A modeling exploration of how synaptic feedback to descending projection neurons shapes the activity of an oscillatory network.

Rhythmic activity which underlies motor output is often initiated and controlled by descending modulatory projection pathways onto central pattern generator (CPG) networks. In turn, these descending pathways receive synaptic feedback from their target CPG network, which can influence the CPG output. However, the mechanisms underlying such bi-directional synaptic interactions are mostly unexplored. We develop a reduced mathematical model, including both feed-forward and feedback circuitry, to examine how the synaptic interactions involving two projection neurons, MCN1 and CPN2, can produce and shape the activity of the gastric mill CPG in the crab stomatogastric nervous system. We use simplifying assumptions that are based on the behavior of the biological system to reduce this model down to 2 dimensions, which allows for phase plane analysis of the model output. The model shows a distinct activity for the gastric mill rhythm that is elicited when MCN1 and CPN2 are co-active compared to the rhythm elicited by MCN1 activity alone. Furthermore, the presence of feedback to the projection neuron CPN2 provides a distinct locus of pattern generation in the model which does not require reciprocally inhibitory interactions between the gastric mill CPG neurons, but is instead based on a half-center oscillator that occurs through a tri-synaptic pathway that includes CPN2. Our modeling results show that feedback to projection pathways may provide additional mechanisms for the generation of motor activity. These mechanisms can have distinct dependence on network parameters and may therefore provide additional flexibility for the rhythmic motor output.