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Discrete attractor dynamics underlies persistent activity in the frontal cortex

Abstract

Short-term memories link events separated in time, such as past sensation and future actions. Short-term memories are correlated with slow neural dynamics, including selective persistent activity, which can be maintained over seconds. In a delayed response task that requires short-term memory, neurons in the mouse anterior lateral motor cortex (ALM) show persistent activity that instructs future actions. To determine the principles that underlie this persistent activity, here we combined intracellular and extracellular electrophysiology with optogenetic perturbations and network modelling. We show that during the delay epoch, the activity of ALM neurons moved towards discrete end points that correspond to specific movement directions. These end points were robust to transient shifts in ALM activity caused by optogenetic perturbations. Perturbations occasionally switched the population dynamics to the other end point, followed by incorrect actions. Our results show that discrete attractor dynamics underlie short-term memory related to motor planning.

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Data availability

Electrophysiological data are available at FigShare (https://figshare.com/; doi:10.25378/janelia.7489253).

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Acknowledgements

We thank N. Brunel, S. Lim, N. Li, G. Card, M. Economo, K. Daie, J. Yu, T. Wang, L. Liu, A. Ebihara and A. Finkelstein for comments on the manuscript, M. Inagaki for animal training, T. Harris, B. Barbarits, J. J. James and W. L. Sun for help with silicon probe recordings and spike sorting, and D. Hansel and S. Druckmann for discussions. This work was funded by Howard Hughes Medical Institute. H.K.I is a Helen Hay Whitney Foundation postdoctoral fellow.

Reviewer information

Nature thanks Ila P. Fiete and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

H.K.I. performed experiments and analysed data, with input from all the authors. L.F. and S.R. performed network modelling. H.K.I. and K.S. wrote the paper, with input from all the authors.

Competing interests

The authors declare no competing interests.

Correspondence to Sandro Romani or Karel Svoboda.

Extended data figures and tables

  1. Extended Data Fig. 1 Continuous and discrete attractor models (one hemisphere).

    a, Schematic of simulated networks. The same architecture was used for the continuous attractor model (bh), single moving attractor model (io) and multiple discrete attractors model (pv). L, lick-left selective excitatory neurons; I, inhibitory interneurons, R, lick-right selective excitatory neurons. Blue and red arrows indicate selective external input. b, Trajectories projected along the CD. Left, activity in unperturbed trials. Right, distribution of end points. Line denotes the mean; shading denotes s.d. Blue, correct lick-right trials; red, correct lick-left trials. c, Left, activity in perturbed correct trials. Right, distribution of end points. Cyan bar on top, photoinhibition. Traces with lighter colours correspond to higher intensity of photoinhibition. d, Left, activity in perturbed incorrect trials. Right, distribution of end points. e, Across-trial fluctuations during the delay epoch in unperturbed correct trials. Across-trial fluctuations are normalized for the value at 2.0 s before the go cue. f, Recovery speed of the CD in perturbed correct trials following perturbations. g, Absolute difference in projection to CD between perturbed and unperturbed trials at the middle delay (green) and end points (magenta). h, Phase line of trajectories. io, Dynamics of single moving attractor model. pv, Dynamics of multiple discrete attractors model. w, Across-trial fluctuations in continuous attractor with decreasing external noise (Methods), normalized by their value 2.0 s before the go cue. x, A summary table comparing three models and data.

  2. Extended Data Fig. 2 Whole-cell recordings example cells.

    Columns represent data from one cell. Top, mean spike rate; second row, mean membrane potential (Vm). Blue, correct lick-right trials; red, correct lick-left trials; third row, spike-triggered median of Vm. Spikes in the pre-sample epoch (black) and the delay epoch (blue) in correct lick-right trials were analysed. Shading denotes s.e.m. (hierarchical bootstrap). P value denotes the probability of the null hypothesis that spike-triggered medians are the same between epochs (Methods, hierarchical bootstrap); fourth row, relationship between Vm and spike rate of the pre-sample epoch (black), the delay epoch (blue) and all epochs (grey). Error bar denotes s.e.m. (hierarchical bootstrap). P value denotes the probability of the null hypothesis that Vm-to-spike rate curves are the same between the pre-sample epoch and the delay epoch (hierarchical bootstrap, Methods). All statistical tests are two-sided. When there was no overlap between the curves from the two epochs, we did not test (P = not applicable (N.A)). Cell 88–130, cells recorded during the auditory task; cell 135–184, cells recorded during the tactile task. Asterisk denotes selective cells. See Supplementary Table 1 for number of trials.

  3. Extended Data Fig. 3 Analysis of Vm.

    a, Relationship between delay spike rate and Vm (delay epoch spike rate or Vm minus pre-sample epoch spike rate or Vm). For each cell, correct lick-right and correct lick-left trials are shown separately (n = 37 cells). Black, selective cells (n = 10 cells). Red line, linear regression. Linear regression, Pearson’s correlation coefficient, and the t-statistic of Pearson correlation coefficient (P) are shown. b, Selectivity of ALM neurons based on spike rate (top) and Vm (bottom). Duplicate of Fig. 2d. Shading denotes s.e.m. (bootstrap, n = 10 cells). c, Autocorrelation of Vm during the pre-sample epoch (left) and the delay epoch in correct lick-right trials (middle). Subtraction of these two autocorrelation curves is shown on right to emphasize the difference between epochs. Thick line denotes mean across cells; thin lines denote individual cells (n = 37 cells). d, Comparison of time constant of membrane fluctuations based on autocorrelation between the pre-sample epoch and the delay epoch. Left, scatter plot of the time constant; right, histogram of the difference in time-constant between the delay epoch compared to the pre-sample epoch (change in time constant). P value determined by two-sided Wilcoxon signed-rank test examining a null hypothesis that the change in time constant is 0. The first P value, all cells (left; n = 37 cells); second P value, selective cells (right; n = 10 cells). The shorter time constant during the delay epoch is presumably due to increase in conductance. e, Distribution of number of spike bursts per trial in correct lick-right trials. White, all cells; black, selective cells. f, Spike raster (top) and spike rates (bottom) of correct lick-right trials in an example cell with high occurrence of spike bursts (cell 120, arrow in e). Blue, regular spikes; green, spikes belonging to spike bursts. Right, example spike bursts. g, Grand average spike rate of cells with more than 0.5 spike bursts per trial in correct lick-right trials (n = 12 cells). Shading denotes s.e.m. Top, spike rate of all spike types (regular spikes and spike bursts), (bottom) spike rate of spike bursts. h, Comparison of number of bursts per trial between the pre-sample epoch and the delay epoch. P value determined by two-sided Wilcoxon signed-rank test examining a null hypothesis that number of bursts per trial are the same between two epochs (n = 12 cells). Blue, correct lick-right trials; red, correct lick-left trials. Spike bursts did not increase during the delay epoch. ip, The same format as in ah for the tactile task. All cells, n = 42; selective cells, n = 10.

  4. Extended Data Fig. 4 Negative current injection.

    a, Five example cells with negative current injection. Top, mean Vm without negative current injection; bottom, mean Vm with negative current injection. Blue, correct lick-right trials; red, correct lick-left trials. b, Input resistance (Rin) of cells with and without current injection (n = 10 cells). Data are pooled from cells analysed in c. P value determined by two-sided Wilcoxon signed-rank test. Central line in the box plot is the median. Top and bottom edges are the 75% and 25% points, respectively. The whiskers show the lowest datum within 1.5 interquartile range (IQR) of the lower quartile, and the highest datum within 1.5 IQR of the upper quartile. c, Delay amplitude of Vm (delay epoch Vm minus pre-sample epoch Vm) with and without current injections (n = 10 cells). Delay amplitude during the current injection was normalized by the change in input resistance. Correct lick-right trials (blue) and correct lick-left trials (red) are shown separately. Crosses denote s.e.m. (bootstrap). Dashed line denotes linear regression. Slope of linear regression, Pearson’s correlation coefficient and the t-statistic of Pearson’s correlation coefficient (P) are shown. d, Lick-right delay selectivity (delay epoch Vm in lick-right trial minus delay epoch Vm in lick-left trial) with and without current injections (n = 10 cells). Crosses denote s.e.m. (bootstrap). Dashed line denotes linear regression. Slope of linear regression, Pearson’s correlation coefficient), and the t-statistic of Pearson correlation’s coefficient (P) are shown. e, Loss of spike bursts after current injection. Top, Vm of two example cells with high occurrence of spike bursts. Overlay of all correct lick-right trials. Black horizontal line, spike threshold. Regular spikes were removed and Vm was averaged over 100 ms. Sharp overshoots above the spike threshold indicate spike bursts. n = 19 and 20 trials (cell 96 and 101, respectively). Right, two example spike bursts indicated by arrows (cell 101). Bottom, Vm of the same example cells with negative current injection. There was no spike to remove. Vm was averaged over 100 ms. Note the loss of sharp depolarizing events. n = 8, and 9 trials (cell 96 and 101, respectively).

  5. Extended Data Fig. 5 Funnelling of Vm.

    a, Four example ALM neurons. Top, mean Vm; middle, all correct lick-right trials overlaid; bottom, all correct lick-left trials overlaid. To remove fast within trial fluctuations, Vm was averaged over 200 ms. b, The same plot as in Fig. 4c, d. n = 79 cells (both auditory and tactile tasks are pooled). Black, selective cells (n = 20 cells). P values were determined by one-sided Wilcoxon signed-rank test (the same applies to ce). The first P value, all cells; second P value, selective cells only. c, As in b for the correct lick-left trials. Statistical methods and n value as in b. d, As in b for comparison between the sample epoch and the delay epoch. Statistical methods and n value as in b. e, As in c for comparison between the sample epoch and the delay epoch. Statistical methods and n value as in b. f, Across-trial fluctuations of all cells (n = 37) (left), and selective cells (n = 10) (right) in the auditory task (as in Fig. 4b). Line, mean of across-trial fluctuations; shading denotes s.e.m. (hierarchical bootstrap). Blue, correct lick-right trials; red, correct lick-left trials. g, Testing for a decrease in across-trial fluctuations. P values reflect a null hypothesis that across-trial fluctuations during the delay epoch were higher than that during the pre-sample epoch (hierarchical bootstrap, n = 1,000 iteration). Across-trial fluctuations were measured as the quartile difference (left) or trimmed s.d. (right) of Vm across the same trial type (blue, correct lick-right trials; red, correct lick-left trials) (Methods). Both methods provided similar results. Vm was averaged over 100 ms (triangle) or 200 ms (square) to remove fast within-trial fluctuations. The result was robust to the averaging bin size. The dashed line, P = 0.025 (α = 0.05 for two-sided test). A schematic of statistical test in g and i is shown in the box below i. Across-trial fluctuations during the pre-sample epoch (0.6 s) was compared with the across-trial fluctuations during the delay epoch (variable durations: window size in g and i). The window ends at the time t, which is t = (time of the go cue) − (bin size)/2, to exclude the signal after the go cue. h, As in f for the tactile task. i, As in g for the tactile task. j, Relationship between Vm and the change in across-trial fluctuations (across-trial fluctuations during the delay epoch minus across-trial fluctuations during the pre-sample epoch). Vm during the delay epoch was averaged and normalized to the spike threshold. Dashed line, linear regression. Slope of linear regression, Pearson’s correlation coefficient, and the t-statistic of Pearson’s correlation coefficient (P) are shown. Pooling both the tactile and auditory tasks, and excluding non-spiking cells (n = 73 cells). The slope of regression line is opposite from what is expected for the ceiling effect.

  6. Extended Data Fig. 6 Robustness of the CD to perturbation.

    a, Schematics. Projection of population activity to the CD. b, The CD is stable during the delay epoch. Pearson’s correlation coefficient of the CD between half of trials (fit trials) and the other half (test trials) (Methods). Grand average of all sessions (n = 11 sessions for bl). c, Projection of individual trials to the CD in two example sessions (seven randomly selected trials per trial type; blue, correct lick-right trials; red, correct lick-left trials). d, Selectivity explained by different modes (dimensions in activity space). Left, selectivity over time. Solid line, unperturbed correct trials, dotted line, perturbed correct trials. Blue, total selectivity; other colours, selectivity along different modes. Middle, selectivity explained by each mode during early delay (first 1 s of the delay epoch). Right, selectivity explained by each mode during late delay (last 1 s of the delay epoch) (mean ± s.e.m.). CDe, CD during early delay; CDs, CD during stimulation; PM, perturbation mode; RM, non-selective ramping mode (Methods). Sum of all modes is shown on top. Selectivity did not increase along any of these modes during perturbations. Central line in the box plot is the median. Top and bottom edges are the 75% and 25% points, respectively. The whiskers show the lowest datum within 1.5 IQR of the lower quartile, and the highest datum within 1.5 IQR of the upper quartile. e, Distribution of projection to the CD at end points in each session is overlaid. Blue, correct lick-right trials; red, correct lick-left trials. f, Distribution of projection to CD at end points in all trial types (both correct and incorrect trials are pooled, but not early lick or no-response trials). Distribution of end points in each session is overlaid. g, Distribution of projection to the CD at end points in Fig. 5b, pooling correct and incorrect trials, but not early lick or no-response trials. Shading denotes s.e.m. (bootstrap). h, The same format as in g for perturbed trial types. i, Decoder based on projection to the CD at a time bin just before the onset of perturbation (Methods). Probability to lick right in trials with projection to CD higher than each value in x axis (blue). Probability to lick left in trials with projection to CD lower than each value in x axis (red). Dashed lines indicate decision boundaries for lick-right (blue) and lick-left (red) trials (Methods). Shading denotes s.e.m. (hierarchical bootstrap). j, Trajectories along the CD in perturbed trials decoded to be correct trials before the onset of perturbation. Dotted line, unperturbed correct trials in Fig. 5e. k, Phase line of trajectories along CD of trials decoded to be correct trials before the onset of perturbation. Solid line, data; dashed line, shuffled data; shading, s.e.m. (hierarchical bootstrap). l, Absolute difference in projection to the CD between perturbed and unperturbed trials at the middle delay (green) and end points (magenta). Grey, individual session; black, mean. P = 0.57, 0.92, 0.0078 and 0.0039 from left to right (two-sided Wilcoxon signed-rank test). P < 0.05. mx, The same format as in bl for the random delay task. n = 13 sessions. In x, P = 0.79, 0.027, 0.00024 and 0.64 from left to right (two-sided Wilcoxon signed-rank test). P < 0.05; P < 0.01.

  7. Extended Data Fig. 7 Characterization of bilateral photoinhibition of ALM.

    a, Schematic of bilateral photoinhibition of ALM. Eight photostimuli were applied to ALM in both hemispheres (spacing, 1-mm interval). These photostimuli are expected to uniformly silence excitatory neurons in ALM6. Photoinhibition started at the onset of the delay epoch (−2 s to the go cue) or at the middle of the delay epoch (−1 s to the go cue) and lasted for 600 ms with additional 400 ms ramping down (Methods). b, Effect of the photoinhibition with different laser powers on behavioural performance. Black, early delay inhibition; magenta, late delay inhibition. Thick lines, grand mean performance (n = 5 mice); thin lines, mean performance of each mouse. Error bars denote s.e.m. (hierarchical bootstrap). Laser power, time-averaged mean power per spot. c, Effect of photoinhibition with different laser powers on early lick rates. Early lick rate after the early delay photoinhibition is shown. The same format as in b. d, Schematic of silicon probe recording during bilateral photoinhibition of ALM in non-behaving mice (relevant to ej). e, Spike rates of fast-spiking neurons (top) and regular-spiking neurons (bottom) during photoinhibition of ALM with eight spots. Each column represents data with different laser powers. Mean spike rate is shown. Cyan bar, time of photoinhibition. f, Spike rate of regular-spiking neurons during the photoinhibition. For each cell, mean spike rate during photoinhibition (100–600 ms) was divided by mean spike rate before photoinhibition (−1–0 s) to calculate the normalized spike rate (as in h and j). Increasing laser power resulted in stronger inhibition. P < 0.01, two-sided Wilcoxon signed-rank test with Bonferroni correction. From left to right: P = 2.1 × 10−19, 2.2 × 10−25, 2.1 × 10−27, 4.2 × 10−27, 1.6 × 10−27 and 2.7 × 10−31 (P values without Bonferroni correction), n = 188 cells. Central line in the box plot is the median. Top and bottom edges are the 75% and 25% points, respectively. The whiskers show the lowest datum within 1.5 IQR of the lower quartile, and the highest datum within 1.5 IQR of the upper quartile. g, Spike rate of regular-spiking neurons after the photoinhibition. For each cell, mean spike rate after photoinhibition (1–2 s) was divided by the mean spike rate before photoinhibition (−1–0 s) to calculate normalized spike rate. Increasing laser power resulted in stronger rebound. P < 0.05, P < 0.01, two-sided Wilcoxon signed-rank test with Bonferroni correction. From left to right: P = 0.37, 7.1 × 10−3, 3.1 × 10−2, 1.4 × 10−2, 3.6 × 10−5 and 1.4 × 10−6 (P values without Bonferroni correction), n = 188 cells. Box plots follow the same format as in f. h, Relationship between depth and spike rate of regular-spiking neurons during the photoinhibition. Photoinhibition affected neurons across layers. i, Spike rate of regular-spiking neurons during the photoinhibition at different locations. Mean spike rate is shown for each laser power (control, black). Distance of recording site (ALM) and centre of laser stimulation (centre of four spots in the same hemisphere) is shown. Laser spots were moved from ALM to posterior locations. j, Spike rate of regular-spiking neurons during the photoinhibition at different locations. Photoinhibition affected neurons 1 mm away from the laser, consistent with a previous report6. P < 0.01, two-sided Wilcoxon signed-rank test with Bonferroni correction. From left to right: P = 1.1 × 10−15, 6.0 × 10−7, 0.61, 0.55, 0.52 (P values without Bonferroni correction), n = 87 cells. Box plots follow the same format as in f.

  8. Extended Data Fig. 8 Effect of photoinhibition on neural populations.

    a, Proportion of cells with significant spike rate difference between unperturbed and perturbed trials at each time point (Methods). Cyan bar, photoinhibition. n = 667 cells. b, Selectivity during bilateral photoinhibition. Line denotes mean of all cells; shadow denotes s.e.m. (bootstrap). Black, unperturbed trials. Cyan bar, photoinhibition. n = 667 cells. c, Recovery speed of selectivity following perturbation (approximately −1.2 to 0 s before the go cue; Methods). P = 0.032 (testing a null hypothesis that recovery speed is the same between trials with 0.1 mW and 0.3 mW photoinhibition, bootstrap, two-sided). n = 667 cells. Central line in the box plot is the median. Top and bottom edges are the 75% and 25% points, respectively. The whiskers show the lowest datum within 1.5 IQR of the lower quartile, and the highest datum within 1.5 IQR of the upper quartile. d, Relationship between selectivity in correct and incorrect trials. Mean selectivity during 1–2 s after the delay onset is shown. Inset, definition of θ (Methods). n = 465 cells. e, Mean spike rate of lick-right preferring neurons with different θ. Lines, grand mean of peri-stimulus time histogram; shading denotes s.e.m. (bootstrap). Blue, correct lick-right trials; red, correct lick-left trials; dark blue, incorrect lick-right trials; dark red, incorrect lick-left trials. Mean peri-stimulus time histogram of unperturbed correct trials (first row) are also shown as dashed lines in the second to fourth row. fj, As in ae for the random delay task. To calculate mean spike rate and selectivity, we pooled spikes before the go cue across trials with different delay durations. Because delay durations were different across trials, the time axis is aligned to the onset of the delay epoch. In h, P = 0.009 (testing a null hypothesis that recovery speed is the same between trials with 0.1 mW and 0.3 mW photoinhibition, bootstrap, two-sided). n = 867 cells for fh, and 487 cells for i. k, Example single units (random delay task). Top, spike raster. Seven and twenty-five trials per trial type were randomly selected for unperturbed trials and perturbed trials, respectively. Bottom, mean spike rate pooling spikes before the go cue across trials with different delay durations. Blue, correct lick-right trials; red, correct lick-left trials; dark blue, incorrect lick-right trials; dark red, incorrect lick-left trials. Cyan bar, photoinhibition. l, Cumulative distribution of increase in spike rate during the delay epoch. Data from four different tasks are compared (Methods).

  9. Extended Data Fig. 9 Modular discrete attractor models.

    We built models consisting of two modules, each corresponding to one ALM hemisphere, in accordance with the previously described functional architecture11. These models are consistent with (1) ramping dynamics during the delay epoch; (2) reproduce the response to transient bilateral inactivation (Fig. 5); and (3) the response to unilateral ALM perturbation11. The circuit architecture in each hemisphere is as in Extended Data Fig. 1. Slow ramping was caused by either external non-selective input (bh; external ramping model; note ramping external non-selective input in a) or internal slow dynamics (io; internal ramping model; note shallower energy landscape in a). All panels show results from the left hemisphere. In bo, we modelled the fixed delay task (ramping activity during the delay epoch.) In p, q, we modelled the random delay task (stationary activity during the delay epoch). To make the activity during the delay epoch stationary, non-selective input was modified to be stationary for the external ramping model, and the energy landscape was modified to be steeper for the internal ramping model. With these modifications the two models are essentially equivalent. Therefore, we show only one model for the random delay task. n = 1,000 trials per model. a, Schematic of two-hemisphere network models. Circuit architecture, common to both models (middle), and time course of external inputs in each model (left and right). R, L and I correspond to lick-right selective excitatory neurons, lick-left selective excitatory neurons and inhibitory interneurons, respectively. Blue and red arrows, selective external input. Black arrows, non-selective external input. b, Trajectories projected along the CD in model with external ramping input. Activity in unperturbed trials (left), and distribution of end points (right). Line denotes mean; shading denotes s.d. Blue, correct lick-right trials; red, correct lick-left trials. c, Projected activity in bilaterally perturbed correct trials (left), and distribution of end points (right). Line denotes mean. Cyan bar on top denotes photoinhibition. Lighter colours correspond to higher intensity of photoinhibition. d, Projected activity in bilaterally perturbed incorrect trials. e, Projected activity in unilaterally perturbed correct trials. Effect of unilateral ALM photoinhibition contralateral (left) or ipsilateral (right) to the analysed hemisphere (left ALM) is shown. f, Phase line of projected trajectories. g, Absolute difference in projection to the CD between perturbed and unperturbed trials at the middle delay (green) and end points (magenta). h, Behavioural performance of the model (Methods). io, As in bh for internal slow dynamics model. p, Schematic of two-hemisphere network models with stationary delay activity. q, Projected activity in bilaterally perturbed correct trials. Same format as in d. r, Recovery speed of the CD in bilaterally perturbed correct trials following perturbation. Note that recovery speed in the external ramping model is similar regardless of delay dynamics (ramping or stationary).

  10. Extended Data Fig. 10 Performance in the random delay task.

    a, Behavioural performance (left), early lick rate (middle) and no-response rate (right) in the random delay task. Thin lines, individual sessions (n = 23); thick line, grand mean among sessions. bd, The same format as in Fig. 5b–d for the random delay task. Trials with 2-s delay duration are shown. Line denotes mean; shading denotes s.e.m. (bootstrap). n = 13 sessions. e, Schematics. Projection of trials to the non-selective ramping mode (RM). f, Projection of trials to non-selective ramping mode in the fixed delay task with 2-s delay. Line, grand mean across sessions (n = 11 sessions); shading denotes s.e.m. (bootstrap). g, As in f for the random delay task (n = 13 sessions). Trials with 2-s delay duration are shown.

Supplementary information

  1. Reporting Summary

  2. Supplementary Table 1

    A list of whole cells recorded. Related to Fig. 2-4 and Extended Data Figs. 2-5.

  3. Supplementary Table 2

    A list of fixed delay task (2s delay) sessions. Related to Fig. 5 and Extended Data Figs. 6 and 8.

  4. Supplementary Table 3

    A list of random delay task sessions. Related to Fig. 6 and Extended Data Figs. 6, 8, and 10.

  5. Supplementary Table 4

    Parameters used for models. Related to Extended Data Figs. 1 and 9.

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Further reading

Fig. 1: Models of persistent preparatory activity.
Fig. 2: Whole-cell recordings in ALM.
Fig. 3: Hyperpolarization of ALM neurons.
Fig. 4: Funnelling of the membrane potential.
Fig. 5: Robustness of discrete trajectories.
Fig. 6: Stationary preparatory activity.
Extended Data Fig. 1: Continuous and discrete attractor models (one hemisphere).
Extended Data Fig. 2: Whole-cell recordings example cells.
Extended Data Fig. 3: Analysis of Vm.
Extended Data Fig. 4: Negative current injection.
Extended Data Fig. 5: Funnelling of Vm.
Extended Data Fig. 6: Robustness of the CD to perturbation.
Extended Data Fig. 7: Characterization of bilateral photoinhibition of ALM.
Extended Data Fig. 8: Effect of photoinhibition on neural populations.
Extended Data Fig. 9: Modular discrete attractor models.
Extended Data Fig. 10: Performance in the random delay task.

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