Chaos in neuronal networks with balanced excitatory and inhibitory activity

Science

Volumn 274, Issue 5293, 1996, Pages 1724-1726

  Van Vreeswijk, C ^a   Sompolinsky, H ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL BEHAVIOR; ANIMAL CELL; ARTICLE; NERVE CELL EXCITABILITY; NERVE CELL INHIBITION; NERVE CELL NETWORK; NONHUMAN; PREDICTION; PRIORITY JOURNAL; SPIKE WAVE; STRUCTURE ANALYSIS;

ANIMALS; CEREBRAL CORTEX; HAPLORHINI; MODELS, NEUROLOGICAL; NERVE NET; NEURONS; NONLINEAR DYNAMICS; PREFRONTAL CORTEX; SYNAPSES;

ANIMALIA;

EID: 0029835892     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.274.5293.1724     Document Type: Article

References (25)

1. B. D. Burns and A. C. Webb, Proc. R. Soc. London Ser. B 194, 211 (1976); R. J. Douglas and K. A. C. Martin, Trends Neurosci. 14, 286 (1991); W. R. Softky and C. Koch, J. Neurosci. 13, 334 (1993).
2. B. D. Burns and A. C. Webb, Proc. R. Soc. London Ser. B 194, 211 (1976); R. J. Douglas and K. A. C. Martin, Trends Neurosci. 14, 286 (1991); W. R. Softky and C. Koch, J. Neurosci. 13, 334 (1993).
3. B. D. Burns and A. C. Webb, Proc. R. Soc. London Ser. B 194, 211 (1976); R. J. Douglas and K. A. C. Martin, Trends Neurosci. 14, 286 (1991); W. R. Softky and C. Koch, J. Neurosci. 13, 334 (1993).
4. G. R. Holt, W. R. Softky, C. Koch, R. J. Douglas, J. Neurophysiol. 75, 1806 (1996); Z. F. Mainen and T. J. Sejnowski, Science 268, 1503 (1995).
5. G. R. Holt, W. R. Softky, C. Koch, R. J. Douglas, J. Neurophysiol. 75, 1806 (1996); Z. F. Mainen and T. J. Sejnowski, Science 268, 1503 (1995).
6. The fluctuations in the total synaptic input can be large if the different individual inputs are strongly synchronized. Model networks with a high degree of connectivity can display chaotic states characterized by strongly synchronized bursts of activity (15). Whether cortical networks exhibit such spatially coherent bursts under normal conditions is questionable.
7. M. N. Shadlen and W. T. Newsome, Curr. Opin. Neurobiol. 4, 569 (1994); ibid. 5, 248 (1995); W. R. Softky, ibid., p. 239; A. Bell, Z. Mainen, M. Tsodyks, T. Sejnowski, Soc. Neurosci. Abstr. 20, 1527 (1994).
8. M. N. Shadlen and W. T. Newsome, Curr. Opin. Neurobiol. 4, 569 (1994); ibid. 5, 248 (1995); W. R. Softky, ibid., p. 239; A. Bell, Z. Mainen, M. Tsodyks, T. Sejnowski, Soc. Neurosci. Abstr. 20, 1527 (1994).
9. M. N. Shadlen and W. T. Newsome, Curr. Opin. Neurobiol. 4, 569 (1994); ibid. 5, 248 (1995); W. R. Softky, ibid., p. 239; A. Bell, Z. Mainen, M. Tsodyks, T. Sejnowski, Soc. Neurosci. Abstr. 20, 1527 (1994).
10. M. N. Shadlen and W. T. Newsome, Curr. Opin. Neurobiol. 4, 569 (1994); ibid. 5, 248 (1995); W. R. Softky, ibid., p. 239; A. Bell, Z. Mainen, M. Tsodyks, T. Sejnowski, Soc. Neurosci. Abstr. 20, 1527 (1994).
11. D. J. Amit and N, Brunel, Cereb. Cortex, in press; M. Tsodyks and T. Sejnowski, Network (Bristol) 6, 111 (1995).
12. D. J. Amit and N, Brunel, Cereb. Cortex, in press; M. Tsodyks and T. Sejnowski, Network (Bristol) 6, 111 (1995).
13. The details of the dynamics are not essential. The simplest model for analytical study is one in which at each time step an updating neuron is chosen at random. Qualitatively similar behavior exists if the neurons are updated sequentially in a fixed order. Another possibility is a smooth dynamic model for analog units (13). These models differ primarily in the details of their short-time correlations. Time is scaled so that excitatory neurons are updated once per unit of time, and inhibitory units are updated every τ time units.
14. k + D)√K.
15. I (t) ≤ 1 denotes the unit activities averaged over all the units in the ℓth population. It represents the firing rate of the neuronal population relative to its maximal rate. A detailed analysis also yields the short-time correlations of the input, which decay on a time scale of order unity. The external input does not contribute to the fluctuations.
16. C typically ranges from 0.5 to 1.5.
17. kℓ between the two network populations. The activities are thresholded to zero when the above relations yield negative values.
18. M. Abeles, H. Bergman, E. Vaadia, unpublished data.
19. kℓ/K. These neurons integrate linearly their input with the same time constants as in the balanced network. The strengths of the synapses from cells outside of the network as well as the thresholds were chosen so that the stationary population rates of this network are the same as those for the balanced network.
20. H. Sompolinsky, A. Crisanti, H. J. Sommers, Phys. Rev. Lett. 61, 259 (1988).
21. B. Derrida, E. Gardner, A. Zippelius, Europhys. Lett. 4, 167 (1987). In this model, the randomness in the sign of the interactions is the result of the random nature of the embedded memories.
22. D. Hansel and H. Sompolinsky, Phys. Rev. Lett. 68, 718 (1992); J. Comput. Neurosci. 3, 5 (1996); P. C. Bush and R. J. Douglas, Neural Comput. 3, 19 (1991).
23. D. Hansel and H. Sompolinsky, Phys. Rev. Lett. 68, 718 (1992); J. Comput. Neurosci. 3, 5 (1996); P. C. Bush and R. J. Douglas, Neural Comput. 3, 19 (1991).
24. D. Hansel and H. Sompolinsky, Phys. Rev. Lett. 68, 718 (1992); J. Comput. Neurosci. 3, 5 (1996); P. C. Bush and R. J. Douglas, Neural Comput. 3, 19 (1991).
25. We thank D. J. Amit, D. Hansel, and T. Sejnowski for extensive discussions. We are grateful to M. Abeles, H. Bergman, and E. Vaadia for permission to present their data.