Journal of Computational Neuroscience

, Volume 30, Issue 2, pp 501–513 | Cite as

A network of spiking neurons that can represent interval timing: mean field analysis

Article
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Abstract

Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.

Keywords

Recurrent network Mean field theory Synaptic plasticity Spontaneous activity Reinforcement learning 
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References

  1. Amit, D. J. (1989). Modeling brain function: The world of attractor neural networks. Cambridge [England], New York: Cambridge University Press. 89015741 Daniel J. Amit. ill.; 24 cm. Includes bibliographies and index.Google Scholar
  2. Amit, D. J., & Brunel, N. (1997). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex, 7(3), 237–252.PubMedCrossRefGoogle Scholar
  3. Amit, D. J., Gutfreund, H., & Sompolinsky, H. (1985). Spin-glass models of neural networks. Physical Review A, 32(2), 1007–1018.PubMedCrossRefGoogle Scholar
  4. Barbieri, F., & Brunel, N. (2008). Can attractor network models account for the statistics of firing during persistent activity in prefrontal cortex? Front Neuroscience, 2(1), 114–122.CrossRefGoogle Scholar
  5. Brody, C. D., Romo, R., & Kepecs, A. (2003). Basic mechanisms for graded persistent activity: Discrete attractors, continuous attractors, and dynamic representations. Current Opinion in Neurobiology, 13(2), 204–211.PubMedCrossRefGoogle Scholar
  6. Brunel, N., & Wang, X. J. (2001). Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition. Journal of Computational Neuroscience, 11(1), 63–85.PubMedCrossRefGoogle Scholar
  7. Budd, J. M. (1998). Extrastriate feedback to primary visual cortex in primates: A quantitative analysis of connectivity. Proceedings of the Royal Society B: Biological Sciences, 265(1400), 1037–1044.PubMedCrossRefGoogle Scholar
  8. Churchland, M. M., Yu, B. M., Cunningham, J. P., Sugrue, L. P., Cohen, M. R., Corrado, G. S., et al. (2009). Stimulus onset quenches neural variability: A widespread cortical phenomenon. Nature Neuroscience, 13(3), 369–378.CrossRefGoogle Scholar
  9. 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.PubMedCrossRefGoogle Scholar
  10. Eliasmith, C. (2005). A unified approach to building and controlling spiking attractor networks. Neural Computation, 17(6), 1276–1314.PubMedCrossRefGoogle Scholar
  11. Gavornik, J. P. (2009). Learning temporal representations in cortical networks through reward dependent expression of synaptic plasticity. Ph.D. dissertation, The University of Texas at Austin.Google Scholar
  12. Gavornik, J. P., Shuler, M. G., Loewenstein, Y., Bear, M. F., & Shouval, H. Z. (2009). Learning reward timing in cortex through reward dependent expression of synaptic plasticity. Proceedings of the National Academy of Sciences of the United States of America, 106(16), 6826–6831.PubMedCrossRefGoogle Scholar
  13. Johnson, R. R., & Burkhalter, A. (1996). Microcircuitry of forward and feedback connections within rat visual cortex. Journal of Comparative Neurology, 368(3), 383–398.PubMedCrossRefGoogle Scholar
  14. Lewis, P. A., & Miall, R. C. (2006). A right hemispheric prefrontal system for cognitive time measurement. Behavioural Processes, 71(2–3), 226–234.PubMedCrossRefGoogle Scholar
  15. Lisman, J. E., Fellous, J. M., & Wang, X. J. (1998). A role for NMDA-receptor channels in working memory. Nature Neuroscience, 1(4), 273–275.PubMedCrossRefGoogle Scholar
  16. Machens, C. K., Romo, R., & Brody, C. D. (2005). Flexible control of mutual inhibition: A neural model of two-interval discrimination. Science, 307(5712), 1121–1124.PubMedCrossRefGoogle Scholar
  17. Mastronarde, D. N. (1987). Two classes of single-input X-cells in cat lateral geniculate nucleus. II. Retinal inputs and the generation of receptive-field properties. Journal of Neurophysiology, 57(2), 381–413.PubMedGoogle Scholar
  18. Mauk, M. D., & Buonomano, D. V. (2004). The neural basis of temporal processing. Annual Review of Neuroscience, 27, 307–340.PubMedCrossRefGoogle Scholar
  19. Miller, P., Brody, C. D., Romo, R., & Wang, X. J. (2003). A recurrent network model of somatosensory parametric working memory in the prefrontal cortex. Cerebral Cortex, 13(11), 1208–1218.PubMedCrossRefGoogle Scholar
  20. Moshitch, D., Las, L., Ulanovsky, N., Bar-Yosef, O., & Nelken, I. (2006). Responses of neurons in primary auditory cortex (A1) to pure tones in the halothane-anesthetized cat. Journal of Neurophysiology, 95(6), 3756–3769.PubMedCrossRefGoogle Scholar
  21. Renart, A., Brunel, N., & Wang, X. (2003). Mean-field theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks. In J. Feng (Ed.), Computational neuroscience: A comprehensive approach (pp. 431–490). Boca Raton: CRC Press.Google Scholar
  22. Renart, A., Moreno-Bote, R., Wang, X. J., & Parga, N. (2007). Mean-driven and fluctuation-driven persistent activity in recurrent networks. Neural Computation, 19(1), 1–46.PubMedCrossRefGoogle Scholar
  23. Roudi, Y., & Latham, P. E. (2007). A balanced memory network. PLoS Computational Biology, 3(9), 1679–1700.PubMedCrossRefGoogle Scholar
  24. Seung, H. S. (1996). How the brain keeps the eyes still. Proceedings of the National Academy of Sciences of the United States of America, 93(23), 13339–13344.PubMedCrossRefGoogle Scholar
  25. Seung, H. S., Lee, D. D., Reis, B. Y., & Tank, D. W. (2000). Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron, 26(1), 259–271.PubMedCrossRefGoogle Scholar
  26. Shouval, H. Z., & Gavornik, J. P. (2010). A single cell with active conductances can learn timing and multi-stability. Journal of Computational Neuroscience. doi: 10.1007/s10827-010-0273-0.Google Scholar
  27. Shuler, M. G., & Bear, M. F. (2006). Reward timing in the primary visual cortex. Science, 311(5767), 1606–1609.PubMedCrossRefGoogle Scholar
  28. Staddon, J. E. (2005). Interval timing: Memory, not a clock. Trends in Cognitive Sciences, 9(7), 312–314.PubMedCrossRefGoogle Scholar
  29. Super, H., Spekreijse, H., & Lamme, V. A. (2001). A neural correlate of working memory in the monkey primary visual cortex. Science, 293(5527), 120–124.PubMedCrossRefGoogle Scholar
  30. Wang, X. J. (2001). Synaptic reverberation underlying mnemonic persistentactivity. Trends in Neurosciences, 24(8), 455–463.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Neurobiology and AnatomyThe University of Texas Medical School at HoustonHoustonUSA
  2. 2.Department of Electrical and Computer EngineeringThe University of Texas at AustinAustinUSA

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