Multiple types of navigational information are independently encoded in the population activities of the dentate gyrus neurons

Significance In this study, we found that multiple types of information (position, speed, and motion direction in an open field and current and future location in a T-maze) are independently encoded in the overlapping, but different, populations of dentate gyrus (DG) neurons. This computational nature of the independent distribution of information in neural circuits is newly found not only in the DG, but also in other hippocampal regions.


Figure S4. Position decoding error in the open field.
Cumulative distribution functions (CDFs) of the position decoding error. The results from all the mice (black; 7 wild-type mice, red; 5 αCaMKII +/mice) are shown. Mean absolute errors (MAE, same as in Figure 2d) of each mouse are also shown in each figure. Note that all of the decoding errors of wild-type mice were smaller than those of αCaMKII +/mice.  Confusion matrices for speed decoding results for all wild-type and αCaMKII +/mice. The xaxis represents the actual mouse speed, and the y-axis represents the estimated mouse speed.
Each column corresponds to the estimated probability distribution over speed for a given true speed (0.1 cm/sec bins). The correlation coefficient (R) between the observed and decoded speeds (same as in Figure 2e) is shown in each mouse.

Wild-type mouse1
Wild-type mouse4 Wild-type mouse7 αCaMKII +/-mouse3 Wild-type mouse5 Wild-type mouse2 Wild-type mouse3 Wild-type mouse6   spatial information from larger ones to smaller ones (solid red line in the right panel), the position decoding error increases faster than when cells are removed randomly (black line).
When neurons are removed from the dataset in the sequence of spatial information from smaller to larger ones (dotted red line), the decoding error increases more slowly than when neurons are removed randomly. (ii) Information is diffusely distributed in the neuron population (e.g.,  suggesting that the distribution of position information is independent of that of speed information. RoCDE(Direction/Speed) is around 0.5 (0.425 ± 0.10), which indicates moderate dependency between direction and speed information. This is probably because speed-off cells tend to be unable to show fine-tuning for motion direction due to their low activity during motion, resulting in their mutually exclusive nature.  e, Color-coded PVO matrices and their mean PVO in the Immobile period (0-1 cm/sec) and Walking / Running period (> 1 cm/sec) is shown for a representative mouse from the wild-type and αCaMKII +/groups.
f, Box plot showing the mean PVO of wild-type and αCaMKII +/mice in the Immobile and Walking / Running period. In the Immobile period, there was no significant difference in the mean PVO of wild-type and αCaMKII +/mice (P = 0.711). On the other hand, the mean PVO of αCaMKII +/mice was significantly larger than wild-type mice (P = 0.0158).  S11c) and LR decoding accuracy in the forced arm period (Fig. 4g). There is a significant negative correlation (R = -0.835). The position decoding performance of αCaMKII +/mice was less precise (MAE = 15.5-17 cm) than that of wild-type but LR decoding accuracy in the forced-arm period (average 65%) is significantly higher than the chance level (50%). Thus, even though the position decoding of x-y coordinates is not so precise (as in Fig. 2d and SI Appendix, Fig. S11c), the decoding performance of the current LR location can be better than the chance level. This may be because the defined area of the current LR location is much larger than the resolution of position decoding of x-y coordinates. c, PVO of the LR-tuning patterns of neurons between the forced arm and decision period. An individual black or red dot corresponds to an individual wild-type or αCaMKII +/mice, respectively. The PVOs of wild-type mice were significantly higher than those of αCaMKII +/mice, but were relatively small (0.00 -0.38).
d, Decoding accuracies on correct-or-error of choices in the forced alternation task. There were no significant differences in the decoding accuracies between Obs. and Shuff. either in wildtype or in αCaMKII +/mice, indicating that correct or error cannot be decoded from activities in dDG neurons. Note that the decoding accuracy of Shuff. of wild-type mice is about 70% because the decoding accuracy expected by chance in correct-or-error is about 70%, due to the correct-error ratio of wild-type mouse is 71.4% (Fig. 4b).  color-coded bins), as well as for shuffled data ("Perm.", dark gray) and scrambled data ("Scram.", white), for a representative wild-type mouse. We repeated random permutation and random scrambling 1000 times each to generate shuffled data, and there was no significant difference between their distributions. c, Decoding accuracy of position, speed, and motion direction by different shuffling methods.
Random permutations and random scrambles were repeated 10 times each to generate shuffled data from a representative wild-type mouse. Decoding analysis was performed on these shuffled data, in which the accuracy was compared, and there was no significant difference between them. Summary of information about the statistics used in the paper.

Supplementary Results
Position and speed information is encoded in the dDG by a different coding principle (SI Fig. S9).

Appendix,
We found the selective impairments of information (position in open field and future location in T-maze) in αCaMKII +/mice (Fig. 2). There are two hypotheses on why a specific type of information is impaired in the DG of these mice.  Fig. S9b).
Thus, the increased position decoding error in αCaMKII +/mice relative to that in wild-type mice (P = 1.12 × 10 -3 , Fig. 2d) might be attributable to the larger mean PVO (P = 0.0208, SI Appendix, Fig. S9b), corresponding to less distinct firing patterns of neural ensembles across different subareas. Next, we investigated how encoding of speed information is associated with overall firing frequency of dDG neurons. We found positive and linear correlations between the speed of the mice and the average Ca 2+ transient rate in the dDG (SI Appendix, Fig. S9c).
We also found a significant correlation between speed decoding accuracy and the change in the average Ca 2+ transient rate with speed (SI Appendix, Fig. S9d), neither of which were significantly different between wild-type and αCaMKII +/mice ( Fig. 2e and SI Appendix, Fig.   S 9d). Thus, information about position and speed might be encoded with different coding principles in the dDG, and only the coding principle for position may be affected in the dDG of αCaMKII +/mice. In addition, we noted that the Ca 2+ transient rate is increased with the increasing moving speed of mice (SI Appendix, Fig. S9c). We then divided all data into the Immobile period (0-1 cm/sec) and Walking / Running period (> 1 cm/sec) and measured the mean PVO of position in an open field (as in SI Appendix, Fig. S9a) in each period. In Immobile periods, the mean PVO of αCaMKII +/mice was not significantly different from those of wildtype (SI Appendix, Fig. S9e and S9f). On the other hand, in the Walking / Running periods, the mean PVO of αCaMKII +/mice was significantly higher than that of wild-type mice (SI Appendix, Fig. S9e and S9f). These results suggest that, in αCaMKII +/mice, the population coding of position information is disorganized when the mice are running and the Ca 2+ transient rate is high but not when the mice are immobile.
Previous studies have reported that increased neuronal excitability 5 and epileptiform activity 6,7 are observed in the DG and CA1 of αCaMKII knockout mice. It is also reported that hippocampal pyramidal neurons of mice with a point mutation in the αCaMKII show a deficit in LTP and stability of place cell 8,9 . Despite such increased excitability of neurons and the brain, in our data, the overall Ca 2+ transient rate of dDG neurons in αCaMKII +/mice was not significantly different from that of wild-type mice (SI Appendix, Fig. S9c). This may be because of the "synaptic homeostasis" that stabilizes the neuronal excitability and the neural firing rate, which was reported to be shared by multiple strains of autism spectrum disorder model mice 10 .
It is also reported that these mice exhibit alternations in neural circuits that lead to abnormally high synchrony of network activity 11 and deficit in sensory information processing 12 . The authors discussed that imperfect homeostasis largely normalized firing rate but maladaptively compromised some aspects of the population coding, like firing synchrony and sensory tuning, in these mice 10 . It is tempting to speculate that, in αCaMKII +/mice, that have dramatically reduced synaptic molecules (such as GluR1, GluR2 and PSD95), synaptic homeostasis could have increased neuronal excitability to stabilize overall firing rate but compromised the coordinated network activity of neurons and population coding of position information. On the other hand, speed information in the dDG of αCaMKII +/mice was not disturbed, possibly because it depends on changes in the overall neural firing frequency, which may not affected by compromised coordinated network activity. Thus, the dDG may utilize different coding principles for encoding different types of information, which supports the notion that individual neurons can independently participate in encoding different types of information. Appendix, Fig. S12).

Neural representation of past and future states in T-maze by populations of dDG neurons (SI
We investigated the relationship between the neural representations of the current location in the forced arm period and those of the future state in the decision period. There are at least two possibilities for these relationships (SI Appendix, Fig. S12a). One is that the representations of information about left and right in the decision and forced arm period are similar to each other, and neural activity in the decision period preplays the predicted future experience in the next forced arm period ((i) in SI Appendix, Fig. S12a). Another is that the representation of future LR information in the decision period is different from those in the forced arm period ((ii) in SI Appendix, Fig. S12a).
In Fig. 5a, we noted a small but significant correlation between the LR indices of the  Fig. S12b). The PVOs of wild-type mice were significantly higher than those of αCaMKII +/mice, but were relatively small (0.00 -0.38, SI Appendix, Fig. S12c). Overall LR-tuning patterns in the forced arm and decision period were slightly but significantly similar to each other. These results suggest that a small number of neurons might be involved in 'preplay'-like activity during the decision period ((i) in SI Appendix, Fig. S12a), while the majority of neurons may not.
Next, we investigated the associations between the importance of neurons in the population coding during the forced arm and decision period. In Fig. 5c, removing neurons that are important for LR decoding in the forced arm period did not have a significant impact on those in the decision period and vice versa. This result indicates that the neuron populations used for the decoding of left and right in the forced arm and decision period are not similar to each other but rather independent. Therefore, the major representation of future LR information in the decision period that was used for decoding is not likely to be 'preplay'-like activities of future experience similar to that in the forced arm period ((i) in SI Appendix, Fig. S12a) but rather predictive representations of the future state that are independent of the representations during the force arm period ((ii) in SI Appendix, Fig. S12a).
The traditional view of place coding in the hippocampal circuit is that the place cells encode the current location of the animal. It has also been known that neural activity patterns in CA1 13,14 , CA3 14,15 , and medial EC 16 are involved in the prospective representation of future states. In our analysis, we were able to decode whether the mice were on the left or right side of the T-maze by the population activity patterns of dDG neurons either after or before a left or right turn. These results suggest that the population activity patterns of dDG neurons not only encode the current location but also may be involved in the predictive representation of future states alongside other hippocampal regions. These two states are represented in the dDG in a partially similar but largely independent manner. Appendix, Fig. S15).

Velocity filtering for position and direction decoding (SI
The activation of hippocampal place cells during immobile periods, which occurs in conjunction with hippocampal sharp wave ripples (SWRs), is known not to represent the current position of animals 17,18 . Therefore, in analyses of position information in the hippocampus, periods of immobility are generally excluded from the data. We did not know whether immobile periods should also be excluded for data obtained from the dDG, as it is not known whether neural activity equivalent to SWRs can be observed in the Ca 2+ imaging in this region. Therefore, to test the validity of this procedure, we examined whether removing periods of immobility would improve the accuracy of position decoding in the dDG (SI Appendix, Fig.   S15, left panel). We removed the time bins in which the movement speed of the mouse was below the threshold (from 0.0 cm/sec to 3.0 cm/sec) and performed position decoding using the remaining data. In wild-type mice, removing time bins in which the speed was below 1.0-1.25 cm/sec reduced the position decoding error (SI Appendix, Fig. S15, left panel). These results suggest that neural activity during periods of immobility that do not represent current location may also be observed in the Ca 2+ imaging data of the dDG. Based on these results, all periods in which the mouse's speed was below 1 cm/sec were eliminated from the analysis of position information. (This threshold is roughly equivalent to those commonly used in hippocampal CA cells (1.0-2.0 cm/sec) 19 ).
The motion direction of the mouse was estimated from the changes in the mouse position in the open field. Even small movements such as grooming, rearing or head turning were calculated as actual mouse movements. To exclude these periods and more accurately measure motion direction, we examined the speed threshold below which movements could be removed from the datasets (SI Appendix, Fig. S15, right panel). We removed all the time bins in which the speed of the mouse was below the threshold (from 0.0 cm/sec to 10.0 cm/sec) and performed direction decoding using the remaining data. In wild-type mice, the decoding error for motion direction decreased after applying a threshold of 4.0-8.0 cm/sec to remove movement periods, suggesting that small movement periods below these thresholds were useless for accurate direction decoding (SI Appendix, Fig. S15, right panel). Based on these results, all periods when the mouse ran slower than 4.0 cm/sec were removed from our datasets for the analysis of motion direction.

On the possibility that information about motion direction is decoded from place-coding cells.
There might be a possibility that motion direction was decoded from the activities of the neurons that encode spatial information, not from those encoding information about motion direction. If the decoding of motion direction was achieved by an activities of neurons encoding spatial information through an association between position and motion direction, deleting neurons in the order of spatial information (red line in Fig.3c right panel) would increase decoding errors faster than that of random order deletion (black line). However, in Fig. 3 and Fig. S8, deleting neurons in the order of spatial information (red line) did not affect the accuracy of direction decoding faster than random order deletion (black line) did.
These results indicate that neurons with relatively larger spatial tuning were not preferentially used for motion direction decoding. Therefore, the decoding accuracy of motion direction is not likely to be achieved by an activity of the neurons encoding position information.
Also, our results of decoding analysis of αCaMKII +/mice supported the idea that our decoding of position and motion direction are independent. In αCaMKII +/mice, position information was selectively impaired, but direction information was not significantly different from wild-type mice ( Fig.2d and 2f). This result also suggests that successful decoding of direction information is not achieved by an association between position and direction.

Estimation of the active population of DG neurons.
Estimation

Behavioral experiments.
Before every behavioral experiment, the OF or T-maze apparatus was cleaned using weakly acidified hypochlorous water (super hypochlorous water; Shimizu Laboratory Supplies, Kyoto, Japan) to prevent bias due to olfactory cues. All behavioral experiments were carried out in a sound-proof room, and the behavior of the mice was monitored through a computer screen located outside the room to minimize artefactual cues due to the presence of the experimenter.
Mouse behavior was recorded at a 3 Hz sampling rate. For the OF and T-maze, different groups of mice were used (OF, 7 wild-type mice and 5 αCaMKII +/mice; T-maze, 7 wild-type mice and 4 αCaMKII +/mice).

Open field test
More than a week after baseplate attachment, mice were habituated to the test environment.
Each mouse was lightly anaesthetized, and a dummy camera (Inscopix, CA) was mounted on the mouse. At least 30 min after recovery from anesthesia, mice were placed for 2 hr in the OF arena (40 cm × 40 cm × 30 cm; width, depth, and height, respectively; O'Hara, Japan), made of opaque white plastic. The OF apparatus was evenly illuminated with 100 lux white LED light installed above the apparatus. This habituation session was repeated for three days. One day after the final habituation session, OF experiment was performed. Prior to the experiment, the mice were weakly anaesthetized with isoflurane, and an nVista miniature microscope was mounted onto the head stage. The mice were then habituated in the testing room for at least 30 min after recovery from the anaesthesia. Following the habituation in the testing room, each mouse was placed in the OF arena, and neuronal activity was recorded for 30 min. In order to obtain the location time sequence of each mouse, the images of the mouse were automatically processed by an ImageJ plugin (Image OF, freely available on the Mouse Phenotype Database website: http://www.mouse-phenotype.org/software.html).

T-maze test
The T-maze test was conducted using an automatic T-maze apparatus (O'Hara, Japan) as previously described 20  pixel grid. The position of the mouse is determined from the centroid of its shadow on the camera. We then assigned a label corresponding to the discrete location of the mouse (e.g., [10, 100]) to each time bin (=1/3 sec).
(ii) Speed: From the distance travelled between 1 sec before and after a given time point, we calculated the speed of the mouse at that moment and assigned this speed (cm/sec) to each time bin.
(iii) Motion direction: The visual tracking system that we used does not allow direct measurement of head direction. Instead, we indirectly estimated the direction of motion from the changes in the position of the mouse. The motion direction (in radians) was computed from the direction of change in two subsequent mouse positions (1 sec before and after a given time point) in the x-y plane and assigned this to each time bin. North was defined as 0 radians; west was defined from 0 to π radians, and east was defined from 0 to -π radians.

Statistical analysis of spatial, speed, and direction information.
To quantify the tuning specificities of neurons with position, speed, and motion direction, we measured their specificity in terms of the information rate of cell activity. We defined them as (i) spatial, (ii) speed, and (iii) direction information 21 . The Ca 2+ event rate in Ca 2+ imaging is considerably lower than in electrophysiological recordings (on average, approximately 30 Ca 2+ transients per 30 min session). If the discretization of position, speed, and motion direction is too fine for the number of events in the recorded cells, we will not be able to obtain a proper null distribution when creating the shuffle data for that cell. Therefore, we set the resolution of the discretization of position and speed to be lower than those commonly performed. where i is the bin number corresponding to the physical parameter (in this case, spatial position in the OF; i = 1-4 from the 2×2 square grid), N is the total number of bins, p is the probability that the mouse occupied bin i, ri is the mean transient rate at bin i, and r is the overall mean transient rate.
(ii) To measure speed information, we applied the same formula to the speed after discretizing it to a binary state: Run (for speeds >1 cm/sec) and Stop (for speeds <1 cm/sec).
(iii) Similarly, we measured direction information by applying the same formula to the motion direction after discretizing the full angle to 8 bins of 45 degrees each.

LR indices of neurons in the T-maze test.
To quantify the left-or right-preference of each neuron's activity for the current and future location in the T-maze, we generated a parameter called the LR index. For each neuron, we measured the average Ca 2+ transient rates during the forced arm and decision periods for the left-and right-choice trials-that is, when the mouse is in the left or right arm of the T-maze, respectively-and computed the LR index as follows: where RL is the average Ca 2+ transient rate across all left-choice trials, and RR is from the rightchoice trials. All neurons are assigned an LR index in both the forced arm and decision periods.
A positive value indicates a neuron's preference for the left arm, whereas a negative value indicates a neuron's preference for the right arm.

Data Shuffling.
To assess the statistical significance of information coding of individual neurons, we computed chance distributions of the shuffled data using two common methods previously described in the literature 19,3,22 .
Random permutation permutates calcium events (SI Appendix, Fig. S14). We divided the calcium event data into 1000 segments along the time axis and randomly sorted them to generate permutated data of calcium events. This method destroys temporal structures of neural activity and temporal correlations between neural activity and behavioral variables (e.g., position, speed, and motion direction in open field test); however, the overall neural activity is maintained across cells. We repeated this procedure 1000 times to obtain the distribution of 1000 shuffled data. For single-cell statistics, we compared the original information of individual cells with the null distributions of 1000 values of shuffled data generated from the original cell (SI Appendix, Fig. S2). If the original value of information of a cell exceeded 3 sigmas from the shuffled distribution, the cells were defined as carrying significant amounts of information. For group comparison (for example, Obs. vs Shuff. in Fig. 1d, 4c, and 4d), we pooled all the shuffled data in a group together, and distributions of the original cells were compared with null distributions of the shuffled data.
Random scrambling is a method that maintains temporal dynamics of neural activity data while disrupting the relationship with behavioral patterns (for example, the calcium event timeseries and the animal's position (SI Appendix, Fig. S14)). We shift the whole vector of the calcium event time series in time by a random amount in a torus; that is, points beyond the data's time limits were reinsert from the other side. This procedure disrupts the relationship between neural activity and animal behavior, but preserves the temporal patterns of these variables. By repeating this procedure while changing the number of frames to be shifted at random, we obtain the null distributions of shuffled data (SI Appendix, Fig. S14). Information statistics are performed in the same way as the first shuffling method.
Since we found that the information statistics and decoding results of the shuffled data did not differ significantly between these shuffling strategies (SI Appendix, Fig. S14), we adopted the random permutation method for the generation of shuffled data.

Decoding position, speed, and motion direction in the open field.
To determine how the OF behavioral parameters are encoded in the DG, we trained decoders with machine learning methods to separately predict position, speed, and motion direction from the population Ca 2+ activity. We assigned the labels of the discretized behavioral parameters of the mouse (position (cm), speed (cm/sec), and motion direction (-π -+π radians)) and the binary values of the Ca 2+ signal (0 or 1) of all neurons to each time bin. We then divided the reported as the correlation between the predicted and actual instantaneous speed. This is because speed, unlike position and motion direction, is not limited to a certain range, and the mean absolute error of speed may depend on the average locomotion speed of each individual mouse, which would be inappropriate for the evaluation of decoding error. To assess the statistical significance of the decoding accuracies, the decoding error from the observed data was compared with that of the shuffled data, which is created by dividing the Ca 2+ imaging data into 1,000 segments and sorting them randomly (see also SI Appendix, Fig. S14).
Furthermore, we compared the decoding accuracies of the three behavioral parameters among the 8 decoders and found that they were not significantly different (SI Appendix, Fig. S3).
Consequently, we reported the decoding results obtained with the LSTM Network, which showed slightly better decoding performance in wild-type mice than others. For decoding position and motion direction, we identified and removed time bins when the mouse moved at speeds below 1.0 cm/sec and 4.0 cm/sec, respectively, to obtain optimal decoding results.
Details on the methods used in thresholding the data according to the movement speeds of the mice are described in the SI Appendix, Supplementary Results "Velocity filtering for position and direction decoding" and SI Appendix, Fig. S15.

Decoding current and future location in the T-maze test.
We similarly sought to decode the left or right preferences for the current and future locations in the T-Maze test using the population Ca 2+ activity with machine learning methods. The decoders used for current and future LR locations are independently trained using neural activities during the forced arm and decision period, respectively. For each trial of the forced arm and decision periods, we assigned a label corresponding to the left or right choice of the mouse and the average Ca 2+ transient rate of each neuron during the period. We then used a support vector machine (SVM) classifier function in MATLAB for binary classification of the left or right decision (MathWorks, MA). All 50 trials from each mouse were used for 25-fold cross-validation; the 50 trials were randomly divided into 48 trials of training data and 2 trials of test data. We repeatedly trained the binary classifier using randomly selected training data and performed left or right predictions for the remaining test data to evaluate the decoding accuracy. We also shuffled the Ca 2+ transient data and performed the same decoding analysis.
As with the open field behavioral parameters, the decoding accuracy was compared between the shuffled and unshuffled data.

Population vector overlap (PVO).
To quantify the similarities in population activity patterns of neurons between different locations in the DG, we calculated the population vector overlap (PVO) 24 . The PVO for a population of N neurons in two different conditions (x, y) was defined as where i is the neuron number; λj(x) and λj(y) are the average Ca 2+ transient rates of neuron j in conditions x and y, respectively; and N is the total number of neurons. For a given population of neurons and a pair of conditions, a lower PVO indicates that the activity patterns of the neurons are distinct between the two conditions.

The ratio of cumulative decoding errors (RoCDE).
RoCDE between speed/direction information and position information and those between position/direction information and speed information are defined as blow: AUCSpatial, AUCSpeed, AUCDirection, and AUCRandom designate the area under the curve (AUC) of the deletion in spatial, speed, direction, and random information order, respectively.
AUCRevSpatial is that in the reverse order of spatial information order. The degree of difference of the distribution between an information type (e.g., speed information or direction information) and position information is evaluated by how the deletion order (e.g., blue or