Phase Coupling by Synaptic Spread in Chains of Coupled Neuronal Oscillators

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Abstract
Many neural systems behave as arrays of coupled oscillators, with characteristic phase coupling. For example, the rhythmic activation patterns giving rise to swimming in fish are characterized by a rostral-to-caudal phase delay in ventral root activity that is independent of the cycle duration. This produces a traveling wave of curvature along the body of the animal with a wavelength approximately equal to the body length. Here a simple mechanism for phase coupling in chains of equally activated oscillators is postulated: the synapses between the cells making up a "unit oscillator" are simply repeated in neighboring segments, with a reduced synaptic strength. If such coupling is asymmetric in the rostral and caudal directions, traveling waves of activity are produced. The intersegmental phase lag that develops is independent of the coupling strength over at least a tenfold range. Furthermore, for the unit oscillator believed to underlie central pattern generation in the lamprey spinal cord, such coupling can result in a phase lag that is independent of frequency.