We trained two rhesus monkeys in an oculomotor spatial working memory task that required them to remember the spatial location of a brief (0.5 s) visual stimulus and execute a saccade toward the remembered location after a delay period of 3 s3. By tracking eye position, we collected a behavioral data set consisting of the coordinates of the saccadic end point for each successful trial in which the saccade correctly reported the approximate location of the memorized cue (Fig. 1a and Online Methods). For each monkey, we computed the mean saccadic end point for each of the eight cues presented. We computed a behavioral measure of accuracy as the angular distance on the screen from each trial's saccadic end point to the mean saccadic end point for the given cue. This measure classifies trials into clockwise and counterclockwise trials (Fig. 1a,b).

Figure 1: Behavioral and neural fingerprints of spatial working memory. (a) Saccade endpoints reporting cue location after a 3-s delay (fixation on black cross) for one monkey. White crosses indicate mean saccade locations for each of eight cues. Color indicates angular deviation from mean responses. CCW, counterclockwise; CW, clockwise. (b) Angular deviations pooled over cues and monkeys. Triangles indicate ± median absolute deviation. (c) PFC neurons represented cue location in selective sustained delay activity. Population activity (100-ms sliding window, n = 204) for preferred (solid) and non-preferred cues (dashed). Cue (C) and response (R) periods are marked in gray. (d) Population delay tuning curve for all neurons (thick line, n = 204) and for n = 102 neurons stronger (thin line) and weaker tuning (dashed line). (e) Distribution of mean delay firing rates (upper histogram, mean = 9 Hz, s.d. = 9.2 Hz), of tuning strength T (right histogram, mean = 0.21, s.d. = 0.15) and their correlation (central plot, P < 0.0001, n = 204). (f) Distribution of a rate modulation index (Online Methods) did not deviate significantly from a Gaussian (Lilliefors test, P = 0.27, n = 204) with zero mean (t test, t = 0.23, P = 0.82, n = 204). Negative (positive) values correspond to a firing rate decrease (increase) during the delay. Filled bars mark neurons with significant changes (Wilcoxon test, P < 0.05). (g) Distribution of modulation indexes for preferred location (top) and tuning strength T (bottom). Filled bars indicate neurons with significant changes (permutation test, P < 0.05). Gray shading shows bootstrap-estimated s.e.m. Full size image

While the monkeys performed the task, we collected single-unit responses from the dorsolateral PFC. A substantial fraction of neurons in this area showed tuned persistent delay activity during the mnemonic phases of the task2,3, and we selected these neurons for our further analyses (n = 204; Fig. 1c). We calculated memory tuning curves by averaging the delay period activity of each neuron across trials as a function of the eight equally spaced cues and determined a preferred cue angle (Online Methods). By aligning tuning curves by their preferred cue and averaging, we formed the population tuning curve (Fig. 1d).

On the other hand, individual neural responses were highly heterogeneous22. Mean firing rates during the delay period varied broadly across the population (Fig. 1e). Moreover, the degree of delay tuning to the cue varied widely among neurons. To quantify this, we calculated the tuning strength T for each neural tuning curve (T = 0 for non-tuned responses, T = 1 indicates response to one single cue; Online Methods). We found T to be broadly distributed (Fig. 1e). Mean firing rate and tuning strength were correlated across neurons (tuning curves for high T and low T neurons; Fig. 1d), with no clustering suggesting separate functional populations (Fig. 1e). Some neurons showed dynamics in their delay firing rate (Fig. 1f), with 30 of 204 (39 of 204) cells having significantly higher (lower) activity for preferred cues in the last compared with the first second of the delay (Wilcoxon test, P < 0.05). However, a majority of neurons (135 of 204) did not show a significant activity change, which was also the result for the population (Wilcoxon test, P > 0.5; Fig. 1f). Fano factors decreased slightly from the first to the last half of the delay period, from 1.29 ± 0.02 to 1.24 ± 0.03 (Wilcoxon test, z = 3.6, P < 0.001, n = 196). However, the tuning of individual neurons was markedly consistent through the delay period: preferred cue angles and tuning strength T did not change significantly between the first and last seconds of the delay (preferred angle: Harrison-Kanji test, χ2 = 0.38, P = 0.8; tuning T: Wilcoxon test, z = –0.83, P = 0.4, n = 204; Fig. 1g). The steadiness of the coding properties through the delay suggests that PFC activity can be described by a bump code, which could be responsible for behavioral performance during the task.

With this data, we tested the bump attractor hypothesis, the idea that trial-averaged memory tuning curves reflect a hill of population activity of invariant shape (bump attractor) that encodes during the delay period the information that will determine the upcoming saccade (Fig. 2a). The center of mass of the bump attractor can be at any position along a continuum and encodes a continuous representation of the visual cue's position. Random fluctuations in bump attractor position6,7,8,21 lead to deviations in the read-out at the end of the delay, which result in inaccurate behavioral responses (Fig. 2b,c). This mechanism produces specific predictions regarding the trial-to-trial relationship between variability in neural activity and variability in behavioral responses that we tested in the data.

Figure 2: Bump attractor dynamics during the delay can explain behavioral inaccuracies. (a) Spatio-temporal representation of network activity during the delay period in an individual trial. Gray levels and z axis elevations schematize neuronal firing rates. (b) The same trial is presented as in a, but represented on the time-network plane. Gray scale represents firing rate elevations. The black triangle shows the location of the initial cue, right before the beginning of the delay (encoded population activity, bottom). The white triangle indicates the behavioral response decoded from network activity at the end of the delay (decoded population activity, bottom). Leftward displacement of the white relative to the black triangle indicates a clockwise behavioral response deviation in this trial. (c) Data are presented as in b but for a different trial. Rightward displacement of the white relative to the black triangle indicates a counterclockwise, inaccurate trial. Full size image

Tuning-curve bias in the delay predicts behavioral biases

According to our hypothesis, population activity displacements at the end of the delay underlie behavioral response deviations. These displacements of population activity should be reflected in a systematic bias of delay tuning curves derived from the sets of trials that led to clockwise and counterclockwise deviations (Supplementary Fig. 1). For each neuron, we separated clockwise and counterclockwise trials for each cue condition (Fig. 3a) and computed the corresponding clockwise and counterclockwise tuning curves (Fig. 3b) as the corresponding trial-averaged firing rate versus the eight angles of the cue location. The tuning bias was defined as the signed angular distance from the counterclockwise to the clockwise tuning curve centers (Online Methods). With this definition, our hypothesis predicts that the tuning bias should become positive during the delay (Supplementary Fig. 1). We computed tuning biases for all neurons in different time windows along the trial and combined them to obtain the time evolution of the population tuning bias. Consistent with the bump attractor hypothesis, the population tuning bias became significantly positive at the end of the delay (tuning bias = 4.4 ± 2.9° in the last second of delay, one-sided permutation test, P = 0.024, n = 204), right before the behavioral response (Fig. 3c). To test for a possible motor origin of this signal, we repeated the analysis, excluding neurons with increasing rates in the delay period (positive modulation index; Fig. 1f), which have been shown to represent saccade preparation23. We still found significantly positive tuning bias in the last second of the delay (tuning bias = 9.9 ± 6.6°, one-sided permutation test, P = 0.014, n = 101), thereby excluding a driving role for saccade preparation neurons in generating the tuning bias during the delay.

Figure 3: Tuning curves computed from clockwise and counterclockwise behavioral trials show model-predicted shift in the delay period. (a) Representation of saccade endpoints for one session. For each cue, trials are separated in half based on their relative clockwise (red) and counterclockwise (blue) saccadic responses. (b) Sample neuron delay-period responses in the clockwise and counterclockwise conditions. Triangles indicate the circular mean of the responses, an estimate of the preferred cue for each condition. The distance between these two circular means is the tuning bias. Error bars represent ±s.e.m. (c) Population average of the tuning bias for all neurons across time showed significantly positive values by the end of the delay (thick horizontal lines; permutation test, P < 0.05). Cue (C) and response (R) periods are indicated with gray areas. Tuning curves were estimated over 1-s sliding windows. Error bars (shaded area) indicate s.e.m. Full size image

In addition, we found a quantitative agreement between the mean tuning bias computed from our 204 neurons and the mean behavioral deviation computed as the difference between the average saccade end points of the corresponding counterclockwise and clockwise trials (mean tuning bias = 4.4 ± 2.9°, mean behavioral deviation = 7 ± 0.2°, Welch's test, t = 0.9, P = 0.36, n = 201). This order-of-magnitude match indicates that the bump attractor hypothesis in PFC can account for the magnitude of behavioral inaccuracies that we observed experimentally.

Correlation between delay activity and behavioral deviations

Thus, average tuning was related to dichotomized behavior (clockwise-counterclockwise; Fig. 3). In addition, the bump attractor model predicts that firing rates should correlate on a trial-by-trial basis with parametric deviations in behavioral response. In particular, a neuron increases its activity as the activity bump moves closer to its preferred location. As a result, trials for which a given neuron had stronger delay responses should result in behavioral deviations toward that neuron's preferred location. Thus, we would expect a positive correlation between firing rate and behavior attraction to the neuron's preferred location. This effect should be especially strong for neurons with strong tuning and for cues at the tuning curve flanks (that is, cues 1–2 positions from preferred), where responses are most sensitive to small variations in bump location (Fig. 4).

For each neuron, we selected the trials with stimuli in its tuning curve flanks (Fig. 4a) and matched the neuron's responses with the corresponding behavioral deviation (Fig. 1b). Defining behavioral deviations to be positive (negative) for saccades closer to (further from) the neuron's preferred location (Fig. 4a), we calculated the correlation coefficient between response deviation and behavioral deviation for each cell (Fig. 4b). We found that the population average of these correlations became positive during the delay period (Fig. 4c), especially for neurons with stronger tuning T (Fig. 4d). This effect persisted when removing neurons with ramping-up delay activity from the analysis (correlation in last second of delay = 0.029 ± 0.016, P = 0.041, n = 101, one-sided permutation test), thereby excluding saccade preparation as the cause of this signal.

Figure 4: Responses to flank stimuli (1 and 2 locations from preferred) become correlated with upcoming behavior during the delay. (a) Sample neuron responses to flank stimuli superimposed on its tuning curve (data from last second of delay). Each circle represents a single trial: y is the neuron's firing rate and x is the angle of saccadic endpoint (also ticked on the line above). Dashed lines indicate cue locations and saccade deviations are marked with horizontal stems. Black (gray) circles indicate behavioral imprecision toward (away from) the neuron's preferred location. (b) Firing rate deviations from tuning curve correlate positively with saccadic deviations from cue location. Saccadic deviations toward the preferred cue have positive sign. The same data are presented as in a. (c) Population average of correlation coefficients computed as in b for tuned (n = 204, solid line) and non-tuned neurons (n = 523, dashed line). Rate-behavior correlations were computed over 1-s sliding windows. Shaded areas indicate bootstrapped s.e.m. Thick lines mark periods of significantly positive correlation (permutation test, P < 0.05). (d) Average rate-behavior correlation over the last 2 s of the delay for tuned (solid) and non-tuned neurons (dashed) with low, medium and high tuning strength T (Supplementary Fig. 2). (e) For the neuron shown in a, R2 values for the linear regression of firing rate in the last 1 s of delay and behavioral deviations (solid line) were highest for individual flank stimuli. The dashed line is the mean R2 for shuffled surrogates, R2 shuffle . (f) Population average of corrected R2 (R2 – R2 shuffle ) was significantly positive for flank stimuli in tuned neurons (P < 0.05). Dashed lines are 95% confidence intervals for R2 shuffled . (g) Corrected R2 averaged over cues became significantly positive for tuned, but not non-tuned, neurons during the delay (late-delay tuned: P = 0.045, n = 204, one-tailed permutation test; 1-s non-overlapping windows). *P < 0.05. Error bars represent ±s.e.m. Full size image

This positive correlation accrued with time into delay (Fig. 4c), suggesting that behavioral deviations result from accumulated errors in prefrontal activity during the delay, as in our hypothesis (Fig. 2). We confirmed this by looking separately at cues at different distances from the preferred location (Fig. 5). If the bump were to diffuse during the delay (Fig. 2), the correlation between firing rate and behavior should appear earlier in trials in which the cue was presented closer to the cell's preferred location. This occurs because it takes more time for the bump to diffuse and modulate neurons with preferred locations more distant from the cue. Indeed, periods of significant correlation between neuronal and behavioral variability appeared later in the delay as we took flank cues more distant from preferred location (Fig. 5).

Figure 5: As predicted by the bump attractor model, neuronal variability correlates with upcoming behavioral responses in a cue-dependent way: maximally for flank stimuli and earlier in the delay for cues closer to the neuron's preferred location. (a) Absence of rate-behavior correlation for trials in which the presented cue coincided with the neuron's preferred location θ pref . (b) Significant rate-behavior correlation (permutation test, P < 0.05), as early as 2 s before saccade, for trials with cues presented just next to θ pref . (c) Late-delay rate-behavior correlation for cues presented two locations away from θ pref . (d) Absence of rate-behavior correlation for cues opposing θ pref . Correlation was computed in 1-s sliding windows. In b and c we evaluated the center of mass (black triangles) of time points with significantly positive correlation (one-sided permutation test, P < 0.05). Center of mass standard errors were evaluated with a bootstrap procedure. The curve shown in Figure 4c is the result of combining trials used in b and c. Error bars (shaded area) represent ±s.e.m. Full size image

The trial-to-trial relationship between firing rate and behavior should be restricted to neurons participating in the bump. To test this, we investigated neurons without significant delay tuning (non-tuned neurons, n = 523; Online Methods and Supplementary Fig. 2). We found no significant correlation between responses to flank stimuli and behavioral deviations for this data set (P > 0.05; Fig. 4c,d). However, this analysis requires computing the preferred cue of each neuron, which probably suffered large estimation errors for such weakly tuned neurons. In addition, alignment to a preferred location could mask a rate-behavior relationship that is not related to the bump attractor hypothesis in these neurons. We therefore performed an additional analysis that did not assume a specific relationship between a neuron's tuning curve and behavioral deviations. For each neuron and each cue, we calculated the R2 value of the linear regression between rate at the end of the delay and behavioral deviation (Fig. 4e). Consistent with the data shown in Figure 4c, the average of R2 across tuned neurons was significant for two flank cues (P >< 0.05; Fig. 4f). Crucially, the mean R2 over all cues, averaged across all cells, became significant for tuned, but not non-tuned, neurons at the end of the delay (P >< 0.05; Fig. 4g). Thus, non-tuned neurons did not show a detectable rate-behavior relationship in our data set.

Late-delay behavioral modulations of Fano factors

We then tested the contribution of bump attractor diffusion to neuronal variability, as captured by the Fano factor. Following our hypothesis, bump displacements in different trials induced behavioral inaccuracies and led to the largest variation in neuronal response for cues in the flanks of a neuron's tuning curve (Fig. 6a,b). For these cues, random diffusion of the bump caused maximal neuronal activation in trials in which the bump drifted toward the neuron's preferred location, and minimal activation when it drifted away (Fig. 6b). Our hypothesis predicts that the variance of neural responses to flank stimuli should be larger for trials with inaccurate compared with more accurate behavior. Moreover, this difference should be specific to flank stimuli and absent, or even inverted, for preferred or tail stimuli (Fig. 6b). Note that the variance of neural responses is also affected by independent spiking noise, typically in proportion to the mean response24,25. This contribution will not interfere qualitatively with our prediction, assuming its invariance across task conditions25.

Figure 6: Fano factors follow the predictions of the bump attractor model. (a) Depending on the response properties of recorded neurons, cues can be classified as preferred, flank and tail cues. (b) Left, schematic representation of four different late-delay population activity profiles in response to the same 90° cue. Magenta lines represent trials with behavior closer to the target (accurate trials) and green lines trials with behavior farther from the target (inaccurate trials). The range of neural responses for these types of trials are marked with vertical rectangles for specific neurons in the network, those for which the presented cue represents a preferred, a flank or a tail cue. Right, according to the bump attractor hypothesis, neural response variability should be higher for inaccurate than accurate trials, selectively for flank stimuli. (c) In the data, when flank stimuli responses are separated into trials with behavioral responses farther or closer from the mean saccadic endpoint for that cue, Fano factor dynamics separate by the end of the delay with inaccurate responses showing higher Fano factors than accurate responses (one-sided permutation test, P < 0.05). (d) The difference between Fano factors in inaccurate and accurate trials at the end of the delay (averaging counts in the last 500 ms) depends on the cue condition. The Fano factor difference between accurate and inaccurate trials is significant for preferred and flank stimuli (*P < 0.05, permutation test, n = 181). Fano factor was computed in 100-ms windows. Error bars (shaded area) represent ±s.e.m. Full size image

We separated inaccurate trials, in which the monkey made saccadic responses beyond the median absolute angular displacement (Fig. 1b), from accurate trials, which contained the same number of trials for each neuron and cue combination as the inaccurate group, but with the smallest angular displacement. In flank-cue trials, the Fano factor for accurate and inaccurate trials differed significantly at the end of the delay period, as predicted (last 0.5 s of delay, one-sided paired t test, t = 1.56, P = 0.05, n = 181; Fig. 6c). This difference increased parametrically as we restricted inaccurate trials to the most extreme saccadic deviations (Supplementary Fig. 3). The effect was specific for flank stimuli (Fig. 6d): modeling Fano factor with a mixed-effects ANOVA with factors cue, accuracy, monkey and neuron identity as random factor yielded a significant interaction effect of cue × accuracy (F 2,897 = 6.69, P = 0.0013, cell size 152 or 29 depending on monkey; Supplementary Fig. 4). Reduced ANOVA models revealed a main effect of cue for inaccurate trials (F 2,360 = 16.01, P < 0.001) and no significant cue effect for accurate trials (F 2,360 = 1.32, P = 0.27).

Late delay–selective negative pairwise correlations

We finally tested a long-standing prediction on how spike count correlations between neurons depend on the neurons' tuning preferences and the cue in a bump attractor representation6,7,20. We expected negative trial-to-trial correlations in the delay activity of two neurons responding to a cue presented right between their two preferred locations, resulting from random bump displacements in different trials (Fig. 7a,b). Only for this condition, when the cue engages the neurons in parts of their tuning curve with slopes of opposite sign, would we expect a negative correlation. Other cue conditions or correlations for neurons with the same selectivity should show positive or vanishing correlations6,7.

Figure 7: Noise correlations between pairs of neurons depend on the stimulus as predicted by the bump attractor model. (a) Scheme of delay population activity profiles in response to three repeated presentations of 180° cue. We focus on two neurons in this schematic network (○ and □) lying at opposite sides of the activity bump. (b) Only in this configuration, trial-to-trial correlations between the two neurons are expected to be negative because a displacement of the bump, illustrated in a, leads to an increase of firing rate in one neuron and a decrease in the other neuron (○ and □ in a). (c) Delay-period tuning curves for a sample pair of PFC neurons with the same preferred cue. Relevant cue conditions are indicated below the x axis. Spike count correlations were computed for each pair in the final 200 ms of the delay. Inset, scatter plot of spike counts for this sample pair. (d) Data presented as in c for a pair of neurons whose preferred cues were separated by one cue. Inset, scatter plot of spike counts for the 'in-flank' stimulus. (e) Pairwise correlation for same-tuning pairs (n = 15) computed separately for peak, flank and tail cue conditions. Significant deviation from zero mean was tested combining the last two 200-ms bins in the delay period (two-tailed t test, P < 0.05, n = 30). (f) Data presented as in e for different-tuning pairs (n = 10). Negative correlation for in-flank stimuli was tested with one-sided t test (t = 2.42, P = 0.026, n = 20). *P < 0.05. Error bars represent ±s.e.m. Full size image

We selected neuron pairs in two conditions: same-tuning pairs, with neurons sharing preferred cue (n = 15; Fig. 7c), and different-tuning pairs, where neurons differed in preferred location with one intervening cue in between (n = 10; Fig. 7d). We computed correlations between responses in the pair (Fig. 7c,d) for various cue conditions (peak, flank and tail, and in-flank, peak and out-flank; Fig. 7c,d) both in early and late delay (200-ms windows). Same-tuning pairs had stronger correlations than different-tuning pairs (three-way ANOVA with factors time, cue and neuron selectivity difference: main effect of selectivity difference, F 1,272 = 25.6, P < 0.001; no interaction effects, P > 0.2; Supplementary Fig. 4e–h). In same-tuning pairs, no other interaction or main effect was significant (factorial ANOVA, factors time and cue, P > 0.5), indicating consistently positive correlations through the delay, independently of the cue (Fig. 7e). Instead, a significant interaction of time and cue emerged for different-tuning pairs (F 2,114 = 3, P = 0.05), which reflected pairwise correlations becoming significantly negative at the end of the delay for in-flank stimuli (Fig. 7f). Thus, spike count correlations changed with cue condition as predicted by the bump attractor hypothesis.

The data can distinguish alternative scenarios

To test the extent to which our experimental data could distinguish the bump attractor model from other alternative encoding hypotheses for memory maintenance in PFC, we formulated two alternative models, the discrete attractor and the decaying bump network models (Supplementary Videos 1, 2 and 3). The continuous bump attractor network features strong topographic connectivity between excitatory neurons, so that a rigid bump attractor stabilized after brief network activation and diffused in the network during the delay period as a result of external noisy inputs (Fig. 8a). The discrete attractor network includes eight populations, each one encoding one of the cue locations, with stronger connections within and weaker connections across populations. An external stimulus brought the system to an attractor that maintained three adjacent populations persistently active and subject to strong external noise (Fig. 8a). Finally, in the decaying bump network, mnemonic information is encoded by individual neurons through an intrinsic depolarizing current that slowly decays away after initial activation by the stimulus. The bump of activity therefore slowly decayed away during the delay period (Fig. 8a).

Figure 8: Comparison of three alternative memory representations in three mechanistic models: a bump attractor model maintained by continuous topographic recurrent excitation (left), a discrete attractor model with eight populations (middle) and a non-attractor decaying bump model sustained by a slow intrinsic current (right). (a) Sample simulated delay activity in one trial for each model (see Supplementary Videos 1, 2 and 3). Triangles mark decoded response. Insets display recurrent excitatory connectivity patterns. (b) Distributions of behavioral responses over 16,000 simulations for each model reveal similar behavioral variability. (c) Tuning bias analysis as in Figure 3 for neural and behavioral data obtained from each model revealed significant positive bias only for the bump attractor model (thick horizontal lines; permutation test, P < 0.05). (d) Correlation between rate and behavioral deviations toward the neuron's preferred location (as in Fig. 4) becomes gradually positive in the delay only for the bump attractor model. Error bars (shaded area) represent ±s.e.m. Full size image

To test whether a neural data set with the characteristics of our experimental data can distinguish between these models, we performed simulations with the three firing rate models (Online Methods and Supplementary Codes 1, 2 and 3), and we generated three surrogate data sets matching the sample sizes in our experiment. We picked parameters for our models that produced similar neural and behavioral data (Fig. 8a,b), in good qualitative agreement with experimental data (Fig. 1). To get a sense of the quantitative effects expected, we also tested non-mechanistic coding models that could match quantitatively the heterogeneity of experimental neural data (Online Methods and Supplementary Figs. 5 and 6).

We analyzed these surrogate data sets exactly as we did before for the experimental data. Data produced by the bump attractor model replicated our experimental findings, but none of the effects were replicated by the discrete attractor or the decaying bump models (tuning curve bias, rate-behavior correlation, Fano factor and pairwise correlations; Fig. 8c,d and Supplementary Fig. 6). For these models, the lack of effects occurred because behavioral variability did not result primarily from collective neuronal variability: both in the discrete attractor and in the decaying bump models behavioral variability emerged largely from independent random fluctuations at the cellular level, and not from correlated population dynamics as in the bump attractor model. Such dynamics can occur in discrete attractor models, in the form of noise-induced transitions to adjacent attractors. However, this leads to large abrupt shifts in behavioral read-out, which result in multimodal behavioral distributions, that were not supported experimentally (Fig. 1b) unless very fine discretization approaching a continuum is assumed. We conclude that our experimental findings can discriminate between distinct mechanisms of working memory maintenance, supporting a neural representation in PFC compatible with the bump attractor hypothesis for spatial working memory.