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Interplay between persistent activity and activity-silent dynamics in the prefrontal cortex underlies serial biases in working memory


Persistent neuronal spiking has long been considered the mechanism underlying working memory, but recent proposals argue for alternative ‘activity-silent’ substrates. Using monkey and human electrophysiology data, we show here that attractor dynamics that control neural spiking during mnemonic periods interact with activity-silent mechanisms in the prefrontal cortex (PFC). This interaction allows memory reactivations, which enhance serial biases in spatial working memory. Stimulus information was not decodable between trials, but remained present in activity-silent traces inferred from spiking synchrony in the PFC. Just before the new stimulus, this latent trace was reignited into activity that recapitulated the previous stimulus representation. Importantly, the reactivation strength correlated with the strength of serial biases in both monkeys and humans, as predicted by a computational model that integrates activity-based and activity-silent mechanisms. Finally, single-pulse transcranial magnetic stimulation applied to the human PFC between successive trials enhanced serial biases, thus demonstrating the causal role of prefrontal reactivations in determining working-memory behavior.

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Fig. 1: Previous-trial stimulus code reactivates before the forthcoming stimulus.
Fig. 2: In human EEG, the delay code also reactivates in the fixation period.
Fig. 3: Cross-correlation selectivity to previous-trial stimulus suggests an activity-silent trace in the PFC.
Fig. 4: Bump-attractor model with STP accounts for serial dependence and neurophysiology.
Fig. 5: Bump reactivation from a hidden trace increases serial biases.
Fig. 6: Single-pulse TMS on the dlPFC during fixation modulates serial biases nonlinearly.

Data availability

All data that support the findings of this study are available at

Code availability

The custom code used in this study is publicly available at


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This work was funded by the Spanish Ministry of Science and Innovation and the European Regional Development Fund (references BFU2015-65315-R and RTI2018-094190-B-I00); by the Institute Carlos III, Spain (grant PIE 16/00014); by the Cellex Foundation; by the “La Caixa” Banking Foundation (reference LCF/PR/HR17/52150001); by the Safra Foundation; by the Generalitat de Catalunya (AGAUR 2014SGR1265 and 2017SGR01565); and by the CERCA Programme/Generalitat de Catalunya. C.C. was supported by NIH grant R01 EY017077. J.B. was supported by the Spanish Ministry of Economy and Competitiveness (FPI program, reference BES-2013-062654) and by the Bial Foundation (reference 356/18). H.S. was supported by the “La Caixa” Banking Foundation (reference LCF/BQ/IN17/11620008) and the European Union’s Horizon 2020 Marie Skłodowska–Curie grant (reference 713673). K.C.S.A. was supported by NIH grant T32-MH020002. We thank the Barcelona Supercomputing Center (BSC) for providing computing resources, and the Neurology Department of the Hospital Clínic de Barcelona for granting access to EEG, TMS and neuronavigation equipment. This work was developed at the building Centro Esther Koplowitz, Barcelona. We thank A. Morató and D. Lozano-Soldevilla for assistance with EEG analyses, L. C. García del Molino for valuable insights during the development of early versions of the model, and A. Renart and J. de la Rocha for their comments on the manuscript.

Author information




J.B. and A.C. performed the monkey data analyses. J.B. and A.C. developed the model. H.S. and A.C. designed the human EEG research. H.S. and A.G.-G. performed the human EEG experiments. H.S., J.B. and A.C. performed the human data analyses. A.C. and J.D. obtained the funding used for the human EEG research. K.C.S.A. performed the preliminary human EEG data analyses. J.B., R.L.M., J.V.-S. and A.C. designed the TMS experiments. R.L.M. performed the TMS experiments and performed the data analyses. S.L. performed the monkey experiments. C.C. designed the monkey research. J.B., H.S. and A.C. discussed the results and wrote the manuscript. All authors revised the manuscript and gave critical comments.

Corresponding author

Correspondence to Albert Compte.

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Competing interests

J.D. receives royalties from Athena Diagnostics for the use of Ma2 as an autoantibody test and from Euroimmun for the use of NMDA as an antibody test. He received a licensing fee from Euroimmun for the use of GABAB receptor, GABAA receptor, DPPX and IgLON5 as autoantibody tests; he has received a research grant from Sage Therapeutics.

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Peer review information Nature Neuroscience thanks Bradley Postle and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Consistent decoding accuracy in delay and reactivation links these two representations at the neural ensemble level.

a, The size of n=94 independent ensembles of simultaneously recorded neurons varies between 1-6. b, Fraction of neural ensembles with significant previous stimulus decoding accuracy (z > 1.96, see Methods) computed for all ensembles (dashed line) and only for those ensembles with strongest previous stimulus code averaged across the whole delay (see Methods). The incidence of stimulus decoding was significant in delay and reactivation, but not at ITI (two-sided binomial test at p=0.05, with n=94 and n=27 ensembles, for ‘all ensembles’ and ‘highest delay code’, respectively). Error bars are bootstrapped ±s.e.m. c, across-ensemble Pearson correlation between delay decoding accuracy (averaged in the entire delay) and decoding accuracy at different time points (two-sided p-values: 6.5e-30, 0.87, 0.035, n=94 ensembles). The ensembles with strongest delay code also had stronger decoding during reactivation, demonstrating the neural association between delay representations and reactivations despite absent code in the ITI. Error bars denote ±s.e.m. computed with a bootstrap procedure. d, Individual ensemble values from c, orange (Pearson correlation, two-sided p=0.035, n=94 ensembles).

Extended Data Fig. 2 Noise correlation between pairs of neurons is negative at reactivation, as predicted by the attractor model.

Bump-attractor dynamics are characterized by negative pairwise noise correlations for cues presented between the preferred locations (within pref) of the two neurons, but not for other cues (outside pref) 6. a, Periods used in noise correlation analyses: early (activity-silent), and late fixation (reactivation; n=94 ensembles, zoom-in of Fig. 1c). Error shading, bootstrapped 95% C.I. b, In the computational model (n=1,000 independent simulations), bump reactivations from subthreshold traces are characterized by negative noise correlations only during reactivation for within-pref trials, following the nonspecific input drive (Fig. 4). c, Noise correlations of PFC pairs with dissimilar preferred angles (60° < Δθ < 120°, n=34 pairs) were lower in late than in early fixation for within-pref trials (bootstrap test, p=0.0001, n=34, Cohen’s d=0.61). d, On average, lower noise correlations occurred only during reactivation and in within-pref trials (ANOVA trial condition x time point, F(4)=2.5, p=0.06, n=34). For within-pref trials, noise correlations differed between early and late fixation (bootstrap test, p=0.0001, Cohen’s d=0.61, n=34), being negative in late (bootstrap test, p=0.035, Cohen’s d=-0.32, n=34), but positive in early fixation (bootstrap test, p=0.018, Cohen’s d=0.37, n=34). Correlations were positive in outside-pref trials both during late and early fixation (bootstrap test, p=0.024 and p=0.06, respectively), with no significant difference (two-sided bootstrap test, p=0.93, n=34). In addition, negative noise correlations diminished when using the previous saccade location rather than the previous stimulus as reference (paired bootstrap test, p=0.005, Cohen’s d=-0.47, n=34), suggesting that the bump diffused only during the delay period, but not after the saccade 6. Unless stated otherwise, all bootstrap tests were one-tailed in the direction of the model predictions in b. All error bars indicate ±s.e.m.

Extended Data Fig. 3 Stimulus selectivity in both cross-correlation peaks and firing rates during the delay period prevents the isolation of activity-based and activity-silent processes.

Same analysis as in Fig. 3, but performed during the current delay period (instead of ITI, Fig. 3) and selecting pref and anti-pref trials based on current stimulus (instead of previous, Fig. 3). Note that these are different trials (no need to be consecutive), so exc (n=33 pairs) and inh (n=21 pairs) might differ from Fig. 3. a, Left, cross-correlation peak selectivity emerged and was sustained in the delay period (left, CCSI as in Fig. 3, computed in centered 500-ms windows sliding in steps of 50 ms) and consisted in enhanced central peaks (troughs) for exc (inh) following a preferred stimulus. Color bars mark the periods where the average CCSI is different from 0 (bootstraped 95% C.I.) Right, cross-correlation averaged over 0.5-3.5 s. Zero-lag correlation for pref and anti-pref are different in exc (p=0.03, n=33, two-sided paired bootstrap test) and inh (p=0.01, n=21, two-sided bootstrap test) conditions. b, Firing rate selectivity (pref - anti-pref) also emerges robustly in the delay period for neurons in exc and inh pairs. The selectivity in cross-correlation peaks (CCSI) can therefore be confounded with firing rate selectivity71 when analyzing data in the delay period. This prevents the unambiguous identification of activity-silent mechanisms in this task period. Our approach of analyzing data in the inter-trial interval, when there is no firing rate selectivity (Fig. 3f), gets around this problem. Gray shading marks the stimulus presentation. In all panels, error-bar shadings indicate ±s.e.m.

Extended Data Fig. 4 In a dataset with unpredictable stimulus-onset time, previous item representations were not reactivated in the pre-stimulus period.

We conducted the same analysis as in human EEG (Fig. 2) in a previously published dataset (n=15 independent subjects for all panels; for experimental details, please refer to the original publication, ref. 33) with unpredictable fixation period durations (range 0.7 s-1.3 s). Decoding analyses were applied separately for data aligned to the onset of fixation (Fn, graded shading indicates range of possible stimulus onset times, upper panels) and aligned to the onset of the stimulus (Sn, graded shading indicates possible fixation onset times, lower panels). a, Tuning to previous-trial location (decoder trained in delay, 0.5s - 1.0s after stimulus onset) during previous-trial delay (left, stimulus aligned) vanishes in current-trial fixation (right, fixation onset aligned). No reactivation occurs. b, Average tuning reconstruction at different epochs for the delay decoder, indicated in a. c, Serial dependence separating trials with high (red curve, top quartile) from all other trials’ (black curve) decoding accuracy in early fixation (orange in a). Unlike in an experiment with predictable stimulus onset (Fig. 5), serial bias did not differ as a function of decoding strength. d, Difference in serial biases (Methods) between high-decoding and other trials were not significant at any time point in fixation. The black triangle marks the center of 0.2 s decoding window for the split in c. e-h, Parallel results were obtained when the analyses of panels a-d were run on data aligned to the time of stimulus onset instead of fixation onset. In d and h, time courses were smoothed using a squared filter of 5 samples. Periods with significant decoding in a,e are marked with black horizontal bars, indicating p<.001 in a two-sided bootstrap test. Shading indicates 95% C.I. in a,d,e,h, and ±s.e.m. in b,c,f,g.

Extended Data Fig. 5 Structured inhibition is necessary for repulsive serial biases at far distances.

Top panel, illustration of two different models that have different inhibitory connectivity profiles. On the left, inhibitory connectivity strength from inhibitory to excitatory neurons is similar for all distances between their preferred locations. On the right, inhibition is structured such that similarly tuned neurons have stronger feedback inhibition. This shows that repulsive biases are caused by repulsive interactions between simultaneously active bumps in the network39,40, and are absent when there is no reignited bump that recruits localized inhibition at the flanks of the pre-cue bump of activity.

Extended Data Fig. 6 Serial bias split between high-decoding and other trials (Fig. 5) is robust to the choice of different percentiles.

a, In monkey behavior b, In human behavior. X-axis indicates quantiles used for the split in high- and low-decoding trials (Fig. 5), from a total of n=1362 trials in a, and a range of 792-908 trials per subject in b. Error bars are ±s.e.m. (over n=1362 trials in a, and over n=15 subjects in b) and colored bars mark where corresponding difference in serial biases is different than zero (p<0.05, two-sided bootstrap test).

Extended Data Fig. 7 The effect on serial biases of targeting dlPFC with TMS diminishes in the course of the experimental session.

Serial bias plots averaged across n=20 independent subjects for trials with TMS applied in vertex (a) and PFC (b), and difference between serial biases computed for sham and weak-tms trials in vertex (black) and in PFC (red) blocks (c). Same analyses as in Fig. 6, but (top) analyzing trials from the full session, (middle) first half session (225 trials, replication of Fig. 6) and (bottom) last half session (225 trials). The behavioral impact of PFC TMS stimulation declined through the session, as if subjects desensitized (prev-curr × TMS intensity × session-half t11083 = –2.38, p = 0.017. Methods, Linear Mixed Models). Serial biases were modulated by TMS in PFC, but not in Vertex (prev-curr × TMS intensity × coil location, t18272 = 2.21, p = 0.027. For dlPFC: prev-curr × TMS intensity, t11087 = 2.13, p = 0.032. For Vertex: t7166 = 0.03, p = 0.97. Methods, Linear mixed models) when analyzing the full session, and analyzing only the first half session (t9133 = 2.51, p = 0.011). x-axis coordinates mark the central value of windows (π/2 radians, sliding by π/30 radians) used to calculate behavioral biases.

Extended Data Fig. 8 Consistent fixation-period single-pulse TMS effects on serial biases: first experiment.

Serial bias plots averaged across n=20 independent subjects for trials with TMS applied in vertex (a) and PFC (b), and difference between serial biases computed for sham and weak-tms trials in vertex (black) and in PFC (red) blocks (c). Same as Extended Data Fig. 6, but only analyzing data from the original study (n=10 subjects). Similarly to when pooling both the original and replication studies together, the behavioral impact of PFC TMS stimulation declined throughout the session, however not significantly (prev-curr × TMS intensity × session-half t5701 = –1.73, p = 0.08. Methods, Linear Mixed Models). Serial biases were modulated by TMS in PFC, but not in Vertex (t5705 = 1.92, p = 0.05) when analyzing the full session, and analyzing only the first half session (t3059 = 2.59, p = 0.009, Methods). x-axis coordinates mark the central value of windows (π/2 radians, sliding by π/30 radians) used to calculate behavioral biases.

Extended Data Fig. 9 Consistent fixation-period single-pulse TMS effects on serial biases: replication experiment.

Serial bias plots averaged across n=20 independent subjects for trials with TMS applied in vertex (a) and PFC (b), and difference between serial biases computed for sham and weak-tms trials in vertex (black) and in PFC (red) blocks (c). Same as Extended Data Fig. 6 and 7, but only analyzing data from the pre-registered ( replication study (n=10 subjects). Similarly to the original experiment, the behavioral impact of PFC TMS stimulation declined throughout the session, however not significantly (prev-curr × TMS intensity × session-half t5375 = –1.63, p = 0.1. Methods, Linear Mixed Models). Similarly to the original study, serial biases were more strongly modulated by TMS in PFC than in Vertex, however not significantly (t5379 = 1.12, p = 0.25) when analyzing the full session and the effect was stronger when analyzing only the first half-session (t2675 = 1.91, p = 0.06, Methods). x-axis coordinates mark the central value of windows (π/2 radians, sliding by π/30 radians) used to calculate behavioral biases.

Extended Data Fig. 10 A phenomenological model of our hypothesis on how long-term physiological effects of single TMS pulses affect serial bias curves in event-related experimental sessions.

Our TMS results show a difference between the effects of sham stimulation at the vertex and sham stimulation over dlPFC (Fig. 6). We interpret this baseline difference as the possible effect of long-term physiological alterations by single pulses 58 (but see ref. 72) that carry over from “strong-tms” trials to “no-tms” trials. We explicitly implemented this interpretation in the following way: we generated trial-by-trial responses biased depending on the sequence of stimuli according to a given baseline serial bias curve (a, “Vertex” condition where TMS is ineffective). In the “PFC” condition the serial bias strength changed depending on TMS conditions: in “weak-tms” trials the pulse had the acute effect of increasing the bias strength momentarily by an additive factor (3 times the baseline bias strength), in “strong-tms” trials the effect of the pulse was chronic: the bias changed with a negative additive component (equal in magnitude to the baseline strength), which decayed slowly through subsequent trials (10% decay/trial). When collapsing together “responses” obtained on the basis of this model through a sequence of randomly selected “no-tms”, “weak-tms” and “strong-tms” trials, serial bias curves showed the pattern observed experimentally, where sham (“no-tms”) trials show repulsion in the “PFC” condition (panel b) and not in the “Vertex” condition (panel a). The difference of serial bias curves for “weak-tms” and “no-tms” then showed the modulation clearly in “PFC” and not in “Vertex” (panel c), as seen in the data (Fig. 6).

Supplementary information

Supplementary Information

Supplementary Figs. 1 and 2.

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Supplementary Data

Mask used to locate right PFC for TMS stimulation. The mask was obtained from a NeuroSynth58 term-based meta-analysis of 53 fMRI studies associated with the key phrase “spatial working memory”.

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Barbosa, J., Stein, H., Martinez, R.L. et al. Interplay between persistent activity and activity-silent dynamics in the prefrontal cortex underlies serial biases in working memory. Nat Neurosci 23, 1016–1024 (2020).

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