Neural ensemble dynamics underlying a long-term associative memory - PubMed (original) (raw)

. 2017 Mar 30;543(7647):670-675.

doi: 10.1038/nature21682. Epub 2017 Mar 22.

Benjamin F Grewe 1 2 3, Lacey J Kitch 1 2 3, Jerome A Lecoq 1 2 3, Jones G Parker 3 5, Jesse D Marshall 1 2 3, Margaret C Larkin 1 3, Pablo E Jercog 1 2 3, Francois Grenier 4, Jin Zhong Li 1 3, Andreas Lüthi 4 6, Mark J Schnitzer 1 2 3

Affiliations

Neural ensemble dynamics underlying a long-term associative memory

Benjamin F Grewe et al. Nature. 2017.

Abstract

The brain's ability to associate different stimuli is vital for long-term memory, but how neural ensembles encode associative memories is unknown. Here we studied how cell ensembles in the basal and lateral amygdala encode associations between conditioned and unconditioned stimuli (CS and US, respectively). Using a miniature fluorescence microscope, we tracked the Ca2+ dynamics of ensembles of amygdalar neurons during fear learning and extinction over 6 days in behaving mice. Fear conditioning induced both up- and down-regulation of individual cells' CS-evoked responses. This bi-directional plasticity mainly occurred after conditioning, and reshaped the neural ensemble representation of the CS to become more similar to the US representation. During extinction training with repetitive CS presentations, the CS representation became more distinctive without reverting to its original form. Throughout the experiments, the strength of the ensemble-encoded CS-US association predicted the level of behavioural conditioning in each mouse. These findings support a supervised learning model in which activation of the US representation guides the transformation of the CS representation.

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Conflict of interest statement

Competing financial interests. M.J.S. is a scientific co-founder of Inscopix, Inc., which produces the miniature fluorescence microscope used in this study.

Figures

Extended Data Fig. 1

Extended Data Fig. 1. Mouse preparation for Ca2+ imaging in excitatory BLA neurons.

(a) Coronal slice of a mouse brain showing expression in the BLA of the GCaMP6m Ca2+ indicator, five weeks after injection of the AAV2/5-CaMK2a-GCaMP6m virus. Scale bar: 1 mm. (b) Schematic of a coronal mouse brain section shown with the reconstructed positions (dashed red lines) of the microendoscope implants in the BLA, for the 12 mice subject to the experimental protocol of Fig. 1c. The focal planes for in vivo Ca2+ imaging were 77–181 µm below the indicated implant positions, as determined through computational modeling of the microendoscope’s optical pathway done using the empirically determined value of the back focal length. Hence, the optical focal plane often spanned ventral parts of lateral amygdala (LA) and dorsal parts of the basal amygdala (BA), motivating our use the joint term basal and lateral amygdala (BLA) throughout the paper. AP: anterior posterior. Ctx: cortex. Scale bar: 1 mm. The mouse brain section in this figure has been reproduced with permission from. (c) Top, Wide-field fluorescence image of BLA tissue acquired through an implanted microendoscope, six weeks after injection of the AAV2/5-CaMK2a-GCaMP6m virus. The outer fiber tract enclosing the BLA does not express GCaMP6m and appears as a vertical dark stripe in the center of the field-of-view. The dashed box shows the position of the camera’s field-of-view, which we positioned over the BLA by using the fiber tract as a reference marker. Bottom, The same image as in the top panel, but with the boundaries of the BLA and endopiriform nucleus (Epn) marked in green and black dashed lines, respectively. Ctx: piriform cortex. Scale bar: 0.2 mm. (d–f) Coronal section of a mouse brain showing, d, inhibitory neurons in the BLA immuno-labeled with a monoclonal anti-GAD67 antibody; e, neurons expressing GCaMP6m under the control of the CaMK2a promoter; and f, the overlay of the images in d and e. Red arrows in d and e mark GAD67-positive interneurons that are not expressing GCaMP6m. Scale bars: 20 μm. (g–i) Coronal brain section showing, g, excitatory neurons in the BLA immuno-labeled using a polyclonal anti-Neurogranin (NRGN) antibody; h, neurons expressing GCaMP6m; and i, an overlay of the images in d and e, showing that the set of NRGN-positive excitatory neurons (labeled red) strongly overlap with the set of cells expressing GCaMP6m (labeled green). Scale bars: 20 μm.

Extended Data Fig. 2

Extended Data Fig. 2. Stimuli of neutral, positive, and negative valence activate sparse, largely distinct, spatially intermingled subsets of neurons in the BLA.

(a) A miniature fluorescence microscope enabled large-scale neural Ca2+ imaging in the BLA of awake behaving mice as we presented stimuli of different valences to the animals. (b) Candidate cells identified using an automated cell sorting routine, were easily segregated into those (left column) with sizes, morphologies and Ca2+ activity traces (gray traces, individual activity transients; black traces, mean waveforms) characteristic of individual neurons, and those that were obviously not neurons (right column). For the 4–10% of candidates with less common characteristics, we were conservative and accepted only those that were plainly cells by human visual scrutiny. We verified every cell included in the analyses by visual inspection. (c) An example cell map in the BLA, as determined from a Ca2+ imaging dataset 28 min in duration. Colors indicate the subsets of BLA neurons that responded to rewards (light blue), electric foot shocks (green) or eyelid shocks (yellow), or neutral tones (red). Scale bar: 20 μm. (Significance threshold: P ≤ 0.01, rank-sum test, comparing evoked Ca2+ signals to baseline levels). (d) Ca2+ responses of six example neurons in the same mouse following the delivery of individual water rewards (left), eyelid shocks (middle) or foot-shocks (right). Gray traces show the Ca2+ responses from eight individual trials. Black traces show the mean responses. (e) Mean ± s.e.m percentages of cells (n = 1251 neurons in total from 8 mice) with significant Ca2+ responses to the four different stimuli (Threshold for a significant response: P ≤ 0.01, comparing evoked versus baseline Ca2+ levels for n = 8 presentations of the stimulus; Wilcoxon rank-sum test). (f) Cumulative probability distributions, each determined as a mean over 8 mice (1251 total cells), of the centroid separations between all pairs of cells in each mouse (dashed black curve), and between pairs of cells that both had significant responses to one of the four different stimuli (colored curves). Inset: The corresponding probability densities. (g) Mean ± s.e.m. percentages of all neurons (n = 8 mice; 1251 cells in total) that had significant responses to each of the two stimuli in each pair listed on the vertical axis. Dashed orange line indicates the expected levels of overlap due to random chance. * denotes P < 0.05 and ** denotes P < 0.01, comparing the actual percentages versus those determined from datasets in which we randomly shuffled the cells’ identities (1000 random shuffles; Wilcoxon signed-rank test). (h) Mean ± s.e.m. Mahalanobis population vector distances (PVD) between the ensemble neural representations of the two stimuli of each pair listed on the vertical axis. All PVD values are normalized to the PVD between the neural representations of eyelid-shock and foot-shock. Pairs of stimuli with smaller PVD values have ensemble neural representations of greater similarity than pairs with larger PVD values. Dashed orange line indicates the PVDs between ensembles in which we randomly shuffled the cells’ identities (1000 random shuffles). * denotes P < 0.05 and ** denotes P < 0.01, comparing the actual PVD values versus those determined for the shuffled datasets (Wilcoxon signed-rank test). Data are based on the same 1251 cells as in e–g. (i) Twenty sets of fluorescence Ca2+ traces, showing evoked responses to presentations of the CS+ and CS– from 20 example neurons prior to fear conditioning. Light gray traces show the cells’ individual responses to each of five stimulus presentations; black traces are average responses. Traces were down-sampled to 5 Hz to aid visualization.

Extended Data Fig. 3

Extended Data Fig. 3. Unilateral implantation of a microendoscope implantation does not alter conditioned freezing; bilateral implantation minimally alters conditioned freezing without affecting locomotion.

(a) Traces of locomotor activity across an entire (22 min) habituation session (Day 1), for one example mouse in each of the three different experimental groups indicated. Scale bar: 5 cm. (b) Mean ± s.e.m. values of the total distance traveled (left), locomotor speed (middle) and acceleration (right) for the three different groups of mice during the Day 1 habituation session. There were no significant differences between the three experimental groups [no-implant control (12 mice); unilateral implant (12 mice); bilateral implant (10 mice)] in any of the three movement-related parameters (One-way Kruskal-Wallis Test; degrees of freedom: dfgroup = 2, dferr = 31_, dftotal_ = 33 for 3 groups and 34 total mice; χ2 = 10–12; P ≥ 0.05 for all three parameters). (c, d) Mean ± s.e.m. percentages of time mice spent freezing before conditioning (Days 1, 2) in response to 5 presentations of the CS–, c, and 5 presentations of the CS+, d, in control mice with no implant (12 mice), mice with a unilateral implant (12 mice), mice with a bilateral implant (10 mice), and mice that had a bilateral implant and received a muscimol injection into the BLA before the Day 3 conditioning session (8 mice). There were no significant differences in freezing time between any of the groups (One-way Kruskal-Wallis Test; degrees of freedom: dfgroup = 3, dferr = 42, dftotal = 45 for 4 groups and 42 total mice; χ2 = 10.2 and 11.8 for CS+ and CS–, P ≥ 0.05 for both CS+ and CS–). (e, f) Mean ± s.e.m. percentages of time mice spent freezing after conditioning (Days 4–6) in response to 4 presentations of the CS–, e, and during 3 sets each comprising 4 presentations of the CS+, f, in the same 42 mice as in panels c, d. * denotes P = 0.005 (Wilcoxon signed-rank test; bilateral muscimol group vs. control; significance threshold = 0.02 after Dunn-Šidák correction for 3 comparisons). These data are consistent with past work showing the necessity of BLA for auditory fear conditioning and further demonstrate that the BLA we are imaging are functional and necessary for the behavior. g) Mean ± s.e.m. percentages of time mice (n = 12) spent freezing during the 20–180 s inter-stimulus intervals following either a CS+ or CS– presentation_._ CS+ and CS– freezing values are averages over the numbers of stimulus presentations shown in Fig. 1c. After fear conditioning, CS–-evoked freezing levels were above those during the inter-stimulus intervals, indicating the CS– did not serve as a learned safety signal.

Extended Data Fig. 4

Extended Data Fig. 4. Ca2+ transient responses of individual BLA neurons to CS presentations closely resemble expectations based on electrical recordings of these responses.

To check whether fluorescence Ca2+ imaging in the BLA captured similar forms of neural activity as prior extracellular electrical recordings in this brain area, we compared individual neurons’ responses to CS presentations, as observed using the two recording modalities in two different sets of mice presented the same CS stimuli. Across the two datasets, there was close agreement between the shapes of the empirically determined Ca2+ transient waveforms and the expected waveforms based on the electrically recorded CS-evoked spiking responses. (a) We took a recording of CS-evoked spiking activity from an individual BLA cell (left), convolved the spike train with a decaying exponential function (700 ms time constant) to account for the kinetics of the GCaMP6m indicator (middle), and subtracted the baseline fluorescence level to yield a predicted CS-evoked Ca2+ fluorescence signal (Δ_F/F_) whose waveform shape closely matched the actual CS-evoked Ca2+ fluorescence signal of a BLA cell that we had monitored using the miniature microscope (right). (b) Six additional examples of individual BLA neurons’ CS-evoked spiking responses, as monitored via extracellular electrical recordings (black traces). From these spike trains, we used the approach of panel a to predict the Ca2+ fluorescence signals that these cells would produce (red traces) and compared these predictions to the actual CS-evoked Ca2+ fluorescence signals of another six BLA cells that we had studied by Ca2+ imaging and that had similar responses (blue traces).

Extended Data Fig. 5

Extended Data Fig. 5. Precise spatial registration of the Ca2+ imaging datasets from different behavioral sessions allows unambiguous tracking of individual cells across multiple days.

Using the spatial filters provided for each neuron by the automated cell sorting algorithm,, we made maps of all active cells detected in the BLA on each day of the study. We then used standard methods of image alignment to register these maps across the different days. Approximately 50% of all neurons observed across the entire experiment were detected as active on individual days. (a) Example maps of active BLA cells from three mice on the first (left), third (middle), and last (right) day of the six-day experimental protocol (Fig. 1c). Circles indicate cells that were active in only one of the three recordings (gray), on two of the three days (blue), or on all three days (red). Scale bar: 30 μm. The maximum number of active cells seen in one session was 192. (b) Thresholded spatial filters from three example cells registered across the six-day experimental protocol. Green asterisks indicate each cell’s centroid position on Day 1. Blue asterisks mark each cell’s centroid positions on subsequent days. Scale bar: 10 μm. (c) Five examples of neighboring cells detected via their activity patterns on different days of the experiment. In each case, the two individual cells are clearly discernible. Scale bar: 10 μm. (d) Cumulative histogram of the distances between the centroids of all pairs of cells detected within the same imaging session, plotted with a logarithmic scale on the y-axis. Inset: A magnified view of the portion of the graph enclosed in the dashed box. No pairs of cells were separated by <6 µm. (**e**) Cumulative histogram of the distances between the centroids of all pairs of active cells registered as being the same neuron seen in different sessions. _Inset_: Magnified view of the plot for _y_-axis values >97%. Because the worst-case alignment error of the image registration algorithm was 1.5 µm, as determined by a bootstrap analysis, and since all pairs of anatomically distinct cells were separated by ≥ 6 µm (panel d), cell pairs separated by < 4.5 µm were virtually guaranteed to be the same neuron seen on two different occasions. This yielded the worst-case estimate that >99.7% of all cell pairs registered as being the same cells were correctly assigned the same identity. This estimate is conservative in that the image registration errors were usually <1 µm. (**f**) A plot of the mean ± s.e.m probability that an active neuron detected in one imaging session will also be active in a subsequent session, for all 3655 neurons in the study (_black points_) and for CS–-responsive neurons (_gray points_)_. Inset_: Mean ± s.e.m. probability that a cell detected on any day in the study was present in each of the imaging sessions, for all 3655 neurons in the study (_black trace_), the CS+-responsive neurons (_red_), and the CS–-responsive neurons (_blue_)_._ These probabilities were constant throughout the study and statistically indistinguishable between the three groups of cells examined for all days and all mice [49 ± 2% (s.e.m.) of all cells were active each day; Two-way Friedman Test; degrees of freedom: _dfdays_ = 5, _dfgroup_ = 2, _dfinteraction_ = 10, _dferr_ = 198, _dftotal_ = 215 for 6 days, 3 groups of cells and 12 mice; χ2 = 1.6–7.5; _P_ > 0.05 for all three _P_-values]. (g) The total number of neurons detected in each mouse was stable across all days of the study (152 ± 14 cells per day; mean ± s.e.m.; n = 12 mice; One-way Friedman Test; degrees of freedom: dfdays = 5, dferr = 55, dftotal = 71 for 6 days and 12 mice; χ2 = 5.9; P = 0.31). (h) Mean ± s.e.m. percentage of all 3655 cells in the study that were detected in one to six sessions.

Extended Data Fig. 6

Extended Data Fig. 6. Conditioning induces bi-directional changes in CS-evoked responses.

Contrary to the predictions of the cellular, Hebbian model of fear learning, conditioning induced substantial bi-directional changes in the CS+-evoked responses of cells that responded to the US and of cells that did not respond to the US. Notably (panel a), a preponderance of cells that responded to both the CS+ and US before training had decreased CS+-evoked responses after training. Further (panel b), many cells with potentiated CS+-evoked responses after training were not US-responsive. Ensemble level analyses showed that cells with up- and down-regulated responses made equally important contributions to the learning-induced changes in ensemble neural coding (Fig. 3e). (a) Mean ± s.e.m percentages of CS–-responsive cells that were also US-responsive (blue) and of CS+-responsive cells that were also US-responsive. The latter data are further divided into those cells that increased their CS+-evoked responses after training (maroon), those that underwent no significant changes in their CS+-evoked responses (pink), and those that decreased their CS+-evoked responses after training (red). (b) Mean ± s.e.m percentages of CS–-responsive cells that were not US-responsive (blue) and of CS+-responsive cells that were not US-responsive. The latter data are further divided into those cells that increased their CS+-evoked responses after training (maroon), those that underwent no significant changes in their CS+-evoked responses (pink), and those that decreased their CS+-evoked responses after training (red). All data are from the same 12 mice.

Extended Data Fig. 7

Extended Data Fig. 7. BLA ensembles provide sufficient information to decode the CS, and the decoding accuracy improves with successive tone presentations in a series of tones.

(a) Left: A three-way decoder has three possible outputs (CS+, CS– and baseline) and hence different categories of possible errors. When a decoder makes a Type A error, it outputs the wrong CS (i.e. CS+ instead of CS–). When a decoder makes a Type B error, it fails to distinguish a CS presentation from baseline activity. Right: When we used all neurons’ activity traces to train the decoders, they determined the correct answer on 97 ± 1% (mean ± s.e.m.) of all trials from a testing set comprising equal numbers of samples of each type. The success rate was 90 ± 2% when we trained the decoders using only those cells with statistically significant responses to at least one of the CS types. (b) For trials that were incorrectly decoded, the pie charts show the proportions of the two types of errors, for decoders trained on the activity traces of all neurons (left), and for those trained using only neurons with statistically significant responses to at least one of the two CS types (right). (c) Type A errors (mean ± s.e.m.) declined sharply during the first 5 of the 25 CS tone pulses (black curve), both before (left panel), and after (right panel) conditioning. After conditioning, as the 25 tone pulses proceeded the mice increasingly distinguished between the CS– (blue curve) and the CS+ (red curve), as seen by the differences in evoked freezing behavior. (d) Schematic showing how we extracted the principal components (PCs) of the BLA ensemble responses to CS tone presentations. Dashed box encloses two PCs, used in panel e for illustration. (e) Plots of the first two PCs, determined as in d for four example mice, illustrate that the ensemble responses to the CS+ (red points) and the CS– (blue points) were generally distinguishable. Black stars mark the first out of 25 tone pulses for each CS presentation and illustrate that the initial tones in the series were generally the hardest to categorize correctly.

Extended Data Fig. 8

Extended Data Fig. 8. Fisher linear discriminant analysis of BLA population activity.

(a) A notional schematic showing the Mahalanobis distance and the discrimination boundary of a Fisher linear discriminant analysis (FLDA) decoder (black dotted line), which discriminates the multi-dimensional, neural ensemble responses to CS presentations from the activity patterns during baseline conditions. For simplicity, the schematic shows a hypothetical case in which the ensemble consisted of only two neurons, but the basic principles readily apply to larger ensembles. For a given set of training data, the Fisher decoder provides the a posteriori probability that a representative data sample will be correctly categorized. (b) Example histogram from one mouse showing BLA ensemble responses (Day 1) to CS presentations, normalized and projected onto the dimension of maximal discriminability. The dashed vertical line marks the classification boundary of the Fisher linear decoder, dividing those ensemble responses classified as baseline from those classified as representing a CS. The separation between the two peaks in the histogram is an empirical estimate of the Mahalanobis distance, which is a multi-dimensional generalization of the discriminability index_, d_’, used in statistics. (c) Mean decoding performance as a function of the number of cells used for training the decoder (open circles) and corresponding parametric fits to a sigmoid function. When the training and testing data came from the same day (black curve), performance asymptotically approached near perfect decoding when more than ~100 cells were used. When the training and testing data came from different days (red curve), our datasets were not large enough to approach the asymptote. However, the sigmoidal fit suggests that the asymptotic performance of time-lapse decoders would be ~90% in cases with more than ~120 cells. Shading indicates s.e.m. (d) Mean ± s.e.m. decoding performance of time-lapse CS– decoders, as a function of the elapsed time between the day on which the training dataset was acquired and the day on which the testing dataset was acquired (n = 12 mice). Despite cells’ declining re-occurrence probabilities as a function of elapsed time (Extended Data Fig. 5f), decoding performance remained stable for time-lapse intervals of 1–5 days.

Extended Data Fig. 9

Extended Data Fig. 9. The Mahalanobis distance quantifies the discriminability of two sets of ensemble responses and takes into account the mean and covariance of each response set.

(a) Left: Schematic illustration of two sets of ensemble neural responses (blue and red clouds of data points). The Euclidean distance (gray line) between the means of the two distributions does not take into account the degree to which the ensemble neural responses are variable from trial to trial. Right: To characterize the differentiability of the two response sets in a way that takes into account neural variability, we determined the Mahalanobis distance (M) between the two distributions. To do this, we first used the covariance matrix of the ensemble neural responses (∑) to map the data points into a space in which the distributions have unity variance in all directions. We determined M by calculating the distance between the means of the two resulting distributions. (b) A change in the Mahalanobis PVD can be due to changes in the means of the two sets of ensemble responses, changes in response variability, or both. The schematic illustrates these two different ways in which the sets of ensemble responses can become more or less differentiable. The top row shows a pair of cases in which changes in the mean ensemble responses dominate the change in the PVD. The bottom row shows a pair of cases in which changes in response variability dominate the change in the PVD. (c) We divided the total change in the CS+–US PVD (red curve) induced by learning into two components, a component due to changes in the mean CS+-evoked response (cyan curve) and a component due to changes in the variability of the CS+-evoked responses (black curve). After conditioning, the CS+-evoked responses became less variable (black curve) but also more similar to the US-evoked ensemble responses (cyan curve). The latter effect substantially outweighed the former, leading to a net ~32% decline (red curve) in the differentiability of the CS+- and US-evoked responses, as quantified by the net decrease in the Mahalanobis distance. Thin lines show the values from each of 12 individual mice. Thick lines show the mean values. Error bars are s.e.m.

Extended Data Fig. 10

Extended Data Fig. 10. Procedure for computational rescue of the CS+ decoders.

Unlike time-lapse CS– decoders, which worked well across all six days of the experiment, time-lapse CS+ decoders did not work well when the training and testing datasets came from a pair of days that spanned across the conditioning session (Fig. 3b). This failure mode for the CS+ decoders arises from the learning-induced changes in the ensemble representation of the CS+ (Fig. 3c,d). However, we found that by extrapolating the changes in the CS+ representation that occur during the training session on Day 3, we could predict the much greater, subsequent changes in the CS+ representation that occur before the next session on Day 4 and thereby rescue the failures of the time-lapse CS+ decoders. This figure schematizes the procedure for the computational rescue. (a) Schematic illustration of how conditioning-induced changes in CS+-evoked ensemble activity (light and dark red dots) can impair the performance of a time-lapse decoder trained on data from before fear conditioning and tested on data from after conditioning. (b) Through five main steps, we computationally simulated the changes in the CS+-representation that occurred during post-training consolidation, by extrapolating by a factor, q, the much smaller changes in the CS+-representation that occurred during the Day 3 training session. (c) To determine the optimal value of q, the extrapolation factor, we simulated the post-training changes in the CS+-representation by computationally adjusting the CS+ population vectors in increments of ΔA, the modest change in coding that occurred on Day 3. Increments of 3–5 times ΔA were optimal, in that they best rescued the capabilities of two-way decoders trained on either of Days 1 or 2 to detect a CS+ presentation when tested on data from after training (Days 4–6), or vice versa. (Each datum shows the mean ± s.e.m decoding performance, averaged across 12 mice and the 12 possible pair-wise combinations per mouse of one pre- and one post-training day). The same analysis of the CS– representation scarcely yielded any change in decoding performance, because the effects of training (ΔA) for the CS– were negligible. Decoders trained on temporally shuffled data (1000 shuffles; gray curve) and those based only on cells with up- (green) or down-regulated (purple) responses to the CS+ after training performed less successfully than decoders based on all cells (brown).

Fig. 1

Fig. 1. Ca2+ imaging of BLA neural activity across a six-day fear conditioning protocol.

(a) A miniature microscope and implanted microendoscope allowed large-scale neural Ca2+ imaging. (b) Traces of spontaneous Ca2+ activity from 15 BLA neurons. (c) Upper, Conditioning protocol, with numbers of stimuli. Lower, Mean ± s.e.m. percentages of time 12 mice froze during CS+ and CS– presentations_._ Values are respectively averaged over 5 and 4 stimulus presentations, before and after conditioning. (d) Activity traces of cells responsive to CS+ or CS– presentations before conditioning. (e) Map of BLA cells in one mouse. Colored cells responded to CS+ or CS– tones. Traces in b and d were down-sampled to 200 ms time bins.

Fig. 2

Fig. 2. Fear conditioning induces bi-directional changes in BLA signaling.

(a) Percentages (± s.e.m.) of cells responding to the CS+, CS–, or both stimuli. (b) Ca2+ signals, showing changes in CS+ encoding and stable CS– encoding for two sets of 125 cells detected throughout the study. Top, Cells responsive to the CS+ on at least one day. Bottom, Cells that either responded to the CS– on one or more days, or lacked responses to both CS types. Colors show each cell’s Ca2+ response averaged over 5 CS presentations on the day the cell responded maximally, for days before and after fear conditioning (FC). Cells are arranged by whether they responded maximally before or after conditioning. (c) Ca2+ signals from four cells, before (left, mean over 5 CS+ presentations), during (middle, single trial), and after (right, mean over 5 CS+ presentations) conditioning, illustrating altered responses to the CS+ (top two traces) or US (bottom two traces). (d) Percentages (± s.e.m.) of cells after conditioning with stable, increased or decreased responses to the CS+ (red), CS– (blue) and US (black), respectively based on 231, 362 and 261 neurons. Cells in the former two charts responded to the CS on at least one day before or after conditioning. Cells in the latter chart responded significantly to the US on Day 3. Traces in b and c were down-sampled to 200 ms time bins. a, b, d are from _N_=12 mice.

Fig. 3

Fig. 3. Learning increases the similarity of the CS+ and US representations.

(a) Accuracies of same-day, three-way decoders discriminating baseline, CS+ and CS– presentations. Decoders based on CS-responsive cells (green curve) nearly matched those using all cells (brown). Decoders based on cells un-responsive to the CS (purple) performed poorly, but better than decoders given temporally shuffled Ca2+ traces (gray dotted line) or shuffled cell identities (green dotted line). 152 ± 14 (s.e.m.) cells per day per mouse (3655 cells total; 12 mice). Shading denotes s.e.m. (b) Accuracies of inter-day, binary decoders distinguishing CS– (left) or CS+ (right) presentations from baseline conditions. (c) Population vector distances (PVD) between US-evoked ensemble activity and that evoked by the CS– (blue) or CS+ (red) during conditioning (Day 3). CS+–US PVDs declined by an amount Δ1 as responses to the two stimuli gained similarity. Dashed vertical line separates early and late CS+–US pairings; to calculate Δ1 we compared these two portions of the session. 155 ± 11 (s.e.m.) cells per mouse on Day 3 (1860 cells total; 12 mice). (d) CS+–US PVDs declined during and after training, indicating increased similarity of the two representations. Δ2 is the difference in PVD values before vs. after training (3655 cells). (e) Upper, Composition of the changes, Δ1, in CS+–US PVDs between early and late phases of training, defined in c. Lower, Analogous graph for Δ2, showing how CS+–US PVDs changed from before (Days 1,2) to after (Days 4–6) conditioning. To decompose Δ1 and Δ2 we examined cells with stable (white), up- (light gray) or down-regulated (dark gray) responses to the CS+, and cells with up- or down-regulated responses to the US (black). Error bars: s.e.m. (f) Before conditioning, population vector representations of the US (blue) and CS+ (pink) were orthogonal [88° ± 4° (s.e.m.); 12 mice]. Afterward, the CS+ population vector (orange) was 210 ± 20% longer, rotated 32° ± 3° from its initial orientation, and had a 61° ± 4° angle to the US representation, indicating the rotation was in the plane defined by the US-representation and that of the initial CS+. These changes differed from predictions of Hebbian potentiation (maroon) [angle and length changes each P < 10-4 ; rank-sum test]. (g) Mean accuracies of time-lapse decoders after computational rescue of their ability to distinguish CS+ presentations from baseline. For each pairing of one pre- and one post-training day (pairs inside gray rectangles), we rescued population vectors from the testing day by applying the optimal transformation, determined as in Extended Data Fig. 10c.

Fig. 4

Fig. 4. During behavioral extinction, the CS+ representation becomes more distinguishable from the US representation but does not revert to its initial form.

(a) Ca2+ signals from two neurons, illustrating bi-directional plasticity of CS+-evoked responses in early (left), middle (center), and late (right) phases of fear extinction on Day 4. Gray lines: Individual CS+ presentations (4 per set). Black lines: Mean responses. Inset: Magnified view of responses to individual CS+ tone pulses. (b) Population vector distances (PVDs) between CS- and US-evoked activity during extinction (Days 4–6), for individual mice (thin lines) and averaged across 12 mice (thick lines) for 12 CS+ and 4 CS– presentations per day (2181 total cells). CS+–US PVDs (red lines) increased by an amount, Δ3, within the sessions after fear conditioning (FC). CS––US PVDs (blue lines) were stable. (c) Composition of the change in PVD, Δ3, in b, from cells with stable (white), increased (light gray), or decreased (dark gray) responses to the CS+ after training. **: P < 0.001 (signed-rank test; 12 mice). (d) Within individual sessions, the CS+ representation changed at similar rates during learning and extinction (quantified by the change in mean CS+–US PVD per CS+ presentation; P = 0.6; signed-rank test; 12 mice). (e) During extinction sessions (Days 4–6), there was little change (Δ4) in the mean PVDs (thick lines) between CS+ and CS– representations and their initial forms before conditioning (averaged over Days 1, 2). Thin lines: data from individual mice. (f) Overnight consolidation induced long-term changes in the CS+ representation 24 h after conditioning (Day 3) but not after extinction training (Days 4, 5). Horizontal line marks where coding changes from training are neither amplified nor diminished in consolidation. Numbers above each dataset denote mean coding changes occurring overnight after each day, i.e. a 450% increase after Day 3, and reductions to 7% and 14% of their values after Ca2+ imaging on Days 4 and 5. Open diamonds: values from 12 individual mice. ***: P < 0.001 (signed-rank test; Day 3 vs. Days 4 or 5). All error bars are s.e.m.

Fig. 5

Fig. 5. The similarity of the CS+ and US representations encodes the CS+–US association strength.

(a) CS+–US PVDs for each CS+ presentation, normalized to the CS+–US PVD for the mouse’s first CS+ presentation, are predictive of the freezing level that each CS+ evoked before and during conditioning (left), and during extinction (middle). CS––US PVDs (right) lack this relationship. a and b are based on 3655 neurons in 12 mice. Black lines: linear fits. (b) Within each 25-s CS+, the 1 s time bins with and without freezing had a near unity ratio between their CS+–US PVD values, irrespective of the evoked freezing level. (c) How much each mouse (individual data points) exhibited post-training changes in the CS+–US PVD was predictive of its learned, CS+-evoked freezing behavior. Black line: linear fit (r = 0.7; _P <_10-3). Error bars: s.e.m. across 6 pair-wise comparisons of one day before (Days, 1, 2) and one day after training (Days 4–6) for each mouse. (d) How much each mouse (data points) exhibited a changed CS+–US PVD between the first 6 CS+ on Day 4 versus the first 6 CS+ on Day 6 was predictive of its loss of CS+-evoked freezing. Black line: linear fit (r = 0.9; _P <_10-3). Blue points denote mice with significant consolidated extinction (signed-rank test comparing time spent freezing between the two sets of CS+ presentations; P < 0.05). Error bars: s.e.m. across the 6 pair-wise comparisons of one CS+ from among the first six presentations on Day 4 and the corresponding CS+ from the first six presented on Day 6. (e) Schematic of CS+ population vector changes during learning and extinction. During learning, this vector doubles in length. It also rotates directly toward and becomes less differentiable from the US population vector, supporting a model in which the US representation provides a learning supervision signal. During acute extinction, the CS+ population vector shrinks ~20% and rotates ~5–8° out of the plane defined by the US and the initial CS+.

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