Prefrontal persistent activity during the delay of spatial working memory tasks is thought to maintain spatial location in memory. A 'bump attractor' computational model can account for this physiology and its relationship to behavior. However, direct experimental evidence linking parameters of prefrontal firing to the memory report in individual trials is lacking, and, to date, no demonstration exists that bump attractor dynamics underlies spatial working memory. We analyzed monkey data and found model-derived predictive relationships between the variability of prefrontal activity in the delay and the fine details of recalled spatial location, as evident in trial-to-trial imprecise oculomotor responses. Our results support a diffusing bump representation for spatial working memory instantiated in persistent prefrontal activity. These findings reinforce persistent activity as a basis for spatial working memory, provide evidence for a continuous prefrontal representation of memorized space and offer experimental support for bump attractor dynamics mediating cognitive tasks in the cortex.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Gnadt, J.W. & Andersen, R.A. Memory related motor planning activity in posterior parietal cortex of macaque. Exp. Brain Res. 70, 216–220 (1988).
Funahashi, S., Bruce, C.J. & Goldman-Rakic, P.S. Mnemonic coding of visual space in the monkey's dorsolateral prefrontal cortex. J. Neurophysiol. 61, 331–349 (1989).
Constantinidis, C., Franowicz, M.N. & Goldman-Rakic, P.S. Coding specificity in cortical microcircuits: a multiple-electrode analysis of primate prefrontal cortex. J. Neurosci. 21, 3646–3655 (2001).
Wilson, H.R. & Cowan, J.D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973).
Amari, S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77–87 (1977).
Ben-Yishai, R., Bar-Or, R.L. & Sompolinsky, H. Theory of orientation tuning in visual cortex. Proc. Natl. Acad. Sci. USA 92, 3844–3848 (1995).
Pouget, A., Zhang, K., Deneve, S. & Latham, P.E. Statistically efficient estimation using population coding. Neural Comput. 10, 373–401 (1998).
Compte, A., Brunel, N., Goldman-Rakic, 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).
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).
Constantinidis, C. & Wang, X.-J. A neural circuit basis for spatial working memory. Neuroscientist 10, 553–565 (2004).
Miller, P. Analysis of spike statistics in neuronal systems with continuous attractors or multiple, discrete attractor states. Neural Comput. 18, 1268–1317 (2006).
Mongillo, G., Barak, O. & Tsodyks, M. Synaptic theory of working memory. Science 319, 1543–1546 (2008).
Goldman, M.S. Memory without feedback in a neural network. Neuron 61, 621–634 (2009).
Barak, O., Tsodyks, M. & Romo, R. Neuronal population coding of parametric working memory. J. Neurosci. 30, 9424–9430 (2010).
Jun, J.K. et al. Heterogenous population coding of a short-term memory and decision task. J. Neurosci. 30, 916–929 (2010).
Hussar, C.R. & Pasternak, T. Memory-guided sensory comparisons in the prefrontal cortex: contribution of putative pyramidal cells and interneurons. J. Neurosci. 32, 2747–2761 (2012).
White, J.M., Sparks, D.L. & Stanford, T.R. Saccades to remembered target locations: an analysis of systematic and variable errors. Vision Res. 34, 79–92 (1994).
Ploner, C.J., Gaymard, B., Rivaud, S., Agid, Y. & Pierrot-Deseilligny, C. Temporal limits of spatial working memory in humans. Eur. J. Neurosci. 10, 794–797 (1998).
Wang, X.J. Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24, 455–463 (2001).
Wu, S., Hamaguchi, K. & Amari, S. Dynamics and computation of continuous attractors. Neural Comput. 20, 994–1025 (2008).
Burak, Y. & Fiete, I.R. Fundamental limits on persistent activity in networks of noisy neurons. Proc. Natl. Acad. Sci. USA 109, 17645–17650 (2012).
Shafi, M. et al. Variability in neuronal activity in primate cortex during working memory tasks. Neuroscience 146, 1082–1108 (2007).
Constantinidis, C., Franowicz, M.N. & Goldman-Rakic, P.S. The sensory nature of mnemonic representation in the primate prefrontal cortex. Nat. Neurosci. 4, 311–316 (2001).
Shadlen, M.N. & Newsome, W.T. The variable discharge of cortical neurons: implications for connectivity, computation and information coding. J. Neurosci. 18, 3870–3896 (1998).
Churchland, A.K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818–831 (2011).
Goldman-Rakic, P.S. Cellular basis of working memory. Neuron 14, 477–485 (1995).
Durstewitz, D., Seamans, J.K. & Sejnowski, T.J. Neurocomputational models of working memory. Nat. Neurosci. 3, 1184–1191 (2000).
Brody, C.D., Hernández, A., Zainos, A. & Romo, R. Timing and neural encoding of somatosensory parametric working memory in macaque prefrontal cortex. Cereb. Cortex 13, 1196–1207 (2003).
Zaksas, D. & Pasternak, T. Directional signals in the prefrontal cortex and in area MT during a working memory for visual motion task. J. Neurosci. 26, 11726–11742 (2006).
Meyers, E.M., Freedman, D.J., Kreiman, G., Miller, E.K. & Poggio, T. Dynamic population coding of category information in inferior temporal and prefrontal cortex. J. Neurophysiol. 100, 1407–1419 (2008).
Compte, A. et al. Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J. Neurophysiol. 90, 3441–3454 (2003).
Renart, A., Song, P. & Wang, X.-J. Robust spatial working memory through homeostatic synaptic scaling in heterogeneous cortical networks. Neuron 38, 473–485 (2003).
Hansel, D. & Mato, G. Short-term plasticity explains irregular persistent activity in working memory tasks. J. Neurosci. 33, 133–149 (2013).
Barbieri, F. & Brunel, N. Irregular persistent activity induced by synaptic excitatory feedback. Front. Comput. Neurosci. 1, 5 (2007).
Britten, K.H., Newsome, W.T., Shadlen, M.N., Celebrini, S. & Movshon, J.A. A relationship between behavioral choice and the visual responses of neurons in macaque MT. Vis. Neurosci. 13, 87–100 (1996).
Jun, J.K. et al. Heterogeneous population coding of a short-term memory and decision task. J. Neurosci. 30, 916–929 (2010).
Machens, C.K., Romo, R. & Brody, C.D. Functional, but not anatomical, separation of 'what' and 'when' in prefrontal cortex. J. Neurosci. 30, 350–360 (2010).
Kilpatrick, Z.P., Ermentrout, B. & Doiron, B. Optimizing working memory with heterogeneity of recurrent cortical excitation. J. Neurosci. 33, 18999–19011 (2013).
Miller, E.K. The prefrontal cortex and cognitive control. Nat. Rev. Neurosci. 1, 59–65 (2000).
Meyer, T., Qi, X.-L. & Constantinidis, C. Persistent discharges in the prefrontal cortex of monkeys naive to working memory tasks. Cereb. Cortex 17, i70–i76 (2007).
Kohn, A. & Smith, M.A. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25, 3661–3673 (2005).
Bair, W., Zohary, E. & Newsome, W.T. Correlated firing in macaque visual area MT: time scales and relationship to behavior. J. Neurosci. 21, 1676–1697 (2001).
Cohen, M.R. & Newsome, W.T. Context-dependent changes in functional circuitry in visual area MT. Neuron 60, 162–173 (2008).
Ponce-Alvarez, A., Thiele, A., Albright, T.D., Stoner, G.R. & Deco, G. Stimulus-dependent variability and noise correlations in cortical MT neurons. Proc. Natl. Acad. Sci. USA 110, 13162–13167 (2013).
Mitchell, J.F., Sundberg, K.A. & Reynolds, J.H. Spatial attention decorrelates intrinsic activity fluctuations in macaque area V4. Neuron 63, 879–888 (2009).
Amit, D.J., Fusi, S. & Yakovlev, V. Paradigmatic working memory (attractor) cell in IT cortex. Neural Comput. 9, 1071–1092 (1997).
Leutgeb, J.K. et al. Progressive transformation of hippocampal neuronal representations in 'morphed' environments. Neuron 48, 345–358 (2005).
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).
Durstewitz, D., Vittoz, N.M., Floresco, S.B. & Seamans, J.K. Abrupt transitions between prefrontal neural ensemble states accompany behavioral transitions during rule learning. Neuron 66, 438–448 (2010).
Balaguer-Ballester, E., Lapish, C.C., Seamans, J.K. & Durstewitz, D. Attracting dynamics of frontal cortex ensembles during memory-guided decision-making. PLoS Comput. Biol. 7, e1002057 (2011).
Constantinidis, C., Williams, G.V. & Goldman-Rakic, P.S. A role for inhibition in shaping the temporal flow of information in prefrontal cortex. Nat. Neurosci. 5, 175–180 (2002).
Constantinidis, C. & Goldman-Rakic, P.S. Correlated discharges among putative pyramidal neurons and interneurons in the primate prefrontal cortex. J. Neurophysiol. 88, 3487–3497 (2002).
Jin, D.Z., Dragoi, V., Sur, M. & Seung, H.S. Tilt aftereffect and adaptation-induced changes in orientation tuning in visual cortex. J. Neurophysiol. 94, 4038–4050 (2005).
Compte, A. & Wang, X.-J. Tuning curve shift by attention modulation in cortical neurons: a computational study of its mechanisms. Cereb. Cortex 16, 761–778 (2006).
Berens, P. CircStat: a MATLAB toolbox for circular statistics. J. Stat. Softw. 31, 1–21 (2009).
We thank M. Goldman, J. de la Rocha and A. Roxin for fruitful discussions. We wish to acknowledge the late P. Goldman-Rakic, in whose laboratory experimental data were collected. This work was funded by the Ministry of Economy and Competitiveness of Spain, the European Regional Development Fund (Ref: BFU2009-09537) and by the National Science Foundation (NSF PHY11-25915 and DMS-0847749). K.W. acknowledges funding from the German Research Foundation (research fellowship Wi 3767/1-1). D.Q.N. was supported by the Generalitat de Catalunya (PIV-DGR 2010 program). C.C. received support from the Tab Williams Family Endowment. The work was carried out at the Esther Koplowitz Centre and partly at the Kavli Institute for Theoretical Physics, and at the Centre de Recerca Matemàtica.
The authors declare no competing financial interests.
Integrated supplementary information
Supplementary Figure 1 Schematic illustration of the first prediction from the bump attractor model regarding the relation between single-neuron delay tuning curves and the direction of small behavioral imprecisions.
(a) Scheme of 2 possible delay population activity profiles (red and blue lines) in response to the repeated presentation of a 90° cue. Repeated presentation of any given cue results in variable behavior, with saccades directed CW (red) and CCW (blue) from the correct cue location. Neural responses are marked for one single neuron in the network (circles, preferred cue 144°). (b) Same as a for a different cue, presented at 180°. Again two network responses for two different trials are plotted, which give rise to CW (red) and CCW (blue) behavioral imprecisions. Responses from the same neuron with preference at 144° are indicated by filled circles. (c) Tuning curves computed for the single neuron indicated in a and b, separately recorded from trials with CCW and CW behavior. The tuning curve is constructed by plotting the neuron's response to different stimuli locations (x-axis). Here panels a and b contribute two points to each tuning curve in panel c, the rest of the points are obtained by presenting all other possible cues to the network (not shown). Notice that CW tuning curves are displaced CCW relative to CCW tuning curves: the tuning bias defined as the distance from the CCW to the CW tuning curve centers is predicted to be positive.
Supplementary Figure 2 Comparison of delay tuning properties of the databases of tuned and non-tuned neurons.
(a) Mean tuning for tuned neurons (solid) is higher than for non-tuned neurons (dashed). Note that the alignment to preferred locations induces a spurious tuning by itself. (b) Histograms of tuning strength T for tuned (black) and non-tuned neurons (gray) differ significantly in their medians (triangles, 0.0832 vs. 0.1757, P < 1e–6, Wilcoxon test) but have a significant overlap. (c) Neurons with similar tuning strength T in the two databases (tuned, black and non-tuned, gray) have lower mean firing rate for non-tuned neurons, thus explaining non-significant tuning in cells with high tuning strength T in the non-tuned neuron database. Low, medium and high tuning was defined using tertiles obtained from the tuned neuron database and splitting the non-tuned database using the same intervals (n = 353, 111 and 59 non-tuned neurons for low, medium and high tuning, respectively).
Supplementary Figure 3 Late-delay Fano factor difference between accurate and inaccurate trials for flank cues increases for more extreme behavioral deviations.
As the fraction of trials used to build accurate and inaccurate response classes is reduced (i.e. the two classes differ more in their mean response accuracy) the difference between Fano Factors computed from neural responses at the end of the delay (last 500 ms) for flank cue stimuli in each of these classes of trials grows parametrically. Significance was assessed with a permutation test (P < 0.05).
Graphical representation of the ANOVA residuals corresponding to the analyses in Fig. 6a-d and Fig. 7e-h. Data deviated mildly from the normality assumption due to long tails (panels a, e) and some outlier points (panel e), and from the homoscedasticity assumption in panels b, d, g, h (Levene's test P < 0.05). Note that despite this significant heteroscedasticity, there is not more than a factor 3 between the various dispersions. Heteroscedasticity is the most worrisome aspect of the data, and it is particularly severe in the case of unequal sample sizes. In our case the sample size corresponding to the different monkeys (d) and the different neuronal pair tunings (h) were different. However, the cases with the smaller sample size had smaller variance and this condition is known to reduce the power of the test rather than inflate the false positive rate. Thus, for both ANOVA tests, non-normality and heteroscedasticity do not question the rejection of the hypotheses, since the corresponding corrections are unlikely to cancel the strong significance of the effects found (P = 0.0013 for the interaction cue × accuracy in Fig. 6 and panels a-d, and P < 0.001 for main effect of selectivity in Fig. 7 and panels e-h).
The models in Fig 8 were in qualitative agreement with experimental behavioral and neural data, but the quantitative match of neuronal firing rates was limited by the network implementation. To evaluate quantitative predictions that took into account the specific firing rates and heterogeneity present in the data (Fig. 1), we tested two coding models for inaccurate memory-guided behavioral responses: the bump attractor model and the decaying bump model. (a) In the bump attractor model, dispersion of behavioral responses is due to noise-induced diffusion of the location of a rigid bump representation. In different trials (red and blue) in response to the same cue the bump diffuses during the delay to different locations (lower panel), giving rise to different read-outs and inaccurate, off-target behavioral responses. (b) In the decaying bump model, the bump is established at cue presentation, but begins to decay once the cue is removed. During the delay, the coding slowly decays away, with different decay rates in different trials. The read-out is inaccurate at the end of the delay due to the decreased selectivity. (c-d) Generation of multiple firing rate trials (8 equidistant cues, 10 trials per cue) and surrogate Poisson spike trains for n = 200 neurons from the models in corresponding panels a and b above generates behavioral and neural data in quantitative agreement with the experimental data (Fig. 1). Behavioral responses from computational models (panel c, left, and panel d, right) are represented as in Fig. 1b. The memory dependence of these behavioral inaccuracies is revealed by comparing with the models' behavioral responses for a brief 0.5 s delay (black dashed curve). Average tuning curves of model neurons (panel c, right and panel d, left) in the delay period computed as in Fig. 1d.
Supplementary Figure 6 Model-derived surrogate data supports a bump attractor representation, not a decaying bump representation.
(a,b) Tuning curve bias analysis (Fig. 3c) performed on surrogate data from the diffusing and decaying bump models (Supplementary Fig. 5), respectively. For the bump attractor, but not the decaying bump model, the tuning curve bias computed from trials with CW versus CCW behaviors (Fig. 3) becomes increasingly positive through the delay. (c,d) Rate-behavior correlation analysis (Fig. 4c) applied to the surrogate data of Supplementary Fig. 5. Only for the bump attractor model spike counts in response to flank stimuli correlated with behavioral deviations in the direction of the neuron's preferred cue as delay progressed. (e,f) For surrogate data generated from the bump attractor model, but not the decaying bump model, Fano Factors computed separately for trials when a flank stimulus was presented are larger when considering inaccurate trials with large behavioral deviations (solid line) as compared to accurate trials (dashed line) (c.f., Fig. 6d). This is shown for average activity in the last 500 ms of delay period, when considering cues presented at different points of the neuronal tuning curve. (g,h) Only surrogate data derived from the bump attractor model mimics the experimental results (Fig. 7e,f) that neuron pair noise correlation is negative for those pairs with dissimilar tuning, when responding to a middle flank stimulus (In-flank condition). Solid lines correspond to labels “Peak,” “Flanks,” and “Tails” as in Fig. 7e. Dashed lines correspond to labels “In-flank,” “Peaks,” and “Out-flanks” as in Fig. 7f.
Supplementary Figures 1–6 (PDF 652 kb)
Matlab code to run the bump attractor network model of Fig. 8. The model is described in Online Methods generically, and this Matlab code specifies all the parameters necessary to run the simulation. (TXT 4 kb)
Matlab code to run the discrete attractor network model of Fig. 8. The model is described in Online Methods generically, and this Matlab code specifies all the parameters necessary to run the simulation. (TXT 4 kb)
Matlab code to run the decaying bump network model of Fig. 8. The model is described in Online Methods generically, and this Matlab code specifies all the parameters necessary to run the simulation. (TXT 4 kb)
Video demonstrating network activity and behavioral read-out in the course of one simulation of the bump attractor network model of Fig. 8.
The upper left panel shows the temporal progress along the task timeline (F=fixation, C=cue, D=delay, R=response) with a red time-stamp marker. The upper right panel shows in black the simulated visual scene: fixating cross and square visual cue, together with the instantaneous network readout during the delay in red. The lower panel shows the activity of excitatory neurons in the network. The 8 possible locations of cue stimuli are indicated on the lower panel with gray dots. When external stimuli are applied to the network, these are indicated with a thick black line on the location of corresponding neurons on the x-axis. This occurs in the cue period of the trial (C in upper panel), and is implemented as a depolarizing current to excitatory neurons around the cue location at θ= 0°), and in the response period (R in upper panel), where a hyperpolarizing current is injected to all excitatory neurons in the network. The location encoded instantaneously in the excitatory population activity is read out continuously with a population vector algorithm (Online Methods and Supplementary Code 1) and it is indicated with a black triangle in the lower panel and with a red radial line in the upper right panel. Parameters for this simulation are as detailed in Supplementary Code 1. (MOV 6610 kb)
Video demonstrating network activity and behavioral read-out in the course of one simulation of the discrete attractor network model of Fig. 8.
Same layout and symbols as for Supplementary Video 1. Parameters for this simulation are as detailed in Supplementary Code 2. (MOV 7248 kb)
Video demonstrating network activity and behavioral read-out in the course of one simulation of the decaying bump network model of Fig. 8.
Same layout and symbols as for Supplementary Video 1. Parameters for this simulation are as detailed in Supplementary Code 3. (MOV 7060 kb)
About this article
Cite this article
Wimmer, K., Nykamp, D., Constantinidis, C. et al. Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory. Nat Neurosci 17, 431–439 (2014). https://doi.org/10.1038/nn.3645
Strong inhibitory signaling underlies stable temporal dynamics and working memory in spiking neural networks
Nature Neuroscience (2021)
Nature Communications (2021)
Frontiers in Cellular Neuroscience (2021)
Interaction between neuronal encoding and population dynamics during categorization task switching in parietal cortex
Cerebral Cortex (2021)