The transformation from sensory representation to graded memory of the sensory stimulus to decision can be seen at the population level. It is apparent in the orientation of the ellipse in , which describes the f1- and f2-dependence of the population for five different time intervals as indicated above each panel. During the first stimulus period (left panel of ) neurons respond primarily to the value of the incoming frequency as shown by the spread along the horizontal axis, demonstrating firing rate dependence on f1. This representation is maintained during the delay period (2nd and 3rd panels from left) which shows the memory of f1 in the population. During the 2nd stimulus period (4th and 5th panels), neurons begin to show activity related to the the comparison between f1 and f2; the population rotates to the line 45 degrees below horizontal, indicating activity related to the difference between f1 and f2.
The averaged population-level view described above obscures the complex dynamics that individual neurons display. The dynamics of each neuron can be very reliable from trial to trial, even while there is great heterogeneity across neurons. illustrates the dynamics of 6 different representative neurons. Some neurons show stimulus-dependent activity throughout all task periods. Other neurons show stimulus-dependent activity only during a portion of each trial (compare with other panels). Furthermore, the nature of the stimulus-dependence can vary greatly from neuron to neuron. For example, the neuron in shows activity that depends only on the value of f1; the f1-dependent activity starts during the f1 period, disappears during the middle portion of the delay, reemerges at the end of delay, and continues into the presentation of f2. In contrast, the neuron of shows stimulus-dependent activity only during the f2/decision period; this neuron’s response is bimodal, and highly correlated with the animal’s choice at the end of the trial.
In terms of their stimulus encoding, neurons with linear coefficients indicating a +f1 f2 dependence (dark red in and ) or −f1+f2 (pink in and ) are directly linked to the animal’s decision in the sense that the task involves computing the sign of (f1−f2). Neurons that encoded this difference, of either sign, are then neurons with firing rates that are directly correlated with the appropriate behavioral choice on each trial. In contrast, neurons with a response during the f2/decision period that encode f1 only, or f2 only, do not allow a direct choice readout.
We attempt to portray the full heterogeneity of the neural data by analyzing each neuron individually and presenting the results for the entire population. As before, each neuron’s firing rate was regressed to stimulus values. From the regression coefficients and their associated confidence regions, we then classified each time point into 8 possible categories, illustrated by the color code in the upper inset of . For presentation clarity, we used two different regression models for different parts of the task, as indicated at the top . Briefly, before f2 presentation, we used a reduced model where we only considered a regression to the value of f1 (a1(t)) plus a constant term (a0(t)). After f2 presentation, we use the full regression model as described earlier in the text and in Materials and Methods. The result of the regression determines the color of each time interval for each cell. If the regression at time interval ti was not significantly different from the origin (a1(ti)=0 for the reduced or b1(ti)= b2(ti)=0 for the full model), the time interval was colored black. If the regression point was significantly different from the origin, than they were labelled using the following scheme: positive f1 (dark green), negative f1 (light green), positive f2 (dark blue), negative f2 (light blue), f1−f2 (red), f2−f1 (pink), and if the point was different from the origin but could not be unambiguously assigned to any of the preceding lines (gray). The reduced regression model eliminates ambiguous points—hence, no gray bins before f2 onset; regression points and associated confidence intervals lie along a line, and therefore they either overlap the origin or they do not and instead are positive or negative.
Using this color scheme, we could illustrate the stimulus-dependence of each neuron as a function of time. Each cell is placed on its own horizontal row of colored bins with time progressing from left to right, and the color of each time interval representing the cell’s encoding during that time point. The results of analyzing every neuron in this manner are shown in . Neurons were further sorted and sub-sorted by the timing of their encodings. The first six sorting criteria was earliest time of f1−f2, f2−f1, +f2, −f2, +f1, −f1 during the f2/decision period respectively; the sorting criteria naturally produces six groups of neurons—indicated by the colored brackets.
The largest two groups are composed of neurons that are decision-correlated during the f2/decision period, encoding either +f1 −f2 (“yes”) (dark red, n=25%, 227/912) or −f1+f2 (“no”) (pink, n=29%, 261/912). We examined the average encoding of each of these groups during the f1 period and during the delay period (). Most of these decision-correlated neurons did not encode f1 during the f1-period or delay (black in main panel and in pie charts). However, for those decision-correlated neurons that do show
f1-encoding during the delay, a pattern in the encoding relationship between delay period and f2/decision period emerges: +f1 −f2 decision-correlated neurons tend, by a factor of 2:1, to spend their time encoding +f1 during the delay ( right), while −f1+f2 decision-correlated neurons tend to encode −f1 during the delay ( right). Given that the transition from the f1 period to the delay period shows a relatively low number of encoding sign switches (Romo et al., 1999
), we might expect a similar relationship to hold between the first stimulus period and the second stimulus/decision period. Nevertheless, this is not the case: both groups of decision-correlated neurons spend equal time encoding +f1 as −f1 during the f1-stimulus period ( left).
Two groups of neurons respond to the second stimulus, f2, in a manner predominantly dependent on f2 only (dark blue and light blue in ). Of these neurons, those encoding +f2 predominantly encode +f1 during the f1-period ( left); conversely, those encoding −f2 predominantly encode −f1 during the f1-period ( left). These neurons might thus appear to be purely sensory neurons, responding only to the current stimulus in a manner consistent across the two stimulus periods. However, to our surprise, we found that a very high fraction of these “quasi-sensory” neurons also encode f1 during the delay period ( right), thus showing a strong short-term memory response in addition to their sensory responses. Although relatively small in number, of all the groups we studied, the “quasi-sensory” group of neurons spent the highest fraction of time encoding f1 during the delay period, suggesting that this category of cells might be particularly important for maintenance of short-term memory.
Two more groups of neurons were those formed by neurons encoding f1, the first stimulus, during f2, the second stimulus. These neurons, like the sensory driven neurons described above, maintain their sign of encoding throughout the task. For example, the +f1 cells (dark green) have 51% +f1-encoding during f1 presentation and 33% +f1-encoding during the delay versus 1% and 3% to −f1 respectively (). The −f1 cells (light green) maintain 38% and 21% −f1-encoding versus 0% and 3% +f1-encoding during f1 presentation and delay respectively ().
Finally, near the top of the , starting at neuron 651, we sorted all other cells based on their first time of +f1 and −f1 significance during the f1 period and delay, followed by the first time of ambiguous encoding in the f2/decision period. Quite a few cells show significance to +f1 and −f1 (91 and 62 neurons respectively) during limited portions of the task; many other cells show ambiguous significance during f2/decision but not during any other time (67 neurons starting at 804).
While we have described some of the gross trends observable in , we note here some of the finer details. These generally indicate the high level of heterogeneity in response properties across neurons. We point out three such properties: (1) within each of the bracketed response groups during the f2/decision period that we defined, we further subsorted the neurons vertically according to the latency of the onset of their response category. In Supplementary Figs.1A–C
, we show the distribution of (A) all decision significant time intervals for all cells in the dark red and pink groups, (B) the median of the decision time for each cell, and (C) the first decision time; the distributions are broad indicating that cells become decision related throughout the f2/decision period. Taking neurons that encode +f1 −f2 (dark red) as an example, some neurons acquire their +f1 −f2 encoding almost as soon as f2 is presented—although one should not, from this fact, conclude that cells are making the discrimination immediately since spikes are convolved with Gaussians kernels—while other neurons encode +f1 −f2 only towards the end of stimulus f2. A similar wide spread in latencies can be observed for the other groups in . (2) In addition to latencies being widely different across neurons, so are the durations of the period of time over which the neurons encode the decision, observable in as the various horizontal extents of encoding in different cells. (3) At different points in time, even looking only within the f2/decision period, different neurons encode different stimulus properties. For example, a few neurons encode −f1 during the delay and start of the f2/decision period, but then encode −f2, and only later encode +f1−f2 (neurons numbers 145–150). Many different such patterns are visible. Some of the most remarkable are neurons that invert their encodings: as can be seen in , some neurons encode +f1−f2 (dark red), but later reverse themselves, encoding −f1+f2 (pink); the converse also occurs, with neurons encoding f2−f1 (pink) and later +f1−f2 (dark red). We emphasize that the patterns thus described are not simply noise: shows only the encodings that are highly significant (see Significance of Regression in Materials and Methods).
In , we show the average PSTH of each group from . The “decision”-related groups, , show strong binary activity depending on whether the trial was f1>f2 or f1<f2. In contrast, the +f2 and −f2 groups, , show graded activity during the f2/decision period. The +f1 and −f1 groups, , show graded activity related to f1 during the beginning of the f2/decision period, but then segregate between yes and no trials towards the end; however, rather than a purely binary spike rate as in , activity is graded based on the (f1,f2) combination.
Figure 4 Activity and average choice probability for all cells by group. A, Average PSTHs of all cells within a group broken up by frequency. The rainbow color code indicates the value of the f1 stimulus during the f1 and delay periods, and for panel Aii only, (more ...)
To quantify the correlation between spike rate and behavior for each group, we computed the behavioral ACP for each neuron and averaged the values in each group. shows the results. Within each of the six groups, neurons were further subdivided by whether they possessed f1-memory during the delay. Across all six groups, neurons encoding f1 have a higher-than-chance ACP at the end of the delay period (purple traces), consistent with these neurons being part of the neural substrate used to hold the short-term memory of f1. But after the f2 stimulus begins, the different groups show very different properties. Neurons encoding +f1 −f2 or −f1+f2, , show very high ACP, consistent with their being involved in computing the choice that the subject will subsequently report with its behavior. Furthermore, only the +f1 −f2 memory cells, left, showed a significant difference in ACP from the non-memory cells during f2 presentation (p<0.01, random permutation test). Neurons encoding +f2 or −f2, , show ACP indistinguishable from chance after f2 onset, even for those memory-carrying neurons that had higher than chance ACP values before the onset of f2. Neurons in the +f1 and −f1 groups, , do show an increase in the ACP after f2 onset, however the increase is less pronounced than in the “yes” and “no” groups, compare with . The difference in the ACP of the two populations is evident from the PSTHs, . The “yes” and “no” cells spike in a strong binary pattern during the two different trial categories, whereas the +f1 and −f1 cells spike in a graded pattern.
hints at some differences between cells that carry memory related activity during the delay period and those that do not. In , memory cells from the “yes” group show an elevated ACP during the second stimulus period as compared to those with no memory. On the other hand, cells from the “no” group do not show a difference between the two populations. To further examine this relationship, we disregarded the group structure from and simply categorized cells into two groups: memory and decision cells and decision only cells. We used strict criteria (see Materials and Methods) to ensure that only those cells with significant decision and memory related activity are included in the analysis thereby reducing noise from cells that show marginal or transient significance. Memory and decision cells outnumber decision only cells 225 to 173. To determine if one group becomes associated with the decision faster than the other, we calculated the regression angle of both populations separately using a weighted Gaussian fit, see Materials and Methods. shows snapshots of the two population regressions at four different time intervals. By the first 100 ms of the second stimulus turning on, neither population has moved towards the 45 degree decision line. Just 70 ms later, however, both populations have begun to rotate, reaching the 45 degree line somewhere between 275 ms to 300 ms after f2 onset. shows the population angle as a function of time. Neither population reaches the decision line clearly before the other. We also tested the correlation of the activity with the behavioral choices of the monkey for both populations (). The memory and decision population appears to be greater than the decision only population. We found that the difference between the means in the second half of the f2 period was significant with p=0.0176 using a random permutation test with 10000 shuffles of labels between memory and non-memory cells. The ACP measures spike activity relative to behavioral performance. We also tested the theoretical discriminability of spike rates between “yes” trials and “no” trials using correct trials only (). Again, we found that memory cells elevated versus their non-memory counterparts. The difference between means in the second half of the stimulus period was highly significant (p<0.001).
Comparison of data with existing models
Two competing computational models, by distinct subsets of the current authors, have proposed different mechanisms by which neural circuits could achieve the memory-to-decision transformation displayed in the current data. Both the Machens-Romo-Brody (MRB) model (Machens et al., 2005
) and the Miller-Wang (MW) model (Miller and Wang, 2006
) have assumed that PFC is the locus of both the memory of f1 and the discrimination between f1 and f2. But the mechanism differs in the two models, leading to different predictions for how the core computational cells encode task variables. Given the great diversity of responses seen in PFC, e.g. in , we asked how well-supported are each of the models in the data—that is, we ask what fraction of cells observed in the data fit the predicted response characteristics described by each model. Below, we first describe an overview of the stimulus encoding found in the data (). We then summarize the basic properties of each of the two models, and describe the cell classes that each model predicts. We then make the comparison between models and data ().
Figure 6 Overview of stimulus encoding in the population. A, Fraction of cells in the population showing significant regression to stimuli broken down by type and sign. Color scheme is identical to the one used in . Gray lines before f2 onset appear here (more ...)
In order to examine this question, we need to categorize the activity of each cell to stimulus values. We again apply our standard regression analysis using strict criteria to ensure that cell responses are robust to task stimuli. In this analysis, we will focus on how cells change encoding signs from one task epoch to another; e.g. if a cell encoded +f1 during the first stimulus period does it remain positive during the delay or switch signs to become negative or possibly lose f1-encoding altogether? Since the models have different predictions for f1-sensory, f1-memory, and comparison encoding in PFC cells, we may be able to disambiguate the two models from the evidence in the data.
In , we show an overview of stimulus encoding in the population. shows the total fraction of cells that have significant regression coefficients (see Significance of Regression in Materials and Methods) broken down by stimulus type and sign as a function of time. In essence, is a summary of showing the total fraction of cells in each color for every time bin. However, in we used the full regression model for the entire task rather than just after the second stimulus. We did this to show more clearly how the representation of the comparison (solid red and dashed pink lines) is stronger than the representation of f1 during the first stimulus presentation and delay (solid dark green and dashed light green lines). In comparing the two models, we will be emphasizing transitions in encoding signs from one epoch to another. shows an overview of the number of significant transitions that occur throughout the task. Anytime a cell regressed significantly different from the origin at one time interval then switched sign significantly at a later time interval, we counted that as a sign switch at the latter time. In , very few of the sign switches occur before the onset of the second stimulus. After second stimulus however, many cells switch signs. Interestingly when the sign switch is triggered on the f2 sign (gray line), a large peak at the beginning of the f2 period appears. When the switch is triggered on f1 (black line), however, there is no initial sharp peak; after a short delay the number of flips rises to f2 levels and falls with it to the end of the f2 period. Another interesting feature is the sharp peak for both lines after the f2 period. Many cells reverse their decision encoding, e.g. from f1−f2 to f2−f1, during this time; this is also evident in where many cells in the red group turn pink and cells in the pink group turn red between 4 and 4.5 s.
When comparing the two models, we required that cells be significant over extended periods in each epoch; something that cannot be gleaned from alone. Therefore, we applied a strict criteria to the number of time bins that a cell has significant regression coefficients in order to categorize encoding types (see Categorization in Materials and Methods). shows a Venn diagram depicting the intersection of three categories of cells: 1) f1-sensory encoding during the f1-stimulus period, 2) f1-memory encoding during the delay, and 3) comparison encoding during the f2-stimulus period. By category, 361/912 (40%) of cells were f1-sensory encoding, 455/912 (50%) of cells were f1-memory encoding, and 398/912 (44%) of cells were comparison encoding. There are 703/912 (77%) cells that fit into at least one category and are shown in . Of these, many neurons were counted in one category but not in any of the others (296/703, 42%). Many neurons were counted in some combination of two of the categories (303/703, 43%). A smaller number of neurons fit into all three categories (104/703, 15%). As a comparison, if one randomly shuffles the three categories for all 912 cells, the expected number of cells fitting at least one category is 756, with 377/756 (50%) of cells fitting only a single category, 300/756 (40%) of cells fitting two categories, and 79/756 (10%) of cells fitting all three categories. We performed a Pearson’s chi-squared test that the percent of cells fitting exactly one, exactly two, and all three categories are different from the null random expected values. We found that all three percentages were significant with p-values of 5.3E-6, 0.0048, and 6.0E-4 for exactly one, two, and three categories respectively. The significance of our findings suggests that being in one category is correlated with being in another category, more than expected by chance. In other words, we found more combined f1-sensory encoding, f1-memory encoding, and comparison encoding than expected by chance. We note here that in , the fraction of cells with significant regression to the decision is much higher than the fraction of cells with significant regression to f1 during the delay at any given time. However, the number of cells categorized as f1-memory encoding during the delay is comparable to the number of cells categorized as comparison encoding during the second stimulus period. This is primarily due to differences in regression models (and associated significance analysis) used for the two periods. Also, since the delay period is longer and cells can be memory encoding during anytime of the delay, there are more opportunities to be categorized as an f1-memory encoding neuron. However, the categorization is not simply due to noise as we had strict requirements for inclusion in each category. Also, shuffling stimulus pair labels for the regression produced very few cells in each category: 3/912 for f1-sensory encoding during the f1-period, 28/912 for f1-memory encoding during the delay, and 0/912 for comparison encoding during the f2-period. We tested a number of different criteria for categorization (data not shown), with little difference to the general trend of the data presented here and in the comparison of the two theoretical models that follows.
With the overall picture in hand, we now turn to the specifics of the two theoretical models. The two models predict distinct neural signatures that would be observed using the analysis tools of . As we will describe below, the MRB model predicts the presence of 2 neural signatures, and the MW model predicts the presence of 6 signatures. No class belongs to both models, and we therefore expect that determining which classes predominate in the data should allow us to distinguish between the models. We now discuss each of the predicted signatures in turn.
A key assumption of the MRB model is that the same set of PFC neurons both encode the memory of f1 during the delay and perform the binary comparison during f2. The core of the MRB model is a demonstration of how a single neural circuit in PFC, with a fixed architecture, can accomplish both graded persistent activity and binary decision-making. In this model, the populations of cells that have positive monotonic encoding of f1 (“plus” cells) and those that have negative monotonic encoding (“minus” cells) mutually inhibit one another to form a line attractor circuit (Seung, 1996
) during the delay period. A decrease in tonic excitation to such a circuit transforms it from a line attractor, capable of graded persistent activity, to a bistable circuit, capable of binary decision-making. This dual capacity is a result of the mutual inhibition architecture. Thus, in the MRB model both the plus and the minus populations are required for the system’s operation.
Although the circuit within PFC is fixed in the MRB model, the connections from sensory areas to PFC do change. The MRB model depends on the assumption that a within-trial switch in effective connectivity between sensory areas and PFC exists. That is, the effective connectivity from secondary somatosensory cortex (S2) to PFC must change in sign at some time from the f1 to the f2 period. Machens et al. (2005)
observed that most neurons that are plus during the delay subsequently fire most during f2 in trials where f1 > f2, i.e. they encode f1−f2 (“yes” decisions; see right). This means that during f2, the lower
the value of f2, the higher the firing rate, which is the opposite of the stimulus dependence observed during the delay period. Thus, the sign of the dependence on the sensory stimulus had switched from plus to minus. Similarly, neurons that are minus during the delay also display a sign switch, but in the opposite direction (see right). This experimental observation, combined with the observation that few neurons change the sign of their encoding from f1 presentation to delay, led to the postulate that between the f1 period and the f2 period, there should be a switch in the sign of the effective connectivity between sensory areas and PFC. The MRB model was constructed based on the assumption that this postulate was correct. Biophysically, such a switch could be accomplished using either a context dependent signal and an inhibitory switch in S2 (Machens et al., 2005
), or by using appropriately chosen, fixed synaptic weights from S2 to PFC (Chow and Brody, 2009
In the MRB model, then, neurons that are plus (minus) f1-sensory encoding during f1-presentation should remain plus (minus) f1-memory encoding during the delay and become f1−f2 (“yes”) comparison encoding during f2-presentation. Such neurons, if analyzed using the standard method illustrated in , would display the dynamics cartooned in left (plus) and right (minus).
Struck by the inelegance of requiring a within-trial sign switch in effective connectivity from sensory areas to PFC, and motivated by considering the existence of such a switch implausible, Miller and Wang (2006)
devised a competing model in which no switch or connectivity change is required anywhere in the circuit. In contrast to the MRB model, the MW model uses two separate neural populations for the memory and the comparison/decision operations. Sensory stimuli from S2 drive a population of comparison/decision cells (labelled “C” cells), which in turn drive a bank of cells capable of graded memory (“M” cells, configured as a line attractor/integrator). The M cells perfectly integrate incoming signals from the “C” cells and in turn provide negative feedback to the “C” cells. An f1 sensory stimulus thus causes an increase in the activity of “C” cells, which in turn causes an increase in the activity of “M” cells, and this increase continues until the activity of the “M” cells has grown to the point where their negative feedback to the “C” cells exactly cancels the sensory input. At this point the “C” cells no longer drive an increase in “M” cell activity. When the sensory stimulus turns off, the “M” cells continue to fire persistently at a rate that depends on the value of the previously presented f1 stimulus. The “M” cells thus encode a memory of f1 throughout the delay. The “C” neurons are inhibited by the “M” neurons and hence are quiescent. During f2, sensory stimuli driving the “C” cells will encounter the incoming stimulus input and the continuing negative feedback from the “M” cells which is in proportion to the memory of f1. Thus, “C” cells will only respond to f2 if it is sufficiently large to overcome the negative feedback. That is, the “C” cells only fire if f2>f1. As a result, these cells in the MW model perform the f1 vs f2 comparison without requiring any switch in effective connectivity.
If analyzed using the standard method of , the “C” cells would be driven into “plus” activity during f1; the inhibition from the “M” cells would silence the “C” cells again by the end of f1, leading the “C” cells to have no encoding during the delay; finally, during f2 these cells would fire when f2 is greater than f1. A cartoon of the dynamics of such “C” cells is shown in left. “M” cells analyzed in the same way would become “plus” during f1-presentation, remain “plus” during the delay, and then during f2 would fire in a manner that increased as a function of f1+f2; this is illustrated in left.
The MW model does not strictly require having both a “plus” and a “minus” population. Nevertheless, the model can be constructed in either the “plus” configuration or in the “minus” configuration. Furthermore, having both configurations greatly facilitates the final readout of the decision. Thus the MW model also predicts activity patterns cartooned in right and 7C right, which are the “minus” circuit versions of left.
As described thus far, the MW model does not account for neurons that change the sign of their stimulus-dependency from the delay to f2. Miller and Wang observed that their model could be modified to account for such cells by having some of the integrator “M” cells ignore inputs below a minimum threshold θ. This has the advantage of increasing the robustness of the “M” cell integrator. The MW model further proposes that throughout each trial, a tonic input drives “C” cells to fire at θ. Thanks to this input, an extra input from the f1 stimulus drives the “C” cells to a firing rate above the “M” cell threshold, therefore affecting the “M” cells and leading to the negative integral feedback process: the negative feedback from the “M” cells would increase until it brought the “C” cells back to the firing rate θ, thus canceling the f1 input. After this, when the f1 input ceases at the end of the first stimulus period, the “M” cells continue firing at a rate proportional to f1, thus holding the f1 memory; and the inhibitory input from the “M” cells, combined with the lack of the f1 sensory input and the tonic excitation, drives the “C” cells to a firing rate proportional to θ − f1. That is, the sign of the “C” cell encoding to f1 switches from “plus” during f1 to “minus” during the delay. When f2 is presented, “C” cells will be initially driven to a firing rate proportional to θ + (f2 − f1). Thus values of f2 that are greater than the previously presented f1 will lead “C” cells to fire above θ, while values of f2 less than f1 will lead the “C” cells to fire below θ. The “C” cell firing rate can therefore be used to form the appropriate decision (f1 > f2? Y or N), with θ forming the decision boundary. Using again the tools of , the “plus” circuit version of these “C” cells is illustrated in left, and the “minus” circuit version is illustrated in right.
In summary, the analysis tools of lead us to seek 2 different signatures compatible with the MRB model () and 6 different signatures compatible with the MW model (). No class belongs to both models, and we therefore expect that determining which classes predominate in the data should allow us to distinguish between the models. We analyzed the firing rates of 912 recorded neurons and classified each into the eight different classes defined in . Additionally, we classified cells into categories not predicted in either model, .
Categorization was based on regression and significance analysis. Details can be found in Materials and Methods. Briefly, for the two stimulus periods, we require that at least half of the time bins within the middle 250 ms have significant regression coefficients with all significant bins having the same encoding sign. For the delay period, we divided the 3 s into 6 equal 500 ms segments. Within each segment, we required that at least half of the bins regressed significantly and were of the same sign. If any one segment passed criteria, we defined the cell as having memory. Cells with multiple segments passing criteria would also need to have all signs be identical. For situations where cells were required specifically to not encode any stimuli, we set a lower threshold for the number of significant bins which a cell had to be under in order to pass. Regressions for this analysis was performed on PSTHs created using a Gaussian kernel with a standard deviation of 50 ms during stimulus periods and 150 ms during all other times. Gaussians were truncated and normalized for edge effects at epoch boundaries. Therefore, for example, memory of f1 during the delay is not attributable to convolving spikes from the stimulus periods. In our analysis, we do not consider the temporal dynamics of each neuron. In principle, the MRB and MW models rely on fixed-points in order to maintain f1-memory encoding during the delay period. Therefore, average firing rates should remain steady throughout the delay. Many cells, however, show strong temporal dynamics which are reliable on a trial-to-trial basis. To simplify our analysis, we did not attempt to define cells based on temporal characteristics.
shows the total number of cells conforming to each cell type at the top of each panel and the total for each model along the sides of the panels. Overall, only a small fraction of cells (80/912, 9%) fit into one of the eight categories outlined above for both models. Of those, a total of 47 fit into the MRB model categories while a total of 33 fit into the MW model categories. The two numbers that are most readily comparable in this analysis are between the MRB neurons of and the MW “C” neurons with memory of . These cells have the most similar set of criteria, differing only in the signs of the combinations of encodings. When these two sets are compared, the MRB model has the same 47 cells, while the MW model has 19 cells. Thus, the MRB model, based on these numbers alone, would appear to be better represented in the data.
One might be concerned that the paucity of numbers reported here are due to overly zealous selection criteria or that if the statistical power on all cells were increased that we may have found more favorable accounting for each model. To demonstrate that this is not the case, in we show 8 cell categories that are not predicted by either the MRB or the MW models. The numbers for these categories were generated using the same set of criteria used for both models and can be compared to one another. For example, purely sensory cells, , account for 45 cells that show f1 activity during the first stimulus and delay followed by f2 activity during the second stimulus and account for 31 cells that show f1 activity throughout the entire task. A few categories that show decision related activity but are not predicted by either model are shown in . Of these, a small number, 17, show activity like MRB cells during f1 and the delay, but then show decision activity opposite to that predicted by the model. A far greater number, 77, show no stimulus related activity throughout the f1 and delay period, but then show decision related activity during f2.
The 16 categories shown in are only a sample of the total possible categories. In the Supplementary Material, Table S1
shows the numbers of cells that fit into all possible categories, including those enumerated here, and using the same strict categorization criteria throughout. This procedure leads to a well-defined category for 568/912 (62%) neurons. The remaining 344 (38%) neurons cannot be unambiguously categorized with these methods.
Therefore, as a second approach, we applied a simpler set of categorization criteria, Fig. S4 in Supplementary Materials
. During the f1-period and separately for the delay period, we placed one of three labels on each cell: positive f1-encoding, negative f1-encoding, or non-encoding. During the f2-period, we used the following three labels: “yes” decision-encoding, “no” decision-encoding, and non-decision-encoding (but could encode f1 or f2), see Methods and Materials for more details. The three labels in three epochs provides 27 non-overlapping encoding combinations. Two combinations represent neurons that are most similar to the predictions of the MRB model (); a total of 105 out of 912 neurons (12%) best fit this profile (46 of the 105 best fit the left panel of , while the remaining 59 best fit the right panel). Two combinations represent neurons that are most similar to the “C” cells without memory in the MW model (); a total of 32/912 neurons (4%) best fit this profile (24 of the 32 best fit the left panel, while the remaining 8 fit the right panel). Two combinations represent neurons that are most similar to the “C” cells with memory in the MW model (); a total of 55/912 neurons (6%) best fit this profile (28 of the 55 best fit the left panel, while the remaining 27 best fit the right panel). These numbers can be compared to two unpredicted decision cell types shown in . A total of 61/912 neurons (7%) best fit the profiles shown in (29 of the 61 best fit the left panel, while the remaining 32 best fit the right panel). A total of 81/912 (9%) neurons best fit the profiles shown in (43 of the 81 best fit the left panel, while the remaining 38 best fit the right panel). Figure S4 of the Supplementary Material
reports the number of cells that best fit each of the 27 combinations, including the ones described above. It also re-plots by showing the neurons sorted according to the simplified categorization scheme described above.
In this analysis, of all the cells showing decision related behavior, the two MRB profiles had the highest number of cells that best fit their encoding combinations. However, the numbers were only a few percent higher than other leading categories. Also, the simplified categorization has the disadvantage of underestimating non-encoding categories—a single bin of significance places a cell as encoding in this set of criteria—which is a disadvantage for the MW “C” neuron without memory (). Note that this is an unavoidable problem as determining non-encoding is not simply the negative of determining encoding; there is a substantial middle ground where cells may show weak or barely significant encoding. Nevertheless, taken together with the more stringent set of criteria, we conclude that the cell types predicted by either model do not dominate the data. This suggests a highly heterogenous code in PFC for solving the task.
Given the heterogeneity found in the data, can we constrain future models of this task? sketches the outlines of four circuit architectures that could solve the task. In , the set of neurons supporting short-term memory of f1 is separate from those supporting the comparison between f1 and f2 and/or the formation of the binary decision. The scenario is simple in the sense that each module, or group of neurons, has a single, fixed, and well-defined computation. In this scenario, we would not expect memory neurons to carry binary decision-related signals, nor would we expect decision-related neurons to carry memory signals. Neurons with these properties are found in the experimental data. shows 91 neurons that are stimulus-sensitive only during the delay and 130 neurons that are stimulus-sensitive only during f2-presentation; they might be the basis of the circuit sketched in . Other neuronal types (e.g. neurons that are stimulus-sensitive during both
the delay and f2-presentation) might be epiphenomenal with respect to the current task and driven by the neurons fully compatible with . Such a view predicts that neurons carrying both memory and decision-related signals, i.e., the “epiphenomenal” cells, should have lower average choice probability (ACP) than those carrying purely memory signals during the delay and purely decision signals during f2. In , we compared the ACP of memory and decision cells to non-memory and decision cells; we found ACP favors memory and decision cells during f2. To test the former prediction, we calculated the ACP during the delay period for memory-only cells and memory and decision cells. In Figure S1
, we show the ACP as a function of time within the delay; we further break down the population of cells based on when they show significant memory activity: early (0–1 second of delay only), middle (1–2 second of delay only), late (2–3 second of delay only), persistent (entire delay), and all others (anything remaining from the above). No difference between the two populations (memory only vs memory+decision) are apparent; again, if anything, the memory+decision cells have a higher ACP when the memory component is persistent. The data, therefore, suggests the scenario of unlikely.
Figure 8 Schematic of several possible architectures capable of performing the stimulus/memory/comparison transformation required in the task. A, A network that completely separates memory and comparison/decision. B, Similar to A, except that feedback from comparison/decision (more ...)
A variation on the scenario of is shown in . Once again the memory module and the comparison/decision module are kept separate, except that once the decision is formed, the result is fed back to the memory module, thus leading to neurons that carry both memory and decision information, as commonly observed in the data. In the scenario of , such feedback is not necessary for the circuit to perform the task; the purpose of the feedback could be related to other tasks that the prefrontal cortex participates in. Nevertheless, if such feedback were present, the 225 neurons (out of 912 neurons, 25%) that have both memory and decision-related activity could be accounted for. In such a scenario, we would expect decision-related activity to arise slightly earlier in decision-only neurons than in memory-and-decision neurons, since the former drive the latter. Furthermore, we would expect decision-only neurons to have higher choice probability than memory-and-decision neurons, since they would be more closely linked to the circuit’s decision output. Yet, shows precisely the opposite of these two predictions, namely, that memory-and-decision neurons have higher choice probabilities and shorter decision latencies than decision-only neurons. For these reasons, we consider the scenario of unlikely.