Abstract
Shortterm memories link events separated in time, such as past sensation and future actions. Shortterm memories are correlated with slow neural dynamics, including selective persistent activity, which can be maintained over seconds. In a delayed response task that requires shortterm 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 shortterm 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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References
 1.
Kubota, K. & Niki, H. Prefrontal cortical unit activity and delayed alternation performance in monkeys. J. Neurophysiol. 34, 337–347 (1971).
 2.
Tanji, J. & Evarts, E. V. Anticipatory activity of motor cortex neurons in relation to direction of an intended movement. J. Neurophysiol. 39, 1062–1068 (1976).
 3.
Funahashi, S., Bruce, C. J. & GoldmanRakic, P. S. Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex. J. Neurophysiol. 61, 331–349 (1989).
 4.
Romo, R., Brody, C. D., Hernandez, A. & Lemus, L. Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399, 470–473 (1999).
 5.
Maimon, G. & Assad, J. A. A cognitive signal for the proactive timing of action in macaque LIP. Nat. Neurosci. 9, 948–955 (2006).
 6.
Guo, Z. V. et al. Flow of cortical activity underlying a tactile decision in mice. Neuron 81, 179–194 (2014).
 7.
Erlich, J. C., Bialek, M. & Brody, C. D. A cortical substrate for memoryguided orienting in the rat. Neuron 72, 330–343 (2011).
 8.
Shenoy, K. V., Sahani, M. & Churchland, M. M. Cortical control of arm movements: a dynamical systems perspective. Annu. Rev. Neurosci. 36, 337–359 (2013).
 9.
Inagaki, H. K., Inagaki, M., Romani, S. & Svoboda, K. Lowdimensional and monotonic preparatory activity in mouse anterior lateral motor cortex. J. Neurosci. 38, 4163–4185 (2018).
 10.
Svoboda, K. & Li, N. Neural mechanisms of movement planning: motor cortex and beyond. Curr. Opin. Neurobiol. 49, 33–41 (2018).
 11.
Li, N., Daie, K., Svoboda, K. & Druckmann, S. Robust neuronal dynamics in premotor cortex during motor planning. Nature 532, 459–464 (2016).
 12.
Guo, Z. V. et al. Maintenance of persistent activity in a frontal thalamocortical loop. Nature 545, 181–186 (2017).
 13.
Gao, Z. et al. A corticocerebellar loop for motor planning. Nature 563, 113–116 (2018).
 14.
Johnston, D. & Wu, S. M.S. Foundations of Cellular Neurophysiology (MIT Press, Cambridge, 1995).
 15.
Chaudhuri, R. & Fiete, I. Computational principles of memory. Nat. Neurosci. 19, 394–403 (2016).
 16.
Lim, S. & Goldman, M. S. Balanced cortical microcircuitry for maintaining information in working memory. Nat. Neurosci. 16, 1306–1314 (2013).
 17.
Wang, X. J. Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24, 455–463 (2001).
 18.
Goldman, M. S. Memory without feedback in a neural network. Neuron 61, 621–634 (2009).
 19.
Amit, D. J. & Brunel, N. Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex 7, 237–252 (1997).
 20.
Wimmer, K., Nykamp, D. Q., Constantinidis, C. & Compte, A. Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory. Nat. Neurosci. 17, 431–439 (2014).
 21.
Koulakov, A. A., Raghavachari, S., Kepecs, A. & Lisman, J. E. Model for a robust neural integrator. Nat. Neurosci. 5, 775–782 (2002).
 22.
Zylberberg, J. & Strowbridge, B. W. Mechanisms of persistent activity in cortical circuits: possible neural substrates for working memory. Annu. Rev. Neurosci. 40, 603–627 (2017).
 23.
Cannon, S. C., Robinson, D. A. & Shamma, S. A proposed neural network for the integrator of the oculomotor system. Biol. Cybern. 49, 127–136 (1983).
 24.
Brody, C. D., Romo, R. & Kepecs, A. Basic mechanisms for graded persistent activity: discrete attractors, continuous attractors, and dynamic representations. Curr. Opin. Neurobiol. 13, 204–211 (2003).
 25.
Machens, C. K., Romo, R. & Brody, C. D. Flexible control of mutual inhibition: a neural model of twointerval discrimination. Science 307, 1121–1124 (2005).
 26.
Barak, O. & Tsodyks, M. Working models of working memory. Curr. Opin. Neurobiol. 25, 20–24 (2014).
 27.
Mongillo, G., Barak, O. & Tsodyks, M. Synaptic theory of working memory. Science 319, 1543–1546 (2008).
 28.
Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).
 29.
Amari, S. I. Learning patterns and pattern sequences by selforganizing nets of threshold elements. IEEE Trans. Comput. C21, 1197–1206 (1972).
 30.
BenYishai, R., BarOr, R. L. & Sompolinsky, H. Theory of orientation tuning in visual cortex. Proc. Natl Acad. Sci. USA 92, 3844–3848 (1995).
 31.
Seung, H. S. How the brain keeps the eyes still. Proc. Natl Acad. Sci. USA 93, 13339–13344 (1996).
 32.
Loewenstein, Y. et al. Bistability of cerebellar Purkinje cells modulated by sensory stimulation. Nat. Neurosci. 8, 202–211 (2005).
 33.
Egorov, A. V., Hamam, B. N., Fransen, E., Hasselmo, M. E. & Alonso, A. A. Graded persistent activity in entorhinal cortex neurons. Nature 420, 173–178 (2002).
 34.
Kim, S. S., Rouault, H., Druckmann, S. & Jayaraman, V. Ring attractor dynamics in the Drosophila central brain. Science 356, 849–853 (2017).
 35.
Anderson, J. S., Lampl, I., Gillespie, D. C. & Ferster, D. The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science 290, 1968–1972 (2000).
 36.
Aksay, E., Gamkrelidze, G., Seung, H. S., Baker, R. & Tank, D. W. In vivo intracellular recording and perturbation of persistent activity in a neural integrator. Nat. Neurosci. 4, 184–193 (2001).
 37.
Williams, S. R. & Mitchell, S. J. Direct measurement of somatic voltage clamp errors in central neurons. Nat. Neurosci. 11, 790–798 (2008).
 38.
Camperi, M. & Wang, X. J. A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability. J. Comput. Neurosci. 5, 383–405 (1998).
 39.
Churchland, A. K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818–831 (2011).
 40.
Burak, Y. & Fiete, I. R. Fundamental limits on persistent activity in networks of noisy neurons. Proc. Natl Acad. Sci. USA 109, 17645–17650 (2012).
 41.
Churchland, M. M., Yu, B. M., Ryu, S. I., Santhanam, G. & Shenoy, K. V. Neural variability in premotor cortex provides a signature of motor preparation. J. Neurosci. 26, 3697–3712 (2006).
 42.
Strogatz, S. H. Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering (AddisonWesley, Boston, 1994).
 43.
Janssen, P. & Shadlen, M. N. A representation of the hazard rate of elapsed time in macaque area LIP. Nat. Neurosci. 8, 234–241 (2005).
 44.
Komura, Y. et al. Retrospective and prospective coding for predicted reward in the sensory thalamus. Nature 412, 546–549 (2001).
 45.
Wills, T. J., Lever, C., Cacucci, F., Burgess, N. & O’Keefe, J. Attractor dynamics in the hippocampal representation of the local environment. Science 308, 873–876 (2005).
 46.
Kopec, C. D., Erlich, J. C., Brunton, B. W., Deisseroth, K. & Brody, C. D. Cortical and subcortical contributions to shortterm memory for orienting movements. Neuron 88, 367–377 (2015).
 47.
Piet, A. T., Erlich, J. C., Kopec, C. D. & Brody, C. D. Rat prefrontal cortex inactivations during decision making are explained by bistable attractor dynamics. Neural Comput. 29, 2861–2886 (2017).
 48.
Suzuki, M. & Gottlieb, J. Distinct neural mechanisms of distractor suppression in the frontal and parietal lobe. Nat. Neurosci. 16, 98–104 (2013).
 49.
Freedman, D. J., Riesenhuber, M., Poggio, T. & Miller, E. K. Categorical representation of visual stimuli in the primate prefrontal cortex. Science 291, 312–316 (2001).
 50.
Shadlen, M. N. & Newsome, W. T. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophysiol. 86, 1916–1936 (2001).
 51.
Hippenmeyer, S. et al. A developmental switch in the response of DRG neurons to ETS transcription factor signaling. PLoS Biol. 3, e159 (2005).
 52.
Madisen, L. et al. A toolbox of Credependent optogenetic transgenic mice for lightinduced activation and silencing. Nat. Neurosci. 15, 793–802 (2012).
 53.
Zhao, S. et al. Cell typespecific channelrhodopsin2 transgenic mice for optogenetic dissection of neural circuitry function. Nat. Methods 8, 745–752 (2011).
 54.
Guo, Z. V. et al. Procedures for behavioral experiments in headfixed mice. PLoS ONE 9, e88678 (2014).
 55.
Taberner, A. M. & Liberman, M. C. Response properties of single auditory nerve fibers in the mouse. J. Neurophysiol. 93, 557–569 (2005).
 56.
Ison, J. R., Allen, P. D. & O’Neill, W. E. Agerelated hearing loss in C57BL/6J mice has both frequencyspecific and nonfrequencyspecific components that produce a hyperacusislike exaggeration of the acoustic startle reflex. J. Assoc. Res. Otolaryngol. 8, 539–550 (2007).
 57.
Anderson, J. S., Carandini, M. & Ferster, D. Orientation tuning of input conductance, excitation, and inhibition in cat primary visual cortex. J. Neurophysiol. 84, 909–926 (2000).
 58.
Yu, J., Gutnisky, D. A., Hires, S. A. & Svoboda, K. Layer 4 fastspiking interneurons filter thalamocortical signals during active somatosensation. Nat. Neurosci. 19, 1647–1657 (2016).
 59.
Monier, C., Chavane, F., Baudot, P., Graham, L. J. & Fregnac, Y. Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning. Neuron 37, 663–680 (2003).
 60.
Efron, B. & Tibshirani, R. An Introduction to the Bootstrap, 1 edn (Chapman and Hall/CRC, 1994).
 61.
van der Leeden, R. in Handbook of Multilevel Analysis (eds J. de Leeuw & E. Meijer) 401–433 (Springer, 2008).
 62.
Aarts, E., Verhage, M., Veenvliet, J. V., Dolan, C. V. & van der Sluis, S. A solution to dependency: using multilevel analysis to accommodate nested data. Nat. Neurosci. 17, 491–496 (2014).
 63.
Jun, J. J. et al. Realtime spike sorting platform for highdensity extracellular probes with groundtruth validation and drift correction. Preprint at https://www.bioRxiv.org/content/early/2017/01/19/101030 (2017).
 64.
Compte, A., Brunel, N., GoldmanRakic, P. S. & Wang, X. J. Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cereb. Cortex 10, 910–923 (2000).
 65.
Wilson, H. R. & Cowan, J. D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1–24 (1972).
 66.
Murray, J. D. et al. Stable population coding for working memory coexists with heterogeneous neural dynamics in prefrontal cortex. Proc. Natl Acad. Sci. USA 114, 394–399 (2017).
 67.
Murphy, B. K. & Miller, K. D. Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61, 635–648 (2009).
 68.
Barak, O. & Tsodyks, M. Persistent activity in neural networks with dynamic synapses. PLoS Comput. Biol. 3, e35 (2007).
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
Affiliations
Contributions
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.
Corresponding authors
Correspondence to Sandro Romani or Karel Svoboda.
Extended data figures and tables
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 (b–h), single moving attractor model (i–o) and multiple discrete attractors model (p–v). L, lickleft selective excitatory neurons; I, inhibitory interneurons, R, lickright 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 lickright trials; red, correct lickleft 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, Acrosstrial fluctuations during the delay epoch in unperturbed correct trials. Acrosstrial 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. i–o, Dynamics of single moving attractor model. p–v, Dynamics of multiple discrete attractors model. w, Acrosstrial 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.
Extended Data Fig. 2 Wholecell recordings example cells.
Columns represent data from one cell. Top, mean spike rate; second row, mean membrane potential (V_{m}). Blue, correct lickright trials; red, correct lickleft trials; third row, spiketriggered median of V_{m}. Spikes in the presample epoch (black) and the delay epoch (blue) in correct lickright trials were analysed. Shading denotes s.e.m. (hierarchical bootstrap). P value denotes the probability of the null hypothesis that spiketriggered medians are the same between epochs (Methods, hierarchical bootstrap); fourth row, relationship between V_{m} and spike rate of the presample 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 V_{m}tospike rate curves are the same between the presample epoch and the delay epoch (hierarchical bootstrap, Methods). All statistical tests are twosided. 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.
Extended Data Fig. 3 Analysis of V_{m}.
a, Relationship between delay spike rate and V_{m} (delay epoch spike rate or V_{m} minus presample epoch spike rate or V_{m}). For each cell, correct lickright and correct lickleft 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 tstatistic of Pearson correlation coefficient (P) are shown. b, Selectivity of ALM neurons based on spike rate (top) and V_{m} (bottom). Duplicate of Fig. 2d. Shading denotes s.e.m. (bootstrap, n = 10 cells). c, Autocorrelation of V_{m} during the presample epoch (left) and the delay epoch in correct lickright 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 presample epoch and the delay epoch. Left, scatter plot of the time constant; right, histogram of the difference in timeconstant between the delay epoch compared to the presample epoch (change in time constant). P value determined by twosided Wilcoxon signedrank 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 lickright trials. White, all cells; black, selective cells. f, Spike raster (top) and spike rates (bottom) of correct lickright 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 lickright 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 presample epoch and the delay epoch. P value determined by twosided Wilcoxon signedrank test examining a null hypothesis that number of bursts per trial are the same between two epochs (n = 12 cells). Blue, correct lickright trials; red, correct lickleft trials. Spike bursts did not increase during the delay epoch. i–p, The same format as in a–h for the tactile task. All cells, n = 42; selective cells, n = 10.
Extended Data Fig. 4 Negative current injection.
a, Five example cells with negative current injection. Top, mean V_{m} without negative current injection; bottom, mean V_{m} with negative current injection. Blue, correct lickright trials; red, correct lickleft trials. b, Input resistance (R_{in}) of cells with and without current injection (n = 10 cells). Data are pooled from cells analysed in c. P value determined by twosided Wilcoxon signedrank 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 V_{m} (delay epoch V_{m} minus presample epoch V_{m}) with and without current injections (n = 10 cells). Delay amplitude during the current injection was normalized by the change in input resistance. Correct lickright trials (blue) and correct lickleft 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 tstatistic of Pearson’s correlation coefficient (P) are shown. d, Lickright delay selectivity (delay epoch V_{m} in lickright trial minus delay epoch V_{m} in lickleft 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 tstatistic of Pearson correlation’s coefficient (P) are shown. e, Loss of spike bursts after current injection. Top, V_{m} of two example cells with high occurrence of spike bursts. Overlay of all correct lickright trials. Black horizontal line, spike threshold. Regular spikes were removed and V_{m} 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, V_{m} of the same example cells with negative current injection. There was no spike to remove. V_{m} was averaged over 100 ms. Note the loss of sharp depolarizing events. n = 8, and 9 trials (cell 96 and 101, respectively).
Extended Data Fig. 5 Funnelling of V_{m}.
a, Four example ALM neurons. Top, mean V_{m}; middle, all correct lickright trials overlaid; bottom, all correct lickleft trials overlaid. To remove fast within trial fluctuations, V_{m} 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 onesided Wilcoxon signedrank test (the same applies to c–e). The first P value, all cells; second P value, selective cells only. c, As in b for the correct lickleft 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, Acrosstrial fluctuations of all cells (n = 37) (left), and selective cells (n = 10) (right) in the auditory task (as in Fig. 4b). Line, mean of acrosstrial fluctuations; shading denotes s.e.m. (hierarchical bootstrap). Blue, correct lickright trials; red, correct lickleft trials. g, Testing for a decrease in acrosstrial fluctuations. P values reflect a null hypothesis that acrosstrial fluctuations during the delay epoch were higher than that during the presample epoch (hierarchical bootstrap, n = 1,000 iteration). Acrosstrial fluctuations were measured as the quartile difference (left) or trimmed s.d. (right) of V_{m} across the same trial type (blue, correct lickright trials; red, correct lickleft trials) (Methods). Both methods provided similar results. V_{m} was averaged over 100 ms (triangle) or 200 ms (square) to remove fast withintrial fluctuations. The result was robust to the averaging bin size. The dashed line, P = 0.025 (α = 0.05 for twosided test). A schematic of statistical test in g and i is shown in the box below i. Acrosstrial fluctuations during the presample epoch (0.6 s) was compared with the acrosstrial 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 V_{m} and the change in acrosstrial fluctuations (acrosstrial fluctuations during the delay epoch minus acrosstrial fluctuations during the presample epoch). V_{m} 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 tstatistic of Pearson’s correlation coefficient (P) are shown. Pooling both the tactile and auditory tasks, and excluding nonspiking cells (n = 73 cells). The slope of regression line is opposite from what is expected for the ceiling effect.
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 b–l). c, Projection of individual trials to the CD in two example sessions (seven randomly selected trials per trial type; blue, correct lickright trials; red, correct lickleft 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, nonselective 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 lickright trials; red, correct lickleft 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 noresponse 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 noresponse 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 lickright (blue) and lickleft (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 (twosided Wilcoxon signedrank test). ^{∗}P < 0.05. m–x, The same format as in b–l for the random delay task. n = 13 sessions. In x, P = 0.79, 0.027, 0.00024 and 0.64 from left to right (twosided Wilcoxon signedrank test). ^{∗}P < 0.05; ^{∗∗}P < 0.01.
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, 1mm interval). These photostimuli are expected to uniformly silence excitatory neurons in ALM^{6}. 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, timeaveraged 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 nonbehaving mice (relevant to e–j). e, Spike rates of fastspiking neurons (top) and regularspiking 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 regularspiking 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, twosided Wilcoxon signedrank 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 regularspiking 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, twosided Wilcoxon signedrank 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 regularspiking neurons during the photoinhibition. Photoinhibition affected neurons across layers. i, Spike rate of regularspiking 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 regularspiking neurons during the photoinhibition at different locations. Photoinhibition affected neurons 1 mm away from the laser, consistent with a previous report^{6}. ^{∗∗}P < 0.01, twosided Wilcoxon signedrank 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.
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, twosided). 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 lickright preferring neurons with different θ. Lines, grand mean of peristimulus time histogram; shading denotes s.e.m. (bootstrap). Blue, correct lickright trials; red, correct lickleft trials; dark blue, incorrect lickright trials; dark red, incorrect lickleft trials. Mean peristimulus time histogram of unperturbed correct trials (first row) are also shown as dashed lines in the second to fourth row. f–j, As in a–e 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, twosided). n = 867 cells for f–h, and 487 cells for i. k, Example single units (random delay task). Top, spike raster. Seven and twentyfive 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 lickright trials; red, correct lickleft trials; dark blue, incorrect lickright trials; dark red, incorrect lickleft trials. Cyan bar, photoinhibition. l, Cumulative distribution of increase in spike rate during the delay epoch. Data from four different tasks are compared (Methods).
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 architecture^{11}. 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 perturbation^{11}. The circuit architecture in each hemisphere is as in Extended Data Fig. 1. Slow ramping was caused by either external nonselective input (b–h; external ramping model; note ramping external nonselective input in a) or internal slow dynamics (i–o; internal ramping model; note shallower energy landscape in a). All panels show results from the left hemisphere. In b–o, 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, nonselective 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 twohemisphere 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 lickright selective excitatory neurons, lickleft selective excitatory neurons and inhibitory interneurons, respectively. Blue and red arrows, selective external input. Black arrows, nonselective 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 lickright trials; red, correct lickleft 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). i–o, As in b–h for internal slow dynamics model. p, Schematic of twohemisphere 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).
Extended Data Fig. 10 Performance in the random delay task.
a, Behavioural performance (left), early lick rate (middle) and noresponse rate (right) in the random delay task. Thin lines, individual sessions (n = 23); thick line, grand mean among sessions. b–d, The same format as in Fig. 5b–d for the random delay task. Trials with 2s delay duration are shown. Line denotes mean; shading denotes s.e.m. (bootstrap). n = 13 sessions. e, Schematics. Projection of trials to the nonselective ramping mode (RM). f, Projection of trials to nonselective ramping mode in the fixed delay task with 2s 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 2s delay duration are shown.
Supplementary information
Reporting Summary
Supplementary Table 1
A list of whole cells recorded. Related to Fig. 24 and Extended Data Figs. 25.
Supplementary Table 2
A list of fixed delay task (2s delay) sessions. Related to Fig. 5 and Extended Data Figs. 6 and 8.
Supplementary Table 3
A list of random delay task sessions. Related to Fig. 6 and Extended Data Figs. 6, 8, and 10.
Supplementary Table 4
Parameters used for models. Related to Extended Data Figs. 1 and 9.
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Further reading

The what, where and how of delay activity
Nature Reviews Neuroscience (2019)
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