Functional (ir)Relevance of Posterior Parietal Cortex during Audiovisual Change Detection

Data and code availability

The data and code that support the findings of this study are available from authors M.N.O.L., C.M.A.P. and U.O., on reasonable request.

Animals

All animal experiments were approved by the Dutch Commission for Animal Experiments and by the Animal Welfare Body of the University of Amsterdam. A total of 24 male mice was used from two transgenic mouse lines: PVcre (JAX 008069) and F1 offspring of Pvcre (JAX 008069) and Ai9-TdTomato cre-reporter mice (JAX 007909). Mice were at least 8 weeks of age at the start of experiments and group-housed under a reversed day-night schedule (lights were switched off at 8:00 and back on at 20:00). All experimental procedures were performed during the dark period.

Head bar implantation

Before the start of any experiment, mice were implanted with a custom-made titanium head bar to allow head fixation. Mice were anesthetized with isoflurane and fixed in a stereotaxic apparatus. A circular head bar was positioned to include V1 and PPC bilaterally and glued and cemented to the exposed skull. Areas of interest were located based on stereotaxic coordinates (V1 relative to lambda: AP 0.0, ML ± 3.0, PPC relative to bregma: AP 1.9, ML ± 1.6) (Goard et al., 2016; Song et al., 2017; Le Merre et al., 2018). Mice were allowed to recover for 2-7 d after implantation and were then habituated to handling and head-fixation before the start of the training procedure.

Audiovisual change detection task

Throughout experiments, mice were water-deprived and earned their daily ration of liquid by performing the behavioral task. Mice were head-fixed, and two lick spouts were positioned symmetrically on the left and right side within reach of their tongue. Licks were detected by capacitance-based (training setups) or piezo-electric-based detectors (recording setup). Upon correct licking, 5-8 µl of liquid reward (Infant formula, Nutrilon) was delivered through the lick spout using gravitational force and solenoid pinch valves (Biochem Fluidics).

Stimuli were continuously presented throughout behavioral sessions. Visual stimuli were drifting square-wave gratings with a temporal frequency of 1.5 Hz and spatial frequency of 0.08 cpd at 70% contrast. Stimuli were presented with a 60 Hz refresh rate on an 18.5 inch monitor positioned at a straight angle with the body axis from the mouse at 21 cm from the eyes. In trials with a visual change, the orientation of the drifting grating was instantaneously changed (e.g., from 150° to 180°) while preserving the phase. The auditory stimulus was a stationary Shepard tone (Shepard, 1964) composed of a center tone and multiple harmonics (2 lower and 2 higher harmonics). The center tones ranged a full octave spanning from 2¹³ Hz (8372 Hz) to 2¹⁴ Hz (16,744 Hz). For each given Shepard tone in this stimulus set, the weight of the center and harmonic tones are taken from a fixed Gaussian weight distribution over all center and harmonic tones, in this case centered at 2^13.5 (11,585 Hz). Stimuli were presented with a sampling rate of 192 kHz. Stimuli were high-pass filtered (Beyma F100, Crossover Frequency 5-7 kHz) and delivered through two bullet tweeters (300 W) directly below the screen. Sound pressure level was calibrated at the position of the mouse, and volume was adjusted per mouse to the minimum volume that maximized performance (average ±70 dB). In trials with an auditory change, the stimulus was modified instantaneously from one Shepard tone to another with a different center frequency and associated harmonics, while preserving the phase across all compound tones. For example, an auditory change of ¼ octave would jump from 213 to 213^.25. The amount of change determined stimulus difficulty (see also below).

Animals were trained to respond in a lateralized manner to sensory changes in each modality: lick to one side to report visual changes, to the other side for auditory changes (modality-side pairing was counterbalanced across mice). In other words, mice were required to simultaneously monitor both the auditory and visual modality and identify the sensory modality in which a change occurred.

Trials were separated by a random intertrial interval (taken from an exponential distribution with a mean of 6 s, minimum 3 s, and maximum 20 s). Trial types were pseudorandomly ordered by block-shuffling: every block of 10 trials contained a mixture of trial types in a fixed proportion but random order (8% catch trials = no change, 46% visual trials, 46% auditory trials). For instance, each block contained on average 46% of visual trials randomly interspersed among the other trial types. Directly after stimulus change, a response window of 1500 ms followed in which mice could obtain a reward by licking the correct side (no reward available in catch trials). The first lick on the correct side during the response window was immediately rewarded (median reaction time was 324 ms across all auditory hits and 407 ms across all visual hits).

It is not likely that mice solved the task using short-term memory or prolonged evidence accumulation, as mice could respond immediately and the observed reaction times are shorter than the time windows usually considered in behavioral tasks explicitly including evidence accumulation or working memory (∼1000 ms) (Brunton et al., 2013; Akrami et al., 2018; Odoemene et al., 2018). However, it can still be argued that this task could be solved, for instance, by keeping the previous orientation in memory and comparing it with the previous one.

For each trained animal, we presented five levels of auditory and visual amount of change that spanned the perceptual range. We fitted this psychophysical data (see below) to establish the perceptual threshold for the visual and auditory domains for each animal. To sample sufficient trials per condition in recording sessions, we used two levels of change (threshold and maximal). For noncontingently exposed (NE) mice, we used threshold values that matched those from trained animals.

As visual and auditory feature changes were associated with different motor actions (in trained but not in NE animals), a simultaneous auditory and visual change would present the animal with conflicting signals (the visual change predicts reward for licking left, auditory change predicts reward for licking right). In a subset of sessions, we introduced these conflict trials (25% of the trials, replacing unimodal trials) and registered the choice (side of the first lick). Both sides were rewarded in conflicting trials.

We compared multisensory trained animals (MST, n = 17) with NE animals (n = 7). For NE animals, the sensory environment was identical; both the auditory and visual stimuli were continuously presented with the same distribution of trial types and temporal statistics as for trained animals. However, these animals received rewards if they licked during a hidden response window that was temporally decorrelated from the stimuli. Spontaneous licks were therefore occasionally rewarded, and this allowed us to compare intermittent licks, rewards, and stimuli between trained and NE mice. Each session was terminated after 20 trials of unresponsiveness, and these last 20 trials were always discarded from all analyses.

We further excluded a subset of sessions from trained animals with poor behavioral performance because of (1) a high false alarm rate to auditory or visual spout (>50%, one session excluded), (2) a high lapse rate on easiest auditory or visual trials (a threshold of >30% hit rate on both visual and audio trials with a maximal amount of change had to be met, two sessions excluded for low auditory performance, nine sessions for low visual performance). In this two-alternative unforced choice task, performance at chance level is not 50% with three response options (lick to visual spout, auditory spout, no lick) and depends on spontaneous lick rates and trial type distribution.

Viral injection

Once animals were trained to asymptotic performance, we aimed at optogenetically inactivating PPC by locally expressing Channelrhodopsin-2 in a cre-dependent manner in PVcre mice, therefore driving inhibitory interneurons. Mice were subcutaneously injected with the analgesic buprenorphine (0.025 mg/kg) and maintained under isoflurane anesthesia (induction at 3%, maintenance at 1.5%-2%) throughout the surgery. Small craniotomies (∼100 µm) were made over the area of interest (V1 or PPC) using a dental drill. A glass micropipette backfilled with AAV2.1-EF1a-double floxed-hChR2(H134R)-EYFP-WPRE-HGHpA (titer: 7 × 10¹² vg/ml, 20 298-AAV1 Addgene) was slowly lowered in the cortex, and 25 nl was injected at 700 µm and 400 µm below the dura each using a Nanoject pressure injection system (Drummond Scientific). Additional experiments continued after 3 weeks to allow for viral expression. A potential concern is that expression of ChR2 in deep parvalbumin-expressing (PV) pyramidal neurons (Tanahira et al., 2009) led to an increase rather than a decrease of activity in deep layers. We observed no such expression in deep pyramidal neurons of PPC (see Fig. 6B).

Neuronal recordings in PPC

We performed craniotomies on the day before starting extracellular recording sessions. Mice were anesthetized with isoflurane and small (∼300-500 µm) craniotomies over the areas of interest were made using a dental drill leaving the dura intact. Craniotomies were made in the left hemisphere over V1, PPC, as well as primary auditory cortex, and medial PFC. Only data from V1 and PPC were analyzed for this study. The data presented from these areas were partly recorded in the same animals. Data regarding optogenetic manipulations of V1 and PPC activity were gathered in different animals.

Extracellular recordings were performed on consecutive days with a maximum of 4 d to minimize damage to the cortical tissue. Microelectrode arrays of 32 or 64 channels (NeuroNexus, A1x32-Poly2-10 mm-50s-177, A1x64-Poly2-6 mm-23s-160) were slowly inserted perpendicularly to the cortical surface until all recording sites were in contact with the tissue. To allow for tissue stabilization, the start of the behavioral task commenced at least 15 min after array insertion. For the recording session on the final day before perfusion, the array was covered in DiI (Thermo Fisher Scientific) to facilitate post hoc visualization of the electrode tract. Neurophysiological signals were pre-amplified, bandpass filtered (0.1 Hz to 9 kHz), and acquired continuously at 32 kHz with a Digital Lynx 128 channel system (Neuralynx).

Optogenetics

In sessions with optogenetic interventions, a random subset of trials (50% of trials) was associated with photostimulation. Photostimulation started at stimulus onset and continued until the animal made a choice. Two fiber-optic cannulas (ID 200 µm, NA 0.48, Doric lenses) were connected to a 473 nm laser (Eksma Optics, DPSS 473 nm H300) and positioned within 1 mm directly over the thinned skull at the area of interest. We performed extracellular recordings simultaneous with photostimulation in all mice to verify the effectiveness of inactivation, and we adjusted the laser power for each animal to the minimum power that maximally inhibited neural activity. The horizontal offset between the fiber tip and insertion site of the microelectrode array was minimized within the limited space constraints and measured ∼200-400 µm (for comparison: PPC measures ∼1.0-1.5 by 1.0-1.5 mm, depending on delineation) (Lyamzin and Benucci, 2019). The range of laser powers used was the same for PPC animals compared with V1 animals (2-15 mW at the tip of each fiber-optic cannula, corresponding to 15.9-119.3 mW mm⁻²). This laser power in combination with our optogenetic approach was previously shown to lead to effective spatial inhibition across our infected target area (Li et al., 2019). To allow rapid control over light delivery, laser beam continuity was controlled by a shutter (Vincent Associates LS6 Uniblitz). We stimulated with 10 ms pulses at 20 Hz (40 ms off, 20% duty cycle). For the photoinactivation of V1, a stimulation scheme was used in which the pulse and interpulse duration was variable with an average of 20 Hz and 75% duty cycle. The higher duty cycle of V1 inhibition versus PPC inhibition (75% vs 20%) is unlikely to explain the difference in effect on task performance for two reasons. First, when we investigated spiking activity relative to single laser pulses, we observed no rebound activity during the interpulse interval (see Fig. 6D). Second, the same stimulation protocol has been used in the same laboratory to effectively silence higher visual areas to study the impact on V1 (Oude Lohuis et al., 2021). To prevent light from reaching the eye of the mouse, the fiber-optic cannulas were sealed with black tape, leaving only the tip exposed. Furthermore, animals performed the task in an environment with ambient blue pulsating light.

Pupil monitoring

The left eye was illuminated with an off-axis infrared light source (IR-LEDs, 850 nm) positioned to yield high contrast illumination of both the eye and whisker pad. A near-infrared monochrome camera (CV-A50 IR, JAI) coupled with a zoom lens (Navitar 50 mm F/2.8 2/3 inch 10MP) was positioned at ∼30 cm from the mouse to capture a view of the lick spouts and face of the mouse. A frame-grabber acquired images of 752 × 582 pixels at 25 frames per second. The pupil size and position were extracted from the obtained videos by labeling the pupil center and 6 radially symmetric points on the edge of the pupil using DeepLabCut (Mathis et al., 2018), and pupil size was quantified as the surface area of an ellipse fit to these points.

Histology

At the end of the experiment, mice were overdosed with pentobarbital and perfused (4% PFA in PBS). The brains were recovered for histology to verify viral expression and recording sites. We cut coronal and flattened cortical sections as described previously (Lauer et al., 2018). For coronal sections, area borders were drawn by aligning and overlaying the reference section from the atlas (Paxinos and Franklin, 2004). For flattened cortical sections, areas were identified based on cell densities aligned to reference maps (Gămănuţ et al., 2018).

Data analysis

Unless otherwise stated, all data were analyzed using custom-made software written in MATLAB (The MathWorks).

Behavior: analysis of performance

Behavioral hit rates were fit with a multialternative signal detection model (Sridharan et al., 2014). This model extends signal detection theory (Green and Swets, 1966) for multiple signals and has been designed to accurately and parsimoniously account for observer behavior in a detection task with multiple signals. In our behavioral task, these are the auditory and visual signals to be reported at different lick spouts. In this model, the decision is based on a bivariate decision variable whose components encode sensory evidence in each modality, and decision space is partitioned in three regions (miss: neither evidence is strong enough, auditory response, and visual response). In a given trial, the observer either chooses to report nothing (no licking) or report visual or auditory stimuli (by licking left or right) if the decision variable exceeds a particular cutoff value, the “criterion” for each signal (the animal's internal signal threshold for responding, in terms of signal detection framework). We fit two versions of this model. In sessions with two levels of change per modality (threshold and maximum), we fit the d′ and criterion (c) to the behavioral response rates for each stimulus difficulty separately. This consists of fitting four free parameters: the d′ parameters (d′_vis, d′_aud) and criterion parameters (c_vis, c_aud). In sessions with four levels of change per modality, we fit the behavioral response rates by fitting a fixed criterion and a d′ at each stimulus difficulty that was described by psychophysical function (three-parameter hyperbolic function). The d′ at each stimulus difficulty follows from: d′i=d′max*xin/(xin + s50n)(1) where d′_max is the asymptotic d′, s₅₀ is the stimulus strength at 50% of the asymptotic value, n is the slope of the psychometric function, and x_i is the amount of change. This consisted of fitting a total of 8 free parameters: d′_max, n, s₅₀, and c for each modality. These eight parameters are presented in Figure 8.

For a detailed description of how the d′ and criterion subsequently relate to response rates, we refer the reader to Sridharan et al. (2014). This analysis was used before the start of experimental sessions to establish for each animal the perceptual threshold and therefore auditory and visual stimulus difficulty to use, as well as quantify behavioral performance on control and optogenetic trials.

Behavior: regression model of choice

To test whether PPC inactivation affected other factors beyond performance averaged over trial types, we constructed a regression model of behavioral choice (Busse et al., 2011; Hwang et al., 2017; Akrami et al., 2018). We selected a multinomial logistic regression model, as in our behavioral task the animal was presented with three discrete choice options (lick to visual spout, lick to auditory spout, or no-go). In this model, each regressor has two weights, where positive weights increase the probability of responding relative to a third reference option. We chose no-go (not licking) as the reference option, such that the linear sum of weights across regressors determine the probabilities of the choice on a given trial through the following: log(paudiopno−go)=baudio + βaudio*X(2) log(pvisualpno−go)=bvisual + βvisual*X(3)

Where b is a bias parameter, β are sets of regression coefficients (or weights), and X is the matrix with the values of regressor variables for every trial. As regressors, we used information from the current and the previous trial. Only information from up to one trial in the past was used, as this captured the strongest effects on behavioral choice and allowed us to test the effects of PPC inactivation. First, to construct a null model, we included a random predictor with random values between 0 and 1 (abbreviated to N in Fig. 9). This null model can already predict behavioral choice above chance by matching choice fractions. Second, we included the within-session trial number to account for nonstationarity in behavioral choice because of satiation (T). Third, for sensory information, we used the amount of visual and auditory change (degree of grating orientation and pitch change, respectively) as a scalar variable (both log-transformed to account for logarithmic sensitivity in sensory systems) (S_v, S_A), and sensory stimuli on the previous trial (S_V-1, S_A-1). Fourth, reward on the previous trial was captured in two binary regressors per modality (R_V-1, R_A-1; 0 = not-rewarded, 1 = rewarded). Fourth, we included choice history (C_-1). Because this was a detection task with sensory stimuli at or near the perceptual threshold, licks outside “trials” to the auditory or visual lick spout could be interpreted as reports of perception. Therefore, we included for choice history a binary predictor that reflected the side of the last lick (0 = last auditory lick; 1 = last visual lick). Last, to capture the effect of PPC photoinactivation on choice, a binary predictor of photostimulation was included (O).

All sessions of single animals were concatenated as if it were one session (N = 7.2 sessions on average). The model was fit on this concatenated trial data per animal (N = 17 animals, 58.652 trials in total) using the glmnet package in MATLAB (Friedman et al., 2010) with elastic-net regularization (α = 0.95) and threefold cross-validation. Regularization parameter λ was maximized while not decreasing cross-validated performance. Model fit quality was assessed as the fraction of held-out test trials in which the estimated choice (choice with the highest probability) matched the actual choice. We term this cross-validated model performance, and it is shown in the figure in partial models. We used a subset of variables and performed the same regression procedure: for instance, a model with and without including photostimulation as a predictor to assess the effect of PPC inactivation on model performance. The analysis of the effects of photoinactivation was done on the 5 animals with PPC inactivation.

Neural data processing

Before spike sorting, the median of the raw trace of nearby channels (within 400 µm) was subtracted to remove common noise artifacts. Automated spike sorting and manual curation were done using Klusta and the Phy GUI, respectively (Rossant et al., 2016). During manual curation, each putative single unit was inspected based on its waveform, autocorrelation function, and its firing pattern across channels and time. High-quality single units were included as having (1) an isolation distance >10 (Schmitzer-Torbert et al., 2005); (2) <0.1% of their spikes within the refractory period of 1.5 ms (Vinck et al., 2016; Bos et al., 2017); and (3) stable presence throughout the session. This latter was quantified by binning the firing across the entire session (∼50 min) in 100 time bins and only including neurons that spiked in >90 time bins. We recorded a total of 671 neurons from 14 animals over 32 sessions that met our criteria.

For Figure 1D, F, spike times were binned in 1 ms bins, convolved with a Gaussian window with 50 ms SD, and z-scored by subtracting the mean baseline activity and dividing by the SD of all baseline periods (−1 to −0.2 s before stimulus). For the single neuron encoding model, spikes were binned in 25 ms bins and convolved with a Gaussian window with a 50 ms SD.

Single-neuron encoding model

We constructed an encoding model that allowed us to model, for single neurons, the time-dependent effects of all measured variables related to the task and the animal's behavior simultaneously on single-trial neuronal activity. This approach is particularly useful to disentangle the different events that contribute to heterogeneous responses in associative regions, such as parietal cortex (Park et al., 2014).

We included six categories of predictors: visual stimuli, auditory stimuli, reward, licking movement, pupil size, and trial history. Binary variables (stimulus present or not, last trial rewarded or not; all variables except for pupil size were binary) were modeled with a series of temporal basis functions (raised cosines) that spanned the relevant epoch of influence to fit time-dependent modulation of neuronal responses by these predictors.

For the auditory and visual predictors, we used two kernels with 100 ms SD that spanned the first 200 ms after stimulus to capture the early spiking activity and 10 kernels with 200 ms SD that spanned from 0 to 2000 ms after stimulus to capture the late, sustained response. A separate predictor set was used per combination of orientation/frequency × amount of change. For reward variables, we used 10 kernels with 200 ms SD that spanned from 0 to 2000 ms relative to stimulus change in hit trials (visual hit, audio hit) and 10 predictors that spanned −500 ms to 1500 ms relative to reward. We used reward as a single term to refer to hit-trial specific activity (rewarded visual and auditory hits). This definition was used also in tensor component analysis (TCA) and population decoding (see below). This definition captures activity related to correct detection and report as well as reward-related activity, and this encoding model dissociated this from other confounds (e.g., licking and arousal) by exploiting the trial-by-trial variability in timing. For licking movement, we used three kernels that spanned −200 to 400 ms relative to each lick, split by lick side. To capture arousal effects, the z-scored pupil area was included in the predictor set: with original timing and two temporal offsets (−800 and −400 ms). We included three binary history-dependent predictors, capturing the modality of the previous trial (visual or auditory), reward (hits or not), and choice (lick to visual or auditory spout). Last, the trial number was included to account for nonstationarity in firing rate across the entire session because of, for example, motivational signals and electrode drift, but was not reported in figures.

The number, width, and spacing of temporal basis functions were selected by optimizing the variance explained on a diverse subset of representative neurons (Runyan et al., 2017). For example, the use of trial-spanning history predictors was based on the fact that history had an offset effect throughout the trial duration in example neurons (Fig. 3). Explained variance (EV) both on trial averages and single trials was comparable to previously reported studies (Runyan et al., 2017; Steinmetz et al., 2019).

This resulted in a predictor matrix of size P × T for each neuron, where P is the number of predictors and T is the number of total time bins. The encoding model was fit on concatenated single trials, and T is therefore the number of trials (typically 200-500 trials) multiplied by the number of time bins per trial (100 time bins; −0.5 to 2 s relative to stimulus change, 25 ms time bins). The encoding model (a GLM) was fit with a Poisson link function to single neuron activity with the glmnet package in MATLAB (Friedman et al., 2010). We used elastic-net regularization (α = 0.95) and fivefold cross-validation. To maximally punish weights without losing model fit quality, λ was maximized while keeping the cross-validated error within 1 SE of the minimum. We quantified model performance by assessing the fivefold cross-validated EV in two ways. First, we computed EV over all concatenated firing rate bins (over all single trials). Second, we computed EV on the concatenated firing rate bins of the average firing rate for four main trial type conditions with most trial counts (visual and auditory hits and misses) (Runyan et al., 2017; Musall et al., 2019).

To quantify the contribution of subsets of predictors, we calculated the single-trial EV for a firing rate prediction based on only those predictors. In other words, we computed how much of the firing rate variance is explained by only considering the weights from, for example, visual variables. This value was compared with a shuffled distribution where the EV was computed using the predicted firing rate and the actual firing rate from shuffled trials (N = 1000 shuffles). A neuron was deemed to significantly encode this variable if it exceeded the 99% percentile of this shuffled distribution. This permutation test approximately labeled variable encoding in single neurons if at least 1% of the single-trial variance was explained, as we found very similar results when we simply thresholded on 1% EV.

To quantify whether the joint encoding of variables was significantly different from a random distribution across neurons, we shuffled (N = 1000) the vectors of neuron indices that significantly encoded visual, auditory, and reward variables relative to each other and recomputed joint or unique encoding (i.e., recomputing the Venn diagram). For instance, with 50% of neurons encoding visual and 50% encoding auditory variables, this shuffling procedure would generate percentages of joint audiovisual encoding neurons at ∼25%, against which the actual percentage was tested (exceeding the 2.5% or 97.5% percentile, corresponding to a two-sided test with p < 0.05).

Population decoding analysis

We tested whether PPC ensembles were responsive to audiovisual stimuli and reward by training decoders to classify (1) audio versus catch trials, (2) visual versus catch trials, (3) visual versus audio trials, and (4) rewarded versus nonrewarded trials. In 1, 2, and 3, we included only trials with large stimulus changes. Decoding was performed on recordings that contained at least 15 neurons and 15 trials per class. Spikes were binned using a sliding window of 100 ms with 50 ms increments, whereas for the insets, showing broader temporal dynamics, we used a window of 500 ms moved with 250 ms increments. Trials were aligned to the moment of stimulus change (Fig. 4A–H) or the timing of the first response lick (i.e., the first lick occurring at least 100 ms after stimulus change, Fig. 4I,J). When trials were aligned to stimulus change, temporal bins containing data before and after stimulus change (t = 0) were excluded from the analysis. Decoding was performed using a random forest classifier with 200 trees, as implemented in Scikit-learn (Pedregosa et al., 2011), and we used a 5 × 5 cross-validation routine with stratified folds (which preserves the proportions of samples of the two classes in each fold). The average accuracy obtained in the cross-validation routine was corrected by subtracting the average accuracy on 300 surrogate datasets in which the trial labels were randomly permuted to obtain the improvement in decoding accuracy beyond chance level. For every time point, we tested whether the corrected accuracy was significantly different from 0 using Wilcoxon signed-rank test; p values were corrected for multiple comparisons using the Benjamini–Yekutieli method, with a significance level of 0.05. We additionally trained decoders to classify the orientation of the drifting gratings and the frequency of the audio tone (Fig. 4G,H). Before decoding visual and auditory stimulus identity, we grouped the two pairs of orientations/frequencies, to obtain a two-class classification problem, and included only trials in which the stimulus changed from one pair of stimuli to the other (max changes).

Tensor component analysis (TCA)

We applied TCA (Williams et al., 2018) to recordings that contained at least 15 neurons. As the objective and similarity plot did not demarcate a fixed number of components to decompose our data, we chose a rank of 8 and tested the robustness of our analysis to different choices of rank (5 and 10 components, data not shown). As a way of identifying components representing noise and drift in the recordings, we filtered out components that were expressed in <20% of units or <20% of trials. For each component, we measured with a ROC-AUC score how well the trial factors discriminated (1) audio trials versus catch trials, (2) visual trials versus catch trials, and (3) correct trials versus incorrect trials. For each AUC score, we computed an associated p value by generating a null distribution of AUC values calculated on randomly permuted trial labels and computing the fraction of values in the null distribution which were equal or larger than the observed AUC score. AUC scores were considered significant with p < 0.05. For Figure 5B, C, components were labeled based on the contrast associated with the highest AUC score and included if the highest AUC score had an associated p < 0.05.

Statistics

We used Bayesian statistics throughout the manuscript (Jeffreys, 1939; Rouder et al., 2009) to facilitate intuitive interpretation of the strength of evidence as well as establish evidence of the absence of effects (Keysers et al., 2020). Bayesian statistics assess the likelihood of the data under both the null and the alternative hypotheses (H0 and H1, respectively). In most cases, we report the Bayes factor that corresponds to the ratio of likelihoods p(data|H₁)/p(data|H₀), abbreviated to BF. For instance, BF = 10 would mean that the data are 10 times more likely under H₁ than H₀ providing very strong support for H₁, while BF = 0.1 would mean that the data are 10 times more likely under H₀ than H₁ providing very strong support for H₀. Generally, a BF between 1/3 and 3 indicates that the data are similarly likely under H₁ and H₀ and that the data thus does not adjudicate which is more likely. A BF below 1/3 or >3 is interpreted as supporting H₀ or H₁, respectively, corresponding roughly to p < 0.05 for moderate sample sizes (Jeffreys, 1939). Evidence of absence of an effect, where the null hypothesis is more likely given the data, is denoted by the hashtag symbol (#) in figures, next to the standard asterisk symbol (*) for evidence for the alternative hypothesis.

We also performed classical frequentist statistics (i.e., calculating the probability of observing the data given a hypothesis) for each test and found nearly identical results, except for one statistical test in Figure 8C, where the auditory threshold was slightly affected by PPC inactivation.

We made four exceptions and used the classical frequentist test when we required a significance threshold without an available Bayesian alternative: (1) χ² test for fractions for significant increased and decreased fractions of PPC neurons (Fig. 1D) and (2) AUC values per TCA component versus a shuffled distribution (Fig. 5), (3) significant time points of decoding performance (Fig. 4), and (4) significant (joint) encoding of stimulus and behavioral variables versus shuffled distributions (Fig. 3).