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 (s ¼ 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 (s ¼ 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).

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... actual data and require the user to precisely understand these elaborate procedures involving complex multistep mathematical processes ( Kobak et al., 2016;Aoi et al., 2020). Although these analytical tools describe the temporal structure of neural modulation as a latent component in the multidimensional neural space ( Kobak et al., 2016, their Fig. 3B; Aoi et al., 2020, their Fig. 3A) the extracted modulation structures do not simply correspond to the results from the rate-coding analyses. Thus, it is worthwhile to develop a simple, user-friendly method to extract temporal structures of neural modulations that are compatible with the rate-coding ...

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... to precisely understand these elaborate procedures involving complex multistep mathematical processes ( Kobak et al., 2016;Aoi et al., 2020). Although these analytical tools describe the temporal structure of neural modulation as a latent component in the multidimensional neural space ( Kobak et al., 2016, their Fig. 3B; Aoi et al., 2020, their Fig. 3A) the extracted modulation structures do not simply correspond to the results from the rate-coding analyses. Thus, it is worthwhile to develop a simple, user-friendly method to extract temporal structures of neural modulations that are compatible with the rate-coding ...

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... 2; see Materials and Methods). In Exp. 1, we examined how the probability and magnitude of rewards were encoded and integrated by the activity of OFC neurons immediately after cue presentation. Linear regression analysis revealed that cOFC neurons encode both probability and magnitude to some extent after cue onset, as shown in an example neuron (Fig. 3A,B; n ¼ 119 trials; coefficient/intercept: À0.74; t ¼ À0.72, p ¼ 0.47; probability: 8.55, t ¼ 6.91, p , 0.001; magnitude: 11.1, t ¼ 8.95, p , 0.001). In the cOFC populations, approximately half of the neurons were modulated by the probability and magnitude of rewards during the 1 s time window (0-1 s after cue onset; probability: 44%, 84 ...

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... p , 0.001; magnitude: 11.1, t ¼ 8.95, p , 0.001). In the cOFC populations, approximately half of the neurons were modulated by the probability and magnitude of rewards during the 1 s time window (0-1 s after cue onset; probability: 44%, 84 of 190; magnitude: 49%, 94 of 190). Modulations for either or both probability and magnitude were found ( Fig. 3C; Both: 30%, 57 of 190; P: 14.2%, 27 of 190; M: 19.5%, 37 of 190; Nonmodulated (NO): 36.3%, 69 of 190). The analysis with 0.02 s time bins showed that the percentage of neurons modulated by these two parameters increased, reached a maximum percentage at ;0.25 s, and then gradually decreased during the 1.0 s after the onset of the ...

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... 3C; Both: 30%, 57 of 190; P: 14.2%, 27 of 190; M: 19.5%, 37 of 190; Nonmodulated (NO): 36.3%, 69 of 190). The analysis with 0.02 s time bins showed that the percentage of neurons modulated by these two parameters increased, reached a maximum percentage at ;0.25 s, and then gradually decreased during the 1.0 s after the onset of the lottery cue (Fig. ...

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... item and location after the sample presentation. The analyses were aimed at examining how the item information was encoded and integrated with the location information by the neurons immediately after the sample presentation. ANOVA revealed that HPC neurons encoded both item and location information to some extent, as shown in an example neuron (Fig. 3F,G; two-way ANOVA, n ¼ 120 trials; item: F (5,96) ¼ 52.1, p , 0.0001; location: F (3,96) ¼ 4.4, p ¼ 0.006). In the HPC population, neurons were modulated by these two factors (0.08-1 s after sample onset; Item, 39%, 232 of 590; Location, 39%, 233 of 590). Modulations for either or both factors were found ( Fig. 3H; Both: 23%, 138 of 590; ...

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... as shown in an example neuron (Fig. 3F,G; two-way ANOVA, n ¼ 120 trials; item: F (5,96) ¼ 52.1, p , 0.0001; location: F (3,96) ¼ 4.4, p ¼ 0.006). In the HPC population, neurons were modulated by these two factors (0.08-1 s after sample onset; Item, 39%, 232 of 590; Location, 39%, 233 of 590). Modulations for either or both factors were found ( Fig. 3H; Both: 23%, 138 of 590; Item: 16%, 95 of 590; Location: 16%, 94 of 590; NO: 45%, 263 of 590). The analysis with the 0.02 s time bins showed that the percentage of neurons modulated by these two factors increased, reached a maximum percentage at ;0.25 s, and then gradually decreased during the 1.0 s after the onset of the sample ...

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... ( Fig. 3H; Both: 23%, 138 of 590; Item: 16%, 95 of 590; Location: 16%, 94 of 590; NO: 45%, 263 of 590). The analysis with the 0.02 s time bins showed that the percentage of neurons modulated by these two factors increased, reached a maximum percentage at ;0.25 s, and then gradually decreased during the 1.0 s after the onset of the sample stimulus (Fig. 3I). We note that the percentage of neural modulation by the presented location did not change with time because the monkeys already knew the item location before the sample presentation (Fig. 3I, see blue), whereas the percentage change in neural modulations was because of an increase in item information (Fig. 3I, see green). Thus, for ...

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... these two factors increased, reached a maximum percentage at ;0.25 s, and then gradually decreased during the 1.0 s after the onset of the sample stimulus (Fig. 3I). We note that the percentage of neural modulation by the presented location did not change with time because the monkeys already knew the item location before the sample presentation (Fig. 3I, see blue), whereas the percentage change in neural modulations was because of an increase in item information (Fig. 3I, see green). Thus, for both neural populations, typical changes in neural modulation were observed as a percentage increase, followed by a decrease after visual stimulus onset in the conventional ...

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... the onset of the sample stimulus (Fig. 3I). We note that the percentage of neural modulation by the presented location did not change with time because the monkeys already knew the item location before the sample presentation (Fig. 3I, see blue), whereas the percentage change in neural modulations was because of an increase in item information (Fig. 3I, see green). Thus, for both neural populations, typical changes in neural modulation were observed as a percentage increase, followed by a decrease after visual stimulus onset in the conventional ...

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... then examined a regression coefficient that describes the extent of neural modulations in each neural population. In Exp. 1, the regression coefficients for the probability and magnitude of rewards in the case of continuous variables were visualized in the cOFC population (Fig. 3E). The extent of neural modulations increased between 0.2 and 0.4 s after cue onset, as seen in the larger positive or smaller negative regression coefficients for probability and magnitude. For the categorical parameters in Exp. 2, we plotted the regression coefficients represented in the ANOVA table for the best and worst items ...

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... as seen in the larger positive or smaller negative regression coefficients for probability and magnitude. For the categorical parameters in Exp. 2, we plotted the regression coefficients represented in the ANOVA table for the best and worst items detected in each neuron because we mainly focused on the neural modulation by the visual item ( Fig. 3J; data not shown for all visual items). The distribution of coefficients for the best items seemed to be wider at 0.2-0.5 s (see xaxis, especially larger positive values), compared with that just after the sample onset (0-0.02 s plots within a range of À20 to 20). Thus, for both neural populations, an increase in neural modulation was ...

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... step captures the across-trial variance caused by task-related parameters moment-by-moment at a population level, which demonstrates the extent of neural modulations by the task parameters across time. This corresponds to the estimation of the regression coefficients shown in Figure 3, E and J (for all time bins and conditions), which constructs the regression matrices detected in each neural population with a fine time resolution (Fig. 4, middle row, step 1, X). Second, we applied PCA one time to the time series of neural activity in the regression subspace in each neural population (Fig. 4, bottom row, step 2). ...

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... consistent with our previous results even when the analysis window sizes differed: a whole cue period of 2.7 s previously, but here, only the initial 0.6 s were analyzed ( Yamada et al., 2021, their Fig. 7B). These straight geometric changes (i.e., stable vectors in angle) indicate that almost equal neural modulations by probability and magnitude (Fig. 3E) evolved across the 0.6 s time period at the neural population level. Thus, the two neural modulation ratios were kept ...

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... only explained ;10% of the variance (Fig. 6A, gray arrowhead). Because the percentage of modulated neurons was similar between the two neural populations (Fig. 3C,H), this would not be because of the weaker influence of task parameters in Exp. 2 on the recorded HPC population. This may be partly because of the larger regression matrix composed of 10 vectors at each time point (six items and four locations) and a larger neural population containing 590 neurons: total X of size N (590) Â M (300) , ...

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... eigenvectors in the first three PCs appeared to describe neural population dynamics in the HPC. For example, the extracted eigenvectors for each visual item evolved within a reasonable range of time with an increase and a subsequent decrease at ;0.2-0.5 s (Fig. 6B), which is consistent with our findings using typical conventional analyses, ANOVA (Fig. 3H,I). In contrast, the eigenvectors for locations did not exhibit clear trends over time (Fig. 6C), as location information was provided to the monkeys before the sample presentations. This is also consistent with our findings using ANOVA, in which percentages modulated by locations did not change over time (Fig. 3I, blue). If we plotted ...

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... conventional analyses, ANOVA (Fig. 3H,I). In contrast, the eigenvectors for locations did not exhibit clear trends over time (Fig. 6C), as location information was provided to the monkeys before the sample presentations. This is also consistent with our findings using ANOVA, in which percentages modulated by locations did not change over time (Fig. 3I, blue). If we plotted eigenvectors in the space of the first three PCs, they consistently evolved in one direction in the PC1 and PC2 spaces (I2, I3, and I6), or PC3 spaces (I1, I4, and I5; Fig. 6D, left). In contrast, the eigenvectors for locations were positioned in a constant location over time (Fig. 6D, top right). Unambiguously, the ...

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... the arrangements of the eigenvectors for item and location were orthogonalized, as seen in item representations in the second and fourth quadrants and in location representations in the first and third quadrants (Fig. 6D, top row). The increase and subsequent decrease in vector sizes at ;0.2-0.5 s were similar to those in the neural modulations (Fig. 3J). Thus, our state-space analysis in the regression subspace may capture the neural modulation dynamics in HPC populations similar to that in cOFC populations, while reflecting continuous and categorical parameters in their neural ...

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... to PC2, item: n ¼ 52, df ¼ 51, W ¼ 502, p ¼ 0.002; PC2 to PC3, item: n ¼ 52, df ¼ 51, W ¼ 588, p , 0.001; PC1 to PC2, location: n ¼ 52, df ¼ 51, W ¼ 600, p , 0.001; PC2 to PC3, location: n ¼ 52, df ¼ 51, W ¼ 542, p , 0.001). This is because the regression coefficients for the best item were considerably different from their mean neural modulation (Fig. 3J, x-axis) in contrast to those for the worst item (y-axis). Thus, the vector sizes captured temporal changes in neural modulation at the population level, which is consistent with the results obtained from the rate-coding analyses (Fig. ...

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... the regression coefficients for the best item were considerably different from their mean neural modulation (Fig. 3J, x-axis) in contrast to those for the worst item (y-axis). Thus, the vector sizes captured temporal changes in neural modulation at the population level, which is consistent with the results obtained from the rate-coding analyses (Fig. ...

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... subspace described neural modulation dynamics in the cOFC and HPC during two different cognitive tasks composed of continuous and categorical parameters. These dynamic structures, evaluated qualitatively (Figs. 5-7) and quantitatively ( Fig. 8), reflected the neural modulation properties described by the conventional rate-coding analyses (Fig. 3). The straight dynamics observed in both cOFC and HPC populations were captured by a combination of changes in vector size and stable vector angle across time, which cannot be captured by the conventional rate-coding ...

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... for item and location in line with the rate-coding analysis. These analyses showed that straight dynamics were derived from the optimal and nonoptimal activity of neurons (Fig. 7C, Extended Data Fig. 7-1B). In the rate-coding analysis, the time course of neural modulation by item and location was observed in the percentages of modulated neurons (Fig. 3I) and in the magnitudes of regression coefficients (Fig. 3J). In the dynamic analysis, these characteristics were observed on the time course of the vector size (Fig. 8A,B), while the neural modulation structures were evaluated in terms of their similarity across time. Thus, the classical rate-coding analysis was well incorporated into ...

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... These analyses showed that straight dynamics were derived from the optimal and nonoptimal activity of neurons (Fig. 7C, Extended Data Fig. 7-1B). In the rate-coding analysis, the time course of neural modulation by item and location was observed in the percentages of modulated neurons (Fig. 3I) and in the magnitudes of regression coefficients (Fig. 3J). In the dynamic analysis, these characteristics were observed on the time course of the vector size (Fig. 8A,B), while the neural modulation structures were evaluated in terms of their similarity across time. Thus, the classical rate-coding analysis was well incorporated into the dynamic analyses, which specifically captured their ...

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... consisted of separately recorded single-neuron activities after visual stimulus presentations, and we extracted both neural modulation dynamics using an original state-space analysis. These straight geometries with unidimensional features of neural modulations indicated that modulation structures by task parameter remained similar across time (Fig. 3E,J). We would like to caution researchers against using nonmodulated task parameters in PCA (i.e., task parameters that show minimal neural modulation), as the PCs derived in such cases were less biologically meaningful (Björklund, 2019). Our simple extractions of neural modulation dynamics indicate that all types of data can be easily ...