Misclassification in memory modification in AppNL-G-F knock-in mouse model of Alzheimer’s disease
Figures
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 Materials 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, 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.
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Figure 1—source data 1
Simulation data and experimental data shown in Figure 1C–E.
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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 conditioned stimulus (CS) was accompanied with the unconditioned stimulus (US) three 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–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 Supplementary file 1b. (F–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 Supplementary file 1c and d. (B–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.
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Figure 2—source data 1
Freezing % and Aβ plaque quantification data shown in Figure 2 and Figure 2—figure supplements 1 and 2.
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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 sections of AppNL-G-F mice. (A, 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, 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–E) 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).
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-F mice. 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–D) The first row shows the trace of observed conditioned response (CR) and simulated CR. The observed CR is the median freezing rate during the conditioned stimulus (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.
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Figure 3—source data 1
Simulation data and median of experimental data shown in Figure 3.
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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 conditioned response (CR). The signed prediction error between observed and simulated CR in the 6-month-old group (D) and 12-month-old group (E). (A–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 Supplementary file 1e and f. (D, E). The gray areas indicate the test phases. *p<0.05 by Mann-Whitney U test comparing control and AppNL-G-F mice 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–E) Colors in the boxplot indicate different groups: orange represents 6-month-old control (n = 15), light blue represents 6-month-old AppNL-G-F mice (n = 12), pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18).
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Figure 3—figure supplement 1—source data 1
Simulation data shown in Figure 3—figure supplement 1.
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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 (ρ) 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–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–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 (Supplementary file 1g). 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–H) Pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18). Detailed statistical results are provided in Supplementary file 1g, h, and i.
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Figure 4—source data 1
Estimated parameter values of the 12-month-old group.
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Figure 4—source data 2
Simulation data shown in Figure 4C–H and Figure 4—figure supplement 3.
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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 (ρ), 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, B) Spearman’s correlation coefficient (ρ) 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 conditioned response (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–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-F mice (n = 18).
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–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–H) Orange represents 6-month-old control (n = 15), and light blue represents 6-month-old AppNL-G-F mice (n = 12). Detailed statistical results are provided in Supplementary file 1j, k, and l.
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Figure 5—source data 1
Estimated parameter values of the 6-month-old group.
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Figure 5—source data 2
Simulation data shown in Figure 5C–H and Figure 5—figure supplement 3.
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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 conditioned response (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–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).
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 1–6), the first reversal training (days 9–11), and the second reversal training (days 12–14) 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 1–6), the first reversal training (days 9–11), and the second reversal training (days 12–14) 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, 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 the 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, 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 Supplementary file 1n, o, and p for the 12-month-old group results and Supplementary file 1r, s, and t for the 6-month-old group results.
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Figure 6—source data 1
Behavioral data of the reversal Barnes maze experiment shown in Figure 6 and Figure 6—figure supplements 1 and 3.
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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, 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 Supplementary file 1m. (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 Supplementary file 1p.
Strategy analysis in the Barnes maze task.
(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 Supplementary file 1q for panels A and B; Supplementary file 1t for panel C.
Model fit of the Rescorla-Wagner model and the latent state model to the behavioral data.
(A) Simulation of reinstatement in the 6-month-old control mice in the RW model. The estimated parameter value: αCS = 0.1, αcontext = 1, β = 0.504. (B) Simulation of reinstatement in the 6-month-old AppNL-G-F mice in the RW model. The estimated parameter value: αCS = 0.1, αcontext = 1, β = 0.302. (C) Simulation of reinstatement in the 12-month-old control mice in the RW model. The estimated parameter value: αCS = 0.1, αcontext = 1, β = 0.614. (D) Simulation of reinstatement in the 12-month-old AppNL-G-F mice in the RW model. The estimated parameter value: αCS = 0.1, αcontext = 1, β = 0.596. (E) Simulation of reinstatement in the 6-month-old contol mice in the latent state model (LSM). The estimated (parameter value: α0 = 0.012, α1 = 0.020, α2 = 0.040, γ = 0.020, ncop = 10, η = 2.369, χ = 3, σ0 = 0.99). (F) Simulation of reinstatement in the 6-month-old AppNL-G-F mice in the LSM. The estimated parameter value: α0 = 0.078, α1 = 0.058, α2 = 0.418, γ = 0.258, ncop = 10, η = 2.290, χ = 7, σ0 = 0.69. (G) Simulation of reinstatement in the 12-month-old control mice in the LSM. The estimated parameter value: α0 = 0.043, α1 = 0.191, α2 = 0.376, γ = 0.099, ncop = 10, η = 0.044, χ = 8, σ0 = 0.58. (H) Simulation of reinstatement in the 12-month-old AppNL-G-F mice in the LSM. The estimated parameter value: α0 = 0.069, α1 = 0.020, α2 = 0.495, γ = 0.886, ncop = 32, η = 0.040, χ = 9, σ0 = 0.62. (A–H) The observed conditioned response (CR) is the median freezing rate during the conditioned stimulus (CS) presentation over the mice within each group; both observed and simulated CR of each group were divided by their maximum over all trials. The vertical dashed lines indicate the boundaries of phases. In the RW model, 6-month-old control (A), 6-month-old AppNL-G-F (B), and 12-month-old control (C) were marked as anomalies in parameter estimation.
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Appendix 1—figure 1—source data 1
Data shown in Appendix 1—figure 1.
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Number of excluded samples during parameter estimation in each model.
The number of samples that did not pass the accepted criteria in the 6-month-old group (A) and 12-month-old group (B). LCM: latent cause model; LSM: latent state model; RW: Rescorla-Wagner model. 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). The transparency of the color indicates accepted samples (dark) and anomalies (light).
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Appendix 1—figure 2—source data 1
Data shown in Appendix 1—figure 2.
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The squared prediction error in the Rescorla-Wagner model (A) and the latent state model (B).
The squared prediction error across trials is shown as median with interquartile range. In the RW model, data from all samples are used. In the LSM, only accepted samples are shown (the exact numbers are shown in Appendix 1—figure 2).
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Appendix 1—figure 3—source data 1
Data shown in Appendix 1—figure 3.
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Comparison of squared prediction error among models in the 6-month-old group (A) and 12-month-old group (B).
The data are shown as median with interquartile range. In the RW model, data from all samples are used. In the LSM and LCM, only accepted samples are shown (the exact numbers are shown in Appendix 1—figure 2). LCM: latent cause model; LSM: latent state model; RW: Rescorla-Wagner model. *p < 0.05, **p < 0.01, and ***p < 0.001 by Mann-Whitney U test comparing LCM and LSM. The RW model was excluded from the statistical comparison because of the low sample number.
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Appendix 1—figure 4—source data 1
Data shown in Appendix 1—figure 4.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig4-data1-v1.xlsx
The number of latent states inferred in different phases and their posterior probability in test 3.
(A–E) The figure format is the same as that in Figures 4C–E–5C–E for the latent cause model. The latent states were classified based on the trial they were initially inferred: during the acquisition trials (first row), extinction trials (second row), and trials after extinction (third row). The first and third columns show the count of latent states in the 6-month-old group and 12-month-old group, respectively. The second and fourth columns show the posterior probability of latent states in test 3 in the 6-month-old group and 12-month-old group, respectively. The horizontal axis indicates the proportion of the value in each group. Colors in the histogram indicate different groups: orange represents 6-month-old control (n = 6), light blue represents 6-month-old AppNL-G-F mice (n = 13), pink represents 12-month-old control (n = 10), and dark blue represents 12-month-old AppNL-G-F mice (n = 11). Each black dot represents one animal.
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Appendix 1—figure 5—source data 1
Data shown in Appendix 1—figure 5.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig5-data1-v1.xlsx
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 conditioned response (CR) in the latent state model.
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 by one-way ANCOVA with age as a covariate; No significant difference between control and AppNL-G-F mice within the same age was detected by Student’s t-test comparing. Colors in the box plot indicate different groups: orange represents 6-month-old control (n = 6), light blue represents 6-month-old AppNL-G-F mice (n = 13), pink represents 12-month-old control (n = 10), and dark blue represents 12-month-old AppNL-G-F mice (n = 11). Each black dot represents one animal.
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Appendix 1—figure 6—source data 1
Data shown in Appendix 1—figure 6.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig6-data1-v1.xlsx
The sum posterior probability (A), the sum of associative weight of CS (B), and the sum of associative weight of context (C) of acquisition and extinction latent causes in Figure 1D and 1E.
Simulation (A) and parameter estimation (B and C) in the extended Rescorla-Wagner model.
Leaving trials out in parameter estimation in the latent cause model.
(A – F) The observed CR (colored line) is the median freezing rate during the CS presentation over the mice within each group, which is the same as that in Figure 3. The colors indicate different groups: orange represents 6-month-old control, light blue represents 6-month-old AppNL-G-F mice, pink represents 12-month-old control, and dark blue represents 12-month-old AppNL-G-F mice. Under six different leave-out conditions (i – vi), parameters were estimated and used for generating simulated CR (gray line). In each condition, trials were categorized as acquisition (light-shaded area), training data (white area), and test data (dark-shaded area) based on the error threshold during parameter estimation. Only the error threshold of the test data trial was different from the original method (see Material and Method) and set to 1. In conditions i to vi, the number of test data trials is 27, 25, 19, and 19 in extinction phases. In condition v, the number of test data trials is 2 (trials 35 and 36). In condition vi, test data trials were the 3 test phases (trials 4, 34, and 36). (G) Each subplot shows the mean squared prediction error for the test data trial (gray circles), training data trial (white squares), and acquisition trial (gray triangles) in each group. The left y-axis corresponds to data from test and training trials, and the right y-axis corresponds to data from acquisition trials. The dashed line indicates the results calculated from Figure 3 as a baseline.
Freezing rate across reinstatement paradigm in the 17-month-old AppNL-G-F mice.
Dashed and solid lines indicate the median freezing rate over 34 mice before (preCS) and during (CS) tone presentation, respectively. Red, blue, and yellow backgrounds represent acquisition, extinction, and unsignaled shock in Figure 2A. The dashed vertical line separates the extinction 1 and extinction 2 phases.
Net freezing rate in test 2 and test 3.
Net freezing rate is defined as the CS freezing rate (i.e., freezing rate during 1 min CS presentation) minus the preCS freezing rate (i.e., 1 min before CS presentation). The dashed horizontal line indicates no freezing rate change from the preCS period to the CS presentation. *p < 0.05 by paired-sample Student’s t-test, and the alternative hypothesis specifies that test 2 freezing rate change is less than test 3. 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. Statistical results were as follows: t(23) = -1.927, p = 0.033, Cohen’s d = -0.393 in 6-month-old control; t(24) = -1.534, p = 0.069, Cohen’s d = -0.307 in 6-month-old AppNL-G-F; t(23) = -1.775, p = 0.045, Cohen’s d = -0.362 in 12-month-old control; t(24) = 0.86, p = 0.801, Cohen’s d = 0.172 in 12-monthold AppNL-G-F.
Simulation of context effect in test 3.
Estimated parameter sets of each sample were used to run the simulation that only context or context with CS was present in test 3 (trial 36). The data are shown as median with interquartile range, where white bars with colored lines represent CR for context only and colored bars represent CR for context with CS. Colors indicate different groups: orange represents 6-month-old control (n = 15), light blue represents 6-month-old AppNL-G-F mice (n = 12), pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18). Each black dot represents one animal. **p < 0.01, and ***p < 0.001 by Wilcoxon signed-rank test comparing context only and context + CS in each group, and the alternative hypothesis specifies that CR in context is not equal to CR in context with CS. Statistical results were as follows: W = 15, p = 0.008, effect size r = -0.66 in 6-month-old control; W = 0, p < 0.001, effect size r = -0.88 in 6-month-old AppNL-G-F; W = 25, p = 0.002, effect size r = -0.67 in 12-month-old control; W = 9, p = 0.002 , effect size r = -0.75 in 12-month-old AppNL-G-F.
Magnified view of wcontext and wCS in the last 3 trials in Figure 3D.
The graph format is the same as in Figure 3D. The weight for CS (wCS) and that for context (wcontext) in each latent cause across trial 34 (test 2), 35 (unsignaled shock), and 36 (test 3) in 12-month-old AppNL-G-F in Figure 3D was magnified in the upper and lower magenta box, respectively.
Posterior probability of acquisition, extinction, and after extinction latent causes in test 3.
The values within each bar indicate the mean posterior probability of acquisition latent cause (darkest shade), extinction latent cause (medium shade), and latent causes inferred after extinction (lightest shade) in test 3 over mice within genotype. Source data are the same as those used in Figure 4C–E (posterior of z).
Tables
| Reagent type (species) or resource | Designation | Source or reference | Identifiers | Additional information |
|---|---|---|---|---|
| Strain, strain background (mouse) | C57BL/6-App<tm3(NL-G-F)Tcs> (KI/KI) | https://doi.org/10.1038/nn.3697 | RRID:IMSR_RBRC06344 | Denoted as AppNL-G-F mice in this study |
| Strain, strain background (mouse) | C57BL/6J-Tg(Thy1-G-CaMP7,-DsRed2);C57BL/6-App<tm3(NL-G-F)Tcs>(KI/KI) | https://doi.org/10.1523/JNEUROSCI.0208-21.2021 | N/A | Denoted as AppNL-G-F mice in this study |
| Strain, strain background (mouse) | C57BL/6JmsSIc | SLC Japan | RRID:IMSR_JAX:000664 | Denoted as control in this study |
| Strain, strain background (mouse) | C57BL/6J-Tg(Thy1-G-CaMP7,-DsRed2) | https://doi.org/10.1523/JNEUROSCI.0208-21.2021 | N/A | Denoted as control in this study |
| Software, algorithm | MATLAB R2022a, R2023a | MathWorks Inc, MA, US | RRID:SCR_001622 | Simulation and parameter estimation; Barnes maze results analysis; http://www.mathworks.com/ |
| Software, algorithm | LabVIEW 2013 | National Instruments, TX, US | RRID:SCR_014325 | Barnes maze experiment; http://www.ni.com/labview/ |
| Software, algorithm | QuickNII | https://doi.org/10.1371/journal.pone.0216796 | RRID:SCR_016854 | IHC image analysis; https://www.nitrc.org/projects/quicknii |
| Software, algorithm | VisuAlign | N/A | RRID:SCR_017978 | IHC image analysis; https://www.nitrc.org/projects/visualign |
| Software, algorithm | Ilastik | https://doi.org/10.1038/s41592-019-0582-9 | RRID:SCR_015246 | IHC image analysis; https://www.ilastik.org/ |
| Software, algorithm | Nutil v0.8.0 | https://doi.org/10.3389/fninf.2020.00037 | RRID:SCR_017183 | IHC image analysis; https://nutil.readthedocs.io/en/latest/ |
| Software, algorithm | JASP 0.18.3.0 | JASP team, 2024 | RRID:SCR_015823 | Statistical analysis; https://jasp-stats.org/ |
| Software, algorithm | Python 3.11.5 | N/A | RRID:SCR_008394 | Visualization; https://www.python.org/ |
| Antibody | anti-β-Amyloid (mouse monoclonal) | Biolegend | Cat # 803001, RRID:AB_2564653 | 1:1000 |
| Antibody | anti-GFAP (rat monoclonal) | Invitrogen | Cat # 13–0300, RRID:AB_2532994 | 1:1000 |
| Antibody | anti-Iba1 (rabbit polyclonal) | FUJIFILM Wako Pure Chemical Corporation | Cat # 019–19741, RRID:AB_839504 | 1:1000 |
| Antibody | Alexa Fluor 488 Donkey Anti-Rat IgG (H+L) Antibody | Molecular probes | A21208, RRID:AB_2535794 | 1:500 |
| Antibody | Alexa Fluor 568 Donkey Anti-Mouse IgG (H+L) Antibody | Molecular probes | A10037, RRID:AB_11180865 | 1:500 |
| Antibody | Alexa Fluor 647 Donkey Anti-Rabbit IgG (H+L) Antibody | Molecular probes | A31573, RRID:AB_2536183 | 1:500 |
The initial value, lower bound, and upper bound of parameters in slice sampling in the latent state model.
| Description | Parameters | Initial value | Lower bound | Upper bound |
|---|---|---|---|---|
| learning rate for associative strength | α0 | 0.05 | 0.005 | 0.1 |
| learning rate for variance | α1 | 0.06 | 0.005 | 0.5 |
| learning rate for covariance | α2 | 0.04 | 0.005 | 0.5 |
| transition probability between states | γ | 0.1 | 0.01 | 1 |
| maximum number of latent states | ncop | 15 | 1 | 36 |
| threshold to activate new state | η | 2.5 | 0.01 | 3.05 |
| number of rumination updates | χ | 5 | 1 | 10 |
| initial standard deviation | σ0 | 0.5 | 0.1 | 1 |
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Note. τ and δ were fixed at 10 and 0.6, respectively, in the present simulation.
The initial value, lower bound, and upper bound of parameters in slice sampling.
| Parameters | Initial value | Lower bound | Upper bound |
|---|---|---|---|
| α | 1.5 | 1 | 3 |
| g | 1 | 0.01 | 2 |
| η | 0.1 | 0.01 | 1 |
| maxIter* | 3 | 1 | 5 |
| w0 | 0 | –0.01 | 0.01 |
| σr2 | 0.4 | 0.01 | 3 |
| σx2 | 1 | 0.01 | 3 |
| θ | 0.01 | 0.002 | 0.02 |
| λ | 0.01 | 0.002 | 0.02 |
| K | 33 | 1 | 36 |
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*
max. no. of iterations.
Effect of α and η on test trials conditioned response (CR), number of latent causes, and test 3 internal states.
| α | η | Test 1 | Test 2 | Test 3 | Kacq | Kext | Krem | Test 3 | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pacq | Pext | Prem | wcontext, acq | wcontext, ext | wcontext, rem | ||||||||
| 1 | 0.01 | 0.78 | 0.18 | 0.19 | 2 | 2 | 1 | 0.026 | 0.477 | 0.497 | 0.010 | 0.006 | 0.000 |
| 1 | 0.5 | 1.00 | 0.64 | 0.93 | 2 | 2 | 1 | 0.017 | 0.482 | 0.502 | 0.147 | 0.288 | 0.000 |
| 3 | 0.01 | 0.19 | 0.17 | 0.18 | 3 | 30 | 0 | 0.043 | 0.957 | 0.000 | 0.010 | 0.006 | 0.000 |
| 3 | 0.5 | 1.00 | 0.49 | 1.00 | 2 | 30 | 1 | 0.049 | 0.863 | 0.089 | 0.155 | 0.049 | 0.243 |
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Note. This table is used for the reply to reviewer comment #14. The fixed parameter value: g = 1, max. no. of iteration = 3, w0 = 0, σr2 = 0.4, σx2 = 1, θ = 0.01, λ = 0.01, K = 33. Test 1, Test 2, Test 3: the simulated CR in each test. Kacq, Kext, Krem: the number of latent causes inferred during acquisition phases, extinction phases, and the remaining trials. Pacq, Pext, Prem: the posterior probability of latent causes inferred during acquisition phases, extinction phases, and the remaining trials in test 3. wcontext, acq, wcontext, ext, wcontext, rem: the associative weight between context and US in the latent causes inferred during acquisition phases, extinction phases, and the remaining trials in test 3.
Effect of w0, θ, and λ on conditioned response (CR) at each trial in the acquisition phase.
| w0 | θ | λ = 0.01 | λ = 0.02 | ||||
|---|---|---|---|---|---|---|---|
| Trial 1 | Trial 2 | Trial 3 | Trial 1 | Trial 2 | Trial 3 | ||
| –0.01 | 0.002 | 0.080757 | 0.999969 | 1 | 0.241964 | 0.977479 | 1 |
| 0 | 0.002 | 0.42074 | 1 | 1 | 0.460172 | 0.994947 | 1 |
| 0.01 | 0.002 | 0.841345 | 1 | 1 | 0.691462 | 0.999156 | 1 |
| –0.01 | 0.01 | 0.013903 | 0.999333 | 1 | 0.135666 | 0.945672 | 0.999999 |
| 0 | 0.01 | 0.158655 | 0.999993 | 1 | 0.308538 | 0.98508 | 1 |
| 0.01 | 0.01 | 0.57926 | 1 | 1 | 0.539828 | 0.996929 | 1 |
| –0.01 | 0.02 | 0.000687 | 0.986396 | 1 | 0.054799 | 0.865261 | 0.999994 |
| 0 | 0.02 | 0.02275 | 0.999588 | 1 | 0.158655 | 0.952757 | 1 |
| 0.01 | 0.02 | 0.211855 | 0.999996 | 1 | 0.344578 | 0.987459 | 1 |
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Note. This table is used for the reply to reviewer comment #26. The fixed parameter value: α = 1.5, g = 1, η = 0.1, max. no. of iteration = 3, σr2 = 0.4, σx2 = 1, K = 33
Effect of α and g on the number of latent causes inferred at each phase.
| α | g | Kacq | Kext | Krem |
|---|---|---|---|---|
| 1 | 0.01 | 2 | 0 | 0 |
| 2 | 0.01 | 2 | 0 | 0 |
| 1 | 1 | 2 | 2 | 1 |
| 2 | 1 | 2 | 30 | 1 |
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Note. This table is used for the reply to reviewer comment #29. The fixed parameter value: η = 0.1, max. no. of iteration = 3, w0 = 0, σr2 = 0.4, σx2 = 1, θ = 0.01, λ = 0.01, K = 33. Kacq, Kext, Krem: the number of latent causes inferred during acquisition phases, extinction phases, and the remaining trials.
Variance inflation factor of each parameter.
| Parameter | Variance inflation factor | |
|---|---|---|
| 6-month-old group | 12-month-old group | |
| α | 3.368 | 3.420 |
| g | 2.966 | 1.472 |
| η | 3.941 | 1.370 |
| maxIter* | 1.878 | 1.373 |
| w0 | 2.232 | 1.644 |
| σr2 | 2.292 | 1.610 |
| σx2 | 2.240 | 3.343 |
| θ | 2.579 | 1.547 |
| λ | 1.431 | 1.923 |
| K | 1.612 | 2.789 |
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Note. This table is used for the reply to reviewer comment #31.
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*
max. no. of iterations.
The joint effect of K, α, and σx2 on conditioned responses (CRs) (test 1 and 3), discrimination index (DI) (test 3 vs. test 1), and the number of latent causes.
| K | α | σx2 | Test 1 | Test 3 | DI (test 3 vs test 1) | Kacq | Kext | Krem |
|---|---|---|---|---|---|---|---|---|
| 4 | 1 | 0.01 | 1.00 | 0.34 | 0.26 | 2 | 0 | 1 |
| 1 | 3 | 1.00 | 0.81 | 0.45 | 2 | 2 | 0 | |
| 3 | 0.01 | 1.00 | 0.35 | 0.26 | 2 | 0 | 1 | |
| 3 | 3 | 0.42 | 0.74 | 0.64 | 3 | 1 | 0 | |
| 36 | 1 | 0.01 | 1.00 | 0.34 | 0.26 | 2 | 0 | 1 |
| 1 | 3 | 1.00 | 0.34 | 0.26 | 2 | 3 | 2 | |
| 3 | 0.01 | 1.00 | 0.35 | 0.26 | 2 | 0 | 1 | |
| 3 | 3 | 0.42 | 0.19 | 0.31 | 3 | 31 | 2 |
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Note. This table is used for the reply to reviewer comment #31. The fixed parameter value: g = 1, η = 0.1, max. no. of iteration = 3, w0 = 0, σr2 = 0.4, θ = 0.01, λ = 0.01. Test 1, Test 3: the simulated CR. Kacq, Kext, Krem: the number of latent causes inferred during acquisition phases, extinction phases, and the remaining trials.
Effect of w0 on conditioned response (CR) in test trials and number of latent causes.
| w0 | Test 1 | Test 2 | Test 3 | Kacq | Kext | Krem |
|---|---|---|---|---|---|---|
| –0.01 | 1 | 0.22 | 0.13 | 2 | 2 | 1 |
| –0.005 | 1 | 0.27 | 0.24 | 2 | 2 | 1 |
| 0 | 1 | 0.32 | 0.37 | 2 | 2 | 1 |
| 0.005 | 1 | 0.38 | 0.52 | 2 | 2 | 1 |
| 0.01 | 1 | 0.44 | 0.66 | 2 | 2 | 1 |
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Note. This table is used for the reply to reviewer comment #33. The fixed parameter value: α = 1.5, g = 1, η = 0.1, max. no. of iteration = 3, σr2 = 0.4, σx2 = 1, θ = 0.01, λ = 0.01, K = 33. Test 1, Test 2, Test 3: the simulated CR in each test. Kacq, Kext, Krem: the number of latent causes inferred during acquisition phases, extinction phases, and the remaining trials.
Additional files
-
Supplementary file 1
Tables corresponding to the statistical results.
- https://cdn.elifesciences.org/articles/105347/elife-105347-supp1-v1.docx
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MDAR checklist
- https://cdn.elifesciences.org/articles/105347/elife-105347-mdarchecklist1-v1.docx
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Appendix 1—figure 1—source data 1
Data shown in Appendix 1—figure 1.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig1-data1-v1.xlsx
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Appendix 1—figure 2—source data 1
Data shown in Appendix 1—figure 2.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig2-data1-v1.xlsx
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Appendix 1—figure 3—source data 1
Data shown in Appendix 1—figure 3.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig3-data1-v1.xlsx
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Appendix 1—figure 4—source data 1
Data shown in Appendix 1—figure 4.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig4-data1-v1.xlsx
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Appendix 1—figure 5—source data 1
Data shown in Appendix 1—figure 5.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig5-data1-v1.xlsx
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Appendix 1—figure 6—source data 1
Data shown in Appendix 1—figure 6.
- https://cdn.elifesciences.org/articles/105347/elife-105347-app1-fig6-data1-v1.xlsx