Article Figures & Data
Figures
- Figure 1.
Schematic depictions of the state-space analysis in the regression subspace. The state-space analysis in the regression subspace provides the neural dynamics for activity modulations. In a particular experimental condition, neural population activity composed of multiple neurons is modulated by the task variables [e.g., location (L1, L2) and stimulus (S1, S2; left)]. By applying PCA (principal component analysis) for neural modulations (left), predominant components of the neural modulations are extracted (middle) and depicted as the neural trajectory (right). Typical examples of neural population structures observed previously are straight, curvy, and rotational structures. imp/s indicates impulse per second. PC1 to 3 indicates first to third principle components, respectively.
- Figure 2.
Behavioral task and recording location of neurons. A, The sequence of events during the single-cue task in Exp. 1. A single visual pie chart containing green and blue pie segments was presented to the monkeys. Neural activity was analyzed during the initial 0.6 s after cue onset, that is, for the same duration as in Exp. 2. B, Payoff matrix: each of the magnitudes was fully crossed with each probability resulting in a pool of 100 lotteries. C, Illustration of neural recording areas based on coronal magnetic resonance (MR) images for the cOFC (13 M, medial part of area 13) at the A31–A34 anterior–posterior level. D, The sequence of events during the ILR task in Exp. 2. The cue stimulus during the response phase was the same as the sample stimulus during the encoding phase in the match trial, whereas the two stimuli differed in the nonmatch trial. Neural activity was analyzed during the initial 0.6 s after sample onset, that is, for the same duration as in Exp. 1. E, Six visual item stimuli and spatial composition for the sample stimulus. F, Coronal MR images from monkey A for the HPC population showing the recording area at A16–A10.5, depicted in purple within the red box. A was published previously in the study by Yamada et al. (2021). D–F was published previously in the study by Chen and Naya (2020).
- Figure 3.
Example activity of neurons during the single-cue and ILR tasks. A, An example activity histogram of a cOFC neuron modulated by the probability and magnitude of rewards during the single-cue task. Activity aligned with cue onset is represented for three different levels of probability (P, 0.1–0.3, 0.4–0.7, 0.8–1.0) and magnitude (M, 0.1–0.3 ml, 0.4–0.7 ml, 0.8–1.0 ml) of rewards. Gray hatched areas indicate the 1 s time window used to estimate the neural firing rates shown in B. Histograms smoothed using a Gaussian kernel (σ = 50 ms). B, An activity plot of the cOFC neuron during the 1 s time window shown in A against the probability and magnitude of rewards. C, The percentage of neural modulation types detected in 1 s time window shown in A: the P, M, Both, and NO. D, Percentages of neural modulation type detected in the 0.02 s time bins during the 1.0 s after cue onset. Calibration: 0.2 s. E, Regression coefficient plots for the probability and magnitude of rewards estimated for all cOFC neurons in Exp. 1. Regression coefficients in the 0.02 s time bin shown every 0.1 s during the 0.6 s after cue onset (0–0.02 s, 0.10–0.12 s, 0.20–0.22 s, 0.30–0.32 s, 0.40–0.42 s, 0.50–0.52 s, and 0.58–0.60 s). Filled gray indicates significant regression coefficient for either Probability or Magnitude at p < 0.05. F, An example of an HPC neuron showing sample-triggered sample–location signals and item signals. A 0.08–1.0 s time window after sample onset was used to estimate the neural firing rates shown in G. Histograms are smoothed using a Gaussian kernel (σ = 20 ms). G, An activity plot of the HPC neuron during the time window shown in F against item and location. H, The percentage of neural modulation types detected in the 0.08–1.0 s window shown in F; Item, Location, Both, and NO. I, Percentages of neural modulation types detected in the 0.02 s time bins during the 1.0 s after sample onset. J, Regression coefficient plots for the best and worst items estimated for all HPC neurons in Exp. 2. Filled gray indicates significant regression coefficient for item at p < 0.05 using ANOVA without interaction term. The location modulation was not shown because we showed changes of neural modulation by the sample stimulus, whereas the location had already been provided to the monkeys. A, B, and D were published previously in the study by Yamada et al. (2021).
- Figure 4.
Graphic methods for the conventional rate-coding analysis and state-space analysis in the regression subspace. Conventional analysis (top and middle rows): in each single neuron, activity modulations by task variables are detected in the fixed time window (top row) using linear regression and ANOVA for continuous (left, Exp. 1) and categorical (right, Exp. 2) task parameters (Fig. 2, see for the task details), respectively. The same analyses were applied in a fine time resolution in Exp. 1 and Exp. 2 (middle row). The conventional analyses using a general linear model (linear regression and ANOVA) provide the extent of neural modulations as the coefficients in the analysis table of the statistical software. These are neural modulations in a fine time resolution observed at the level of population. i represents the number of neurons in each neural population (Exp. 1, 190 neurons; Exp. 2, 590 neurons). t represents the number of time bins (30 for both Exp. 1 and Exp. 2). In our state-space analysis as step 1, the time series of neural population activity was projected onto a regression subspace composed of probability and magnitude (left, Exp. 1) and item and location (right, Exp. 2). The middle row, therefore, represents the neural population activity in the regression subspace X. By applying PCA to X, eigenvectors for probability and magnitude were extracted and plotted after coordinate transformation against PC1 and PC2 (step 2, left, Exp. 1). Eigenvectors for item and location were plotted after coordinate transformation against PC1 and PC2 (right, Exp. 2). A series of eigenvectors was obtained by applying PCA once to the cOFC and HPC populations, respectively. The number of eigenvectors obtained by PCA was 0.6 s, divided by the analysis window size, 0.02 s, for P and M; in total, 30 eigenvectors for each (left, Exp. 1), and for the six items and four locations; in total, 30 eigenvectors for each. Extended Data Figure 4-1 represents detail of the vector analyses.
- Figure 5.
The state-space analysis provides a temporal structure of neural modulation in the cOFC. A, Cumulative variance explained by PCA in the cOFC population. The arrowhead indicates the percentage of variance explained by PC1 and PC2. B, Time series of eigenvectors, PC1 to PC3 in the cOFC population. C, A series of eigenvectors for PC1 to PC3 are plotted against PC1 and PC2, and PC2 and PC3 dimensions in the cOFC population. Plots at the beginning and end of the series of vectors are labeled as start (s) and end (e), respectively. a.u., Arbitrary unit.
- Figure 6.
Temporal structure of neural modulation in the HPC population. A, Cumulative variance explained by PCA in the HPC population. The arrowhead indicates the percentages of variances explained by PC1 and PC2. B, Time series of eigenvectors for six items in the HPC population. The top three PCs are shown. C, Time series of eigenvectors for four locations. D, A series of eigenvectors for PC1 to PC3 are plotted against PC1 and PC2, and PC2 and PC3 dimensions in the HPC population. a.u., Arbitrary unit. Extended Data Figure 6-1 represents shuffled control results.
- Figure 7.
Effects of preference ordering on the HPC categorical data. A, Three examples of HPC neurons for preference ordering. The activities were ordered by their preference to the items and locations (right, shown best to worst), while their activity have a preference to item or location during the 0.08–0.6 s after sample presentation. B, Cumulative variance explained by PCA in the HPC population when item and location were arranged in the order of their activity preferences (see Materials and Methods). The arrowhead indicates the percentages of variances explained by PC1 and PC2. C, Series of eigenvectors for PC1 to PC3 when item and location were arranged in the order of their preferences, plotted against the PC1 and PC2, and PC2 and PC3 dimensions in the HPC population. Ib and Iw indicate the best and worst items, respectively. I2 to I5 indicate the second to fifth best items. Lb and Lw indicate the best and worst locations, respectively. L2 and L3 indicate the second and third best locations, respectively. NA, No significant difference using ANOVA at p < 0.05. *p < 0.05, ***p < 0.001. Extended Data Figure 7-1 represents results for optimal response analysis.
- Figure 8.
Quantitative evaluations of eigenvector properties in the cOFC and HPC populations. A, Time series of vector size estimated in the cOFC population for P and M of rewards. Vector sizes are estimated in the PC1–PC2 plane (top) and PC2–PC3 plane (bottom), respectively. a.u., Arbitrary unit. The solid-colored lines indicate interpolated lines using a cubic spline function to provide a resolution of 0.005 s. B, Time series of vector size estimated in the HPC population for the best and worst items. C, Boxplots of vector size estimated in the cOFC population for probability and magnitude of rewards. D, Boxplots of vector size in the HPC population for the best and worst items and locations. E, F, Boxplots of vector angle estimated in the cOFC (E) and HPC (F) populations. G, H, Boxplots of vector deviance from the mean estimated in the cOFC (G) and HPC (H) populations. In C–H, data after 0.1 s are used. *p < 0.05, ***p < 0.001.
- Figure 9.
Thematic depiction of the difference between dPCA and PCArs. Illustration of the procedure to construct the neural population dynamics by dPCA and ours (PCArs). dPCA decomposes the neural activity into the dynamics as a linear summation of the multiple components for categorical variables (Kobak et al., 2016). Our method first projects the neural population dynamics into a regression subspace that removes the activity change other than the neural modulations by task parameters and demonstrates the modulation dynamics. dPCA figures are represented in the study by Kobak et al. (2016, their Fig. 8). PSTH indicates peristimulus time histogram.
Extended Data
Figure 4-1
Schematic depictions of eigenvector evaluations. Characteristics of the eigenvectors evaluated quantitatively. Angle, vector angle from the horizontal axis obtained from –180° to 180°; Size, eigenvector length; Deviance, difference between vectors. Download Figure 4-1, file.
Figure 6-1
Explained variances by PCA in shuffled controls. A, A boxplot of explained variances by PCA for PC1 to PC6 for the cOFC population under the three shuffled conditions (for details, see Materials and Methods). The plot is not cumulative. The boxplot was made with 1000 repeats of the shuffle in each condition. B, A boxplot of explained variances by PCA for PC1 to PC12 for the HPC population. In A and B, the colored circles indicate variances explained by PCA in each neural population without the shuffles. C, Examples of a series of eigenvectors for PC1 to PC2, plotted in the cOFC population under the three shuffle conditions. D, Examples of a series of eigenvectors for PC1 to PC2, plotted in the HPC population under the three shuffle conditions. Download Figure 6-1, file.
Figure 7-1
Optimal response analysis in the HPC population. A, Cumulative variance explained by PCA in the HPC population when the best and worst conditions for item and location were used for the regression subspace. The gray dots indicate the percentage variance explained by PCA upon using the full matrix. The first 12 PCs are shown. B, Time series of the eigenvectors for PC1 to PC3 when the best and worst items and locations were used. Ib and Iw indicate the best and worst items, respectively. Lb and Lw indicate the best and worst locations, respectively. s and e indicate the start and end of the time series of vectors, respectively. C, A boxplot of explained variances by PCA for PC1 to PC12 under the three shuffled conditions (for details, see Materials and Methods). The plot is not cumulative. The boxplot was made with 1000 repeats of the shuffle in each condition. The colored circles indicate the variances explained by PCA in the HPC population without the shuffles. Download Figure 7-1, file.
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