Conditions for multi-functionality in a rhythm generating network inspired by turtle scratching

Rhythmic behaviors such as breathing, walking, and scratching are vital to many species. Such behaviors can emerge from groups of neurons, called central pattern generators, in the absence of rhythmic inputs. In vertebrates, the identification of the cells that constitute the central pattern generator for particular rhythmic behaviors is difficult, and often, its existence has only been inferred. For example, under experimental conditions, intact turtles generate several rhythmic scratch motor patterns corresponding to non-rhythmic stimulation of different body regions. These patterns feature alternating phases of motoneuron activation that occur repeatedly, with different patterns distinguished by the relative timing and duration of activity of hip extensor, hip flexor, and knee extensor motoneurons. While the central pattern generator network responsible for these outputs has not been located, there is hope to use motoneuron recordings to deduce its properties. To this end, this work presents a model of a previously proposed central pattern generator network and analyzes its capability to produce two distinct scratch rhythms from a single neuron pool, selected by different combinations of tonic drive parameters but with fixed strengths of connections within the network. We show through simulation that the proposed network can achieve the desired multi-functionality, even though it relies on hip unit generators to recruit appropriately timed knee extensor motoneuron activity, including a delay relative to hip activation in rostral scratch. Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay. This framework is harnessed to consider bistability and to make predictions about the responses of the scratch rhythms to input changes for future experimental testing