Skip to main content
SpringerLink
Log in

Synaptic efficacy shapes resource limitations in working memory

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

Working memory (WM) is limited in its temporal length and capacity. Classic conceptions of WM capacity assume the system possesses a finite number of slots, but recent evidence suggests WM may be a continuous resource. Resource models typically assume there is no hard upper bound on the number of items that can be stored, but WM fidelity decreases with the number of items. We analyze a neural field model of multi-item WM that associates each item with the location of a bump in a finite spatial domain, considering items that span a one-dimensional continuous feature space. Our analysis relates the neural architecture of the network to accumulated errors and capacity limitations arising during the delay period of a multi-item WM task. Networks with stronger synapses support wider bumps that interact more, whereas networks with weaker synapses support narrower bumps that are more susceptible to noise perturbations. There is an optimal synaptic strength that both limits bump interaction events and the effects of noise perturbations. This optimum shifts to weaker synapses as the number of items stored in the network is increased. Our model not only provides a circuit-based explanation for WM capacity, but also speaks to how capacity relates to the arrangement of stored items in a feature space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Almeida, R., Barbosa, J., Compte, A. (2015). Neural circuit basis of visuo-spatial working memory precision: a computational and behavioral study. Journal of Neurophysiology, 114(3), 1806–1818.

    Article  PubMed  PubMed Central  Google Scholar 

  • Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27(2), 77–87.

    Article  PubMed  CAS  Google Scholar 

  • Amari, S. (2014). Heaviside world: excitation and self-organization of neural fields. In Neural fields (pp. 97–118). Springer.

  • Avitabile, D., Desroches, M., Knobloch, E. (2017). Spatiotemporal canards in neural field equations. Physical Review E, 95(4), 042,205.

    Article  CAS  Google Scholar 

  • Barak, O., & Tsodyks, M. (2014). Working models of working memory. Current Opinion in Neurobiology, 25, 20–24.

    Article  PubMed  CAS  Google Scholar 

  • Bays, P.M. (2014). Noise in neural populations accounts for errors in working memory. Journal of Neuroscience, 34(10), 3632–3645.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Bays, P.M. (2015). Spikes not slots: noise in neural populations limits working memory. Trends in Cognitive Sciences, 19(8), 431–438.

    Article  PubMed  Google Scholar 

  • Bays, P.M., & Husain, M. (2008). Dynamic shifts of limited working memory resources in human vision. Science, 321(5890), 851–854.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Bays, P.M., Catalao, R.F., Husain, M. (2009). The precision of visual working memory is set by allocation of a shared resource. Journal of Vision, 9(10), 7–7.

    Article  PubMed  PubMed Central  Google Scholar 

  • Bressloff, P.C. (2005). Weakly interacting pulses in synaptically coupled neural media. SIAM Journal on Applied Mathematics, 66(1), 57–81.

    Article  Google Scholar 

  • Bressloff, P.C. (2009). Stochastic neural field theory and the system-size expansion. SIAM Journal on Applied Mathematics, 70(5), 1488–1521.

    Article  Google Scholar 

  • Bressloff, P.C. (2012). Spatiotemporal dynamics of continuum neural fields. Journal of Physics A: Mathematical and Theoretical, 45(3), 33,001–33,109.

    Article  Google Scholar 

  • Bressloff, P.C., & Kilpatrick, Z.P. (2015). Nonlinear langevin equations for wandering patterns in stochastic neural fields. SIAM Journal on Applied Dynamical Systems, 14(1), 305–334.

    Article  Google Scholar 

  • Bressloff, P.C., & Webber, M.A. (2012). Front propagation in stochastic neural fields. SIAM Journal on Applied Dynamical Systems, 11(2), 708–740.

    Article  Google Scholar 

  • Burak, Y., & Fiete, I.R. (2012). Fundamental limits on persistent activity in networks of noisy neurons. Proceedings of the National Academy of Sciences, 109(43), 17,645–17,650.

    Article  Google Scholar 

  • Buschman, T.J., Siegel, M., Roy, J.E., Miller, E.K. (2011). Neural substrates of cognitive capacity limitations. Proceedings of the National Academy of Sciences, 108(27), 11,252–11,255.

    Article  Google Scholar 

  • Carroll, S., Josic, K., Kilpatrick, Z. (2014). Encoding certainty in bump attractors. Journal of Computational Neuroscience, 37(1), 29–48.

    Article  PubMed  Google Scholar 

  • Compte, A., Brunel, N., Goldman-Rakic, P.S., Wang, X.J. (2000). Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cerebral Cortex, 10(9), 910–923.

    Article  PubMed  CAS  Google Scholar 

  • Constantinidis, C., & Klingberg, T. (2016). The neuroscience of working memory capacity and training. Nature Reviews Neuroscience, 17(7), 438–449.

    Article  PubMed  CAS  Google Scholar 

  • Coombes, S., & Laing, C. (2011). Pulsating fronts in periodically modulated neural field models. Physical Review E, 83(1), 011,912.

    Article  CAS  Google Scholar 

  • Coombes, S., & Owen, M.R. (2005). Bumps, breathers, and waves in a neural network with spike frequency adaptation. Physical Review Letters, 94(14), 148,102.

    Article  CAS  Google Scholar 

  • Coombes, S., & Schmidt, H. (2010). Neural fields with sigmoidal firing rates: approximate solutions. Discrete and Continuous Dynamical Systems Series 28, 1369–1379.

  • Coombes, S., Schmidt, H., Bojak, I. (2012). Interface dynamics in planar neural field models. The Journal of Mathematical Neuroscience, 2(1), 9.

    Article  PubMed  Google Scholar 

  • Cowan, N. (2010). The magical mystery four: how is working memory capacity limited, and why? Current Directions in Psychological Science, 19(1), 51–57.

    Article  PubMed  PubMed Central  Google Scholar 

  • Edin, F., Klingberg, T., Johansson, P., McNab, F., Tegnér, J., Compte, A. (2009). Mechanism for top-down control of working memory capacity. Proceedings of the National Academy of Sciences, 106(16), 6802–6807.

    Article  Google Scholar 

  • Ermentrout, B. (1998). Neural networks as spatio-temporal pattern-forming systems. Reports on Progress in Physics, 61(4), 353.

    Article  Google Scholar 

  • Folias, S., & Ermentrout, G. (2011). New patterns of activity in a pair of interacting excitatory-inhibitory neural fields. Physical Review Letters, 107(22), 228,103.

    Article  CAS  Google Scholar 

  • Fougnie, D., Suchow, J.W., Alvarez, G.A. (2012). Variability in the quality of visual working memory. Nature Communications, 3, 1229.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Funahashi, S., Bruce, C.J., Goldman-Rakic, P.S. (1989). Mnemonic coding of visual space in the monkey9s dorsolateral prefrontal cortex. Journal of Neurophysiology, 61(2), 331–349.

    Article  PubMed  CAS  Google Scholar 

  • Gardiner, C. (2009). Handbook of stochastic methods, Vol. 4, Springer, Berlin.

  • Gazzaley, A., & Nobre, A.C. (2012). Top-down modulation: bridging selective attention and working memory. Trends in Cognitive Sciences, 16(2), 129–135.

    Article  PubMed  Google Scholar 

  • Gökçe, A., Avitabile, D., Coombes, S. (2017). The dynamics of neural fields on bounded domains: an interface approach for dirichlet boundary conditions. Journal of Mathematical Neuroscience, 7(1), 1–12.

    Article  Google Scholar 

  • Goldman-Rakic, P.S. (1995). Cellular basis of working memory. Neuron, 14(3), 477–485.

    Article  PubMed  CAS  Google Scholar 

  • Gorgoraptis, N., Catalao, R.F., Bays, P.M., Husain, M. (2011). Dynamic updating of working memory resources for visual objects. Journal of Neuroscience, 31(23), 8502–8511.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Guo, Y., & Chow, C.C. (2005). Existence and stability of standing pulses in neural networks: II. Stability. SIAM Journal on Applied Dynamical Systems, 4(2), 249–281.

    Article  Google Scholar 

  • Ikkai, A., & Curtis, C.E. (2011). Common neural mechanisms supporting spatial working memory, attention and motor intention. Neuropsychologia, 49(6), 1428–1434.

    Article  PubMed  Google Scholar 

  • Keshvari, S., Van den Berg, R., Ma, W.J. (2013). No evidence for an item limit in change detection. PLoS Computational Biology, 9(2), e1002,927.

    Article  CAS  Google Scholar 

  • Kilpatrick, Z.P. (2013). Interareal coupling reduces encoding variability in multi-area models of spatial working memory. Frontiers in Computational Neuroscience, 7(82), 1–14.

    Google Scholar 

  • Kilpatrick, Z.P. (2016). Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction. Discrete Contin Dyn Syst Ser B, 21, 2211–2231.

    Article  Google Scholar 

  • Kilpatrick, Z.P. (2017). Synaptic mechanisms of interference in working memory. bioRxiv 149435.

  • Kilpatrick, Z.P., & Ermentrout, B. (2013). Wandering bumps in stochastic neural fields. SIAM Journal on Applied Dynamical Systems, 12(1), 61–94.

    Article  Google Scholar 

  • Kilpatrick, Z.P., Ermentrout, B., Doiron, B. (2013). Optimizing working memory with heterogeneity of recurrent cortical excitation. The Journal of Neuroscience, 33(48), 18,999–19,011.

    Article  CAS  Google Scholar 

  • Laing, C.R., & Troy, W.C. (2003a). Pde methods for nonlocal models. SIAM Journal on Applied Dynamical Systems, 2(3), 487–516.

  • Laing, C.R., & Troy, W.C. (2003b). Two-bump solutions of amari-type models of neuronal pattern formation. Physica D: Nonlinear Phenomena, 178(3), 190–218.

  • Laing, C.R., Troy, W.C., Gutkin, B., Ermentrout, G.B. (2002). Multiple bumps in a neuronal model of working memory. SIAM Journal on Applied Mathematics, 63(1), 62–97.

    Article  Google Scholar 

  • Lara, A.H., & Wallis, J.D. (2012). Capacity and precision in an animal model of visual short-term memory. Journal of Vision, 12(3), 13–13.

    Article  PubMed  Google Scholar 

  • Lim, S., & Goldman, M.S. (2014). Balanced cortical microcircuitry for spatial working memory based on corrective feedback control. Journal of Neuroscience, 34(20), 6790–6806.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Lu, Y., Sato, Y., Si, Amari. (2011). Traveling bumps and their collisions in a two-dimensional neural field. Neural Computation, 23(5), 1248–1260.

    Article  PubMed  Google Scholar 

  • Luck, S.J., & Vogel, E.K. (1997). The capacity of visual working memory for features and conjunctions. Nature, 390(6657), 279.

    Article  PubMed  CAS  Google Scholar 

  • Luck, S.J., & Vogel, E.K. (2013). Visual working memory capacity: from psychophysics and neurobiology to individual differences. Trends in Cognitive Sciences, 17(8), 391–400.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ma, W.J., Husain, M., Bays, P.M. (2014). Changing concepts of working memory. Nature Neuroscience, 17(3), 347–356.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Macoveanu, J., Klingberg, T., Tegnér, J. (2006). A biophysical model of multiple-item working memory: a computational and neuroimaging study. Neuroscience, 141(3), 1611–1618.

    Article  PubMed  CAS  Google Scholar 

  • Mante, V., Sussillo, D., Shenoy, K.V., Newsome, W.T. (2013). Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature, 503(7474), 78–84.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Murray, J.D., Bernacchia, A., Roy, N.A., Constantinidis, C., Romo, R., Wang, X.J. (2017). Stable population coding for working memory coexists with heterogeneous neural dynamics in prefrontal cortex. In Proceedings of the National Academy of Sciences, (Vol 114, No. 2, pp. 394–399).

  • Novikov, E.A. (1965). Functionals and the random-force method in turbulence theory. Soviet Physics – JETP, 20(5), 1290–1294.

    Google Scholar 

  • Pinto, D.J., & Ermentrout, G.B. (2001). Spatially structured activity in synaptically coupled neuronal networks: II. Lateral inhibition and standing pulses. SIAM Journal on Applied Mathematics, 62(1), 226–243.

    Article  Google Scholar 

  • Ploner, C.J., Gaymard, B., Rivaud, S., Agid, Y., Pierrot-Deseilligny, C. (1998). Temporal limits of spatial working memory in humans. European Journal of Neuroscience, 10(2), 794–797.

    Article  PubMed  CAS  Google Scholar 

  • Rosenbaum, R., Smith, M.A., Kohn, A., Rubin, J.E., Doiron, B. (2017). The spatial structure of correlated neuronal variability. Nature Neuroscience, 20(1), 107.

    Article  PubMed  CAS  Google Scholar 

  • Schneegans, S., & Bays, P.M. (2017). Neural architecture for feature binding in visual working memory. Journal of Neuroscience, 37(14), 3913–3925.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • van den Berg, R., Shin, H., Chou, W.C., George, R., Ma, W.J. (2012). Variability in encoding precision accounts for visual short-term memory limitations. Proceedings of the National Academy of Sciences, 109 (22), 8780–8785.

    Article  Google Scholar 

  • Wei, Z., Wang, X.J., Wang, D.H. (2012). From distributed resources to limited slots in multiple-item working memory: a spiking network model with normalization. Journal of Neuroscience, 32(33), 11,228–11,240.

    Article  CAS  Google Scholar 

  • White, J.M., Sparks, D.L., Stanford, T.R. (1994). Saccades to remembered target locations: an analysis of systematic and variable errors. Vision Research, 34(1), 79–92.

    Article  PubMed  CAS  Google Scholar 

  • Wilken, P., & Ma, W.J. (2004). A detection theory account of change detection. Journal of Vision, 4(12), 11–11.

    Article  Google Scholar 

  • Wimmer, K., Nykamp, D.Q., Constantinidis, C., Compte, A. (2014). Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory. Nature Neuroscience, 17(3), 431–439.

    Article  PubMed  CAS  Google Scholar 

  • Zhang, W., & Luck, S.J. (2008). Discrete fixed-resolution representations in visual working memory. Nature, 453(7192), 233.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Zylberberg, J., & Strowbridge, B.W. (2017). Mechanisms of persistent activity in cortical circuits: possible neural substrates for working memory. Annual Review of Neuroscience, 40, 603–627.

    Article  PubMed  CAS  PubMed Central  Google Scholar 

Download references

Acknowledgements

NK was supported by EXTREEMS - QED: Directions in Data Discovery in Undergraduate Education (NSF DMS-1407340). ZPK was supported by an NSF grant (DMS-1615737).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, 80309, USA

    Nikhil Krishnan & Zachary P. Kilpatrick

  2. Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Daniel B. Poll

Authors
  1. Nikhil Krishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel B. Poll
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zachary P. Kilpatrick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zachary P. Kilpatrick.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Action Editor: A. Compte

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krishnan, N., Poll, D.B. & Kilpatrick, Z.P. Synaptic efficacy shapes resource limitations in working memory. J Comput Neurosci 44, 273–295 (2018). https://doi.org/10.1007/s10827-018-0679-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-018-0679-7

Keywords

Search

Navigation