We have created a computational model of the timing network that paces the heartbeat of the medicinal leech, Hirudo medicinalis. The rhythmic activity of this network originates from two segmental oscillators located in the third and fourth midbody ganglia. In the intact nerve cord, these segmental oscillators are mutually entrained to the same cycle period. Although experiments have shown that the segmental oscillators are coupled by inhibitory coordinating interneurons, the underlying mechanisms of intersegmental coordination have not yet been elucidated. To help understand this coordination, we have created a simple computational model with two variants: symmetric and asymmetric. In the symmetric model, neurons within each segmental oscillator called oscillator interneurons, inhibit the coordinating interneurons. In contrast, in the asymmetric model only the oscillator interneurons of one segmental oscillator inhibit the coordinating interneurons. In the symmetric model, when two segmental oscillators with different inherent periods are coupled, the faster one leads in phase, and the period of the coupled system is equal to the period of the faster oscillator. This behavior arises because, during each oscillation cycle, the oscillator interneurons of the faster segmental oscillator begin to burst before those of the slower oscillator, thereby terminating spike activity in the coordinating interneurons. Thus there is a brief period of time in each cycle when the oscillator interneurons of the slower segmental oscillator are relieved of inhibition from the coordinating interneurons. This “removal of synaptic inhibition” allows, within certain limits, the slower segmental oscillator to be sped to the period of the faster one. Thus the symmetric model demonstrates a plausible biophysical mechanism by which one segmental oscillator can entrain the other. In general the asymmetric model, in which only one segmental oscillator has the ability to inhibit the coordinating interneurons, behaves similarly, except only one segmental oscillator can control the period of the system. In addition, we simulated physiological experiments in which a “driving” stimulus, consisting of alternating positive and negative current steps, was used to control a single oscillator interneuron and thereby entrain the activity of the entire timing network.
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