A neuromechanical model for the neuronal basis of curve walking in the stick insect

The coordination of the movement of single and multiple limbs is essential for the generation of locomotion. Movement about single joints and the resulting stepping patterns are usually generated by the activity of antagonistic muscle pairs. In the stick insect, the three major muscle pairs of a leg are the protractor and retractor coxae, the levator and depressor trochanteris, and the flexor and extensor tibiae. The protractor and retractor move the coxa, and thereby the leg, forward and backward. The levator and depressor move the femur up and down. The flexor flexes, and the extensor extends the tibia about the femur-tibia joint. The underlying neuronal mechanisms for a forward stepping middle leg have been thoroughly investigated in experimental and theoretical studies. However, the details of the neuronal and mechanical mechanisms driving a stepping single leg in situations other than forward walking remain largely unknown. Here, we present a neuromechanical model of the coupled three joint control system of the stick insect's middle leg. The model can generate forward, backward, or sideward stepping. Switching between them is achieved by changing only a few central signals controlling the neuromechanical model. In kinematic simulations, we are able to generate curve walking with two different mechanisms. In the first, the inner middle leg is switched from forward to sideward and in the second to backward stepping. Both are observed in the behaving animal, and in the model and animal alike, backward stepping of the inner middle leg produces tighter turns than sideward stepping.