Neuronal responses during auditory omission paradigm

In this study, we focused on the right auditory cortex of Urethane-anesthetized rats, utilizing extracellular recordings to monitor responses to auditory stimuli. Across 18 electrode penetrations involving 10 rats, we successfully captured the activity of 990 single units. For each rat, we first used a surface microelectrode array (NeuroNexus, Ann Arbor, MI, USA) (Fig 1A) to map the various parts of the auditory cortex (Fig 1B) [29–31]. We then used a Neuropixels electrode array to record different layers of the chosen area for each penetration (Fig 1C).

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Fig 1. Neuronal recording and experimental paradigm.

(A) Surface microelectrode array used to map the auditory cortex in urethane-anesthetized rats. (B) Representative auditory-evoked potentials in the cortex elicited by click stimuli. The color bar represents P1 amplitude (see “Methods”). A1, AAF, and VAF represent the primary auditory cortex, anterior auditory field, and ventral auditory field, respectively. (C) Neuropixels electrode array inserted through the holes on the surface array into the mapped regions to record neural activity across different cortical layers. (D) Experimental design featuring eight conditions with two distinct tones (A and B) and a 5% omission rate, presented in random order. Each condition comprised 1,000 stimulus items, varying the probability of Tones A and B to achieve different predictability levels. (E) Example of a neuron that responds to tones but not to omissions. The raster plot shows spikes (black dots) with time (ms) on the x-axis and trials on the y-axis. The PSTH displays firing rate over time, with tone stimuli (blue shading) and omissions (gray shading). The black line represents the firing rate, the red line shows omission responses, and the green line indicates the omission baseline. (F) Example of a neuron that selectively responds to the omission of specific tones. The same representation is used as in panel E.

https://doi.org/10.1371/journal.pbio.3003242.g001

To explore the neural response to auditory stimuli and their omission, we devised eight experimental conditions (Fig 1D). Each condition featured an oddball sequence of two tones with distinct probabilities, along with a consistent occurrence of tone omissions at a rate of 5%. To create varied prediction contents while maintaining a fixed omission rate, we utilized two tones and controlled their relative predictability. We selected two distinct pure tones (denoted as Tones A and B), one octave apart, that consistently elicited responses from most neurons for each penetration (see details in “Methods”). The sequences were systematically designed but presented in a random order. Each sequence comprised 1,000 stimulus items, including omissions, and featured Tones A and B at varying probabilities to achieve distinct levels of predictability. The specific ratios of Tones A and B were carefully controlled as follows: 95% Tone A and 0% Tone B (exclusively Tone A), 90% and 5%, 85% and 10%, and 75% and 20%. This pattern continued, adjusting further to 20% and 75%, 10% and 85%, 5% and 90%, until reaching 0% and 95% (exclusively Tone B).

We observed diverse patterns of neural responses to omissions. Fig 1E and 1F illustrate responses from three exemplary neurons to tone omissions during two distinct tone sequences: one with 95% Tone A and 5% omissions, and the other with 95% Tone B and 5% omissions. Some neurons exhibited strong responses when either tone was presented but did not respond to their omission (Fig 1E), and some neurons displayed selective responses to the absence of specific tones, with the intensity and nature of these responses varying depending on which tone was omitted (Fig 1F).

Omission responses encode tone probability

To determine whether omission responses encode negative prediction errors, we investigated how neurons’ responses to omissions were modulated by the predictability of the omitted stimuli. For neurons encoding negative prediction errors, their response should correlate with the content of the prediction. In our experimental design, the content is determined by the probabilities of the two tones, which is equivalent to the probability of one tone, since their total is fixed at 95%. Therefore, we first evaluated which neurons’ omission response correlated with the probability of tone presentation. The omission response was defined as the neuron’s mean firing rate during a 5–120 ms window after the omission, with a local baseline subtracted on a per-trial basis. This baseline was calculated as the mean firing rate from –24 to 5 ms relative to the expected tone onset, capturing the neuron’s state just before the tone was omitted [32]. We then computed the Spearman’s correlation between each neuron’s average omission response under each condition and the corresponding probability of tone presentation (either Tone A or B). For each neuron, the tone whose omission response increased with higher probability was designated the “omission preferred” (O_P) tone, while the other was termed the “omission non-preferred” (O_NP) tone. Under this definition, the correlation coefficients measured against the O_P tone were all positive, unlike those measured against the O_NP tone, which would be negative.

Next, we examined whether distinct groups exist based on how strongly each neuron’s omission response correlated with predictability of the O_P tone. To achieve this, we performed k-means clustering on the correlation coefficients and used an unbiased elbow analysis to determine the optimal number of clusters (see details in “Methods”). The elbow analysis revealed that it is optimal to cluster the data into two distinct neuronal subpopulations (see the elbow analysis in S1 Fig): one comprising 771 neurons with little or no modulation of omission responses by tone probability (mean Spearman’s ρ = 0.048), and a second comprising 219 neurons exhibiting a robust positive correlation (mean ρ = 0.18) (Fig 2A).

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Fig 2. Split-Data analysis for probability encoding.

(A) Distribution of Spearman’s correlation coefficients (rho) between each neuron’s omission response and OP tone probability. The histogram (gray bars) shows in how many neurons each correlation magnitude occurs, and the two overlaid curves represent separate clusters identified via k-means clustering analysis. (B) Omission responses from two example neurons across eight conditions ranging from 0% to 95% probability of the O_P tone. Each panel displays single‐trial spike raster plot (dots, right y‐axis) and a peristimulus time histogram (black line, left y‐axis) aligned to the expected onset of the omitted tone (time = 0 ms). The red line shows omission responses, and the green line indicates the omission baseline. The omission period is indicated by gray shading, and a local baseline is shown in green. The right plots in each row depict the mean omission response (blue curve) for that probability condition, with the x‐axis showing O_P tone percentage and the y‐axis showing firing rate. (C) Proportion of neurons classified using ODD trials as: PEONs (neurons showing both significant Spearman’s correlation between omission response and O_P tone probability plus significant omission response in Wilcoxon sign-rank test when comparing omission responses to baseline in conditions where O_P tone was standard), neurons with correlation only (showing significant correlation but no significant omission response), and neurons with no significant correlation. (D) Box plot summarizing omission responses for PEON_ODD, tested on EVEN trials. The x-axis represents the O_P tone probability (0%–95%), and the y-axis indicates mean baseline-subtracted firing rate in response to the omission, calculated over a 5–120 ms window after the expected tone onset. Boxes correspond to the interquartile range (IQR) with a horizontal line marking the median. Whiskers extend to 1.5× IQR. Individual data points are shown as overlaid dots, with means at each probability level marked by red diamonds connected by a dashed line. The text annotation shows the Spearman’s rank correlation coefficient (rho) and associated p-value, quantifying the strength and statistical significance of the monotonic relationship between probability and neural response. Underlying data are provided in S1 Data. (E) Laminar distribution of the recorded population (gray bars) and the neurons classified as PEON_ODD (blue bars), shown as a function of cortical depth (y‐axis). Horizontal dashed lines indicate the approximate boundaries between supragranular (0–600 μm), granular (600–900 μm), and infragranular (900–1,400 μm) layers, based on current source density analysis. (F) Distribution of PEONs across auditory cortical fields. Three pie charts illustrate the proportion of PEONs (blue slice) vs. other recorded neurons (gray slice) within A1 (left), VAF (middle), and AAF (right). Labels on each slice indicate the neuron category, the absolute count, and the percentage relative to the total number of neurons recorded in that specific field (indicated in the title of each chart). The p-value shown below reflects the result of a bootstrap analysis comparing the observed PEON count in each area to a simulated null distribution; the asterisk denotes statistical significance (p < 0.05).

https://doi.org/10.1371/journal.pbio.3003242.g002

Fig 2B illustrates the omission responses of two example neurons across eight different conditions. These range from scenarios with 0% O_P tone (95% O_NP and 5% omission) to scenarios with 95% O_P tone (0% O_NP and 5% omission). The peri-stimulus time histograms (PSTHs), aligned to the expected onset of the omitted tone, have been baseline-subtracted to isolate the omission response. Neuron 1 (from Cluster 1 in Fig 2A) exhibited only a weak correlation (Spearman’s ρ = 0.12), while Neuron 2 (from Cluster 2) showed a pronounced increase in omission response as the probability of the O_P tone increased (rho = 0.36).

To further examine these PEONs without introducing double-dipping biases, we conducted a split-data analysis by dividing trials into two independent subsets (odd and even trials, denoted as ODD and EVEN trials) to ensure the robustness of our analyses. All PEONs were identified using only one half (e.g., ODD) and subsequently tested on the complementary half (e.g., EVEN), ensuring that selection and evaluation were fully independent. Using the ODD trials, we identified 123 PEONs according to two criteria: (1) a significant correlation (p < 0.05) between their omission responses and the probability of the corresponding O_P tone, as verified by Spearman’s correlation test; and (2) a significant omission response (p < 0.05, Wilcoxon sign‐rank test) to this O_P tone in the four conditions where it was presented as standard (75%, 85%, 90%, and 95%), when the O_P tone is most predictable and omission responses should be greatest (see details in “Methods”). We refer to these PEONs as PEON_ODD. To confirm the reliability of our selection criteria and ensure that the identified neurons were not specific to one trial subset, we applied the same classification procedure to the EVEN trials, identifying a separate group of PEONs referred to as PEON_EVEN. For additional comparison, maximizing statistical power and evaluating probability encoding without trial-based data splitting, we identified PEON_ALL, a group classified using all available trials.

Out of a total of 990 neurons, we identified 123 (13%) PEON_ODD, 60 neurons (6%) showed correlation with probability but no omission response, and 807 neurons (82%) showed no correlation (Fig 2C, top). On the other hand, when using the EVEN trials, 145 neurons were classified as PEON_EVEN, 69 showed correlation but no response, and 776 showed no correlation. Although the precise numbers varied slightly between subsets, the classification proportions were broadly similar, supporting the robustness of the procedure. To assess consistency more directly, we quantified the overlap between the two independently identified PEON subsets. A total of 61 neurons were classified as PEONs in both ODD and EVEN trial sets, significantly exceeding the overlap expected by chance (expected: 18 neurons; hypergeometric test, p << 0.001). This result supports the stability of the classification approach, even when applied to trial-split subsets with reduced statistical power. For comparison, when using all trials without splitting, 200 neurons were classified as PEON_ALL, 70 showed correlation but no response, and 720 showed no correlation. Pie charts for both PEON_EVEN and PEON_ALL classifications are shown in S2 Fig.

Fig 2D presents a box plot that aggregates the omission response of all PEON_ODD on EVEN trials. To quantify the relationship between omission response and O_P tone probability, we performed a direct Spearman’s correlation analysis using all individual neuron data points, which revealed a significant positive relationship (Spearman’s ρ = 0.34, p = 1.6 × 10⁻²⁷, n = 984, representing 123 neurons × 8 probability conditions). The strength of this relationship indicates that neural responses systematically increase as the probability of the O_P tone increases, providing strong evidence that these neurons encode stimulus probability.

This significant relationship confirmed the robustness of the probability-encoding property, which is likewise replicated in the analysis of PEON_EVEN on ODD trials and PEON_ALL using all trials (see S2 Fig). From here onward, we present the results from the PEON_ODD group. Equivalent analyses for PEON_EVEN and PEON_ALL are provided in the S2–S5 Figs to further support the robustness and generalizability of our findings.

Spatial distribution of PEONs in auditory cortex

To investigate the anatomical basis of predictive coding in the auditory system, we analyzed the laminar and areal distribution of PEON_ODD. We used current source density (CSD) analysis of local field potential (LFP) responses to determine cortical layer depths and categorized neurons into layers based on established criteria (see “Methods”). Fig 2E illustrates the distribution of these neurons across cortical depths, demonstrating that PEON_ODD are distributed across all cortical layers, with a higher proportion found in the supragranular (16.2%) and granular (13.4%) layers compared to the infragranular layers (9.8%). A similar distribution was also discovered from PEON_EVEN and PEON_ALL (see S3 Fig).

To assess whether these distributions differed significantly from a random distribution, we performed a two-sided bootstrap analysis with 300,000 samples. The analysis revealed a marginal trend in the supragranular layer (p = 0.058) and a significant difference in the infragranular layer (p = 0.029), whereas the granular layer did not show a significant deviation (p = 0.62). Further examination of these results indicated that PEONs were present at a lower-than-expected rate in the infragranular layer. We similarly examined neuron distribution across different auditory fields, summarized in Fig 2F, using bootstrap analysis with 300,000 samples. This analysis revealed a significantly higher proportion of PEONs in A1 (p = 0.0036), whereas VAF (p = 0.9442) and AAF (p = 0.9926) did not show significant deviations from the distribution expected under the null hypothesis. Further examination suggested that PEONs were present at a higher-than-expected rate specifically in A1 relative to the other auditory fields.

Omission responses build up throughout the trials

To confirm that PEONs encode negative prediction errors, it is essential to show that their responses to omissions increase over time as predictions are gradually formed, reflecting a growing discrepancy between the predicted and actual outcomes. We analyzed PEON_ODD from EVEN trials and focused on omissions of the O_P tone in sequences where it was the standard (75%, 85%, 90%, and 95%), and therefore expected to evoke the largest omission responses. We grouped these responses by their sequence position and computed the mean firing rate (±standard error) for each bin. This grouping tests whether the omission response increases as more tones precede the omission, which is the expected pattern if these neurons are indeed signaling a negative prediction error that strengthens with increasing prediction.

Our analysis revealed a notable pattern: the magnitude of the PEONs response to these omissions progressively increased throughout the sequence, achieving a steady state or plateau after approximately 400 standards were presented (Fig 3A). The dynamics of the trial-by-trial omission response were fitted by a logistic growth curve, expressed as:

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Fig 3. Trial-by-trial dynamics of omission responses and standard tone adaptation.

(A) Firing rate of PEON_ODD for omission events (on EVEN trials) in the four conditions where the O_P tone was the standard (75%, 85%, 90%, 95%), grouped by sequence position. The x-axis represents the bin center (i.e., its sequence position), and the y-axis represents the firing rate in spikes per second. The black dots indicate the mean firing rate across all PEON_ODD for each bin, and the error bars represent the standard error of the mean (SEM), showing variability across neurons. The blue line represents the logistic growth curve fit to the data, illustrating how omission responses evolve over successive standards. Data were averaged across sequences where the O_P tone was the standard (95%, 90%, 85%, and 75%). (B) Firing rate of PEON_ODD in response to the presentation of tones across the first 50 trials. The x-axis represents the trial number, and the y-axis represents the firing rate in spikes per second. The black dots indicate the mean firing rate across all PEON_ODD for each trial, and the error bars represent SEM, showing variability across neurons. The blue line represents the exponential decay model’s fit to the data, indicating a rapid decline in response intensity over the initial trials as the neurons adapt to the repeated tone presentations.

https://doi.org/10.1371/journal.pbio.3003242.g003

where represents the firing rate as a function of n, and n is the bin center corresponding to the sequence position of the omissions (i.e., the number of tones presented preceding each omission). The logistic function depicts a saturating increase in response magnitude. Here, an R² value of 0.51 indicates the model’s moderate success in capturing the variability in responses. To demonstrate that the observed increase in omission response was not caused by gradual changes in network activation over time, we also examined how PEONs responded to standard tones over the first 50 trials (Fig 3B). The results indicated a rapid decline in response intensity over successive trials. This decay was fitted using an exponential decay model:

where is the firing rate at trial . An R² value of 0.75, indicating a substantial fit to the data. As expected, this encapsulates the phenomenon of stimulus-specific adaptation or a decrease in positive prediction error, where the response to an expected stimulus diminishes rapidly. These trends were consistent also for PEON_EVEN during ODD trials and PEON_ALL over all trials (see S4 Fig).

PEONs selectively respond to omissions while broadly reacting to tones

Finally, we investigated whether PEONs are exclusively responsive to omissions or if they also react to tone stimuli. The population responses of PEON_ODD from EVEN trials revealed a pronounced asymmetry in omission and tone responses (Fig 4A, top). Omission responses showed tone selectivity based on probability: as described before for PEON_ODD, the response strength systematically increased with the probability of the O_P tone. In contrast, tone-evoked responses for both O_P and O_NP tones exhibited an inverse relationship with probability. Specifically, the response to the O_P tone (blue line) decreased as the probability of the O_P tone increased (Spearman’s ρ = –0.19, p = 2.1 × 10⁻⁸, n = 861, representing 123 neurons × 7 probability conditions), showing adaptation to the increasingly standard O_P tone (Fig 4A, bottom). Similarly, the response to the O_NP tone (orange line) increased as the probability of the O_P tone increased (Spearman’s ρ = 0.20, p = 6.7 × 10⁻⁹, n = 861, representing 123 neurons × 7 probability conditions), which means it also shows an inverse relationship with probability, but with respect to the O_NP tone’s own decreasing probability, reflecting deviant detection of the increasingly rare O_NP tone. In essence, PEONs selectively signal negative prediction errors only for O_P tone omissions, while their responses to both tones exhibit symmetrical adaptation to the standard tone and deviant detection of the deviant tone, without tone-specific selectivity in the direction of probability modulation.

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Fig 4. Selective omission and broad tone responses in PEONs.

(A) Top: Population-level firing rates comparing omission responses (black), tone responses to the O_P tone (blue), and tone responses to the O_NP tone (red), plotted against the probability of the O_P tone. The y-axis indicates firing rate (spikes/s), and error bars show standard error of the mean. All data are drawn from the EVEN trials of PEON_ODD. Bottom: Spearman’s correlation coefficients between neural responses and tone probability. Bars show the correlation strength and direction for responses to the O_P tone (blue), responses to the O_NP tone (red), and omission responses (black). Asterisks indicate statistical significance (*p < 0.05). Underlying data are provided in S2 Data. (B) Raster plots (dots) and PSTHs (black lines) with omission and tone responses (red line) and baselines (green line). from a single PEON (identified in ODD trials, shown here on 25 EVEN trials), illustrating omission responses (left column), tone responses to the O_P tone (middle), and tone responses to the O_NP tone (right). Gray shading marks the omission period (expected stimulus timing), and light blue shading indicates tone presentation. For tone responses (middle and right columns), trials were subsampled to match the statistical power of omission trials, ensuring equalized trial counts across conditions. PSTHs are shown after subtracting the mean baseline (green line), and the red line highlights the evoked response. Each row corresponds to a different probability of the O_P tone (0%–95%). (C) The left chart categorizes the 90 PEONs validated on EVEN trials, meaning they were originally identified in ODD trials and continued to show significant omission responses to O_P in EVEN trials (90 of 123 PEON_ODD). These neurons were divided into selective PEONs, which responded significantly to omissions only when O_P was the standard, and non-selective PEONs, which exhibited significant omission responses when either O_P or O_NP was the standard. The right chart further classifies the 59 O_P omission-selective PEONs based on their tone responses—those responding to both tones, only to the O_P tone, only to the O_NP tone, or to neither.

https://doi.org/10.1371/journal.pbio.3003242.g004

When examining individual neurons, we found that, as expected from the definition of PEONs, their omission responses were highly selective. A substantial proportion of PEONs detected the absence of one tone while responding to both. This is illustrated in Fig 4B, which shows the responses on EVEN trials of an example PEON_ODD. This neuron’s omission response (left column) increased with O_P probability, exhibiting robust firing at high probabilities (90%–95%). Despite its selective omission response, it showed significant responses to both O_P tone (center column) and O_NP tone (right column), especially when the tone probabilities were low (5%–10%).

To ensure that the selectivity observed in omission responses is not merely due to residual effects from the previous trial’s tone responses—such as lingering activity or altered baseline activity—we verified that omission selectivity is independent of tone selectivity. To do this, we measured the omission selectivity index (OSI) and the tone selectivity index (TSI) for each PEON (see details in “Methods”). The results showed no significant correlation between OSI and TSI across the PEON population (Spearman’s ρ = –0.03, p = 0.78, n = 123 neurons). This lack of correlation indicates that a PEON’s preference for a specific tone (e.g., Tone A over Tone B) does not predict its preference for the omission of that tone. Therefore, omission selectivity was not a residual effect from the previous trials.

To quantify this selectivity across the population, we examined how many PEONs exhibited significant omission responses under different conditions. Out of 123 PEON_ODD, 90 demonstrated significant O_P-omission responses in EVEN trials (with an additional 5 showing significant responses only to O_NP omissions). Of these 90 neurons with O_P omission responses, 59 (66%) were selective for O_P omissions, whereas 31 (34%) were non-selective, exhibiting significant omission responses for both tones (Fig 4C, left). To further characterize the omission-selective group, we examined their responses to tone presentations to determine whether they responded exclusively to one tone or to both (Fig 4C, right), 41 (or 69%) exhibited significant responses to both the O_P and O_NP tones across experimental conditions (see details in “Methods”). Additionally, 3 PEONs responded exclusively to the O_P tone, 9 solely to the O_NP tone, and 6 did not significantly respond to either tone.

Similar trends in tone responses were observed when validating PEON_EVEN validated on ODD trials and in PEON_ALL (see S5 Fig). In both cases, most omission-selective neurons responded to both tones, while smaller subsets responded exclusively to one tone or to neither. This consistency across datasets further supports the robustness of the omission response selectivity and its relationship to tone-evoked activity. In summary, these characteristic responses—observed in a considerable subpopulation of individual PEONs, which are selective for omissions but broadly responsive to tones—mirror the population responses and indicate an intriguing functional asymmetry. This raises the question of how computational principles and circuitry give rise to this phenomenon.

Neural circuit model for asymmetric predictive-coding processing

To further understand how PEONs, which we presume to be negative prediction-error neurons, can display this observed asymmetry in top–down and bottom–up processing, we developed a neural circuit model consisting of multiple streams within a “predictive-coding module” (Fig 5A). This model was based on the framework proposed by Keller and Mrsic-Flogel, which describes a circuit module that integrates negative prediction error computation [6].

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Fig 5. Neural circuit model for asymmetric predictive-coding processing.

(A) Basic circuit module showing interconnections between neurons. P: prediction neuron, PE+: positive prediction error neuron, PE–: negative prediction error neuron, I+/I–: inhibitory interneurons, I: sensory input neuron. The connection types are also indicated. (B) Temporal profiles of sensory and prediction signals. (C) Lateral connections between two example circuit modules processing different sensory streams. (D) Full model with 5 sensory streams showing tonotopic organization. Streams 2 and 4 receive full strength input for tones A and B, respectively. The numbers below illustrate the strength of sensory signal (S_strength) in each stream. (E) Distance-dependent properties of lateral connections, showing delay and weight as a function of the distance between streams (see more details in “Methods”).

https://doi.org/10.1371/journal.pbio.3003242.g005

Each predictive-coding module includes six leaky integrate-and-fire (LIF) neurons divided into two streams: one stream calculates the positive prediction error and upregulates the prediction, while the other stream calculates the negative prediction error and downregulates the prediction. A sensory neuron (denoted as I) receives the sensory signal and propagates the information in a bottom–up manner. In contrast, a prediction neuron (P) receives the prediction signal and propagates the information in a top–down manner. A positive prediction-error neuron (PE+) receives excitatory synaptic input from the sensory neuron and is suppressed by the prediction neuron via an inhibitory interneuron (I+). Conversely, a negative prediction-error neuron (PE–) receives excitatory synaptic input from the prediction neuron and is suppressed by the sensory neuron via an inhibitory interneuron (I–). All synaptic connections are static synapses that include three variables: synaptic weight, time constant, and synaptic delay (see details in “Methods”). The activity of PE+ enhances the prediction signal through excitatory analog feedback, while the activity of PE– suppresses the prediction signal via inhibitory analog feedback.

In our simulation, the sensory signal was designed to replicate the experiment, featuring an analog pulse stimulus with an intensity of S_strength (ranging between 0 and 1) and a duration of 20 ms, delivered with a stimulus onset asynchrony (SOA) of 150 ms (see Fig 5B, top). Conversely, the prediction signal was modeled as a similar analog pulse as the sensory signal, but varied in intensity (P_strength), which could be enhanced by excitatory feedback from PE+ or diminished by inhibitory feedback from PE– (Fig 5B, bottom). It is important to recognize that our model assumes the temporal profile of the prediction signal is learned through a separate mechanism, while the predictive-coding module adjusts only the signal’s magnitude based on prediction error.

Predictive coding modules from different streams, each processing a specific frequency according to a tonotopic organization, are interconnected through lateral excitatory synaptic connections. These connections run from PE+ of one module to PE– of another (as illustrated between streams A and B in Fig 5C). Intuitively, this setup enables PEONs, represented as PE–, in one stream to respond to stimuli in another stream, endowing them with a broader bottom–up receptive field. Moreover, this configuration allows an unexpected stimulus in one stream to inhibit the predictive signal in other streams. For example, as shown in Fig 5C, if the sensory signal in Stream B is unexpected, PE+ in Stream B will activate, causing PE– in Stream A to also activate through the lateral connection. This activation will then suppress the predictive signal in Stream A. Thus, when an unexpected Tone B is detected, indicating that Tone A (or other tones) is unlikely, the prediction for Tone A (or other tones) is consequently reduced. Conversely, since the absence of an expected Tone B does not necessarily suggest the presence of Tone A (or other tones), our model does not include lateral connections running from PE– to PE+.

Our comprehensive model includes five streams: Stream 2 is tuned to detect the O_P tone (Tone A), while Stream 4 detects the O_NP tone (Tone B) (see Fig 5D). The model incorporates a simple receptive field structure for sensory signals. Specifically, Stream 2 receives Tone A at full strength (S_strength = 1), whereas the adjacent Streams 1 and 3 receive Tone A at half strength (S_strength = 0.5). Similarly, Stream 4 receives Tone B at full strength, and the adjacent Streams 3 and 5 receive Tone B at half strength. Additionally, the model features lateral excitatory connections between streams that are distance-specific (Fig 5E). The synaptic delay between any two streams is proportional to their spatial separation, and the synaptic weight decreases with the inverse square of their distance (see more details in “Methods”).

Asymmetric activities in modelled PEON

We conducted multiple simulations using the model, each featuring unique probability combinations of tones A and B, along with a consistent 5% omission rate, mirroring the conditions of our rodent experiments. Each simulation included 500 stimuli—either tone A, B, or an omission (O)—across a total of 75 s. Importantly, every simulation began with no initial predictions across all streams (P_strength = 0).

Here, we demonstrate the model’s responses using the example where the sensory inputs consist of 90% A, 5% B, and 5% O, randomly ordered as shown in Fig 6A. The spiking activities of Neurons I, P, PE+, and PE− across the five streams are illustrated in Fig 6B. Notably, Neuron P began firing after a few seconds, particularly in Streams 1–3, which are responsive to Tone A. This activity indicated that the prediction for Tone A was beginning to be established. Consequently, the positive prediction error, reflected by PE+’s spiking activity, began to diminish. Additionally, the spiking activity of PE−, primarily associated with the omission of Tone A, was also observed in Streams 4 and 5. This was largely due to lateral connections from PE+ in Streams 1–3. The prediction signals across the five streams, detailed in Fig 6C, show that P_strength increased and plateaued in Streams 1–3, caused by PE+’s firing, with Stream 2 displaying the highest value.

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Fig 6. Asymmetric activities in modelled PEON.

(A) Sensory input sequences over 75 s, showing occurrences of tones A (90%), B (5%), and omissions (5%). (B) Spiking activities of neurons I, P, PE+, and PE– across five streams. Colors represent different streams. (C) Prediction signal strength (P_strength) over time for different streams. The same color scheme is used as in panel B. (D) Raster plots (top 3 panels) and PSTHs (bottom panel) for PEON in Stream 2 under: 90% A, 5% B, 5% O. Responses to tones A (red vertical line), B (blue vertical line), and omissions (O, black dotted vertical line) are shown separately. PSTHs display firing rate over time, with colored lines indicating responses to different stimuli. In the top three panels, spike rasters are plotted across the same set of 500 trials. Because Tone B occurs in only 5% of trials, fewer spikes are displayed for B compared to A. The bottom panel shows the corresponding firing rates for each condition. (E) Raster plots and PSTHs for PEON in Stream 2 under: 5% A, 90% B, 5% O.

https://doi.org/10.1371/journal.pbio.3003242.g006

To explore asymmetric predictive-coding processing, we focused on the PEON in Stream 2, the target neuron for modeling our experimental results. Our goal was to reproduce the experimentally observed asymmetry: selective responses to omissions of the preferred tone, but broad responses to both tones. The raster plots of this PEON, presented in Fig 6D for a simulation containing 90% A, 5% B, and 5% O, characterize responses to different stimuli: Tones A, B, and omissions O. The PSTH reveals that while the PEON consistently responded to omissions, it did not respond to Tone A (in later trials), which was anticipated. Importantly, the PEON did respond to Tone B, a response enabled by lateral connections. In Fig 6E, we present raster plots from a different simulation with 5% A, 90% B, and 5% O. Similar to the previous simulation, the PEON in Stream 2 responded to Tone B via lateral connections. It also reacted to Tone A, facilitated by the lateral connections from nearby Streams 1 and 3, where PE+ was activated by the deviant Tone A. Notably, there was no response to omissions, as the prediction in Stream A was not effectively established due to the minimal occurrence of only 5% A. In conclusion, the PEON in Stream 2 demonstrated the asymmetry of receptive fields in bottom–up sensory and top–down predictive processing, reflecting the findings in the rodent experiment.

Note that this asymmetry requires that the weights of the lateral excitatory connections from nearby neurons (as shown in Fig 5E) exceed the inhibitory weights within the module (see S1 Table). This setup ensures that sensory inputs from the neighboring streams can overcome inhibition to elicit a response on PEONs. When the number of lateral neighbor neurons increases (there are only two in our model), reduced excitatory weights can remain effective. Furthermore, we believe these lateral connections could be activity-dependent (e.g., via spike-timing-dependent plasticity) and further refined through self-organization. However, this lies beyond the scope of our current study.

Alternative models and evaluation

To assess the validity of the proposed model with lateral connections (the model labeled “Lateral PE+ to PE–”), we evaluated two alternative models and compared their predictions against the experimental data. The alternatives included: a model with lateral connections from Neuron I to PE– across different streams (termed “Lateral I to PE–”, depicted in Fig 7A), and a model with no lateral connections at all (referred to as “No lateral”). For each model, we measured the responses of the PEON in Stream 2 to Tones A, B, and omission O under different probabilities of Tone A (Prob(A)): from 0% (95% B and 5%O) to 95% (0% B and 5%O). The results are shown in Fig 7B, together with the correlation between the firing rate and Prob(A).

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Fig 7. Alternative models and evaluation.

(A) Schematic of the alternative model with lateral connections from input neurons (I) to negative prediction error neurons (PE–) across streams A and B. (B) Evaluation of alternative models: Lateral PE+ to PE–, Lateral I to PE–, and No Lateral. Top panels show the firing rates of PEON in Stream 2 in response to Tone A (red), Tone B (blue), and omissions (O, gray) across varying probabilities of Tone A (Prob(A)). Bottom panels display correlations between firing rates and probabilities for Tones A, B, and omissions for each model.

https://doi.org/10.1371/journal.pbio.3003242.g007

In our proposed model, the PEON’s response to omission significantly correlated with Prob(A) (Spearman’s ρ = 0.79, p = 2.1 × 10⁻¹⁰⁸, n = 500 trials; see “Methods” for further details), indicating that the PEON did encode the probability of the stimulus within its stream. For Tone A, the PEON exhibited reduced responses as Prob(A) increased, demonstrating a significant negative correlation between firing rate and Prob(A) (r = –0.73, p < 1 × 10⁻²⁵⁰, n = 4,750 trials). This occurred because PE+ in nearby Streams 1 and 3 detected less surprise at higher Prob(A) values, leading to less activation of the PEON in Stream 2 through lateral connections (as also noted in Fig 5E). Conversely, for Tone B, the PEON’s response positively correlated with Prob(A) (r = 0.81, p < 1 × 10^-250, n = 4,750 trials). At higher Prob(A) values, Tone B emerged as the deviant tone. This led to an enhanced detection of surprise by PE+ near Stream 4 for Tone B, which subsequently activated the PEON in Stream 2 more strongly through lateral connections.

In the alternative “Lateral I to PE–” model, the PEON’s response to omission was also correlated with Prob(A) (r = 0.82, p = 4.3 × 10⁻¹²³, n = 500 trials). For Tone A, unlike the proposed model, the PEON in Stream 2 did not exhibit decreased responses at high Prob(A) values. This occurred because the PEON directly received sensory input from Neuron I, which remained unchanged across different Prob(A) settings. Despite this, a positive correlation between the firing rate and Prob(A) was observed (r = 0.82, p = 4.3 × 10⁻¹²³, n = 4,750 trials). This was due to slightly increased responses from Neuron I in nearby Streams 1 and 3, which were caused by an elevated membrane potential resulting from frequent stimulation by Tone A. Conversely, for Tone B, the opposite effect occurred: Neuron I near Stream 4 showed an increase in membrane potential due to frequent stimulation of Tone B at low Prob(A) levels. Therefore, despite only minor changes in firing rate across different Prob(A) values, a negative correlation was observed (r = –0.42, p = 3.5 × 10⁻²⁰⁴, n = 4,750 trials).

In the alternative “No lateral” model, the PEON’s response to omission correlated with Prob(A) (r = 0.38, p = 9.2e⁻¹⁹, n = 500 trials), as this encoding occurs within the stream without the need for lateral connections. For Tone A, the PEON displayed no responses, which was anticipated since it could only react to an omission in the absence of lateral connections. For Tone B, the PEON exhibited similar responses as to omissions, since in Stream 2, any stimulation differing from Tone A was treated as an omission. Consequently, a similar positive correlation was observed (r = 0.58, p < 1 × 10⁻²⁵⁰, n = 4,750 trials).

To validate these models, each demonstrating unique encoding characteristics, we compared them to data from our rodent experiment. In our analysis, Tones A and B corresponded to the O_P and O_NP Tones, respectively. The correlation patterns we observed in our experimental data (see Fig 4A) align closely with the predictions of our proposed model. The positive correlation for omission responses, negative correlation for responses to O_P tone, and positive correlation for responses to O_NP tone are all successfully captured by the model with lateral PE+ to PE− connections. These results support the proposed model with its lateral connections facilitating positive prediction errors, distinguishing it from the alternative models.

The models discussed so far have not taken into account that the strength of sensory signals could diminish due to frequent exposure to a specific stimulus. To address this, we analyzed responses from neurons in the thalamus (n = 130 neurons) across various probabilities of the O_P Tone (see S6A Fig and “Methods” for details). Accordingly, we modeled the sensory signal strength, S_strength, as a function of Prob(A) (S6B Fig) and conducted simulations. By simulating various levels of sensory adaptation (see “Methods”), our results reaffirmed that only the proposed model successfully replicated the probability encoding characteristics observed in the rodent data (S6C Fig).

Computational benefits of lateral connections

Our next step was to explore the potential computational benefits of the proposed lateral connections, particularly in terms of enhancing prediction encoding. How do these connections influence prediction signals? Without lateral connections, not only would Stream 2 predict Tone A, but also the neighboring streams (e.g., Stream 1), due to their broad sensory receptive fields receiving half-strength sensory signals. However, with lateral connections, these predictions are reduced not only by the omission of Tone A but also by the presence of Tone B. Particularly, we theorized that this additional reduction would suppress the already low prediction signals in the neighboring streams. This leads to a scenario where the prediction signal is predominantly strong in Stream 2, thus resulting in a more precise encoding of Prob(A) across streams.

To test this, we first assessed the steady value of P_strength after the prediction signal stabilized across various stimulation sequences (as in Fig 6C). These sequences varied Prob(A) from 0% to 95%, with increments of 1%. In Fig 8A, we plotted the time courses of P_strength for each 75-s simulation under different Prob(A) settings, focusing on Stream 2, where our target PEON was situated, and the adjacent Stream 1. For comparison, the time courses for Streams 1 and 2 in the model without lateral connections (“No lateral”) are shown in Fig 8B. The steady value of P_strength was determined by averaging values over the last 50 s (from 25 to 75 s). It was plotted as a function of Prob(A) for both models, with and without lateral connections, across Streams 1 and 2 (as shown in Fig 8C). In both streams, P_strength increased as Prob(A) rose. However, the increase was less pronounced in the model with lateral connections, especially at lower Prob(A) values. We further analyzed the contrast in P_strength between Streams 1 and 2 by calculating the decibel value (logarithmic ratio of P_strength in Stream 2 to that in Stream 1). This contrast was significantly greater in the model with lateral connections compared to the model without, particularly when Prob(A) was less than 0.5 (Fig 8D). This suggested that the lateral connections enhance the contrast of prediction signals across streams.

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Fig 8. Computational benefits of lateral connections.

(A) Time courses of prediction strength (P_strength) in Streams 2 and 1 with the lateral connections for varying probabilities of Tone A. Colors indicate the magnitude of P_strength. (B) Time courses of prediction strength in Streams 2 and 1 without the lateral connection. The same representation is used as in the panel A. (C) Steady-state P_strength in Stream 2 (solid lines) and Stream 1 (dotted lines) as a function of Prob(A) with (red) and without (blue) lateral connections. (D) Contrast in P_strength between Streams 1 and 2 (log scale) with and without lateral connections, plotted against Prob(A). (E) Steady-state P_strength across all streams (S1 to S5) as a function of Prob(A), with and without lateral connections. (F) Mean P_strength across all streams for different Prob(A) settings, comparing the network with (blue) and without (red) lateral connections.

https://doi.org/10.1371/journal.pbio.3003242.g008

We also hypothesized that the additional suppression of prediction signals facilitated by lateral connections could enhance prediction encoding efficiency. This is supported by the observation that P_strength was generally lower with lateral connections (as shown in Fig 8C). To investigate this further, we measured P_strength across Prob(A) for all streams in both models (Fig 8E) and then calculated the average P_strength across streams for each Prob(A) setting (Fig 8F). The findings suggest that with lateral connections, the network requires less “energy” or smaller prediction signals to effectively encode sequences, particularly in less predictable scenarios where the occurrences of Tones A and B are equal, such as Prob(A) = 0.5. This demonstrates a more efficient encoding strategy. Conversely, without lateral connections, the network expends more energy to manage more unpredictable sequences.

Auditory omission responses as correlates of negative prediction error

Omission paradigms are a powerful tool for isolating negative prediction-error signals, as they eliminate the confounding influence of sensory input present in positive prediction error paradigms (e.g., oddball sequences). In human studies using EEG and MEG, mismatch negativity (MMN) responses to unexpected omissions in tone sequences have been reported, which are interpreted as evidence for predictive coding mechanisms [17,20,22–24,33]. More recently, single-neuron recordings in animals have begun to reveal the neural mechanisms underlying these auditory prediction errors. Studies have reported omission-responsive neurons in the auditory cortex of both awake and anesthetized rodents. One study found that 35.6% of neurons in awake animals and 19.5% of neurons in anesthetized rats and mice exhibited significant responses to the omission of expected tones [34,35]. Another study, using more complex stimuli involving the omission of expected gaps within auditory sequences, also demonstrated robust omission responses in unanesthetized rats [25]. Alongside these auditory findings, multiple studies in mouse visual cortex have documented sensorimotor prediction-error signals, specifically negative prediction errors, in response to unexpected reductions in expected sensory input [7,36,37]. These studies demonstrate that neurons in V1 exhibit negative mismatch responses when expected visual flow is weakened or omitted during locomotion. A molecularly distinct population of neurons in V1 has been identified that selectively responds to unexpected omissions of predicted visual stimuli [9] Extending this sensorimotor framework to the auditory system, a recent study showed that neurons in the auditory cortex responded to unexpected reductions in movement-contingent sound within a virtual reality environment, signaling a negative prediction error [28]. Building upon this foundation, our study’s conceptual advance stems from our paradigm design that systematically varies tone probabilities while maintaining consistent omission rates, allowing us to characterize negative prediction error as a continuous, probability-encoding mechanism rather than simply a binary deviance detector. This approach also reveals the dynamic nature of these prediction signals, which develop gradually through repeated exposure to statistical patterns in the environment. The subsequent sections will explore how these findings, along with our observations of asymmetry in predictive processing, led us to develop a circuit-level model that offers a new perspective on information flow in predictive coding networks.

Top–down “predictive field”

Our model builds upon the framework proposed by Keller and Mrsic-Flogel, which describes predictive coding as a canonical cortical computation [6]. Their model emphasizes hierarchical processing with distinct neuron populations computing positive and negative prediction errors. Consistent with this framework, our findings provide evidence for both types of prediction error in the rat auditory cortex. While we focused on characterizing negative prediction errors in PEONs, we also observed oddball responses in the broader population of non-PEON neurons (S7 Fig), with enhanced responses to unexpected tones. Since such responses have been interpreted as positive prediction-error signals in previous studies, we infer that at least some of these neurons encode positive prediction error [16,18,38–41]. More importantly, our model additionally describes how predictive coding modules, which process bidirectional information, interact both vertically and horizontally across sensory streams. This provides a means for prediction errors to integrate across bottom–up receptive fields. Moreover, we hypothesize that there is also a receptive field for top–down signaling. Traditionally, a neuron’s receptive field is defined by the range of external stimuli that can directly evoke its activity, a concept rooted in bottom–up sensory processing. However, neurons like PEONs are influenced not only by bottom–up sensory input but also by prediction signals generated in other brain areas. Therefore, their effective response properties – what we might term their “predictive field” – are shaped also by the specificity of the prediction. We believe that the asymmetry between the bottom–up receptive field and the top–down predictive field provides a means to integrate predictions and prediction errors, and that it could be inverted (i.e., a larger predictive field than receptive field) at other hierarchical levels.

Lateral connections in predictive coding networks

Our circuit model proposes that unexpected stimuli in one frequency stream inhibit predictive signals in adjacent streams via lateral prediction suppression. This enhances the contrast between the predicted frequency and others, sharpening the prediction signal and facilitating more efficient updates to the internal model, conceptually analogous to lateral inhibition in sensory systems, which serves to enhance the contrast of bottom–up sensory input [42]. That is, the lateral prediction suppression we propose for the top–down predictive field is functionally analogous to lateral inhibition in the bottom–up receptive field.

Biological evidence strongly supports the existence of excitatory lateral connections between adjacent frequency channels in A1. These connections play a crucial role in spectral integration and the processing of complex auditory stimuli [43–45]. Anatomical studies have revealed that pyramidal neurons in A1 exhibit long-range horizontal collaterals that form connections across different frequency representations, often aligning with isofrequency bands [46,47]. Physiological investigations have demonstrated that these intracortical pathways contribute significantly to the breadth of subthreshold frequency receptive fields, which can span up to five octaves [48,49]. The strength and probability of these connections are distance-dependent, with stronger and more probable connections between neurons tuned to close frequencies, weakening as the frequency distance increases [50,51]. This organized network of lateral connections facilitates the integration of spectral information across different frequency channels, supporting complex auditory processing and cortical plasticity in A1.

Similar patterns of lateral connectivity have been observed in other sensory modalities, such as orientation-specific connections in visual cortex [52] and whisker-related connections in somatosensory barrel cortex [53], suggesting a common organizational principle across different sensory areas. The development of these lateral connections might involve both innate and learned components. While the basic framework of these connections may be genetically predetermined, their refinement occurs during early postnatal development through experience-dependent plasticity [54]. This developmental process allows for the fine-tuning of these connections based on sensory experience, optimizing the auditory cortex for processing the specific acoustic environment encountered during critical periods of development.

In our model, the one-way excitation from PE+ to PE− neurons allows for rapid recalibration of expectations across streams. This asymmetry enables efficient updating of predictions based on positive surprises while avoiding false alarms from mere absences. Integration across frequency channels enables complex interactions, with sequences of tones providing predictive information about subsequent tones. Naturalistic sounds like tone clouds can activate multiple streams simultaneously, leveraging the network’s capacity for sophisticated auditory processing [55].

Lateral prediction suppression and the free energy principle

Building upon these anatomical and functional observations of lateral connectivity, we can consider how our proposed circuit model might be interpreted through theoretical principles. The free energy principle [1,56] potentially offers an elegant explanatory framework for understanding why these lateral connections may have evolved. Could the lateral prediction suppression we observed be more than just a convenient circuit mechanism? When viewed through the lens of free energy minimization, these connections might represent an optimal solution for efficient predictive processing. In S1 Text, we provide a mathematical treatment that suggests when a simplified form of the free energy principle is applied to a two-tone paradigm similar to our experimental design, lateral interactions between prediction errors across different streams emerge naturally from the formalism.

In our mathematical exploration, we considered a simplified generative model where auditory tones at different frequencies are represented as hidden variables with linear relationships to sensory inputs. By deriving the update rules for prediction signals under free energy minimization, we found that the resulting equations comprise three key components: updates based on prediction errors within the same frequency stream, lateral interactions of prediction errors across different frequency streams, and a temporal decay term. Notably, the lateral interaction term emerges from the correlation structure of sensory inputs across different frequencies—a statistical regularity well-documented in natural auditory environments [57]. These theoretical derivations align remarkably well with our proposed circuit model, where lateral connections between PE+ and PE− neurons across different frequency streams play a crucial role in shaping prediction signals.

This theoretical perspective raises intriguing possibilities about why the brain might implement the asymmetric receptive fields we observed. The efficient coding strategy—where unexpected stimuli in one frequency channel not only signal prediction errors within that channel but also laterally modulate predictions in neighboring channels—could represent an evolutionarily advantageous solution for minimizing computational costs while maximizing predictive accuracy. Such a theoretical framing might also explain the directionality of lateral connections we proposed, flowing primarily from positive to negative prediction error neurons rather than bidirectionally. While experimental validation of these theoretical predictions remains a challenge for future work, the mathematical alignment between our empirical findings and free energy principles suggests that lateral prediction suppression could be a fundamental computational motif in predictive processing, potentially extending beyond the auditory system to other sensory modalities.

Layer and area specificity of PEONs

Our finding that PEONs are more prevalent in granular and supragranular layers aligns with current views on the laminar organization of predictive coding circuits [4]. These layers are thought to be primary sites for prediction error computation and integration of top–down predictions with bottom–up sensory input. The relative scarcity of PEONs in infragranular layers suggests these neurons may be less involved in generating feedback predictions to earlier processing stages. Regarding their distribution across different auditory fields (A1, VAF, AAF), while PEONs were present in all areas examined, they showed a significantly higher proportion in A1 compared to VAF and AAF (based on bootstrap analysis). This potential enrichment in A1 might suggest functional specializations within primary auditory cortex related to negative prediction error signals, although the presence of PEONs across fields still supports the idea that predictive coding is a widespread cortical computation [6]. However, this raises questions about potential functional specializations not captured by our current paradigm.

Dynamics of omission responses

A notable feature of the PEON omission responses is their shape; rather than exhibiting a sharp, transient peak as seen in typical tone responses, they often display a more gradual onset and prolonged duration [27,32,34] compared to both typical auditory evoked responses and the idealized, instantaneous prediction-error signals assumed in simplified predictive coding models, including our own. While our model effectively captures the probability encoding and asymmetry of PEON responses, it does not explicitly model the detailed temporal dynamics. Functionally, a more gradual negative prediction-error signal might help prevent drastic responses to slightly delayed expected input—contrasting with the rapid responses needed for unexpected stimuli. Furthermore, the negative prediction-error signal could reflect a prediction not only about the content (i.e., the tone) but also about its timing. In other words, the prediction signal could be gradually ramped up according to a hazard function, modeling how the brain adjusts its anticipation of an event as time passes [58–61], and the negative prediction-error signal could follow a similar pattern. We suspect that this ramp-up response involves a recurrent cortical circuit normally inhibited by sensory input; when the input is omitted and disinhibition occurs, the negative prediction-error signal gradually increases. Future computational modeling that explicitly incorporates recurrent connectivity and temporal integration mechanisms will be crucial for elucidating the precise neural mechanisms underlying this observed latency.

Establishment of prediction signals

A notable limitation of our study is the absence of explicit “prediction neurons” in both our experimental findings and computational model. While we identified neurons responding to prediction errors, we did not find neurons directly representing predictions about upcoming stimuli. Predictive signals might be generated in higher-order auditory areas, non-auditory regions providing top–down input, or encoded in a distributed manner across neuronal populations. Further computational modeling of distributed prediction encoding could help guide future experiments by suggesting specific patterns or population-level dynamics to look for in neural data.

It is important to consider whether the observed omission responses might themselves be a prediction signal, rather than solely a prediction error. However, several aspects of the PEON activity argue against this interpretation. First, a prediction signal should precede the expected time of the stimulus, while PEON omission responses occur after the expected tone onset. Second, prediction signals should appear consistently across all trials, regardless of whether the stimulus is presented or omitted. Instead, we observe that PEONs exhibit markedly different activity patterns between presentation and omission trials—in some cases showing smaller responses when tones are presented compared to when they are omitted. Thus, the PEON activity pattern is more consistent with a negative prediction-error signal, reflecting the mismatch between expectation and reality, rather than just the expectation itself.

Future research should address the limitations of our study, such as the potential effects of anesthesia on neural responses, by comparing findings with those from awake and behaving animals. Additionally, employing more complex stimuli and varying spectral distances between tones could further probe the limits of the proposed lateral prediction suppression mechanism. Another important direction is identifying the specific neuronal populations involved in prediction-error signaling. While our study focused on firing rate dynamics, different neuronal subtypes may play distinct roles in encoding positive and negative prediction errors. Techniques such as optogenetic tagging, juxtacellular recording, or genetic labeling could help determine whether PEONs correspond primarily to excitatory pyramidal neurons or specific subtypes of inhibitory interneurons, providing critical insights into the circuit mechanisms underlying predictive processing in the auditory cortex.

Animals

The study involved 10 male Wistar rats, aged 11–12 weeks, and weighing between 250 and 350 gms. The animals were housed in a carefully controlled environment with a 12-h light/dark cycle, ensuring optimal conditions for their well-being. Food and water were provided ad libitum throughout the study. To minimize animal suffering, all surgical procedures were conducted under appropriate anesthesia. Upon completion of the experiments, the animals were humanely euthanized using an overdose of pentobarbital sodium (160 mg/kg, administered intraperitoneally), following established guidelines for the humane termination of animal studies.

Surgical procedures

The rats were anesthetized using urethane, with an initial dose of 1.5 g/kg administered intraperitoneally and supplementary doses of 0.5 g/kg provided as needed to ensure stable and deep anesthesia. This depth of anesthesia was confirmed by the absence of corneal and pedal reflexes. The animals were secured using a custom-made head-holding apparatus. Atropine sulfate (0.1 mg/kg) was administered subcutaneously at the onset of the procedure to reduce bronchial secretion viscosity. Local anesthetic xylocaine (0.3–0.5 ml) was applied at the incision site before making the skin incision. A needle electrode was inserted subcutaneously into the right forepaw to serve as ground. A small craniotomy was performed near the bregma landmark to place a reference electrode, ensuring electrical contact with the dura. A larger craniotomy was performed over the right auditory cortex (4.0 mm posterior and 6.0 mm lateral to bregma), and the right temporal muscle, cranium, and dura covering the auditory cortex were surgically removed. The exposed cortical surface was kept moist with saline to prevent drying. Cisternal cerebrospinal fluid drainage was conducted to minimize cerebral edema. Throughout the experiment, an adequate and stable level of anesthesia was ensured by monitoring the animals’ respiratory rate, heart rate, and hind-paw withdrawal reflexes.

Electrophysiological recordings

Neuronal activity was recorded using both a custom-designed surface microelectrode array [62] and a Neuropixels 1.0 electrode array (IMEC, Belgium) [63].

Mapping auditory cortex using the surface array

To record neuronal activity epipially over the auditory cortex, a surface array (NeuroNexus, Ann Arbor, MI, USA) comprising 64 platinum electrodes was employed. Each electrode had a diameter of 100 μm and a center-to-center distance of 500 μm, covering an area of 4.5 × 3.0 mm. The array featured 0.3-mm diameter holes between the electrodes to allow the insertion of a Neuropixels array. Auditory evoked potentials (AEPs) were recorded using amplifiers with a gain of 1,000, a digital filter bandpass of 0.3–500 Hz, and a sampling frequency of 1 kHz, employing the Cerebus Data Acquisition System (Blackrock Microsystems LLC, Salt Lake City, UT, USA).

We mapped the click-evoked responses to pinpoint the location of the auditory cortex (AC). A click was defined as a monophasic positive wave lasting 20 ms. 60 clicks were administered at a rate of 1 Hz, and LFPs were recorded. The peak amplitude of the middle-latency auditory-evoked potential (P1) within the first 50 ms following the stimulus onset was measured from the grand averaged LFP. To identify three subfields within the AC—A1, AAF, and VAF—we analyzed the spatial distribution of the P1 response.

Neuropixels recordings

For recording neuronal activity across different cortical layers, we used the Neuropixels 1.0 electrode array [63]. The array features 384 active recording sites (out of 960 sites total) located at the bottom approximately 4 mm of an approximately 10 mm shank (70 µm wide, 24 µm thick, 20 µm electrode spacing), with the reference and ground, shorted together. The probe’s ground and reference pads were soldered to a pin, which was then connected to a skull screw on the animal. Recordings were made in internal reference mode.

Data acquisition for the Neuropixels arrays was performed using Neuropixels version 1.0 acquisition hardware, specifically the National Instruments PXIe-1071 chassis and PXI-6133 I/O module for recording analog and digital inputs (Neuropixels version 1.0, IMEC, Belgium). The signal was collected from the most distal 384 recording sites (bank 0) at a 30 kHz sampling rate. Raw voltage traces from the Neuropixels arrays were filtered, amplified, multiplexed, and digitized on-probe. Data acquisition and initial processing were managed using Open Ephys software (www.open-ephys.org). Spike sorting was conducted using Kilosort 3 [64], and further manual curation was performed with Phy software (https://phy.readthedocs.io/en/latest/). This process involved removing artifacts, merging duplicate clusters, and discarding units with insufficient refractory periods, intermingled waveforms, or unstable firing patterns. Only well-isolated neurons meeting strict inclusion criteria were retained for analysis. The cortical depth of the recording site, estimated via CSD analysis, had to be within 0 µm to +1,800 µm from the pial surface. The lower bound of 1,800 µm was chosen to confine recordings to the auditory cortex, preventing the inclusion of neurons from subcortical areas or unintended regions. Additionally, neurons had to fire at least 200 spikes per session to ensure sufficient statistical power, while those exhibiting strong drift in firing rate or waveform shape were excluded to maintain stationarity.

Characterization of the frequency response area

To assess the frequency-tuning properties of all recorded neurons, we measured the frequency response area (FRA) at each recording site. The auditory stimuli consisted of pure tone bursts with a 5-ms rise/fall time and a 20-ms steady-state duration. The tones covered a wide range of frequencies, spanning 18 distinct values from 1.6 to 64 kHz, and were presented at seven different sound pressure levels, ranging from 20 to 80 dB SPL in 10-dB steps. In total, 126 unique tone bursts were used to characterize the FRA. The stimuli were delivered in a pseudorandom sequence with an inter-tone interval of 600 ms, and each tone was repeated 20 times. FRA maps were generated for each neuron based on their responses to the presented tones. After examining the FRA maps, we selected two tones that were one octave apart and elicited robust responses from most recorded neurons. These two tones were then used as the stimuli for the subsequent experiments investigating the neural responses to tone sequences and omissions using an intensity well above the threshold of a typical neuron.

Experimental design

To investigate the neural responses to tone sequences and omissions, we designed eight experimental conditions, each employing an oddball paradigm with two distinct tones and a fixed 5% probability of tone omissions. The stimuli were the two sinusoidal tones chosen before with a duration of 50 ms, including 5-ms rise and fall ramps. These tones were arranged in sequences of 1,000 stimuli, with an SOA of 150 ms. In the first condition, one tone (Tone A) comprised 95% of the sequence, while the other tone (Tone B) was absent. Across the subsequent conditions, the proportion of Tone B gradually increased by 5% increments, while the proportion of Tone A decreased accordingly. This resulted in the following sequences:

1. Sequence 1: 95% Tone A, 0% Tone B, 5% omissions
2. Sequence 2: 90% Tone A, 5% Tone B, 5% omissions
3. Sequence 3: 85% Tone A, 10% Tone B, 5% omissions
4. Sequence 4: 75% Tone A, 20% Tone B, 5% omissions
5. Sequence 5: 50% Tone A, 45% Tone B, 5% omissions
6. Sequence 6: 20% Tone A, 75% Tone B, 5% omissions
7. Sequence 7: 10% Tone A, 85% Tone B, 5% omissions
8. Sequence 8: 0% Tone A, 95% Tone B, 5% omissions

This design allowed us to systematically manipulate the relative probabilities of the two tones while maintaining a consistent rate of omissions. By progressively shifting the balance between the tones across conditions, we could examine how the neural responses to tone omissions were influenced by the statistical context provided by the sequence.

Data analysis

Tone and omission selectivity indices.

To assess the relationship between tone-evoked selectivity and omission selectivity, we computed selectivity indexes – TSI and OSI for each neuron. TSI was calculated as:

and represent the neuron’s mean firing rate in response to the and tones, respectively, averaged across the seven probability conditions in which each tone was presented. OSI was calculated as:

and denote the neuron’s mean firing rate in response to omissions occurring in the 4 sequences where the and tones were standard, respectively. To test whether a neuron’s tone selectivity predicted its omission selectivity, we computed Spearman’s correlation between TSI and OSI.

Computational modeling.

We constructed a circuit of leaky integrate-and-fire neurons following

with membrane time constant and membrane resistance . When , neurons emitted a spike () and were reset to for a refractory period of 2 ms. Synaptic currents and were modeled with instantaneous rise and exponential decay,

and equivalently for , with time constants and . Spikes from presynaptic neurons were delivered with a synapse-specific delay and weight as detailed in S1 Table within each stream module. Lateral connections between streams and delivered spikes with delay and weight . Sensory stimulation was presented through the input neuron I by setting its to a constant (target stream) or (adjacent streams) for 20 ms. Similarly, prediction signals were fed to the P neuron by setting with identical timing. P_strength was initialized to 0 and updated by spikes in prediction neurons as follows:

and clipped to ensure at all times. Both and were raised to their respective values for 20 ms at the start of each trial, then reset to for the remaining 130 ms.

The model was written in Brian2 [65], which allowed calculating exact solutions for the internal neurons of the circuit (PE+, PE–, I+, I–). The remaining neurons (P and I), synapses and P_strength were integrated with a time step of 0.1 ms by forward Euler integration. Simulations were run over 500 trials.

Sensory adaptation.

To model sensory adaptation, we adjusted the input by using an adaptation factor a, which is greater than zero, and a base firing factor b, which is between 0 and 1. The input strength for the A and B streams under different values of Prob(A) was adjusted as follows:

Examples of S_strength_A versus Prob(A) are shown in S6 Fig, with 12 combinations of a (0.01, 0.05, 0.1, 0.5) and b (0.1, 0.3, 0.5).