Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in insect locomotion

Neuromuscular systems are stabilized and controlled by both feedforward and feedback signals. Feedforward pathways driven by central pattern generators (CPGs), in conjunction with preflexive mechanical reaction forces and nonlinear muscle properties, can produce stable stereotypical gaits. Feedback is nonetheless present in both slow and rapid running, and preflexive mechanisms can join with neural reflexes originating in proprioceptive sensors to yield robust behavior in uncertain environments. Here, we develop a single degree-of-freedom neuromechanical model representing a joint actuated by an agonist/antagonist muscle pair driven by motoneurons and a CPG in a periodic rhythm characteristic of locomotion. We consider two characteristic feedback modes: phasic and tonic. The former encodes states such as position in the timing of individual spikes, while the latter can transmit graded measures of force and other continuous variables as spike rates. We use results from phase reduction and averaging theory to predict phase relationships between CPG and motoneurons in the presence of feedback and compare them with simulations of the neuromechanical model, showing that both phasic and tonic feedback can shift motoneuronal timing and thereby affect joint motions. We find that phase changes in neural activation can cooperate with preflexive displacement and velocity effects on muscle force to compensate for externally applied forces, and that these effects qualitatively match experimental observations in the cockroach.