Short Duty Cycle Destabilizes a Half-Center Oscillator, But Gap Junctions Can Restabilize the Anti-Phase Pattern

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Abstract
Mutually inhibitory pacemaker neurons with duty cycle close to 50% operate as a half-center oscillator (anti-phase coordination, i.e., 180° out of phase), even in the presence of weak to modest gap junctional coupling. For electrical coupling strength above a critical value synchronization occurs. But, as shown here with modeling studies, the effects of electrical coupling depend critically on a cell's duty cycle. Instead of oscillating either in-phase or anti-phase, model cells with short duty cycle express additional rhythmic patterns, and different transitions between them, depending on electrical coupling strength. For weak or no electrical coupling, cells do not oscillate in anti-phase but instead exhibit almost in-phase activity. Strengthening this weak coupling leads to stable anti-phase activity. With yet stronger electrical coupling stable inphase (synchrony) emerges but it coexists with the anti-phase pattern. Thus the network shows bistability for an intermediate range of coupling strength. For sufficiently strong electrical coupling synchrony is the network's only attracting rhythmic state. Our results, numerical and analytical (phase plane analysis), are based on a minimal but biophysically motivated pacemaker model for the slowly oscillating envelope of bursting neurons. However, illustrations for an Hodgkin–Huxley model suggest that some of our results for short duty cycle may extend to patterning of repetitive spikes. In particular, electrical coupling of intermediate strength may promote anti-phase activity and provide bistability of anti-phase and in-phase spiking.