Phase-Locking in Chains of Half-Center Oscillators: Mechanisms Underlying Phase Constancy in the Crayfish Swimmeret System

In a previous paper we computed the phase response curve (PRC) of a half-center oscillator (HCO), a pair of reciprocally inhibitory model neurons that exhibit alternating rhythms, based on the minimal ionic model. It was showed that the two intrinsic mechanisms of the local HCO, “release” and “escape”, gave rise to two different shapes of PRCs. In this paper we use the theory of weakly coupled oscillators to compute the phase-locking property of crayfish’s swimmeret system based on the PRC of the local HCO. We show analytically and numerically that in our 2-HCO system T/4 is the unique stable phase-locked state under both the “escape” and “release” mechanisms with either one of the two configurations of intersegmental synaptic connections defined in [2] and [3]. We also show that in our 4-HCO system model with nearestneighbor couplings only the configuration defined in [2] under the “escape” mechanism and the configuration defined in [3] under the “release” mechanism produce a stable uniform phase-locked state of approximately T/4 as observed in experiments. We also show that phase-locking is insensitive to changes in system frequency and that ascending or descending connection alone is able to produce the phase-locking with a slight perturbation. 1 Background Crayfish’s swimmeret system can be modeled as four half-center oscillators (HCOs) weakly coupled together [2], each of which can be modeled as a postinhibitory rebound (PIR) system consisting of a pair of reciprocally inhibitory model neurons that exhibit alternating rhythms based on the minimal ionic model proposed by Wang and Rinzel [6]. In a previous paper we demonstrated that the two distinct underlying mechanism of each HCO, “release” and “escape”, give rise to two different shapes of PRCs. [7] (Note that the PRCs in this paper are infinitesimal PRCs.) In this paper, using the theory of weakly coupled oscillators, we compute the phase-locked states