Rhythm generation, robustness, and control in stick insect locomotion: modeling and analysis

Stick insect stepping patterns have been studied for insights about locomotor rhythm generation and control, because the underlying neural system is relatively accessible experimentally and produces a variety of rhythmic outputs. Harnessing the experimental identification of effective interactions among neuronal units involved in stick insect stepping pattern generation, previous studies proposed computational models simulating aspects of stick insect locomotor activity. While these models generate diverse stepping patterns and transitions between them, there has not been an in-depth analysis of the mechanisms underlying their dynamics. In this study, we focus on modeling rhythm generation by the neurons associated with the protraction-retraction, levation-depression, and extension-flexion antagonistic muscle pairs of the mesothoracic (middle) leg of stick insects. Our model features a reduced central pattern generator (CPG) circuit for each joint and includes synaptic interactions among the CPGs; we also consider extensions such as the inclusion of motoneuron pools controlled by the CPG components. The resulting network is described by an 18-dimensional system of ordinary differential equations. We use fast-slow decomposition, projection into interacting phase planes, and a heavy reliance on input-dependent nullclines to analyze this model. Specifically, we identify and eludicate dynamic mechanisms capable of generating a stepping rhythm, with a sequence of biologically constrained phase relationships, in a three-joint stick insect limb model. Furthermore, we explain the robustness to parameter changes and tunability of these patterns. In particular, the model allows us to identify possible mechanisms by which neuromodulatory and top-down effects could tune stepping pattern output frequency.