Optimal Intrinsic Dynamics for Bursting in a Three-Cell Network

Previous numerical and analytical work has shown that synaptic coupling can allow a network of model neurons to synchronize despite heterogeneity in intrinsic parameter values. In particular, synchronous bursting oscillations can arise in a network with excitatory synaptic coupling, even in the absence of intrinsically bursting neurons. In this work, we explore how the intrinsic dynamics of neurons within a reduced three-cell network influence its ability to exhibit synchronous bursting and the frequency range over which such activity can occur. We establish necessary and sufficient conditions for the existence of synchronous bursting solutions and perform related numerical experiments in three-cell networks that include a quiescent cell, a tonically active cell, and a third added cell. Our results show that, in most cases, the addition of a quiescent cell is optimal for synchronous network bursting, in a variety of ways, and that intrinsically bursting cells can be detrimental to synchronous bursting, and we explain the mechanisms underlying these effects. These findings may help explain how robust synchronous oscillations arise in neuronal central pattern generators, such as the mammalian inspiratory network, despite the presence of significant cellular heterogeneity. They also support the idea that intrinsic burst capabilities of individual cells need not be central to these networks' rhythms.