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

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 twocell 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 Wangfrom Seventeenth Annual Computational Neuroscience Meeting: CNS*2008 Portland, OR, USA. 19–24 July 2008