Posterior parietal cortex represents sensory history and mediates its effects on behaviour


Many models of cognition and of neural computations posit the use and estimation of prior stimulus statistics1,2,3,4: it has long been known that working memory and perception are strongly impacted by previous sensory experience, even when that sensory history is not relevant to the current task at hand. Nevertheless, the neural mechanisms and regions of the brain that are necessary for computing and using such prior experience are unknown. Here we report that the posterior parietal cortex (PPC) is a critical locus for the representation and use of prior stimulus information. We trained rats in an auditory parametric working memory task, and found that they displayed substantial and readily quantifiable behavioural effects of sensory-stimulus history, similar to those observed in humans5,6 and monkeys7. Earlier proposals that the PPC supports working memory8,9 predict that optogenetic silencing of this region would impair behaviour in our working memory task. Contrary to this prediction, we found that silencing the PPC significantly improved performance. Quantitative analyses of behaviour revealed that this improvement was due to the selective reduction of the effects of prior sensory stimuli. Electrophysiological recordings showed that PPC neurons carried far more information about the sensory stimuli of previous trials than about the stimuli of the current trial. Furthermore, for a given rat, the more information about previous trial sensory history in the neural firing rates of the PPC, the greater the behavioural effect of sensory history, suggesting a tight link between behaviour and PPC representations of stimulus history. Our results indicate that the PPC is a central component in the processing of sensory-stimulus history, and could enable further neurobiological investigation of long-standing questions regarding how perception and working memory are affected by prior sensory information.

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Figure 1: Rat performance and contraction bias.
Figure 2: Sensory history biases behaviour.
Figure 3: The PPC is specifically necessary for the behavioural effect of previous sensory stimuli.
Figure 4: PPC neurons carry more information about previous-trial sensory stimuli than about current trial stimuli, which predicts behavioural bias.


  1. 1

    Steyvers, M., Griffiths, T. L. & Dennis, S. Probabilistic inference in human semantic memory. Trends Cogn. Sci. 10, 327–334 (2006)

    Article  Google Scholar 

  2. 2

    Chater, N., Tenenbaum, J. B. & Yuille, A. Probabilistic models of cognition: conceptual foundations. Trends Cogn. Sci. 10, 287–291 (2006)

    Article  Google Scholar 

  3. 3

    Pouget, A., Beck, J. M., Ma, W. J. & Latham, P. E. Probabilistic brains: knowns and unknowns. Nat. Neurosci. 16, 1170–1178 (2013)

    CAS  Article  Google Scholar 

  4. 4

    Schapiro, A. & Turk-Browne, N. in Brain Mapping: An Encyclopaedic Reference Vol. 3, (ed. Toga, A. W.) 501–506 (Academic, 2015)

    Google Scholar 

  5. 5

    Ashourian, P. & Loewenstein, Y. Bayesian inference underlies the contraction bias in delayed comparison tasks. PLoS ONE 6, e19551 (2011)

    CAS  ADS  Article  Google Scholar 

  6. 6

    Fassihi, A., Akrami, A., Esmaeili, V. & Diamond, M. E. Tactile perception and working memory in rats and humans. Proc. Natl Acad. Sci. USA 111, 2331–2336 (2014)

    CAS  ADS  Article  Google Scholar 

  7. 7

    Romo, R. & Salinas, E. Flutter discrimination: neural codes, perception, memory and decision making. Nat. Rev. Neurosci. 4, 203–218 (2003)

    CAS  Article  Google Scholar 

  8. 8

    Harvey, C. D., Coen, P. & Tank, D. W. Choice-specific sequences in parietal cortex during a virtual-navigation decision task. Nature 484, 62–68 (2012)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Carandini, M. & Churchland, A. K. Probing perceptual decisions in rodents. Nat. Neurosci. 16, 824–831 (2013)

    CAS  Article  Google Scholar 

  10. 10

    Visscher, K. M., Kahana, M. J. & Sekuler, R. Trial-to-trial carryover in auditory short-term memory. J. Exp. Psychol. Learn. Mem. Cogn. 35, 46–56 (2009)

    Article  Google Scholar 

  11. 11

    Lockhead, G. R. & King, M. C. A memory model of sequential effects in scaling tasks. J. Exp. Psychol. Hum. Percept. Perform. 9, 461–473 (1983)

    CAS  Article  Google Scholar 

  12. 12

    Ernst, M. O. & Banks, M. S. Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415, 429–433 (2002)

    CAS  ADS  Article  Google Scholar 

  13. 13

    Körding, K. P. & Wolpert, D. M. Bayesian integration in sensorimotor learning. Nature 427, 244–247 (2004)

    ADS  Article  Google Scholar 

  14. 14

    Hollingworth, H. L. The central tendency of judgment. J. Philos. Psychol. Sci. Methods 7, 461–469 (1910)

    Google Scholar 

  15. 15

    Karim, M., Harris, J. A., Langdon, A. & Breakspear, M. The influence of prior experience and expected timing on vibrotactile discrimination. Front. Neurosci. 7, 255 (2013)

    Article  Google Scholar 

  16. 16

    Hernández, A., Salinas, E., García, R. & Romo, R. Discrimination in the sense of flutter: new psychophysical measurements in monkeys. J. Neurosci. 17, 6391–6400 (1997)

    Article  Google Scholar 

  17. 17

    Raviv, O., Ahissar, M. & Loewenstein, Y. How recent history affects perception: the normative approach and its heuristic approximation. PLoS Comput. Biol. 8, e1002731 (2012)

    CAS  ADS  Article  Google Scholar 

  18. 18

    Busse, L. et al. The detection of visual contrast in the behaving mouse. J. Neurosci. 31, 11351–11361 (2011)

    CAS  Article  Google Scholar 

  19. 19

    Abrahamyan, A., Silva, L. L., Dakin, S. C., Carandini, M. & Gardner, J. L. Adaptable history biases in human perceptual decisions. Proc. Natl Acad. Sci. USA 113, E3548–E3557 (2016)

    CAS  Article  Google Scholar 

  20. 20

    Hwang, E. J., Dahlen, J. E., Mukundan, M. & Komiyama, T. History-based action selection bias in posterior parietal cortex. Nat. Commun. 8, 1242 (2017)

    ADS  Article  Google Scholar 

  21. 21

    Olkkonen, M., McCarthy, P. F. & Allred, S. R. The central tendency bias in color perception: effects of internal and external noise. J. Vis. 14, 5 (2014)

    Article  Google Scholar 

  22. 22

    Fritsche, M., Mostert, P. & de Lange, F. P. Opposite effects of recent history on perception and decision. Curr. Biol. 27, 590–595 (2017)

    CAS  Article  Google Scholar 

  23. 23

    Lu, Z. L., Williamson, S. J. & Kaufman, L. Behavioral lifetime of human auditory sensory memory predicted by physiological measures. Science 258, 1668–1670 (1992)

    CAS  ADS  Article  Google Scholar 

  24. 24

    Sinclair, R. J. & Burton, H. Discrimination of vibrotactile frequencies in a delayed pair comparison task. Percept. Psychophys. 58, 680–692 (1996)

    CAS  Article  Google Scholar 

  25. 25

    Preuschhof, C., Schubert, T., Villringer, A. & Heekeren, H. R. Prior information biases stimulus representations during vibrotactile decision making. J. Cogn. Neurosci. 22, 875–887 (2010)

    Article  Google Scholar 

  26. 26

    Papadimitriou, C., Ferdoash, A. & Snyder, L. H. Ghosts in the machine: memory interference from the previous trial. J. Neurophysiol. 113, 567–577 (2015)

    Article  Google Scholar 

  27. 27

    Fischer, J. & Whitney, D. Serial dependence in visual perception. Nat. Neurosci. 17, 738–743 (2014)

    CAS  Article  Google Scholar 

  28. 28

    Pasternak, T. & Greenlee, M. W. Working memory in primate sensory systems. Nat. Rev. Neurosci. 6, 97–107 (2005)

    CAS  Article  Google Scholar 

  29. 29

    Erlich, J. C., Brunton, B. W., Duan, C. A., Hanks, T. D. & Brody, C. D. Distinct effects of prefrontal and parietal cortex inactivations on an accumulation of evidence task in the rat. eLife 4, e05457 (2015)

    Article  Google Scholar 

  30. 30

    Raposo, D., Kaufman, M. T. & Churchland, A. K. A category-free neural population supports evolving demands during decision-making. Nat. Neurosci. 17, 1784–1792 (2014)

    CAS  Article  Google Scholar 

  31. 31

    Paxinos, G. & Watson, C. The Rat Brain in Stereotaxic Coordinates 5th edn (Elsevier, 2004)

  32. 32

    Nogueira, R. et al. Lateral orbitofrontal cortex anticipates choices and integrates prior with current information. Nat. Commun. 8, 14823 (2017)

    CAS  ADS  Article  Google Scholar 

  33. 33

    Paninski, L., Shoham, S., Fellows, M. R., Hatsopoulos, N. G. & Donoghue, J. P. Superlinear population encoding of dynamic hand trajectory in primary motor cortex. J. Neurosci. 24, 8551–8561 (2004)

    CAS  Article  Google Scholar 

  34. 34

    Hanks, T. D. et al. Distinct relationships of parietal and prefrontal cortices to evidence accumulation. Nature 520, 220–223 (2015)

    CAS  ADS  Article  Google Scholar 

  35. 35

    Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    MathSciNet  Article  Google Scholar 

  36. 36

    Rieke, F., Warland, D. & Bialek, W. Coding efficiency and information rates in sensory neurons. Europhys. Lett. 22, 151–156 (1993)

    ADS  Article  Google Scholar 

  37. 37

    Treves, A. & Panzeri, S. The upward bias in measures of information derived from limited data samples. Neural Comput. 7, 399–407 (1995)

    Article  Google Scholar 

  38. 38

    Nemenman, I., Bialek, W. & de Ruyter van Steveninck, R. Entropy and information in neural spike trains: progress on the sampling problem. Phys. Rev. E 69, 056111 (2004)

    ADS  Article  Google Scholar 

  39. 39

    Ince, R. A. A., Mazzoni, A., Petersen, R. S. & Panzeri, S. Open source tools for the information theoretic analysis of neural data. Front. Neurosci. 4, 62–70 (2010)

    PubMed  PubMed Central  Google Scholar 

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We thank C. Duan, R. Low, A. Piet, L. Pinto, B. Scott and I. Witten for their comments on the manuscript. We thank K. Osorio and J. Teran for animal and laboratory support.

Author information




A.A. and C.D.B. conceived the project. A.A. carried out all experiments and analysed the data, with the optogenetic inactivations carried out with assistance from C.D.K. A.A. gathered human tactile data in M.E.D.’s laboratory. A.A. and C.D.B. wrote the manuscript, based on a first draft by A.A., with extensive comments from C.D.K. and M.E.D.

Corresponding authors

Correspondence to Athena Akrami or Carlos D. Brody.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks L. Busse and J. de la Rocha for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Full stimulus set, learning curves, mean performance and reward bias.

a, Each stimulus is composed of a series of SPL values sampled from a zero-mean normal distribution, and standard deviation of s. For each trial, SPL values are randomly drawn and therefore, owing to sampling statistics, the actual standard deviation value of the stimulus always differed slightly from its designated value. The coordinates of each small box represent the actual joint values of (sa, sb) for one sample training session. b, Individual grey lines show learning curves presented as the change in percentage correct over months of training, for n = 25 rats. An average rat (black line) reaches 70% of performance after 90 sessions. c, Learning curve presented as the ratio of the best fit weights for the second stimulus, sb, to the first stimulus, sa, using the model described in Fig. 2e (three-parameter, no-history version). d, Rat auditory working memory performance, data from 21 rat subjects (total of 468,165 trials) are grouped according to (sa, sb) pair but averaged across subjects and over different delay durations (2–8 s). e, Human auditory working memory performance. For humans, the interstimulus delay varied randomly from 2 s to 6 s. (11 subjects, 12,623 trials). f, Human tactile working memory performance; similar to e but for humans engaged in the tactile version of the task. In this task, the interstimulus delay varied randomly from 2 s to 8 s. Data from 14 human subjects (total of 4,694 trials) are pooled together. g, Reward history bias. Left, the y axis shows, for turn-left trials and as a function of k, the percentage of subjects that went left when the kth trial back was rewarded on the left, minus the percentage that went left when the kth trial back was rewarded on the right. Right, the complementary plot for turn-right trials: the percentage that went right when the kth trial back was rewarded on the right, minus the percentage that went right when the kth trial back was rewarded on the left. Data from n = 21 rats. Each point shows the mean value of the bias over subjects. Error bars show 95% confidence intervals. h, i, Similar to g for human auditory (h, n = 11 subjects) and tactile (i, n = 14 subjects) PWM tasks.

Extended Data Figure 2 Contraction bias grows as a function of the working memory delay interval of the current trial.

a, Slopes from linear fits to the percentage leftward bias (as in Fig. 2a), for rats that were each trained on delay intervals of 2, 4, and 6 s (n = 21). The plot on the left shows the behavioural bias (percentage that went left minus the average) as a function of working memory delay interval of the current trial. The plot on the right shows the behavioural bias as a function of working memory delay interval from one trial back. Each dot represents a rat; lines connect the different delay intervals for each rat. Left: from a one-sided paired t-test, 2 versus 4 s: P = 0.012, 2 versus 6 s: P < 0.001; 4 versus 6 s: P < 0.001 *P < 0.001, one-sided paired t-test. Right: 2 versus 4 s: P = 0.76, 2 versus 6 s: P = 0.37; 4 versus 6 s: P = 0.65. The behavioural bias increases with greater current working memory delay period, but no significant dependence on the working memory delay period of the previous trial is found26. b, Percentage correct averaged across all bias+ trials or all bias trials, relative to overall average performance, as a function of working memory delay interval on the current trial. Data are pooled from a dataset in which different rats were trained on different sets of delay intervals; data for each delay interval may therefore contain different rats than data for other delay intervals (n = 25 rats total). Error bars show s.d. As in a, behavioural effect grows as a function of the current working memory delay period. *P < 0.001, one-sided t-test. c, Schematics of stimuli used for three different psychometric curves: high sb, in which contraction bias would lead all the sa stimuli to be treated as lower than they actually were (indicated by the leftward arrows), producing a rightward shift of the psychometric curve; mid sb, in which contraction bias would lead all the sa stimuli to be treated as closer to sb than they actually were, producing a flattening of the psychometric curve; and low sb, in which contraction bias would lead all the sa stimuli to be treated as higher than they actually were, producing a leftward shift of the psychometric curve. d, Psychometric curves for low-sb trials, averaged across rats and separately for each individual rat, for trials with a 2-s working memory delay interval, and for trials with a 6-s working memory delay interval. Curves are fits to a four-parameter logistic function (see Methods). As the working memory delay interval grows, the leftward shift predicted by contraction bias shift is more pronounced. For each individual rat, n = 120 sessions of data were used. Error bars show the s.e.m. over sessions. e, as in d but for the mid-sb trials. As the working memory delay interval grows, the flattening predicted by contraction bias is more pronounced. f, as in d but for the high-sb trials. As the working memory delay interval grows, the rightward shift predicted by contraction bias is more pronounced.

Extended Data Figure 3 Sensory-history matrix, from one to five trials back.

a, Stimulus-history matrix, as described in Fig. 2a, when percentage left is shown given any combination of the stimuli in the current trial (x axis) and n-trials back (y axis), n = 1, 2, 3, 4, 5. Trial numbers indicate pairs of (sa, sb), values in dB. 1: (68, 60); 2: (76, 68); 3: (84, 76); 4: (92, 84); 5: (60, 68); 6: (68, 76); 7: (76, 84); 8: (92, 84). Data from n = 21 rats, comprising a total of 468,165 trials used in this analysis. b, Similar to a, for the human auditory task. Trial numbers, with values in dB: 1: (62.7, 60); 2: (65.4, 62.7); 3: (68.1, 65.4); 4: (70.8, 68.1); 5: (73.5, 70.8); 6: (60, 62.7); 7: (62.7, 65.4); 8: (65.4, 68.1); 9: (68.1, 70.8); 10: (70.8, 73.5). c, Similar to a, for the human tactile task. Trial numbers, in mm s−1: 1: (33, 23); 2: (46, 33); 3: (64, 46); 4: (90, 64); 5: (125, 90); 6: (175, 125); 7: (245, 175); 8: (23, 33); 9: (33, 46); 10: (46, 64); 11: (64, 90); 12: (90, 125); 13: (125, 175); 14: (245, 175).

Extended Data Figure 4 Sensory-history matrix, controlled for reward and choice.

Similar to Extended Data Fig. 2, except that in this plot only trials for which the previous trial resulted in the same action and reward status are included. Therefore, modulation by previous trial cannot be due to action history or reward history. Trial numbers are similar to those in Extended Data Fig. 3.

Extended Data Figure 5 Short-term and long-term sensory history, and estimating the optimal window of 〈s〉.

a, Slopes from linear fits to the percentage leftward bias from n-back trials (n = 1–7, as in Fig. 2a where n = 1 was used), and also 〈s〉 which is a window of 17 trials, from n = 4 to n = 20, in grey. Each point shows the mean of the slope values over n = 25 rats. Error bars show 95% confidence intervals. b, For each rat the optimal exponential window over the past trials was estimated such that it would maximize the cross-validation bit/trial measurement. Two models are compared here: green shows the distribution of τ values from a model that has five regressors to account for the sensory history—the first and second stimulus from the two trials back and a separate exponential window over the remaining past trials (Fig. 2d). The results shown in orange are from a model containing only one regressor: a single exponential window over all the past trials accounts for the sensory history. In the single-exponential model, the best-fit value of τ is very small, practically as if only past one or two trials back are inducing most of the effect. c, The five-parameter model of sensory history outperforms the single-exponential model. Two hundred iterations of fivefold cross validation were used to calculate the cross-validated bit/trial (see Methods). Accordingly, each bar shows the mean of n = 1,000 data points. Error bars denote s.d.

Extended Data Figure 6 Model comparison.

a, Model comparisons, 200 runs of fivefold cross validation were performed, on data from each rat, in order to find the best fit parameters and to compare different model fits using the cross-validated bit/trial quantity defined as the relative value of the log likelihood of each model, to the null log likelihood, normalized in log2. Removing one parameter by constraining the regression weights on the sa stimulus of the current trial plus the weights on previous sensory stimuli to add to 1 (constrained model, in red) improved performance on cross-validated data compared to the unconstrained model (in black). A total of 12 different variants of the model are compared. Regressors are described in the box. b, Mean value of cross-validated bit/trial for different variants of the model as in a, over n = 20 rats. Error bars show s.e.m. Unconstrained models are shown in black, constrained models are shown in red. c, Top, raster plots of versus (t = 1, 2, from model 9). Each dot represents a subject. Pearson correlation values (r), and corresponding two-sided P values are shown for each plot. Bottom, median value of and (t = 1, 2), across rats. Error bars show median absolute deviation. d, Similar to c, for human subjects (auditory and tactile tasks are pooled together). Similar to rat subjects, model 9 shows the best performance for human subjects as well (data not shown). e, To compare the sensory-history matrix from the real data to the ones predicted from the best model fits (Fig. 2f, g), Frobenious distance norm was used, defined as the square root of the sum of the absolute squares of the difference between elements of two matrices. Frobenious distance is a measure of similarity, and the smaller the value, the more similar the two matrices. Frobenious distance is calculated separately for individual rats and each bar shows its mean value over n = 20 rats. Error bars show s.e.m. Models are models A–F from Fig. 2e. f, Scatter plot of slopes from linear fits to percentage leftward bias (Fig. 2a) versus short-term sensory history (that is, sum of weights for , , and ) from model 9. This plot shows significant correlation between the two measurements (Pearson correlation, r = −0.66, two-sided P = 0.0084, n = 17 rats), suggesting that when our logistic fit coefficients are particularly large, the subjects also have a particularly large contraction bias. g, Examining the weights in regression model 9, which is determined to be the best model, shows that the weights for sensory-history terms are significantly larger than those for the correct-side history term (paired-sample t-test, P < 0.0001, n = 22 rats). Data from individual rats are used to fit the model and bars show the mean value of sensory-history weights (in blue), and correct-side history weight (in green), over fit values from n = 22 rats. Error bars show s.e.m. Moreover, the sensory history regressor term, that is, sum of sensory-history weights × regressors produces larger variance over trials (0.38) compared to the correct-side regressor (0.11), indicating a bigger impact on trial-by-trial behaviour.

Extended Data Figure 7 Physiological and histological confirmations.

a, Physiological confirmation of optogenetic inactivation effect in an anesthetized rat. Left, single trace of acute extracellular activity of an example cell in the PPC, expressing eNpHR3.0, is shown in response to light stimulation. Laser illumination period (8 s) is marked by the light green bar. Right, raster-plot for 32 trials, for variable durations of light stimulation. The green vertical dashed line indicates the start of the laser illumination. The laser was on for variable durations of 750, 1,500, 3,000, 6,000 or 8,000 ms. The laser turning off is indicated by the vertical red dashed line. Recordings continued for 2 s after the laser was turned off. b, Histological localization of electrodes targeting the PPC. The inset shows an example of electrode locations in a coronal slice at anteroposterior = 3.48 from the bregma. In all cases, the electrode and fibre placements in the PPC were within between 2.8 and 4 mm posterior the bregma and between 2 and 3.5 mm lateral to the midline. Atlas panel is taken from Paxinos and Watson, 2004 (ref. 31).

Extended Data Figure 8 Optogenetics: PPC inhibition reduces leftward bias owing to past sensory stimuli.

a, Sensory-history matrix and leftward biases due to past sensory stimuli, similar to Fig. 2a–c, but now for three types of trials: laser-off trials (two leftmost panels) that consist of trials with no PPC inactivation on either the current or the previous trial; laser-on trials (two middle panels) that consist of trials with PPC inactivation on the current trial; and laser-off-after-laser-on trials (two rightmost panels) that consist of trials immediately after the laser-on trials. This last set controls for number of trials, as it contains equal numbers of trials to the laser-on condition. Modulation along the vertical indicates a previous trial effect behavioural bias as a function of the stimuli of the previous trial, for trials for which rats went left, and were rewarded, therefore history of reward and choice is held fixed. Grey lines are different current trial (sa, sb) pairs, the black line is the average over pairs. b, Similar to a, for trials for which rats went right and were rewarded. c, Similar to a for all combinations of current and previous stimuli.

Extended Data Figure 9 Optogenetics: impact on contraction bias on the full stimulus set, individual data points and best fit parameters for non-sensory-history weights.

a, Stimulus set and performance during optogenetic inhibition sessions, averaged over 37 sessions from 3 rats (delay interval of 2 s). Trials are grouped based on laser-off (left) and laser-on (right) conditions. The boxes represent the set of (sa, sb) pairs used in a session, with the colour representing the percentage that went left and the numbers above each box indicating the percentage correct. The plot in the bottom shows the difference between laser-off and laser-on conditions, with positive values indicating improved performance in laser-on conditions and negative values indicating impaired performance. b, c, Similar to Fig. 3d–f, with all data points overlaid on the bar plots. For b, n = 37 for each bar plot (equal to the total number of inactivation sessions); for c, n = 600, from 200 iterations of threefold cross-validation data; *P < 0.01 from one sided t-test. d, Best-fit parameter values for all weights from the nine-parameter model (short-term sensory-history model, constrained version, Fig. 2d, e). Values are plotted as their mean once the average value from the laser-off condition is subtracted. Except for the sensory history, none of the other weights were significantly affected by optogenetic inactivation of the PPC. Error bars show s.d. (n = 600, 200 iterations of threefold cross-validation; *P < 0.01 from one sided t-test). e, Similar to d, for period-selective optogenetic inhibitions, in which the PPC is selectively inhibited during the first stimulus sa (left), delay interval (middle) or second stimulus sb (right).

Extended Data Figure 10 Mutual information.

a, Sensory-history coding, one trial back, population analysis, each row represents the time course of significant values of mutual information between the firing rate of a cell and the stimulus pair (sa, sb) presented on the previous trial. Data from all trials with variable delay duration (minimum of 2 s) were pooled and plots are aligned to the beginning of sa. Data from n = 5 rats, and only cells with significant values of mutual information values are included. When estimating the mutual information, spurious information values can be attributed to the inherent correlations between task parameters, such as sensory stimuli and choice. To overcome this, conditional mutual information was calculated only when trials with same previous choice and reward status were considered, and sensory inputs were the only variable. Left, on the previous trial rats went right and were rewarded. Right, on the previous trial rats went left and were rewarded. b, Sensory-history coding, one trial back, percentage of cells with significant coding of stimuli presented on the previous trial (trial i − 1), aligned to the start of trial i. Only trials with a delay interval larger than 4 s are included in this analysis. c, Sensory-history coding, two trials back, percentage of cells with significant coding of stimuli presented two trials in the past (trial i − 2), aligned to the start of trial i. Shaded horizontal areas show the mean ± s.d. of the percentage of neurons with significant mutual information (MI), calculated from random sets built by shuffling the firing rates of neurons and conditions. d, Percentage of cells with significant coding of a rat’s choice and reward status, on both the current trial (solid lines) and previous trial (dashed lines), when time is aligned to the current trial, either sa (left), or sb (right). Shaded horizontal areas show the mean ± s.d. of the percentage of neurons with significant mutual information, calculated from random sets built by shuffling the firing rates of neurons and conditions. e, In the standard stimulus set (Fig. 1b, (sa, sb) pairs along the diagonal lines), knowledge of the rat’s choice of side, whether it was rewarded or not, and one of either sa or sb enables unique identification of the other stimulus (sb or sa). Therefore, in order to probe whether neurons carried information for different values of sa itself (as opposed to a combination of choice, reward and sb), we ran recording sessions with psychometric stimuli added to the standard stimulus set (top left). In this way, three different values of sa are assigned to one fixed value of sb and one fixed action (left in different shades of red, and right in different shades of blue). The firing rate of an example neuron is shown in response to different values of sa, only for trials in which the rat responded by going left (middle graph) or right (right graph) after the ‘go’ cue, was rewarded, and the delay interval was 4 s. Even though choice, reward and sb are fixed, firing rates clearly differentiate values of sa. The bottom graph shows a summary of population analysis from psychometric recording sessions (as in the examples in the graphs above), showing the percentage of cells with significant coding of sa from trial i (red) or trial i − 1 (blue, n = 142 cells). Shaded horizontal areas show the mean ± s.d. of the percentage of neurons with significant mutual information, calculated from random sets built by shuffling the firing rates of neurons and conditions.

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Akrami, A., Kopec, C., Diamond, M. et al. Posterior parietal cortex represents sensory history and mediates its effects on behaviour. Nature 554, 368–372 (2018).

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