A mathematical model of motorneuron dynamics in the heartbeat of the leech

The heartbeat of the medicinal leech is driven by direct contact between two arrays of motorneurons and two lateral blood vessels. At any given time, motorneurons exhibit one of two alternating states so that, on one side of the animal, the heart beats in a rear-to-front fashion (peristaltic), while on the other side the heart beats synchronously. Every 20 heartbeats, approximately, the two sides switch modes. It is known that the heartbeat rhythm is generated through burst of oscillatory activity produced by a central pattern generator (CPG) network of neurons. However, to the best of our knowledge, how the CPG activity is translated into peristaltic and synchronous rhythms in the motorneurons is yet unknown. In this work, we use symmetric systems of differential equations, accompanied with computational simulations, to investigate possible mechanisms for generating the motorneuron activity that characterizes the heartbeat of leeches and in particular the switching scenario.