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Nature Neuroscience | Article

Balanced cortical microcircuitry for maintaining information in working memory

Journal name:
Nature Neuroscience
Volume:
16,
Pages:
1306–1314
Year published:
DOI:
doi:10.1038/nn.3492
Received
Accepted
Published online

Abstract

Persistent neural activity in the absence of a stimulus has been identified as a neural correlate of working memory, but how such activity is maintained by neocortical circuits remains unknown. We used a computational approach to show that the inhibitory and excitatory microcircuitry of neocortical memory-storing regions is sufficient to implement a corrective feedback mechanism that enables persistent activity to be maintained stably for prolonged durations. When recurrent excitatory and inhibitory inputs to memory neurons were balanced in strength and offset in time, drifts in activity triggered a corrective signal that counteracted memory decay. Circuits containing this mechanism temporally integrated their inputs, generated the irregular neural firing observed during persistent activity and were robust against common perturbations that severely disrupted previous models of short-term memory storage. These results reveal a mechanism for the accumulation and storage of memories in neocortical circuits based on principles of corrective negative feedback that are widely used in engineering applications.

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  1. Memory networks with negative-derivative feedback.
    Figure 1: Memory networks with negative-derivative feedback.

    (a–c) Simple models of a neural population and their energy surfaces with positive feedback (a), derivative feedback (b), and hybrid positive and derivative feedback (c). Persistent activity can be maintained at different levels (horizontal axis of energy surface) either by a positive-feedback mechanism that effectively flattens the energy surface (a,c, bottom) or by a negative derivative–feedback mechanism that acts like a viscous drag force opposing changes in memory activity (b,c, bottom). The wall at the left of the energy surface represents the constraint that activity cannot be negative. (d) Illustration of how a negative derivative–feedback mechanism detects and corrects deviations from persistent activity. (e–g) Effective time constant of activity from equation (2) as a function of the strengths of positive feedback Wpos (e,g) and derivative feedback Wder (f,g). As Wder increases, the network time constant τeff becomes less sensitive to changes in Wpos (g).

  2. Negative derivative-feedback networks of excitatory and inhibitory populations.
    Figure 2: Negative derivative–feedback networks of excitatory and inhibitory populations.

    (a) Derivative-feedback network structure (top) and component feedback pathways onto the excitatory population (bottom). (b) In response to external input that steps the excitatory population between two fixed levels, the recurrent feedback pathways mediate a derivative-like signal resulting from recurrent excitation and inhibition that arrive with equal strength, but different timing. (c,d) Maintenance of graded persistent firing in response to transient inputs (c) and integration of step-like inputs into ramping outputs (d) with linear (top) and nonlinear (bottom) firing rate (f) versus input current (I) relationships.

  3. Negative-derivative feedback with mixture of NMDA and AMPA synapses in all excitatory pathways.
    Figure 3: Negative-derivative feedback with mixture of NMDA and AMPA synapses in all excitatory pathways.

    (a) Derivative feedback network structure. Blue, cyan and red curves represent NMDA-mediated, AMPA-mediated and GABA-mediated currents, respectively. qEE and qIE are the fractions of NMDA-mediated synaptic inputs in each excitatory pathway. (b) Time constant of decay of network activity, τnetwork, as a function of the average time constants of excitatory connections, aver(τEE) and aver(τIE). Each average time constant is varied either by varying the fractions or by varying the time constants of NMDA-mediated synaptic inputs in each connection. The region in the red rectangle corresponds to a set of possible aver(τEE) and aver(τIE) obtained when varying qEE and qIE and holding the synaptic time constants fixed at values matching the experimental observations in ref. 13. (c) Time constant of decay of network activity τnetwork as a function of the connectivity strengths Jij and the time constants of positive and negative feedback, τ+ and τ−. τnetwork increases linearly with the balanced amount of positive and negative-derivative feedback Jder ~ JEE ~ JIEJEI/JII, and with the difference between τ+ and τ−, as Wder ~ Jder (τ+ − τ−).

  4. Robustness to common perturbations in memory networks with derivative feedback.
    Figure 4: Robustness to common perturbations in memory networks with derivative feedback.

    (a–f) Non-robustness of persistent activity in positive-feedback models. (a) Positive-feedback models with recurrent excitatory (left) or disinhibitory (right) feedback loops. (b) Effective time constant of network activity, τnetwork, as a function of connectivity strength. Green asterisks correspond to 5% deviations from perfect tuning. (c–f) Time course of activity in perfectly tuned networks (black) and following small perturbations of intrinsic neuronal gains (c) or synaptic connection strengths (d–f). (g–k) Robust persistent firing in derivative-feedback models. To clearly distinguish the hybrid models with derivative and positive feedback, purely negative derivative–feedback models with no positive feedback are shown. All excitatory synapses are mediated by both NMDA and AMPA receptors as in Figure 3, with parameters chosen to coincide with experimental observations13. (h) τnetwork increases linearly with the strength of recurrent feedback J. (i–k) Robustness to 5% changes (green asterisks in h) in neuronal gains or synaptic connection strengths. (l) Disruption of persistent activity in derivative-feedback models following perturbations of NMDA-mediated synaptic currents. (m) Hybrid model with positive and derivative feedback. (n–q) As the strength of negative-derivative feedback is increased, τnetwork decreases less rapidly with mistuning than in purely positive-feedback models (n) and the network becomes robust against perturbations (o–q, shown for Jder/Jpos = 150). (r) Disruption of persistent activity in the hybrid model following perturbations of NMDA-mediated currents.

  5. Irregular firing in spiking networks with graded persistent activity.
    Figure 5: Irregular firing in spiking networks with graded persistent activity.

    (a) Experimentally measured irregular firing (coefficients of variation of inter-spike intervals, CVisi, higher than 1) during persistent activity in a delayed-saccade task. Adapted from ref. 16. (b) Structure of network of spiking neurons with negative-derivative feedback. (c–k) Network response to a brief (100 ms) stimulus applied at time 0. Raster plots illustrating irregular persistent firing are shown in c–e for 50 example excitatory neurons. Instantaneous, population-averaged activity of excitatory neurons, computed in 1-ms (gray) or 10-ms (black) time bins are shown in f–h. The balance between population-averaged excitation and inhibition following offset of external input can be seen in i–k. (l–n) Histogram of CVisi of active excitatory neurons during the persistent firing. Note that, for activity with strong input, a small subset of neurons fire regularly at high rate and exhibit low CVisi (n). This reflects that the heterogeneity resulting from our simple assumption of completely randomly connected networks can result in excess positive feedback in some clusters of neurons.

  6. Synaptic inputs in derivative-feedback and common positive-feedback models.
    Figure 6: Synaptic inputs in derivative-feedback and common positive-feedback models.

    (a–c) Network structures of positive-feedback models (a,b) and derivative-feedback models (c) with two competing populations. (d–f) Relation between firing rates of excitatory and inhibitory neurons. Firing rates of the E2 (black points) and inhibitory (red points) populations are plotted as a function of E1 firing rate. (g–i) Relation between excitation and inhibition for different levels of maintained firing. x and y axes are normalized by the amount of excitation and inhibition received when the left and right excitatory populations fire at equal levels of 30 Hz. (j–l) Persistent activity in the two competing excitatory populations (solid: E1; dashed, E2). Perturbing the networks by uniformly increasing the intrinsic gain in E1 leads to gross disruptions of persistent firing in positive-feedback models (green curves in j,k), but not negative derivative–feedback models (l). See Supplementary Figure 5 for robustness to other perturbations.

References

  1. Jonides, J. et al. The mind and brain of short-term memory. Annu. Rev. Psychol. 59, 193–224 (2008).
  2. Fuster, J.M. & Alexander, G.E. Neuron activity related to short-term memory. Science 173, 652–654 (1971).
  3. Major, G. & Tank, D. Persistent neural activity: prevalence and mechanisms. Curr. Opin. Neurobiol. 14, 675–684 (2004).
  4. Durstewitz, D., Seamans, J.K. & Sejnowski, T.J. Neurocomputational models of working memory. Nat. Neurosci. 3, 1184–1191 (2000).
  5. Wang, X.J. Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24, 455–463 (2001).
  6. 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).
  7. Seung, H.S. How the brain keeps the eyes still. Proc. Natl. Acad. Sci. USA 93, 13339–13344 (1996).
  8. Machens, C.K., Romo, R. & Brody, C.D. Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science 307, 1121–1124 (2005).
  9. Wang, X.J. Decision making in recurrent neuronal circuits. Neuron 60, 215–234 (2008).
  10. Haider, B. & McCormick, D.A. Rapid neocortical dynamics: cellular and network mechanisms. Neuron 62, 171–189 (2009).
  11. Wang, H., Stradtman, G.G., Wang, X.J. & Gao, W.J. A specialized NMDA receptor function in layer 5 recurrent microcircuitry of the adult rat prefrontal cortex. Proc. Natl. Acad. Sci. USA 105, 16791–16796 (2008).
  12. Wang, H.X. & Gao, W.J. Cell type–specific development of NMDA receptors in the interneurons of rat prefrontal cortex. Neuropsychopharmacology 34, 2028–2040 (2009).
  13. Rotaru, D.C., Yoshino, H., Lewis, D.A., Ermentrout, G.B. & Gonzalez-Burgos, G. Glutamate receptor subtypes mediating synaptic activation of prefrontal cortex neurons: relevance for schizophrenia. J. Neurosci. 31, 142–156 (2011).
  14. Wang, M. et al. NMDA receptors subserve persistent neuronal firing during working memory in dorsolateral prefrontal cortex. Neuron 77, 736–749 (2013).
  15. Softky, W.R. & Koch, C. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334–350 (1993).
  16. 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).
  17. Haider, B., Duque, A., Hasenstaub, A.R. & McCormick, D.A. Neocortical network activity in vivo is generated through a dynamic balance of excitation and inhibition. J. Neurosci. 26, 4535–4545 (2006).
  18. Shu, Y., Hasenstaub, A. & McCormick, D.A. Turning on and off recurrent balanced cortical activity. Nature 423, 288–293 (2003).
  19. Murphy, B.K. & Miller, K.D. Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61, 635–648 (2009).
  20. Lisman, J.E., Fellous, J.M. & Wang, X.J. A role for NMDA-receptor channels in working memory. Nat. Neurosci. 1, 273–275 (1998).
  21. Wang, X.J. Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory. J. Neurosci. 19, 9587–9603 (1999).
  22. Koulakov, A.A., Raghavachari, S., Kepecs, A. & Lisman, J.E. Model for a robust neural integrator. Nat. Neurosci. 5, 775–782 (2002).
  23. Goldman, M.S., Levine, J.H., Major, G., Tank, D.W. & Seung, H.S. Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron. Cereb. Cortex 13, 1185–1195 (2003).
  24. Nikitchenko, M. & Koulakov, A. Neural integrator: a sandpile model. Neural Comput. 20, 2379–2417 (2008).
  25. Shen, L. Neural integration by short term potentiation. Biol. Cybern. 61, 319–325 (1989).
  26. Wang, Y. et al. Heterogeneity in the pyramidal network of the medial prefrontal cortex. Nat. Neurosci. 9, 534–542 (2006).
  27. Mongillo, G., Barak, O. & Tsodyks, M. Synaptic theory of working memory. Science 319, 1543–1546 (2008).
  28. Barbieri, F. & Brunel, N. Can attractor network models account for the statistics of firing during persistent activity in prefrontal cortex? Front. Neurosci. 2, 114–122 (2008).
  29. Vogels, T.P., Rajan, K. & Abbott, L.F. Neural network dynamics. Annu. Rev. Neurosci. 28, 357–376 (2005).
  30. van Vreeswijk, C. & Sompolinsky, H. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724–1726 (1996).
  31. Knill, D.C. & Pouget, A. The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci. 27, 712–719 (2004).
  32. Boerlin, M. & Deneve, S. Spike-based population coding and working memory. PLoS Comput. Biol. 7, e1001080 (2011).
  33. Romo, R., Brody, C.D., Hernandez, A. & Lemus, L. Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399, 470–473 (1999).
  34. Roitman, J.D. & Shadlen, M.N. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci. 22, 9475–9489 (2002).
  35. Robinson, D.A. Integrating with neurons. Annu. Rev. Neurosci. 12, 33–45 (1989).
  36. 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).
  37. Shadlen, M.N., Britten, K.H., Newsome, W.T. & Movshon, J.A. A computational analysis of the relationship between neuronal and behavioral responses to visual motion. J. Neurosci. 16, 1486–1510 (1996).
  38. Shadlen, M.N. & Newsome, W.T. Noise, neural codes and cortical organization. Curr. Opin. Neurobiol. 4, 569–579 (1994).
  39. Destexhe, A., Rudolph, M. & Pare, D. The high-conductance state of neocortical neurons in vivo. Nat. Rev. Neurosci. 4, 739–751 (2003).
  40. Renart, A., Moreno-Bote, R., Wang, X.J. & Parga, N. Mean-driven and fluctuation-driven persistent activity in recurrent networks. Neural Comput. 19, 1–46 (2007).
  41. Roudi, Y. & Latham, P.E. A balanced memory network. PLoS Comput. Biol. 3, 1679–1700 (2007).
  42. Major, G., Polsky, A., Denk, W., Schiller, J. & Tank, D.W. Spatiotemporally graded NMDA spike/plateau potentials in basal dendrites of neocortical pyramidal neurons. J. Neurophysiol. 99, 2584–2601 (2008).
  43. Liu, G. Local structural balance and functional interaction of excitatory and inhibitory synapses in hippocampal dendrites. Nat. Neurosci. 7, 373–379 (2004).
  44. Tao, H.W. & Poo, M.M. Activity-dependent matching of excitatory and inhibitory inputs during refinement of visual receptive fields. Neuron 45, 829–836 (2005).
  45. Vogels, T.P., Sprekeler, H., Zenke, F., Clopath, C. & Gerstner, W. Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks. Science 334, 1569–1573 (2011).
  46. Xie, X. & Seung, H.S. Spike-based learning rules and stabilization of persistent neural activity. in Advances in Neural Information Processing Systems Vol. 12 (eds. Solla, S.A., Leen, T.K. & Müller, K.-R.) 199–205 (2000).
  47. Csete, M.E. & Doyle, J.C. Reverse engineering of biological complexity. Science 295, 1664–1669 (2002).
  48. Ganguli, S. et al. One-dimensional dynamics of attention and decision making in LIP. Neuron 58, 15–25 (2008).
  49. Coyle, J.T., Tsai, G. & Goff, D. Converging evidence of NMDA receptor hypofunction in the pathophysiology of schizophrenia. Ann. NY Acad. Sci. 1003, 318–327 (2003).
  50. Wilson, H.R. Spikes, Decisions and Actions (Oxford University Press, 1999).
  51. McCormick, D.A., Connors, B.W., Lighthall, J.W. & Prince, D.A. Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J. Neurophysiol. 54, 782–806 (1985).
  52. Salin, P.A. & Prince, D.A. Spontaneous GABAA receptor–mediated inhibitory currents in adult rat somatosensory cortex. J. Neurophysiol. 75, 1573–1588 (1996).
  53. Xiang, Z., Huguenard, J.R. & Prince, D.A. GABAA receptor-mediated currents in interneurons and pyramidal cells of rat visual cortex. J. Physiol. (Lond.) 506, 715–730 (1998).
  54. Hansel, D., Mato, G., Meunier, C. & Neltner, L. On numerical simulations of integrate-and-fire neural networks. Neural Comput. 10, 467–483 (1998).

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Author information

Affiliations

  1. Center for Neuroscience, University of California, Davis, Davis, California, USA.

    • Sukbin Lim &
    • Mark S Goldman

  2. Department of Neurobiology, Physiology and Behavior, University of California, Davis, Davis, California, USA.

    • Mark S Goldman

  3. Department of Ophthalmology and Visual Science, University of California, Davis, Davis, California, USA.

    • Mark S Goldman

  4. Present address: Department of Neurobiology, University of Chicago, Chicago, Illinois, USA.

    • Sukbin Lim

Contributions

S.L. and M.S.G. designed the study, analyzed the data and wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

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    Supplementary Figures 1–7 and Supplementary Modeling

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