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Minimally dependent activity subspaces for working memory and motor preparation in the lateral prefrontal cortex

  1. Cheng Tang
  2. Roger Herikstad
  3. Aishwarya Parthasarathy
  4. Camilo Libedinsky  Is a corresponding author
  5. Shih-Cheng Yen  Is a corresponding author
  1. Institute of Molecular and Cell Biology, A*STAR, Singapore
  2. The N1 Institute for Health, National University of Singapore (NUS), Singapore
  3. Department of Psychology, NUS, Singapore
  4. Innovation and Design Programme, Faculty of Engineering, NUS, Singapore
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Cite this article as: eLife 2020;9:e58154 doi: 10.7554/eLife.58154

Abstract

The lateral prefrontal cortex is involved in the integration of multiple types of information, including working memory and motor preparation. However, it is not known how downstream regions can extract one type of information without interference from the others present in the network. Here, we show that the lateral prefrontal cortex of non-human primates contains two minimally dependent low-dimensional subspaces: one that encodes working memory information, and another that encodes motor preparation information. These subspaces capture all the information about the target in the delay periods, and the information in both subspaces is reduced in error trials. A single population of neurons with mixed selectivity forms both subspaces, but the information is kept largely independent from each other. A bump attractor model with divisive normalization replicates the properties of the neural data. These results provide new insights into neural processing in prefrontal regions.

Introduction

Complex flexible behaviors require the integration of multiple types of information, including information about sensory properties, task rules, items held in memory, items being attended, actions being planned, and rewards being expected, among others. A large proportion of neurons in the lateral prefrontal cortex (LPFC) encode a mixture of two or more of these types of information (Rigotti et al., 2013; Parthasarathy et al., 2017; Masse et al., 2019; van Ede et al., 2019; Marcos et al., 2019). This mixed selectivity endows the LPFC with a high-dimensional representational space (Rigotti et al., 2013), but it also presents the challenge of understanding how downstream regions that receive mixed-selective input from the LPFC can read out meaningful information. One possible solution would be to have multiple low-dimensional information subspaces, embedded within the high-dimensional state space of LPFC, which could enable the independent readout of different types of information with minimal interference from changes of information in other subspaces (Remington et al., 2018; Parthasarathy, 2019; Semedo et al., 2019; Mante et al., 2013; Wolff et al., 2019; Druckmann and Chklovskii, 2012). Information subspaces have been identified in the medial frontal cortex (Wang et al., 2018), lateral prefrontal cortex (Parthasarathy, 2019), early visual areas (Semedo et al., 2019), and motor cortex (Kaufman et al., 2014; Elsayed et al., 2016). However, no studies to date have explicitly tested whether information about two separate cognitive processes can be simultaneously encoded in subspaces within a single biological neural network. Here, we demonstrate the existence of two minimally dependent information subspaces in the LPFC network: (1) a working memory subspace in which target information emerged in Delay 1, and was maintained till the end of Delay 2; and (2) a motor preparation subspace in which information emerged only in Delay 2 after the presentation of the distractor, possibly due to the initiation of saccade preparation after the last sensory cue that reliably predicted the timing of the Go cue (i.e. the offset of the distractor). Both subspaces exhibited behavioral relevance with significantly decreased information in error trials only in the subspace, and not in the null space. Interestingly, we found a reduction in information in the memory subspace when information in the movement preparation subspace emerged. At the same time, we found that the average firing rate of the neurons across the population remained unchanged. This suggested that a normalization mechanism could have been acting on the population activity (Ruff and Cohen, 2017; Duong et al., 2019). We subsequently found that a bump attractor model (Compte et al., 2000) with divisive normalization allowed us to replicate the observed neurophysiological properties. We believe these results provide insights into the neural mechanisms of cognitive flexibility and cognitive capacity.

Results

We measured LPFC activity from two monkeys while they performed a delayed saccade task with an intervening distractor. Briefly, the monkeys had to remember the location (out of eight possibilities) of a briefly presented visual target for 2.3 s. One second after the target disappeared, a distractor was presented briefly in a different location. At the end of an additional 2.3 s, the monkeys reported the location of the remembered target using an eye movement (Figure 1a). We recorded single-unit activity from the LPFC and FEF of both monkeys while they performed the task. We only analyzed data collected for seven target locations for both animals, since one animal had difficulty making saccades to the lower-right location. Figure 1b shows the different electrode positions in the LPFC and FEF on an anatomical map. Additionally, FEF electrodes were differentiated from LPFC electrodes using microstimulation (see Materials and methods). We previously reported that the presentation of the distractor led to code-morphing in the LPFC (which was not observed in the FEF), such that a decoder trained in the delay period that preceded the distractor (Delay 1) could not be used to decode memory locations during the delay period that followed the distractor (Delay 2), and vice versa (Parthasarathy et al., 2017; Figure 2a). In other words, there were two stable population codes in the LPFC, one in Delay 1 and one in Delay 2, but they did not generalize to each other. In this paper, the presence of code-morphing in the LPFC motivated us to analyze the 226 single neurons recorded from the LPFC, which did not include those recorded from the FEF. Single neurons in the LPFC showed sustained selectivity to target locations during both delay periods, with some maintaining the same target tuning in both delays (Figure 1c, left), while some changed target tuning from Delay 1 to Delay 2 (Figure 1c, right). The latter category of neurons was characterized as non-linearly mixed selective neurons and was shown to drive code-morphing in the LPFC (Parthasarathy et al., 2017). On the population level, most of the cells with target selectivity in one delay also showed selectivity in the other delay (Figure 1d).

Experimental design and responses of example neurons.

(a) Behavioral task: Each trial began when the animal fixated on a fixation spot at the center of the screen. The animal was required to maintain fixation throughout the trial until the fixation spot disappeared. A target (red square) was presented for 300 ms followed by a 1000 ms delay period (Delay 1). A distractor (green square) was then presented for 300 ms in a random location that was different from the target location and was followed by a second delay of 1000 ms (Delay 2). After Delay 2, the fixation spot disappeared, which was the Go cue for the animal to report, using an eye movement, the location of the target. (b) Implant locations of 16-channel and 32-channel electrode arrays (with electrode lengths ranging from 5.5 mm closer to the sulci, to 1 mm further from the sulci) in the LPFC (red dots) and the FEF (blue dots) in the two animals. Analyses were carried out only on LPFC data. (c) Peristimulus time histograms (PSTH) for two single neurons in the LPFC. Time 0 marks the onset of target presentation; responses to the different target locations are color-coded according to the legend shown in the top right; the colored regions surrounding each line indicates the standard error. (d) Venn diagram showing the number of LPFC neurons selective in Delay 1, in Delay 2, and their overlap. Target selectivity was tested using one-way ANOVA (p < 0.05) with spike counts averaged during 800–1300 ms for Delay 1 and 2100–2600 ms for Delay 2.

Figure 2 with 7 supplements see all
Code morphing, and two minimally dependent subspaces.

(a) Heat map showing the cross-temporal population-decoding performance in the LPFC. White lines indicate target presentation (0–0.3 s), distractor presentation (1.3–1.6 s), and cue onset (2.6 s). (b) Schematic illustration of the projection of the full-space activity into Subspace 1 and Subspace 2. Delay 1 activity (purple and green filled circles) projected into the Subspace 1 would cluster according to target location (filled circles in the red subspace), and because this was a stable subspace, the Delay 2 activity for each target location (purple and green unfilled circles) would overlap with those for Delay 1 (open circles in the red subspace). In Subspace 2, Delay 1 activity would not cluster according to location (filled circles in the blue subspace), and the clustering by location would emerge only from the Delay 2 activity (open circles in the blue subspace) after the emergence of the new information. (c) We projected the trial-averaged full-space population activity for each time bin across the whole trial into Subspace 1 and Subspace 2 and calculated the magnitude of the projections. For each subspace, the magnitude was normalized to have a maximum value of 1. The projections into Subspace 1 and Subspace 2 exhibited different temporal profiles. (d) Cross-temporal decoding performance after projecting full-space activity into Subspace 1. (e) Cross-temporal decoding performance after projecting full-space activity into Subspace 2. (f) Projection of single-trial activity for two target locations (actual locations shown in the upper left corner) onto the first three principal components. Delay 1 is depicted as closed circles, and Delay 2 as open circles. Re-projections into the Subspace 1 (red plane) and Subspace 2 (blue plane) are shown and guided by projection cones (green and purple cones connecting the PCA projections into the subspace re-projections).

Two minimally dependent subspaces coexisted within the LPFC

Two different and stable population activity patterns in the LPFC were observed in Delay 1 and Delay 2 (Figure 2a), which implied that a downstream region would need to use different decoders in the two periods to extract the working memory information (neural codes supporting the discrimination of different intended items), and would need to know which of them to use in the appropriate delay period. Alternatively, the difference observed between Delay 1 and Delay 2 activity could be explained by a superposition of different types of information in independent subspaces, such that each downstream region can use the same decoder to extract a specific type of information invariantly across time, even if the mixing of different types of information is dynamic across time. We have previously shown that a time-invariant (henceforth stable) working memory subspace can be identified in the LPFC (Parthasarathy, 2019). However, significant information about the target was present outside of this space (null space decoding performance of 35.7 ± 1.7% in Delay 1, and 31.6 ± 1.5% in Delay 2) (Parthasarathy, 2019) suggesting the existence of a non-trivial additional subspace that contains target information. The incorporation of the new information from the additional subspace into the neuronal population, alongside the existing information from the working memory subspace, would have then resulted in code morphing in the full space (illustrated in Figure 2b). One possible source of the new information could be motor preparation activity. The stable population activity in Delay 2 suggested that the animals could have initiated preparatory activity right after distractor offset, as the distractor was the last signal that reliably predicted the Go cue. In order to assess this possibility, we looked for a subspace decomposition that could maximally differentiate the neural codes for working memory and motor preparation. Standard methods for such decompositions are regression (Mante et al., 2013; Brody et al., 2003) (resulting in a one-dimensional component for each task-dependent variable) and, more interestingly, Demixed Principal Component Analysis (dPCA) (Brendel et al., 2011; Kobak et al., 2016), which selectively isolates and constructs a subspace for one task-dependent variable at a time by averaging out all the other task-dependent variables. However, these methods are not suitable for our data, because we always had the same target location label for working memory and motor preparation in each trial. As a result, for regression, the working memory and motor preparation variables will not have different coefficients; for dPCA, we cannot differentially represent the neural activity by averaging trials according to working memory or motor preparation locations to find different subspaces. Instead, we developed a novel method to identify the two subspaces even given that working memory and motor preparation always had the same target labels in each trial by regarding the trial-averaged and time-averaged Delay 1 and Delay 2 activity (each had a size 226 × 7, where 226 was the number of neurons, and seven was the number of target locations) as a mixture of working memory and motor preparation activity, and assumed that working memory and motor preparation activity themselves to be minimally dependent on each other. Our objective was then to find, through an optimization technique, the best unmixing coefficients to apply to Delay 1 and Delay 2 activity that could recover the working memory and motor preparation activity with the lowest mutual information possible between them (see Materials and methods). The original Delay 1 and Delay 2 activity exhibited 0.33 bits of mutual information. Using our method, we found two unmixed elements (representations of unmixed population activity that were each of size 226 × 7) from D1 and D2 activity with a minimum mutual information of 0.08 bits (Figure 2—figure supplement 1). The two elements we identified consisted of seven vectors in the 226-dimensional space, and according to the unmixing coefficients we identified, the magnitude of one element (Element 1) in Delay 2 was 65% of that in Delay 1, and the magnitude of the other element (Element 2) in Delay 1 was 12% of that in Delay 2. The orthonormal bases of the two elements defined two subspaces (Subspace 1 and Subspace 2). The temporal dynamics of the full-space population activity projected into these subspaces showed that the magnitude of activity in Subspace 1 increased early after target presentation and was maintained until the saccade cue, while the magnitude of activity in Subspace 2 increased after distractor presentation and stayed relatively high even after the Go cue (Figure 2c, single-session results are shown in Figure 2—figure supplement 2). Next, we used the decoding performance of a linear decoder (LDA) as a proxy of target information and evaluated target information in each subspace. We trained an LDA decoder at each time point of the trial, and tested the decoder against all other time points across the trial to evaluate the temporal generalization of the population activity (cross-temporal decoding, see Materials and methods). Cross-temporal decoding after projecting the full-space neural activity into Subspace 1 showed that information emerged right after target presentation, and although the information was higher in Delay 1 (60.5 ± 1.3%), it was present throughout the whole trial, even during the distractor period (Figure 2d). This was qualitatively consistent with our hypothesis, aside from the decrease in information in Delay 2 (39.9 ± 1.1%). Cross-temporal decoding of full-space neural activity projected into Subspace 2 showed that information emerged after distractor presentation (42.6 ± 1.1%), and was stable throughout Delay 2 (Figure 2e). In Delay 1, Subspace 1 and Subspace 2 accounted for 14.6% and 10.3% of the variance in the full space; in Delay 2, Subspace 1 and Subspace 2 accounted for 5.8% and 8.1% of the variance in the full space. Full-space data in the two subspaces had an effective dimensionality of 6 dimensions each – after projecting single-trial full-space data into the subspaces, we performed a PCA on the projected data, and the first six out of the seven principal components cumulatively accounted for more than 95% of the variance within each subspace (Figure 2—figure supplement 3). This indicated that the true dimensionality of the neural code could be smaller than the number of discrete target locations imposed by the experiment. In addition, as the number of discrete target locations increases in the experiment (for example, 24 target locations), we expect the effective dimensionality of data in the subspaces will asymptote to the true dimensionality of the neural codes supporting the cognitive processes.

Figure 2f shows single-trial projections of two different target locations (purple and green locations shown in the top-left corner) onto the top three principal components (PCs). These projections were then re-projected into Subspace 1 (red plane) and Subspace 2 (blue plane). The low-dimensional visualizations are merely used to provide intuitions underlying the cross-temporal decoding results, which were all obtained using high-dimensional data (see Materials and methods). Consistent with our hypothesis, Delay 1 and Delay 2 projections into Subspace 1 clustered according to target location, although they overlapped less than we expected (we will revisit this deviation from our expectation later on). However, the separation between the projected points was small enough that target location information could be decoded in both delays, regardless of whether the classifier was trained using Delay 1 or Delay 2 activity (Figure 2d).

On the other hand, projections into Subspace 2 behaved differently, such that Delay 1 projections for multiple target locations overlapped, whereas Delay 2 projections remained separated. This explained why in Subspace 2, target location information could not be decoded in Delay 1, but could be decoded in Delay 2 (Figure 2e). Projections into Subspace 1 and Subspace 2 for all target locations confirmed that these observations generalized to the rest of the locations (Figure 2—figure supplement 4, which also illustrates the reason for the difference in performance in the two off-diagonal quadrants in Figure 2d).

The two minimally dependent subspaces corresponded to working memory and motor preparation

Since Subspace 1 contained target information throughout the trial, and working memory of the target location was presumably required throughout the trial, we hypothesized that Subspace 1 corresponded to a working memory subspace. We previously showed that the LPFC contained a working memory subspace that encoded stable working memory information (Parthasarathy, 2019). In order to assess whether Subspace 1 corresponded to the working memory subspace previously described (Parthasarathy, 2019), we calculated the principal angles between these subspaces, as a measure of similarity (see Materials and methods). We found that Subspace 1 was significantly closer than chance to the working memory subspace, while Subspace 2 was not (Figure 3—figure supplement 1). This result supported the interpretation that Subspace 1 corresponded to a working memory subspace. Thus, henceforth, we will refer to Subspace 1 as the ‘working memory subspace’ and Element 1 as the unmixed working memory element.

Since Subspace 2 contained target information only after the distractor disappeared, and motor preparation presumably began after the last sensory cue that reliably predicted the timing of the Go cue (i.e. the offset of the distractor), we hypothesized that Subspace 2 corresponded to a motor preparation subspace. Activity between the Go cue and the saccade onset contained information about saccade execution (45% of LPFC neurons we recorded were selective in the period between the Go cue and saccade onset, assessed using a one-way ANOVA, p < 0.05). In order to test whether Subspace 2 corresponded to a motor preparation subspace, we compared the original unmixed elements using Delay 1 and Delay 2 activity with a new pair of unmixed elements using Delay 1 and pre-saccadic period activity (150 ms to 0 ms prior to saccade). If Subspace 2 corresponded to a motor preparation subspace, we should observe similarities between the second element in both pairs of unmixed elements, that is the unmixed motor preparation activity and the unmixed pre-saccade activity (see Materials and methods). In the new pair of unmixed elements, we obtained two elements with relative vector magnitudes similar to those found in the first pair of unmixed elements (for Element 1’, the vector magnitude in the pre-saccade period was 70% of that in Delay 1, while for Element 2’, the vector magnitude in Delay 1 was 0% of that in the pre-saccade period, Figure 3—figure supplement 2). We found that Element 1 and Element 1’ were significantly correlated (Figure 3a left, Pearson correlation r > 0.99, p < 0.01). Importantly, Element 2 and Element 2’ were also significantly correlated (Figure 3a right, Pearson correlation r = 0.62, p < 0.01). This result supported our hypothesis that Subspace 2 corresponded to a motor preparation subspace.

Figure 3 with 3 supplements see all
Preparatory and pre-saccadic activity.

(a) Correlation between unmixed elements found from Delay 1/Delay 2 activity (Elements 1 and 2) and the unmixed elements from Delay 1/pre saccadic activity (Elements 1’ and 2’). The matrices were flattened into 1-d for the correlation analysis. Elements 1 and 1’ were almost identical (r > 0.99, p < 0.01, left), while Elements 2 and 2’ were highly correlated (r = 0.62, p < 0.01, right). (b) Left, the percentage of cells that exhibited significant correlation between Elements 2 and 2’. Right, the percentage of cells that exhibited significant correlation between Elements 1 and 2’. The shaded area shows the 5th and 95th percentiles of the chance percentage obtained by shuffling the tuning across cells. (c) Response tuning of four representative cells that showed significant correlation between their activity in Elements 2 and 2’.

In an additional test of the hypothesis that Subspace 2 corresponded to a motor preparation subspace, we examined the relationship between the unmixed motor preparation activity and the unmixed pre-saccade activity at the level of single cells. First, we identified cells with spatial tuning in both Delay 2 and the pre-saccade period (73 cells, two one-way ANOVAs, both p < 0.05). Then, for each cell, we measured the correlation between the unmixed motor preparation activity and the unmixed pre-saccade activity across different target locations. We found that 47% of these neurons showed significant correlation (Pearson correlation, p < 0.05), which exceeded the number expected by chance (Figure 3b, left bar, p < 0.001, g = 10.82). As a control, we carried out the same analysis between the unmixed working memory activity and the unmixed pre-saccade activity, and found no evidence of a higher number of correlated cells than expected by chance (Figure 3b, right bar, p > 0.19, g = 1.51). Examples of neurons with significant correlation are shown in Figure 3c. This result provided additional support to our hypothesis that Subspace 2 corresponded to a motor preparation subspace. Thus, henceforth, we will refer to Subspace 2 as the ‘motor preparation subspace’. Alongside the working memory and motor preparation activity for target locations, there could also be activity representing distractor locations in Delay 2. By grouping trials according to distractor labels, we indeed found significant distractor information in the full space (Figure 3—figure supplement 3). However, the distractor activity in Delay 2 was not related to the Element 2 or the motor preparation subspace we identified, because the distractor activity and the motor preparation activity were obtained from data grouped by different trial labels (target and distractor labels were uncorrelated). Very little distractor information (17.9 ± 0.7%) was successfully decoded in the motor preparation subspace (Figure 3—figure supplement 3).

Activity of neurons with mixed working memory and motor preparation selectivity formed the two subspaces

The existence of two minimally dependent subspaces could be mediated by one of two possible mechanisms: (1) two distinct subpopulations of neurons with exclusive working memory or motor preparation selectivity within the LPFC, or (2) the same population of LPFC neurons with mixed selectivity to both working memory and motor preparation. In order to distinguish between these two possible mechanisms, we projected the unit vector representing each neuron in the full space into the working memory and motor preparation subspaces, and quantified the magnitude of the two projections for each neuron (i.e. loading weight, Figure 4a). A clustering of the loading weights along the x- and y-axes would support the first mechanism, and if not this case, a non-significant or positive correlation would support the second mechanism. In order to test if the points clustered along the x- and y-axes, we computed the ratio of points near the x- or y-axes (above 67.5° line or below 22.5° line) for 1,000 bootstraps, with a random 10% data exclusion in each bootstrap. We found that there were significantly more points away from the x- or y-axes (88% to 90%, corresponding to the 5th and 95th percentile of 1,000 bootstraps), which rejected the first mechanism. In addition, to our surprise, we found a significant positive correlation between the loading weights in each subspace (r = 0.68, which was significantly higher than the 95th percentile of 1,000 shuffles, where in each shuffle we randomly permuted the population’s loading weights for both subspaces), which not only supported the second mechanism, but further suggested that neurons with stronger contribution to the working memory subspace would also have a stronger contribution to the motor preparation subspace. As a measure of the relative contribution to each subspace, we calculated the ratio between the loading weights for each cell, and analyzed their distribution (Figure 4b). We found that only 14 (6%) of the neurons had ‘exclusive’ loading for the working memory (red) or motor preparation (blue) subspaces. However, these cells were not necessary to identify the subspaces (Figure 4—figure supplement 1).

Figure 4 with 4 supplements see all
Loading weights for individual neurons.

(a) The loading weight of each neuron in the working memory subspace and the motor preparation subspace. (b) Histogram of the ratio between the loading weights for each cell. For cells with larger loading for the working memory subspace, the values are plotted to the right of the plot, while for cells with larger loading for the motor preparation subspace, the values are plotted to the left of the plot. Red dots (in a) and bars (in b) represent cells with ‘exclusive’ loading for the working memory subspace, while blue dots (in a) and bars (in b) represent cells with ‘exclusive’ loading for the motor preparation subspace. These cells were identified as those with ratios that exceeded two standard deviations from the mean. (c) Illustration of how overlapping codes can be read out. Different loading weights of the two subspaces (expressed as connection weights between the readout neurons and Neurons 1 and 2) unambiguously read out working memory or motor preparation information from the conjunctive population code formed by both Neuron 1 and Neuron 2, whereas it would have been ambiguous to look only at Neuron 1's change of firing rate in Delay 2.

In order to understand how a single population of neurons with mixed selectivity could have contributed minimally dependent information to the two subspaces, we created a simple illustration (Figure 4c). Working memory and motor preparation information were read out by separate readout neurons with different connection weights to Neurons 1 and 2 that reflected the loading weights of each subspace. In isolation, the activity of Neuron 1 would be ambiguous for both readout neurons, as an increase of activity in Delay 2 could be interpreted as a new memory at a different spatial location, or as the same memory as in Delay 1, but with superimposed motor preparation activity. In order to disambiguate the meaning of a change in the activity of one neuron, it would be necessary to interpret that change in the context of changes in the activity of the rest of the neuronal population (i.e. in this example, Neuron 2). In the illustration, a superimposed increase of activity in Neurons 1 and 2 signals a change in memory (i.e. only the readout activity in the working memory subspace changed), whereas the same increase in Neuron 1, but with a superimposed decrease of activity in Neuron 2, signals that the memory has not changed, but that a motor preparation plan has emerged in Delay 2 (i.e. only the readout activity in the motor preparation subspace changed). This concept can be extended to the 212 neurons with mixed selectivity to understand how the coordinated activity between those neurons can contribute minimally dependent information to the working memory and motor preparation subspaces through different loading weights that we found in the LPFC (low-dimensional visualizations of neural data provided in Figure 2f and Figure 2—figure supplement 4).

Information in one subspace led to a small amount of interference in information in the other subspace

Since one population of neurons with mixed selectivity contributed to both the working memory and motor preparation subspaces, it was possible that information in one of the subspaces interfered with information in the other, and vice versa. We checked if the two subspaces were orthogonal to each other by comparing their principal angles with those between two random subspaces of the same dimension (Figure 5a). All the principal angles between the working memory and motor preparation subspaces were significantly smaller than chance, indicating non-orthogonality between the two subspaces and the likelihood of interference of information between them. One way to assess the interference between the information in both subspaces is to ask whether the emergence of motor preparation activity in Delay 2 (added on top of working memory activity) changes the amount of readable information in the working memory subspace, compared to the situation where there is only working memory activity in Delay 2. In order to quantify this interference of information, we compared the decoding performance of an LDA classifier trained and tested on the unmixed single-trial working memory activity (see Materials and methods) projected into the working memory subspace (Figure 5a: projMSub(M)), with decoding performance of a classifier trained and tested on single-trial working memory activity plus motor preparation activity (i.e. Delay 2 activity) projected into the working memory subspace (Figure 5a: projMSub(M+P)). A similar analysis was carried out in the motor preparation subspace (Figure 5b: projPSub(P) and projPSub(M+P)). We found no evidence of a drop in performance between projMSub(M) and projMSub(M+P) (p > 0.73, g = 0.61), and between projPSub(P) and projPSub(M+P) (p > 0.22, g = 2.63), suggesting a lack of interference between these subspaces.

Figure 5 with 3 supplements see all
Comparisons between working memory and motor preparation subspaces.

(a) The principal angles between the working memory subspace and the motor preparation subspace are shown in the magenta lines in ascending order. The black boxplots illustrate the distribution of principal angles between two random subspaces with the same dimensions as the working memory and motor preparation subspaces. The borders of the box represented the 25th and the 95th percentile of the distribution, while the whiskers represent the 5th and the 95th percentiles. (b) Decoding performance in the working memory subspace. M stands for unmixed single-trial working memory activity; projMSub(M), decoding of the unmixed single-trial working memory activity projected into the working memory subspace; projMSub(M+P), decoding of the single-trial Delay 2 activity projected into the working memory subspace; projMSub(ME), decoding of the unmixed single-trial working memory activity in error trials projected into the working memory subspace using a classifier built on unmixed single-trial working memory activity in correct trials projected into the working memory subspace; (c) Decoding performance in the motor preparation subspace. P stands for unmixed single-trial motor preparation activity. Same conventions as in a, but for unmixed single-trial motor preparation activity and the motor preparation subspace. We verified that the drop in performance in error trials was specific to the two subspaces, and not due to a non-specific increase in noise in the population (see Materials and methods). (d) Inter-to-Intra cluster ratio of unmixed single-trial working memory activity projected into the working memory subspace (projMSub(M)), and of single-trial full-space activity projected into the working memory subspace (projMSub(M+P)). (e) Same conventions as in d, but for unmixed single-trial motor preparation activity and motor preparation subspace.

As we used LDA’s decoding performance as a proxy of target information, the lack of interference between two non-orthogonal subspaces indicated that the shift of clusters in the state space caused by superimposed activity were not large enough to cross the classification boundaries, and thus did not affect the classification performance. So we performed a more sensitive state-space analysis on Delay 2 activity to assess whether the working memory and motor preparation subspaces interfered with each other. We quantified interference by projecting the unmixed single-trial activity into the two subspaces, and calculated the average distance between clusters of points corresponding to different target locations (inter-cluster distance). The inter-cluster distance was then normalized by the average intra-cluster distance for all clusters, which was a measure of trial-by-trial variability in the population activity (see Materials and methods). This inter-to-intra cluster distance ratio was compared between projections of unmixed single-trial working memory activity into the working memory subspace (Figure 5d: projMSub(M)), and projections of single-trial working memory plus motor preparation activity (i.e. Delay 2 activity) into the working memory subspace (Figure 5d: projMSub(M+P)). A similar analysis was carried out in the motor preparation subspace (Figure 5e). We found a small decrease (7.1%) of the inter-to-intra cluster distance ratio when both working memory and motor preparation activity were projected into the subspaces, suggesting the existence of a small, but significant interference between both subspaces (p < 0.001, g = 4.81 between projMSub(M) and projMSub(M+P), p < 0.001, g = 6.63 between projPSub(P) and projPSub(M+P)).

Less information was found in error trials in both subspaces

In a subset of trials, the animals maintained fixation until the Go cue, but failed to report the correct target location with a saccade. These failures could be due to the animals reporting other locations, including the location of the distractor, or simply saccading to a completely different location, such as the edge of the monitor. Classifiers trained on unmixed single-trial working memory activity of correct trials projected into the working memory subspace, projMSub(M), were tested on unmixed single-trial working memory activity of error trials (see Materials and methods), which was also projected into the working memory subspace, projMSub(ME). Decoding performance was significantly reduced in error trials (Figure 5a,) compared to correct trials (Figure 5a, p < 0.001, g = 13.9 between projMSub(M) and projMSub(ME)), suggesting that failures in memory encoding occurred during error trials. A similar analysis on the motor preparation subspace yielded equivalent results (Figure 5b, p < 0.001, g = 13.8 between projPSub(P) and projPSub(PE)), which were consistent with the fact that in error trials, saccades were made to different locations than in correct trials. These results suggested that the subspaces we found could have been used by the animals to perform the task.

Artificial neural networks with divisive normalization recapitulated the properties of LPFC activity

An unexpected observation in our results was that decoding performance in the working memory subspace decreased in Delay 2 compared to Delay 1 (Figure 2d). This decrease coincided with an increase of decoding performance in the motor preparation subspace (Figure 2e). The reduction of working memory decoding performance was not expected in the schematic diagram of the subspace dynamics (Figure 2b), but was captured by the state space visualization of real neural data (Figure 2f, inter-cluster distance in Subspace 1 reduced in Delay 2). A more rigorous state space analysis revealed that the decrease of working memory decoding performance was due to a decrease in the inter-to-intra cluster distance ratio of working memory activity in Delay 2, and the increase of motor preparation decoding performance was due to an increase in the inter-to-intra cluster distance ratio of motor preparation activity in Delay 2 (Figure 2—figure supplement 5). In addition, we noticed that the mean population firing rate did not change between Delay 1, Delay 2 and pre-target fixation periods (Figure 2—figure supplement 6). This observation was consistent with a population normalization mechanism to maintain the mean population firing rate at a constant level in the LPFC (Ruff and Cohen, 2017; Duong et al., 2019). In order to assess whether a normalization mechanism was responsible for the decrease of working memory information in Delay 2, we built artificial neural network models with and without population normalization, and compared their behavior with the LPFC data.

Bump attractor models have been shown to replicate several properties of LPFC activity, including code-morphing in the full space, the existence of a stable subspace with stable working memory information, and non-linear mixed selectivity of individual neurons (Parthasarathy, 2019; Compte et al., 2000; Wimmer et al., 2014). Here, we created a model that incorporated subsets of neurons that represented information in the working memory and motor preparation subspaces (Figure 4—figure supplement 2), and looked at the effect of adding divisive normalization to keep the mean population firing rate constant. We constrained the attractor model to utilize neurons with mixed selectivity by matching the selectivity properties to those found in the LPFC data (Figure 4—figure supplement 3). We also used the same unmixing method to identify working memory and motor preparation subspaces from the activity in the attractor model. We found that only the attractor model with divisive normalization qualitatively replicated all the features of the neural data (Figure 4—figure supplement 2). We also explored an alternative model that supported the implementation of subspaces – a linear subspace model (Murray et al., 2017). Similarly, only the linear subspace model with divisive normalization replicated all the main findings in the neural data (Figure 4—figure supplement 4). The results of the model simulations supported the idea that divisive normalization was needed to faithfully replicate the properties of neural data, and suggested that such a mechanism constituted part of the function of the LPFC. The similarity between the results obtained from two different categories of models – the bump attractor model and the linear subspace model, also indicated the conceptual convergence between the two models in replicating the sustained-activity aspect of the LPFC activity.

Discussion

Here, we demonstrate that two minimally dependent subspaces coexist within the LPFC population. These subspaces contain largely independent information about target location, and appear to encode working memory and motor preparation information. We show that there is a small, but significant interference of information when both subspaces encode information simultaneously, and during error trials information in the working memory subspace is reduced. Assessment of activity properties of individual neurons revealed that a single population of neurons with mixed selectivity generates both subspaces. Finally, we show that a bump attractor neural network model with divisive normalization can capture all these properties described. Overall, our results show that working memory and motor preparation subspaces coexist in a single neural network within the LPFC.

Our results provided the first evidence suggesting that information about two separate cognitive processes can be simultaneously encoded in subspaces within the same brain region. The majority of the literature on information subspaces in the brain has reported a single subspace (Parthasarathy, 2019; Druckmann and Chklovskii, 2012; Inagaki et al., 2019; Svoboda and Li, 2018), multiple subspaces in different regions (Semedo et al., 2019), or multiple subspaces in the same region where information transited from one subspace to another but did not coexist simultaneously in different subspaces (Kaufman et al., 2014; Elsayed et al., 2016; Yoo and Hayden, 2020; Kimmel et al., 2020). Mante et al., 2013. showed coexistence of information in three subspaces in the prefrontal cortex, but two of the subspaces encoded color and motion (stimulus subspace), and only one subspace encoded action choice (cognitive subspace). Minxha et al., 2020. reported the existence of two cognitive subspaces for ‘memory’ and ‘categorization’ tasks, but the two subspaces were employed asynchronously in different types of trial blocks. Thus, the identification of two coexisting cognitive subspaces (working memory and motor preparation) in our work could provide new insights into the brain’s mechanisms underlying our cognitive flexibility.

It is important to minimize interference between different types of information. For example, a visual area may read out working memory information (Yeterian et al., 2012; Merrikhi et al., 2017), while a premotor region may read out motor preparation information from the LPFC (Yeterian et al., 2012; Churchland et al., 2012; Schall and Hanes, 1993). If large interference existed between subspaces, the computations of downstream regions would be compromised. We found a small, but significant interference between the subspaces, such that some working memory information was reflected in the motor preparation subspace (and vice versa). It is not surprising that there is some degree of interference, since the method we used to decompose the signals did not impose a constraint to ensure maximal orthogonality between subspaces, and while the mutual information was low, it was not zero. In order to assess whether imposing orthogonality between subspaces was feasible, we fixed Delay 1 activity as the first activity subspace and rotated each column vector in Delay 2 activity matrix to be orthogonal to Delay 1 activity (Gram-Schmidt algorithm) to obtain the second activity matrix, such that the two activity matrices would be orthogonal to each other. To our surprise, the two simple orthogonal subspaces were highly similar to our working memory and motor preparation subspaces (Figure 5—figure supplement 1). The reason for this similarity could be that the unmixing method showed that there was very little motor preparation activity in Delay 1, so the assumption that Delay 1 activity exclusively contains working memory information would largely align with the unmixing results. However, the unmixing method was in principle a more flexible approach to identify the subspaces, and also provided a less constrained viewpoint to interpret the neural data (details discussed in Figure 5—figure supplement 1). We also considered alternative methods to identify the subspaces, but these produced subspaces with larger interference (Figure 5—figure supplements 2 and 3). The interference we found suggests that under conditions that stress the working memory and motor preparation systems (such as a task that requires the concurrent memorization of four targets, and preparation of four movements) a predictable bias should be observable for both the recalled target locations and eventual movements. This prediction remains to be tested.

We also found an indirect way in which information in subspaces interfere with each other: divisive normalization of population activity. This led to a decrease of working memory information in Delay 2 once motor preparation information emerged. Divisive normalization, which has been described before in the LPFC (Ruff and Cohen, 2017; Duong et al., 2019), could be useful as an energy saving mechanism, since it maintains the population activity at a low level when new information is added. A bump attractor model and a linear subspace model with divisive normalization allowed us to replicate the properties of LPFC activity. However, the models only provide high-level support for this mechanism, and a mechanistic implementation is still needed.

In this work, we derived two subspaces, and analyzed the benefits of decoding from those subspaces, from data in which the memory location and the motor preparation location were identical. However, there are situations where the LPFC is required to store multiple pieces of information that are uncorrelated, for example if the animal has to remember the location and color of a target to perform a task, where these are uncorrelated (Warden and Miller, 2010; Cavanagh et al., 2018). We have verified that our approach can be extended to identify the relevant subspaces in tasks with uncorrelated information as well (see Materials and methods). We show that in tasks with uncorrelated information, decoding in the full space could result in higher interference as compared to tasks with correlated information (Figure 2—figure supplement 7a,b). However, the use of subspaces could reduce interference in both cases (Figure 2—figure supplement 7c,d), suggesting a possible advantage of encoding information in minimally dependent subspaces in a broad range of cognitive tasks that we typically associate with the LPFC.

Our results support a framework in which low-dimensional subspaces could be a general property of cortical networks (Remington et al., 2018; Ruff and Cohen, 2019). Under this framework, downstream regions could extract specific information from these subspaces (Semedo et al., 2019). This could provide a mechanism for selective routing of information between regions (Yang et al., 2016), which could in turn be a building block of our cognitive flexibility capacity. The dimensionality of a network’s full state space constrains the number and dimensionality of the different information subspaces that could coexist within the network. The LPFC is a densely connected brain hub, anatomically connected to more than 80 regions, compared to the roughly 30 connected to the primary visual cortex (Markov et al., 2014). Given the variety of inputs to the LPFC, it is not surprising that a large number of its neurons show mixed selective activity (Rigotti et al., 2013; Parthasarathy et al., 2017), which in turn endow the LPFC with high dimensionality (Rigotti et al., 2013). This property would allow a higher number of subspaces to coexist within the network. The number of items that can be simultaneously maintained in working memory is limited, which may be the result of encoding constraints within the working memory subspace. However, the types of information that can be encoded in working memory seem limitless. These include memories of external events (such as the visual stimuli in the current study), as well as memories of internally-generated events (such as the task rules stored in long-term memory in the current study, which previous studies have shown to be reflected in LPFC activity; Wallis et al., 2001). It is possible that underlying this ability to encode such diverse types of information is the extremely large number of possible information subspaces that could coexist within regions of the LPFC.

Materials and methods

Subjects and surgical procedures

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We used two male adult macaques (Macaca fascicularis), Animal A (age 4) and Animal B (age 6), in the experiments. All animal procedures were approved by, and conducted in compliance with the standards of the Agri-Food and Veterinary Authority of Singapore and the Singapore Health Services Institutional Animal Care and Use Committee (SingHealth IACUC #2012/SHS/757). The procedures also conformed to the recommendations described in Guidelines for the Care and Use of Mammals in Neuroscience and Behavioral Research (Van Sluyters and Obernier, 2003). Each animal was implanted first with a titanium head-post (Crist Instruments, MD) before arrays of intracortical microelectrodes (MicroProbes, MD) were implanted in multiple regions of the left frontal cortex. In Animal A, we implanted six arrays of 16 electrodes and one array of 32 electrodes in the LPFC, and two arrays of 32 electrodes in the FEF, for a total of 192 electrodes. In Animal B, we implanted one array of 16 electrodes and two arrays of 32 electrodes in the LPFC, and two arrays of 16 electrodes in the FEF, for a total of 112 electrodes. The arrays consisted of platinum-iridium wires with either 200 or 400 µm separation, 1–5.5 mm of length, 0.5 MΩ of impedance, and arranged in 4 × 4 or 8 × 4 grids. Surgical procedures followed the following steps. 24 hr prior to the surgery, the animals received a dose of Dexamethasone to control inflammation during and after the surgery. They also received antibiotics (amoxicillin 7–15 mg/kg and Enrofloxacin 5 mg/kg) for 8 days, starting 24 hr before the surgery. During surgery, the scalp was incised, and the muscles retracted to expose the skull. A craniotomy was performed (~2×2 cm). The dura mater was cut and removed from the craniotomy site. Arrays of electrodes were slowly lowered into the brain using a stereotaxic manipulator. Once all the arrays were secured in place, the arrays’ connectors were secured on top of the skull using bone cement. A head-holder was also secured using bone cement. The piece of bone removed during the craniotomy was repositioned to its original location and secured in place using metal plates. The skin was sutured on top of the craniotomy site, and stitched in place, avoiding any tension to ensure good healing of the wound. All surgeries were conducted using aseptic techniques under general anesthesia (isofluorane 1–1.5% for maintenance). The depth of anesthesia was assessed by monitoring the heart rate and movement of the animal, and the level of anesthesia was adjusted as necessary. Analgesics were provided during post-surgical recovery, including a Fentanyl patch (12.5 mg/2.5 kg 24 hr prior to surgery, and removed 48 hr after surgery), and Meloxicam (0.2–0.3 mg/kg after the removal of the Fentanyl patch). Animals were not euthanized at the end of the study.

Recording techniques

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Neural signals were initially acquired using a 128-channel and a 256-channel Plexon OmniPlex system (Plexon Inc, TX) with a sampling rate of 40 kHz. The wide-band signals were band-pass filtered between 250 and 10,000 Hz. Following that, spikes were detected using an automated Hidden Markov-Model-based algorithm for each channel (Herbst et al., 2008). The eye positions were obtained using an infrared-based eye-tracking device from SR Research Ltd. (Eyelink 1000 Plus). The behavioral task was designed on a standalone PC (stimulus PC) using the Psychophysics Toolbox (Brainard, 1997) in MATLAB (Mathworks, MA). In order to align the neural and behavioral activity (trial epochs and eye data) for data analysis, we generated strobe words denoting trial epochs and performance (rewarded or failure) during the trial. These strobe words were generated on the stimulus PC and were sent to the Plexon and Eyelink computers using the parallel port.

Microstimulation

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For arrays positioned in the prearcuate region (FEF), we used standard electrical microstimulation to confirm that saccades could be elicited with low currents. These electrodes had a depth of 5.5 mm inside the sulcus and tapered to 1 mm away from the sulcus. We conducted these microstimulation experiments after we finished our recording experiments. During the microstimulation experiment, each electrode implanted in the FEF was tested for its ability to evoke fixed-vector saccadic eye movements with stimulation at currents of 50 μA. Electrical microstimulation consisted of a 200 ms train of biphasic current pulses (1 ms, 300 Hz) with no interphase delays, delivered with a Plexon Stimulator (Plexon Inc, TX). We mapped the saccade vector elicited via microstimulation at each electrode to verify that the electrodes were implanted in the FEF. Sites at which stimulation of 50 μA or less elicited eye movements at least 50% of the time, plus regions within 2–3 mm of these locations, were considered to be in the FEF.

Behavioral task

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Each trial started with a mandatory period (500 ms) where the animal fixated on a white circle at the center of the screen. While continuing to fixate, the animal was presented with a target (a red square) for 300 ms at any one of eight locations in a 3 × 3 grid. The center square of the 3 × 3 grid contained the fixation spot and was not used. The presentation of the target was followed by a delay of 1,000 ms, during which the animal was expected to maintain fixation on the white circle at the center. At the end of this delay, a distractor (a green square) was presented for 300 ms at any one of the seven locations (other than where the target was presented). This was again followed by a delay of 1000 ms. The animal was then given a cue (the disappearance of the fixation spot) at the end of the second delay to make a saccade toward the target location that was presented earlier in the trial. Saccades to the target location within a latency of 150 ms and continued fixation at the saccade location for 200 ms was considered a correct trial. An illustration of the task is shown in Figure 1a. One of the animals was presented with only seven of the eight target locations because of a behavior bias in the animal.

Cross-temporal decoding

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A decoder based on linear discriminant analysis (LDA) was built using the classify function in MATLAB to predict the location of the target. We trained a decoder for each time point in the trial, and tested the decoder with all other time points throughout the trial. We pooled the activity across recording sessions to create a pseudo-population of 226 neurons. In the pseudo-population, for each pseudo-trial with target location T, we randomly picked one trial from each neuron with target location T, and stacked the activity from all neurons together as if they were simultaneously recorded. We constructed 1,750 pseudo-trials (250 for each target location) as the training set, and 1,750 pseudo-trials as the testing set. The training set and testing set were sampled from non-overlapping sets of trials from each neuron. When performing cross-temporal decoding in the full space (226 dimensions, Figure 1b), we denoised the training and testing data using principal components analysis (PCA) at every time point by reconstructing the data with the top n principal components that explained at least 95% of the variance. When performing cross-temporal decoding in the subspace (seven dimensions, Figure 1e,f), the PCA projection matrix described in the previous step was replaced by the matrix specifying the desired subspace (working memory or motor preparation subspace), and the resulting data in the subspace would thus be seven dimensional.

Activity unmixing and subspace identification

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The subspaces where identified using a pseudo-population of 226 neurons. For each trial condition (which was one of seven possible target locations), we trial-averaged and time-averaged the neural activity in Delay 1 (800 to 1300 ms from target onset) and Delay 2 (2000 to 2500 ms from target onset) for each neuron to obtain two activity matrices of 226 x 7. We then normalized the two activity matrices to the mean of the baseline by subtracting neural activity in the fixation period (300 ms before target onset), and obtained activity matrices D1¯ and D2¯ of size 226 x 7, where each column represented the change in population activity under one condition. After flattening D1¯ and D2¯ activity into 1-D arrays (each of size 1 x 1,582, denoted as D1 and D2), we found high mutual information (0.33 bits) between D1 and D2 (Figure 2—figure supplement 1). We hypothesized that the highly correlated D1 and D2 resulted from a mixture of working memory and motor preparation activity, while working memory and motor preparation activity themselves were minimally dependent on each other. In matrix expression, we have:

[D1D2]=[1ab1][MP]

where M and P are the underlying working memory and motor preparation activity in a flattened shape (each with size 1 x 1,582);  a and b are the mixing coefficients of M and P. We used a standard optimization function fmincon in MATLAB to find out a pair of (a, b) that would recover the two activity arrays M and P with the least mutual information between them. The objective function we used was the mutual information for two discrete distributions:

IX;Y=y=Yx=XpX,Y(x,y)log(pX,Y(x,y)pX(x)pY(y))

where pX,Y is the joint probability mass function of X and Y; pX and pY are the marginal probability mass function of X and Y, respectively. To discretize our data, we chose the number of bins according to Sturges’ rule, which is conservative in estimating the number of bins (ensuring there are enough data points in each bin):

Numberofbins=ceil(1+log2(N))

where N is the number of total data points from a distribution. Since a scaling operation on the two distributions would not change their mutual information, we could always stipulate the coefficient matrix to have an identity diagonal such that the interpretation of a and b would be intuitive: a indicated the fraction of motor preparation activity in Delay 1 if we assumed the magnitude of motor preparation activity in Delay 2 was one; b indicated the fraction of working memory activity in Delay 2 if we assumed the magnitude of working memory activity in Delay 1 was one. To obtain a robust optimization result, we ran the optimization function 1,000 times with random initialization and examined the results. The values for (a, b) were well centered around the valley of the objective function landscape (a = 0.118 ± 0.04, b = 0.654 ± 0.027, Figure 2—figure supplement 1) and the minimum mutual information obtained was 0.076 bits when we rounded a to 0.12 and b to 0.65 (Figure 2—figure supplement 1). We then reshaped M and P arrays into matrices with size 226 x 7 (denoted as M¯ and P¯, which were also referred to as two unmixed elements), and the orthonormal bases of M¯ and P¯ defined the working memory and motor preparation subspaces. The column vectors in M¯ and P¯ were regarded as the trial-averaged and time-averaged population activity for working memory and motor preparation, respectively, for the different target locations. The working memory and motor preparation subspaces captured all target information from time-averaged data in Delay 1 and Delay 2. This was because the columns of D1¯ and D2¯ essentially represented the cluster means of each target location in the state space, so all the cluster means collapsed to zero in the null space of D1¯ and D2¯ (there was no linearly decodable information in the null space). Hence, the space spanned by D1¯ and D2¯ captured all target information in Delay 1 and Delay 2. Because M¯ and P¯ spanned the same space as D1¯ and D2¯, the working memory and motor preparation subspaces also captured all target information in Delay 1 and Delay 2.

A similar optimization was performed between activity in Delay 1 and the pre-saccadic period (150 to 0 ms prior to saccade onset):

[D1Ds]=[1ab1][MS]

where Ds was the activity in the pre-saccade period. Using the same approach as described above, we obtained M  and S with a minimum mutual information of 0.086 bits when a=0.01(± 0.014) and b = 0.706 (± 0.033) (Figure 3—figure supplement 2). We reshaped S into a matrix with size 226 x 7 (denoted as S¯), and regarded the column vectors as the trial-averaged and time-averaged pre-saccade activity.

In order to extract the unmixed working memory and motor preparation activity in the full space with single-trial variability, we used:

M1=D1a×P¯, M2=D2P¯P1=D1M¯, P2=D2b×M¯

where M¯ and P¯ are the unmixed trial-averaged memory and preparation activity, D1 and D2 were the single-trial Delay 1 and Delay 2 activity matrices of size 226 x 1,750 (250 random single trials per condition); M and P (number indicates in Delay 1 and Delay 2) were the unmixed single-trial working memory and motor preparation activity in the full space (of size 226 x 1750). Subspace memory and preparation activity were obtained by projecting the unmixed full-space single-trial activity into their respective subspaces derived from M¯ and P¯.

In the error trial analysis, single-trial full-space memory and preparation activity in error trials were estimated by:

M1E=D1Ea×P¯, M2E=D2EP¯P1E=D1EM¯, P2E=D2Eb×M¯

where D1E and D2E were similar to D1 and D2, but from error trials. The decoder was trained and validated on the data from correct trials in the subspace and tested on the data from error trials in the same subspace. Although we interpreted the decrease in decoding performance in the two subspaces in error trials to be evidence of the link between these subspaces and the behavior of the animal, an alternative interpretation could be that there was a general increase in noise in the population in error trials (perhaps due to factors like inattention), and this led to a non-specific decrease in information in all subspaces, including the memory and preparation subspaces. In order to rule this possibility out, we quantified the intra-cluster variance in the full space across locations for correct and error trials in both Delays 1 and 2 (refer to Figure 2—figure supplement 5). We found no evidence supporting the fact that the intra-cluster variance in Delay 1 was higher in error trials than in correct trials (p > 0.46, g = 0.85), and found the intra-cluster variance in error trials in Delay 2 to actually be lower than correct trials (p < 0.01, g = 6.6), presumably due to the effects of divisive normalization. These results indicated that the drop in performance in the working memory and motor preparation subspaces in error trials was not due to a non-specific increase in noise, but were more likely due to the fact that the activity in error trials deviated significantly from those in correct trials, resulting in lower information in the two subspaces.

Principal angles between subspaces

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Let X and Y be two subspaces in an N dimensional full space (X has rank xN, Y has rank yN), and all the columns of X and Y be the orthonormal bases of each subspace. We perform a Singular Value Decomposition (SVD) on the matrix product of X and Y:

[U,S,V] = SVD(XTY)

where U, V are orthonormal matrices and S a diagonal matrix. The number of principal angles between X and Y is min(x,y), and these angles are obtained by computing the inverse-cosine of the diagonal elements of S and converting radians into degrees. The principal angles in all our analyses were arranged in ascending order such that the leading principal angles are more indicative of the overall alignment of two subspaces. To test if subspace X is significantly closer to subspace Y than chance (e.g. Figure 3—figure supplement 1), we first compute the principal angles between X and Y, and next sample the principal angles between subspace Y and 1,000 random subspaces with the same dimensionality as X to obtain min(x,y) number of chance distributions corresponding to the min(x,y) number of principal angles between X and Y. X is significantly closer to Y subspaces if the principal angels between X and Y are smaller than the 5th percentile of their corresponding chance distributions.

Inter-to-intra cluster distance ratio

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To compute the inter-to-intra cluster distance ratio for working memory activity in the full space (Figure 2—figure supplement 5), we bootstrapped 250 unmixed single-trial working memory activity for seven target locations. First, to compute the mean inter-cluster distance, we computed the pairwise distances between all cluster means, and then computed the grand mean of all the pairwise cluster distances. Inter-cluster distance could be intuitively understood as the measure of separation between clusters. Second, to compute the mean intra-cluster distance, we first computed the intra-cluster distance in each cluster (mean pairwise distance among all the data points in one cluster), and then computed the grand mean of the intra-cluster distance among all the clusters. Intra-cluster distance could be intuitively understood as the trial-by-trial variability among all the target conditions. The inter-to-intra cluster distance ratio is then a concept similar to the signal-to-noise ratio of the working memory activity in the state space. We repeated this procedure for 1,000 times to get a distribution of the inter-to-intra cluster distance ratio, and presented the 5th to 95th percentile of this distribution in the boxplot in Figure 2—figure supplement 5. The same procedure was repeated for the motor preparation activity.

To compute the inter-to-intra cluster distance ratio in subspaces (Figure 4c,d), we first projected the full-space activity into the desired subspaces, and then repeated the procedure mentioned above.

Statistics

We considered two bootstrapped distributions to be significantly different if the 95th percentile range of the two distributions did not overlap. We also computed an estimated p-value for this comparison using the following formula (Fi and Garriga, 2010),

1+XN+1

where X represents the number of overlapping data points between the two distributions and N represents the number of bootstraps. With this computation, and the N = 1000 bootstraps we used throughout the paper, two distributions with no overlap will result in a p-value < 0.001, and two distributions with x% of overlap will result in a p-value ~ x/100.

In addition to the estimated p-value, we also computed the effect size of the comparison using a measure known as Hedges’ g, computed using the following formula (Fisher, 1936),

(134(n1+n2)9)(x1¯x2¯s)

where

s=(n11)s12+(n21)s22n1+n22

x¯ refers to the mean of each distribution, n refers to the length of each distribution, and s refers to the standard deviation of each distribution.

No statistical methods were used to pre-determine sample sizes, but our sample sizes were similar to those reported in previous publications (Murray et al., 2017; Stokes et al., 2013; Jacob and Nieder, 2014). The majority of our analyses made use of nonparametric permutation tests, and as such, did not make assumptions regarding the distribution of the data. No randomization was used during the data collection, except in the selection of the target and distractor locations for each trial. Randomization was used extensively in the data analyzed to test for statistical significance. Data collection and analysis were not performed blind to the conditions of the experiments. No animals or data points were excluded from any of the analyses. Please see additional information in the Life Sciences Reporting Summary.

Cell selectivity classification

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For Figure 4—figure supplement 3, in order to match the selectivity properties of neurons in the model with those of LPFC data, we first quantified the selectivity of LPFC activity as follows. First, using a two-way ANOVA with independent variables of target locations (seven locations) and task epoch (Delay 1 and Delay 2), we categorized cells as those with pure working memory selectivity (those with target information in both Delay 1 and Delay 2, and those with selectivity to target location and task epoch, but no interaction, 27.6% of cells), those with mixed selectivity to target location and task epoch (those with a significant main effect of target location and task epoch, as well as a significant interaction between target location and task epoch, 43.9% of cells). And using two one-way ANOVAs of target location (one in Delay 1 and one in Delay 2), we categorized cells as those with pure motor preparation selectivity (those with significant selectivity in Delay 2, but not Delay 1, 28.6% of cells).

Artificial neural networks

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For the bump attractor model in Figure 4—figure supplement 2, we used two populations of firing-rate units for the memory and preparation input (N = 80 for each, and the whole population consisted of the working memory and motor preparation populations), and tested the model’s performance with different overlapping ratios between the two populations (if the overlapping ratio was 0%, then the full network consisted of 160 units, whereas if the overlapping ratio was 100%, then the full network consisted of 80 units). The firing rate of the population was characterized by:

τdrdt=-r+φWrecr+WinI+σ

where τ was a uniform decay constant; r was the population firing rate; Wrec was the recurrent connection weight between units; I was the external input; Win was the loading weight of input signal to the population; σ was a Gaussian noise term. For numerical simulation, we used Newton’s method:

rt+1=rt+-rt+φ(Wrecrt+WinI+σ)×dtτ
rt=rt/αt

where we set τ=20 ms and dt=2 ms; αt was a scalar obtained by mean(rt)/mean(r0), and it was applied uniformly to each unit of the whole population to maintain the mean population firing rate at the baseline level (divisive normalization). φ(x) was a piecewise nonlinear activation function adopted from Wimmer et al., 2014:

φ(x)={0, x<0x2, 0<x<14x3 , x>1

The matrix, Wrec, had a diagonal shape with stronger positive values near the diagonal, and weaker negative values elsewhere, such that only a few neighboring units were connected via excitatory weights to each other while being connected via inhibitory weights to the rest. In this way, a structured input signal to adjacent units was able to generate a local self-sustaining bump of activity. There were eight input units, representing the eight spatial target locations in the animal’s task. For each input unit, the loading weight matrix Win specified a random group of 10 adjacent units in the working memory population, as well as the motor preparation population, to receive the signal. The input to the working memory population was transiently active in the target presentation period, and the input to the motor preparation population was transiently active in the distractor presentation period. In each trial, the label for working memory and motor preparation inputs was always the same. Distractors used the same input loadings as the working memory input did, but the strength was only 50%, and the distractor label was always different from the target label.

For the linear subspace model in Figure 4—figure supplement 4, we used a total of N = 112 units where the firing rate of the population was characterized by:

τdrdt=-r+Wrecr+WinI+σ

where τ was a uniform decay constant r was the population firing rate; Wrec was the recurrent connection weight between units; I was the external input; Win was the loading weight of input signal to the population; σ was a Gaussian noise term. For numerical simulation, we used Newton’s method:

rt+1=rt+-rt+Wrecrt+WinI+σ×dtτ
rt=rt/αt

where we set τ=20 ms and dt=2 ms; αt was a scalar obtained by mean(rt)/mean(r0), and was applied uniformly to each unit of the whole population to maintain the mean population firing rate at the baseline level (divisive normalization). We constructed the recurrent weight matrix from eigendecomposition:

Wrec=QΛQ-1

where Q was a random square matrix whose columns were the eigenvectors of Wrec, and Λ was a diagonal matrix whose diagonal elements were the corresponding eigenvalues for each eigenvector. The first 17 eigenvalues in Λ were 1 (thus there were 17 stable eigenvectors), while the rest of the eigenvalues were randomly chosen between 0 and 1 using a uniform distribution. In a network of N neurons, the simultaneous activity of all the neurons represents a vector in an N dimensional space, and hence the vector notation and the network activity can be used interchangeably. The population activity will stay stable across time if it is a linear combination of the stable eigenvectors (Murray et al., 2017). In each simulation, we assigned 1 stable eigenvector as baseline activity (with entries selected from a uniform distribution U(0,1)), 8 stable eigenvectors for working memory activity, and 8 stable eigenvectors for motor preparation activity (with entries selected from U(1,2)). In order to ensure that decoding performance in Delay 1 and Delay 2 were the same, we imposed a positive mean for the motor preparation activity, so that the incorporation of motor preparation in Delay 2 would elevate the population mean, and divisive normalization would reduce the mean activity of both working memory and motor preparation information. Otherwise, if the motor preparation activity had zero mean, there would be a significant increase of decoding performance in Delay 2. In the input weight matrix, the input activity for working memory corresponded to the 8 working memory eigenvectors, and the input activity for motor preparation corresponded to the 8 motor preparation eigenvectors. For each target location, there was a one-to-one mapping of working memory activity and motor preparation activity. The distractor inputs had the same input loading as did the target inputs, but with a lower magnitude (0.2 compared to target). At the beginning of each trial, the population started with baseline activity equal to the stable baseline eigenvector, then the input for working memory was transiently active in the target presentation period, and the input for motor preparation was transiently active in the distractor presentation period. When the input activity had the same direction as a stable eigenvector, the resultant population activity would stay stable across time because it was still a linear combination of stable eigenvectors. As all the input activity corresponded to stable eigenvectors, all target information, distractor information, and motor preparation information were maintained stably across time.

Subspaces for uncorrelated information

Request a detailed protocol

Due to our experimental design, the working memory location and the motor preparation locations were identical in each trial, and thus correlated. We can imagine another case where there are two types of information that do not have a one-to-one mapping (for example, in a task that requires memorizing locations of items - one out of two possible locations, and their colors - one out of three possible colors, which are uncorrelated). When each target location is associated with only one stimulus color (similar to our working memory and motor preparation locations), the incorporation of stimulus color information in Delay 2 would add only one out of three possible shifts (representing the three possible stimulus colors) to the clusters representing target location (Figure 2—figure supplement 7a). However, when target location and stimulus color are uncorrelated (each stimulus color is equally likely to appear in each target location), the incorporation of stimulus color information could add any of the three possible shifts to the clusters representing target location activity, leading to much more diffuse clusters (Figure 2—figure supplement 7b). In this latter case, we propose a more general formulation to estimate the information subspaces for target location and stimulus color. First, we group trials by target location and obtain the trial-averaged and time-averaged activity in Delay 1 (G1¯). Next, we group trials by stimulus color and obtain the trial-averaged and time-averaged activity in Delay 2 (G2¯). Finally, we estimate the subspaces by:

G1¯=L¯+a×E[CL¯]G2¯=C¯+b×E[LC¯]

where L¯ and C¯ define the subspaces for target location and stimulus color, while and b are scalars representing the mixing coefficients. E[CL¯] represents the expectation of stimulus color activity associated with particular target locations, and E[LC¯] represents the expectation of target location activity associated with particular stimulus colors. At one extreme, the correlation between target location and stimulus color could be 0 (completely random pairing), in which case the expectation value will reduce to 0 if averaging across the other variable does not result in a net translation (which also means there will be no code morphing). In this case, there is no need to minimize mutual information, as the L¯ and C¯ vectors will remain unchanged. On the other hand, if there is a net translation, code morphing will be present, and there will be a need to minimize the mutual information to recover the angles between the subspaces. At the other extreme, the correlation could be 1 (one-to-one mapping), in which case the expectation value will reduce to C¯ and L¯. We can verify that the decorrelation method used for working memory and motor preparation elements in this work was a special case of this formulation (G1¯ and G2¯ become D1¯ and D2¯ as memory and preparation have the same grouping, and the expectations reduce to P¯ and M¯ as there is one-to-one mapping). We would perform the same optimization on (a,b) that will give the least mutual information between L¯ and C¯.

Data and code availability statement

Request a detailed protocol

The code package and data needed to perform the analyses used in the paper is available at https://github.com/chengtang827/MemoryPreparationSubspace (Tang, 2020; copy archived at https://github.com/elifesciences-publications/MemoryPreparationSubspace).

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Decision letter

  1. John T Serences
    Reviewing Editor; University of California, San Diego, United States
  2. Michael J Frank
    Senior Editor; Brown University, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Thank you for submitting your article "Minimally dependent activity subspaces for working memory and motor preparation in the lateral prefrontal cortex" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Michael Frank as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

As the editors have judged that your manuscript is of interest, but as described below that additional experiments are required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv (if it is not already there) along with this decision letter and a formal designation that the manuscript is "in revision at eLife". Please let us know if you would like to pursue this option. (If your work is more suitable for medRxiv, you will need to post the preprint yourself, as the mechanisms for us to do so are still in development.)

Summary:

After consultation, the two reviewers and I wish to highlight the following points that will need to be addressed (along with any other issues raised in the reviews below).

1) Were the data pooled across FEF and 9/46? FEF and 9/46 cytoarchitecture is different and they may work as interrelated but somewhat independent modules (e.g. FEF is an eye field and 9/46 is not based on the work of Schiller, Tehovnik, Goldberg, Schall, etc). To assess the potentially different roles of these areas, it will be important to perform a separate analysis of the data per area, as well as a more complete presentation of the data, anatomy, and recording sites.

2) Clarity of the data analysis method. The authors are using a novel method for data analysis and some more effort is needed to explain concepts more carefully and coherently. See reviewer comments for more specifics.

3) We all agree that there are some issues with the model design and assumptions that limit the insights gained. Given that we are requesting more information about FEF/9-46 and about recording sites etc, we suggest that the model, after revising, might be moved to the supplementary materials.

4) The working memory and motor preparation functions alluded to in the manuscript are very difficult to separate given the design of this experiment (see reviews for more details). An analysis of error trials may help to address this issue, as has been done in some rodent studies (e.g., work from Karel Svoboda, as in Inagaki et al., 2018).

Reviewer #1:

This manuscript examines the coding of working memory signals in two areas of the macaque frontal cortex, the Frontal Eye Fields and the Lateral Prefrontal Cortex. The paper concludes that there are two different subspaces in the DLPFC, one encoding WM signals and the other motor preparation signals, and that neurons with mixed selectivity contribute to both subspaces. They conduct an analysis of multielectrode data recordings in monkeys performing an ODR task with an intervening distractor. This is an interesting study that follows up on two previous publications by the same group (Parthasarathy et al., 2017 and 2019). The study has potential to make a contribution to our knowledge or how worming memory and movement signals segregate within the frontal lobe. Below I will provide a summary of what I believe are strengths and weaknesses of the current manuscript and suggestion on how, in my opinion, the manuscript could be improved.

Strengths:

1) The paper conducts and elegant and novel analysis of multielectrode data recordings using a standard working memory task (ODR), to which a distracter has been added. The methods are state-of-the-art and this reviewer acknowledges the difficulties of conducting the experiments and achieving good isolation of units with relatively large amount of electrodes implanted in the cortex. These procedures are challenging, and the authors should be praised for that.

2) The idea of different subspaces encoding working memory signals and motor preparation within the LPFC is interesting and controversial. Neurons in the LPFC have been hypothesized encode representations that are dissociated from motor signals (Funahashi et al., 1993). However, studies in the same area have also reported neurons that respond before a saccadic eye movement is made (Bullock et al., 2017). The engagement of the LPFC in motor preparation is not clear, mainly because must studies do not dissociate the location of the saccade and the relevant task location (but see Lebedev et al., 2004). In the latter study, however, there was again no dissociation of attention and movement goal. On the other hand, neurons in the neighboring to FEF and more posterior premotor cortex do encode movement plans (Cisek and Kalaska., 2005, see their Figure 5 for recording locations). Regarding neurons in the FEF there is also a consensus they encode movement goals (See Tehovnik, 2000 for a review and Vernet et al., 2014). To summarize this is an interesting issue that has not been clarified yet. Would LPFC encode motor preparation signals rather than abstract representations of space?

Weaknesses and suggestions:

1) One main issue is that the authors pool together the data from FEF and the LPFC. These are two different brain areas and it has been shown that although some neurons exhibit similar properties they are not the same. Neurons in the FEF have a more direct connection to motor centers (e.g., stimulation of the FEF with low current intensities <50microAmps produces saccades, see also Tehovnik, 2000 for a review). This is not the case in LPFC. One issue is that the area of the LPFC where recordings were conducted is not described in the paper, although presumably this is the same data set as Parthasarathy et al., 2017 where there is a figure describing the location of the arrays. By examining the data in the previous publication by the same group (Parthasarathy et al., 2017) my guess the LPFC areas are 9/46, in the vicinity of the principal sulcus (Petrides, 2005). This needs to be detailed in the manuscript. From the point of view that neurons in FEF and 9/46 share some properties, it may make sense pooling the data. However, from the anatomical and other physiological properties point of view it is not justified. Something the authors should take into account is the FEF is not considered by many as part of the granular prefrontal cortex. The cytoarchitecture of the FEF is disgranular, not granular, as areas 9/46 (see Figure 1 of Petrides, 2005). The FEF also has large pyramidal neurons in layer V (Stanton et al., 1989), which is different from areas 9/46, where the largest pyramidal cell bodies are in layers 2/3. The connectivity with other areas is also different (see below). A comprehensive review of FEF anatomy and function across species is in Vernet et al. 2014. Although the review of Tehovnik, 2000, used here as a reference seems to allocate FEF to the DLPFC, this does not seem compatible with the structure of the area in terms of granularity (Petrides, 2005). Other reviews such as Thompson, 2005 make the distinction between FEF and the area around the principal sulcus (9/46). The latter is the area where Goldman-Rakic and coworkers conducted many studies of working memory and I believe some of the arrays in this study were implanted. What I am trying to get at is that FEF does not have the same features as areas 46/9, and therefore it justifies separate analyses rather than pooling the data. It is hard to conceive that a read-out mechanism is using data from these regions simultaneously, not impossible but it would not be the first assumption to make. I would suggest analyzing the data from FEF and areas 9/46 separately. This may reveal that the premotor subspace is biased towards the FEF and the memory towards areas 9/46.

2) One issue in this dataset is the fact that the task does not dissociate the memorized location and the location of the saccade. This is problematic because one needs to assume the memory for the location ends when the saccade starts, some sort of sequential order in the task. This may be the case but there is data from Funahashi and Goldman-Rakic in which they use an antisaccade task and show that the LPFC neurons in areas 46/9 encode the remembered location rather than the location of the saccade (Funahashi et al., 1993). This suggest that motor codes, or preparatory motor signals for saccades may not be encoded in the LPFC. In the FEF this is very different, as commented above, the FEF seems to be directly connected to oculomotor centers such as the SC (see Hanes and Wurtz, 2001). I am not aware of similar connectivity between areas 9/46 and SC, at least not to the same degree, which is relevant to the ODR task employed in this study (see Field et al., 2008). The FEF seems to be part of an oculomotor network while 46/9 are not. This brings me to suggesting the authors again to perform separate analyses for the FEF and LPFC data and to include a diagram in the paper that shows the recording locations superimposed to an anatomical map (e.g., Petrides, 2005).

3) The existence of a distracter in the middle of the delay period is problematic in this task. The animals are supposed to ignore the distracter and they did so as evidenced in the performance data. One question regarding the distracter in the task is whether the second subspace the authors find is encoding a memory for the distracter that diverges from the code in the first subspace. It has been shown that neurons in the LPFC encode visual/perceptual and memory signals and that this can be different populations (Mendoza-Halliday et al., 2017). One possibility is that the authors group the trials according to the distracter location and repeat the analysis. One would anticipate some neurons in the population respond to the distracter. Whether the animal is aware of the distracter location at the time of the saccade is impossible to know for sure. However, if one analyses the pattern of errors and one sees a bias making saccades to the distracter location that would suggest there was a memory for that component of the task that it may be maintained together with the one for the target or in some cases deleted the memory for the target. The authors seem to be aware of the issues with the distracter but they concentrate on color rather than location. Color signals are encoded in the LPFC (Schwedhelm et al., 2020), making the pooling difficult if the authors had several colors of the distracter. But again, pooling by distracter location should be doable. I suggest repeating the analyses as a function of distracter location and examine whether a subspace may encode the distracter location. This would not be surprising, working memory can hold more than 1 item at the time.

4) The paper contains few main figures with very little information about the recordings sites, responses of single neurons. It is heavy on the analysis and data modeling side but does not show single cell or population data visualizations. I am not sure if the authors consider this or they show these data in the previous manuscript. But this should be an independent manuscript. For a modeling paper this may be fine but this is not my view of this manuscript. In this case it is critical to show characterization of responses of single units, levels of firing rates, examples, analysis of selectivities for remembered location, saccade location, etc. The paper could be much more appealing if incorporating these suggestions.

Reviewer #2:

The work by Tang and colleagues pertains to the identification of neural subspaces that are computationally relevant to a task that requires representation of a target across two delay periods, robustness to distractors, and motor execution to the initially acquired target. It builds upon previous work that showed “code morphing” of working memory representations during a delay period following distractor presentation (Parathasurathy et al., 2017). A notable aspect of the present study is the description of an optimization algorithm to identify neural subspaces that does not rely on “classical” dimensionality reduction techniques such as orthogonal decomposition (e.g., PCA, dPCA, etc). The authors claim that the algorithm leads to the existence of two distinct yet concurrent cognitive subspaces within the same task and period: a working memory and a motor preparation subspace. In principle, these results constitute a valuable addition to the literature on population analyses as well as on the interaction between memory and motor processes. The lack of clarity of the presentation of the method, however, obscures the overall interpretation of the data that supports the authors' claims, while making the description challenging for the reader. With respect to the computational model, many important details require revision and/or clarification. Moreover, the model limits itself to reproducing decoding performance, but says much less about the biophysical mechanisms that underlie the existence and/or deployment of working memory and motor preparation subspaces. Although I commend the authors on relating population activity patterns to neural circuit mechanisms, the model in its current form is not particularly insightful.

Below I provide a detailed summary of my three main concerns. The first two points (“Details of subspace identification method” and “Modeling”) are critical:

1) Details of subspace identification method:

a) Rigor and consistency in definitions:

Subsection “Two minimally dependent subspaces coexisted within the LPFC”: Several technical terms related to matrix decomposition are introduced but many of them are used ambiguously throughout, and there is conceptual overlap between them: activity, unmixing matrix, component, and subspace.

“…the magnitude of one component in Delay 2 was 65% of that in Delay 1 (Component 1), and the magnitude of the other component in Delay 1 was 12% of that in Delay 2 (Component 2).”: Components are conflated with their magnitude

“The temporal dynamics of the full space population activity projected into these subspaces showed that activity in the first subspace emerged early after target presentation and was maintained until the saccade cue…”: Projections or magnitude of the projections?

In what sense is the term “information” used throughout the manuscript? (In the vernacular sense or as a measure of uncertainty in bits?)

“…information emerged right after target presentation, and although the information was stronger in Delay 1 (60.5 ± 1.3%),”: What is the relationship between target information and decoder performance? are both variables measured with a percentage?

“Cross-temporal decoding of full space neural activity projected into the second subspace showed that information emerged after distractor presentation (42.6 ± 1.1%), and was stable throughout Delay 2 (Figure 1F). In Delay 1 and Delay 2, the first subspace explained 14.6% and 10.3% of the full space variance, while the second subspace explained 5.8% and 8.1% of the full space variance, respectively.”: What is the relationship here between the variance explained by subspaces and the components? The distinction between “component” and “subspace” is not always clear.

“…and the first 6 out of the 7 principal components cumulatively accounted…”: In standard dimensionality reduction, for example, the goal is to reduce the dimensionality of the neuron state space (226 neurons) to a lower number (e.g., Santhanam et al., 2009). What do the 6 effective dimensions refer to?

Subsection “Information in one subspace led to a small amount of interference in information in the other subspace”, “We found no evidence of a drop in performance between projMSub(M) and projMSub(M+P) (p > 0.73, g = 0.61), and between projPSub(P) and projPSub(M+P) (p > 0.22, g = 2.63), suggesting a lack of interference between these subspaces”: How is this result interpreted in light of the finding that the subspaces are not orthogonal?

b) Novelty and relationship to established methods:

Subsection “Two minimally dependent subspaces coexisted within the LPFC”: There is a discussion of the difficulty of obtaining labels for working memory and motor preparation subspaces, and the subsequent application of a novel method to obtain them. How is this different from orthogonalization? In other words, how is considering mutual information between components a more general framework?

Aforementioned subsection, “Our objective was then to find through an optimization technique the best unmixing matrix, to apply to Delay 1 and Delay 2 activity, that could recover the working memory and motor preparation activity with the lowest mutual information possible between them (see Materials and methods).”: How is this different from the optimization method used in Parathasurathy et al., 2019? Is this a general framework to identify any pair of subspaces?

“This was qualitatively consistent with our hypothesis, aside from the decrease in information in Delay 2 (39.9 ± 1.1%).”: Is the decrease in “information” in Delay 2 related to the fact that this subspace is morphed in Delay 2 (Parathasarathy et al., 2017)?

“Our results provided the first evidence showing that information about two separate cognitive processes can be simultaneously encoded in subspaces within the same brain region.”: This is a strong statement for at least three reasons: (a) there are other studies that have shown some decomposition related to what can arguably be called cognitive processes, including some from the rodent literature which were not referenced (e.g., Inagaki et al., 2019, Svoboda and Li, 2018); (b) this work has not conclusively/causally shown that these subspaces indeed contain information about memory and motor preparation, as lesion studies would; and (c) the word subspace in this study does not imply reduced dimensionality as in many other studies (e.g. Kaufman et al., 2014). I suggest rewriting in a more modest form.

c) Overall clarity in description:

A method is described to obtain working memory and motor preparation subspaces. However, the logical presentation is not adequate. In Figure 1, for example, subspaces are already introduced to be related to working memory and motor preparation, without any evidence. An alternative is to name the two subspaces in Figure 1 only after showing that they correspond to functional subspaces (before they are, Subspace 1 and Subspace 2).

“Since the second subspace contained target information only after the distractor disappeared, and motor preparation presumably began after the last sensory cue that reliably predicted the timing of the Go cue (i.e. the offset of the distractor), we hypothesized that the second subspace corresponded to a motor preparation subspace”: Can motor preparation and working memory be distinguished in terms of behavior during error trials (e.g., Inagaki et al., 2018)?

“In Delay 1 and Delay 2, the first subspace explained 14.6% and 10.3% of the full space variance, while the second subspace explained 5.8% and 8.1% of the full space variance, respectively.”: This sentence about explained variance is difficult to parse, because of the existence of two delays, two subspaces and the full space. What would be the expected total variance? Are the subspaces explaining a fraction of the variance of the full space?

2) Modeling

a) model construction:

i) Equation in subsection “Model” describes the dynamics of the “bump attractor” model. A “leak” term, which reflects a decay towards a baseline firing rate, seems to be missing. From a modeling point of view, the leak is crucial for the dynamics, as its existence is what motivated recurrent synaptic circuitry to counterbalance the decay mediated by the leak for integration and working memory computations as mediated by “bump attractor” dynamics (e.g., compare to Wimmer et al., 2014, which was cited).

ii) There are no details of how “normalization” was implemented. Was it applied to all units uniformly? What is the form of the normalization equation and what are the values of the parameters? It seems like an ad-hoc step, while some models have shown that normalization arises naturally in some implementations of the bump attractor model (e.g., Ardid et al., 2007).

iii) Subsection “Model” paragraph two: The description of the inputs here (i.e., working memory and motor preparation) is missing some details. Are the inputs correlated? How does the distractor input affect the overall dynamics? What are their values?

iv) In subsection “A bump attractor artificial neural network with divisive normalization recapitulated the properties of LPFC activity” there is a description of how the model is constrained by selectivity of the neural data, as well as by the “ 43 % overlap” in inputs (Figure 5). How this related to the loadings found in Figure 3?

b) Model significance:

i) What are the activities of the model neurons? In particular, it is not clear whether the neurons are mixed selective, i.e., whether any given (simulated) neuron participates in both working memory and motor preparation. A hint is given in Figure 4—figure supplement 2, but this should be expanded.

ii) In Figure 5, a direct comparison between model and data is missing, although it is described qualitatively in the text.

iii) What are the model predictions?

3) Additional analyses or plots to improve clarity

a) Is Figure 1C necessary, given a similar Figure 1G with actual data? A general schematic is always welcome, perhaps illustrating distinct possibilities of overlap between the subspaces.

b) “In an additional test of the hypothesis that the second subspace corresponded to a motor preparation subspace, we examined the relationship between the unmixed motor preparation activity and the unmixed pre-saccade activity at the level of single cells”: This is a continuation, at a single cell level, of the previous hypothesis of relating delay 2 period activity to pre-saccadic activity. For an independent analysis, can the activity in error trials be used to distinguish motor preparation from working memory representations?

c) “Importantly, Component 2 and Component 2’ were also significantly correlated (Figure 2A right, Pearson correlation r = 0.62, P <0.01).”: Can the similarity between the components be defined in terms of angles, as done between the subspaces? Moreover, the correlation component2-component2' = 0.62 is high, but could be higher. How does the motor preparation subspace relate to distractor encoding? Could this explain why the correlation 2-2' is not higher?

d) “…concurrent increase of activity in Neurons 1 and 2 signals a change in memory (i.e. the population activity in state space moved along the working memory subspace)…”: This has not been shown explicitly with the neural activity, namely, that moving along the working memory subspace, corresponds to a (discrete) change in the target representation. Such a figure would be much more informative than the illustration in Figure 3C (which is appreciated, but would actually be valid for any orthogonal subspace decomposition, not necessarily working memory/motor preparation).

https://doi.org/10.7554/eLife.58154.sa1

Author response

Summary:

After consultation, the two reviewers and I wish to highlight the following points that will need to be addressed (along with any other issues raised in the reviews below).

1) Were the data pooled across FEF and 9/46? FEF and 9/46 cytoarchitecture is different and they may work as interrelated but somewhat independent modules (e.g. FEF is an eye field and 9/46 is not based on the work of Schiller, Tehovnik, Goldberg, Schall, etc). To assess the potentially different roles of these areas, it will be important to perform a separate analysis of the data per area, as well as a more complete presentation of the data, anatomy, and recording sites.

We have clarified the recording sites used in this current analysis in the main text and in the response to reviewers (see below for more details). In summary, we only used neurons recorded from electrodes in area 9/46 for this analysis, since cells recorded in those electrodes were the ones that showed a higher degree of mixed selectivity and code morphing (in Parthasarathy et al., 2017). We did not include neurons in the FEF (which were confirmed using microstimulation in Parthasarathy et al., 2017), as they exhibited a stable code that implied a single subspace.

2) Clarity of the data analysis method. The authors are using a novel method for data analysis and some more effort is needed to explain concepts more carefully and coherently. See reviewer comments for more specifics.

We realize that the methods were not explained clearly enough, so we have modified the explanation extensively (as explained below in the response to reviewers and as reflected in the changes to the main text of the manuscript). We hope that the changes make it clearer why we needed a new method, and what this method entailed.

3) We all agree that there are some issues with the model design and assumptions that limit the insights gained. Given that we are requesting more information about FEF/9-46 and about recording sites etc, we suggest that the model, after revising, might be moved to the supplementary materials.

We agree with this point, and have moved the model to the supplement, as suggested.

4) The working memory and motor preparation functions alluded to in the manuscript are very difficult to separate given the design of this experiment (see reviews for more details). An analysis of error trials may help to address this issue, as has been done in some rodent studies (e.g., work from Karel Svoboda, as in Inagaki et al., 2018).

It would have been great to have more error trials to be able to carry out this analysis. Unfortunately, the elevated performance of our monkeys prevented us from obtaining enough error trials to run a meaningful analysis. Furthermore, even if we did have enough error trials, the suggested analysis would be challenging, since an error could be due to failures in memory encoding and/or motor preparation. We expand on these points in the response to reviewers below.

Reviewer #1:

[…]

Weaknesses and suggestions:

1) One main issue is that the authors pool together the data from FEF and the LPFC. These are two different brain areas and it has been shown that although some neurons exhibit similar properties they are not the same. Neurons in the FEF have a more direct connection to motor centers (e.g., stimulation of the FEF with low current intensities <50microAmps produces saccades, see also Tehovnik, 2000 for a review). This is not the case in LPFC. One issue is that the area of the LPFC where recordings were conducted is not described in the paper, although presumably this is the same data set as Parthasarathy et al., 2017 where there is a figure describing the location of the arrays. By examining the data in the previous publication by the same group (Parthasarathy et al., 2017) my guess the LPFC areas are 9/46, in the vicinity of the principal sulcus (Petrides, 2005). This needs to be detailed in the manuscript. From the point of view that neurons in FEF and 9/46 share some properties, it may make sense pooling the data. However, from the anatomical and other physiological properties point of view it is not justified. Something the authors should take into account is the FEF is not considered by many as part of the granular prefrontal cortex. The cytoarchitecture of the FEF is disgranular, not granular, as areas 9/46 (see Figure 1 of Petrides, 2005). The FEF also has large pyramidal neurons in layer V (Stanton et al., 1989), which is different from areas 9/46, where the largest pyramidal cell bodies are in layers 2/3. The connectivity with other areas is also different (see below). A comprehensive review of FEF anatomy and function across species is in Vernet et al., 2014. Although the review of Tehovnik, 2000, used here as a reference seems to allocate FEF to the DLPFC, this does not seem compatible with the structure of the area in terms of granularity (Petrides, 2005). Other reviews such as Thompson, 2005 make the distinction between FEF and the area around the principal sulcus (9/46). The latter is the area where Goldman-Rakic and coworkers conducted many studies of working memory and I believe some of the arrays in this study were implanted. What I am trying to get at is that FEF does not have the same features as areas 46/9, and therefore it justifies separate analyses rather than pooling the data. It is hard to conceive that a read-out mechanism is using data from these regions simultaneously, not impossible but it would not be the first assumption to make. I would suggest analyzing the data from FEF and areas 9/46 separately. This may reveal that the premotor subspace is biased towards the FEF and the memory towards areas 9/46.

We thank the reviewer for pointing out that we provided incomplete information about our recording sites and neural data involved in the analyses. We did not pool together FEF and LPFC neurons in our analyses; the data from what we called LPFC in this paper were only from Areas 46 and 9/46, and did not include what we previously identified as FEF in Parthasarathy et al., 2017.

We have added a new figure (Figure 1B) to show the recording sites of the LPFC cells, and highlight the difference between LPFC and FEF electrode positions.

We have added a sentence in Results to state that the data used in the analyses did not involve FEF neurons:

“Figure 1B shows the different electrode positions in the LPFC and FEF on an anatomical map. Additionally, FEF electrodes were differentiated from LPFC electrodes using microstimulation (see Materials and methods).”

We have also added a section in Materials and methods to describe how we functionally differentiated the FEF from the LPFC using microstimulation.

In Parthasarathy et al., 2017, one of the main findings was that LPFC neurons exhibited code-morphing (i.e. there were two different population codes in Delay 1 and Delay 2 for the same target location), whereas the population code in FEF did not morph (i.e. there was one stable code throughout Delay 1 and Delay 2). This motivated us to use only LPFC data, rather than FEF data, to identify the two subspaces in the current work.

We have added a line in Results to highlight this motivation.

“In this paper, the presence of code-morphing in the LPFC motivated us to analyze the 226 single neurons recorded from the LPFC, which did not include those recorded from the FEF.”

2) One issue in this data set is the fact that the task does not dissociate the memorized location and the location of the saccade. This is problematic because one needs to assume the memory for the location ends when the saccade starts, some sort of sequential order in the task. This may be the case but there is data from Funahashi and Goldman-Rakic in which they use an antisaccade task and show that the LPFC neurons in areas 46/9 encode the remembered location rather than the location of the saccade (Funahashi et al., 1993). This suggest that motor codes, or preparatory motor signals for saccades may not be encoded in the LPFC. In the FEF this is very different, as commented above, the FEF seems to be directly connected to oculomotor centers such as the SC (see Hanes and Wurtz, 2001). I am not aware of similar connectivity between areas 9/46 and SC, at least not to the same degree, which is relevant to the ODR task employed in this study (see Field et al., 2008). The FEF seems to be part of an oculomotor network while 46/9 are not. This brings me to suggesting the authors again to perform separate analyses for the FEF and LPFC data and to include a diagram in the paper that shows the recording locations superimposed to an anatomical map (e.g., Petrides, 2005).

We thank the reviewer for raising two good points in this comment, which we address below.

First, while it is true that the task does not dissociate the memorized location and the location of the saccade (which is the reason why we developed this novel method to identify the 2 subspaces), it is not the case that we required a sequential order in the task, as working memory and motor preparation information overlapped in Delay 2. Our interpretation of the 2nd subspace as a motor preparation subspace is consistent with the interpretation that the monkeys begin the preparation of the movement after the last stimulus that reliably predicts the Go cue (which is the offset of the distractor, that reliably occurs 1 second prior to the Go cue). But it is worth highlighting that this is our interpretation of the results, rather than a guiding hypothesis. In other words, our method to identify the 2 subspaces included no constraint or bias towards finding a subspace where information emerged in Delay 2. Rather, the fact that we did find a subspace with information that emerged during Delay 2 led us to interpret this subspace as a motor preparation subspace.

Second, the concern in Point 2 stems from the same problem raised in the Point 1. Following the reviewer’s suggestion, we have added a diagram to visually show the electrode locations on an anatomical map, and stated explicitly that all our analyses with LPFC neurons was not mixed with FEF neurons (please refer to the responses to Point 1).

3) The existence of a distracter in the middle of the delay period is problematic in this task. The animals are supposed to ignore the distracter and they did so as evidenced in the performance data. One question regarding the distracter in the task is whether the second subspace the authors find is encoding a memory for the distracter that diverges from the code in the first subspace. It has been shown that neurons in the LPFC encode visual/perceptual and memory signals and that this can be different populations (Mendoza-Halliday et al., 2017). One possibility is that the authors group the trials according to the distracter location and repeat the analysis. One would anticipate some neurons in the population respond to the distracter. Whether the animal is aware of the distracter location at the time of the saccade is impossible to know for sure. However, if one analyses the pattern of errors and one sees a bias making saccades to the distracter location that would suggest there was a memory for that component of the task that it may be maintained together with the one for the target or in some cases deleted the memory for the target. The authors seem to be aware of the issues with the distracter but they concentrate on color rather than location. Color signals are encoded in the LPFC (Schwedhelm et al., 2020), making the pooling difficult if the authors had several colors of the distracter. But again, pooling by distracter location should be doable. I suggest repeating the analyses as a function of distracter location and examine whether a subspace may encode the distracter location. This would not be surprising, working memory can hold more than 1 item at the time.

We didn’t find evidence that the animals are more prone to make an error saccade to the distractor location, as shown in Author response image 1.

Author response image 1
Each point represents the probability of making a saccade into the distractor location in a single session.

Blue line, chance probability (1/8). No significant evidence was found against chance (T-test, P > 0.31).

Although there was no tendency to saccade to the distractor location, there was still significant information for distractor locations in the population activity (Figure 3—figure supplement 3A). But the distractor information was not encoded in the motor preparation subspace, as we have shown that the decoding performance for distractor locations in the motor preparation subspace was significantly lower than that in the full space (Figure 3—figure supplement 3B).

We have added this supplementary figure and a section in Results to clarify this point.

“Alongside the working memory and motor preparation activities for target locations, there could also be activities representing distractor locations in Delay 2. By grouping trials according to distractor labels, we indeed found significant distractor information in the full space (Figure 3—figure supplement 3). However, the distractor activity in Delay 2 was not related to the Element 2 or the motor preparation subspace we identified, because the distractor activity and the motor preparation activity were obtained from data grouped by different trial labels (target and distractor labels were uncorrelated). Very little distractor information (17.9 ± 0.7%) was successfully decoded in the motor preparation subspace (Figure 3—figure supplement 3).”

4) The paper contains few main figures with very little information about the recordings sites, responses of single neurons. It is heavy on the analysis and data modeling side but does not show single cell or population data visualizations. I am not sure if the authors consider this or they show these data in the previous manuscript. But this should be an independent manuscript. For a modeling paper this may be fine but this is not my view of this manuscript. In this case it is critical to show characterization of responses of single units, levels of firing rates, examples, analysis of selectivities for remembered location, saccade location, etc. The paper could be much more appealing if incorporating these suggestions.

We agree with the reviewer that these changes will make the manuscript more readable and appealing. Together with the diagram showing the anatomical location of electrodes (Figure 1B), we added diagrams showing two single cell responses (Figure 1C) and a characterization of the population selectivity (Figure 1D) to form a new Figure 1.

We also changed our Results section accordingly:

“We recorded single unit activity from the LPFC and FEF of both monkeys while they performed the task. Figure 1B shows the different electrode positions in the LPFC and FEF on an anatomical map. Additionally, FEF electrodes were differentiated from LPFC electrodes using microstimulation (see Materials and methods).”

“In this paper, the presence of code-morphing in the LPFC motivated us to analyze the 226 single neurons recorded from the LPFC, which did not include those recorded from the FEF. Single neurons in the LPFC showed sustained selectivity to target locations during both delay periods, with some maintaining the same target tuning in both delays (Figure 1C, left), while some changed target tuning from Delay 1 to Delay 2 (Figure 1C, right). The latter category of neurons was characterized as non-linearly mixed selective neurons, and was shown to drive code-morphing in LPFC. On the population level, most of the cells with target selectivity in one delay also showed selectivity in the other delay (Figure 1D).”

Reviewer #2:

[…]

1) Details of subspace identification method:

a) Rigor and consistency in definitions:

Subsection “Two minimally dependent subspaces coexisted within the LPFC”: Several technical terms related to matrix decomposition are introduced but many of them are used ambiguously throughout, and there is conceptual overlap between them: activity, unmixing matrix, component, and subspace.

We thank the reviewer for the suggestions to enhance the clarity and readability of this manuscript.

We have chosen to use “activity” to refer to the raw firing rate of neurons (spikes/s), such as Delay 1 or Delay 2 activity; it is also used to refer to the contribution that the firing rate makes to working memory (working memory activity) or motor preparation (motor preparation activity).

We used the term “unmixing matrix” to refer to the matrix of coefficients used to unmix the original Delay 1 and Delay 2 activity. We have renamed it to “unmixing coefficients”.

We used “component” to refer to the seven 226-dimensional vectors obtained from the optimization. To avoid confusion with the meaning of “component” in other technical contexts like principal component analysis, we have changed it to “element”, and explicitly defined an “element” as the 7 vectors obtained by the optimization. When talking about “elements”, we are always referring to the 226 x 7 vector sets.

A “subspace” is the orthonormal bases of an “element” (7 vectors). We have also added this definition.

We have modified the text as follows:

“Using our method, we started with Delay 1 and Delay 2 activity exhibiting 0.33 bits mutual information, and found two unmixed elements (each of size 226 x 7) from D1 and D2 activity with a minimum mutual information of 0.08 bits (Figure 2—figure supplement 1). The two elements we identified consisted of 7 vectors in the 226-dimensional space, and according to the unmixing coefficients we identified, the magnitude of one element (Element 1) in Delay 2 was 65% of that in Delay 1, and the magnitude of the other element (Element 2) in Delay 1 was 12% of that in Delay 2. The orthonormal bases of the two elements defined two subspaces (Subspace 1 and Subspace 2).”

“…the magnitude of one component in Delay 2 was 65% of that in Delay 1 (Component 1), and the magnitude of the other component in Delay 1 was 12% of that in Delay 2 (Component 2).”: Components are conflated with their magnitude.

We have reordered the sentences to avoid confusion:

“The two elements we identified consisted of 7 vectors in the 226-dimensional space, and according to the unmixing coefficients we identified, the magnitude of one element (Element 1) in Delay 2 was 65% of that in Delay 1, and the magnitude of the other element (Element 2) in Delay 1 was 12% of that in Delay 2.”

“The temporal dynamics of the full space population activity projected into these subspaces showed that activity in the first subspace emerged early after target presentation and was maintained until the saccade cue…”: Projections or magnitude of the projections?

We were referring to the magnitude of the projections. We have rewritten the text:

“The temporal dynamics of the full space population activity projected into these subspaces showed that the magnitude of activity in the first subspace increased early after target presentation and was maintained until the saccade cue, while the magnitude of activity in the second subspace increased after distractor presentation and stayed relatively high even after the Go cue (Figure 1C, single-session results are shown in Figure 2—figure supplement 2).”

In what sense is the term “information” used throughout the manuscript? (In the vernacular sense or as a measure of uncertainty in bits?)

We used the term “information” in a general sense throughout the paper, which mostly referred to the neural code enabling the decoding of different intended locations, with the only exception of “mutual information”, which is a measure of uncertainty in bits.

We have added a brief definition of the general “information” in Results:

“Two different stable population activity in LPFC were observed in Delay 1 and Delay 2, which implied that a downstream region would need to use different decoders in the two periods to extract the stable working memory information (neural codes supporting the discrimination of different intended items)…”

“…information emerged right after target presentation, and although the information was stronger in Delay 1 (60.5 ± 1.3%),”: What is the relationship between target information and decoder performance? are both variables measured with a percentage?

Decoder performance is a proxy of target information, and more specifically, it only speaks for linearly decodable information. Only decoder performance is measured with a percentage.

We have added a brief description in the text:

“Next, we used the decoding performance of a linear decoder (LDA) as a proxy of target information and evaluated target information in each subspace.”

“Cross-temporal decoding of full space neural activity projected into the second subspace showed that information emerged after distractor presentation (42.6 ± 1.1%), and was stable throughout Delay 2 (Figure 1F). In Delay 1 and Delay 2, the first subspace explained 14.6% and 10.3% of the full space variance, while the second subspace explained 5.8% and 8.1% of the full space variance, respectively.”: What is the relationship here between the variance explained by subspaces and the components? The distinction between “component” and “subspace” is not always clear.

We have changed the term “Component” into “Element”, and an “Element” refers to a 226 x 7 vector set identified using the optimization method.

“The two elements we identified consisted of 7 vectors in the 226-dimensional space…”

The 7 vectors in an “Element” were not orthogonal to each other, and a “subspace” refers to the orthonormal bases spanned by the vectors from the vector set.

“The orthonormal bases of the two elements defined two subspaces (Subspace 1 and Subspace 2).”

“…and the first 6 out of the 7 principal components cumulatively accounted…”: In standard dimensionality reduction, for example, the goal is to reduce the dimensionality of the neuron state space (226 neurons) to a lower number (e.g., Santhanam et al., 2009). What do the 6 effective dimensions refer to?

From the optimization, we identified two elements, each consisted of 7 226-dimensional vectors. The subspace spanned by each vector set is surely 7 dimensional, given that all the 7 vectors are independent. However, this does not guarantee that the projection of full space data into this subspace will still be 7 dimensional – it is possible that the projection spans an even smaller dimension in the subspace. Hence, we performed a PCA after projecting full space data into the subspace, and the “6 effective dimensions” were referring to the 6 PCA components that explained more than 95% variance. In other words, the “6 effective dimensions” were describing the data projected into the subspace, rather than the subspace per se. We have modified our text to clarify this point.

“Full-space data in the two subspaces had an effective dimensionality of 6 dimensions each – after projecting single-trial full space data into the subspaces, we performed a PCA on the projected data, and the first 6 out of the 7 principal components cumulatively accounted for more than 95% of the variance within each subspace (Figure 2—figure supplement 3).”

Figure 2—figure supplement 3 title:

“Effective dimension of full-space data in the subspaces.”

Subsection “Information in one subspace led to a small amount of interference in information in the other subspace”, “We found no evidence of a drop in performance between projMSub(M) and projMSub(M+P) (p > 0.73, g = 0.61), and between projPSub(P) and projPSub(M+P) (p > 0.22, g = 2.63), suggesting a lack of interference between these subspaces”: How is this result interpreted in light of the finding that the subspaces are not orthogonal?

Because we used LDA’s decoding performance as a proxy of target information, the lack of interference between two non-orthogonal subspaces indicated that the shift of clusters in the state space were not large enough to cross the classification boundaries, and thus did not affect the classification performance. These cases can be observed in Figure 2F and Figure 2—figure supplement 4.

We have more clearly stated this interpretation in the main text.

“As we used LDA’s decoding performance as a proxy of target information, the lack of interference between two non-orthogonal subspaces indicated that the shift of clusters in the state space caused by superimposed activity were not large enough to cross the classification boundaries, and thus did not affect the classification performance.”

b) Novelty and relationship to established methods:

Subsection “Two minimally dependent subspaces coexisted within the LPFC”: There is a discussion of the difficulty of obtaining labels for working memory and motor preparation subspaces, and the subsequent application of a novel method to obtain them. How is this different from orthogonalization? In other words, how is considering mutual information between components a more general framework?

We discussed an alternative orthogonalization method in the Discussion.

“In order to assess whether imposing orthogonality between subspaces was feasible, we fixed Delay 1 activity as the first activity subspace and rotated each column vector in Delay 2 activity matrix to be orthogonal to Delay 1 activity (Gram-Schmidt algorithm) to obtain the second activity matrix, such that the two activity matrices would be orthogonal to each other.”

The limitation of the orthogonalization method is discussed further in Figure 5—figure supplement 1.

“First, imposing orthogonality between subspaces, while possible, may hide interesting properties in the data, since activity subspaces could be perfectly orthogonal, but they could also be non-orthogonal, such that interference between them was possible (which may account for interference between cognitive processes). As such, imposing orthogonality would prevent us from identifying interference between subspaces. Instead, the unmixing method allows for both possibilities, and hence is a more unbiased way to understand our data. Second, the unmixing method has fewer assumptions and is more flexible for subspace identification. Orthogonal decomposition imposes one fixed subspace to begin with, and the second subspace is entirely contingent to the blind choice of the first subspace. Instead, the unmixing method simultaneously identifies two subspaces without biasing towards either one.”

Aforementioned subsection, “Our objective was then to find through an optimization technique the best unmixing matrix, to apply to Delay 1 and Delay 2 activity, that could recover the working memory and motor preparation activity with the lowest mutual information possible between them (see Materials and methods).”: How is this different from the optimization method used in Parathasurathy et al., 2019? Is this a general framework to identify any pair of subspaces?

It is true that both methods are under the optimization framework, but their objectives are quite different.

The 2019 paper aimed to find a single subspace in which the projection of Delay 1 and Delay 2 activity overlapped, and the objective function to be minimized was the distance between the Delay 1 and Delay 2 clusters projected into the subspace.

This paper aimed to find two subspaces that were minimally dependent on each other, and the objective function to be minimized was the mutual information between the two unmixed elements.

Given good evidence that there are two distinct subspaces in the data, our method does provide a general framework to identify the subspaces.

“This was qualitatively consistent with our hypothesis, aside from the decrease in information in Delay 2 (39.9 ± 1.1%).”: Is the decrease in “information” in Delay 2 related to the fact that this subspace is morphed in Delay 2 (Parathasarathy et al., 2017)?

Yes, the decrease in decoding performance in the working memory subspace was related to code morphing. This is because in Delay 2, the motor preparation code was superimposed onto the working memory code (which resulted in code-morphing); in the presence of divisive normalization, working memory activity was suppressed, and thus the decoding performance also decreased. This observation was replicated in the bump attractor model with normalization.

Figure 4—figure supplement 2:

“e, Cross-temporal decoding performance of the model (with normalization) in the working memory subspace. Decoding performance reduced significantly in the working memory subspace in Delay 2 (84.1 ± 7.7% in LP11, 58.4 ± 4.1% in LP22, P < 0.05, g = 3.39).”

“Our results provided the first evidence showing that information about two separate cognitive processes can be simultaneously encoded in subspaces within the same brain region.”: This is a strong statement for at least three reasons: (a) there are other studies that have shown some decomposition related to what can arguably be called cognitive processes, including some from the rodent literature which were not referenced (e.g., Inagaki et al., 2019, Svoboda and Li, 2018); (b) this work has not conclusively/causally shown that these subspaces indeed contain information about memory and motor preparation, as lesion studies would; (c) the word subspace in this study does not imply reduced dimensionality as in many other studies (e.g. Kaufman et al., 2014). I suggest rewriting in a more modest form.

We acknowledge the limitations in causality evidence as pointed out in (b) by the reviewer, so we softened our gap statement as:

“Our results provided the first evidence suggesting that information about two separate cognitive processes can be simultaneously encoded in subspaces within the same brain region.”

The two rodent studies the reviewer mentioned in (a) (Inagaki et al., 2019, Svoboda and Li ,2018) only explored premotor activity and the premotor subspace, which is still different from our results showing two simultaneous cognitive subspaces (working memory and motor preparation). We have added references to them, together with other work showing the existence of one subspace.

“The majority of the literature on information subspaces in the brain has reported a single subspace (Druckmann and Chklovskii, 2012; Inagaki et al., 2019; Parthasarathy et al., 2019; Svoboda and Li, 2018)…”

Additionally, we have added a reference to another recent human study (Minxha et al., 2020), where they reported two cognitive subspaces for a “memory” task and a “categorization” task. However, the two subspaces were employed in different types of trial blocks in an “alternating” fashion, still different from our simultaneous activation of both working memory and motor preparation subspaces.

“Minxha et al., 2020, reported the existence of two cognitive subspaces for “memory” and “categorization” tasks, but the two subspaces were employed asynchronously in different trial blocks.”

The 7-dimensional working memory subspace were identified from experimental data containing 7 target locations, but the real encoding subspace for working memory could require fewer dimensions than 7. For Point (c), we think the fact that the effective dimensions of the data in the working memory subspace was 6, rather than 7, indicated that there was a reduction in dimensionality. We further believe that if there were more task conditions (24 target locations for example), the reduction of effective dimension of data in the subspace will be more prominent, as it will asymptote to the true dimensionality of the working memory code. We have added a few lines after the presentation of “effective dimension” to elaborate on this point.

“Full-space data in the two subspaces had an effective dimensionality of 6 dimensions each … This indicated that the true dimensionality of the neural code could be smaller than the number of discrete target locations imposed by the experiment. In addition, as the number of discrete target locations increases in the experiment (for example, 24 target locations), we expect that the effective dimensionality of data in the subspaces will asymptote to the true dimensionality of the neural codes supporting the cognitive processes.”

c) Overall clarity in description:

A method is described to obtain working memory and motor preparation subspaces. However, the logical presentation is not adequate. In Figure 1, for example, subspaces are already introduced to be related to working memory and motor preparation, without any evidence. An alternative is to name the two subspaces in Figure 1 only after showing that they correspond to functional subspaces (before they are, Subspace 1 and Subspace 2).

We agree with the reviewer and have renamed the subspaces as Subspace 1 and 2 before the presentation of evidence.

“Since the second subspace contained target information only after the distractor disappeared, and motor preparation presumably began after the last sensory cue that reliably predicted the timing of the Go cue (i.e. the offset of the distractor), we hypothesized that the second subspace corresponded to a motor preparation subspace”: Can motor preparation and working memory be distinguished in terms of behavior during error trials (e.g., Inagaki et al., 2018)?

Unfortunately, we do not think we can distinguish them with error trials. This is because in correct trials, the working memory location was always the same as the motor preparation location. When an error was made, we would not know if it was due only to incorrect preparation, or due to an incorrect memory plus an incorrect preparation (our error trial analysis suggested that it was likely to be the latter case, as the decoding performance using error trial data decreased in both subspaces, Figure 5B,C). This analysis will only be possible in another experimental setup where the animals’ behavioral responses dissociated memory and saccade locations, and could report both labels separately in a trial.

Additionally, we did not have enough error trials for this analysis. For example, if we looked for trials where the correct location was A, but an incorrect saccade was made to Location B, the number of such trials were no more than 9 among all (A, B) pairs in any single session, making it hard to reach any statistical conclusions.

“In Delay 1 and Delay 2, the first subspace explained 14.6% and 10.3% of the full space variance, while the second subspace explained 5.8% and 8.1% of the full space variance, respectively.”: This sentence about explained variance is difficult to parse, because of the existence of two delays, two subspaces and the full space. What would be the expected total variance? Are the subspaces explaining a fraction of the variance of the full space?

Yes, the subspaces explained a fraction of the variance in the full space. The variance explained by the subspaces were analogous to the variance explained by principal components, and the total variance would be 100% of the variance in the full space. We have rewritten the sentence for better readability.

“In Delay 1, Subspace 1 and Subspace 2 accounted for 14.6% and 10.3% of the variance in the full space; in Delay 2, Subspace 1 and Subspace 2 accounted for 5.8% and 8.1% of the variance in the full space.”

2) Modeling

a) Model construction:

i) Equation in subsection “Model” describes the dynamics of the “bump attractor” model. A “leak” term, which reflects a decay towards a baseline firing rate, seems to be missing. From a modeling point of view, the leak is crucial for the dynamics, as its existence is what motivated recurrent synaptic circuitry to counterbalance the decay mediated by the leak for integration and working memory computations as mediated by “bump attractor” dynamics (e.g., compare to Wimmer et al., 2014, which was cited).

The “leak” term was technically not missing in the previous version of our model, it was just hidden. With a “leak” term, the dynamics defining the model would look like: τdrdt=r+φ(Wrecr+WinI+σ) where r is the firing rate of the population; Wrecr+WinI+σ represents the sum of the recurrent input, external input, and noise; τ is the decaying time constant. To enable numerical simulation, we use Newton’s method to discretize the equation: rt+1=rt+(rt+φ(Wrecrt+WinI+σ))×dtτ where dt is the length of the simulation time step. In the previous version of the model, we made dt=τ, and the “leak” term was canceled out, so the dynamics looked like: rt+1=φ(Wrecrt+WinI+σ) Now we have set τ=20ms, and dt=2ms, which essentially makes the approximation steps 10 times finer than the previous simulation. We have verified that this change does not result in any qualitative changes to the model results, and have updated the model description and results to the revised version.

“The firing rate of the population was characterized by:

τdrdt=r+φ(Wrecr+WinI+σ) where τ was a uniform decay constant; . . . For numerical simulation, we used Newton’s method: rt+1=rt+(rt+φ(Wrecrt+WinI+σ))×dtτrt=rt/αt where we set τ=20ms and dt=2ms; αt was a scalar obtained by mean(rt)/mean(r0), and it was applied uniformly to each unit of the whole population to maintain the mean population firing rate at the baseline level (divisive normalization)…”

ii) There are no details of how “normalization” was implemented. Was it applied to all units uniformly? What is the form of the normalization equation and what are the values of the parameters? It seems like an ad-hoc step, while some models have shown that normalization arises naturally in some implementations of the bump attractor model (e.g., Ardid et al., 2007).

The divisive normalization step in the model was inspired by an observation in the neural data – the mean population firing rate in the delay periods was not different from that in the baseline period. This was different from the normalization described in Ardid et al., 2007, because in that paper, the mean population firing rates before stimulus presentation and during the mnemonic delay were different.

The divisive normalization was applied uniformly to all the units. We divided the firing rate of each neuron by the same factor (derived from the sum of the population activity) to maintain the overall population activity at a constant level. We have added more details to the description of the divisive normalization:

rt+1=rt/αtαt was a scalar obtained by mean(rt)/mean(r0), and it was applied uniformly to all units to maintain the mean population firing rate at the baseline level (divisive normalization).”

We acknowledge that this implementation of normalization simulated only the high-level operation of divisive normalization; more biological-plausible mechanisms and detailed modeling on the single-neuron level could be explored for future work.

iii) Subsection “Model” paragraph two: The description of the inputs here (i.e., working memory and motor preparation) is missing some details. Are the inputs correlated? How does the distractor input affect the overall dynamics? What are their values?

Yes, the working memory input and the motor preparation were correlated (1-to-1 mapping) in the model. In each trial, the distractor location was always different from the target location; the input loadings of the distractor was the same as that of the working memory input, but the strength was only 50%. In other words, working memory input was provided during target presentation period, and distractor input and motor preparation input were provided during distractor presentation period. We have added the following description:

“In each trial, the target label for working memory and motor preparation input was always the same. Distractors used the same input loadings as the working memory input, but the strength was only 50% and the distractor label was always different from the target label.”

We have added a new analysis to show that distractor activity does not relate to the second subspace (Figure 3—figure supplement 3) or drive code-morphing in bump attractor models (Parthasarathy et al., 2019). Stronger distractor input would decrease the Delay 2 decoding performance as it increased the within-cluster variance if data was grouped by target labels. We have added a new panel (Panel J) to Figure 4—figure supplement 2 to show the relationship between Delay 2 performance and strength of distractor input.

iv) In subsection “A bump attractor artificial neural network with divisive normalization recapitulated the properties of LPFC activity” there is a description of how the model is constrained by selectivity of the neural data, as well as by the “43 % overlap” in inputs (Figure 5). How this related to the loadings found in Figure 3?

We reported that in the neural data, 43% of the neurons exhibited selectivity to both working memory and motor preparation (Figure 4—figure supplement 3), and the “43% overlap” in the inputs in the model replicated this observation: 43% of the units in the model received both working memory and motor preparation inputs, and hence were selective to both.

Loading and selectivity are slightly different. Loading measures how a neuron’s activity aligns to a subspace, but it does not guarantee selectivity in the subspace; selectivity is only provided when the responses of the neuron are different for different stimuli. We only constrained the model by selectivity ratio, not loadings for the subspaces.

b) Model significance:

i) What are the activities of the model neurons? In particular, it is not clear whether the neurons are mixed selective, i.e., whether any given (simulated) neuron participates in both working memory and motor preparation. A hint is given in Figure 4—figure supplement 2, but this should be expanded.

We have added diagrams showing single-unit activity in the model in Figure 4—figure supplement 2G.

ii) In Figure 5, a direct comparison between model and data is missing, although it is described qualitatively in the text.

We compared the bump attractor model with data quantitatively in Figure 4—figure supplement 2. Now we have also added quantitative comparisons between the linear subspace model and data in Figure 4—figure supplement 4.

“…b, Cross-temporal decoding of the model (without normalization) in the full space. Delay 2 decoding performance (86.9 ± 1.3%) was significantly higher than Delay 1 performance (65.8 ± 1.2%). This was inconsistent with our observations from the neural data. c, Cross-temporal decoding of the model (with normalization) in the full space. Code morphing was replicated in the full space; Delay 2 decoding performance (65.0 ± 1.5%) was not significantly different from Delay 1 performance (65.0 ± 2.0%). d, Cross-temporal decoding performance of the model (with normalization) in the working memory subspace. The decay of working memory information was replicated in the working memory subspace identified by the unmixing method; decoding performance reduced significantly in the working memory subspace in Delay 2 (81.5 ± 1.0% in LP11, 58.8 ± 2.6% in LP22, P < 0.01, g = 11.3). e, Cross-temporal decoding performance of the model (with normalization) in the motor preparation subspace. As expected, target information in the motor preparation subspace emerged in Delay 2…”

iii) What are the model predictions?

If the two ring attractor networks for working memory and motor preparation indeed overlaps as the model assumes, then it predicts that if we sort the neurons according to Delay 1 activity to form a ring structure, we would expect new “bumps” representing motor preparation activity in Delay 2. We are currently conducting new analysis on more neural data to test this hypothesis. We have added this prediction to Figure 4—figure supplement 2.

“This architecture predicts that if we sort neurons according to the working memory “bumps” in Delay 1, we would be able to see the “bumps” representing motor preparation in Delay 2.”

3) Additional analyses or plots to improve clarity

a) Is Figure 1C necessary, given a similar Figure 1G with actual data? A general schematic is always welcome, perhaps illustrating distinct possibilities of overlap between the subspaces.

(The two plots are now Figure 2B and Figure 2F.)

Figure 2B is different from Figure 2F, in that it is a more intuitive prediction of the dynamics in the subspaces. One important aspect in Figure 2F, which the schematic (Figure 2B) failed to predict, is the divisive normalization of activity. We have highlighted the difference due to divisive normalization between Figure 2B and Figure 2F:

“The reduction of working memory decoding performance was not expected in the schematic diagram of the subspace dynamics (Figure 2B), but was captured by the state space visualization of real neural data (Figure 2F, inter-cluster distance in Subspace 1 reduced in Delay 2).”

b) “In an additional test of the hypothesis that the second subspace corresponded to a motor preparation subspace, we examined the relationship between the unmixed motor preparation activity and the unmixed pre-saccade activity at the level of single cells”: This is a continuation, at a single cell level, of the previous hypothesis of relating delay 2 period activity to pre-saccadic activity. For an independent analysis, can the activity in error trials be used to distinguish motor preparation from working memory representations?

Unfortunately, we do not think we can distinguish them in error trials with our data. Details are discussed in point c.

c) “Importantly, Component 2 and Component 2’ were also significantly correlated (Figure 2A right, Pearson correlation r = 0.62, P <0.01).”: Can the similarity between the components be defined in terms of angles, as done between the subspaces?

(We have now renamed a “component” as an “element”, which is a 226 x 7 vector set.)

The two subspaces are the orthonormal bases of the two elements, and because the principal angles between two elements are essentially the principal angles between their orthonormal bases, such an analysis is the same as in Figure 5A.

Moreover, the correlation component2-component2' = 0.62 is high, but could be higher. How does the motor preparation subspace relate to distractor encoding? Could this explain why the correlation 2-2' is not higher?

The second subspace is not related to distractor encoding (see response to question 3 of reviewer #1). We have added a new section and a supplementary figure to address this point.

“Alongside the working memory and motor preparation activities for target locations, there could also be activities representing distractor locations in Delay 2. By grouping trials according to distractor labels, we indeed found significant distractor information in the full space (Figure 3—figure supplement 3). However, the distractor activity in Delay 2 was not related to the Element 2 or the motor preparation subspace we identified, because the distractor activity and the motor preparation activity were obtained from data grouped by different trial labels (target and distractor labels were uncorrelated). Very little distractor information (17.9 ± 0.7%) was successfully decoded in the motor preparation subspace (Figure 3—figure supplement 3).”

And see the new Figure 3—figure supplement 3.

Even though motor preparation and pre-saccade activity are correlated, we do not expect them to be identical, as there could be other transformations between preparatory and execution activities (Churchland et al., 2012; Kaufman et al., 2014). We believe this should be the main reason why the correlation between 2-2’ is not higher.

d) “…concurrent increase of activity in Neurons 1 and 2 signals a change in memory (i.e. the population activity in state space moved along the working memory subspace)…”: This has not been shown explicitly with the neural activity, namely, that moving along the working memory subspace, corresponds to a (discrete) change in the target representation. Such figure would be much more informative than the illustration in Figure 3C (which is appreciated, but would actually be valid for any orthogonal subspace decomposition, not necessarily working memory/motor preparation).

We agree with the reviewer that real neural activity would be more informative than a schematic, and we indeed showed the low-dimensional state space visualization of the neural activity in the working memory/motor preparation subspaces (Figure 2F, Figure 2—figure supplement 4), which should be more informative than showing single-unit activity. We have changed our text to refer to these two figures for neural activity visualization.

“This concept can be extended to the 212 neurons with mixed selectivity to understand how the coordinated activity between those neurons can contribute minimally dependent information to the working memory and motor preparation subspaces through different loading weights that we found in the LPFC (low-dimensional visualizations of neural data provided in Figure 2F and Figure 2—figure supplement 4).”

The purpose of this schematic is more than a visualization of population activity. What we wanted to emphasize was the “readout” aspect of the population coding – how could the subspaces with specific loading weights read out different and minimally dependent information from a single population of mixed-selective neurons. We have changed the figure and text to elaborate on this point.

“In order to understand how a single population of neurons with mixed selectivity could have contributed minimally dependent information to the two subspaces, we created a simple illustration (Figure 4C). Working memory and motor preparation information were read out by separate readout neurons with different connection weights to Neurons 1 and 2 that reflected the loading weights of each subspace. In isolation, the activity of Neuron 1 would be ambiguous for both readout neurons, as an increase of activity in Delay 2 could be interpreted as a new memory at a different spatial location, or as the same memory as in Delay 1, but with superimposed motor preparation activity. In order to disambiguate the meaning of a change in the activity of one neuron, it would be necessary to interpret that change in the context of changes in the activity of the rest of the neuronal population (i.e. in this example, Neuron 2). In the illustration, a superimposed increase of activity in Neurons 1 and 2 signals a change in memory (i.e. only the readout activity in the working memory subspace changed), whereas the same increase in Neuron 1, but with a superimposed decrease of activity in Neuron 2, signals that the memory has not changed, but that a motor preparation plan has emerged in Delay 2 (i.e. only the readout activity in the motor preparation subspace changed).”

https://doi.org/10.7554/eLife.58154.sa2

Article and author information

Author details

  1. Cheng Tang

    Institute of Molecular and Cell Biology, A*STAR, Singapore, Singapore
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5183-1387
  2. Roger Herikstad

    The N1 Institute for Health, National University of Singapore (NUS), Singapore, Singapore
    Contribution
    Conceptualization, Software, Investigation, Methodology
    Competing interests
    No competing interests declared
  3. Aishwarya Parthasarathy

    Institute of Molecular and Cell Biology, A*STAR, Singapore, Singapore
    Contribution
    Conceptualization, Data curation, Investigation, Methodology
    Competing interests
    No competing interests declared
  4. Camilo Libedinsky

    1. Institute of Molecular and Cell Biology, A*STAR, Singapore, Singapore
    2. The N1 Institute for Health, National University of Singapore (NUS), Singapore, Singapore
    3. Department of Psychology, NUS, Singapore, Singapore
    Contribution
    Conceptualization, Resources, Supervision, Validation, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing
    Contributed equally with
    Shih-Cheng Yen
    For correspondence
    camilo@nus.edu.sg
    Competing interests
    No competing interests declared
  5. Shih-Cheng Yen

    1. The N1 Institute for Health, National University of Singapore (NUS), Singapore, Singapore
    2. Innovation and Design Programme, Faculty of Engineering, NUS, Singapore, Singapore
    Contribution
    Conceptualization, Resources, Supervision, Validation, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing
    Contributed equally with
    Camilo Libedinsky
    For correspondence
    shihcheng@nus.edu.sg
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7723-0072

Funding

Ministry of Education - Singapore (MOE2016-T2-2-117)

  • Camilo Libedinsky
  • Shih-Cheng Yen

Ministry of Education - Singapore (MOE2017-T3-1-002)

  • Camilo Libedinsky
  • Shih-Cheng Yen

National University of Singapore and National University Health System Strategic Research Award

  • Shih-Cheng Yen

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work was supported by startup grants from the Ministry of Education Tier 1 Academic Research Fund and SINAPSE to CL, a grant from the NUS-NUHS Memory Networks Program to S-CY, a grant from the Ministry of Education Tier 2 Academic Research Fund to CL and S-CY (MOE2016-T2-2-117), and a grant from the Ministry of Education Tier 3 Academic Research Fund to CL and S-CY (MOE2017-T3-1-002).

Ethics

Animal experimentation: All animal procedures were approved by, and conducted in compliance with the standards of the Agri-Food and Veterinary Authority of Singapore and the Singapore Health Services Institutional Animal Care and Use Committee (SingHealth IACUC #2012/SHS/757). The procedures also conformed to the recommendations described in Guidelines for the Care and Use of Mammals in Neuroscience and Behavioral Research (National Academies Press, 2003).

Senior Editor

  1. Michael J Frank, Brown University, United States

Reviewing Editor

  1. John T Serences, University of California, San Diego, United States

Publication history

  1. Received: April 22, 2020
  2. Accepted: August 21, 2020
  3. Version of Record published: September 9, 2020 (version 1)

Copyright

© 2020, Tang et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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