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Synchronization and Oscillatory Dynamics in Heterogeneous, Mutually Inhibited Neurons

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Abstract

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10–200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials (τs/T), where T can be determined either from the network or from a single, self-inhibiting neuron. With τs/T > 2, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With τs/T < 1, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.

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References

  • Bose A, Terman D, Kopell N (1997) Manuscript in preparation.

  • Bragin A, Jandó G, Nádasdy 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.

    PubMed  Google Scholar 

  • Buzsáki G (1986) Hippocampal sharp waves: Their origin and significance. Brain Res. 398:242-252.

    Article  PubMed  Google Scholar 

  • Chow CC, White JA, Ritt J, Kopell N (1997) Manuscript submitted.

  • Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comp. 8:979-1001.

    Google Scholar 

  • Ernst U, Pawelzik K, Geisel T (1995) Synchronization induced by temporal delays in pulse-coupled oscillators. Phys. Rev. Lett. 74:1570-1573.

    Article  PubMed  Google Scholar 

  • Friesen W (1994) Reciprocal inhibition, a mechanism underlying oscillatory animal movements. Neurosci. Behavior 18:547-553.

    Article  Google Scholar 

  • Gerstner W, van Hemmen JL, Cowen J (1996) What matters in neuronal locking? Neural Comp. 8:1653-1676.

    Google Scholar 

  • Golomb D, Rinzel J (1993) Dynamics of globally coupled inhibitory neurons with heterogeneity. Phys. Rev. E 48:4810-4814.

    Article  Google Scholar 

  • Gray CM (1994) Synchronous oscillations in neuronal systems: Mechanisms and functions. J. Comput. Neurosci. 1:11-38.

    PubMed  Google Scholar 

  • Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Comp. 7:307-337.

    Google Scholar 

  • Jeffreys JGR, Traub RD, Whittington MA (1996) Neuronal networks for induced “40 Hz” rhythms. Trends Neurosci. 19:202-207.

    Article  PubMed  Google Scholar 

  • Katsumaru H, Kosaka T, Heizman CW, Hama K (1988) Gap-junctions on GABAergic neurons containing the calcium-binding protein parvalbumin in the rat hippocampus (CA1 regions). Exp. Brain Res. 72:363-370.

    PubMed  Google Scholar 

  • Llinás R, Ribary U (1993) Coherent 40-Hz oscillation characterizes dream state in humans. Proc. Natl. Acad. Sci. USA 90:2078-2081.

    PubMed  Google Scholar 

  • Perkel D, Mulloney B (1974) Motor patterns in reciprocally inhibitory neurons exhibiting postinhibitory rebound. Science 185:181-183.

    PubMed  Google Scholar 

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

    PubMed  Google Scholar 

  • Skinner F, Kopell N, Marder E (1994) Mechanisms for oscillations and frequency control in networks of mutually inhibitory relaxation oscillators. J. Comp. Neurosci. 1:69-87.

    Google Scholar 

  • Terman D, Bose A, Kopell N (1996) Functional reorganization in thalamocortical networks: Transition between spindling and delta sleep rhythms. Proc. Natl. Acad. Sci. USA 93:15417-15422.

    Article  PubMed  Google Scholar 

  • Traub RD (1995) Model of synchronized population bursts in electrically coupled interneurons containing active dendritic conductances. J. Comp. Neurosci. 2:283-289.

    Article  Google Scholar 

  • Traub RD, Whittington M, Colling S, Buzsáki G, Jefferys J (1996a) Analysis of gamma rhythms in the rat hippocampus in vitro and in vivo. J. Physiol. 493:471-484.

    PubMed  Google Scholar 

  • Traub RD, Jefferys JGR, Whittington MA (1996b) Simulation of gamma rhythms in networks of interneurons and pyramidal cells. J. Comput. Neurosci. (In press).

  • Tsodyks M, Mitkov I, Sompolinsky, H (1993) Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions. Phys. Rev. Lett. 71:1280-1283.

    Article  PubMed  Google Scholar 

  • van Vreeswijk C, Abbott L, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci. 1:313-321.

    PubMed  Google Scholar 

  • Wang X-J, Rinzel J (1992) Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comp. 4:84-97.

    Google Scholar 

  • Wang X-J, Buzsáki G (1996) Gamma oscillation by synaptic inhibition in an interneuronal network model. J. Neurosci. 16:6402-6413.

    PubMed  Google Scholar 

  • Whittington MA, Traub RD, Jefferys JGR (1995) Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation. Nature 373:612-615.

    Article  PubMed  Google Scholar 

  • Ylinen A, Bragin A, Nádasdy Z, Jandó G, Szabó I, Sik A, Buzsáki G (1995) Sharp wave-associated high-frequency oscillation (200 Hz) in the intact hippocampus: Network and intracellular mechanisms. J. Neurosci. 15:30-46.

    PubMed  Google Scholar 

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White, J.A., Chow, C.C., Rit, J. et al. Synchronization and Oscillatory Dynamics in Heterogeneous, Mutually Inhibited Neurons. J Comput Neurosci 5, 5–16 (1998). https://doi.org/10.1023/A:1008841325921

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  • DOI: https://doi.org/10.1023/A:1008841325921

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