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Model for a robust neural integrator

Nature Neuroscience volume 5, pages 775–782 (2002)Cite this article

Abstract

Integrator circuits in the brain show persistent firing that reflects the sum of previous excitatory and inhibitory inputs from external sources. Integrator circuits have been implicated in parametric working memory, decision making and motor control. Previous work has shown that stable integrator function can be achieved by an excitatory recurrent neural circuit, provided synaptic strengths are tuned with extreme precision (better than 1% accuracy). Here we show that integrator circuits can function without fine tuning if the neuronal units have bistable properties. Two specific mechanisms of bistability are analyzed, one based on local recurrent excitation, and the other on the voltage-dependence of the NMDA (N-methyl-D-aspartate) channel. Neither circuit requires fine tuning to perform robust integration, and the latter actually exploits the variability of neuronal conductances.

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Figure 1: The oculomotor system as an example of an integrator.
Figure 2: The fine-tuning hypothesis.
Figure 3: Qualitative explanation of the new model containing bistable units.
Figure 4: Multistability in circuits with hysteretic units.
Figure 5: Robust integrator network using circuit-based bistability.
Figure 6: Response to weak inputs.
Figure 7: Integrator network based on the voltage-dependence of the NMDA conductance.
Figure 8: Robust integrator function when conductances are randomly chosen.

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References

  1. Miyashita, Y. & Chang, H.S. Neuronal correlate of pictorial short-term memory in the primate temporal cortex. Nature 331, 68–70 (1988).

    Article  CAS  Google Scholar 

  2. Gnadt, J.W. & Andersen, R.A. Memory related motor planning activity in posterior parietal cortex of macaque. Exp. Brain Res. 70, 216–220 (1988).

    CAS  PubMed  Google Scholar 

  3. DeSouza, J.F. et al. Eye position signal modulates a human parietal pointing region during memory-guided movements. J. Neurosci. 20, 5835–5840 (2000).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  5. Fuster, J.M. Memory in the Cerebral Cortex: An Empirical Approach to Neural Networks in the Human and Nonhuman Primate (MIT Press, Cambridge, Massachusetts, 1995).

    Google Scholar 

  6. Romo, R., Brody, C.D., Hernandez, A. & Lemus, L. Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399, 470–473 (1999).

    Article  CAS  Google Scholar 

  7. Wang, X.J. Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24, 455–463 (2001).

    Article  CAS  Google Scholar 

  8. 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).

    Article  CAS  Google Scholar 

  9. Fukushima, K., Kaneko, C.R. & Fuchs, A.F. The neuronal substrate of integration in the oculomotor system. Prog. Neurobiol. 39, 609–639 (1992).

    Article  CAS  Google Scholar 

  10. Arnold, D.B. & Robinson, D.A. A learning network model of the neural integrator of the oculomotor. Biol. Cybern. 64, 447–454 (1991).

    Article  CAS  Google Scholar 

  11. Robinson, D.A. Integrating with neurons. Annu. Rev. Neurosci. 12, 33–45 (1989).

    Article  CAS  Google Scholar 

  12. Aksay, E., Baker, R., Seung, H.S. & Tank, D.W. Anatomy and discharge properties of pre-motor neurons in the goldfish medulla that have eye-position signals during fixations. J. Neurophysiol. 84, 1035–1049 (2000).

    Article  CAS  Google Scholar 

  13. Seung, H.S., Lee, D.D., Reis, B.Y. & Tank, D.W. Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron 26, 259–271 (2000).

    Article  CAS  Google Scholar 

  14. Seung, H.S. How the brain keeps the eyes still. Proc. Natl. Acad. Sci. USA 93, 13339–13344 (1996).

    Article  CAS  Google Scholar 

  15. Seung, H.S., Lee, D.D., Reis, B.Y. & Tank, D.W. The autapse: a simple illustration of short-term analog memory storage by tuned synaptic feedback. J. Comput. Neurosci. 9, 171–185 (2000).

    Article  CAS  Google Scholar 

  16. Wilson, H.R. & Cowan, J.D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical J. 12, 1–24 (1972).

    Article  CAS  Google Scholar 

  17. Hopfield, J.J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).

    Article  CAS  Google Scholar 

  18. Wang, X.J. Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory. J. Neurosci. 19, 9587–9603 (1999).

    Article  CAS  Google Scholar 

  19. Koulakov, A.A. Properties of synaptic transmission and the global stability of delayed activity states. Network 12, 47–74 (2001).

    Article  CAS  Google Scholar 

  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).

    Article  CAS  Google Scholar 

  21. Schiller, J. & Schiller, Y. NMDA receptor–mediated dendritic spikes and coincident signal amplification. Curr. Opin. Neurobiol. 11, 343–348 (2001).

    Article  CAS  Google Scholar 

  22. Nowak, L., Bregestovski, P., Ascher, P., Herbet, A. & Prochiantz, A. Magnesium gates glutamate-activated channels in mouse central neurons. Nature 307, 462–465 (1984).

    Article  CAS  Google Scholar 

  23. Mayer, M.L., Westbrook, G.L. & Guthrie, P.B. Voltage-dependent block by Mg2+ of NMDA responses in spinal cord neurons. Nature 309, 261–263 (1984).

    Article  CAS  Google Scholar 

  24. Aksay, E., Gamkrelidze, G., Seung, H.S., Baker, R. & Tank, D.W. In vivo intracellular recording and perturbation of persistent activity in a neural integrator. Nat. Neurosci. 4, 184–193 (2001).

    Article  CAS  Google Scholar 

  25. Godaux, E., Cheron, G. & Mettens, P. Ketamine induces failure of the oculomotor neural integrator in the cat. Neurosci. Lett. 116, 162–167 (1990).

    Article  CAS  Google Scholar 

  26. Mettens, P., Cheron, G. & Godaux, E. NMDA receptors are involved in temporal integration in the oculomotor system of the cat. Neuroreport 5, 1333–1336 (1994).

    CAS  PubMed  Google Scholar 

  27. Priesol, A.J., Jones, G.E., Tomlinson, R.D. & Broussard, D.M. Frequency-dependent effects of glutamate antagonists on the vestibulo-ocular reflex of the cat. Brain Res. 857, 252–264 (2000).

    Article  CAS  Google Scholar 

  28. Taube, J.S., Muller, R.U. & Ranck, J.B. Jr. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10, 420–435 (1990).

    Article  CAS  Google Scholar 

  29. Blair, H.T. & Sharp, P.E. Anticipatory head direction signals in anterior thalamus: evidence for a thalamocortical circuit that integrates angular head motion to compute head direction. J. Neurosci. 15, 6260–6270 (1995).

    Article  CAS  Google Scholar 

  30. Shadlen, M.N. & Newsome, W.T. Neural basis of a perceptual decision in the parietal cortex (area lip) of the rhesus monkey. J. Neurophysiol. 86, 1916–1936 (2001).

    Article  CAS  Google Scholar 

  31. Lisman, J.E. A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase. Proc. Natl. Acad. Sci. USA 82, 3055–3057 (1985).

    Article  CAS  Google Scholar 

  32. Petersen, C.C., Malenka, R.C., Nicoll, R.A. & Hopfield, J.J. All-or-none potentiation at CA3-CA1 synapses. Proc. Natl. Acad. Sci. USA 95, 4732–4737 (1998).

    Article  CAS  Google Scholar 

  33. Cimino, A. & Hervagault, J.F. Irreversible tansitions in a model substrate cycle. An experimental illustration. FEBS Lett. 263, 199–205 (1990).

    Article  CAS  Google Scholar 

  34. Novick, A. & Weiner, M. Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci. USA 43, 553–566 (1957).

    Article  CAS  Google Scholar 

  35. McAdams, H.H. & Arkin, A. Simulation of prokaryotic genetic circuits. Annu. Rev. Biophys. Biomol. Struct. 27, 199–224 (1998).

    Article  CAS  Google Scholar 

  36. Segel, L.A., Jager, E., Elias, D. & Cohen, I.R. A quantitative model of autoimmune disease and T-cell vaccination: does more mean less? Immunol. Today 16, 80–84 (1995).

    Article  CAS  Google Scholar 

  37. Pinsky, P. & Rinzel, J. Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J. Comput. Neurosci. 1, 39–60 (1994).

    Article  CAS  Google Scholar 

  38. Kepecs, A. & Raghavachari, S. in Advances in Neural Information Processing Systems Vol. 14 (eds. Dietterich, T. G., Becker, S. & Ghahramani, Z.) (MIT Press, Cambridge, Massachusetts, 2002).

    Google Scholar 

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Acknowledgements

The authors are grateful to C. Kaneko and H. Sompolinsky for encouragement and to S. Seung and his group for numerous helpful suggestions. A.A.K. and A. K. were supported by fellowships from the Swartz and Alfred P. Sloan Foundations. We also acknowledge grants NIH 461434 and NSF 450578.

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Authors and Affiliations

  1. Salk Institute for Biological Studies, 10010 North Torrey Pines Road, La Jolla, 92037, California, USA

    Alexei A. Koulakov

  2. Department of Physics, University of Utah, 115 South 1400 East, Salt Lake City, 84112, Utah, USA

    Alexei A. Koulakov

  3. Volen Center for Complex Systems, Mailstop 013, Brandeis University, Waltham, 02454, Massachusetts, USA

    Sridhar Raghavachari, Adam Kepecs & John E. Lisman

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Correspondence to Alexei A. Koulakov.

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Koulakov, A., Raghavachari, S., Kepecs, A. et al. Model for a robust neural integrator. Nat Neurosci 5, 775–782 (2002). https://doi.org/10.1038/nn893

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