Subharmonic Coordination in Networks of Neurons with Slow Conductances

We study the properties of a network consisting of two model neurons that are coupled by reciprocal inhibition. The study was motivated by data from a pair of cells in the crustacean stomatogastric ganglion. One of the model neurons is an endogenous burster; the other is excitable but not bursting in the absence of phasic input. We show that the presence of a hyperpolarization activated inward current (ih) in the excitable neuron allows these neurons to fire in integer subharmonics, with the excitable cell firing once for every N ≥ 1 bursts of the oscillator. The value of N depends on the amount of hyperpolarizing current injected into the excitable cell as well as the voltage activation curve of ih. For a fast synapse, these parameter changes do not affect the characteristic point in the oscillator cycle at which the excitable cell bursts; for slower synapses, such a relationship is maintained within small windows for each N. The network behavior in the current work contrasts with the activity of a pair of coupled oscillators for which the interaction is through phase differences; in the latter case, subharmonics exist if the uncoupled oscillators have near integral frequency relationships, but the phase relationships of the oscillators in general change significantly with parameters. The mechanism of this paper provides a potential means of coordinating subnetworks acting on different time scales but maintaining fixed relationships between characteristic points of the cycles.