A Distributed Neural Code in the Dentate Gyrus and in CA1.

Resource Availability

Lead contact Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Stefano Fusi ( sf2237@columbia.edu ).

Materials Availability

This study did not generate new unique reagents.

Data and Code Availability

The datasets and analysis code supporting the current study are available from the lead contact on request.

Experimental Model and Subject Details Mice

All procedures were conducted in accordance with the U.S. NIH Guide for the Care and Use of Laboratory Animals and the institutional Animal Care and Use Committees at New York State Psychiatric Institute and UCSF. Adult male C57BL/6J mice were supplied by Jackson Laboratory and were used beginning at 8–12 weeks of age. Mice were co-housed with litter mates (2–5 per cage). Mice were maintained with unrestricted access to food and water on a 12-hour light/dark cycle.

Viral Constructs

For calcium imaging, AAVdj-CaMKII-GCaMP6m was packaged and supplied by Stanford Vector Core at titers of ~ 4 X 10 12 vg/ml, and AAV1-Syn-GCaMP6f.WPRE.SV40 was packaged and supplied by U Penn Vector Core at titers of ~ 2 X 10 12 vg/ml. Method Details Calcium imaging. Mice were prepared for in vivo calcium imaging as previously described ( Resendez et al., 2016 ). For dorsal DG imaging, mice were injected with a virus encoding GCaMP6m (AAVdj-CaMKII-GCaMP6m) at the following coordinates: −1.95AP, 1.4ML, 2.2, 2.1, 2.0, 1.9 DV, ~ 90 nl per site) and a ~ 1.0 mm diameter, ~ 4 mm long GRIN lens (Inscopix, Palo Alto, CA) was implanted at (−2.0AP, −1.4ML, −1.95 DV). For dorsal CA1 imaging, mice were injected with a virus encoding GCaMP6f (AAV1-Syn-GCaMP6f.WPRE.SV40) at the following coordinates: (-2.15AP, 1.85ML, −1.55, −1.65DV, 256nl per site) and a GRIN lens was implanted at (-2.15AP, 1.30ML, −1.30DV). Three weeks after surgery, mice were checked for GCaMP expression with a miniaturized microscope (Inscopix, Palo Alto, CA) with procedures previously described ( Resendez et al., 2016 ). Anesthetized mice were checked for GCaMP+ neurons and a baseplate was attached to the skull at the optimal imaging plane. For all the mice presented in this report the histology confirmed the adequate placement of the lens ( Fig. S22 ). For dorsal DG imaging, one week later, mice were imaged during foraging in an open field task and were habituated to the room and enclosure (30min), then 24 hours later they were imaged as they foraged for sucrose pellets in an open field enclosure (50cm 2 ). For dorsal CA1 imaging, mice were imaged during exploration of an open field enclosure. Mice were habituated to the room and enclosure (10 minutes) and then imaged 30 minutes later. Imaging frames were recorded with nVista acquisition software (Inscopix, Palo Alto, CA), and time-synced behaviour was acquired using EthoVision XT 10. Calcium imaging videos were acquired at 15 frames per second with 66.56 ms exposure.

Quantification and Statistical Analysis

Behaviour data pre-processing. The behaviour was recorded using a webcam (Logitech) mounted on the ceiling about 3 feet above the arena. The instantaneous position of the animal was then extrapolated from the video using custom code written in Python using the Scikit-image library (version 0.13.0). We first applied a 9 points piecewise affine transformation to correct for barrel camera distortions. We then applied a smoothing filter with a Gaussian profile to reduce the effect of pixel intensity noise due to low lighting and low image resolution and applied a threshold to the gray-scale converted image to get a few contiguous regions of pixels as candidate animal tracking. We then used a method based on the determinant of the Hessian to identify blobs in the pre-processed images and verified that the largest blob was consistently found to be corresponding to the animal silhouette. Hence, we used the centre of the largest blob as the tracked position of the mouse. We further temporally aligned the position data to the imaging data using linear interpolation and smoothed them with a 7 frames time window. Lastly, we identified the time bins in which the speed of the animal was lower than 2 cm/s for more than 1 s and discarded them from the analysis, unless specified. Signal extraction and spike deconvolution. All calcium movies were initially processed in Mosaic (Inscopix, Palo Alto, CA) for spatial binning and motion correction and subsequently analysed using a recently developed software algorithm written in Matlab (Mathworks) called CNMF-e ( Zhou et al., 2018 ). Briefly, the algorithm separates the large, low-frequency fluctuating background components from the signal produced by of multiple sources in the data, allowing the accurate source extraction of cellular signals. It involves a constrained non-negative matrix factorization problem optimized for endoscopic data whereby calcium temporal dynamics and the shape of spatial footprints are used as constraints. It includes 3 main steps which are iterated: obtain a first estimate of spatial and temporal components of single neurons without direct estimation of the background; estimate the background given the estimated neurons’ spatio-temporal activity; update the spatial and temporal components of all neurons while fixing the estimated background fluctuations. In each of these steps, manual intervention guided by visual inspection based on temporal profile and spatial footprint shape allowed to further improve the quality of the signal extraction. The result of this process consists of a list of deconvolved calcium events for each cell with associated time-stamp and magnitude and the convolved trace with a calcium decay profile estimated for each cell independently on the basis of the raw trace. For our decoding analysis, we did not use the original traces, rather we used the events extracted with CNMF-e convolved with an exponential kernel. The time constant of the kernel was optimized to maximize the cross-validated position decoding performance and was equal for all neurons. The results depend only weakly on the kernel time constant, and qualitatively are the same (see Fig. S1 ). All other quantities derived from the calcium traces were computed using the calcium events, unless specified otherwise, and therefore their values do not depend on the shape of the kernel. Place fields and heading direction tuning. Place fields for each extracted source were constructed in a manner similar to established method applied to electrophysiology data ( Leutgeb et al., 2007 ). We used the calcium events of each cell as its putative spiking activity. We then summed the total number of events that occurred in a given location, divided by the amount of time the animal spent in the location and smoothed using a Gaussian kernel centered on each bin. The rate in each location × was estimated as r ( x ) = ∑ i = 1 n g ( s i − x h ) ∫ 0 T g ( y ( t ) − x h ) d t where g is a Gaussian smoothing kernel, h = 5 sets the spatial scale for smoothing, n is the number of events, s i is the location of the i -th event, y ( t ) the location of the animal at time t and [0, T ) the period of the recording. In this and all subsequent analysis we removed the time bins in which the animal had a speed of less than 2 cm/s for more than 1 s, unless specified otherwise. Similarly, for heading direction tuning, we first discretized the directions of motion into 8 angular bins of 45 degrees each and then computed the mean event rate for each cell in each of the 8 bins. Spatial information statistics. To quantify the statistical significance of the rate maps we measured their specificity in terms of the information content of cell activity ( Skaggs et al., 1993 ; Danielson et al., 2017 ; Allegra et al., 2019 ). We used a 16×16 square grid and computed the amount of Shannon information that a single event conveys about the animal’s location. The spatial information content of cell discharge was calculated as a mutual information score between event occurrence per cell and animal position or equivalently using the formula: S I = ∑ i = 1 N p i r i r log 2 r i r where i is the spatial bin number, p is the probability for occupancy of bin i , r i is the mean event rate at bin i and r is the overall mean event rate. We applied the same formula to the direction of motion after discretizing the full angle to 8 bins of 45 degrees. For both measures, we corrected for the sampling bias problem in information measures ( Panzeri et al., 2007 ) using shuffled distributions of event occurrences as follows. For each cell independently, we discretized time, generating a long vector of 0’s (no event) and 1’s (event). We then randomly permuted the elements of this vector and for each permutation we computed the resulting spatial information. We repeated this procedure 1000 times, therefore obtaining 1000 values of spatial information to which we compared the original information content ( Ziv et al., 2013 ; Danielson et al., 2017 ; Meshulam et al., 2017 ; Allegra et al., 2019 ). We labeled a cell as place cells or a heading direction cell if the original value of spatial information exceeded 3 sigmas from the shuffled distribution (see also S2 and S3 and Table S1 ). Decoding position. For all the datasets, unless otherwise specified, we used 10-fold cross validation to validate the performance of the decoders. We divided the trial in 10 temporally contiguous periods of equal size in terms of number of datapoints after excluding datapoints corresponding to immobility. We then trained the decoders using the data from 9 of them and tested on the remaining data. To decode the position of the animal, we first divided the arena into 8×8 equally sized, squared locations. We then assigned at each time bin the label of the discrete location in which the animal was found. For each pair of locations, we trained a Support Vector Machine (SVM) classifier ( Cortes and Vapnik, 1995 ) with a linear kernel to classify the cell activities into either one of the two assigned locations using all the identified cells, unless specified otherwise. We used only the data corresponding to the two assigned locations and to correct for unbalanced data due to inhomogeneous exploration of the arena we balanced the classes with weights inversely proportional to the class frequencies ( Pedregosa et al., 2012 ). The output of the classifiers was then combined to identify the location with the largest number of votes as the most likely location ( Bishop, 2006 ). For each choice of train and test set, we computed the median decoding error as the median of the physical distance between the centre of the decoded discrete location and the actual position of the mouse in each time bin of the test set, unless otherwise specified. The final decoding performance was then computed as the mean of all the median errors across the different choices of train and test sets. Chance level decoding performance To assess the statistical significance of our decoders, we computed chance distributions of decoding errors from shuffled data. This can be done in different ways and we chose a conservative procedure that maintained some structure of the data while destroying the relation between the behavior, e.g., the animal’s position, and the calcium event time series. Briefly, we discretized time obtaining a vector of positions (or other behavioral variables). We then flipped this vector in time (e.g., the last data point of position became the first datapoint and vice versa) an then shifted the whole vector in time by a random amount in a torus, i.e., points that went beyond the time limits of the data were reinserted from the other side. This procedure destroys the relation between behavior and neural activity, but preserves the time correlations of both the time series representing behavior and, of course, the time series of the neural activity (which remains untouched). For each random shift, we trained a new decoder on the data and pooled all the errors obtained. We finally assessed the statistical significance of the decoding error for the 10-fold cross-validation of the original data by comparing it to the distribution of errors obtained from the manipulated data using the non-parametric Mann-Whitney U test, from which we obtained a p-value of significance. We implicitly assumed that the 10 folds are statistically independent (the 10 testing time intervals considered for the 10 folds did not have any overlap). This is the procedure we used in all our figures unless specified otherwise. Another less conservative shuffling strategy is to manipulate the calcium events. We assigned a random time bin to each calcium event for each cell independently while maintaining the overall density of calcium events across all cells, i.e., by choosing only time bins in which there were calcium events in the original data and keeping the same number and magnitude of the events in each time bin. This method destroys spatial information as well as temporal correlations but keeps the overall activity across cells. We verified that our results did not depend on the particular strategy adopted (see Fig. S3 and Table S1 ). Decoding the direction of motion. One behaviourally relevant quantity that was available to us was the direction of motion of the animal. Unfortunately, the visual tracking didn’t allow for a direct estimate of the direction of motion. The head direction was also not easily measurable so we resorted to using the positional information to extract the direction of motion. We computed it by using two subsequent datapoints in the animal x-y trajectory. We discretized the values into 8 angles and then applied similar decoding strategies as for position decoding, i.e., we used a battery of linear-kernel SVM decoders to distinguish between pairs of angles after balancing the dataset through class weighting. We report the median error in radiant on the left-out data of the 10-fold cross validation. We applied the methods described above for position decoding for assessing the statistical significance of the results. Decoding speed. To decode the speed of movement of the animal we first computed the speed of motion using two consecutive positions and assigned the computed speed to the later time bin among the two. To decode the instantaneous speed of motion we used Lasso ( Tibshirani, 1996 ), a linear regression analysis method that minimizes the sum of squared errors while selecting a subset of the input cells to improve decoding accuracy and interpretability of the results. We applied the methods described above for position decoding for assessing the statistical significance of the results. 0.0.0.15. Bayesian decoder. The Bayesian decoder is a theoretical optimal probabilistic method to decode information for the activity of the neural population. It is based on the Bayes rule and has been extensively used to decode position from electrophysiological data from the hippocampus ( Zhang et al., 1998 ; Wilson and McNaughton, 1993 ). Briefly, if x is a discrete position in the arena, we estimate the position using: P ( x | r i ) = P ( r t | x ) P ( x ) / P ( r t ) where r t is the activity of the population at time t and assuming independent activity of different neurons. The algorithm computes P ( x | r t ) for all discrete positions and assigns the predicted position to the one that maximises it: x ^ t = arg max x P ( x | r t ) . Importance index. The importance index was introduced to quantify the contribution of each cell in a population to the decoding of a given quantity. We applied a modified version of a traditional method for feature selection in machine learning. In our analysis, a feature of the input space consists of one DG cell. Feature selection is performed using the weights of the decoder after fitting model to the data. In our case, since we employed multiple decoders, one for each pair of physical location in the arena, we introduced a method to combine the weights assigned to the cells by each decoder. We defined the importance index of cell i as: ω i = ∑ k | w i k | ∑ j | w j k | where w ik is the weight of the k -th decoder assigned to the i -th cell (and equivalently w jk is the weight of the k -th decoder assigned to the j -th cell). The indices i , j run through all cells in the population and k runs through all the binary decoders. Procedure to destroy correlations. To destroy correlations without impacting the spatial information of single neurons, we considered multiple passes through single discrete locations in the arena. We then shuffled the calcium event occurrences between different passes in the same location. Importantly, we corrected the activity of each pass for the different amount of time spent in each pass by radomly sampling events instead of replacing them in order to reduce artifacts. We verified that the correction does not impact decoding when sampling from the same pass (see Fig. S14 ).

Software

The data analysis has been performed using custom code written in Python (version 2.7.12) and routines from the Scipy (ver. 0.19.0), Numpy (ver. 1.11.3) and the Scikit-learn (0.19.1) ( Pedregosa et al., 2012 ) packages. The source extraction has been performed using Matlab (Mathworks, R2016a) and CNMF-e ( Zhou et al., 2018 ) using the same parameters across animals and minimal manual intervention only for obvious non-cell like sources based on spatial profile shape and temporal profile dynamics.

Materials Availability

This study did not generate new unique reagents.

Experimental Model and Subject Details Mice

All procedures were conducted in accordance with the U.S. NIH Guide for the Care and Use of Laboratory Animals and the institutional Animal Care and Use Committees at New York State Psychiatric Institute and UCSF. Adult male C57BL/6J mice were supplied by Jackson Laboratory and were used beginning at 8–12 weeks of age. Mice were co-housed with litter mates (2–5 per cage). Mice were maintained with unrestricted access to food and water on a 12-hour light/dark cycle.

Viral Constructs

For calcium imaging, AAVdj-CaMKII-GCaMP6m was packaged and supplied by Stanford Vector Core at titers of ~ 4 X 10 12 vg/ml, and AAV1-Syn-GCaMP6f.WPRE.SV40 was packaged and supplied by U Penn Vector Core at titers of ~ 2 X 10 12 vg/ml.

Method Details Calcium imaging. Mice were prepared for in vivo calcium imaging as previously described ( Resendez et al., 2016 ). For dorsal DG imaging, mice were injected with a virus encoding GCaMP6m (AAVdj-CaMKII-GCaMP6m) at the following coordinates: −1.95AP, 1.4ML, 2.2, 2.1, 2.0, 1.9 DV, ~ 90 nl per site) and a ~ 1.0 mm diameter, ~ 4 mm long GRIN lens (Inscopix, Palo Alto, CA) was implanted at (−2.0AP, −1.4ML, −1.95 DV). For dorsal CA1 imaging, mice were injected with a virus encoding GCaMP6f (AAV1-Syn-GCaMP6f.WPRE.SV40) at the following coordinates: (-2.15AP, 1.85ML, −1.55, −1.65DV, 256nl per site) and a GRIN lens was implanted at (-2.15AP, 1.30ML, −1.30DV). Three weeks after surgery, mice were checked for GCaMP expression with a miniaturized microscope (Inscopix, Palo Alto, CA) with procedures previously described ( Resendez et al., 2016 ). Anesthetized mice were checked for GCaMP+ neurons and a baseplate was attached to the skull at the optimal imaging plane. For all the mice presented in this report the histology confirmed the adequate placement of the lens ( Fig. S22 ). For dorsal DG imaging, one week later, mice were imaged during foraging in an open field task and were habituated to the room and enclosure (30min), then 24 hours later they were imaged as they foraged for sucrose pellets in an open field enclosure (50cm 2 ). For dorsal CA1 imaging, mice were imaged during exploration of an open field enclosure. Mice were habituated to the room and enclosure (10 minutes) and then imaged 30 minutes later. Imaging frames were recorded with nVista acquisition software (Inscopix, Palo Alto, CA), and time-synced behaviour was acquired using EthoVision XT 10. Calcium imaging videos were acquired at 15 frames per second with 66.56 ms exposure.

Procedure to destroy correlations. To destroy correlations without impacting the spatial information of single neurons, we considered multiple passes through single discrete locations in the arena. We then shuffled the calcium event occurrences between different passes in the same location. Importantly, we corrected the activity of each pass for the different amount of time spent in each pass by radomly sampling events instead of replacing them in order to reduce artifacts. We verified that the correction does not impact decoding when sampling from the same pass (see Fig. S14 ).

Supplementary Material 1 Supplemental Video 1, related to Fig. 2 : Decoding video for DG representative animal. 2 Supplemental Video 2, related to Fig. 2 : Decoding video for CA1 representative animal. 3 5