Balancing the Robustness and Efficiency of Odor Representations during Learning.

Subjects

All procedures were in accordance with protocols approved by the UCSD Institutional Animal Care and Use Committee and guidelines of the National Institute of Health.

Mice

(Pcdh21-Cre) were originally acquired from RIKEN BRC and backcrossed at least 4 times to C57bl/6. Mice were housed in disposable plastic cages with standard bedding in a room with a reversed light cycle (12h-12h), and all experiments were performed during the dark period.

Surgeries

Adult mice (6 weeks or older, male) were anesthetized with isoflurane and surgeries were performed to implant a headplate and perform craniotomy as described previously ( Kato at al 2012 ). Briefly, a stainless-steel headplate was glued to the skull, followed by the implantation of an optical glass window (1×2 mm oval) above the right olfactory bulb and securement with dental cement. To obtain mitral cell specific expression of GCaMP6f, virus containing a Cre-dependent GCaMP6f-expression construct (AAV2.1 hsyn-FLEX-GCaMP6f, UPenn Vector Core, 1:4 dilution in saline, 20 nl / site, 4 sites) was injected into the olfactory bulb of Pcdh21-cre mice at the depth of 250 μm during craniotomy. Odorant delivery Odorants were first diluted in mineral oil to a calculated vapor pressure of 200 ppm. A custom-built olfactometer mixed saturated odorant vapor 1:1 with filtered, humidified air for a final concentration of 100 ppm. Final air flow rate was controlled at 1 L / min.

Behavior

Mice were water-restricted starting ∼1 week after surgeries and weight was maintained at 80-85 % of initial value. The pre-training phase started 2 weeks after water restriction. The behavioral program was controlled by a real-time system (C. Brody). Each daily training session consisted of 150 trials, and odorants were delivered pseudo-randomly, with no more than 3 successive trials of the same odorant. Each trial included an odorant delivery time of 4 seconds. This was followed by a 2-second answer period where the mouse had the opportunity to respond. If the odorant was the rewarded odorant (S+) and the mouse licked the lickport at least once during the answer period, a water reward is given (∼6-7 μl). Any other action (i.e. not licking to S+ or unrewarded odorant (S-), or licking to S-) did not result in a water reward and the trial would then proceed to the inter-trial interval (ITI). No punishment was delivered for error trials. Licking during the odorant period was ignored. During the pre-training phase, mice were first trained with a single odorant pair, citral (S+) and limonene (S-), with an ITI of 3 seconds. After mice performed above 80% success rate, the ITI was incrementally extended by two seconds every half-session until an ITI of 15 seconds was reached. Once the mice performed at a success rate above 80% for the first odorant pair with an ITI of 15 seconds (∼7-10 days), odorants were changed to a second pair, +-carvone (S+) and cumene (S-). Once mice performed above 80% for the second odorant pair (∼3-4 days) and mitral cells expressed GCaMP6f at levels sufficient for imaging, we began the week-long imaging period, where mitral cell activity was monitored while mice simultaneously performed a discrimination task with a novel odorant pair or experienced the novel odorants passively. For passive odorant experience, the trial structure, including odorant delivery time (4 sec) and ITI (15 sec), was the same as during discrimination training, with the exception that no water reward was given. Licking during passive exposure was rare, decreasing from 6.3 ± 2.5 % and 5.2 ± 1.5 % of trials on Day 1 for easy and difficult odorants, respectively, to 1.9 ± 0.6 % and 1.4 ± 0.6 % of trials on Day 7. The odorants used for the imaging experiments, Heptanal and Ethyl Tiglate, were chosen on the basis of their structural dissimilarity.

Image acquisition

Two-photon imaging was done with a commercial microscope (B-scope, Thorlabs) with 925 nm excitation from a Ti-Sa laser (Spectra-physics) at a framerate of approximately 28 Hz. Each imaging frame was made up of 512 × 512 pixels, spanning 765 × 655 μm. Imaging was performed continuously during segments of about 2.4 minutes long, with inter-segment intervals of 7 seconds. Data from trials which occurred during the intervals were not analyzed. Full-frame cross-correlation correction on imaging frames was performed using a custom program written in MATLAB.

Data Analysis

In a small number of sessions, we were not able to collect imaging data due to error and these sessions were excluded from analysis. These excluded sessions were: Difficult odorant discrimination- Day 6 (1 mouse) and Day 7 (2 mice); Difficult odorants, passive exposure- Day 3 (1 mouse); Easy odorant discrimination- Day 7 (2 mice). Unless otherwise stated, all values are reported as mean ± SEM. Determining ROIs Regions of Interest (ROIs) were manually drawn around mitral cells by using a custom MATLAB program on the average image of the first session. For each ROI, a background ROI was also manually drawn in a nearby area that was unoccupied by other labeled cells or neurites. For each subsequent day, each ROI was manually moved to accommodate small shifts and if any ROI was not visible in any of the imaging days, that ROI was excluded. Pixels values within each ROI were averaged to create fluorescence time series and values from the corresponding background ROI was subtracted. For each trial for each mitral cell, the time series was normalized to the average fluorescence value during the baseline period (5-sec period before odorant onset) to calculate dF/F. The total number of cells and animals imaged for each condition are: 731 cells and 10 mice (Difficult discrimination training); 736 cells and 11 mice (Difficult odors, passive exposure), 467 cells and 8 mice (Easy discrimination training), 479 cells and 8 mice (Easy odors, passive exposure).

Classifying responsive and divergent mitral cells

Responsive and divergent mitral cells were identified in each session using trial traces smoothed with the MATLAB ‘smooth’ function with the time constant of 6 frames (∼0.25 seconds). A mitral cell was classified as divergent if both the following two criteria were met: Criterion 1: dF/F is significantly different (p < 0.05) between odorant-1 and odorant-2 trials in at least 75% of the time points within any 0.5 second window during the odorant period. P-value for each time point was calculated by Wilcoxon rank sum test between dF/F values for odorant 1 and odorant 2 trials. Criterion 2: The difference between trial-averaged dF/F of odorant-1 and odorant-2 trials exceeds 0.225 in at least one time point during the 0.5-sec window that meets the first criterion. A mitral cell was classified as responsive to a given odorant in a given session if one of the following two criteria were met: Criterion 1 : The cell is classified as divergent as above. Criterion 2 : Both of the following criteria are met: dF/F is significantly different (p < 0.05) from baseline in at least 75% of the time points (i.e. image frames) within any 0.5 second window during the odorant period. P-value for each time point was calculated by Wilcoxon rank sum test between dF/F at that time point from all trials of a given odorant and dF/F of all baseline frames from all trials. The difference between trial-averaged and time-averaged baseline dF/F and trial-averaged dF/F of a given time point exceeds 0.20 in at least one time frame during the 0.5-sec window that meets the first criterion. Based on these classification methods, the false discovery rate calculated by comparisons with shuffled data ( Komiyama et al., 2010 ) was 0 % for the criterion 2 of responsive classification (0 / 2,704,800 cell- odorant-session pairs, calculated by shuffling time points within trials) and 0.33 % for divergent classification (420 /1,352,400 cell-session pairs, calculated by shuffling trial labels). Calculating d-prime for divergent neurons On each day, the sensitivity index, or d′ ( Macmillan, N.A., & Creelman, 2005 ), for divergent neurons for each mouse was calculated. First, all trial traces were smoothed with the MATLAB ‘smooth’ function with the time constant of 6 frames (-0.25 seconds). If a cell was divergent on a given day, d′ was calculated for each time frame during the odorant period (0 to 4 seconds after odorant onset). d ' = | mean d F F odorant 1 − mean d F F odorant 2 | pooled standard deviation odorant 1 and 2 Then, each divergent neuron was assigned the maximum d′ value of all frames during the odorant period, and the average of these maximum d′ values of divergent neurons for each mouse on each session was calculated and plotted in Figures 2F and 3F .

Decoder Analysis

For each mouse, decoder analysis was performed on 100 iterations. In each iteration, 16 mitral cells used for the decoder were randomly drawn from a pool of all mitral cells that were classified as responsive in at least one session. The population size of n=16 cells was determined by the mouse with the lowest number of responsive mitral cells. Nearest-centroid decoder For the nearest-centroid classifier ( Kato et al., 2012 ), the mitral cell population response in each trial was expressed as an activity vector, which was a concatenation of the time-averaged dF/F from the first and second 2-sec windows during the 4-sec odorant period of each mitral cell (16 neurons × 2 values per neuron = 32 dimensional vector). For each trial, centroids for odorant-1 and odorant-2 trials were calculated from all trial activity vectors excluding the trial being scored. The decoder assigned the trial in question the identity of the odorant with the closest centroid. For each iteration, the accuracy of the decoder was calculated as the prediction success rate of the decoder for all trials on each day. For each mouse, the daily accuracy was calculated by taking the average of the 100 iterations. We next assessed the contributions of individual variables to decoder accuracy. For each iteration, the distance between odor centroids was assessed by first calculating odor centroids, which are the population vectors created from the mean of all trial activity vectors belonging to each odorant in a session. Then the mean square distance was calculated as the square of the Euclidean distance between odor centroids, divided by the number of neurons in the activity vector. For each mouse, the daily mean square distance was calculated by averaging across 100 iterations. The trial-to-trial variability for each odorant was assessed by calculating the total variance on each day. For each iteration, the total variance for each odorant on each day was calculated by summing the diagonal of the covariance matrix (summing the variance across each dimension of the activity vector). Mean daily total variance for each mouse and odorant was calculated by averaging across 100 iterations. The contributions of interneuronal correlations were assessed by disrupting noise correlations through the shuffling of trial responses independently for each neuron. Decoder accuracy was recalculated using activity vectors reconstructed from these shuffled responses for 100 iterations of shuffling. The change in decoder accuracy after disrupting noise correlation was calculated for each mouse in each session by subtracting the original decoder accuracy (without shuffling) from the decoder accuracy after shuffling. Wilcoxon signed rank test was performed, for each condition, on the dataset of concatenated mouse-day pairs of decoder accuracy values for before and after trial shuffling. To assess how distributed odorant identity information is across mitral cells, the decoder analysis was repeated after removing subsets of 16 neurons. Decoder accuracy was calculated after removing one additional neuron in each iteration in the descending order of their contribution to decoder accuracy (i.e. the drop in decoder accuracy after removal). 100 iterations were performed for each mouse, where different 16-neuron populations were resampled for each iteration. Average scores were calculated for each mouse by averaging across iterations.

Linear discriminant analysis

For the linear discriminant analysis (LDA)-based classifier, the mitral cell population response in each trial used the same trial activity vectors as in the nearest-centroid decoder (see above). The linear classification was performed using the MATLAB function classify . For each day, the classifier went through each trial as the test set, using the other remaining trials as the training set. The accuracy of the decoder was calculated as the prediction success rate of the decoder for all trials on each day. For each mouse, the daily accuracy was calculated by taking the average score of the 100 iterations of randomly selected subsets of 16 cells. The contributions of interneuronal correlations for LDA were assessed in the same way as in nearest-centroid decoder, by the shuffling of trial responses independently for each neuron. The change in decoder accuracy after disrupting noise correlation was calculated for each mouse in each session by subtracting the original decoder accuracy (without shuffling) from the decoder accuracy after 100 iterations of shuffling. Support Vector Machine For the support vector machine (SVM)-based classifier, the mitral cell population response in each trial used the same trial activity vectors as in the nearest-centroid classifier (see above). The classification was performed using the MATLAB's svmtrain function. The classifier went through each single trial as the test set, using the other remaining trials as the training data set. The accuracy of the decoder was calculated as the prediction success rate of the decoder for all trials on each day. For each mouse, the daily accuracy was calculated by taking the average of the 100 iterations of randomly selected subsets of 16 cells. The contributions of interneuronal correlations for SVM were assessed in the same way as in nearest-centroid decoder, with 10 iterations of shuffling.

Principal Component Analysis

For individual mice, principal component analysis was performed on a matrix made by concatenating all trial response vectors (defined as above, using all mitral cells that are classified as responsive in at least one session) from Day 1 and Day 7. For pooling across mice, a matrix of trial response vectors was created for each mouse using the first n trials. A pooled response vector was then created by concatenating across animals. The number of trials n , determined by the session with the lowest number of trials for a single odorant, was 31 for easy discrimination and 29 for difficult discrimination. Calculating Correlation Coefficients To calculate correlation coefficients for each day, a mitral cell population response vector was constructed for each trial by concatenating the time-averaged dF/F from the first and second 2-sec windows during the 4-sec odorant period of each mitral cell. Correlation coefficient between response vectors for each pair of trials was calculated using the MATLAB function corrcoef . Averages of trial pairs from two different odorants and same odorants were used as the inter-odorant and intra-odorant correlation coefficient for each mouse, respectively.

Supplementary Material supplement