Dissociable cortical contributions to impulse control during waiting

Abstract

Self-control requires regulating actions over time, particularly suppressing impulsive actions to obtain future rewards. Using a delayed-response task in mice, we identified distinct cortical contributions to impulse control during waiting. Optogenetic inhibition revealed that the dorsomedial frontal cortex (dmFC) promotes patience, the anterior insular cortex (AIC) drives impulsivity, and the posterior parietal cortex (PPC) regulates temporal precision in waiting. Calcium imaging uncovered region-specific computations: PPC neurons predominantly encoded absolute elapsed time through time cell-like activity, tiling the waiting period independently of patience levels. Their activity predicted the waiting precision. Meanwhile, dmFC and AIC neurons exhibited opposing lick-related activity—dmFC neurons preferentially decreasing and AIC neurons increasing activity during licking. Furthermore, their activity changes during waiting predicted patience. These findings reveal distinct yet complementary mechanisms underlying impulse control during waiting: The PPC encodes temporal information crucial for regulating waiting behavior, while the dmFC-AIC circuit orchestrates a push-pull dynamic to regulate patience.

Triple dissociation in waiting behavior: PPC encodes time, while dmFC/AIC exert opposing control over patience/impulsivity.

INTRODUCTION

Self-control is fundamental to adaptive behavior, enabling individuals to prioritize goals over immediate impulses. Deficits in this capacity are associated with various neuropsychiatric conditions, including attention-deficit hyperactivity disorder, substance use disorder, and impulsivity-related personality disorders (1). The delayed-response paradigm, which requires withholding immediate actions in favor of future rewards, provides a useful framework for studying the neural mechanisms of self-control. This paradigm captures the dynamic interplay between patience and impulsivity (2), requiring not only the suppression of premature actions but also the ability to estimate and track time to guide goal-directed behavior (3).

Human neuroimaging studies have identified a distributed network of brain regions involved in self-control, with the prefrontal cortex (PFC) consistently emerging as a central hub (2, 4, 5). The PFC has been strongly implicated in suppressing impulsive responses and facilitating intertemporal decision-making. Increased PFC activity is positively associated with successful self-control, enabling the prioritization of long-term larger rewards over short-term smaller ones (2, 4, 5). Conversely, damage or perturbation of the PFC impairs intertemporal decision-making and the suppression of automatic responses (6–10). In rodents, the medial frontal regions, including the medial PFC and secondary motor cortex, have been extensively studied, revealing their critical role in patient waiting behaviors and the suppression of impulsive responses. Neurophysiological and inactivation studies have consistently demonstrated medial frontal involvement in such tasks, underscoring its essential function in sustaining patience (10–15).

The anterior insular cortex (AIC) integrates interoceptive states with external information to regulate cognitive and motivational processes (16, 17). Traditionally associated with interoception, the AIC has recently been implicated in decision-making tasks that require motivation-driven control (16, 18–20). Activation of the AIC during intertemporal choice tasks and response inhibition (21) highlights its relevance to impulsivity regulation. Extensive reciprocal connections with the medial frontal area (20, 22, 23), combined with the functional imaging findings, suggest that the AIC serves as a critical hub for integrating internal states to guide waiting behavior.

The posterior parietal cortex (PPC) is implicated in diverse cognitive functions, including sensory integration, attention, and decision-making (24–28). Although its direct contributions to waiting behavior have not been extensively explored, there are indications of its involvement. Neurophysiological studies demonstrate PPC contributions to evidence accumulation, sensory and choice history representation, and subjective value coding to guide decision-making, suggesting a role in maintaining task-relevant representations during delay periods preceding behavioral responses (28–33). The PPC’s connectivity with the medial frontal area (22, 27, 34) further implicates its potential role in delayed responses, yet the specific mechanisms by which PPC activity influences waiting behavior remain to be elucidated.

Despite these advances, the precise cellular mechanisms by which these cortical regions regulate impulse control during waiting, as well as their relative contributions, remain to be fully delineated. To address this, we used a delayed-response task in mice, integrating optogenetic inhibition and calcium imaging to dissect region-specific roles. Optogenetic manipulations revealed a remarkable triple dissociation: dorsomedial frontal cortex (dmFC) inhibition reduced waiting times, AIC inhibition extended waiting times, and PPC inhibition increased waiting time variability without altering the mean of waiting times. Calcium imaging further elucidated the distinct neural dynamics underlying these effects. PPC neurons primarily encoded elapsed time through distributed, tiling activity spanning the waiting period, independent of patience levels. In contrast, dmFC neurons were more likely to exhibit lick-related activity suppression, while AIC neurons preferentially showed lick-related activity enhancement, with both activity changes during waiting correlating with patience. These findings highlight the specialized contributions of each region, with the dmFC promoting patience, the AIC driving impulsivity, and the PPC encoding precise temporal information. By integrating causal manipulations with neural population analyses, this study provides a comprehensive understanding of the cortical circuits governing impulse control during waiting.

RESULTS

Optogenetic inhibition reveals distinct cortical contributions to waiting behavior

To examine waiting behavior in mice, we used a modified delayed response task (Fig. 1A). Each trial began with a 0.5-s tone stimulus marking the trial’s onset, followed by a 2-s delay period during which mice were required to suppress licking behavior. In 50% of the trials, designated as “nonprobe” trials, a brief airpuff stimulus was delivered at the end of the delay, indicating the start of a 2-s response window during which mice could lick a water port to receive a water droplet reward. In the remaining 50% of trials, termed “probe” trials, no airpuff was delivered, requiring mice to rely on internal timing to initiate licking after the 2-s delay without an external cue. The response window in probe trials was extended to 6 s, allowing for the assessment of endogenous impulsivity during the waiting period. Trials were classified as follows: (i) hit trials: trials where mice successfully inhibited licking during the delay period and responded appropriately within the response window; (ii) premature response trials: trials where mice failed to suppress licking during the delay period; and (iii) miss trials: trials where mice did not lick during the response window.

Fig. 1. Optogenetic inhibition during the modified delayed response task.

(A) Schematic of a PV-ChR2 mouse performing the modified delayed response task, which includes two trial types: nonprobe trials and probe trials (with or without an explicit cue signaling the end of the delay period). A 473-nm laser was applied in 30 to 50% of trials, beginning at delay period onset and continuing until 2 s after the first lick response. (B) Optogenetic inhibition was applied to different cortical regions by delivering a 473-nm blue laser via an optic fiber in PV-ChR2 mice. Bottom: Representative histology images of each cortical region showing the optic fiber track (white lines). Scale bars, 500 μm. (C) Effect of optogenetic inhibition on hit rate, combining both probe and nonprobe trials. (D) Effect of optogenetic inhibition on mean waiting time during probe trials. (E) A logistic function was fitted to the cumulative distribution of waiting times to extract two parameters: the inflection point, where smaller values indicate greater impulsivity, and the rate constant, where smaller values indicate higher variability in waiting times. (F and G) Mean frequency (F) and cumulative (G) distribution of waiting times, averaged across sessions. Error bars, means ± SEM. (H) Example session showing optogenetic inhibition in each cortical region. Black: laser OFF trials; cyan: laser ON trials. (I and J) Effect of optogenetic inhibition on the inflection point (I) and rate constant (J). n = 40 sessions, 8 mice for the dmFC; n = 56 sessions, 6 mice for the AIC; n = 51 sessions, 6 mice for the PPC. ***P < 0.001; **P < 0.01; not significant, n.s.; P > 0.5, Wilcoxon signed-rank test.

To investigate the role of each cortical region in impulse control during waiting, we applied bilateral optogenetic inhibition to each cortical region, including the dmFC, the AIC, and the PPC (Fig. 1B and fig. S1). Optogenetic inhibition was applied in 30 to 50% of randomly selected trials, starting from the onset of the delay period and continuing until 2 s after the first lick response (Fig. 1, A and B). To assess the balance between patience and impulsive behavior, the hit rate was calculated as the number of hit trials divided by the total number of hit and premature trials, independently of the miss rate. Optogenetic inhibition of the dmFC significantly reduced the hit rate across all trials, indicating an increase in impulsive (premature) responses (P = 3.6 × 10⁻⁸, Wilcoxon signed-rank test; Fig. 1C). This effect remained significant when analyzed separately in probe and nonprobe trials (P = 1.4 × 10⁻⁷ and 3.5 × 10⁻⁷, respectively; fig. S2, A and B). In contrast, inhibition of the AIC increased the hit rate [P = 8.0 × 10⁻¹¹ for all trials (Fig. 1C); P = 1.4 × 10⁻⁹ for probe trials and P = 9.0 × 10⁻¹⁰ for nonprobe trials (fig. S2, A and B)]. Meanwhile, inhibition of the PPC had no effect on the hit rate [P = 0.85 for all trials (Fig. 1C); P = 0.50 for probe trials and P = 0.78 for nonprobe trials (fig. S2, A and B)].

To further evaluate the impact of optogenetic inhibition on endogenous waiting behavior, we analyzed the mean and distribution of waiting times in probe trials, where the animal waited without an external cue signaling the end of the delay (Fig. 1F). By fitting a logistic function to the cumulative waiting time distribution in those trials (Fig. 1, E, G, and H), we extracted two parameters: (i) the inflection point, which represents the mean waiting time, and (ii) the rate constant, which reflects the variability of waiting times. Consistent with the reduced hit rate, dmFC inhibition decreased both the mean waiting time and the inflection point (P = 3.3 × 10⁻⁷ and 9.9 × 10⁻⁷; Fig. 1, D and I), indicating increased impulsivity. In addition, it increased the rate constant (P = 5.3 × 10⁻⁷; Fig. 1J), suggesting reduced waiting time variability. In contrast, AIC inhibition had the opposite effect, increasing the mean waiting time and inflection point (P = 4.5 × 10⁻⁹ and 7.0 × 10⁻⁸; Fig. 1, D and I), indicative of reduced impulsivity, while decreasing the rate constant (P = 0.004; Fig. 1J), reflecting greater waiting time variability. PPC inhibition did not alter the mean waiting time or the inflection point (P = 0.69 and 0.99; Fig. 1, D and I) but significantly decreased the rate constant, suggesting increased waiting time variability without affecting impulsivity (P = 1.7 × 10⁻⁶; Fig. 1J). Sham laser stimulation, achieved by blocking the laser pathway, confirmed that the behavioral effects were not attributable to nonspecific factors, including procedural artifacts such as the laser on/off trial structure or light leakage at the patch cable-ferrule interface (P > 0.05 for all comparisons; fig. S3, A to D). We also observed distinct behavioral effects across different target region groups in the optogenetic experiments. These dissociable outcomes cannot be explained by generalized nonspecific factors, such as tissue heating or intracranial light perception, further reinforcing the specificity of our findings.

We next examined the effects of optogenetic inhibition on additional behavioral metrics, including reaction time and miss rate in nonprobe trials. dmFC inhibition significantly decreased reaction time (P = 0.004; fig. S2D) without affecting miss rate (P = 0.15; fig. S2C). In contrast, AIC inhibition significantly increased both reaction time and miss rate (P = 9.1 × 10⁻⁸ and 8.2 × 10⁻⁹, respectively; fig. S2, C and D). PPC inhibition had no significant effect on either measure (P > 0.05; fig. S2, C and D). The significant changes to the reaction time and/or miss rate during dmFC and AIC inhibition were not observed in sham laser stimulation (P > 0.05 for all comparisons; fig. S3, E and F).

Given that both dmFC and AIC inhibition altered reaction times, we considered the possibility that the observed behavioral effects reflect changes in motor readiness rather than self-control. To address this, we analyzed impulsivity-related measures less dependent on movement speed. Specifically, we quantified lick rates during premature and hit trials in probe trials. dmFC inhibition significantly increased lick rates, whereas AIC inhibition decreased them (P = 0.009 and 0.005 for dmFC inhibition, P = 0.008 and 2 × 10⁻⁴ for AIC inhibition; fig. S2, G and H).

To further support this interpretation, we revisited our earlier analysis of hit rate, defined as the number of hit trials divided by the sum of hit and premature trials. As previously shown, dmFC inhibition significantly reduced hit rate, while AIC inhibition significantly increased it during both probe and nonprobe trials (P < 0.001; Fig. 1C and fig. S2, A and B), indicating a corresponding increase and decrease in premature trial rate, respectively. These consistent, directionally opposing effects across multiple impulsivity-related measures reinforce the conclusion that dmFC and AIC play contrasting roles in regulating impulsivity and patience.

Together, these findings reveal a triple dissociation among the three cortical regions, highlighting the distinct contributions of the dmFC, AIC, and PPC to impulse control and temporal precision during waiting. This underscores their specialized yet complementary roles in regulating waiting behavior in delayed response tasks.

Drift diffusion model captures optogenetic effects

To elucidate the factors underlying waiting behavior modulated by optogenetic inhibition, we used a drift diffusion model (DDM) simulating waiting behavior dynamics. In this model, a decision variable accumulates over time with a specific drift rate and noise level, reaching a threshold that determines waiting time (Fig. 2A; Materials and Methods). In this framework, the drift rate represents the internal bias toward maintaining waiting behavior versus initiating a response. A lower drift rate indicates a stronger tendency toward patient waiting, while a higher drift rate reflects a stronger tendency toward impulsive responding. The noise level in the model captures the precision of temporal estimation during waiting, with higher noise leading to more variable waiting times.

Fig. 2. DDM of waiting behavior dynamics.

(A) Schematic of optogenetic effects on waiting time variability, modeled using DDM. In DDM, a decision variable accumulates over time at a specified drift rate, with an added noise component, until reaching a decision threshold that determines the waiting time for each trial. The drift rate reflects an internal bias between maintaining waiting behavior and initiating a lick response: Lower drift rates indicate a stronger tendency for prolonged waiting, while higher drift rates indicate a stronger tendency for shorter, impatient waiting. The noise level represents variability in time estimation during waiting, where increased noise leads to greater fluctuations in waiting times. (B) Example model-generated trajectories illustrating changes in waiting dynamics. Compared to a control condition (black), blue represents an increased drift rate, red represents a decreased drift rate, and green represents increased noise input. (C, E, and F) Effects of manipulating drift rate and noise on mean waiting time (C), inflection point (E), and rate constant (F). n = 30 iterations per condition. ***P < 0.001; n.s., P > 0.1, Wilcoxon signed-rank test. (D) Example logistic fits of the cumulative frequency distribution of waiting times simulated by increased drift rate (blue), decreased drift rate (red), and increased noise input (green) relative to a control drift rate and noise input (black).

Increasing the drift rate without altering the noise level reduced both the mean and variance of waiting times [P = 5.6 × 10⁻⁶; Fig. 2, B (blue) to D]. Logistic fits showed that this manipulation lowered the inflection points (P = 1.5 × 10⁻⁵; Fig. 2E, left) and increased the rate constant (P = 8.2 × 10⁻⁵; Fig. 2F, left). These simulated outcomes closely mirrored the behavioral effects of dmFC inhibition. Conversely, decreasing the drift rate without changing the noise levels (Fig. 2B, red) replicated the extended waiting times observed with AIC inhibition (mean waiting time: P = 1.7 × 10⁻⁶, inflection point: P = 1.9 × 10⁻⁶, rate constant: P = 1.8 × 10⁻⁵; Fig. 2, C to F). Increasing the noise level without altering the drift rate (Fig. 2B, green) increased waiting time variability without affecting the mean, aligning with the behavioral outcomes of PPC inhibition (mean waiting time: P = 0.83, inflection point: P = 0.31, rate constant: P = 0.0001; Fig. 2, C to F).

These results highlight distinct cortical contributions to waiting behavior regulation. The dmFC and AIC appear to function as part of a push-pull system governing patience and impulsivity, wherein opposing modulations of the drift rate regulate the balance between these behaviors. Meanwhile, the PPC serves a complementary role in reducing noise, ensuring stability and precision in temporal decision-making.

Calcium imaging of neural dynamics during a delayed response task

To investigate the neural mechanisms underlying waiting behavior, we conducted cellular-resolution microendoscopic calcium imaging of pyramidal neurons in the dmFC, AIC, and PPC while animals performed the same delayed-response task used in the optogenetic experiments (Fig. 3A). Task performance across groups was comparable, with similar hit rates and waiting times (Fig. 3, B to E). To selectively label pyramidal neurons, we injected adeno-associated virus (AAV) encoding the calcium indicator GCaMP6f (35) under the control of a calcium- and calmodulin-dependent protein kinase IIα (CaMKIIα) promoter into each cortical region of C57BL/6 mice (fig. S4, A to C). Imaging was performed using a gradient refractive index (GRIN) lens coupled to a miniaturized integrated fluorescence microscope (36–38), enabling simultaneous recording of activity from multiple single neurons (Fig. 3, F to H). For analyses of neural activity in hit trials (waiting time of >2.5 s), we included only probe trials, since nonprobe trials involved an airpuff stimulus that evoked licking responses. In contrast, for premature trials (waiting time of <2.5 s), we included both probe and nonprobe trials, as mice initiated licking before the possible onset of the airpuff, making the two trial types functionally equivalent in this context.

Fig. 3. Microendoscopic calcium imaging and behavioral performance.

(A) Schematic illustration of microendoscopic calcium imaging in head-fixed mice injected with AAV-CaMKIIα-GCaMP6f. (B to E) Comparison of behavioral performance across the three brain region groups. No significant differences were observed in hit rate (B), mean waiting time (C), inflection point (D), or rate constant (E). n = 28 sessions, 6 mice for the dmFC; 36 sessions, 6 mice for the AIC; and 23 sessions, 6 mice for the PPC. n.s., P > 0.05, one-way ANOVA with Bonferroni post hoc test. Error bars, means ±SEM. (F) Schematic of GRIN lens placement in the cortical regions, alongside a histological image confirming its actual position. The green-shaded region indicates GCaMP6f calcium indicator expression. Scale bars, 250 μm. (G) Example field of view (maximum intensity projection of dF/F movie). Scale bars, 250 μm. (H) Activity traces from 10 example regions of interest (ROIs). Black vertical line: trial onset; blue and red vertical lines: first lick detection in hit and premature trials, respectively; black triangles: probe trials. AID, dorsal anterior insular cortex; AIV, ventral anterior insular cortex; Cg, cingulate cortex; LPtA, lateral parietal association cortex.

To capture the primary features of population activity dynamics in each cortical region, we applied principal components analysis (PCA) to neural activity data, selecting a random subset of 100 neurons per region to ensure fair comparisons across regions (Materials and Methods). PCA revealed differences in the degree of heterogeneity across cortical regions. In the PPC, the first 22 ± 0.1 components (means ± SEM across iterations) explained 95% of the variance in population activity, whereas the dmFC and AIC required fewer components [21 ± 0.1 and 17 ± 0.1, respectively; P < 0.001, one-way analysis of variance (ANOVA) with Bonferroni post hoc test; Fig. 4, A and B, and fig. S5, A to C]. These findings were consistent with the population dimensionality of each region, as measured by the participation ratio (PR) index. The PR index quantifies how evenly variance is distributed across the principal components, with higher values indicating greater heterogeneity in the population (39). Among the regions, the PPC exhibited the highest PR index, reflecting a more heterogeneous population of neurons, followed by the dmFC, while the AIC showed the lowest PR index, indicating the most homogeneous neuronal activity (Fig. 4C; P < 0.001, one-way ANOVA with Bonferroni post hoc test). These results suggest that the PPC has a more diverse neuronal population compared to the AIC, which exhibits relatively uniform activity patterns.

Fig. 4. Dimensionality reduction of population activity in each cortical region.

(A) Cumulative explained variance from PCA across cortical regions. To compare dimensionality across regions, a resampling procedure was performed, where 100 neurons were randomly selected with replacement in each of 100 iterations. (B) Mean minimum number of principal components required to explain >95% of the variance, averaged across iterations. (C) PR index across cortical regions (n = 100 iterations, 100 neurons per iteration). (D) Schematic of dPCA, isolating two components: the waiting component (the waiting dPC; hit versus premature trials) and the condition-independent time component. (E and F) Population activity projected onto the waiting dPC (E) and the condition-independent time component (F). For each region, the projected activity is shown for each waiting time bin, aligned to tone stimulus onset (n = 2237 dmFC neurons, 2026 AIC neurons, and 2297 PPC neurons). (G) Single-trial projections onto the waiting dPC (randomly selected 30 trials per waiting time bin). (H) Decoding accuracy for discriminating hit (HT) versus premature (PM) trials based on activity 1 s after tone stimulus onset (n = 100 iterations, randomly selected 2000 neurons for each region, using five hit trials and five premature trials per iteration). (I) Persistency index, measuring the temporal stability of projected population activity onto the waiting dPC (n = 100 iterations, five trials per waiting time bin per iteration). (J) Rotation prevalence index, quantifying the prevalence of rotational dynamics in population activity (n = 100 iterations, 300 neurons per iteration). ***P < 0.001, one-way ANOVA with Bonferroni post hoc test. Error bars, means ± SEM.

Next, we assessed the temporal dynamics of the PCA components. The first component, which accounted for the largest explained variance, exhibited similar patterns across all three regions. These components displayed ramping activity during the delay period following the tone stimulus and modulation time-locked to licking (fig. S5A). This pattern is consistent with previous reports from similar delayed-response tasks in brain regions such as the medial frontal cortex and striatum (12, 13, 40–42), suggesting that those dynamics capture global, shared brain-wide dynamics associated with delayed response processes.

To identify behaviorally relevant features in neural population dynamics, we applied a targeted dimensionality reduction approach, demixed principal components analysis (dPCA) (43), by including the “waiting” component (waiting dPC), which distinguishes hit from premature trials, and the condition-independent time component (Fig. 4D; Materials and Methods). Projections onto the waiting dPC revealed dynamics that varied with waiting time, while the condition-independent component showed similar temporal profiles across waiting durations (Fig. 4, E to G). Aligning activity to lick onset further demonstrated waiting time–modulated patterns along the waiting dPC across regions, with consistent timing patterns along the condition-independent dPC (fig. S5, D and E).

Unlike the dmFC and AIC, PPC activity projected onto the waiting dPC aligned to tone onset showed notable fluctuations during waiting (Fig. 4, E and G). Due to its high temporal variability, the PPC demonstrated the lowest decoding accuracy for distinguishing hit versus premature trials using the waiting dPC as a linear classifier (P < 0.001, one-way ANOVA with Bonferroni post hoc test; Fig. 4H). In addition, the PPC had the lowest persistency index (P < 0.001; Fig. 4I), reflecting reduced temporal consistency in its projected population activity. These fluctuations suggest that PPC dynamics exhibit a strong rotational structure that is not well captured by the one-dimensional linear axis used in dPCA (44). Supporting this, the PPC had the highest rotation prevalence index (P < 0.001; Fig. 4J), as quantified using a joint principal components analysis (jPCA)–based analysis designed to detect rotational dynamics in population activity (45). While all three cortical regions exhibited some degree of rotational dynamics, these dynamics were most prominent in the PPC. Together, these findings suggest that, in contrast to the more persistent and stable waiting-related activity in the dmFC and AIC, the PPC operates through more dynamic, rotational trajectories, implying a distinct computational role in waiting behavior.

Rotational dynamics were originally observed in motor cortex population activity during reaching movements (45), where they emerged consistently across diverse movement conditions despite the aperiodic nature of the behavior. This led to the proposal that such dynamics reflect an intrinsic dynamical system in motor cortex, rather than a simple encoding of movement parameters by individual neurons (45, 46). However, subsequent work has shown that similar rotational structures can arise from various mechanisms, including oscillatory activity or sequential neuronal firing (47, 48). Therefore, while rotational dynamics offer insight into the collective behavior of neural populations, they are not sufficient to define the underlying computational function. To resolve this ambiguity and more directly link neural population dynamics to behavior, we next conducted single neuron–level analyses across brain regions, as detailed in the following sections.

Neural activity related to temporal processing during waiting

Optogenetic inhibition of the PPC increased the variance of waiting times in probe trials without affecting impulsivity (Fig. 1, D and F to J). This, combined with the PPC’s less persistent yet highly rotational population activity (Fig. 4, E and G to J), suggests that PPC neurons may encode temporal information essential for guiding waiting behavior, allowing animals to rely on internal time estimation for a 2-s delay. Supporting this idea, some PPC neurons exhibited peak activity at distinct moments during the waiting period, despite the lack of explicit temporal cues in probe trials (Fig. 5, A and B). This activity resembled “time cells” previously identified in the hippocampus (49, 50). Time cells were defined as neurons whose activity was significantly modulated by the elapsed time since tone onset, as determined by a two-way ANOVA with waiting time bin and elapsed time bin as factors (see Materials and Methods). The PPC contained a significantly higher fraction of time cells compared to the dmFC and AIC (P < 0.001, one-way ANOVA with Bonferroni post hoc test; Fig. 5E). Moreover, the peak activity of PPC time cells at the population level provided more comprehensive coverage of the entire waiting period (Fig. 5, C and D).

Fig. 5. Neural dynamics underlying temporal processing.

(A and B) Activity of example PPC time cells with high ASI (>0.9), sorted by waiting time bin. (C) Distribution of peak timings of time cells. (D) Trial-averaged activity of time cells, sorted by peak time. (E) Mean fraction of time cells (dmFC: 28, AIC: 36, and PPC: 23 sessions). ***P < 0.001; **P < 0.01; *P < 0.05, one-way ANOVA with Bonferroni test. (F) High versus low PE. (G) Distribution of the entropy of peak times. Black bars, mean. ***P < 0.001, one-way ANOVA with Bonferroni test. (H) High versus low population vector dissimilarity across time. (I) Cosine dissimilarity of population vectors across time bins and their distribution. ***P < 0.001, Bonferroni test following two-way ANOVA (region × time lag). (J) Example PPC neurons with different ASI. (K) Distribution of ASI across all neurons (PPC: 2297, dmFC: 2237, and AIC: 2026 neurons). Horizontal colored lines, median, first, and third quartiles. ***P < 0.001; **P < 0.01; *P < 0.05, one-way ANOVA with Bonferroni test. (L) Correlation between the PE of time cells and the rate constant across imaging sessions. (M) Correlation between cosine dissimilarity of population vectors and the rate constant across imaging sessions. Only the correlation in the PPC was significant (PPC: ***P = 7.1 × 10⁻⁷, dmFC: P = 0.23, and AIC: P = 0.051, one-sample Wilcoxon signed-rank test). One-way ANOVA with Bonferroni test for across-region comparisons (***P < 0.001; *P < 0.05; n.s., P > 0.05). (N) Decoding accuracy of elapsed time. (O) Mean decoding error, calculated as the absolute difference between predicted and actual time bin labels, averaged across all elapsed times. (P) Decoding error for each elapsed time. ***P < 0.001, two-way ANOVA (region × time bin) with Bonferroni test. Error bars and shadings, means ± SEM.

To systematically evaluate the distribution of peak activity, we calculated peak entropy (PE) for each imaging session (51), which measures how evenly peak activity covers the waiting period (Materials and Methods). A high PE indicates a uniform distribution of peak activity throughout the waiting period, whereas a low PE reflects a nonuniform, biased distribution (Fig. 5F). The PPC exhibited significantly higher PE than the dmFC and AIC (P < 0.001, one-way ANOVA with Bonferroni post hoc test; Fig. 5G), indicating that PPC time cells were better suited to represent evenly distributed temporal information across the waiting time.

We further analyzed the temporal evolution of population activity during the waiting period. If population activity encodes the elapsed time, the population vectors at different time points should change dynamically rather than remain static. To quantify this, we calculated the cosine dissimilarity between cross-temporal population vectors as a function of the time separation, quantifying how distinct the activity patterns were at two different time points (Fig. 5H). Across all cortical regions, cosine dissimilarity increased with greater time separation, reflecting the dynamic nature of neural activity during waiting (Fig. 5I). However, the PPC exhibited consistently higher cosine dissimilarity across all time separations compared to the dmFC and AIC (P < 0.001, Bonferroni post hoc test following two-way ANOVA with brain region and time lag factors; Fig. 5I). These results suggest that PPC activity patterns are the most dynamic and are particularly well suited for encoding distinct moments throughout the waiting period.

We observed that some neurons displayed activity independent of waiting time, while others exhibited activity modulated by waiting time (Fig. 5J). To quantify whether a neuron’s temporal activity pattern remains fixed or adjusts flexibly based on trial duration, we calculated the absolute-scaling index (ASI) (51). A high ASI indicates that a neuron’s activity follows a preserved temporal pattern, independent of waiting time, whereas a low ASI reflects flexible scaling, with activity stretching or compressing based on trial duration. The PPC exhibited a significantly larger ASI than the dmFC and AIC (P < 0.001, one-way ANOVA with Bonferroni post hoc test; Fig. 5K). Notably, the dmFC displayed a significantly lower ASI than both the PPC and AIC, showing the minimum ASI among the regions. These results indicate distinct roles of cortical regions in temporal encoding. The PPC’s high ASI suggests that it provides a robust, absolute representation of elapsed time, with neural activity patterns remaining consistent across trials, regardless of how long the animal waited. In contrast, the dmFC’s lower ASI indicates a more flexible encoding strategy, where neural activity dynamically scales with the waiting duration, potentially integrating temporal information with impulse control.

The results suggest that PPC activity is well suited for temporal estimation. To further investigate whether fluctuations in PPC activity were linked to the animal’s temporal estimation, we used the rate constant as a measure of temporal precision, where a higher rate constant indicates more precise temporal estimation (Fig. 1E). We examined whether variations in (i) PE of time cells, and (ii) the cosine dissimilarity between cross-temporal population vectors, correlated with the rate constant across imaging sessions. The PPC exhibited the strongest correlation between the PE of time cells and the rate constant (P < 0.001, one-way ANOVA with Bonferroni post hoc test; Fig. 5L). Similarly, the PPC showed the strongest correlation between the cosine dissimilarity of cross-temporal population vectors and the rate constant (P < 0.001; Fig. 5M). These findings strongly suggest that these temporal characteristics in the PPC contribute to the behavioral precision of temporal estimation.

To further probe the role of the PPC in temporal processing, we conducted a decoding analysis of elapsed time using population neural activity across brain regions (Fig. 5N). Although all regions showed robust decoding performance, the PPC exhibited the highest overall accuracy, underscoring its critical role in temporal processing. Moreover, the PPC showed the smallest decoding error, both when averaged across all elapsed time bins (Fig. 5O) and when evaluated at each individual elapsed time bin (Fig. 5P).

Overall, these findings highlight the PPC’s dominant role in encoding temporal information through an evenly distributed and absolute representation of elapsed time during waiting. In contrast, the dmFC adaptively modulates temporal activity patterns based on waiting duration. This interplay underscores the complementary roles of the PPC and dmFC in guiding time-dependent decision-making.

While we excluded the 300-ms time window preceding the first lick onset in our analyses of neural activity related to waiting time to minimize motor-related confound (see the “Binning of trials into waiting time bins and window of analysis” section in Materials and Methods), it remains possible that mice performed small, undetected licks prior to the first detected lick. To investigate this possibility, we analyzed video recordings from a subset of imaging sessions (n = 65 sessions, 15 mice) to assess potential orofacial movements preceding the first detected lick. Specifically, we performed a motion energy analysis (52), z-scoring the motion energy traces within each session and aligning them to the first lick onset (fig. S6A). We then identified the time point at which motion energy significantly increased relative to baseline (defined as 1 to 1.5 s before lick onset). This analysis revealed a significant rise in motion energy starting 800 ms before the detected lick (fig. S6A), suggesting the presence of orofacial movements, likely reflecting undetected licks, beginning at that time. To address this potential motor confound, we reanalyzed our key results using a more conservative time window, excluding at least 800 ms prior to the first detected lick from the lower bound of the assigned waiting time bin. Notably, even with this stringent adjustment, we observed qualitatively the same main findings, including dimensionality and rotation prevalence (fig. S6, B to E) as well as the series of temporal processing analyses (fig. S6, F to K), consistent with the original results (Figs. 4 and 5). Together, these additional video-based analyses confirm that our main conclusions are not explained by, nor contaminated with, motor-related activity, including undetected licking.

Functional characterization of neurons related to licking

To further investigate area specificity, we examined the functional properties of individual neurons in relation to licking behavior, a key measure of impulsiveness. Neurons were classified based on activity changes during the licking epoch, defined as 0.5 to 1 s after the first lick during the response period. Neurons were categorized as “motor-decreased” (Mdec) neurons if their activity significantly decreased during the licking epoch compared to the prelicking epoch (−0.5 to 0 s from the first lick onset; Fig. 6A, left) or as “motor-increased” (Minc) if their activity significantly increased during the licking epoch relative to the prelicking epoch (Fig. 6A, right) (see Materials and Methods). The dmFC exhibited a significantly higher proportion of Mdec neurons compared to Minc neurons (P = 0.002, Wilcoxon signed-rank test), whereas the AIC showed the opposite pattern, with a significantly greater proportion of Minc neurons (P = 0.032) (Fig. 6B).

Fig. 6. Functional characterization of motor neurons.

(A) Example Mdec and Minc neurons in the dmFC, AIC, and PPC. Trial-averaged activity in each waiting time bin was aligned on the tone stimulus or lick onset, as indicated by the dashed lines. Shaded regions, ±SEM. (B) Fraction of Mdec and Minc neurons across regions (dmFC: n = 28, AIC: 36, and PPC: 23 sessions). ***P = 0.0005; **P = 0.002; *P = 0.032, Wilcoxon signed-rank test. (C) Distribution of waiting-offset correlation index for Mdec neurons, with filled colors indicating neurons with significant correlations. (D) Top: Median waiting-offset correlation index for Mdec neurons with significant correlations. Bottom: Median waiting-offset correlation index for all Mdec neurons. Mdec neurons with significant positive/negative correlation (all Mdec neurons): dmFC: n = 84/20 (968), AIC: 31/27 (806), and PPC: 117/88 (1109). (E and F) same as in (C) and (D) but for Minc neurons. Minc neurons with significant positive/negative correlation (all Minc neurons): dmFC: n = 18/103 (692), AIC: 6/158 (905), and PPC: 28/140 (696). (G) Distribution of waiting-onset correlation index for Mdec neurons, with filled colors indicating neurons with significant correlations. (H) Top: Median waiting-onset correlation index for Mdec neurons with significant correlations. Bottom: Median waiting-onset correlation index for all Mdec neurons. Mdec neurons with significant positive/negative correlation (all Mdec neurons): dmFC: n = 18/48 (968), AIC: 9/26 (806), and PPC: 41/46 (1109). (I and J) same as in (G) and (H) but for Minc neurons. Minc neurons with significant positive/negative correlation (all Minc neurons): dmFC: n = 57/9 (692), AIC: 83/25 (905), and PPC: 69/17 (696) [(C), (E), (G), and (I)]. Colored triangles represent the median of the distribution of the indices of all Mdec/Minc neurons. Scale bars, 10 neurons [(D), (F), (H), and (J)]. ***P < 0.001; **P < 0.01; n.s., P > 0.05, one-way ANOVA with Bonferroni post hoc test. Error bars indicate the 95% confidence interval.

To examine the relationship between neuronal activity patterns and waiting, we calculated the waiting-offset correlation index for each neuron (Materials and Methods). This index was defined as the correlation between (i) waiting time and (ii) the change in activity from the baseline epoch (0 to 0.5 s before tone stimulus onset) to the premotor epoch (−1 to −0.8 s from the first lick onset), calculated as premotor activity minus baseline activity. Among Mdec neurons, those in the dmFC exhibited the highest positive waiting-offset correlation indices, followed by neurons in the PPC and AIC (P < 0.001, one-way ANOVA with Bonferroni post hoc test; Fig. 6, C and D). These findings suggest that the increased activity of dmFC-Mdec neurons during waiting is closely associated with longer waiting times. Next, we analyzed the activity of the same neuronal population during licking. For this, we defined the motor correlation index for each neuron as the correlation between (i) waiting time and (ii) the change in activity from the premotor epoch to the motor epoch (0.5 to 1.5 s from the first lick onset), calculated as premotor activity minus motor activity. dmFC-Mdec neurons showed the highest motor correlation index compared to Mdec neurons in the PPC and AIC (P < 0.05; fig. S7, A and B), indicating that the suppressed activity of dmFC-Mdec neurons during licking is strongly linked to patient waiting.

In contrast to Mdec neurons, Minc neurons tended to exhibit negative waiting-offset correlation indices, indicating that reduced activity during waiting is associated with longer waiting times (Fig. 6, E and F). Among the three regions, AIC-Minc neurons displayed the strongest negative waiting-offset correlation indices (P < 0.05; Fig. 6F), suggesting that the suppression of AIC-Minc neuronal activity during waiting is closely tied to prolonged patient waiting. A similar pattern was observed for the motor correlation index, with AIC-Minc neurons exhibiting the strongest motor correlation indices compared to those in other regions (P < 0.001; fig. S7, C and D). This indicates that increased activity of AIC-Minc neurons during licking is strongly linked to patient waiting.

The PPC contained both Mdec and Minc neurons, with Mdec neurons being more prevalent than Minc neurons (P = 0.0005, Wilcoxon signed-rank test; Fig. 6B). However, their activity correlation with waiting time was modest compared to their counterparts in the dmFC and AIC. Specifically, PPC-Mdec neurons exhibited a weaker waiting-offset correlation index (P < 0.01; Fig. 6, C and D) and a lower motor correlation index compared to dmFC-Mdec neurons (P < 0.05; fig. S7, A and B). Similarly, PPC-Minc neurons showed a weaker waiting-offset correlation index (P < 0.01; Fig. 6, E and F) and a weaker motor correlation index compared to AIC-Minc neurons (P < 0.001; fig. S7, C and D). These findings suggest that the PPC plays a limited role in licking control and in regulating patience or impulsivity, aligning with the optogenetic inhibition results.

These findings reveal distinct regional dynamics in licking-related neuronal activity. The dmFC is characterized by an enrichment of Mdec neurons, whose heightened activation during waiting and suppressed activity during licking are strongly linked to patient waiting, highlighting its critical role in promoting patience. In contrast, the AIC is dominated by Minc neurons, whose activity suppression during waiting and enhanced activation during licking are associated with patient waiting, emphasizing its role in driving impulsivity. These region-specific neuronal dynamics are consistent with optogenetic findings, which demonstrated opposing behavioral roles for the dmFC and AIC, with the dmFC fostering patience and the AIC facilitating impulsivity.

We next examined whether neural activity at the onset of waiting predicts subsequent waiting behavior. We calculated a waiting-onset correlation index, defined as the correlation between activity in the first 0 to 0.2 s after tone onset and waiting time. Across regions, Mdec neurons exhibited negative waiting-onset correlation indices (Fig. 6, G and H), whereas Minc neurons exhibited positive indices (Fig. 6, I and J), with no clear regional specificity in either case. To visualize these relationships, we plotted the population activity of Mdec and Minc neurons aligned to tone onset and sorted by waiting time (fig. S8). The trajectories revealed time-evolving dynamics that varied with waiting time. Consistent with Fig. 6, G to J, the waiting-onset activity of Mdec neurons was negatively correlated with waiting time, whereas the waiting-onset activity of Minc neurons was positively correlated. For example, dmFC-Mdec neurons showed minimal early activity in long-wait trials (green traces) followed by a gradual ramp-up, while in short-wait trials (red and blue traces), they were rapidly activated shortly after tone onset. Conversely, AIC-Minc neurons exhibited a steeper ramp-down in short-wait trials compared to long-wait trials. Unlike waiting-offset activity, the relationship between waiting-onset activity and waiting time showed no clear regional differences, suggesting that waiting-onset activity reflects region-general rather than region-specific processes.

Last, we examined the relationship between time cells and Minc/Mdec neurons across cortical regions (fig. S9, A and B). To better characterize functional diversity and specialization, we categorized neurons based on their response properties, including, but not limited to, Minc and Mdec neurons. Specifically, we identified the following functional categories: sensory-responsive (tone and/or tactile), reward-modulated, ramping, and motor-modulated (Minc or Mdec) neurons (fig. S9C; see Materials and Methods). We then assessed the overlap between these functional classes and time cells to explore how temporal coding properties relate to other task-related signals. To intuitively capture the relative prevalence of functional categories and their relationship to temporal coding, we generated polar plots for each cortical region (fig. S9C). These visualizations depict both the overall proportion of neurons within each functional category and the fraction of time cells contained within each category. We further overlaid the fraction of time cells among each category across cortical regions for the ease of comparison (fig. S9C). While the overall distributions of functional categories were comparable across cortical regions, time cells were prevalent across all functional categories in the PPC compared with the dmFC and AIC. PPC time cells exhibited relatively uniform overlap across all functional classes (fig. S9D), suggesting a more integrative role in encoding multiple task-related variables. These observations highlight the functional versatility of temporal coding in the PPC and support the notion that the PPC acts as a central hub for integrating timing information with diverse cognitive and sensorimotor processes during task execution.

DISCUSSION

Our findings reveal distinct contributions of three cortical regions to impulse control during waiting, demonstrating a triple dissociation in their roles. Through a combination of optogenetic manipulation and calcium imaging, we identified specialized functions of the dmFC, AIC, and PPC in regulating different aspects of waiting behavior. DDM provides a unifying theoretical framework for these findings, suggesting that each region contributes distinct computational components to the waiting process. Specifically, the dmFC and AIC modulate drift rates in opposite directions, while the PPC regulates noise levels in the waiting decision process.

The dmFC emerged as a critical promoter of patience, with its inhibition resulting in decreased waiting times and more impulsive behavior. This finding aligns with its established role in impulse control and delayed gratification in humans (2, 4, 53–55). Our findings offer specific cellular mechanisms underlying the enhancement of patience. The predominance of lick-suppressive type neurons (Mdec) in the dmFC, whose enhanced activity during the waiting period correlates with waiting time, suggests that sustained activation of these neurons during waiting actively promotes patient behavior. The strong correlation between Mdec neuron activity and waiting time suggests that these neurons may serve as a neural substrate for maintaining goal-directed behavior in the face of immediate temptation. These findings align with earlier neurophysiological studies showing that activity in medial frontal regions, including the dorsomedial PFC, anterior cingulate cortex, and secondary motor cortex, is associated with the suppression of impulsive actions and the promotion of patient behavior (11–13, 42). Furthermore, the causal role of the medial frontal regions in waiting behavior is supported by evidence from pharmacological and optogenetic manipulations (10, 13, 56), particularly involving the projection from the medial frontal regions to the striatum (14, 42, 57, 58).

In sharp contrast, the AIC was identified as a key regulator of impulsivity, with its inhibition significantly extending waiting times. This finding aligns with its well-established role in motivation-driven decision-making tasks (16, 18, 19, 21, 59) and reinforces the view of the AIC as an integrative hub for interoceptive functions, where internal physiological states are integrated with external environmental cues (16, 17, 60). The predominance of lick-activated neurons (Minc) in the AIC, whose suppression during the waiting period correlates with patient behavior, suggests a push-pull mechanism in opposition to the dmFC. This cellular-level finding marks an essential advance in understanding how self-control is implemented in the brain, revealing an antagonistic relationship between these regions. Such opposition provides a mechanistic basis for behavioral flexibility, enabling the brain to dynamically shift between patient and impulsive states as situational demands change.

However, given the anatomical and functional proximity of the dmFC and AIC to motor-related areas, an alternative interpretation of our findings is that the observed effects may reflect changes in motor readiness or response threshold, rather than impulsivity per se. While our data support the view that these regions play distinct roles in modulating patient and impulsive behaviors, the current experimental design does not allow for a full dissociation between cognitive aspects of impulsivity and motor-related processes. Future studies incorporating measures of motor preparation or dissociating motor execution from decision variables will be necessary to further clarify this distinction.

The antagonistic relationship between the dmFC and the AIC aligns with and extends prior studies demonstrating their opposing roles across various contexts. In addiction, the medial frontal cortex contributes to the successful inhibition of drug-seeking behavior (61, 62), whereas the AIC promotes relapse of addiction (60, 63, 64). Similarly, in risk-based decision-making, the medial frontal area is involved in risk-averse choices (65, 66), while the AIC promotes risk-seeking behavior (67, 68). These findings reflect a broader organizational principle in cognitive control circuits: The medial frontal area functions as a “brake” promoting behavioral inhibition, while the AIC acts as an “accelerator” driving action initiation based on interoceptive states. Our identification of distinct neuronal populations with opposing activity patterns, coupled with the contrasting behavioral effects of optogenetic inhibition, provides a mechanistic framework for understanding how these regions implement their antagonistic functions in regulating impulsivity. Anatomical studies reveal elaborate reciprocal connections between the medial frontal area and AIC (20, 22, 23, 69), offering a structural basis for their dynamic competition in behavioral control. However, the relationship between the medial frontal area and AIC extends beyond simple opposition. Recent studies highlight that these regions, especially the medial PFC, can cooperate to optimize behavior in specific contexts, such as working memory and taste information processing (20, 23, 70). This suggests a dynamic model in which the medial frontal area and AIC adjust their interaction patterns based on behavioral demands, enabling flexible cognitive control.

Our results indicate that the PPC plays a pivotal role in precise temporal processing and reducing the variability of waiting times. We found prevalent time cells in the PPC that encode elapsed time during the waiting period through their distinct peak activity. While earlier studies have reported temporal information processing and elapsed time encoding by medial frontal neurons, particularly in the medial PFC (71, 72), our findings suggest that the PPC is more specialized for tracking elapsed time across several dimensions. First, the prevalence of time cells in the PPC is markedly greater than in the dmFC. Second, the PPC exhibits higher PE, signifying that its peak activity uniformly covers the entire waiting period, thereby underscoring its superior temporal processing capabilities. Third, the PPC demonstrates a higher ASI compared to other regions, indicating that it primarily encodes absolute elapsed time independently of the waiting duration. While absolute coding predominates, neurons with scaling-like responses were also observed in the PPC, reflecting a mixture of absolute and relative temporal representations. In contrast, the dmFC exhibited the lowest ASI, suggesting a more flexible, waiting duration–dependent temporal code. Together, these findings reveal a division of labor in temporal processing: The PPC primarily provides a stable temporal framework, while the dmFC dynamically scales its activity dependent on waiting behavior. This distinction underscores the complementary roles of these regions in regulating temporally sensitive behaviors.

In the present study, we used GRIN lens implantation for calcium imaging, a technique that can cause tissue disruption and potentially alter the physiological properties of imaged neurons. In particular, targeting the PPC with this approach likely resulted in damage to superficial cortical layers. Nevertheless, the persistence of time cell activity under these conditions suggests that the underlying temporal dynamics are robust, even in the absence of intact superficial input. To ensure consistency across experimental conditions, we used the same GRIN lens and miniscope imaging approach across all groups, targeting three distinct brain regions. This standardized methodology minimized variability due to imaging technique and enabled more direct and reliable comparisons of neural dynamics across regions. While this approach offers broad access to deep-layer activity, future studies using two-photon imaging, which allows high-resolution access to both superficial and deep layers with minimal tissue disruption, will be valuable for confirming the widespread presence of time cells in the PPC.

During PPC inhibition, we observed an increase in premature errors at the early onset of the waiting period (Fig. 1, F and G, third row). At first glance, this might appear to challenge the interpretation that the PPC is critical for temporal processing, as the early phase of the waiting period is when temporal processing is arguably least relevant. However, we propose that waiting behavior emerges from a dynamic interplay between impulse control and temporal processing. Impulse control, supported by regions such as the dmFC and AIC, enables suppression of premature actions, while the PPC contributes to the internal estimation of elapsed time, informing when to act. Under normal conditions, animals integrate these systems, using internal temporal estimates to time their licks appropriately, with impulse control helping to prevent premature responses. When the PPC is inhibited, we suggest that temporal precision deteriorates, forcing animals to rely more heavily on the impulse control system to regulate behavior. Without accurate temporal information, animals are effectively blind with respect to when 2 s have elapsed, making their decision to lick more susceptible to trial-by-trial fluctuations in impulsivity and leading to a broader, more variable distribution of waiting times. Consequently, some trials may show premature licking even at the onset of the waiting period, as behavior becomes primarily governed by impulse control in the absence of temporal guidance. Therefore, the increase in early premature errors under PPC inhibition does not contradict the role of the PPC in temporal processing. Rather, it supports a model in which the PPC provides essential temporal structure to behavior, and when this structure is compromised, decision-making becomes increasingly dominated by nontemporal factors such as impulse control.

Our finding that the PPC is involved in temporal processing aligns with previous human neuroimaging studies identifying the parietal cortex as a key region for time estimation during tasks requiring judgments of stimulus or interval duration (73–77). In addition, damage to or transcranial magnetic stimulation of the human parietal cortex impairs time perception, highlighting its causal role in temporal processing (78, 79). Complementing this, single-unit recordings in monkeys have demonstrated that ramping activity in PPC neurons tracks elapsed time relative to a remembered interval, supporting duration judgments (80, 81). Notably, the temporal coding observed in our study diverges from these previously reported ramping dynamics. Our findings extend this body of work by revealing a high prevalence of time cells in the mouse PPC that encode precise temporal information, rather than ramping signals. Together, the causal contribution of the mouse PPC to time estimation suggests evolutionarily conserved temporal processing properties of the PPC across species.

Similar time cells were also found in the hippocampus and medial entorhinal cortex, where they are tightly linked to memory processes (49, 50, 82–86). In these regions, temporal coding emerges as animals learn temporally structured tasks, with distinct time cell sequences becoming associated with specific memory episodes or contents. Moreover, the integrity of these temporal codes has been shown to predict memory performance, suggesting that hippocampal time cells contribute to the temporal organization and retrieval of memory content. In contrast, our study reveals a dense population of time cells in the PPC that are active during a behaviorally relevant waiting period requiring action restraint rather than memory processing. In our delayed response task, mice were not required to remember specific items, cues, or spatial locations; their only demand was to withhold licking for a fixed time interval. During this interval, PPC time cells displayed sequential peak activity that tiled the entire waiting period. This temporal pattern was consistent across trials and largely unaffected by differences in patience or motivation, suggesting that the activity primarily encodes the passage of time itself. Because the task minimized memory demands, the sequential activity is best interpreted as a relatively pure temporal signal, rather than one shaped by memory-related processes such as holding or retrieving task-relevant information. Thus, while PPC and hippocampal/medial entorhinal time cells share similarities in their temporal firing patterns, they may support different cognitive functions. Our findings indicate that PPC time cells may play a greater role in time-based decision-making and self-control, rather than mnemonic processing per se. However, the precise functional distinctions among time cells in the PPC, hippocampus, and medial entorhinal cortex remain to be fully elucidated. Future studies using unified behavioral paradigms will be critical for directly comparing the structure and function of temporal representations across these regions.

Although the PPC and the hippocampus do not have direct anatomical connections, they are indirectly connected through the entorhinal cortex (22, 34, 87). Just as spatial information is known to be shaped through interactions between the PPC and hippocampus (82), our findings suggest that temporal information may be similarly processed through this anatomical pathway. This interaction may enable the PPC to transform hippocampal temporal signals into behaviorally relevant representations, supporting its role in maintaining task-relevant temporal aspects of self-control. The PPC’s temporal processing capabilities, characterized by absolute time encoding and comprehensive coverage, stand in marked contrast to the more flexible, duration-dependent temporal representations observed in the dmFC.

These findings collectively advance our understanding of the neural basis of self-control by clarifying the complementary functions of the dmFC, AIC, and PPC in impulse control during waiting. However, it is likely that other regions also contribute to this process or to broader functions such as delayed gratification. For instance, research has shown that the lateral orbitofrontal cortex (OFC), a region near the AIC, encodes the time-discounted value of expected rewards (88–90). Moreover, recent studies have demonstrated that serotonin stimulation in the OFC promotes waiting, while serotonin in the medial PFC specifically enhances waiting when the timing of future rewards is uncertain (91). Further research is needed to elucidate the OFC’s role, its interactions with the dmFC, AIC, and PPC, and the influence of neuromodulatory systems in shaping cortical activity to regulate patience and impulse control during waiting.

MATERIALS AND METHODS

Animals

All experimental procedures were approved by the Institutional Animal Care and Use Committee at Nanyang Technological University (protocol #A19062). For calcium imaging experiments, C57BL/6 mice were used (aged 1 to 5 months). For targeting the dmFC, the AIC, and the PPC, n = 6 mice were used, respectively. For optogenetic inactivation experiments, PV-ChR2 mice [PV-Cre mice (the Jackson laboratory stock 017320) crossed with Ai32 mice (the Jackson laboratory stock 012569); aged 1 to 5 months] were used (n = 8 mice for targeting the dmFC, n = 6 mice for targeting the PPC, and n = 6 mice for targeting the AIC). As described in (37), animals were housed on a 12-hour dark/12-hour light cycle (light on between 07:00 and 19:00) at around 21°C and 62% humidity. All the experiments were carried out between 07:00 and 23:00.

Surgery

Adult mice were anesthetized with isofluorane (3% for induction and 1.5 to 2% for maintenance in oxygen) and placed on a stereotaxic frame (RWD Life Science), following procedures previously described in (37). The mice received buprenorphine (0.05 mg/kg) before and after surgery and supplementary analgesia (meloxicam, 5 mg/kg) after surgery.

For imaging experiments, animals underwent the following surgical procedures. First, a craniotomy of ~500 μm was made to target the dmFC [anteroposterior (AP) +1.8 to 2.1 mm, mediolateral (ML) 0.3 to 0.5 mm from bregma, dorsoventral (DV) 0.6 to 1.2 mm from pia surface, the right hemisphere], the AIC (AP +1.6 to 1.8 mm, ML 3.1 to 3.3 mm from bregma, DV 1.9 to 2.1 mm from pia surface, the right hemisphere), and PPC (AP −1.8 to −2.1 mm, ML 1.6 to 1.8 mm from bregma, DV 0.6 to 1.2 mm from pia surface, the right hemisphere) where 600 to 800 nl of AAV1-CaMKIIα-GCaMP6f (100834-AAV1, Addgene; titer 1.2 × 10¹³ vg/ml, 3× dilution factor) was injected through a borosilicate glass pipette using a microinjector (Nanoliter 2010, World Precision Instruments). After a week of recovery, a second surgical procedure was conducted to implant cuffed GRIN lenses (Inscopix) for targeting specific brain regions. GRIN lenses with a diameter of 1 mm, length of 4.2 mm, pitch of 0.5, and numerical aperture of 0.5 were used for implantation in the dmFC and PPC. The target coordinates for the dmFC were centered at AP +1.8 to 2.1 mm, ML 0.3 to 0.5 mm from bregma, and DV 0.6 to 1.2 mm from the pia surface in the right hemisphere. Similarly, the PPC was targeted at AP −1.8 to −2.1 mm, ML 1.6 to 1.8 mm from bregma, and DV 0.6 to 1.2 mm from the pia surface in the right hemisphere. For the AIC, a GRIN lens with a 0.5-mm diameter was used, targeting coordinates centered at AP +1.6 to 1.8 mm, ML 3.1 to 3.3 mm from bregma, and DV 1.9 to 2.1 mm from the pia surface in the right hemisphere. The craniotomy was carefully expanded to ~1 mm for the dmFC and PPC, while a ~0.5-mm opening was made for the AIC. Superficial tissue was aspirated using a blunt 27-gauge needle connected to a vacuum pump. To avoid blood clotting during the procedure, the exposed tissue was continuously irrigated with sterile Ringer’s solution. A stainless steel headplate was affixed to the skull using machine screws and black dental cement (Contemporary Ortho-Jet, Black, Lang Dental). After ensuring the absence of active bleeding, the cuffed GRIN lens was gently placed upon the tissue and the lens was fixed to the skull with super glue (Scotch Super Glue AD125, 3M). The GRIN lens was then cemented to the rest of the implant, and the surface of the cuffed lens was covered with a silicone elastomer (Kwik-Cast).

After a week of recovery, the mice underwent behavioral training. Once the mice reached criterion performance (see the “Behavioral procedure” section below), the baseplate was implanted for chronic imaging under 1 to 1.5% isoflurane anesthesia. Silicone sealant was removed to expose the surface of the lens, and the miniature microscope attached to the baseplate was lowered with a micromanipulator to the desired focal plane. The baseplate was then cemented to the rest of the implant and covered with a protective cap after retraction of the microscope. For optogenetic inactivation experiments, a head plate and fiber optic cannula (Ø1.25 mm ceramic ferrule, Ø400 μm core, 0.39 numerical aperture (NA); Thorlabs) were implanted bilaterally to deliver light to the dmFC, AIC, and PPC.

Histology

We performed histology to confirm the location of the implanted GRIN lens in imaging experiments and the optic fiber used in optical stimulation experiments, following procedures previously described in (37). At the end of the experiments, the mice were deeply anesthetized with isoflurane and immediately perfused with chilled 0.1 M phosphate-buffered saline (PBS) followed by 4% paraformaldehyde (w/v) in PBS. The brain was removed and postfixed overnight at 4°C. After fixation, the brain was placed in 30% sucrose (w/v) in PBS solution at least for 1 to 2 days at 4°C. After embedding and freezing, the brain was sectioned into 50-μm coronal slices using a cryostat (Leica CM1950). The slides were mounted with Fluoroshield with 4′,6-diamidino-2-phenylindole (Sigma-Aldrich) and imaged with a slide scanner (ZEISS Axio Scan.Z1).

Behavioral procedure

Modified delayed response task training

Behavioral training for head-fixed mice was conducted through a set of customized codes within Presentation software (Neurobehavioral Systems), following procedures similar to those previously described in (37). Habituation (1 to 2 days) was conducted first, where no stimulus was presented, and the mice were given free water rewards (~2 to 3 μl) for each lick on a metal lickport placed in front of the subject. Licks were detected by the lickport via an electrically coupled circuit board. If mice were able to achieve at least 100 licks within 30 min from the start of a habituation session, mice training would be transited to the training phase. In the training phase, mice were initially trained with only nonprobe trials of the delayed response task. Mice were trained to lick in response to an airpuff stimulus (presented to the right cheek) after a delay period of 2 s. The onset of the delay period was signaled by a 0.5-s auditory tone stimulus (2 kHz, ~75 dB), which in turn also signaled the trial onset. The airpuff stimulus also signaled the onset of a 2-s response window that accepted licking responses. In the nonprobe trials, licking during the response window was rewarded (hit), and licking during the delay period was punished (premature) with a beep sound and a longer intertrial interval (additional 1 s plus the default 1 s). If no lick was detected during the response window (miss), a water reward was given after the response window ended. When the mean reaction time of a training session is less than 1 s, probe trials were included in the subsequent training sessions in equal proportion (50% of trials) to the nonprobe trials. In contrast to nonprobe trials, the airpuff stimulus that signaled the onset of the response window was omitted in probe trials, and the duration of the response window was extended to 6 s. Similar to nonprobe trials, licking during the response window was rewarded (hit), and licking during the delay period of 2 s was punished (premature) with a beep sound and a longer intertrial interval (additional 1 s plus the default 1 s). However, in contrast to the initial training sessions, if no licks were detected during the response window (miss), no water reward was given after the response window ended. Behavioral performance in a training session is computed in the following manner: (i) hit rate: percentage of hit trials divided by the sum of hit and premature trials; (ii) miss rate: percentage of miss trials divided by all trials; and (iii) mean waiting time: the geometric mean of waiting times obtained from probe trials. Before commencing calcium imaging and optogenetic experiments, mice were required to achieve a miss rate of less than 10% in a training session. Once this criterion was met, their hit rate typically ranged from ~40 to 50%, comparable to similar behavioral paradigms in related studies (81, 92).

Optogenetic inactivation

For optogenetic inactivation, a blue laser was delivered through a patch cable connected with a diode-pumped solid-state (DPSS) laser (473 nm; Shanghai Laser) under the control of a custom-made LabVIEW software (step pulse, 0.7 to 1 mW at fiber tip), following procedures previously described in (37). The patch cable was connected with the ferrule end of the optic fiber cannula (implanted in the brain) via a mating ceramic sleeve (Thorlabs). Laser stimulation was applied in 30 to 50% of randomly selected trials, and the same condition never occurred in more than two to three consecutive trials. Laser was delivered from the start of the delay onset and continued to cover the duration of the waiting time and ceased 2 s after the detection of the first lick. In miss trials where no licks were detected, laser cessation occurred at the end of the trial, before the onset of the intertrial interval. Each session was terminated after 10 consecutive miss trials. For the sham optogenetic experiment, three layers of black vinyl tape were placed at the junction between the patch cable and the ferrule end of the optic fiber cannula to block the laser pathway while the other laser stimulation parameters were kept the same.

Microendoscopic calcium imaging

The detailed procedure was described elsewhere (37, 38, 93). Briefly, we performed cellular-resolution microendoscopic calcium imaging from genetically defined cell types in the right dmFC, AIC, and PPC using a miniaturized integrated fluorescence microscope (Inscopix; 20× objective; light-emitting diode power: 0.2 to 0.7 mW; complementary metal-oxide semiconductor (CMOS) sensor resolution: 1200 by 800 pixels) coupled to a GRIN lens. Images were acquired at 15 frames/s and spatially downsampled by a factor of 2 using nVista3 (Inscopix). Behavioral events were registered offline with imaging frames by acquiring analog voltage output from both the nVista3 system and the behavioral control system via NI PCIe-6321 with a custom code in LabVIEW (National Instruments).

Quantification and statistical analysis

Behavioral data analysis

Fitting of logistic function to the distribution of waiting times. To assess the differences in the distribution of waiting times (obtained from probe trials) during the optogenetic inhibition experiments and DDM, the cumulative distribution of waiting times was analyzed using logistic curve fitting. Waiting times, from 0.5 to 8.5 s, were first binned into 0.1-s intervals to calculate normalized probabilities. Cumulative distributions were then computed for each condition by summing the binned probabilities sequentially. A logistic function was used to model the cumulative distributions

$$f\left(x\right)=\frac{L}{1+e^{-k(x-x0)}}$$ (1)

where L is the maximum value (asymptote) the function approaches, k is the steepness or rate constant that determines how quickly the function changes and thus represents the variance of the waiting time distribution, and x0 is the inflection point that represents the central tendency or the peak of the distribution. Curve fitting was performed using the nonlinear least squares method (“lsqcurvefit” function in MATLAB) to estimate L, k, and x0 for the different conditions. The bin centers, calculated as the midpoints of the bin edges, were used as the independent variable for the fitting procedure.

Drift diffusion modeling. The behavioral effects that resulted from the optogenetic inhibition experiments were simulated using a DDM, a widely used framework to model decision-making processes. In this model, a decision variable $x$ evolves according to a combination of deterministic drift and stochastic noise. For each trial (out of n = 40 trials), the decision variable $x$ was initialized at $x=0$ and evolved according to the function

$$x_{t+\mathrm{\Delta }t}=x_t+v·\mathrm{\Delta }t+\mathrm{\sigma }·\sqrt{\mathrm{\Delta }t}·\mathrm{\eta }$$ (2)

where $v$ is the drift rate determining the systematic tendency of the decision variable toward the threshold, $\mathrm{\sigma }$ is the noise level governing the magnitude of random fluctuations in the decision variable, $\mathrm{\Delta }t$ is the time step at a fixed interval of 0.001 s, and $\mathrm{\eta }\backsim N(0,1)$ is the Gaussian noise (adjusted by subtracting a constant offset of 0.02 to introduce skewness as in a typical distribution of waiting times). The simulation continued iteratively until $x\ge$ decision threshold set at 1 or $t\ge T_{\text{max}}$ , the maximum duration of 8.5 s. The time $t$ at which $x$ crossed the threshold was recorded as the waiting time for that trial. Trials that did not reach the threshold before T_max were excluded.

The drift rates reflecting the decision variable accumulation speed used to simulate the effects of optogenetic inhibition in the three cortical regions are as follows: control: 0.62, dmFC inhibition: 0.68, AIC inhibition: 0.52, and PPC inhibition: 0.62. The noise levels representing the variability in the accumulation process used to simulate the effects of optogenetic inhibition in the three cortical regions are as follows: control: 0.35, dmFC inhibition: 0.35, AIC inhibition: 0.35, and PPC inhibition: 0.5. The waiting times obtained from the DDM simulations using the different conditions (n = 30 iterations for each condition) were similarly analyzed as in the behavioral data analysis: computing the mean waiting time and obtaining the inflection point and rate constant by fitting the cumulative distribution with a logistic function.

Imaging data analysis

Preprocessing and ROI identification. Image stacks were first corrected for small displacements of the brain by registering to the first frame of the image sequences, following procedures previously described in (37, 38). To remove scattered fluorescence and background neuropil signal, a spatial Gaussian high-pass filter was applied (σ = 50 μm) and the relative changes in fluorescence

$$\mathit{dF}\left(t\right)/F0=[F\left(t\right)–F0]/F0$$ (3)

were computed for each pixel, where F0 indicates the mean activity of each pixel during the entire session and dF(t) is the mean subtracted fluorescence at each time point t. The successive application of principal components and independent components analyses (PCA/ICA algorithm) was performed for the dF(t)/F0 videos to extract the activity of individual neurons (94). Regions of interest (ROIs) that have signal-to-noise ratio of >3 and only one component from the output of the PCA/ICA algorithm were accepted as real neurons. To correct for decreases in baseline fluorescence due to bleaching of the calcium indicator, we subtracted slow fluctuations in baseline according to the expression

$$F_{\text{corrected}}\left(t\right)=F\left(t\right)-G\left(t\right)+<F\left(t\right)>$$ (4)

where F(t) represents the output trace obtained from the PCA/ICA algorithm, brackets indicate time average over the entire recording session, and G(t) is the average of F(t) over a 300-s sliding window. Last, the corrected calcium traces F_corrected(t) were z-scored using whole traces in each ROI. Unless otherwise stated, we used the z-scored activity for all the analyses. Since the corrected calcium traces F_corrected(t) were z-scored, the addition of the time-averaged fluorescence <F(t)> in Eq. 4 is not strictly necessary for downstream analysis. However, we included this operation because we routinely inspect both unnormalized and z-scored traces. In this context, adding <F(t)> serves to preserve the overall baseline level of the calcium signal after correcting for slow drifts G(t). Subtracting G(t), a smoothed version of F(t), removes slow fluctuations, but also shifts the mean of the signal toward zero. By adding back the global mean <F(t)>, we restore the original baseline level while retaining the correction for slow drift.

Binning of trials into waiting time bins and window of analysis

Unless otherwise specified, most imaging data analyses used 0.5-s waiting time bins: 0.5 to 1 s, 1 to 1.5 s, 1.5 to 2 s, 2 to 2.5 s, 2.5 to 3 s, and 3 to 3.5 s. For analyses of activity aligned to tone stimulus onset, trials were included only up to a duration that excluded at least 0.3 s from the lower bound of their assigned waiting time bin. For example, trials in the 2 to 2.5 s waiting time bin were analyzed for up to 1.7 s after tone onset. This minimized contamination from motor-related activity preceding licking.

Estimating dimensionality of neuronal population

To assess the dimensionality of neuronal population in each cortical region, we computed the PR index. For each cortical region, PCA was performed on the matrix $Q\in {ℝ}^{n\times \mathit{ct}}$ , where n is the number of neurons, c is the number of waiting time bins, and t is the number of time points per waiting time bin. Neural activity included both tone-aligned activity and lick-aligned activity (−0.5 to 2 s from the first lick) for each waiting time bin. The PR index was computed from PCA eigenvalues as the square of the sum of eigenvalues divided by the sum of squared eigenvalues (39). This metric provides a measure of the dimensionality by capturing the distribution of eigenvalues within the neuronal population.

To compare dimensionality across cortical regions, we performed a resampling procedure in each region. In each of 100 iterations, 100 neurons were randomly selected with replacement to construct the matrix $Q$for PCA and compute the PR index. In addition, we determined the minimum number of principal components required to explain more than 95% of the variance.

Demixed principal components analysis

dPCA was used to obtain a low-dimensional representation of neural responses (43) by including the “waiting” component (waiting dPC), which distinguishes hit from premature trials, and the condition-independent time component. Briefly, trials were categorized as hit or premature, and dPCA aimed to preserve maximal variance associated with this waiting variable. Neural activity was represented as a three-dimensional matrix of size n × c × t, where n is the number of neurons, c is the number of conditions (two conditions: hit or premature trials), and t is the number of time points. Since dPCA reconstructs neural activity, the loss function was concerned only with the neural activity of the two conditions averaged across trials. Since waiting times varied across trials, dPCA was applied on neural activity traces from two time windows defined to represent the “start” and “end” of the waiting time: (i) 0 to 0.5 s after tone onset and (ii) −1 to −0.8 s before the first lick. These extracted traces were concatenated for each trial and baseline-subtracted using the mean activity in the baseline window (−0.5 to 0 s from tone onset) before applying dPCA. Only trials with waiting times exceeding 1 s were included in the analysis.

The dPCA output included (i) a decoder matrix W and an encoder matrix V, both of size n × l (where l is the number of principal components specified), and (ii) a vector, whichMarg, which identifies the task-relevant components. X is the three-dimensional activity matrix transposed and concatenated across the last three dimensions. The product XW, of size (ct × l), provided the readout of each demixed principal component across task conditions and time. The matrix V represented the loading of each principal component onto individual neurons. Using the decoder matrix W derived from the dPCA, the trial-averaged activity across waiting time bins was projected onto the first waiting dPC and the condition-independent dPC. This projection allowed for the visualization of key features of population activity across different waiting times.

Decoding accuracy using hit versus premature axis

The waiting dPC obtained from dPCA was used as a linear classifier to decode hit versus premature trials in each cortical region. To estimate the variance of the decoder, a resampling procedure was performed. In each of 100 iterations, 2000 neurons were randomly selected from each cortical region, and their trial-averaged activity for hit and premature trials was used to compute dPCA. Next, five hit trials and five premature trials were randomly selected, and the population activity at 1 s after tone onset was projected onto the waiting dPC. This projection served as a linear classifier to determine trial identity. The 1-s time point was chosen due to prominent fluctuations in waiting dPC–projected population activity observed at that moment.

Persistency index

To quantify the persistence of population activity during waiting, we computed the persistency index, which reflects the temporal variance of population activity along the waiting dPC obtained from dPCA (95). First, the population activity from five randomly sampled trials per waiting time bin was projected onto the waiting dPC. To isolate temporal activity variance from across-trial variability, we subtracted the mean projected activity from each trial’s projected activity trace. The mean-centered activity traces were then concatenated across all waiting time bins. The temporal activity variance was calculated as the variance across time of this concatenated trace. To derive the persistency index, the variance of the mean activity across trials was divided by this temporal activity variance along the waiting dPC. A higher persistency index indicates more persistent neural activity along the waiting dPC, whereas a lower index suggests more dynamic or variable temporal activity patterns.

To ensure a fair comparison across cortical regions, we applied a resampling procedure to compute the persistency index in each region. In each of 100 iterations, 2000 neurons were randomly selected, and their activity was decomposed using dPCA to extract the waiting dPC. Then, five trials from each waiting time bin were randomly selected with replacement, and the population activity of these trials was projected onto the waiting dPC to compute the persistency index.

Rotation prevalence index

To quantify rotational dynamics in population activity during waiting, we computed the rotation prevalence index using jPCA (45). Trials with waiting times between 2.5 and 4.0 s were binned into 0.5-s intervals. For each cortical region, we constructed a matrix $Q\in {ℝ}^{n\times \mathit{ct}}$ , where n is the number of neurons, c is the number of waiting time bins, and t is the number of time points within a 0- to 2.2-s window. Before applying jPCA, we followed standard preprocessing steps (45). Neural responses were normalized using a “soft” normalization method, ensuring that neurons with strong responses were scaled to approximately unity while weaker responses remained below unity. In addition, each neuron’s data were mean-centered by subtracting the across-condition average response, isolating condition-dependent variations. We then performed PCA to reduce the dimensionality of $Q$ from n × ct to k × ct, retaining k = 6 principal components. This step ensured that subsequent jPCA analysis captured only prominent activity patterns across neurons. The reduced Q_red matrix (6 × ct) represented the neural state across time and conditions.

To extract rotational dynamics, we computed ${\dot{Q}}_{\text{red}}$ [6 × c(t − 1)] by taking time derivatives of Q_red. We then fit the relationship between Q_red and ${\dot{Q}}_{\text{red}}$ using two matrices: M, an unconstrained matrix obtained via linear regression, and M_skew, a skew-symmetric matrix capturing rotational dynamics, characterized by purely imaginary eigenvalues. The quality of these fits was assessed using R², which measured how well ${\dot{Q}}_{\text{red}}$ was predicted from Q_red. Last, the rotation prevalence index quantified how well M_skew explained the data relative to the unconstrained M, as skew-symmetric matrices form a restricted subset of all possible transformations.

To enable a fair comparison across cortical regions, we used a resampling approach to calculate the rotation prevalence index for each region. In each of 100 iterations, 300 neurons were randomly selected with replacement to construct the matrix Q for jPCA, from which the rotation prevalence index was then computed.

Classification of time cells

Trials with waiting times between 1 and 3.5 s were grouped into 0.5-s intervals (waiting time bins) for the classification of time cells. Within each waiting time bin, neuronal activity from tone onset to 3.5 s after tone onset was further divided into 10 equally spaced “elapsed time bins,” and the activity within each bin was averaged. Time cells were identified using a two-way ANOVA with waiting time and elapsed time as factors. Neurons that showed a significant main effect for the elapsed time factor were classified as time cells. The peak activity of each time cell was defined as the elapsed time bin in which its activity was highest.

PE of time cells

To evaluate the uniformity of peak activity distribution among time cells across an interval, we computed the PE index

$$\text{PE}={\displaystyle \sum _{j=1}^M}-p_j\text{log}\left(p_j\right)/\text{log}\left(M\right)$$ (5)

where $M$ is the number of bins for estimating the peak time distribution (21 bins) and $p_j$ is the proportion of neurons peaking in time bin j (i.e., the number of neurons with peak activity in bin j divided by the total number of neurons). Since PE computation does not allow negative values, the z-scored activity of neurons was normalized to the range [0,1]. To estimate the variance of the PE index in each cortical region, a resampling procedure was performed. In each of 100 iterations, 30 time cells were randomly selected from a cortical region with replacement. In addition, 10 trials with waiting times between 2.5 and 3 s were randomly selected with replacement. The neuronal activity during waiting (0 to 2.1 s from tone onset) was then used to compute the PE index.

Population vector dissimilarity across time

To evaluate the temporal dynamics of population activity, we computed population vector dissimilarity over time by measuring the cosine dissimilarity between the population vector at each time point and its future time points. To estimate the variance of cosine dissimilarity, a resampling procedure was performed. In each of 100 iterations, 100 neurons and one trial from each waiting time bin (waiting times ranging from 0.5 to 3.5 s, binned in 0.5-s intervals) were randomly selected with replacement. For each trial, population vector dissimilarity was quantified as the cosine dissimilarity (1 – cosine similarity) between the population vector at a given time point and all possible future lags. The average dissimilarity for each lag was then computed across trials.

Absolute-scaling index

To assess the degree of absolute time encoding in neurons, we computed the ASI (51). The ASI quantifies whether a neuron’s temporal firing profile remains unchanged across different interval durations (absolute timing) or dilates proportionally (temporal scaling). The ASI identifies the optimal transformation to align the response profile of the long interval [y(t)] with that of the short interval [x(t)]. This was achieved by concatenating an absolute portion of the long response [y^abs(t)] with a scaled portion of the long response [y^scale(t’)]. Specifically, a breakpoint τ was determined to divide y(t) into absolute and scaled segments, minimizing the Euclidean distance [Dist(τ)] between the transformed long response and x(t). An ASI of 1 indicates absolute timing, where the entire short response aligns with the unscaled early portion of the long response (τ = t_max), meaning the first half of the long interval matches the entire short interval. Conversely, an ASI of 0 corresponds to τ = 0, implying that the response profiles for short and long intervals match when plotted in normalized time. ASI was computed through the following steps

$$\begin{array}{c}\text{Dist}\left(\mathrm{\tau }\right)=\sqrt{\sum _{t=0}^{\mathrm{\tau }}{[x\left(t\right)-y\left(t\right)]}^2+\sum _{t=\mathrm{\tau }}^{t_{\text{max}}}{\left\{x\left(t\right)-y[\mathrm{\tau }+\mathrm{\alpha }(t-\mathrm{\tau })]\right\}}^2}\hfill \end{array}$$ (6)

$${\mathrm{\tau }}_{\text{min}}=\text{argmi}{\mathrm{n}}_{\mathrm{\tau }}\text{[Dist}\left(\mathrm{\tau }\right)\text{]}$$ (7)

$$W^{\text{abs}}\left({\mathrm{\tau }}_{\text{min}}\right)=1/N_{1:{\mathrm{\tau }}_{\text{min}}}\sum _{t=0}^{{\mathrm{\tau }}_{\text{min}}}\left|[x\left(t\right)-x\left(0\right)][y\left(t\right)-y\left(0\right)]\right|$$ (8)

$$\begin{array}{c}{W}^{\text{scale}}\left({\mathrm{\tau }}_{\text{min}}\right)=1/N_{{\mathrm{\tau }}_{\text{min}}:t_{\text{max}}}\hfill \\ \sum _{t={\mathrm{\tau }}_{\text{min}}}^{t_{\text{max}}}\left|[x\left(t\right)-x\left({\mathrm{\tau }}_{\text{min}}\right)]\{y[{\mathrm{\tau }}_{\text{min}}+\mathrm{\alpha }(t-{\mathrm{\tau }}_{\text{min}})]-y\left({\mathrm{\tau }}_{\text{min}}\right)\}\right|\hfill \end{array}$$ (9)

$$\text{Abs}R\left({\mathrm{\tau }}_{\text{min}}\right)=\frac{W^{\text{abs}}\left({\mathrm{\tau }}_{\text{min}}\right)}{W^{\text{scale}}\left({\mathrm{\tau }}_{\text{min}}\right)+W^{\text{abs}}\left({\mathrm{\tau }}_{\text{min}}\right)}$$ (10)

$$\text{ASI}=[\frac{{\mathrm{\tau }}_{\text{min}}}{t_{\text{max}}}+\text{Abs}R\left({\mathrm{\tau }}_{\text{min}}\right)]/2$$ (11)

where breakpoint τ spans all possible values from 0 to t_max (for the short interval). The segment before τ represents the absolute period, while the segment after τ is scaled by α = (2 × t_max − τ)/(t_max − τ) to match the long response. The optimal breakpoint τ_min corresponds to the value that minimizes the Euclidean distance Dist(τ). In Eqs. 8 and 9, the absolute and scaling weights were computed by comparing the dynamics of the short interval with the time-warped dynamics of the long interval. Here, N_a:b refers to the number of time points between time points a and b, and the absolute ratio AbsR(τ_min) at τ_min is calculated. The absolute temporal factor is given by τ_min/t_max, and the ASI is defined as the average of the absolute temporal factor and AbsR(τ_min). The shorter interval was computed from trials with waiting times ranging from 1.5 to 2 s, while the longer interval was computed from trials with waiting times ranging from 2.5 to 3 s.

Correlations between PE and rate constant

To assess whether the PE of time cells was related to behavioral temporal estimation, we computed a Pearson’s correlation between PE and the rate constant across imaging sessions. The rate constant served as a measure of temporal precision, with higher values indicating more precise temporal estimation (Fig. 1E). To control for potential confounds related to the number of time cells recorded in each session, we implemented a resampling procedure. In each of 10 iterations, we randomly sampled 30 time cells with replacement and computed the PE of the sampled cells. This ensured that variability in PE across sessions was not merely driven by differences in the number of recorded time cells.

Correlations between population vector dissimilarity across time and rate constant

To evaluate whether population vector dissimilarity over time was associated with the rate constant, we computed a Pearson’s correlation between the cosine dissimilarity of population vectors over time and the rate constant across sessions. To control for potential confounds related to the number of neurons recorded in each session, we implemented a resampling procedure. In each of 100 iterations, we randomly selected 30 neurons and one trial per waiting time bin (waiting times ranging from 0.5 to 3.5 s, binned in 0.5-s intervals) with replacement. For each trial, population vector dissimilarity was quantified as the cosine dissimilarity (1 – cosine similarity) between the population vector at a given time point and its representations at all possible future lags. The average dissimilarity for each lag was then computed across trials. This approach ensured that variability in temporal population vector dissimilarity across sessions was not simply driven by differences in the number of recorded neurons.

Decoding of elapsed time

To assess how well temporal dynamics in the dmFC, AIC, and PPC encoded elapsed time from tone onset, we implemented a support vector machine (SVM) decoder. A one-versus-one multiclass SVM with a linear kernel was used to decode elapsed time on a trial-by-trial basis. The decoder was trained on population activity from 0 to 2 s after tone onset, divided into 30 time bins, using trials with waiting times longer than 2.8 s. For each trial, the decoder predicted the time bin label for each activity vector, effectively estimating elapsed time. Performance was evaluated using fivefold cross-validation. Decoding performance was quantified as the Pearson’s correlation between the true and predicted time bins across all test trials, while decoding error was defined as the average absolute difference between them. To compare decoding accuracy across the dmFC, AIC, and PPC, we applied a resampling procedure. For each of 10 iterations, 50 neurons and 100 trials were randomly selected (with replacement) to train the SVM. Final decoding performance and error were computed as the average correlation coefficient and average absolute error across all iterations and trials.

Classification of Minc and Mdec neurons

To examine a neuron’s responsiveness to motor actions (licking) during the task, we performed a Wilcoxon signed-rank test (P < 0.05) comparing activity during the prelicking epoch (−0.5 to 0 s relative to lick onset) with activity during the licking epoch (0.5 to 1.0 s after the first detected lick). Based on their modulation by licking, neurons were classified as Minc neurons (positively modulated), Mdec neurons (negatively modulated), or nonresponsive neurons (no significant modulation).

Classification of other task-relevant neurons

To better characterize the functional diversity and specialization across cortical regions, we classified neurons into several functional categories based on their response properties:

Sensory-responsive neurons included tone- and/or tactile-responsive neurons. Tone responsiveness was determined by comparing neural activity during the tone epoch (0 to 0.3 s from tone onset) to the baseline epoch (−0.5 to 0 s before tone onset) (P < 0.05, Wilcoxon signed-rank test). Tactile responsiveness was determined by comparing activity during the airpuff epoch (0 to 0.1 s after airpuff onset) to the pre-airpuff baseline (−0.3 to 0 s before airpuff). Only nonprobe hit trials containing airpuff stimuli were used for this analysis.

Reward-modulated neurons were defined based on differential activity between rewarded probe trials and nonrewarded trials. We compared the change in activity from the prelicking epoch (−0.5 to 0 s before the first lick) to the early-licking epoch (0 to 0.3 s after the first lick) between hit (rewarded) and premature (nonrewarded) trials (P < 0.05, Wilcoxon rank-sum test).

Ramping neurons were identified by analyzing trial-averaged activity across waiting time bins (1 to 3 s, in 0.2-s intervals), as previously described for neurons exhibiting a ramp-to-threshold pattern (12, 13, 42). Threshold crossings were assessed within a 0- to 4-s window from tone onset. For each neuron, 10 threshold levels were tested. The lowest threshold was defined as the minimum activity at which threshold crossing occurred in at least 9 of the 10 waiting time conditions; the highest threshold was similarly defined as the maximum activity meeting this criterion. Eight additional thresholds were evenly spaced between these two values. At each threshold, the correlation between threshold crossing time and waiting time was calculated. A neuron was classified as a ramp-to-threshold neuron if it met the following criteria: (i) There is a significant correlation between crossing time and waiting time (Pearson’s correlation, P < 0.05) for at least 2 of the 10 thresholds; (ii) for these significant thresholds, crossing occurred before lick onset (i.e., positive prediction time); and (iii) at least one significant threshold with positive prediction time had a regression slope between 0.8 and 1.2, indicating near-linear scaling of crossing time with waiting time. Prediction time was defined as the average difference between waiting time and threshold crossing time across all bins.

Motor-modulated neurons corresponded to the previously defined categories of Minc and Mdec neurons (see definitions above).

Waiting-offset correlation index

To quantify the relationship between neuronal activity at the end of the waiting period and waiting behavior, we computed a waiting-offset correlation index for each Minc and Mdec neuron. For each trial, activity change was calculated as the difference between the baseline epoch (−0.5 to 0 s relative to tone onset) and the premotor epoch (−1.0 to −0.8 s relative to the first lick). Waiting times were divided into 0.3-s bins from 1.0 to 3.4 s, with an additional bin for trials exceeding 3.4 s (bin edges: 1.0 to 1.3 s, 1.3 to 1.6 s, 1.6 to 1.9 s, 1.9 to 2.2 s, 2.2 to 2.5 s, 2.5 to 2.8 s, 2.8 to 3.1 s, 3.1 to 3.4 s, and 3.4 to 8.5 s). For each waiting time bin, we computed the mean waiting time and mean activity change and then calculated the Pearson correlation between these two variables using the “corrcoef” function in MATLAB.

Waiting-onset correlation index

To assess whether neuronal activity at the start of the waiting period predicts subsequent waiting behavior, we computed a waiting-onset correlation index for each Minc and Mdec neuron. In this case, activity change was measured as the mean activity from 0 to 0.2 s after tone onset, relative to the baseline epoch (−0.5 to 0 s relative to tone onset). Waiting times were binned using the same procedure as for the waiting-offset correlation index, and the Pearson correlation between mean waiting time and mean activity was calculated for these bins.

Motor correlation index

To examine the relationship between Minc and Mdec neuron activity and licking behavior, we calculated a motor correlation index for each neuron. For each trial, the activity change was defined as the difference between the premotor epoch (−1.0 to −0.8 s relative to the first lick) and the motor epoch (0.5 to 1.5 s relative to the first lick), computed as premotor minus motor. Waiting times were binned into 0.3-s intervals from 1.0 to 3.4 s, with an additional bin for trials exceeding 3.4 s, as in the waiting correlation index analysis. For each bin, we calculated the mean waiting time and mean activity change and then computed the Pearson correlation between these values.

Video-based motion energy analysis for orofacial movements

Motion energy was quantified from video recordings acquired at 30 frames per second to capture frame-by-frame changes in pixel intensity within a user-defined ROI encompassing the mouse’s orofacial area. A representative video frame was used to manually select the ROI. Each frame was converted to grayscale, and the absolute difference in each pixel intensity between consecutive frames was computed within the ROI. These differences were then averaged across all pixels to generate a time series of motion energy values. To allow fair comparisons across sessions, motion energy time series were z-scored. To assess potential undetected lick-related movements prior to lick-sensor detection, Wilcoxon signed-rank test was performed comparing a baseline period without overt movement (−1.5 to −1 s before detected lick) to subsequent time bins (67-ms resolution) spanning −1 to 2 s relative to the detected lick.

Statistics

Statistical analyses are described in the main text and the figure legends. Statistical analyses were performed using MATLAB and GraphPad (GraphPad PRISM v.9). All statistical tests were two-sided unless otherwise stated. No statistical method was used to predetermine sample sizes, but our sample sizes are similar to those reported in previous publications (37, 38, 93).

Supplementary Materials

This PDF file includes:

Figs. S1 to S9