Bursting emerges from the complementary roles of neurons in a four-cell network.

Reciprocally inhibitory modules that form half-center oscillators require mechanisms for escaping or being released from inhibition. The central pattern generator underlying swimming by the nudibranch mollusc, Dendronotus iris, is composed of only four neurons that are organized into two competing modules of a half-center oscillator. In this system, bursting activity in left-right alternation is an emergent property of the network as a whole; none of the neurons produces bursts on its own. We found that the unique synaptic actions and membrane properties of the two neurons in each module (Si2 and the contralateral Si3) play complementary roles in generating stable bursting in this network oscillator. Although Si2 and Si3 each inhibits its contralateral counterpart, Si2 plays a dominant role in evoking fast and strong inhibition of the other module, the termination of which initiates postinhibitory rebound in the Si3 of that module by activating a hyperpolarization-activated inward current. Within each module, the synaptic actions and membrane properties of the two neurons complement each other: Si3 excites Si2, which then feeds back slow inhibition to Si3, terminating the burst. Using dynamic clamp, we showed that the magnitude of the slow inhibition sets the period of the oscillator. Thus, the synaptic actions of Si2 provide the hyperpolarization needed for the other module to rebound stably, whereas the membrane properties of Si3 in each module cause it to rebound first and excite Si2 to maintain the burst until terminated by the slow inhibition from Si2, which releases the other module to become active.NEW & NOTEWORTHY Half-center oscillators composed of reciprocally inhibitory neurons have been posited for over a century to underlie the production of rhythmic movements. The Dendronotus swim central pattern generator may be the simplest such circuit with only two pairs of bilaterally represented neurons. This study completes the description of the mechanism by which this network oscillator functions, showing how stable rhythmic activity arises from the complementary membrane and synaptic properties of the two neurons in the competing modules.