Internal state in the latent cause model in the Pavlovian fear conditioning, extinction, and reinstatement.

(A) Schematic diagram of latent cause framework in a simple Pavlovian fear conditioning paradigm. An experimental mouse observes a tone, a context, and an electrical shock, which are set down in a parallelogram. Among the stimuli, the tone is designed as the conditioned stimulus (CS), and the electrical shock is designed as the unconditioned stimulus (US) with additional consideration of context effect. The mouse has an internal model such that a latent cause z generates the observation where the tone and the context induce the shock at an associative weight wcs and wcontext, respectively. The latent cause is a latent variable represented by a white square. The posterior probability of z is represented by a black arrow from z to the observation. The stimuli (i.e., tone, context, and shock) are observed variables represented in shaded circles, and the associative weight w is represented by a black arrow between the two. Since latent causes are unobservable, the mouse infers which latent cause is more likely from posterior distribution over latent causes given the observation following Bayes’ rule.

(B) Schematic diagram of internal state posited in the latent cause model demonstrating the memory modification process in the fear conditioning paradigm. The mouse has acquired zA through two observations of the CS accompanied by the US in the same context. Now, the mouse observes the tone alone, then infers a new latent cause zB generating the CS and context without US as wcs and wcontext equal to 0. The internal state at the time consists of zA with largely decreased posterior probability and thereby slightly decreased wcs and wcontext, in addition to zB. The mouse in this panel is likely to differentiate the current observation from zA, as it assigns a higher probability for zB. The posterior probability of zA and zB is represented by the relative size of their diagram. If the mouse generalizes zA to the current observation without inferring zB, it would largely decrease wcs and wcontext of zA to minimize prediction error. (C) Observed and simulated conditioned response (CR) during reinstatement in fear conditioning. In the acquisition phase, a CS was accompanied by a US, inducing associative fear memory in the animal, as it exhibits a higher CR to the CS. In the extinction phase, the CS was presented without the US, inducing extinction memory with decreased CR. After an unsignaled shock without the preceding CS, the CR increases again, and this is called reinstatement. The observed CR was sampled from a 2-month-old male wild-type C57BL/6J mouse (magenta line plot with square markers), where the vertical and horizontal axis indicate CR and cumulative trial, respectively. The latent cause model parameters were estimated so as to minimize the prediction error between the observed and the simulated CR given the parameter (gray line with square markers). The estimated parameter value: α = 2.4, g = 0.316, η = 0.64, max. no. of iteration = 9, w0 = –0.006, σr2 = 4.50, σx2 = 4.39, θ = 0.03, λ = 0.02, K = 6. Trials with red, blue, and yellow backgrounds correspond to the acquisition, extinction, and unsignaled shock, where the first and second extinction consists of 19 and 10 trials, respectively (see Material and Methods). Three trials with white backgrounds are tests 1, 2, and 3 to evaluate if conditioning, extinction, and reinstatement are established. The vertical dashed lines separate the phases. (D) The evolution of the posterior probability and (E) the associative weight of each latent cause across the reinstatement experiment, where wcs (top panel) and wcontext (bottom panel) were computed. (D and E) Each latent cause is indicated by a unique subscript number and color, wcs and wcontext. The latent causes acquired during the acquisition phase and their associative weight are termed zA and wA, respectively. Meanwhile, latent causes acquired during the extinction phase and their associative weight are termed zB and wB, respectively.

AppNL-G-F mice exhibited successful associative learning and extinction but a lower extent of reinstatement.

(A) Schematic diagram of reinstatement paradigm in this study. In the acquisition phase, the CS was accompanied with the US 3 times. In the following phase, either the CS or the US was presented at certain times. The context was the same throughout the experiment. (B) Freezing rate during CS presentation across reinstatement paradigm. The markers and lines show the median freezing rate of each group in each trial. Red, blue, and yellow backgrounds represent acquisition, extinction, and unsignaled shock in (A). The dashed vertical line separates the extinction 1 and extinction 2 phases. Freezing rate during CS presentation in test 1 (C), test 2 (D), and test 3 (E). Discrimination index (DI) between test 2 and test 1 (F), between test 3 and test 2 (G), and between test 3 and test 1 (H) calculated from freezing rate during CS presentation.

(C to E) The data are shown as median with interquartile range. *p < 0.05, **p < 0.01, and ***p < 0.001 by one-way ANCOVA with age as covariate; #p < 0.05, ##p < 0.01, and ###p < 0.001 by Student’s t-test comparing control and AppNL-G-F mice within the same age. Detailed statistical results are provided in Table S2. (F to H) The dashed horizontal line indicates DI = 0.5, which means no discrimination between the two phases. †p < 0.05 by one-sample Student’s t-test, and the alternative hypothesis specifies that the mean differs from 0.5; *p < 0.05, **p < 0.01, and ***p < 0.001 by one-way ANCOVA with age as a covariate; #p < 0.05, ##p < 0.01, and ###p < 0.001 by Student’s t-test comparing control and AppNL-G-F mice within the same age. Detailed statistical results are provided in Tables S3 and S4. (B to H) Colors indicate different groups: orange represents 6-month-old control (n = 24), light blue represents 6-month-old AppNL-G-F mice (n = 25), pink represents 12-month-old control (n = 24), and dark blue represents 12-month-old AppNL-G-F mice (n = 25). Each black dot represents one animal.

The divergence of internal states between control and AppNL-G-F mice differed in age.

(A) Simulation of reinstatement in the 6-month-old control mice given a set of estimated parameters of the latent cause model. The estimated parameter value: α = 2.4, g = 0.05, η = 0.42, max. no. of iteration = 2, w0 = 0.009, σr2 = 2.90, σx2 = 0.49, θ = 0.008, λ = 0.018, K = 10. (B) Simulation of reinstatement in 6-month-old AppNL-G-F mice. The estimated parameter value: α = 1.1, g = 0.61, η = 0.51, max. no. of iteration = 2, w0 = 0.004, σr2 = 1.51, σx2 = 0.32, θ = 0.015, λ = 0.019, K = 30. (C) Simulation in 12-month-old control mice. The estimated parameter value: α = 1.1, g = 0.92, η = 0.82, max. no. of iteration = 5, w0 = 0.009, σr2 = 1.88, σx2 = 0.51, θ = 0.010, λ = 0.017, K = 4. (D) Simulation in 12-month-old AppNL-G-Fmice. The estimated parameter value for: α = 1.0, g = 1.10, η = 0.04, max. no. of iteration = 2, w0 = 0.0025, σr2 = 1.51, σx2 = 0.18, θ = 0.011, λ = 0.011, K = 36.

(A to D) The first row shows the trace of observed CR and simulated CR. The observed CR is the median freezing rate during the CS presentation over the mice within each group; the observed CR of each group was divided by its maximum over all trials. The second row shows the posterior probability of each latent cause in each trial. The third and fourth rows show the associative weight of tone to shock (wcs) and that of context to shock (wcontext) in each trial. Each marker and color corresponds to a latent cause up to 5. Each latent cause is represented by the same color as that in the second row and contains wcs and wcontext. The vertical dashed lines indicate the boundaries of phases.

Individual parameter estimation and internal state in the 12-month-old group.

(A) The estimated latent cause model parameter. (B) Correlation between discrimination index (DI) and estimated parameter values in the 12-month-old group. The count of latent causes initially inferred during the acquisition trials (C, left), extinction trials (i.e., test 1, extinction, test 2) (D, left), and trials after extinction (i.e., the unsignaled shock and test 3) (E, left), with the sum of posterior probabilities (C, D, E, right), and the sum of associative weights at test 3 in these latent causes (F, G, H).

(A) Each black dot represents one animal. *p < 0.05, and **p < 0.01 by the Mann-Whitney U test. (B) The y-axis shows the DI between test 3 and test 1. Spearman’s correlation coefficient (⍴) was labeled with significance, where *p < 0.05 and ***p < 0.001. The blue line represents the linear regression model fit, and the shaded area indicates the confidence interval. Each dot represents one animal. (C to E) In the first column, the histogram of the number of latent causes (z) acquired in each phase is shown. The maximum number of latent causes that can be inferred is 3, 31, and 2 in panels C, D, and E. In the second column, the histogram of the sum of the posterior probabilities of the latent causes is shown. The horizontal axis indicates the proportion of the value in each group. (F to H) In the first and second columns, the sum of wcs and wcontext of latent causes are shown in the boxplot, respectively. Note that the initial value of associative weight could take non-zero values, though those were comparable between groups (Table S7). Each black dot represents one animal. *p < 0.05, and **p < 0.01 by the Mann-Whitney U test comparing control and AppNL-G-F mice, and p-values greater than 0.1 were not labeled on the plot. (A to H) Pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-Fmice (n = 18). Detailed statistical results are provided in Tables S7, S8, and S9.

Individual parameter estimation and internal state in the 6-month-old group.

(A) The estimated parameters of the latent cause model. (B) Correlation between discrimination index (DI) and estimated parameter values in the 6-month-old group. The count of latent causes initially inferred during the acquisition trials (C, left), extinction trials (i.e., test 1, extinction, test 2) (D, left), and trials after extinction (i.e., the unsignaled shock and test 3) (E, left), with the sum of posterior probabilities (C, D, E, right), and the sum of associative weights at test 3 in these latent causes (F, G, H).

(A) Each black dot represents one animal. *p < 0.05 by the Mann-Whitney U test. (B) The y-axis shows the DI between test 3 and test 1. Spearman’s correlation coefficient (⍴) was labeled with significance, where *p < 0.05 and **p < 0.01. The blue line represents the linear regression model fit, and the shaded area indicates the confidence interval. Each dot represents one animal. (C to H) The configuration of the figure is the same as in Figure 4. All the p-values of the Mann-Whitney U test comparing control and AppNL-G-F mice were greater than 0.05 and were not labeled on the plot. (A to H) Orange represents 6-month-old control (n = 15), and light blue represents 6-month-old AppNL-G-Fmice (n = 12). Detailed statistical results are provided in Tables S10, S11, and S12.

AppNL-G-F mice failed to infer coexisting spatial memories in the reversal Barnes maze task.

(A) Schematic diagram of the reversal Barnes maze task. The largest circle represents the Barnes maze field. The filled and open small circles represent the target hole with the escape box and the remaining holes in the field, respectively. The small arrow pointing to the hole indicated the position of the target hole without an escape box in the probe test. The same color of the filled circle and arrow indicates the same position. (B) Strategy usage in initial training (days 1 to 6), the first reversal training (days 9 to 11), and the second reversal training (days 12 to 14) in the 12-month-old group. Time spent around each hole at probe test 1 (C) and probe test 2 (D) in the 12-month-old group. (E) Discrimination index (DI) of the second target hole between probe test 2 and probe test 1 in the 12-month-old group. (F) Strategy usage in initial training (days 1 to 6), the first reversal training (days 9 to 11), and the second reversal training (days 12 to 14) in the 6-month-old group. Time spent around each hole at probe test 1 (G) and probe test 2 (H) in the 6-month-old group. (I) Discrimination index (DI) of the second target hole between probe test 2 and probe test 1 in the 6-month-old group.

(B and F) *p < 0.05 of perimeter strategy, #p < 0.05 of confirmatory strategy, †p < 0.05 of serial strategy, ‡p < 0.05 of spatial strategy by Wilcoxon rank-sum test comparing control and AppNL-G-F mice at the same age. (C, D, G, and H) The data are shown as mean with 95% confidence interval. *p < 0.05, **p < 0.01, and ***p < 0.001 by mixed-design two-way [Genotype (control, AppNL-G-F) × Hole (1-12)] ANOVA; †p < 0.05 by Tukey’s HSD test at the specific hole to compare control and AppNL-G- F mice at the same age. (E and I) The dashed horizontal line indicates DI = 0.5, which means no discrimination between the two phases. †p < 0.05 by the Wilcoxon signed-rank test, and the alternative hypothesis specifies that the mean differs from 0.5; *p < 0.05 by Mann-Whitney U test comparing control and AppNL-G-F mice. (C-E, G-I) Each black dot represents one animal. Colors indicate the different groups: pink represents 12-month-old control (n = 18), dark blue represents 12-month-old AppNL-G-F mice (n = 18), orange represents 6-month-old control (n = 24), and light blue represents 6-month-old AppNL-G-F mice (n = 17). Detailed statistical results are provided in Tables S14 to S16 for the 12-month-old group results and Tables S18 to S20 for the 6-month-old group results.

Representative image of immunofluorescence staining using Iba1 (blue), GFAP (green), and Aβ (red) antibodies on anterior

(A) and posterior (B) coronal brain sections. Quantification results of Aβ plaque area in anterior (C) and posterior (D) coronal brain section of AppNL-G-F mice.

(A and B) The scale bar on the images in the first row represents 1 mm. The images in the second row of the panel are the magnified view of the inlet in the same column, where the scale bar on the images represents 150 μm in panel A and 250 μm in panel B. (C and D) The data are shown as mean with 95% confidence interval. Each black dot represents one animal. n = 5 in 6-month-old AppNL-G-F mice; n = 10 in 12-month-old AppNL-G-F mice. Student’s t-test was performed to compare 6– and 12-month-old AppNL-G-F mice. The results were t(14)=2.555, p = 0.023* in (C) and t(14)=3.536, p = 0.003** in (D).

Freezing rate before tone presentation in the reinstatement paradigm

Freezing rate before and during tone presentation across reinstatement paradigm in the 6-month-old group (A) and 12-month-old group (B). The markers and lines show the median of each group in each trial. Dashed and solid lines indicate the freezing rate for 1 min before the CS presentation (preCS) and that for 1 min during the tone presentation (CS), respectively. Red, blue, and yellow backgrounds represent acquisition, extinction, and unsignaled shock as in Figure 2A. The dashed vertical line separates the extinction 1 and extinction 2 phases. Freezing rate before CS presentation in test 1 (C), test 2 (D), and test 3 (E). The data are shown as median with interquartile range. Each black dot represents one animal. *p < 0.05, **p < 0.01, and ***p < 0.001 by one-way ANCOVA with age as covariate; #p < 0.05, ##p < 0.01, and ###p < 0.001 by Student’s t-test comparing control and AppNL-G-F mice within the same age.

(A to E) Colors indicate different groups: orange represents 6-month-old control (n = 24), light blue represents 6-month-old AppNL-G-Fmice (n = 25), pink represents 12-month-old control (n = 24), and dark blue represents 12-month-old AppNL-G-F mice (n = 25).

Replication of DI in the test phases and prediction error across trials in the latent cause model.

Discrimination index (DI) between test 2 and test 1 (A), between test 3 and test 2 (B), and between test 3 and test 1 (C) calculated from simulated CR. The signed prediction error between observed and simulated CR in the 6-month-old group (D) and 12-month-old group (E).

(A to C) Each black dot represents one animal. The dashed horizontal line indicates DI = 0.5, which means no discrimination between the two phases. †p < 0.05 by one-sample Student’s t-test, and the alternative hypothesis specifies that the mean differs from 0.5; *p < 0.05, and **p < 0.01 by one-way ANCOVA with age as a covariate; #p < 0.05 by Student’s t-test comparing control and AppNL-G-F mice within the same age. Detailed statistical results are provided in Tables S5 and S6. (D and E) The gray areas indicate the test phases. *p < 0.05 by Mann-Whitney U test comparing control and AppNL-G-Fmice within the same age. Statistical results are as follows: U = 93.5, p = 0.883 for test 1, U = 110, p = 0.347 for test 2, U = 67, p = 0.277 for test 3 in the 6-month-old group; U = 229, p = 0.156 for test 1, U = 167, p = 0.718 for test 2, U = 101, p = 0.02 for test 3 in the 12-month-old group. (A to E) Colors in the boxplot indicate different groups: orange represents 6-month-old control (n = 15), light blue represents 6-month-old AppNL-G-Fmice (n = 12), pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18).

Correlation matrix of estimated parameters in the 12-month-old group.

The lower triangle shows the scatter plots of pairwise combinations of two parameters where the colors of the dot in the scatterplot indicate groups: pink represents 12-month-old control mice (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18). The square outline highlights parameter pairs with statistically significant correlations. The upper triangle shows the heatmap of Spearman’s correlation coefficient (⍴), where colors indicate the strength and direction of the correlation, as shown in the color bar. Significant correlations are annotated in the heatmap: *p < 0.05, **p < 0.01, and ***p < 0.001.

Correlations between DI and estimated parameters within the 12-month-old control group

(A) and AppNL-G-F group (B).

(A to B) Spearman’s correlation coefficient (⍴) was labeled with significance, where *p < 0.05, **p < 0.01, and ***p < 0.001. The blue line represents the linear regression model fit, and the shaded area indicates the confidence interval. Each dot represents one animal and its color indicates groups: pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18).

Simulated CR (A), and posterior probabilities (B), associative weights (C) of latent causes initially inferred during the acquisition trials in the 6-month-old group in test 1 phase.

(A) The data are shown as median with interquartile range. Each black dot represents one animal. Control (Mdn = 0.84, IQR = 0.44) vs. AppNL-G-F (Mdn = 1, IQR = 0.13), Mann-Whitney U = 247, p = 0.041. (B) The horizontal axis of the histogram indicates the proportion of the value in each group. Control (Mdn = 0.60, IQR = 0.10) vs. AppNL-G-F (Mdn = 1, IQR = 0), Mann-Whitney U = 255, p = 0.008. (C) Each dot represents one animal. Control (Mdn = 0.308, IQR = 0.482) vs. AppNL-G-F (Mdn = 0.373, IQR = 0.401), Mann-Whitney U = 197, p = 0.633 for wcs; Control (Mdn = 0.075, IQR = 0.088) vs. AppNL-G-F (Mdn = 0.077, IQR = 0.091), Mann-Whitney U = 179, p = 0.988 for wcontext. (A to C) Colors in the bar plot or boxplot indicate groups: pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-Fmice (n = 18).

Correlation matrix of estimated parameters in the 6-month-old group.

The figure format is the same as in Figure 4–figure supplement 1, except that the colors of the dots in the scatterplot indicate groups: orange represents 6-month-old control (n = 15), and light blue represents 6-month-old AppNL-G-F mice (n = 12). Significant correlations are annotated in the heatmap: *p < 0.05, *p < 0.01, and ***p < 0.001.

Correlation between DI and selected parameters in 6-month-old control (A) and AppNL-G-F mice (B).

The figure format is the same as in Figure 4–figure supplement 2, the colors of the dots indicate groups: orange represents 6-month-old control (n = 15), and light blue represents 6-month-old AppNL- G-F mice (n = 12).

Simulated CR (A), and posterior probabilities (B), associative weights (C) of latent causes initially inferred during the acquisition trials in the 6-month-old group in test 1 phase.

The figure format is the same as in Figure 4–figure supplement 3. (A) The data are shown as median with interquartile range. Each black dot represents one animal. Control (Mdn = 0.73, IQR = 0.34) vs. AppNL- G-F (Mdn = 1, IQR = 0.18), Mann-Whitney U = 110, p = 0.325. (B) The horizontal axis of the histogram indicates the proportion of the value in each group. Control (Mdn = 0.08, IQR = 0.10) vs. AppNL-G-F (Mdn = 1, IQR = 0.62), Mann-Whitney U = 112, p = 0.249. (C) Each dot represents one animal. Control (Mdn = 0.196, IQR = 0.414) vs. AppNL-G-F (Mdn = 0.203, IQR = 0.476), Mann-Whitney U = 91, p = 0.981 for wcs; Control (Mdn = 0.049, IQR = 0.095) vs. AppNL-G-F (Mdn = 0.054, IQR = 0.074), Mann-Whitney U = 94, p = 0.867 for wcontext. (A to C) Colors in the bar plot or boxplot indicate groups: orange represents 6-month-old control (n = 15), and light blue represents 6-month-old AppNL-G-F mice (n = 12).

Conventional analysis for initial

(A) and reversal (B) training day in the Barnes maze task and discrimination index of the first target hole between probe test 2 and probe test 1 (C) in the 12-month-old group. Colors indicate different groups: pink represents 12-month-old control (n = 18), and dark blue represents 12-month-old AppNL-G-F mice (n = 18).

(A and B) The left, middle, and right panels show the number of errors, latency, and travel distance during training days. The data are shown as mean with 95% confidence interval. *p < 0.05, **p < 0.01, and ***p < 0.001 by mixed-design two-way [Genotype (control, AppNL-G-F) × Day (1-6)] ANOVA. Detailed statistical results are provided in Table S13. (C) Each black dot represents one animal. The dashed horizontal line indicates DI = 0.5, which means no discrimination between the two phases. †p < 0.05 by the Wilcoxon signed-rank test, and the alternative hypothesis specifies that the mean differs from 0.5; *p < 0.05 by Mann-Whitney U test comparing control and AppNL-G-F mice. Detailed statistical results are provided in Table S16.

(A) Animal trajectory examples and definition of each strategy. The red solid circle indicates the target hole, and the black solid circle indicates other holes in the field. The dotted line represents the animal’s trajectory, and the color reflects the time in the trial. (B) The algorithm of strategy analysis.

Conventional analysis for initial

(A) and reversal (B) training day in the Barnes maze task and discrimination index of the first target hole between probe test 2 and probe test 1 (C) in the 6-month-old group. The configuration of the figure is the same as in Figure 6–figure supplement 1. Colors indicate the different groups: orange represents 6-month-old control (n = 24), and light blue represents 6-month-old AppNL-G-F mice (n = 17). Detailed statistical results are provided in Table S17 for panels A and B; Table S20 for panel C.