Inhibitory feedback promotes stability in an oscillatory network

Reliability and variability of neuronal activity are both thought to be important for the proper function of neuronal networks. The crustacean pyloric rhythm (∼1 Hz) is driven by a group of pacemaker neurons (AB/PD) that inhibit and burst out of phase with all follower pyloric neurons. The only known chemical synaptic feedback to the pacemakers is an inhibitory synapse from the follower lateral pyloric (LP) neuron. Although this synapse has been studied extensively, its role in the generation and coordination of the pyloric rhythm is unknown. We examine the hypothesis that this synapse acts to stabilize the oscillation by reducing the variability in cycle period on a cycle-by-cycle basis. Our experimental data show that functionally removing the LP-pyloric dilator (PD) synapse by hyperpolarizing the LP neuron increases the pyloric period variability. The increase in pyloric rhythm stability in the presence of the LP-PD synapse is demonstrated by a decrease in the amplitude of the phase response curve of the PD neuron. These experimental results are explained by a reduced mathematical model. Phase plane analysis of this model demonstrates that the effect of the periodic inhibition is to produce asymptotic stability in the oscillation phase, which leads to a reduction in variability of the oscillation cycle period.