial per neuron and concatenating their firing rates into an N-dimensional vector. Because neurons were recorded across different sessions, pseudo-ensembles were generated by independently sampling trials across neurons at each resampling iteration. Within each neuron, trial numbers were balanced across conditions by subsampling the larger condition to match the smaller (at least four trials). Trials were partitioned into training and test pools using a fixed holdout fraction (25%). Pseudo-population vectors were generated separately from the training and test pools to ensure independence between model fitting and evaluation. The SVM classifier was trained to discriminate action contents (A → B vs. B → A) using training population vectors. Decoding accuracy was computed exclusively on held-out test vectors (N = 10, 20, 30, 40, or 50). This procedure was repeated across multiple ensemble sizes and resampling iterations to obtain stable estimates of decoding performance. Shuffle controls were implemented by randomly permuting training labels while keeping test labels unchanged, thereby preserving population statistics while eliminating condition identity (Hung et al., 2005; Meyers, 2013).

To quantify spatial information coding, firing rate maps for individual neurons were constructed using 1 × 1 cm spatial bins in NeuroExplorer and smoothed with a Gaussian filter (filter width, 3 bins) before being exported to MATLAB for further analyses. Spatial information for each neuron was calculated using the following formula:SpatialInformation(bits/spike)=∑ipiλiλlog2λiλ,\begin{document}$$\displaystyle Spatial\, Information\, \left (bits/spike\right)=\underset{\mathrm{i}}{\sum }\mathrm{p}_{\mathrm{i}}\frac{\mathrm{\lambda }_{i}}{\mathrm{\lambda }}\mathrm{log}_{2}\frac{\mathrm{\lambda }_{\mathrm{i}}}{\mathrm{\lambda }},$$\end{document}

where λ_i is the mean firing rate in the ith bin, λ is the overall mean firing rate, and p_i is the probability of the animal’s being in the ith bin, as described previously (Liu et al., 2024; Skaggs et al., 1996).

To mark the final recording sites, we made electrical lesions by passing 10 s, 10-μA currents through multiple tetrodes. Mice were deeply anesthetized and intracardially perfused with ice-cold PBS or saline, followed by 10% formalin. The brains were removed and postfixed in formalin for at least 24 hr. The brains were sliced into coronal sections of 50 μm thickness using a Leica vibratome. Brain sections were mounted with Mowiol mounting medium for microscopic examination of electrode array placements.

Sample sizes were based on previous similar studies (Liu et al., 2024; Liu et al., 2021). All statistics were conducted in SPSS 30.0. Statistical analyses include repeated measures ANOVA, the nonparametric Friedman test by post hoc test (pairwise Wilcoxon signed-rank test and Bonferroni correction), the Wilcoxon signed-rank test (paired), and Student’s t test (paired). All statistical tests are two-sided; p-values of 0.05 or lower were considered significant.