To functionally determine the precise anatomical location of PPC, we first identified retinotopic and somatotopic organizations with intrinsic signal optical imaging (ISOI) in anesthetized mice ^38–42. Retinotopic mapping revealed locations of each HVA including AM (Figure 1A), which has been considered to be the core of mice PPC in recent studies ^4,27. To map the boundary of the primary somatosensory (S1) area anterior to the HVAs, we used tactile vibration of the body parts including a trunk as trunk S1 is known to be located at the most posterior portion of the S1 ³³. As expected, the trunk S1 (S1t) was located at a posterior region within S1 (Figure 1B; Figure S1A,B). The distance from the center of the AM to the center of the S1t was ∼900 μm (894 ± 18.3 (mean ± s.d.), n = 8 mice). Assuming that the diameter of AM and S1t are 600 μm and 400 μm, respectively, we could estimate that there would be a space 400 μm wide along the rostrocaudal axis between these two areas. Here, we defined this space as area A (Figure 1C), because it roughly overlaps with the HVA identified as area A in a landmark anatomical study of mouse HVAs ²⁰. Our definition of area A likely includes a larger area than this original definition.

Often, PPC is determined using stereotaxic coordinates, and we considered this approach. However, systematic mapping of visual areas relative to the lambda and midline showed that each HVA location based on the stereotaxic coordinates was unreliable. The mean distance from the center position of each HVA in each mouse to the average center position across mice was 244 μm, (range: 198 – 316 μm, n = 12 mice) (Figure S1C,D) when the positions were measured relative to the lambda landmark. We confirmed that the variability in locations was not explained by the age or sex (Figure S1E). Instead, the variation of HVAs substantially decreased after the registration of the areas by translation based on the location of V1 and RL. After this registration, the mean distance from the center position of each HVA to the average center position across mice was ∼91.5 μm (range: 38.6 - 141 μm), n = 12 mice): a reduction in variability by more than half (Figure S1F-I). This improvement indicates that relative locations of HVAs are similar across mice ⁴³, but HVA locations relative to skull landmarks are more than twice as variable. Thus, localizing these small HVAs and components of PPC by stereotaxic coordinates can introduce variability and decrease the fidelity of localization. We concluded that functional imaging of retinotopic and somatotopic organization must be obtained in each individual mouse to precisely and rigorously map HVAs and PPC, and to ascribe functions to neurons therein.

ISOI was supplemented with two-photon calcium imaging to observe the activity of neurons within and surrounding PPC including area A (Figure 1D-F). In awake mice, somatosensory stimuli including tail, trunk, neck, and whiskers resulted in responses in PPC areas. In S1, somatosensory stimulation evoked localized neuronal responses that exhibited somatotopic organization. In contrast, area A neurons activated by somatosensory stimuli did not exhibit clear somatotopy (Figure 1G). Likewise, visual responses of neurons in area A did not exhibit clear retinotopy (Figure 1H), in contrast to other HVAs ²⁰. Some area A neurons showed activity by stimulation of multiple body parts such as trunk and tail, or trunk and whiskers, which is similar to area 5 of macaque ⁴⁴ (Figure 1F). Thus, area A integrates multiple somatosensory inputs, potentially contributing to body coordination (e.g., posture) ^14,44. Some neurons in AM were activated by tactile stimuli, and again this activity lacked somatotopy. Based on the multisensory responsiveness of areas A, AM, and RL ^2,45,46, we demarcate the PPC as a three-module structure, consisting of AM, RL, and A (as defined above) (Figure 1I). Note that these areas overlap with HVAs.

After precisely mapping PPC and adjacent cortical areas, we examined layer 2/3 neuronal activity during behavior with single neuron precision across multiple cortical areas simultaneously with large field-of-view, two-photon calcium imaging (Movie S1). We used transgenic mice that express a genetically encoded calcium sensor, GCaMP6s, in cortical neurons ⁴⁷. The field-of-view (Figure S2) typically covered PPC and surrounding areas including HVAs, V1, S1, and a portion of retrosplenial cortex (RSC).

PPC has been reported to have functions including visually guided decision-making and working memory. Do these functions differ among RL, A, and AM? To address this question, we trained the mice in head-fixed conditions to perform vision-guided and history-guided two-alternative forced-choice tasks (Figure S3A-D) and imaged the activity of neurons for each task. First, we investigated the distribution of task-related neurons during a visually-guided task (“vision task”; Figure 2A-D). In this task, mice had to lick one of two waterspouts (left or right) based on the visual stimuli, naturalistic video (Movie S2) or black screen, presented to the left visual field of the mice (imaging in the right hemisphere) (Figure S3A,B). This simple task was designed to clearly map sparse responses of neurons to natural video ⁴⁸, and to map the choice-related activity guided by the visual stimuli at the same time to see segregation or overlapping of the vision and choice-related neurons around PPC.

Large field-of-view calcium imaging during the task enabled us to simultaneously observe ∼10⁴ neurons (n = 5 mice, total of 10 sessions, 47162 neurons). Neurons were robustly activated by specific frames in the naturalistic video, by the black screen, or by left or right choice (Figure 2E,F; Movie S3). Notably, some PPC neurons showed complex dynamics rather than simply encoding specific visual or choice information, indicating integrative roles. To quantitatively identify and map the functional properties of each neuron, we constructed a simple linear regression model (“encoding model”, Figure 2G). In the encoding model, the activity of each neuron was fitted by a weighted sum of the external control parameters such as a video frame and behavior parameters such as choice and reward directions. The linear model was sufficient to estimate the correlation with neural activity, since there is little correlation between task parameters such as visual stimuli, choice, reward, and inter-trial-intervals (materials and methods). The statistical significance (p<0.001) of each parameter corresponding to visual stimulus and chosen direction was used to identify the vision and choice-related neurons, respectively. The functional labels revealed by this encoding model were consistent with the t-SNE clusters, indicating the validity of the encoding model (Figure 2H; Figure S4B; material and methods). The neurons which were selective to video or black screen (“vision neurons”) were found in V1 and HVAs including AM, while the neurons which were selective to the chosen direction (“choice neurons”) were distributed in S1t and A (Figure 2I). Interestingly, the neurons that activated during the choice period irrespective of the choice directions were distributed broadly (Figure S4A). The vision and choice neurons were distributed mostly exclusively, but some overlapping was found around AM as revealed by mapping of the harmonic mean of the percentage of vision and choice neurons (“association index”) (Figure 2J; Figure S4A; Movie S3). This indicates that the AM would be suitable for integrating vision and choice information rather than the A, RL or the other areas around PPC.

The PPC neurons had been thought to be important for decision making, but recently it has also been suggested that the PPC neurons store the history information rather than deciding the upcoming choice. To analyze whether the neurons around PPC represent the upcoming choice or the past choice in our visually guided task, we decoded the choice direction with the activity of 50 neurons before and after the choice (Figure 2K). The decoding accuracies of A and S1 were higher than the other areas at the choice timing and they stored the choice information even 5 s after the choice. On the other hand, the decoding accuracy of the choice 1 s before the choice was very low in any areas recorded. Thus, neurons in areas A and S1t reflect the choice direction immediately after the choice and store it over 5 s. In addition, vision neurons preferred a specific time of the video frame resulting in the vision neurons sequentially firing during the sampling period (Figure 2L). Decoding analysis showed that the vision neurons precisely possessed the temporal information of the video frame (Figure 2M). Such precise decoding of time during the sampling period was not observed in black screen trials (Figure 2N). From the two decoding performances, we divided the imaged areas into four groups (Figure 2O). Note that area AM is the most suitable area for the association of these two parameters, as it possesses a substantial amount of decodable information about both parameters.

Next, we asked whether and where choice history information can be stored in PPC and surrounding areas. We designed a choice history-dependent task (“history task”) with the same set up as the vision task (Figure 2A-C). In this task, the mice had to choose the opposite side of the previous choice. Mice had to store the direction of the choice for 6-10 seconds from the previous choice to the next choice including an inter-trial-interval (ITI) and a sampling period. Since the visual stimuli were randomly presented during the sampling period, the mice had to ignore the visual stimuli. This task was designed to map the history neurons in contrast to the choice neurons and the vision neurons around PPC.

Large FOV calcium imaging during the history task (n=4 mice, 10 sessions, 27059 neurons) revealed that neurons in A and S1t maintained their activity during the ITI in a past-choice-specific manner, indicating that these neurons stored the choice history for making the next choice (Figure 3A). We used the same encoding model as in the vision task to identify the neurons representing the history of the previous choice (“history neurons”) as well as choice and vision neurons. Again, the functional labels revealed by this encoding model were consistent with the t-SNE clusters, indicating the validity of the encoding model (Figure 3B; Figure S4C,D). We found that neurons in area A had a significantly larger ratio of history neurons than all the other areas including S1t that had more choice neurons, and that neurons in AM exhibit large association index (Figure 3C, D). We also found more history neurons in the history task in A compared to those in the vision task (Figure 3E). Thus, A exhibited a task-specific functional change, preferentially representing a parameter when it is relevant, despite being available in both tasks.

PPC neurons are known to store the information of not only the choice history but also the outcome and sensory histories ^11,13. We compared these candidates by decoding analysis (Figure 3F,G). Although the outcome and visual information rapidly decreased in all areas after a trial, the choice information was strongly represented in A and S1t, and stored during the ITI, especially in A. We confirmed that the choice history information was about the past rather than about the future in both A and S1t (Figure 3H). We also asked whether the history neurons in A contributed to the working memory. When the next trials were correct, the decoding accuracy from history neurons in A during the ITI stayed higher than when the next trials were incorrect (Figure 3I). Thus, the choice history information possessed by history neurons led the animal to the correct choice in following trials. In other words, the history neurons exhibited properties of working memory. What kind of dynamics did the history neurons use to store this choice history information? The population activity of the history neurons indicated that each history neurons had a specific time of peak activity, resulting in the sequential activity after the choice (Figure 3J). In this task, left and right selection are alternated, so the activity of the history neuron is a sequence that repeats in two consecutive trials. We used jPCA⁴⁹ to visualize and quantify this activity pattern (Figure 3K). As expected, the population of history neurons showed one-round rotational dynamics in two trials, and the same was true for the A population, but the AM population did not show rotational dynamics. We quantified the extent to which population activity can be approximated by the rotational component (R² of M_skew; materials and methods) and found that the value in A and S1t was not only higher than that in the other areas (Figure 3L) but also significantly correlated with the correct rate of the session (Figure 3M). Interestingly, the sequential activity was also observed in AM, but it was less specific to the choice (Figure 3N), resulting in the decoding accuracy of time after a specific choice being than in A (Figure 3O). These results indicate that the history-related activities of A and S1t encode past behavior histories by creating long sequences, and that these rotational dynamics lead to behaviors that reflect past histories.

Neuronal activity in S1 typically represents simple somatosensory information, and thus the history neurons in S1t may be a consequence of habitual changes of the posture of the animal after making a choice in a trial. In this case, history neurons may not store the choice history internally, but they may simply reflect the posture of the mouse ¹⁴. To test this possibility, we analyzed the posture of the mice performing the tasks using a deep-learning based tracking method (Figure 4A). We found that the angle of the tail was significantly different from the baseline values several seconds after the RP (Figure S5A). Therefore, the position of the tail was useful information for the next choice in the history task. Overall, although the body was tightly restricted in the body-holder, mice still moved the tail and the paws in relation to the choice, the choice history, and the choice timing. Some parameters could potentially explain apparent task-related activities of neurons, which had been largely ignored in previous studies.

We searched for relationships between the activity of neurons and these posture-related parameters during the history task. We constructed a linear model based on these parameters to fit the activity of each neuron during the history task in a similar way to the encoding model for defining task-related neurons (Figure 4B, materials and methods). We found that the neurons related to the tail and forepaws were similarly distributed around the parietal cortex including S1 and A, while the pupil-size related neurons were mapped around visual areas (Figure 4C), although pupil size and pupil size-related neurons would just respond to luminance changes. A and S1 had a comparable ratio of neurons that were related to the tail and the paws. However, it remained unclear whether the activity of history neurons represented an internally stored choice history variable, or just reflected the sensory information that happened to correlate with the choice on the next trial.

If neurons in A retain history information by receiving posture information, perturbing the posture information should decrease A’s history information. To test this, we prevented the mouse from maintaining its posture during the ITI by randomly rotating the body holder (+24 or -24 degrees), forcibly introducing a physical disturbance making it difficult for the mouse to retain information of the previous choice by posture (Figure 4D). Three mice successfully performed the task in this new condition. We conducted a regression analysis and mapped the neurons reflecting the angle of the holder (“holder neurons”; Figure 4F) and found that they had similar distributions to history neurons (n=3 mice). Decoding analysis also showed the close relationship between history and posture information at the area level (Figure 4G). By contrast, the representation of the angle and representation of the choice history were not correlated at the single neuron level (Figure 4H). This result is evidence that the neurons regarding two different spatial features, the direction of choice and angle of the body, may share some neuronal resources in A and S1t, but these neurons process the information independently. Consistently, the percentage of history neurons and decoding accuracy of choice history were almost the same regardless of the holder movement in both A and AM (Figure 4I,J). Thus, history neurons represent an internally stored choice history variable, independent of the posture. Taken together, the history task and posture-perturbation experiments demonstrated that the most specific function of neurons in area A is storing choice history that contributes to the next choice.

PPC has anatomical connections with a variety of surrounding and remote areas ²², but the functional correlation between those areas has not been extensively examined. In particular, based on the critical functional differences between A and AM that we found, A and AM may belong to distinct cortical networks that consist of different sets of densely interacting cortical areas. To address this question, we focused on the correlation in trial-to-trial variability, r_t. In the following, we analyzed r_t on two different levels: pairs of single-neuron activities and pairs of population activities.

First, to obtain r_t between a pair of single neurons, r_{t_single}, we averaged the activity of individual neurons over the sampling period by trial type, and subtracted this from the trial-wise activity. The trial types consisted of four sets of pairs of stimuli and responses, that is, the video stimulation and left choice, the video stimulation and right choice, the black screen and left choice, and the black screen and right choice. This operation extracted the fluctuation components of single-neuron activity that are independent of the trial types. Correlation of these fluctuations was defined as r_{t_single.} The average value of r_{t_single} was small (∼0.01) but larger than 0 even when the distance between neurons was more than 2 mm (Figure 5A). Notably, a small number of pairs had a large positive correlation irrespective of distance (Figure 5B). In fact, kurtosis (0 in the normal distribution) of correlation after Fisher’s z-transformation was a very large value of 3.77 (p < 10^-6). Thus, we focused on neuron pairs with r_{t_single} > 0.3 (shaded areas in Figure 5B) that were very rare in shuffled pairs in the following analysis to capture the dominant correlation structures.

In which regions are neurons tightly functionally coupled to neurons in AM and A? When mapping the “coupling” neurons in surrounding areas possessing r_{t_single} values > 0.3 with randomly chosen “seed” AM or A neurons, consistent spatial patterns emerged (“coupling neurons”, Figure S6A). The coupling neurons were often localized in specific cortical regions. The localized region of the coupling neurons was S1t in most cases when the seed neurons were in A, while the region was variable when the seed neurons were in AM (Figure 5C). To quantify this property, we used the normalized spatial distribution of coupling neurons for each individual seed neuron of A or AM (Figure 5D). Then we clustered these vectors using K-means (k=6) clustering and displayed the six mean vectors (“preference vectors”) for each cluster. The result showed that interaction with most clusters from seed area A was largely dominated by S1t, while each cluster in AM preferred a specific area such as V1, RSC, A, and S1t (Figure 5E). These relationships were observed in both vision and history tasks. Thus, AM had multiple interaction channels with surrounding areas, while A interacted with S1t, regardless of tasks. We quantified the similarities of preference vectors by averaging the angles between all pairs of the two vectors, which we referred to as “coupling diversity”. We confirmed that the difference in the coupling diversity between A and AM was statistically significant by repeating K-means clustering with randomly chosen neurons in A or AM (Figure 5F; materials and methods).

Is there a relationship between the interarea interaction and functional types in the task? We termed the area where the largest number of coupling neurons are located the “preferred area” and examined the relationship between the preferred area and task relevance. We found that both A and AM neurons with S1t in their preferred areas were significantly more likely to be choice and history neurons. Neurons in area A with visual areas (RL, V1, PM, or RSC) in their preferred areas were significantly more likely to be vision neurons (Figure 5G). Moreover, AM neurons preferring A had significant task relevance for all vision, choice, and history. Thus, A and AM neurons determined their functional types by interarea coupling at least in part.

Next, to investigate r_t of the population activity (r_{t_population}), we first reduced the dimension of population activity in each area into 10 by using PCA (principal component analysis) (Figure S6B,C). Then, “fluctuation activity” was again calculated for each dimension by trial type similar to the single neuron case above, this time representing noise in population activation patterns. We applied CCA (canonical correlation analysis) to each pair of areas and obtained an average of top 10 canonical correlation (CC_t) as r_{t_population} The CC_t structure between areas was similar across task types (Figure 5H) indicating that this structure reflects the underlying functional connectivity independent of the task. The CC_t between A and S1t was the largest among all the pairs (Figure 5H), whereas when the CC_t was averaged across all connections for each area, A and AM had the largest and second largest CC_t, respectively (Figure 5I). The dominance in CC_t in A and AM disappeared when the neurons with r_t,single >0.3 were removed. Notably, the CC_t of AM and the other areas was uniform regardless of the paired areas across all 10 dimensions (Figure 5J). Thus, area AM is an integration hub of interareal communication, whereas A simply coupled with S1t, and such correlation structure at the population level critically depends on this subset of neurons.

Next, we asked whether distinct network level interaction of A and AM can be seen in the neuropil activity level observed in the same two-photon calcium imaging data. We examined the correlation of trial-to-trial “fluctuations” in neuropil activity (r_{t_neuropil}). The fluctuation of the neuropil activity was often localized in a specific area or a set of areas (Figure 6A). Consistently, K-means clustering revealed that the cluster boundaries of the neuropil activity approximately corresponded to the area boundaries (Figure 6B). r_{t_neuropil} was similar regardless of the task types (Figure 6C), so we combined these data for the following analysis. The neuropil activity in AM well correlated with PM, RSC, V1, RL, and A, whereas that of A highly correlated with S1t (Figure 6D). The neuropil activity is known to reflect the local average of input in the imaged location ⁵⁰. Indeed, the trial-to-trial variation of a neuropil activity could be approximated by the average of 1,000 - 10,000 neurons within several hundred micrometers from the center (Figure S7). These data indicate that the correlation structures of average activity of neurons differs between A and AM.

Next, we utilized Allen connectivity atlas where the mesoscale connectivity between cortical and subcortical areas are comprehensively described. We used results of the anterograde tracer experiments where the adeno associated virus that delivers the fluorescent protein was injected in cortex or thalamus (Figure 6E). We found that among cortico-cortical interactions only S1t clearly projected to A more than AM, whereas visual cortices (V1, AL, PM) and frontal cortices (orbitofrontal cortex, dorsal and ventral anterior cingulate cortex) preferentially projected to AM rather than to A (Figure S8A). These data are consistent with our results that A represented sensorimotor parameters together with the S1t, and that AM is an interaction hub which was revealed by the mesoscale correlation analysis.

How does information about anatomical connections relate to functional activity correlations at mesoscale? In general, the activity correlation between two neurons is influenced by the common input ⁵¹. In the case of inter-area correlations, we hypothesized that the more common input two areas receive, the higher the activity correlation between the two areas. To address this question, we used the Allen connectivity data to quantify the degree of anatomical input similarity between any two regions as a correlation (r_anatomy, materials and methods; Figure 6E-G). Interarea correlation between the anatomical input correlation and the neuropil correlation was surprisingly high (r = 0.94, Figure 6H,I).This correspondence suggests that the mesoscale interarea correlation is determined by the cortico-cortical common input at mesoscale. The high correlation was more evident when both the cortico-cortical and thalamo-cortical projection data were combined (Fig 6J). Thus, r_{t_neuropil}, which reflects correlation of the average activity of neurons is strictly determined by r_anatomy.

Does this explain the difference in correlation structure between A and AM? The seed analysis reveals that A and AM have distinct patterns of anatomical input (Figure 6K) and the patterns highly resembled the neuropil correlations seen earlier (Figure6D). This surprising similarity between anatomical and functional seed correlation was the case regardless of the seed areas (Figure S8B). Taken together, these data suggest that the distinction of interarea communication in A and AM is led by the cortico-cortical and thalamo-cortical inputs.

Can the anatomical input correlation predict the correlation between population activities? The correlation between CC_t and r_anatomy was moderate (r = 0.60, Figure 6L). This moderate correlation did not change when the coupling neurons were eliminated (r = 0.61). Interestingly, the largest canonical component was the most unpredictable from the anatomical data (Figure 6M). Thus, the canonical correlation analysis adds important information about population dynamics of neurons that is unpredictable by our analysis on the anatomical input correlation.

The correlation between cortical areas can be affected by globally shared activity reflecting brain states or neuromodulator levels. To evaluate the contribution of global activity on the canonical correlation between areas, we first compared the canonical coefficient vectors (CCV). We found that the first CCV had a similar orientation, regardless of the paired areas (Figure6N). This indicates that the largest components of correlated activity in the CCA analysis are globally shared fluctuation. We also directly evaluated the correlated activity components across all 8 areas with generalized canonical correlation analysis. The first CCV also had a similar orientation to the first generalized canonical coefficient vector (GCCV) (Figure 6O). These results indicate that the 1st canonical component reflects a global correlation across all cortical areas imaged. Such global correlation may be caused by factors other than corticocortical or thalamocortical inputs. We also confirmed the robustness of these results by repeating analyses using only the 40% highly active neurons after denoising with non-negative deconvolution (36828 out of 91397 neurons; Figure S9).

All procedures conducted at the University of North Carolina at Chapel Hill were reviewed and approved by the Institutional Animal Care and Use Committee (IACUC) of the University of North Carolina at Chapel Hill, which ensures compliance with the standards of the American Association for Laboratory Animal Science (AALAS). All procedures conducted in the University of California, Santa Barbara were carried out in accordance with the guidelines and regulations of the US Department of Health and Human Services and approved by the Institutional Animal Care and Use Committee at the University of California, Santa Barbara. Mice were imaged at the age of 8-40 weeks. Adult C57BL/6J mice (Jackson labs) or GCaMP6s ⁴⁷ expressing transgenic adult mice of both sex were used in this study. GCaMP6s expressing were induced by the triple crossing of TITL-GCaMP6s line (Allen Institute Ai94), Emx1-Cre line (Jackson Labs #005628) and ROSA:LNL:tTA line (Jackson Labs #011008) ⁶⁸. Intrinsic signal of equal numbers of males and females C57BL/6J mice were imaged for the P60 and P100 groups (6 mice per time point, 3 of each sex for each time point) when the variability of the visual areas was examined.

On the day of imaging, anesthesia was induced with 5% isoflurane. After initial anesthesia induction, 2.5 mg/kg chlorprothixene was administered via intraperitoneal injection. Isoflurane was reduced and maintained between 1-2.5% during surgery. Ophthalmic ointment (Lacri-lube, Allergan) was applied to both eyes and a heating-pad maintained body temperature. The scalp was then resected, exposing the skull over visual cortex. To register functional maps of visual cortical areas to stereotaxic landmarks, three reference points were labeled with a marker near primary visual cortex (0.8 mm anterior to lambdoid suture, 2.3 mm lateral to the midline). Using digital calipers, three separate measurements were taken from the center of each dot to the midline (mediolateral coordinates) and from the center of each dot to the lambdoid suture (rostrocaudal coordinates). For each reference point, the three measurements were averaged. We used the lambdoid suture instead of bregma as a landmark since the position of the bregma is less reliable to define the coordinates of the brain ^69–71. Although it lacks accuracy, one may be able to use the approximate distance between the lambdoid structure and bregma (∼4.0 mm) to convert the coordinates from lambda-based to bregma-based one.

A head-plate was affixed to the skull. A 3.5-4 mm craniotomy was performed over the visual areas when needed. The glass window with a 3 mm diameter was put onto the cortex, and a tissue adhesive was used to seal the space between the glass and the skull. Then, the mouse was transferred to the intrinsic signal optical imaging (ISOI) system. The ophthalmic ointment was removed from the contralateral eye prior to imaging by manually blinking the eye gently. Isoflurane was maintained between 1-1.5% during imaging. The camera was focused on the skull to acquire an image of the dots relative to the head-plate and major vessels visible through the skull. The camera was then adjusted for ISOI imaging and an initial retinotopy set was acquired through the skull ⁴¹. After imaging experiments, the mouse was removed from the ISOI rig and given a second dose of 2.5 mg/kg chlorprothixene. The ophthalmic ointment was reapplied to the contralateral eye.

The brain was illuminated with 700 nm light and imaged with a tandem lens macroscope focused 600 μm into the brain from the vasculature. Images were acquired with a 12-bit CCD camera (Dalsa 1M30), frame grabber and custom software (David Ferster, with in-house modifications by Jeffrey Stirman & R. H.) at 30 frames per second. Visual stimuli were presented to the left eye relative to the imaged hemisphere using a Dell LCD monitor (Dell U2711b, 2560 × 1440 pixels, 60 Hz) sitting 20 cm from the mouse. The monitor was tilted towards the mouse 17.5° from vertical to cover the visual field (110° by 75°). All stimuli were generated and presented using MATLAB and Psychtoolbox (http://psychtoolbox.org/) ^72,73. All stimuli were modified to correct for visual distortions caused by the flatness of the monitor. Retinotopy was initially mapped by showing the animal a single, square-wave white bar drifting across a black background to identify right V1 and right HVAs (horizontally for azimuth and vertically for elevation). This stimulus was presented for 30 – 50 eight-second-long cycles.

For somatosensory stimuli, the vibration of the membrane of a standard computer speaker was used. The speaker was controlled with the same LabVIEW software. One side of a plastic pipette was attached to the membrane with tape, and the other side of the pipette was attached to a body part (tail, trunk, neck, left ear, left whisker pad, left forelimb and left hindlimb) gently with a tape. As a result, the vibration of the speaker membrane was transferred to the body. Fifty Hz pure tone which gives a 50 Hz sinusoidal movement of the membrane for 0.8 sec vibrated the skin of the targeted body part every 8 seconds. Both cutaneous and proprioceptive responses would be obtained by these stimuli. The speaker sound of 50 Hz tone is far outside the mouse hearing range ⁷⁴, and we confirmed that the stimulation did not evoke activity in the auditory areas with ISOI mapping. The room light was turned off when a pinna or a whisker pad was stimulated to prevent the pipette from being seen since the vibrating pipette was just in front of the left eye. The pipette was outside the visual field from the mouse eyes when the tail, trunk, neck, left forelimb and left hind limb were stimulated.

The images with 12-bit pixel data were binned in software four times temporally and 2 × 2 spatially, resulting in images with 16-bit pixel data. From these binned images, Fourier analysis of each pixel’s time course was used to extract the magnitude and phase of signal modulation at the stimulus frequency for mapping of visually evoked areas. The phase of signal modulation was used to generate maps of the phase of the cortical response, mapping retinotopy of the visual cortex. To identify the areas activated by somatosensory stimuli, the mean intensity of each pixel for 2,000 ms after the stimulus onset was subtracted from the mean intensity of the pixel for 1,000 ms before the stimulus onset across all stimulus trials. The negative value of the pixel implies evoked activity in the pixel. The image with evoked activity was filtered with a Gaussian filter with a standard deviation of 10 pixels, and the pixel with the minimal value was identified as a peak location (downward signal is observed in the activated area). The median value of all pixel was set to the baseline. The mean value of the minimal value and baseline was set the threshold, and the pixels with less than the threshold were regarded as the evoked area.

Retinotopic maps were drawn (ImageJ/Fiji) ^75–77 based on the first set of imaging data (obtained through the skull) and then modified as needed with the second set (obtained without the skull) to ensure that boundaries between cortical visual areas were accurately identified. These maps were drawn based on color reversals ²⁰ and other landmarks present in the retinotopy data. For example, when identifying AL, we look for three stereotyped color reversals to identify the border between AL and LM/LI, AL and V1, and AL and RL. We also used the magnitude maps from these stimuli to ensure that the anterior boundary between AL and non-visual areas is accurately restricted to the area that is visually responsive.

The stereotaxic reference coordinates were first plotted, and the registered to the cortical area location by aligning the plotted coordinates with the reference image (image of the stereotaxic reference coordinates marked on the skull). The reference image was then scaled such that 1 mm in the reference image was the equivalent of 1 mm in the coordinate plot. The reference image was then rotated and moved in X-Y (rigid transform) so that the plotted stereotaxic reference coordinates were in agreement with the marks in the reference image. Using the plotted stereotaxic reference markers, the same image transformations were applied to the retinotopically identified ROIs, producing a set of ROIs registered relative to stereotaxic reference coordinates. This was done for each mouse in the data set. The center of mass for each ROI was computed, and this was then converted to millimeters by measuring the number of pixels in 1 mm and dividing the center location by the conversion factor.

Previous studies on the demarcation of HVAs based on anatomical tracers have shown that the HVAs comprised AL, RL, A, AM, PM, LM, LI and posterior areas ²⁰. With functional mapping with ISOI, we and other laboratories have identified comparable areas with the definition based on anatomical tracing, but the definition of area A and RL has been inconsistent between studies. In this paper, we simply followed our previous studies ^38,39,78 on the definition of HVAs (AL, RL, AM, PM, LM, and LI) for HVA mapping (Figure S1) with ISOI.

In the analysis with two-photon imaging, since we found that area A largely lacked retinotopy, we redefined the areas as follows. By data from two-photon calcium imaging (tactile stimuli and visual stimuli), first, the V1, AM, S1t, and S1barrel were determined by retinotopic and somatotopic organizations. When the cortical neurons activated by visual and tactile stimuli were overlaid, we found an area where the evoked activity was almost absent in the medial space of the FOV. The area was determined as RSC. Then, the triangle behind AM between RSC and V1 was determined as PM. Then, the rectangular space between the S1 barrel and V1, and between S1t and AM was determined as RL and A, respectively. We found a borderline between S1t and S1 barrel, a borderline between V1 and AM, and a borderline between V1 and PM lined up in the straight line. We used the line for the border between RL and A. These definitions are largely consistent with the previous anatomical definitions of the Allen Mouse Brain Common Coordinate Framework (CCFv3) ⁷⁹. We did not discriminate the RSPagl and RSPd in this study since we did not find any functional landmarks. When we analyzed the differences or interactions between areas, we selected the neurons in each area excluding the neurons in a 50 μm-wide transition zone, to avoid contamination.

Mice were anesthetized with isoflurane (1.5 – 1.8%) and acepromazine (1.5 – 1.8 mg/kg body weight) when performing a craniotomy over the posterior parietal cortex. Carprofen (5 mg/kg body weight) was administered prior to surgery. Mouse body temperature was maintained using physically activated heat packs during surgery. The mouse’s eyes were kept moist with ointment during surgery. The scalp overlying the dorsal cortex was removed, and a custom head-fixing imaging chamber (⁸⁰; Figure S3B) was mounted to the skull with a self-cure dental adhesive system (Super bond, L-Type Radiopaque; Sun Medical) and luting cement (Micron Luting; PD). The surface of the intact skull was subsequently coated with clear acrylic dental resin (Super bond, Polymer clear; Sun Medical) to prevent drying. Mice were then returned to their cages.

After the behavior training and before the two-photon imaging sessions, a second surgery was done with the same anesthetic conditions described above. A 4-mm diameter craniotomy was performed over the posterior parietal cortex (right hemisphere, centered 2.0 mm lateral and 2.50 mm posterior from bregma) and covered with two #1 thickness coverslips with 3.5 mm diameter and one #1 thickness coverslip with 5 mm diameter, glued together with optical adhesive (NOA68, Norland). The edge of the upper coverslip with 5 mm diameter was sealed with luting cement (Micron Luting; PD). Mice were then returned to their cages. The condition of the cortical surface was typically the worst in the first week but recovered after the second week. We did not image the activity of neurons when the cortical surface above the PPC was not clear.

In all tasks, mice were kept in a body-holder with the head fixed to the stage (Figure S3A). A white square in the left or right position at the display was presented when the mouse licked to the left or right. In the visually guided task (vision task or “V” task, Figure 2A-C), mice had to lick left or right based on the visual stimuli presented in the display located at the left visual field of them. When a natural video taken in the cage (Figure S3B) was presented, the mouse had to lick left after a 4-s sampling period to get a drop of water as a reward (1.5 - 2.0 μl) from the left lick port. When a black screen was shown on the display, the mice had to lick right to get the reward from the right lick port. During the sampling period, the lick-ports were withdrawn. Mice learned to not lick during this sampling period (Figure S3E,F). The visual stimuli were also presented during the response period and for 2 s after the response when the response was correct. The visual stimuli stopped when the response was incorrect. During the inter-trial-interval (ITI), a gray screen was presented. In the vision task, the probability that the correct direction was left was #R / (#L + #R), where #L and #R are the total number of correct choices in left and right trials before the trial in the session, respectively. When the mice were rewarded three times in the same direction, the correct direction was switched on the next trial. These procedures were implemented to avoid biased licking in the same direction.

We also designed a choice history-dependent task (history task or “H” task) with the same set up as the vision task. In this task, the mice had to choose the other side of the choice from the previous trial (Figure 3A). Thus, the information of direction of the previous choice had to be stored for 6-10 s from the previous choice to the next choice including ITI (2 – 6 s) and a sampling period (4 s). Since the visual stimuli were randomly presented during the sampling period, the mice had to ignore the visual stimuli.

In some sessions of the choice history-dependent task, the body-holder was moved randomly to prevent the mice from storing information about the previous trials based on the body-angle. In every trial, the body-holder was reset to the center position when the ITI started and then moved to either a left or right angle (± 24 degrees).

For training sessions before the vision task and history task, we trained the mice with the “V+H” task, where the mice could follow either the visual stimuli and history of the choice. In this task, the correct chosen direction was the opposite of the previous choice as in the history task, and the visual stimuli were consistent with the correct direction. In a few other sessions of history tasks, the display was switched off or the body-holder was randomly moved in the dark environment. We conducted but did not analyze the data of two-photon imaging during the V+H task, the history task in the dark, or the history task in the dark with body-holder movements in this study.

We trained the mice with a serial schedule in custom-made training boxes or under the microscope (Figure S3C). After recovery from the surgery of a headplate attachment to the skull, we started water restriction (1 ml / day) until the weight was 85 – 90% of the original weight. Then, we started to train the mice with “pre-training”. At the first day of pre-training, the mice freely got a drop of water from both left and right licking ports with the head-fixed condition for 30 min. During the pre-training after the second session, the temporal pattern of the task (i.e. SP (sampling period), RP (response period) and ITI (inter-trial-interval)) was introduced as the vision task described above except for that the RP was unlimited. In other words, the incorrect licking did not result in the termination of RP so that the mice could try to lick until they lick to the correct direction and get a drop of water (1.5 - 2.0 μl). The visual stimuli were switched at every trial between a natural video and a black screen, and the correct licking directions were left and right, respectively as in the V+H task. The distance between the two licking ports was set relatively small (∼2 – 4 mm) to allow the mice to find both spouts easily and was gradually increased up to ∼5.5 mm (distance depended on the mice). The experimenter assisted the mice to find the licking port when the mice missed it for several minutes by repositioning it and manual delivery of water. Overall, the pre-training was used to make the mice learn to lick both sides of the licking ports, which took 2 – 5 sessions. When the number of reward mice got exceeded 150 per session (< 2 hours), the task was switched to the V+H task. In this task, the temporal pattern of the task was the same as the vision task, but the correct direction of licking was set the opposite side of the previous direction. Therefore, the mice could either follow visual stimulus or the choice history to get the reward. The experimenter assisted the mice to find the licking port by repositioning the spouts and manual delivery of water when the mice lost motivation, especially in several initial sessions. The V+H task was trained to give the baseline condition where we can retrain the V task and H task from the task. After the acquisition of the V+H task, we switched the task to the vision task. The correct rate immediately dropped after switching from V+H task to V task but recovered after that. The transient decrease in the correct rate indicates that the mice used history information during the V+H task. After reaching the criteria, the mice were trained to perform the task under the microscope. After the V task, we retrained mice with V+H task to recover the baseline condition. After that, we switched the task to the H task. We found that the correct rate dropped immediately after switching the task from V+H task to H task and recovered again. This transient drop demonstrates that the mice also used vision information in the V+H task. In the H task, all the mice reached the criteria under the microscope during two-photon imaging (blue dots in Figure S3D). With two mice, we trained the H task with randomly moving body-holder, and both mice reached the criteria during the two-photon imaging (orange dots in Figure S3D). Throughout the training, mice kept their weight more than 85 % of the original weight and were monitored their health conditions every day for about 4 months.

Two-photon imaging was carried out using a custom Diesel2p microscope controlled by costom LabVIEW software (National instruments). The two-photon excitation laser from an 80-MHz Newport Spectra-Physics Mai Tai DeepSee was scanned by a resonant scanner (CRS 8 KHz, Cambridge Technologies) and two Galvo scanners (62010H, Cambridge Technologies). The photon signal was collected by a PMT (H7422P-40, Hamamatsu) and amplified with a variable high speed current amplifier (#59-179, Edmund Optics). Two-photon imaging of 3 × 3 mm² was collected at 5.6 Hz for imaging. Since the maximum scan angle of the resonant scanner is limited, we made two rectangles with 1.5 × 3 mm² to cover 3 × 3 mm² FOV (Figure S2A,B). With these parameters, a neuron with a 10 μm diameter circle was supposed to have 29 pixels inside the ROI (region of interest), including more than 100 laser pulses on average, which was sufficient to find the single neuron activities (Figure S2C,D). Imaging was performed with <120 mW excitation 910 nm laser out of the front of the custom-made objective lens (0.55 NA). Mice were head-fixed at about 15 cm from a flat monitor, with their left eye facing the display during imaging. An 80° × 45° the left visual field was covered with the display. During imaging, we monitored a diameter and position of the left pupil, movements of whiskers, both forelimbs, a mouth and a tail with four custom-controlled CMOS cameras at 30 fps. Licking to the left or right licking port was also monitored with an electrical circuit ⁸¹. The timing signals for the resonant scanner were used for synchronization of all the other devices and the data. The imaging depth below the dura was between 80 μm and 180 μm (layer 2/3). To ensure the scanning planes were parallel between different sessions, we tilted the stage of the body holder manually before the imaging sessions to make the imaging plane horizontal to the surface of the brain.

Visual stimulation for retinotopic mapping was displayed on a 60 Hz 7” LCD monitor (9.5 x 15 cm²). A white vertical or horizontal bar was drifted from temporal to nasal or top to bottom at a cycle of 8 s. The tactile simulation for mapping of the somatotopic organization was made with a gentle and brief air-puff (20 – 50 ms) to a specified part of the body at a cycle of 4 or 8 s. Both visual and tactile stimuli were repeated at least 20 cycles. When the mouse started to actively move during the stimuli, the imaging was stopped and the data were discarded.

Image analysis was performed using ImageJ (National Institutes of Health) and MATLAB (MathWorks, Natick, MA, USA) software. Image sequences were corrected for focal plane displacement, and region of interest (ROIs) within somata were automatically determined using suite2p (Figure S2E) ⁸². The fluorescence traces and shape of ROIs were inspected visually. Elongated ROIs, which were more likely to be dendrites or axons, were excluded if the ratio of the length of the major axis to the length of the minor axis was greater than 3. To eliminate the effect of background activity, we made a square-shaped mask whose pixels were within 50 μm from the edge of the ROI, excluding pixels less than 5 pixels from the edge of the ROI and pixels within the other ROIs. Then, we subtracted the mean value of this area from the mean value of the ROI. The obtained value was referred to as “activity” of the neuron. Those neurons showing activity with skewness of > 0.3 ⁸⁰ were regarded as “active neurons” and used for analysis. We also obtained active neurons with kurtosis > 5 as and defined them as “highly active neurons”. Non-negative deconvolution was conducted with foopsi⁸³. The values after non-negative deconvolution were thresholded with median + 1.5 × 1.4826 × mad and was shown as the inferred spike.

To analyze neuropil activity, the pixels within each ROI identified with suite2p were filled with each background activity described above. After that, the size of the image was reduced to 120 × 120 pixel², where the size of a single pixel is 25 × 25 μm².

We recorded video data (160 x 120 pixel², 30 fps, ∼ 1 hour / session) from three IR cameras (Basler SCA640-70GM, GIGE, Lens: Basler C125-1218-5M, 12 mm) placed in front of the mouse, at the rear of the mouse, and in front of the left eye during task performance. We analyzed these data with DeepLabCut ⁸⁴ (https://github.com/AlexEMG/DeepLabCut) for tracking the left and right forepaws, the tail and the pupil. We labeled each body part in randomly extracted 100 frames from each video and trained a model for each video data for each session using the 100 labeled data. About 20,000 iterations were performed in training the model. Google Colaboratory was utilized for the training of the model using GPU. We further analyzed the positions of the body parts in frame with estimated relative likelihood was greater than 0.9. The horizontal and vertical position was directly extracted from the result of the tracking, and then we obtained the direction (angle) of the left and right forepaws and the tail from the body center (Figure 4A). The pupil size was calculated by identifying two edges of the left pupil (Figure 4A). We visually inspected the quality of the results and confirmed that all the tracking results were as precise as human vision.

To map the neurons encoding visual, choice and history-related information, we used a simple linear encoding model (Figure 2g). We confirmed that the range of maximum VIF (variance inflation factor) for parameters for visual, choice, and history was 1.7 - 3.5 (mean: 2.5) in the vision task, 1.5 - 3.1 (mean: 2.0) in the history task, and 2.1 - 4.1 (mean: 2.9) in the history task with holder rotation. In total, the range was 1.5 - 4.1 (mean: 2.4), which indicates that simple linear regression is sufficient to estimate the correlation between these parameters and single neuron activity without a serious problem of collinearity. The activity of each neuron was fitted by a set of predictor variables for each session. The 29 - 32 predictors consisted of the timing of the visual stimuli (556 ms each, 11 bins, video (+1) or dark (−1)), chosen directions (left (+1) or right (−1)), choice histories (3.7 - 7.4 s after left (+1) or right (−1) choice), reward directions (2 s after rewarded, left (+1) or right (−1)), rotation of the body holder (left (+1) or right (−1)), and an inter-trial interval. Non-selective parameters were also added for each parameter, to avoid identifying neurons activated by both types of stimuli, choice, history, reward or holder rotation as task-related neurons. For example, the non-selective parameter was +1 on the time of choice regardless of the choice directions. The Bonferroni-corrected p-values for the visual stimuli, choice, choice history, and holder rotation parameters in the encoding model were used to identify the vision, choice, choice history, and holder-related neurons, respectively. P-values (p<0.001) for each parameter of the regression model were used to determine the significance. The t-values in the regression model were used to map the strength and position of each task-related neuron. To map the ratio of task-related neurons, we counted the number of active neurons and the number of task-related neurons within 150 μm of each pixel and divided the latter by the former to calculate the ratio. The association index was determined by the harmonic mean of the rates of vision neurons and choice neurons.

We also mapped the posture/movement parameters by estimating the posture/movement-related neurons with a regression analysis. As some of the VIFs for the predictors including task parameters and posture/movement parameters were very high (typically 300 or more), we used a linear model with L2 parameter penalization (a ridge regression). The predictors consisted of position, speed, and velocity of the left forepaw, the right forepaw, and the tail along the x-y plane and the angle (Figure S5), pupil size, speed and velocity of pupil size change, and task parameters described above (total 59 parameters). The neuronal activity and predictors were z-scored. We determined the lambda value for each neuron (range: 10^-4 ‒ 10⁴) and avoided overfitting with five-fold cross-validation. To estimate the contribution of parameters for the left forelimb, the right forelimb, the tail, and the pupil, we repeated the same analysis with a reduced model where each set of predictors was eliminated from the full model (Figure 4B). Then, the pseudo-R² was obtained for each set of predictors by (MSE_reduced ‒ MSE_full) / MSE_null, where MSE is the mean squared error, MSE_reduced is MSE for the reduced model, MSE_full is the MSE of the full model, and MSE_null is the null model. For example, we constructed a regression model without the parameters regarding the left forelimb (green shade of Figure 4B), obtained MSE_reduced for the left forelimb, and the pseudo-R² was calculated as above by comparing the MSE of the full model and the null model.

The direction of the choice was decoded by the population activity of neurons with a logistic regression model (Matlab built-in function, “glmfit” with binomial distribution and logit link function). For each time bin, the model was trained to predict the chosen direction using the activity of neurons in the time bin except for the trial. Then, the choice in the trial was predicted by the activity of neurons in the trial (leave-one-out). The outcome (reward or punishment) and visual stimulation (video or blank) were similarly decoded by the activity of neurons. The number of trials was matched to the smaller number of the right and left selections in order to align the number of selections between the left and right selections. For example, if the left selection had 150 trials and the right selection had 200 trials, all trials from the left selection were used and 150 trials from the right selection were randomly selected. To avoid bias due to the selection of trials, we repeated the random selection 20 times and averaged the 20 decoding results to determine the accuracy of the decoding. By this manipulation, decoding accuracy is 50% when the neuron has no information at all.

The time after the initiation of the videos (Figure 2L), or the time after the left or right choice (Figure 3F,N) was independently decoded by using a support vector machine (Matlab built-in function, fitcsvm) and the activity of neurons. For decoding the time after the video starts, each imaging frame (185 ms) during the sampling period was used as a label for classification of the time. For decoding the time after the choice, 9.5 seconds after the choice were divided into 17 parts (each part being 555 ms) and each part was used as a label for the classification. We trained multiple support vector machines, each of which classifies whether a given set of neural activities belongs to the ith interval or not (i = 1, 2, …, the total number of parts). A ten-fold cross-validation procedure was used to avoid over-fitting.

To confirm whether the encoding model explains the diversity of single neuron activity, we visualized each set of the task-related neurons with t-SNE. We averaged single neuron activity over trials for each of four trial types: video + left choice, video + right choice, blank + left choice, and blank + right choice. Then, we defined a vector for each neuron by combining the four averaged activities. The Matlab function “tsne” was applied to this set of vectors.

jPCA is a dimensional reduction method for visualizing neural dynamics developed by Mark Churchland (https://churchland.zuckermaninstitute.columbia.edu/content/code) ⁴⁹. It is useful for visualizing not only rotational dynamics but also sequential dynamics because it approximates the direction of change in the population vector over time that is orthogonal to the current activity (M_skew). To apply jPCA analysis, the activity of neurons in the area of interest was smoothed with a Gaussian filter with σ=0.9 s and z-scored. After reducing the dimensionality to 6 using standard PCA, the activity from 1 s before to 5 s after the choice was concatenated on all trials. jPCA was applied and a linear transformation of the jPCA in the first plane was used to show the neural trajectories. To compare the neural dynamics with behavioral performance, we applied jPCA to 10-minute segments of population activity and compared R² for M_skew with the correct rate in those 10 minutes. R² for M_skew is the coefficient of determination of the regression model for approximating the temporal change of population vector by the current population vector ⁴⁹.

Correlation of trial-to-trial variance of activity between a pair of single neurons was defined as r_{t_single}. To calculate r_{t_single}, we averaged the activity of individual neurons over the sampling period, and the average across each trial type was subtracted from this value. The trial types consisted of four sets of pairs of stimuli and responses, that is, the video stimulation and left choice, the video stimulation and right choice, the black screen and left choice, and the black screen and right choice. By this operation, we extracted the fluctuating components of single-neuron activity that are independent of the trial types. We defined a neuron with 0.3 or more r_{t_single} with a neuron in AM or A as a coupling neuron if the neuron was not in the same area. We counted the number of coupling neurons in each area and considered the number as a vector. We normalized this vector so that the sum was 1 (ratio vector) only when the total number was 5 or more. Then we clustered the ratio vectors using K-means (k=6) clustering and defined the mean vector of each cluster as a “preference vector”. We confirmed that repeated K-means clustering with different initial values resulted in that more than 80% of the neuron pairs being classified into the same cluster. We averaged the angles between all pairs of the preference vectors, and referred to this as “coupling diversity”. For comparison of coupling diversity of AM and A, we randomly extracted half of the ratio vectors from AM and A, conducted K-means clustering, and obtained the coupling diversity 1,000 times to know the distribution of the coupling diversities. We defined area X as the “preferred area” of a neuron in A and AM if the neuron had one or more coupling neurons in the area X. We then compared the proportion of task-related neurons (i.e., vision, choice or history neurons) between the neurons whose preferred area includes area X and the other neurons by a chi-square test.

To calculate the trial-to-trial fluctuations in neuropil activity (r_{t_neuropil}), we averaged the neuropil images over sampling period, and the average image across each trial type was subtracted from this image. The trial types consisted of four sets of pairs of stimuli and responses, that is, the video stimulation and left choice, the video stimulation and right choice, the black screen and left choice, and the black screen and right choice. By this operation, we extracted the fluctuating components of neuropil activity that are independent of the trial types.

CCA was used to compare neural population activities in two areas. As a preprocessing step, the data from an area was reduced to N_PCA (=10) dimensions using PCA (principal component analysis). This ensured that CCA did not find dimensions of high correlation but low data variance ⁸⁵. To estimate the area-to-area correlation in the task-independent variables, the CCA was calculated in task-independent spaces, which is practically the same as noise correlation, as follows (Figure S6B,C).

The value of each principal component was averaged over a 4-s sampling period in each trial. Then, we obtained the fluctuation component of the value by subtracting the mean of each four trial-types. Here four trial-types were defined by a combination of visual stimuli and choices: natural video and left choice, natural video, and right choice, black screen and left choice, and black screen and right choice. We call these fluctuating dimensions task-independent space. The fluctuation was concatenated into one column vector per a principal component (N_PCA by N_trial matrix, N_trial is a total number of four trial types). CCA between any pair of the cortical areas was obtained in these task-independent spaces. The N_CCA (=10) CCA values were averaged and the value was referred to as CC_t,X,Y, where X and Y are a cortical areas.

We also used CCA to estimate the amount of shared information between an area and the other areas (Figure 6L, M; Figure S6D, E). Suppose we have time series of the N_PCA variables (principal components) in the task-independent spaces, X and Y_a, from an area X and another area Y_a, respectively, where X_i and Y_a,_i (i=1,2,3,… N_PCA) are column vectors, whose length is equal to the number of trials (N_trial). To calculate N_CCA canonical correlation values, linear transformation of X and Y_a with weight matrices (canonical coefficient vectors, CCVs) A_a and B_a give canonical scores, S_a and T_a, respectively as follows: where both A_a and B_a are N_PCA by N_CCA matrices with N_CCA CCVs (column vectors) of length N_PCA. The n-th CCV transforms the time series of principal components, X and Y_a, to n-th canonical score. As a result, S_a and T_a are the matrixes with N_CCA by N_trial. This transformation was done so that the correlations between the canonical scores are maximized (with the built-in function “canoncorr” in Matlab).

We have seven time series of the N_PCA variables (principal components) in the task-independent spaces, Y₁, Y₃, …, Y₇, from areas Y₁, Y₃, …, Y₇. Then, we can get sets of CCVs, A₂, A₃, …, A₇ and B₁, B₃, …, B₇ and sets of the canonical scores, S₁, S₃, …, S₇ and T₁, T₃, …, T₇. Here, the CCVs of A₁, A₂, …, A₇ defined in the 10-dimensional data space of area X correspond to the linear projections of activity of neurons in the area X that best explain the activities of neurons in each of the other areas (7 areas in total). If area X shares similar information with another seven areas, CCVs, A₁, A₂, …, A₇ will be oriented in a similar direction and therefore the length of the sum of the CCVs will be larger. Accordingly, we defined the “information sharing index” (Figure S6D) of area X as the length of the sum of CCVs as max , where s_i can be 1 or -1, A_i,d is a d-th column vector (CCV) of i-th area, and || denotes the norm.

We also used generalized CCA (GCCA)⁸⁶, which extends the notion of CCA to >2 data sets. We estimated similarity between the first generalized CCV and CCVs for each area by inner product of these vectors. We defined the average of these inner products as “global information sharing index” (Figure S6E).

We used the Allen Mouse Brain Connectivity Atlas (http://connectivity.brain-map.org ³³) to investigate the pattern of the corticocortical and thalamocortical projections around the mouse PPC. In this database, connectivity data are available for mice from injection areas (AAV1-EGFP as an anterograde tracer) to any brain region. For estimating the relative projection density between A and AM, the corticocortical projection density was obtained in each layer at 0, 100, 200, 300, 400, 500, 600, 700 μm from pia, averaged and normalized with the injection volume, then averaged across wild-type mice. This was repeated with the major source areas to the A and AM (V1, PM, AL, vRSC, S1t, OFC, dACC, and vACC; Figure S8A). For seed correlation analysis, we downloaded the data whose injection sites were either isocortex (929 experiments) or thalamus (189 experiments) at 100 μm resolution (Figure 6E). We set a 100 μm-space grid that covered entire dorsal cortical areas including the PPC. Then, a set of injection sites that projected to each grid at the 300 μm from the surface of the brain were identified for each grid (Figure 6F). Thus, each grid has a set of the injection sites where the grid receives its projection from either isocortex or thalamus. Using these binary connectivity matrices, we calculated the correlation coefficient between two sets of injection sites of the two grids. Based on this correlation matrices, we got a map of the correlation coefficient for each grid (seed) (Figure S8B).

Let a binary data matrix P (N_pix × N_inj) be a set of results of the tracer experiments, where N_pix and N_inj is the number of pixel (cortical surface) and the number of injection experiments, respectively (Figure 6G). Let Q (N_pix × N_inj) be a set of the injected volume (area), ad let W (N_pix × N_pix) be a pixel-to-pixel connection matrix. By definition, Here, we need a correlation matrix, WW^T. However, there are no direct data for W or Q. Therefore, we estimated it by P as follows If the injection volume is small and random enough, QQ^T → Id as the number of experiments gets large. If so, we can approximate WW^T by PP^T. In reality, QQ^T should work as a spatial filter of WW^T. As the injection volume would be <500 μm on average, the seed correlation map should capture the structure with a resolution of several hundred micrometers, which would be sufficient for our analysis. This resolution could be improved with decreasing injection volume, or kernel regression ⁸⁷.

To effectively visualize these maps, we developed a software that users can explore cortical surface point (seeds) to see the cortical areas that shared either the corticocortical input, thalamocortical input or both types of input (Figure S8C, https://web.ece.ucsb.edu/~riichirohira/TopBM-2.05/index.html).

Wilcoxon’s rank-sum test and chi-squared test were used for pairwise comparison. For multiple comparison, we used one-way ANOVA and showed confidence intervals (p=0.05) in the figures. No statistical tests were performed to predetermine sample size. No blinding or randomization was performed.