How noise affects the synchronization properties of recurrent networks of inhibitory neurons

Neural Computation

Volumn 18, Issue 5, 2006, Pages 1066-1110

  Brunel, Nicolas ^a   Hansel, David ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646397012     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2006.18.5.1066     Document Type: Article

References (57)

1. Abbott, L. F., & van Vreeswijk, C. (1993). Asynchronous states in a network of pulse-coupled oscillators. Phys. Rev. E, 48, 1483-1490.
2. Abramowitz, M., & Stegun, I. A. (1970). Tables of mathematical functions. New York: Dover.
3. 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, 237-252.
4. Amit, D. J., & Tsodyks, M. V. (1991). Quantitative study of attractor neural network retrieving at low spike rates I: Substrate-spikes, rates and neuronal gain. Network, 2, 259-274.
5. Anderson, J. S., Lampl, I., Gillespie, D. C., & Ferster, D. (2000). The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science, 290, 1968-1972.
6. Bragin, A., Jando, G., Nadasdy, Z., Hetke, J., Wise, K., & Buzsáki, G. (1995). Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat. J. Neurosci., 15, 47-60.
7. Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci., 8, 183-208.
8. Brunel, N., Chance, F., Fourcaud, N., & Abbott, L. (2001). Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys. Rev. Lett., 86, 2186-2189.
9. Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comp., 11, 1621-1671.
10. Brunel, N., & Wang, X.-J. (2003). What determines the frequency of fast network oscillations with irregular neural discharges? J. Neurophysiol., 90, 415-430.
11. Buzsaki, G., Urioste, R., Hetke, J., & Wise, K. (1992). High frequency network oscillation in the hippocampus. Science, 256, 1025-1027.
12. Compte, A., Constantinidis, C., Tegnér, J., Raghavachari, S., Chafee, M., Goldman-Rakic, P. S., & Wang, X.-J. (2003). Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J. Neurophysiol., 90, 3441-3454.
13. Csicsvari, J., Hirase, H., Czurko, A., Mamiya, A., & Buzsáki, G. (1999a). Fast network oscillations in the hippocampal CA1 region of the behaving rat. J. Neurosci., 19, RC20.
14. Csicsvari, J., Hirase, H., Czurko, A., Mamiya, A., & Buzsáki, G. (1999b). Oscillatory coupling of hippocampal pyramidal cells and interneurons in the behaving rat. J. Neurosci., 19, 274-287.
15. Destexhe, A., & Paré, D. (1999). Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J. Neurophysiol., 81, 1531-1547.
16. Ermentrout, G. B., & Kopell, N. (1986). Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math., 46, 233-253.
17. Ermentrout, B., Pascal, M., & Gutkin, B. (2001). The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Comput., 33, 1285-1310.
18. Fourcaud, N., & Brunel, N. (2002). Dynamics of firing probability of noisy integrate-and-fire neurons. Neural Computation, 14, 2057-2110.
19. Fourcaud-Trocmé, N., Hansel, D., van Vreeswijk, C., & Brunel, N. (2003). How spike generation mechanisms determine the neuronal response to fluctuating inputs. J. Neurosci., 23, 11628-11640.
20. Fuhrmann, G., Markram, H., & Tsodyks, M. (2002). Spike frequency adaptation and neocortical rhythms. J. Neurophysiol., 88, 761-770.
21. Geisler, C., Brunel, N., & Wang, X.-J. (2005). Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges. J. Neurophysiol., 94, 4344-4361.
22. Gerstner, W., van Hemmen, L., & Cowan, J. (1996). What matters in neuronal locking? Neural Computation, 8, 1653-1676.
23. Ginzburg, I., & Sompolinsky, H. (1994). Theory of correlations in stochastic neural networks. Phys. Rev. E, 50, 3171-3191.
24. Golomb, D., & Hansel, D. (2000). The number of synaptic inputs and the synchrony of large sparse neuronal networks. Neural Computation, 12, 1095-1139.
25. Golomb, D., Hansel, D., & Mato, G. (2001). Theory of synchrony of neuronal activity. In S. Gielen & F. Moss (Eds.), Handbook of biological physics. Dordrecht: Elsevier.
26. Golomb, D., Hansel, D., Shraiman, D., & Sompolinsky, H. (1992). Clustering in globally coupled phase oscillators. Phys. Rev. A, 45, 3516-3530.
27. Golomb, D., & Rinzel, J. (1993). Dynamics of globally coupled inhibitory neurons with heterogeneity. Phys. Rev. E, 43, 4810-4814.
28. Golomb, D., & Rinzel, J. (1994). Clustering in globally coupled inhibitory neurons. Physica D, 72, 259-282
29. Hansel, D., & Mato, G. (2001). Existence and stability of persistent states in large neuronal networks. Phys. Ren Lett., 86, 4175-4178.
30. Hansel, D., & Mato, G. (2003). Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons. Neural Comp., 15, 1-56.
31. Hansel, D., Mato, G., & Meunier, C. (1993). Phase dynamics for weakly coupled Hodgkin-Huxley neurons. Europhys. Lett., 23, 367-370.
32. Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Computation, 7, 307-337.
33. Hansel, D., & Sompolinsky, H. (1992). Synchronization and computation in a chaotic neural network. Phys. Rev. Lett., 68, 718-721.
34. Hansel, D., & Sompolinsky, H. (1996). Chaos and synchrony in a model of a hyper-column in visual cortex. J. Computational Neurosci., 3, 7-34.
35. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conductance and excitation in nerve, J. Physiol., 117, 500-544.
36. Hormuzdi, S. G., Pais, I., LeBeau, F. F., Towers, S. K., Rozov, A., Buhl, E.H., Whittington, M. A., & Monyer, H. (2001). Impaired electrical signaling disrupts gamma frequency oscillations in connexin 36-deficient mice. Neuron, 31, 487-495.
37. Kuramoto, Y. (1984). Chemical oscillations, waves and turbulence. New York: Springer-Verlag.
38. Lapicque, L. (1907). Recherches quantitatives sur l'excitabilité électrique des nerfs traitée comme une polarisation. J. Physiol. Pathol. Gen., 9, 620-635.
39. Mato, G. (2005). Theory of neural synchrony. In C. Chow, B. Gutkin, D. Hansel, C. Meunier, & J. Dalibard (Eds.), Methods and models in neurophysics. Dordrecht: Elsevier.
40. McCormick, D., Connors, B., Lighthall, J., & Prince, D. (1985). Comparative electro-physiology of pyramidal and sparsely spiny stellate neurons in the neocortex. J. Neurophysiol., 54, 782-806.
41. Neltner, L., Hansel, D., Mato, G., & Meunier, C. (2000). Synchrony in heterogeneous neural networks. Neural Comp., 12, 1607-1641.
42. Pfeuty, B., Golomb, D., Mato, G., & Hansel, D. (2003). Electrical synapses and synchrony: The role of intrinsic currents. J. Neurosci., 23, 6280-6294.
43. Pfeuty, B., Mato, G., Golomb, D., & Hansel, D. (2005). The combined effects of inhibitory and electrical synapses in synchrony. Neural Comp., 17, 633-670.
44. Ricciardi, L. M. (1977). Diffusion processes and related topics on biology. Berlin: Springer-Verlag.
45. Rinzel, J., & Ermentrout, G. B. (1998). Analysis of neural excitability and oscillations. In C. Koch & I. Segev (Eds.), Methods in Neuronal Modeling, pp. 251-291. Cambridge, MA: MIT Press.
46. Siapas, A. C., & Wilson, M. A. (1998). Coordinated interactions between hippocampal ripples and cortical spindles during slow-wave sleep. Neuron, 21, 1123-1128.
47. Softky, W. R., & Koch, C. (1993). The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci., 13, 334-350.
48. Tiesinga, P. H., & Jose, J. V. (2000). Robust gamma oscillations in networks of inhibitory hippocampal interneurons. Network, 11, 1-23.
49. Treves, A. (1993). Mean-field analysis of neuronal spike dynamics. Network, 4, 259-284.
50. Troyer, T. W., & Miller, K. D. (1997). Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Computation, 9, 971-983.
51. Tsodyks, M. V., Mit'kov, I., & Sompolinsky, H. (1993). Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions. Phys. Rev. Lett., 71, 1280-1283.
52. Tuckwell, H. C. (1988). Introduction to theoretical neurobiology. Cambridge: Cambridge University Press.
53. van Vreeswijk, C. (1996). Partial synchronization in populations of pulse-coupled oscillators. Phys. Rev. E, 54, 5522-5537.
54. van Vreeswijk, C., Abbott, L., & Ermentrout, G. B. (1994). When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci., 1, 313-321.
55. van Vreeswijk, C., & Hansel, D. (2001). Patterns of synchrony in neural networks with spike adaptation. Neural Computation, 13, 959-992.
56. Wang, X.-J., & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci., 16, 6402-6413.
57. White, J. A., Chow, C. C., Soto-Treviño, C., & Kopell, N. (1998). Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons. J. Comput. Neurosci., 5, 5-16.