Volume 9 Supplement 1

Seventeenth Annual Computational Neuroscience Meeting: CNS*2008

Open Access

Loss of synchrony in an inhibitory network of type-I oscillators

BMC Neuroscience20089(Suppl 1):P149

DOI: 10.1186/1471-2202-9-S1-P149

Published: 11 July 2008

Understanding the dynamics and synchronization of inhibitory neurons is a question of fundamental importance in neuroscience, since inhibitory networks play a crucial role in rhythmogenesis, both in invertebrate motor pattern generators [1] and in the mammalian hippocampus and neocortex [2]. Invertebrate CPGs in particular often contain simple two-cell inhibitory sub-networks that play a crucial role in the control of rhythmic motor behaviors. Therefore, characterizing the dynamics of two-cell inhibitory networks is relevant for a better understanding of the rhythmic dynamic activity produced by central pattern generators and other inhibitory circuits.

Here we describe the activity states in a network of two cells with type-I excitability coupled by reciprocal inhibition. Weak coupling analysis is very successful in the study of phase-locked activity in such a network, and predicts synchronous or anti-synchronous dynamics, depending on the time scale of inhibition and the intrinsic cell properties [3]. However, it is known that an increase in coupling strength can destabilize synchrony in many neural circuits [4]. In particular, recent work by Maran and Canavier [5] has shown that non-weak coupling leads to alternating-order firing (termed "leap-frog" spiking by G.B. Ermentrout) in an inhibitory network of two Wang-Buzsáki model neurons, whereby the order of spiking of the two cells alternates in each cycle of the oscillation. Here we show that such activity is a generic property of an inhibitory network of oscillators of type-I excitability class. In particular, we demonstrate that leap-frog spiking can also be obtained in a two-cell network of simpler Morris-Lecar model cells, as shown in Figure 1.
Figure 1

Alternating-order (leap-frog) activity in an inhibitory network of two Morris-Lecar cells with type-I excitability. The membrane potentials of the two model cells are shown as black and red traces, respectively.

We examine the phase-plane geometry of such order non-preserving dynamics, and find that it arises when the inhibition is sufficiently strong to allow a presynaptic cell to transiently suppress the postsynaptic cell below its excitability threshold (saddle-node on an invariant cycle bifurcation) in each cycle of the oscillation. Therefore, non-zero synaptic decay time is crucial for obtaining leap-frog spiking in a continuous system. However, we show that alternating-order spiking can also be obtained in an appropriately modified pulse-coupled integrate-and-fire network. Following the approach of Maran and Canavier [5], we show that the entire activity state bifurcation profile of the two-cell Morris-Lecar network can be completely characterized using the phase-resetting properties of each of the two cells, and describe the conditions on the phase resetting curve that lead to the loss of synchrony and the emergence of leap-frog spiking.



This work is partially supported by the National Science Foundation grant DMS-0417416

Authors’ Affiliations

Department of Mathematical Sciences, New Jersey Institute of Technology


  1. Marder E, Calabrese RL: Principles of rhythmic motor pattern generation. Physiol Rev. 1996, 76: 687-717.PubMedGoogle Scholar
  2. White JA, Chow CC, Ritt J, Soto-Treviño C, Kopell N: Synchronization and oscillatory dynamics in heterogeneous, mutually inhibitory networks. J Computational Neurosci. 1998, 5: 5-16. 10.1023/A:1008841325921.View ArticleGoogle Scholar
  3. Ermentrout GB: Type I membranes, phase resetting curves, and synchrony. Neural Computation. 1996, 8: 979-1001. 10.1162/neco.1996.8.5.979.View ArticlePubMedGoogle Scholar
  4. Ermentrout GB, Kopell N: Multiple pulse interactions and averaging in systems of coupled neural oscillators. J Math Biol. 1991, 29: 195-217. 10.1007/BF00160535.View ArticleGoogle Scholar
  5. Maran SK, Canavier CC: Using phase resetting to predict 1:1 and 2:2 locking in two neuron networks in which firing order is not always preserved. J Comput Neurosci. 2008, 24: 37-55. 10.1007/s10827-007-0040-z.PubMed CentralView ArticlePubMedGoogle Scholar


© Oh and Matveev; licensee BioMed Central Ltd. 2008

This article is published under license to BioMed Central Ltd.